MAT_SCI 201-301

MAT_SCI 201 introduces the core topics and basic concepts of Materials Science and Engineering. We cover introductory materials processing, structure, properties, and performance with particular emphasis on the relationship between structure and properties. We focus on conventional materials classes: metals ceramics, and polymers, and discuss their various properties, such as mechanical, electronic, thermal, optical, magnetic, and electrochemical. Broader themes that arise are how materials’ performance influences technological development, the economy, the environment, and society. Prerequisites are Chem 131/151/171.

2 Course Outcomes

At the conclusion of the course students will be able to (broadly):

Correlate various materials properties (mechanical, optical, electronic) with materials structure and composition.
Describe how processing conditions can be controlled to produce difference structures and, consequently, tune materials properties and performance.
Select materials for various applications by assessing how the combination of materials prop-erties defines a material’s performance.
Understand the role materials have in facilitating technological development, the economy, the environment, and society.

These broad course-level outcomes are supplemented by 5-8 more topical outcomes at the beginning of module.

3 Math Primer

There are no specific mathematics prerequisites for MAT_SCI 201. However, success in this course does require the ability to employ basic algebra, vector manipulations, trigonometry, and calculus. No advanced mathematics (differential equations, linear algebra, etc.) is required.

3.1 Basic Rules for Exponents

You will often work with exponents and will have to apply operations to them. You will need to know the following:

Operation	Formula	Example
Multiplication: add exponents	$a^{m} \times a^{n} = a^{m + n}$	$x^{2} \times x^{3} = x^{5}$
Dividing: subtract exponents	$\frac{a^{m}}{a^{n}} = a^{m - n}$	$\frac{x^{8}}{x^{3}} = x^{5}$
Power to a power: multiply exponents	$(a^{m})^{n} = a^{m n}$	$(x^{3})^{4} = x^{12}$
Power of a product: distribute power	$(a b)^{m} = a^{n} b^{n}$	$(2 x)^{4} = 16 x$
power of a quotient: distribute power	$(\frac{a}{b})^{m} = \frac{a^{n}}{b^{n}}$	$(\frac{x}{5})^{2} = \frac{x^{5}}{25}$
Negative exponents: make positive, shift across quotient line	$a^{- n} = \frac{1}{a^{n}}$ or $\frac{1}{a^{- n}} = a^{n}$	$3 x^{- 4} = \frac{3}{x^{4}}$
Zero exponents: always equal to 1	$\frac{a^{m}}{a^{m}} = a^{0} = 1$	$\frac{x^{0}}{4} = \frac{1}{4}$

3.2 Vectors

Working with vectors will be important when navigating crystal lattices. It is important that you recall the form and construction of these vectors as well as 1.) how to calculate the length of a vector, 2.) how to test for orthogonality between two vectors and 3.) how to calculate the angle between two vectors.

We'll be working in Cartesian coordinate system using an orthonormal basis set. The basis vectors are:

\begin{matrix} \hat{x} & = (1, 0, 0) & (3.1) \\ \hat{y} & = (0, 1, 0) & (3.2) \\ \hat{z} & = (0, 0, 1) & (3.3) \end{matrix}

Any vector a can then be expressed in 3-dimensional space as:

\begin{matrix} a = a_{1} \hat{x} + a_{2} \hat{y} + a_{3} \hat{z} & (3.4) \end{matrix}

Or, in column notation:

\begin{matrix} a = [\begin{matrix} a_{1} \\ a_{2} \\ a_{3} \end{matrix}] & (3.5) \end{matrix}

In this class, we will often use crystallographic convention, in which notation for a lattice vector (you'll see this in Ch. 2) is condensed to

[u v w]

. More on that later.

You should know how to add and subtract vectors. For example, the addition of the vectors a and b:

\begin{matrix} a + b = (a_{1} + b_{1}) \hat{x} + (a_{2} + b_{2}) \hat{y} + (a_{3} + b_{3}) \hat{z} & (3.6) \end{matrix}

Subtraction is similar, of course.

You should also know how to calculate the length of a vector. This is:

\begin{matrix} | a | = \sqrt{a_{1}^{2} + a_{2}^{2} + a_{3}^{2}} & (3.7) \end{matrix}

Or, if you are more comfortable putting this in terms of the dot-product:

\begin{matrix} | a | = \sqrt{a \cdot a} & (3.8) \end{matrix}

Finally, it's important to calculate the angle (or at least the cosine of an angle) between two vectors, a and b, which can be done using the definition of the scalar product:

\begin{matrix} a \cdot b & = | a | | b | cos θ & (3.9) \\ cos θ & = \frac{a \cdot b}{| a | | b |} & (3.10) \\ cos θ & = \frac{a_{1} b_{1} + a_{2} b_{2} + a_{3} b_{3}}{\sqrt{a_{1}^{2} + a_{2}^{2} + a_{3}^{2}} \sqrt{b_{1}^{2} + b_{2}^{2} + b_{3}^{2}}} & (3.11) \end{matrix}

When

a \cdot b = 0

cos θ = 1

and

θ = π / 2

or 90

^{○}

. In this case the vectors are orthogonal.

3.3 Differential and Integral Notation

We will generally employ Leibniz's notation for differentiation and anti-differentiation. The derivative of a function of one variable, e.g.

f (x) = f

, where

x

is the independent variable, is written:

\begin{matrix} \frac{d f}{d x} o r \frac{d}{d x} f . & (3.12) \end{matrix}

And higher-order derivatives are written as:

\begin{matrix} \frac{d^{2} f}{d x^{2}}, \frac{d^{3} f}{d x^{3}}, ..., \frac{d^{n} f}{d x^{n}} . & (3.13) \end{matrix}

You will encounter a partial differential equation during this course that describes time-diffusion in one spacial dimension (Fick's second law). You will not be required to solve this equation, but you will have to use it. Partial differential equations with multiple variables use the same notation as above, but are utilize the with the

\partial

character. Here we define the

g (x, t) = g

, where

x

and

t

are independent variables:

\begin{matrix} \frac{\partial g}{\partial x} o r \frac{\partial}{\partial x} g . & (3.14) \end{matrix}

And higher-order derivatives taken with respect to the same variable are written as:

\begin{matrix} \frac{\partial^{2} g}{\partial x^{2}}, \frac{\partial^{3} g}{\partial x^{3}}, ..., \frac{\partial^{n} g}{\partial x^{n}} . & (3.15) \end{matrix}

Antidifferentiation will be denoted using the integral symbol, e.g. for the definite integration of

x^{2}

from

a

b

\begin{matrix} \int_{a}^{b} x^{2} d x & (3.16) \end{matrix}

After integration, evaluation of this definite integral is written as:

\begin{matrix} {. \frac{x^{3}}{3} |}_{a}^{b} & (3.17) \end{matrix}

Below, we use Lagrange shorthand to denote derivatives, i.e.

\frac{d}{d x} f = f' (x)

3.4 Differentiation

The following differentiation rules may used at some point during the course. Note that

c

is a constant. We will not require you to differentiate trigonometric or hyperbolic functions.

3.4.1 General Formulas

\begin{matrix} \frac{d}{d x} (c) = 0 & (3.18) \\ \frac{d}{d x} [f (x) + g (x)] = f' (x) - g' (x) & (3.19) \\ \frac{d}{d x} [g (x) f (x)] = f (x) g' (x) + g (x) f' (x) & (3.20) \\ \frac{d}{d x} f (g (x)) = f' (g (x)) g' (x) & (3.21) \\ \frac{d}{d x} [c f (x)] = c f' (x) & (3.22) \\ \frac{d}{d x} [\frac{f (x)}{g (x)}] = \frac{g (x) f' (x) - f (x) f' (x)}{[g (x)]^{2}} & (3.23) \\ \frac{d}{d x} x^{n} = n x^{n - 1} & (3.24) \end{matrix}

3.4.2 Exponents and Logarithmic Functions

\begin{matrix} \frac{d}{d x} e^{x} = e^{x} & (3.25) \\ \frac{d}{d x} a^{x} = a^{x} ln a & (3.26) \\ \frac{d}{d x} ln | x | = \frac{1}{x} & (3.27) \\ \frac{d}{d x} {log}_{a} x = \frac{1}{x ln a} & (3.28) \end{matrix}

3.5 Integration

The following integration rules may used at some point during the course. Note that

C

is a constant. We will not require you to perform integrations that may involve trigonometric or hyperbolic functions.

3.5.1 Basic Forms

\begin{matrix} \int u^{n} d u = \frac{u^{n + 1}}{n + 1} + C, n \neq - 1 & (3.29) \\ \int u^{- 1} d u = ln | u | + C & (3.30) \\ \int e^{u} d u = e^{u} + C & (3.31) \\ \int a^{u} d u = \frac{a^{u}}{ln (a)} + C & (3.32) \end{matrix}

3.6 Logarithmic Identities

The following logarithmic identities may be used in class. If so, they will be supplied on your equation sheet.

\begin{matrix} log (x y) = log (x) + log (y) & (3.33) \\ log (\frac{x}{y}) = log (x) - log (y) & (3.34) \\ log (x^{d}) = d log (x) & (3.35) \\ log (\sqrt[y]{x}) = \frac{log (x)}{y} & (3.36) \\ log (x^{c} y^{d}) = log (x^{c}) + log (y^{d}) = c log (x) + d log (y) & (3.37) \end{matrix}

html version of math as a test:

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YPqwixhUMOndis6MhbmfvLBKjC8sKKIZKbJk8L11oNkCQzCgvjhyyEiQSuJcgCQSG4Mocfgc0Hkwcjal1UNgP0CBPikYqBIk9tONv4kLtBswH07vUCjEaHiFGlLf8MgXKzSgjp2HolRRccAOh0ILHz9qlGgIFkwAnzHJRjWFhlA7ROwINyB5HFj59PRZHFor6voq7l23EPNRwdWhgawqbivLSjRA4htEYUFkjESu67icTg5S0aW1sOkCiIysfJ9UnIWevOOLGpepcBxy1wEhd2WI3AZg7sr9WBmHWyasxMcvY%2FiOmsLtHSWNUWEGk9hScMPShasUA1AcHOtRZlqMeQ0OzYS9vQvYUjOLrzP07BUAFikcJNMi7gIxEw4pL1G54TcmmmoAQ5s7TGWErJZ2Io4yQ0ljRYhL8H5e62oDtLF8aDpnIvZ5R3GWJyAugdiiJW9hQAVTsnCBHhwu7rkBlBX6r3b7ejEY0k5GGeyKv66v%2B6dg7mcJTrWHbtMywbedYqCQ0FPwoytmSWsL8WTtChZCKKzEF7vP6De4x2BJkkniMgSdWhbeBSLtJZR9CTHetK1xb34AYIJ37OegYIoPVbXgJ%2FqDQK%2BbfCtxQRVKQu77WzOoM6SGL7MaZwCGJVk46aImai9fmam%2BWpHG%2B0BtQPWUgZ7RIAlPq6lkECUhZQ2gqWkMYKcYMYaIc4gYCDFHYa2d1nzp3%2BJ1eCBay8IYZ0wQRKGAqvCuZ%2FUgbQPyllosq%2BXtfKIZOzmeJqRazpmmoP%2F76YfkjzV2NlXTDSBYB04SVlNQsFTbGPk1t%2FI4Jktu0XSgifO2ozFOiwd%2F0SssJDn0dn4xqk4GDTTKX73%2FwQyBLdqgJ%2BWx6AQaba3BA9CKEzjtQYIfAsiYamapq80LAamYjinlKXUkxdpIDk0puXUEYzSalfRibAeDAKpNiqQ0FTwoxuGYzRnisyTotdVTclis1LHRQCy%2FqqL8oUaQzWRxilq5Mi0IJGtMY02cGLD69vGjkj3p6pGePKI8bkBv5evq8SjjyU04vJR2cQXQwSJyoinDsUJHCQ50jrFTT7yRdbdYQMB3MYCb6uBzJ9ewhXYPAIZSXfeEQBZZ3GPN3Nbhh%2FwkvAJLXnQMdi5NYYZ5GHE400GS5rXkOZSQsdZgIbzRnF9ueLnsfQ47wHAsirITnTlkCcuWWIUhJSbpM3wWhXNHvt2xUsKKMpdBSbJnBMcihkoDqAd1Zml%2FR4yrzow1Q2A5G%2Bkzo%2FRhRxQS2lCSDRV8LlYLBOOoo1bF4jwJAwKMK1tWLHlu9i0j4Ig8qVm6wE1DxXwAwQwsaBWUg2pOOol2dHxyt6npwJEdLDDVYyRc2D0HbcbLUJQj8gPevQBUBOUHXPrsAPBERICpnYESeu2OHotpXQxRGlCCtLdIsu23MhZVEoJg8Qumj%2FUMMc34IBqTKLDTp76WzL%2FdMjCxK7MjhiGjeYAC%2Fkj%2FjY%2FRde7hpSM1xChrog6yZ7OWTuD56xBJnGFE%2BpT2ElSyCnJcwVzCjkqeNLfMEJqKW0G7OFIp0G%2B9mh50I9o8k1tpCY0xYqFNIALgIfc2me4n1bmJnRZ89oepgLPT0NTMLNZsvSCZAc3TXaNB07vail36%2FdBySis4m9%2FDR8izaLJW6bWCkVgm5T%2Bius3ZXq4xI%2BGnbveLbdRwF2mNtsrE0JjYc1AXknCOrLSu7Te%2Fr4dPYMCl5qtiHNTn%2BTPbh1jCBHH%2BdMJNhwNgs3nT%2BOhQoQ0vYif56BMG6WowAcHR3DjQolxLzyVekHj00PBAaW7IIAF1EF%2BuRIWyXjQMAs2chdpaKPNaB%2BkSezYt0%2BCA04sOg5vx8Fr7Ofa9sUv87h7SLAUFSzbetCCZ9pmyLt6l6%2FTzoA1%2FZBG9bIUVHLAbi%2FkdBFgYGyGwRQGBpkqCEg2ah9UD6EedEcEL3j4y0BQQCiExEnocA3SZboh%2Bepgd3YsOkHskZwPuQ5OoyA0fTA5AXrHcUOQF%2BzkJHIA7PwCDk1gGVmGUZSSoPhNf%2BTklauz98QofOlCIQ%2FtCD4dosHYPqtPCXB3agggQQIqQJsSkB%2Bqn0rkQ1toJjON%2FOtCIB9RYv3PqRA4C4U68ZMlZn6BdgEvi2ziU%2BTQ6NIw3ej%2BAtDwMGEZk7e2IjxUWKdAxyaw9OCwSmeADTPPleyk6UhGDNXQb%2B%2BW6Uk4q6F7%2Frg6WVTo82IoCxSIsFDrav4EPHphD3u4hR53WKVvYZUwNCCeM4PMBWzK%2BEfIthZOkuAwPo5C5jgoZgn6dUdvx5rIDmd58cXXdKNfw3l%2BwM2UjgrDJeQHhbD7HW2QDoZMCujgIUkk5Fg8VCsdyjOtnGRx8wgKRPZN5dR0zPUyfGZFVihbFRniXZFOZGKPnEQzU3AnD1KfR6weHW2XS6KbPJxUkOTZsAB9vTVp3Le1F8q5l%2BDMcLiIq78jxAImD2pGFw0VHfRatScGlK6SMu8leTmhUSMy8Uhdd6xBiH3Gdman4tjQGLboJfqz6fL2WKHTmrfsKZRYX6BTDjDldKMosaSTLdQS7oDisJNqAUhw1PfTlnacCO8vl8706Km1FROgLDmudzxg%2BEWTiArtHgLsRrAXYWdB0NmToNCJdKm0KWycZQqb%2BMw76Qy29iQ5up%2FX7oyw8QZ75kP5F6iJAJz6KCmqxz8fEa%2FxnsMYcIO%2FvEkGRuMckhr4rIeLrKaXnmIzlNLxbFspOphkcnJdnz%2FChp%2FVlpj2P7jJQmQRwGnltkTV5dbF9fE3%2FfxoSqTROgq9wFUlbuYzYcasE0ouzBo%2BdDCDzxKAfhbAZYxQiHrLzV2iVexnDX%2FQnT1fsT%2Fxuhu1ui5qIytgbGmRoQkeQooO8eJNNZsf0iALur8QxZFH0nCMnjerYQqG1pIfjyVZWxhVRznmmfLG00BcBWJE6hzQWRyFknuJnXuk8A5FRDCulwrWASSNoBtR%2BCtGdkPwYN2o7DOw%2FVGlCZPusRBFXODQdUM5zeHDIVuAJBLqbO%2Ff9Qua%2BpDqEPk230Sob9lEZ8BHiCorjVghuI0lI4JDgHGRDD%2FprQ84B1pVGkIpVUAHCG%2Biz3Bn3qm2AVrYcYWhock4jso5%2BJ7HfHVj4WMIQdGctq3psBCVVzupQOEioBGA2Bk%2BUILT7%2BVoX5mdxxA5fS42gISQVi%2FHTzrgMxu0fY6hE1ocUwwbsbWcezrY2n6S8%2F6cxXkOH4prpmPuFoikTzY7T85C4T2XYlbxLglSv2uLCgFv8Quk%2FwdesUdWPeHYIH0R729JIisN9Apdd4eB10aqwXrPt%2BSu9mA8k8n1sjMwnfsfF2j3jMUzXepSHmZ%2FBfqXvzgUNQQWOXO8YEuFBh4QTYCkOAPxywpYu1VxiDyJmKVcmJPGWk%2Fgc3Pov02StyYDahwmzw3E1gYC9wkupyWfDqDSUMpCTH5e5N8B%2F%2FlHiMuIkTNw4USHrJU67bjXGqNav6PBuQSoqTxc8avHoGmvqNtXzIaoyMIQIiiUHIM64cXieouplhNYln7qgc4wBVAYR104kO%2BCvKqsg4yIUlFNThVUAKZxZt1XA34h3TCUUiXVkZ0w8Hh2R0Z5L0b4LZvPd%2Fp1gi%2F07h8qfwHrByuSxglc9cI4QIg2oqvC%2Fqm0i7tjPLTgDhoWTAKDO2ONW5oe%2B%2FeKB9vZB8K6C25yCZ9RFVMnb6NRdRjyVK57CHHSkJBfnM2%2Fj4ODUwRkqrtBBCrDsDpt8jhZdXoy%2F1BCqw3sSGhgGGy0a5Jw6BP%2FTExoCmNFYjZl248A0osgPyGEmRA%2BfAsqPVaNAfytu0vuQJ7rk3J4kTDTR2AlCHJ5cls26opZM4w3jMULh2YXKpcqGBtuleAlOZnaZGbD6DHzMd6i2oFeJ8z9XYmalg1Szd%2FocZDc1C7Y6vcALJz2lYnTXiWEr2wawtoR4g3jvWUU2Ngjd1cewtFzEvM1NiHZPeLlIXFbBPawxNgMwwAlyNSuGF3zizVeOoC9bag1qRAQKQE%2FEZBWC2J8mnXAN2aTBboZ7HewnObE8CwROudZHmUM5oZ%2FUgd%2FJZQK8lvAm43uDRAbyW8gZ%2BZGq0EVerVGUKUSm%2FIdn8AQHdR4m7bue88WBwft9mSCeMOt1ncBwziOmJYI2ZR7ewNMPiCugmSsE4EyQ%2BQATJG6qORMGd4snEzc6B4shPIo4G1T7PgSm8PY5eUkPdF8JZ0VBtadbHXoJgnEhZQaODPj2gpODKJY5Yp4DOsLBFxWbvXN755KWylJm%2BoOd4zEL9Hpubuy2gyyfxh8oEfFutnYWdfB8PdESLWYvSqbElP9qo3u6KTmkhoacDauMNNjj0oy40DFV7Ql0aZj77xfGl7TJNHnIwgqOkenruYYNo6h724%2BzUQ7%2BvkCpZB%2BpGA562hYQiDxHVWOq0oDQl%2FQsoiY%2BcuI7iWq%2FZIBtHcXJ7kks%2Bh2fCNUPA82BzjnqktNts%2BRLdk1VSu%2BtqEn7QZCCsvEqk6FkfiOYkrsw092J8jsfIuEKypNjLxrKA9kiA19mxBD2suxQKCzwXGws7kEJvlhUiV9tArLIdZW0IORcxEzdzKmjtFhsjKy%2F44XYXdI5noQoRcvjZ1RMPACRqYg2V1%2BOwOepcOknRLLFdYgTkT5UApt%2FJhLM3jeFYprZV%2BZow2g8fP%2BU68hkKFWJj2yBbKqsrp25xkZX1DAjUw52IMYWaOhab8Kp05VrdNftqwRrymWF4OQSjbdfzmRZirK8FMJELEgER2PHjEAN9pGfLhCUiTJFbd5LBkOBMaxLr%2FA1SY9dXFz4RjzoU9ExfJCmx%2FI9FKEGT3n2cmzl2X42L3Jh%2BAbQq6sA%2BSs1kitoa4TAYgKHaoybHUDJ51oETdeI%2F9ThSmjWGkyLi5QAGWhL0BG1UsTyRGRJOldKBrYJeB8ljLJHfATWTEQBXBDnQexOHTB%2BUn44zExFE4vLytcu5NwpWrUxO%2F0ZICUGM7hGABXym0V6ZvDST0E370St9MIWQOTWngeoQHUTdCJUP04spMBMS8LSker9cReVQkULFDIZDFPrhTzBl6sed9wcZQTbL%2BBDqMyaN3RJPh%2Fanbx%2BIv%2BqgQdAa3M9Z5JmvYlh4qop%2BHo1F1W5gbOE9YKLgAnWytXElU4G8GtW47lhgFE6gaSs%2Bgs37sFvi0PPVvA5dnCBgILTwoKd%2F%2BDoL9F6inlM7H4rOTzD79KJgKlZO%2FZgt22UsKhrAaXU5ZcLrAglTVKJEmNJvORGN1vqrcfSMizfpsgbIe9zno%2BgBoKVXgIL%2FVI8dB1O5o%2FR3Suez%2FgD7M781ShjKpIIORM%2FnxG%2BjjhhgPwsn2IoXsPGPqYHXA63zJ07M2GPEykQwJBYLK808qYxuIew4frk52nhCsnCYmXiR6CuapvE1IwRB4%2FQftDbEn%2BAucIr1oxrLabRj9q4ae0%2BfXkHnteAJwXRbVkR0mctVSwEbqhJiMSZUp9DNbEDMmjX22m3ABpkrPQQTP3S1sib5pD2VRKRd%2BeNAjLYyT0hGrdjWJZy24OYXRoWQAIhGBZRxuBFMjjZQhpgrWo8SiFYbojcHO8V5DyscJpLTHyx9Fimassyo5U6WNtquUMYgccaHY5amgR3PQzq3ToNM5ABnoB9kuxsebqmYZm0R9qxJbFXCQ1UPyFIbxoUraTJFDpCk0Wk9GaYJKz%2F6oHwEP0Q14lMtlddQsOAU9zlYdMVHiT7RQP3XCmWYDcHCGbVRHGnHuwzScA0BaSBOGkz3lM8CArjrBsyEoV6Ys4qgDK3ykQQPZ3hCRGNXQTNNXbEb6tDiTDLKOyMzRhCFT%2BmAUmiYbV3YQVqFVp9dorv%2BTsLeCykS2b5yyu8AV7IS9cxcL8z4Kfwp%2BxJyYLv1OsxQCZwTB4a8BZ%2F5EdxTBJthApqyfd9u3ifr%2FWILTqq5VqgwMT9SOxbSGWLQJUUWCVi4k9tho9nEsbUh7U6NUsLmkYFXOhZ0kmamaJLRNJzSj%2Fqn4Mso6zb6iLLBXoaZ6AqeWCjHQm2lztnejYYM2eubnpBdKVLORZhudH3JF1waBJKA9%2BW8EhMj3Kzf0L4vi4k6RoHh3Z5YgmSZmk6ns4fjScjAoL8GoOECgqgYEBYUGFVO4FUv4%2FYtowhEmTs0vrvlD%2FCrisnoBNDAcUi%2FteY7OctFlmARQzjOItrrlKuPO6E2Ox93L4O%2F4DcgV%2FdZ7qR3VBwVQxP1GCieA4RIpweYJ5FoYrHxqRBdJjnqbsikA2Ictbb8vE1GYIo9dacK0REgDX4smy6GAkxlH1yCGGsk%2BtgiDhNKuKu3yNrMdxafmKTF632F8Vx4BNK57GvlFisrkjN9WDAtjsWA0ENT2e2nETUb%2Fn7qwhvGnrHuf5bX6Vh%2Fn3xffU3PeHdR%2BFA92i6ufT3AlyAREoNDh6chiMWTvjKjHDeRhOa9YkOQRq1vQXEMppAQVwHCuIcV2g5rBn6GmZZpTR7vnSD6ZmhdSl176gqKTXu5E%2BYbfL0adwNtHP7dT7t7b46DVZIkzaRJOM%2BS6KcrzYVg%2BT3wSRFRQashjfU18NutrKa%2F7PXbtuJvpIjbgPeqd%2BpjmRw6YKpnANFSQcpzTZgpSNJ6J7uiagAbir%2F8tNXJ%2FOsOnRh6iuIexxrmkIneAgz8QoLmiaJ8sLQrELVK2yn3wOHp57BAZJhDZjTBzyoRAuuZ4eoxHruY1pSb7qq79cIeAdOwin4GdgMeIMHeG%2BFZWYaiUQQyC5b50zKjYw97dFjAeY2I4Bnl105Iku1y0lMA1ZHolLx19uZnRdILcXKlZGQx%2FGdEqSsMRU1BIrFqRcV1qQOOHyxOLXEGcbRtAEsuAC2V4K3p5mFJ22IDWaEkk9ttf5Izb2LkD1MnrSwztXmmD%2FQi%2FEmVEFBfiKGmftsPwVaIoZanlKndMZsIBOskFYpDOq3QUs9aSbAAtL5Dbokus2G4%2FasthNMK5UQKCOhU97oaOYNGsTah%2BjfCKsZnTRn5TbhFX8ghg8CBYt%2FBjeYYYUrtUZ5jVij%2Fop7V5SsbA4mYTOwZ46hqdpbB6Qvq3AS2HHNkC15pTDIcDNGsMPXaBidXYPHc6PJAkRh29Vx8KcgX46LoUQBhRM%2B3SW6Opll%2FwgxxsPgKJKzr5QCmwkUxNbeg6Wj34SUnEzOemSuvS2OetRCO8Tyy%2BQbSKVJcqkia%2BGvDefFwMOmgnD7h81TUtMn%2BmRpyJJ349HhAnoWFTejhpYTL9G8N2nVg1qkXBeoS9Nw2fB27t7trm7d%2FQK7Cr4uoCeOQ7%2F8JfKT77KiDzLImESHw%2F0wf73QeHu74hxv7uihi4fTX%2BXEwAyQG3264dwv17aJ5N335Vt9sdrAXhPOAv8JFvzqyYXwfx8WYJaef1gMl98JRFyl5Mv5Uo%2FoVH5ww5OzLFsiTPDns7fS6EURSSWd%2F92BxMYQ8sBaH%2Bj%2BwthQPdVgDGpTfi%2BJQIWMD8xKqULliRH01rTeyF8x8q%2FGBEEEBrAJMPf25UQwi0b8tmqRXY7kIvNkzrkvRWLnxoGYEJsz8u4oOyMp8cHyaybb1HdMCaLApUE%2B%2F7xLIZGP6H9xuSEXp1zLIdjk5nBaMuV%2FyTDRRP8Y2ww5RO6d2D94o%2B6ucWIqUAvgHIHXhZsmDhjVLczmZ3ca0Cb3PpKwt2UtHVQ0BgFJsqqTsnzZPlKahRUkEu4qmkJt%2Bkqdae76ViWe3STan69yaF9%2BfESD2lcQshLHWVu4ovItXxO69bqC5p1nZLvI8NdQB9s9UNaJGlQ5mG947ipdDA0eTIw%2FA1zEdjWquIsQXXGIVEH0thC5M%2BW9pZe7IhAVnPJkYCCXN5a32HjN6nsvokEqRS44tGIs7s2LVTvcrHAF%2BRVmI8L4HUYk4x%2B67AxSMJKqCg8zrGOgvK9kNMdDrNiUtSWuHFpC8%2Fp5qIQrEo%2FH%2B1l%2F0cAwQ2nKmpWxKcMIuHY44Y6DlkpO48tRuUGBWT0FyHwSKO72Ud%2BtJUfdaZ4CWNijzZtlRa8%2BCkmO%2FEwHYfPZFU%2FhzjFWH7vnzHRMo%2BaF9u8qHSAiEkA2HjoNQPEwHsDKOt6hOoK3Ce%2F%2B%2F9boMWDa44I6FrQhdgS7OnNaSzwxWKZMcyHi6LN4WC6sSj0qm2PSOGBTvDs%2FGWJS6SwEN%2FULwpb4LQo9fYjUfSXRwZkynUazlSpvX9e%2BG2zor8l%2BYaMxSEomDdLHGcD6YVQPegTaA74H8%2BV4WvJkFUrjMLGLlvSZQWvi8%2FQA7yzQ8GPno%2F%2F5SJHRP%2FOqKObPCo81s%2F%2B6WgLqykYpGAgQZhVDEBPXWgU%2FWzFZjKUhSFInufPRiMAUULC6T11yL45ZrRoB4DzOyJShKXaAJIBS9wzLYIoCEcJKQW8GVCx4fihqJ6mshBUXSw3wWVj3grrHQlGNGhIDNNzsxQ3M%2BGWn6ASobIWC%2BLbYOC6UpahVO13Zs2zOzZC8z7FmA05JhUGyBsF4tsG0drcggIFzgg%2Fkpf3%2BCnAXKiMgIE8Jk%2FMhpkc8DUJEUzDSnWlQFme3d0sHZDrg7LavtsEX3cHwjCYA17pMTfx8Ajw9hHscN67hyo%2BRJQ4458RmPywXykkVcW688oVUrQhahpPRvTWPnuI0B%2BSkQu7dCyvLRyFYlC1LG1gRCIvn3rwQeINzZQC2KXq31FaR9UmVV2QeGVqBHjmE%2BVMd3b1fhCynD0pQNhCG6%2FWCDbKPyE7NRQzL3BzQAJ0g09aUzcQA6mUp9iZFK6Sbp%2FYbHjo%2B%2B7%2FWj8S4YNa%2BZdqAw1hDrKWFXv9%2BzaXpf8ZTDSbiqsxnwN%2FCzK5tPkOr4tRh2kY3Bn9JtalbIOI4b3F7F1vPQMfoDcdxMS8CW9m%2FNCW%2FHILTUVWQIPiD0j1A6bo8vsv6P1hCESl2abrSJWDrq5sSzUpwoxaCU9FtJyYH4QFMxDBpkkBR6kn0LMPO%2B5EJ7Z6bCiRoPedRZ%2FP0SSdii7ZnPAtVwwHUidcdyspwncz5uq6vvm4IEDbJVLUFCn%2FLvIHfooUBTkFO130FC7CmmcrKdgDJcid9mvVzsDSibOoXtIf9k6ABle3PmIxejodc4aob0QKS432srrCMndbfD454q52V01G4q913mC5HOsTzWF4h2No1av1VbcUgWAqyoZl%2B11PoFYnNv2HwAODeNRkHj%2B8SF1fcvVBu6MrehHAZK1Gm69ICcTKizykHgGFx7QdowTVAsYEF2tVc0Z6wLryz2FI1sc5By2znJAAmINndoJiB4sfPdPrTC8RnkW7KRCwxC6YvXg5ahMlQuMpoCSXjOlBy0Kij%2BbsCYPbGp8BdCBiLmLSAkEQRaieWo1SYvZIKJGj9Ur%2FeWHjiB7SOVdqMAVmpBvfRiebsFjger7DC%2B8kRFGtNrTrnnGD2GAJb8rQCWkUPYHhwXsjNBSkE6lGWUj5QNhK0DMNM2l%2BkXRZ0KLZaGsFSIdQz%2FHXDxf3%2FTE30%2BDgBKWGWdxElyLccJfEpjsnszECNoDGZpdwdRgCixeg9L4EPhH%2BRptvRMVRaahu4cySjS3P5wxAUCPkmn%2BrhyASpmiTaiDeggaIxYBmtLZDDhiWIJaBgzfCsAGUF1Q1SFZYyXDt9skCaxJsxK2Ms65dmdp5WAZyxik%2FzbrTQk5KmgxCg%2Ff45L0jywebOWUYFJQAJia7XzCV0x89rpp%2Ff3AVWhSPyTanqmik2SkD8A3Ml4NhIGLAjBXtPShwKYfi2eXtrDuKLk4QlSyTw1ftXgwqA2jUuopDl%2B5tfUWZNwBpEPXghzbBggYCw%2Fdhy0ntds2yeHCDKkF%2FYxQjNIL%2FF%2F37jLPHCKBO9ibwYCmuxImIo0ijV2Wbg3kSN2psoe8IsABv3RNFaF9uMyCtCYtqcD%2BqNOhwMlfARQUdJ2tUX%2BMNJqOwIciWalZsmEjt07tfa8ma4cji9sqz%2BQ9hWfmMoKEbIHPOQORbhQRHIsrTYlnVTNvcq1imqmmPDdVDkJgRcTgB8Sb6epCQVmFZe%2BjGDiNJQLWnfx%2BdrTKYjm0G8yH0ZAGMWzEJhUEQ4Maimgf%2Fbkvo8PLVBsZl152y5S8%2BHRDfZIMCbYZ1WDp4yrdchOJw8k6R%2B%2F2pHmydK4NIK2PHdFPHtoLmHxRDwLFb7eB%2BM4zNZcB9NrAgjVyzLM7xyYSY13ykWfIEEd2n5%2FiYp3ZdrCf7fL%2Ben%2BsIJu2W7E30MrAgZBD1rAAbZHPgeAMtKCg3NpSpYQUDWJu9bT3V7tOKv%2BNRiJc8JAKqqgCA%2FPNRBR7ChpiEulyQApMK1AyqcWnpSOmYh6yLiWkGJ2mklCSPIqN7UypWj3dGi5MvsHQ87MrB4VFgypJaFriaHivwcHIpmyi5LhNqtem4q0n8awM19Qk8BOS0EsqGscuuydYsIGsbT5GHnERUiMpKJl4ON7qjB4fEqlGN%2FhCky89232UQCiaeWpDYCJINXjT6xl4Gc7DxRCtgV0i1ma4RgWLsNtnEBRQFqZggCLiuyEydmFd7WlogpkCw5G1x4ft2psm3KAREwVwr1Gzl6RT7FDAqpVal34ewVm3VH4qn5mjGj%2BbYL1NgfLNeXDwtmYSpwzbruDKpTjOdgiIHDVQSb5%2FzBgSMbHLkxWWgghIh9QTFSDILixVwg0Eg1puooBiHAt7DzwJ7m8i8%2Fi%2BjHvKf0QDnnHVkVTIqMvIQImOrzCJwhSR7qYB5gSwL6aWL9hERHCZc4G2%2BJrpgHNB8eCCmcIWIQ6rSdyPCyftXkDlErUkHafHRlkOIjxGbAktz75bnh50dU7YHk%2BMz7wwstg6RFZb%2BTZuSOx1qqP5C66c0mptQmzIC2dlpte7vZrauAMm%2F7RfBYkGtXWGiaWTtwvAQiq2oD4YixPLXE2khB2FRaNRDTk%2B9sZ6K74Ia9VntCpN4BhJGJMT4Z5c5FhSepRCRWmBXqx%2BwhVZC4me4saDs2iNqXMuCl6iAZflH8fscC1sTsy4PHeC%2BXYuqMBMUun5YezKbRKmEPwuK%2BCLzijPEQgfhahQswBBLfg%2FGBgBiI4QwAqzJkkyYAWtjzSg2ILgMAgqxYfwERRo3zruBL9WOryUArSD8sQOcD7fvIODJxKFS615KFPsb68USBEPPj1orNzFY2xoTtNBVTyzBhPbhFH0PI5AtlJBl2aSgNPYzxYLw7XTDBDinmVoENwiGzmngrMo8OmnRP0Z0i0Zrln9DDFcnmOoBZjABaQIbPOJYZGqX%2BRCMlDDbElcjaROLDoualmUIQ88Kekk3iM4OQrADcxi3rJguS4MOIBIgKgXrjd1WkbCdqxJk%2F4efRIFsavZA7KvvJQqp3Iid5Z0NFc5aiMRzGN3vrpBzaMy4JYde3wr96PjN90AYOIbyp6T4zj8LoE66OGcX1Ef4Z3KoWLAUF4BTg7ug%2FAbkG5UNQXAMkQezujSHeir2uTThgd3gpyzDrbnEdDRH2W7U6PeRvBX1ZFMP5RM%2BZu6UUZZD8hDPHldVWntTCNk7To8IeOW9yn2wx0gmurwqC60AOde4r3ETi5pVMSDK8wxhoGAoEX9NLWHIR33VbrbMveii2jAJlrxwytTHbWNu8Y4N8vCCyZjAX%2FpcsfwXbLze2%2BD%2Bu33OGBoJyAAL3jn3RuEcdp5If8O%2Ba4NKWvxOTyDltG0IWoHhwVGe7dKkCWFT%2B%2Btm%2BhaBCikRUUMrMhYKZJKYoVuv%2FbsJzO8DwfVIInQq3g3BYypiz8baogH3r3GwqCwFtZnz4xMjAVOYnyOi5HWbFA8n0qz1OjSpHWFzpQOpvkNETZBGpxN8ybhtqV%2FDMUxd9uFZmBfKXMCn%2FSqkWJyKPnT6lq%2B4zBZni6fYRByJn6OK%2BOgPBGRAJluwGSk4wxjOOzyce%2FPKODwRlsgrVkdcsEiYrqYdXo0Er2GXi2GQZd0tNJT6c9pK1EEJG1zgDJBoTVuCXGAU8BKTvCO%2FcEQ1Wjk3Zzuy90JX4m3O5IlxVFhYkSUwuQB2up7jhvkm%2BbddRQu5F9s0XftGEJ9JSuSk%2BZachCbdU45fEqbugzTIUokwoAKvpUQF%2FCvLbWW5BNQFqFkJg2f30E%2F48StNe5QwBg8zz3YAJ82FZoXBxXSv4QDooDo79NixyglO9AembuBcx5Re3CwOKTHebOPhkmFC7wNaWtoBhFuV4AkEuJ0J%2B1pT0tLkvFVZaNzfhs%2FKd3%2BA9YsImlO4XK4vpCo%2FelHQi%2F9gkFg07xxnuXLt21unCIpDV%2BbbRxb7FC6nWYTsMFF8%2B1LUg4JFjVt3vqbuhHmDKbgQ4e%2BRGizRiO8ky05LQGMdL2IKLSNar0kNG7lHJMaXr5mLdG3nykgj6vB%2FKVijd1ARWkFEf3yiUw1v%2FWaQivVUpIDdSNrrKbjO5NPnxz6qTTGgYg03HgPhDrCFyYZTi3XQw3HXCva39mpLNFtz8AiEhxAJHpWX13gCTAwgm9YTvMeiqetdNQv6IU0hH0G%2BZManTqDLPjyrOse7WiiwOJCG%2BJ0pZYULhN8NILulmYYvmVcV2MjAfA39sGKqGdjpiPo86fecg65UPyXDIAOyOkCx5NQsLeD4gGVjTVDwOHWkbbBW0GeNjDkcSOn2Nq4cEssP54t9D749A7M1AIOBl0Fi0sSO5v3P7LCBrM6ZwFY6kp2FX6AcbGUdybnfChHPyu6WlRZ2Fwv9YM0RMI7kISRgR8HpQSJJOyTfXj%2F6gQKuihPtiUtlCQVPohUgzfezTg8o1b3n9pNZeco1QucaoXe40Fa5JYhqdTspFmxGtW9h5ezLFZs3j%2FN46f%2BS2rjYNC2JySXrnSAFhvAkz9a5L3pza8eYKHNoPrvBRESpxYPJdKVUxBE39nJ1chrAFpy4MMkf0qKgYALctGg1DQI1kIymyeS2AJNT4X240d3IFQb%2F0jQbaHJ2YRK8A%2Bls6WMhWmpCXYG5jqapGs5%2FeOJErxi2%2F2KWVHiPellTgh%2FfNl%2F2KYPKb7DUcAg%2BmCOPQFCiU9Mq%2FWLcU1xxC8aLePFZZlE%2BPCLzf7ey46INWRw2kcXySR9FDgByXzfxiNKwDFbUSMMhALPFSedyjEVM5442GZ4hTrsAEvZxIieSHGSgkwFh%2FnFNdrrFD4tBH4Il7fW6ur4J8Xaz7RW9jgtuPEXQsYk7gcMs2neu3zJwTyUerHKSh1iTBkj2YJh1SSOZL5pLuQbFFAvyO4k1Hxg2h99MTC6cTUkbONQIAnEfGsGkNFWRbuRyyaEZInM5pij73EA9rPIUfU4XoqQpHT9THZkW%2BoKFLvpyvTBMM69tN1Ydwv1LIEhHsC%2BueVG%2Bw%2BkyCPsvV3erRikcscHjZCkccx6VrBkBRusTDDd8847GA7p2Ucy0y0HdSRN6YIBciYa4vuXcAZbQAuSEmzw%2BH%2FAuOx%2BaH%2BtBL88H57D0MsqyiZxhOEQkF%2F8DR1d2hSPMj%2FsNOa5rxcUnBgH8ictv2J%2Bcb4BA4v3MCShdZ2vtK30vAwkobnEWh7rsSyhmos3WC93Gn9C4nnAd%2FPjMMtQfyDNZsOPd6XcAsnBE%2FmRHtHEyJMzJfZFLE9OvQa0i9kUmToJ0ZxknTgdl%2FXPV8xoh0K7wNHHsnBdvFH3sv52lU7UFteseLG%2FVanIvcwycVA7%2BBE1Ulyb20BvwUWZcMTKhaCcmY3ROpvonVMV4N7yBXTL7IDtHzQ4CCcqF66LjF3xUqgErKzolLyCG6Kb7irP%2FMVTCCwGRxfrPGpMMGvPLgJ881PHMNMIO09T5ig7AzZTX%2F5PLlwnJLDAPfuHynSGhV4tPqR3gJ4kg4c06c%2FF1AcjGytKm2Yb5jwMotF7vro4YDLWlnMIpmPg36NgAZsGA0W1spfLSue4xxat0Gdwd0lqDBOgIaMANykwwDKejt5YaNtJYIkrSgu0KjIg0pznY0SCd1qlC6R19g97UrWDoYJGlrvCE05J%2F5wkjpkre727p5PTRX5FGrSBIfJqhJE%2FIS876PaHFkx9pGTH3oaY3jJRvLX9Iy3Edoar7cFvJqyUlOhAEiOSAyYgVEGkzHdug%2BoRHIEOXAExMiTSKU9A6nmRC8mp8iYhwWdP2U%2F5EkFAdPrZw03YA3gSyNUtMZeh7dDCu8pF5x0VORCTgKp07ehy7NZqKTpIC4UJJ89lnboyAfy5OyXzXtuDRbtAFjZRSyGFTpFrXwkpjSLIQIG3N0Vj4BtzK3wdlkBJrO18MNsgseR4BysJilI0wI6ZahLhBFA0XBmV8d4LUzEcNVb0xbLjLTETYN8OEVqNxkt10W614dd1FlFFVTIgB7%2FBQQp1sWlNolpIu4ekxUTBV7NmxOFKEBmmN%2BnA7pvF78%2FRII5ZHA09OAiE%2F66MF6HQ%2BqVEJCHxwymukkNvzqHEh52dULPbVasfQMgTDyBZzx4007YiKdBuUauQOt27Gmy8ISclPmEUCIcuLbkb1mzQSqIa3iE0PJh7UMYQbkpe%2BhXjTJKdldyt2mVPwywoODGJtBV1lJTgMsuSQBlDMwhEKIfrvsxGQjHPCEfNfMAY2oxvyKcKPUbQySkKG6tj9AQyEW3Q5rpaDJ5Sns9ScLKeizPRbvWYAw4bXkrZdmB7CQopCH8NAmqbuciZChHN8lVGaDbCnmddnqO1PQ4ieMYfcSiBE5zzMz%2BJV%2F4eyzrzTEShvqSGzgWimkNxLvUj86iAwcZuIkqdB0VaIB7wncLRmzHkiUQpPBIXbDDLHBlq7vp9xwuC9AiNkIptAYlG7Biyuk8ILdynuUM1cHWJgeB%2BK3wBP%2FineogxkvBNNQ4AkW0hvpBOQGFfeptF2YTR75MexYDUy7Q%2F9uocGsx41O4IZhViw%2F2FvAEuGO5g2kyXBUijAggWM08bRhXg5ijgMwDJy40QeY%2FcQpUDZiIzmvskQpO5G1zyGZA8WByjIQU4jRoFJt56behxtHUUE%2Fom7Rj2psYXGmq3llVOCgGYKNMo4pzwntITtapDqjvQtqpjaJwjHmDzSVGLxMt12gEXAdLi%2FcaHSM3FPRGRf7dB7YC%2BcD2ho6oL2zGDCkjlf%2FDFoQVl8GS%2F56wur3rdV6ggtzZW60MRB3g%2BU1W8o8cvqIpMkctiGVMzXUFI7FacFLrgtdz4mTEr4aRAaQ2AFQaNeG7GX0yOJgMRYFziXdJf24kg%2FgBQIZMG%2FYcPEllRTVNoDYR6oSJ8wQNLuihfw81UpiKPm714bZX1KYjcXJdfclCUOOpvTxr9AAJevTY4HK%2FG7F3mUc3GOAKqh60zM0v34v%2BELyhJZqhkaMA8UMMOU90f8RKEJFj7EqepBVwsRiLbwMo1J2zrE2UYJnsgIAscDmjPjnzI8a719Wxp757wqmSJBjXowhc46QN4RwKIxqEE6E5218OeK7RfcpGjWG1jD7qND%2B%2FGTk6M56Ig4yMsU6LUW1EWE%2BfIYycVV1thldSlbP6ltdC01y3KUfkobkt2q01YYMmxpKRvh1Z48uNKzP%2FIoRIZ%2FF6buOymSnW8gICitpJjKWBscSb9JJKaWkvEkqinAJ2kowKoqkqZftRqfRQlLtKoqvTRDi2vg%2FRrPD%2Fd3a09J8JhGZlEkOM6znTsoMCsuvTmywxTCDhw5dd0GJOHCMPbsj3QLkTE3MInsZsimDQ3HkvthT7U9VA4s6G07sID0FW4SHJmRGwCl%2BMu4xf0ezqeXD2PtPDnwMPo86sbwDV%2B9PWcgFcARUVYm3hrFQrHcgMElFGbSM2A1zUYA3baWfheJp2AINmTJLuoyYD%2FOwA4a6V0ChBN97E8YtDBerUECv0u0TlxR5yhJCXvJxgyM73Bb6pyq0jTFJDZ4p1Am1SA6sh8nADd1hAcGBMfq4d%2FUfwnmBqe0Jun1n1LzrgKuZMAnxA3NtCN7Klf4BH%2B14B7ibBmgt0TGUafVzI4uKlpF7v8NmgNjg90D6QE3tbx8AjSAC%2BOA1YJvclyPKgT27QpIEgVYpbPYGBsnyCNrGz9XUsCHkW1QAHgL2STZk12QGqmvAB0NFteERkvBIH7INDsNW9KKaAYyDMdBEMzJiWaJHZALqDxQDWRntumSDPcplyFiI1oDpT8wbwe01AHhW6%2BvAUUBoGhY3CT2tgwehdPqU%2F4Q7ZLYvhRl%2FogOvR9O2%2BwkkPKW5vCTjD2fHRYXONCoIl4Jh1bZY0ZE1O94mMGn%2FdFSWBWzQ%2FVYk%2BGezi46RgiDv3EshoTmMSlioUK6MQEN8qeyK6FRninyX8ZPeUWjjbMJChn0n%2FyJvrq5bh5UcCAcBYSafTFg7p0jDgrXo2QWLb3WpSOET%2FHh4oSadBTvyDo10IufLzxiMLAnbZ1vcUmj3w7BQuIXjEZXifwukVxrGa9j%2BDXfpi12m1RbzYLg9J2wFergEwOxFyD0%2FJstNK06ZN2XdZSGWxcJODpQHOq4iKqjqkJUmPu1VczL5xTGUfCgLEYyNBCCbMBFT%2FcUP6pE%2FmujnHsSDeWxMbhrNilS5MyYR0nJyzanWXBeVcEQrRIhQeJA6Xt4f2eQESNeLwmC10WJVHqwx8SSyrtAAjpGjidcj1E2FYN0LObUcFQhafUKTiGmHWRHGsFCB%2BHEXgrzJEB5bp0QiF8ZHh11nFX8AboTD0PS4O1LqF8XBks2MpjsQnwKHF6HgaKCVLJtcr0XjqFMRGfKv8tmmykhLRzu%2BvqQ02%2BKpJBjaLt9ye1Ab%2BBbEBhy4EVdIJDrL2naV0o4wU8YZ2Lq04FG1mWCKC%2BUwkXOoAjneU%2FxHplMQo2cXUlrVNqJYczgYlaOEczVCs%2FOCgkyvLmTmdaBJc1iBLuKwmr6qtRnhowngsDxhzKFAi02tf8bmET8BO27ovJKF1plJwm3b0JpMh38%2BxsrXXg7U74QUM8ZCIMOpXujHntKdaRtsgyEZl5MClMVMMMZkZLNxH9%2Bb8fH6%2Bb8Lev30A9TuEVj9CqAdmwAAHBPbfOBFEATAPZ2CS0OH1Pj%2F0Q7PFUcC8hDrxESWdfgFRm%2B7vvWbkEppHB4T%2F1ApWnlTIqQwjcPl0VgS1yHSmD0OdsCVST8CQVwuiew1Y%2Bg3QGFjNMzwRB2DSsAk26cmA8lp2wIU4p93AUBiUHFGOxOajAqD7Gm6NezNDjYzwLOaSXRBYcWipTSONHjUDXCY4mMI8XoVCR%2FRrs%2FJLKXgEx%2BqkmeDlFOD1%2FyTQNDClRuiUyKYCllfMiQiyFkmuTz2vLsBNyRW%2Bxz%2B5FElFxWB28VjYIGZ0Yd%2B5wIjkcoMaggxswbT0pCmckRAErbRlIlcOGdBo4djTNO8FAgQ%2BlT6vPS60BwTRSUAM3ddkEAZiwtEyArrkiDRnS7LJ%2B2hwbzd2YDQagSgACpsovmjil5wfPuXq3GuH0CyE7FK3M4FgRaFoIkaodORrPx1%2BJpI9psyNYIFuJogZa0%2F1AhOWdlHQxdAgbwacsHqPZo8u%2FngAH2GmaTdhYnBfSDbBfh8CHq6Bx5bttP2%2BRdM%2BMAaYaZ0Y%2FADkbNCZuAyAVQa2OcXOeICmDn9Q%2FeFkDeFQg5MgHEDXq%2FtVjj%2Bjtd26nhaaolWxs1ixSUgOBwrDhRIGOLyOVk2%2FBc0UxvseQCO2pQ2i%2BKrfhu%2FWeBovNb5dJxQtJRUDv2mCwYVpNl2efQM9xQHnK0JwLYt%2FU0Wf%2BphiA4uw8G91slC832pmOTCAoZXohg1fewCZqLBhkOUBofBWpMPsqg7XEXgPfAlDo2U5WXjtFdS87PIqClCK5nW6adCeXPkUiTGx0emOIDQqw1yFYGHEVx20xKjJVYe0O8iLmnQr3FA9nSIQilUKtJ4ZAdcTm7%2BExseJauyqo30hs%2B1qSW211A1SFAOUgDlCGq7eTIcMAeyZkV1SQJ4j%2Fe1Smbq4HcjqgFbLAGLyKxlMDMgZavK5NAYH19Olz3la%2FQCTiVelFnU6O%2FGCvykqS%2FwZJDhKN9gBtSOp%2F1SP5VRgJcoVj%2Bkmf2wBgv4gjrgARBWiURYx8xENV3bEVUAAWWD3dYDKAIWk5opaCFCMR5ZjJExiCAw7gYiSZ2rkyTce4eNMY3lfGn%2B8p6%2BvBckGlKEXnA6Eota69OxDO9oOsJoy28BXOR0UoXNRaJD5ceKdlWMJlOFzDdZNpc05tkMGQtqeNF2lttZqNco1VtwXgRstLSQ6tSPChgqtGV5h2DcDReIQadaNRR6AsAYKL5gSFsCJMgfsaZ7DpKh8mg8Wz8V7H%2BgDnLuMxaWEIUPevIbClgap4dqmVWSrPgVYCzAoZHIa5z2Ocx1D%2FGvDOEqMOKLrMefWIbSWHZ6jbgA8qVBhYNHpx0P%2BjAgN5TB3haSifDcApp6yymEi6Ij%2FGsEpDYUgcHATJUYDUAmC1SCkJ4cuZXSAP2DEpQsGUjQmKJfJOvlC2x%2FpChkOyLW7KEoMYc5FDC4v2FGqSoRWiLsbPCiyg1U5yiHZVm1XLkHMMZL11%2Fyxyw0UnGig3MFdZklN5FI%2FqiT65T%2BjOXOdO7XbgWurOAZR6Cv9uu1cm5LjkXX4xi6mWn5r5NjBS0gTliHhMZI2WNqSiSphEtiCAwnafS11JhseDGHYQ5%2BbqWiAYiAv6Jsf79%2FVUs4cIl%2Bn6%2BWOjcgB%2F2l5TreoAV2717JzZbQIR0W1cl%2FdEqCy5kJ3ZSIHuU0vBoHooEpiHeQWVkkkOqRX27eD1FWw4BfO9CJDdKoSogQi3hAAwsPRFrN5RbX7bqLdBJ9JYMohWrgJKHSjVl1sy2xAG0E3sNyO0oCbSGOxCNBRRXTXenYKuwAoDLfnDcQaCwehUOIDiHAu5m5hMpKeKM4sIo3vxACakIxKoH2YWF2QM84e6F5C5hJU4g8uxuFOlAYnqtwxmHyNEawLW%2FPhoawJDrGAP0JYWHgAVUByo%2FbGdiv2T2EMg8gsS14%2FrAdzlOYazFE7w4OzxeKiWdm3nSOnQRRKXSlVo8HEAbBfyJMKqoq%2BSCcTSx5NDtbFwNlh8VhjGGDu7JG5%2FTAGAvniQSSUog0pNzTim8Owc6QTuSKSTXlQqwV3eiEnklS3LeSXYPXGK2VgeZBqNcHG6tZHvA3vTINhV0ELuQdp3t1y9%2BogD8Kk%2FW7QoRN1UWPqM4%2BxdygkFDPLoTaumKReKiLWoPHOfY54m3qPx4c%2B4pgY3MRKKbljG8w4wvz8pxk3AqKsy4GMAkAtmRjRMsCxbb4Q2Ds0Ia9ci8cMT6DmsJG00XaHCIS%2Bo3F8YVVeikw13w%2BOEDaCYYhC0ZE54kA4jpjruBr5STWeqQG6M74HHL6TZ3lXrd99ZX%2B%2B7LhNatQaZosuxEf5yRA15S9gPeHskBIq3Gcw81AGb9%2FO53DYi%2F5CsQ51EmEh8Rkg4vOciClpy4d04eYsfr6fyQkBmtD%2BP8sNh6e%2BXYHJXT%2FlkXxT4KXU5F2sGxYyzfniMMQkb9OjDN2C8tRRgTyL7GwozH14PrEUZc6oz05Emne3Ts5EG7WolDmU8OB1LDG3VrpQxp%2BpT0KYV5dGtknU64JhabdqcVQbGZiAxQAnvN1u70y1AnmvOSPgLI6uB4AuDGhmAu3ATkJSw7OtS%2F2ToPjqkaq62%2F7WFG8advGlRRqxB9diP07JrXowKR9tpRa%2BjGJ91zxNTT1h8I2PcSfoUPtd7NejVoH03EUcqSBuFZPkMZhegHyo2ZAITovmm3zAIdGFWxoNNORiMRShgwdYwFzkPw5PA4a5MIIQpmq%2Bnsp3YMuXt%2FGkXxLx%2FP6%2BZJS0lFyz4MunC3eWSGE8xlCQrKvhKUPXr0hjpAN9ZK4PfEDrPMfMbGNWcHDzjA7ngMxTPnT7GMHar%2BgMQQ3NwHCv4zH4BIMYvzsdiERi6gebRmerTsVwZJTRsL8dkZgxgRxmpbgRcud%2BYlCIRpPwHShlUSwuipZnx9QCsEWziVazdDeKSYU5CF7UVPAhLer3CgJOQXl%2Fzh575R5rsrmRnKAzq4POFdgbYBuEviM4%2BLVC15ssLNFghbTtHWerS1hDt5s4qkLUha%2FqpZXhWh1C6lTQAqCNQnaDjS7UGFBC6wTu8yFnKJnExCnAs3Ok9yj5KpfZESQ4lTy5pTGTnkAUpxI%2ByjEldJfSo4y0QhG4i4IwkRFGcjWY8%2BEzgYYJUK7BXQksLxAww%2FYYWBMhJILB9e8ePEJ4OP7z%2B4%2FwOQDl64iOYDp26DaONPxpKtBxq%2FaTzRGarm3VkPYTLJKx6Z%2FMw2YbBGseJhPMwhhNswrIkyvV2BYzrvZbxLpKwcWJhYmFtVZ%2BlPEq91FzVp1HlQY1bZVLqeNR9SAUn6n0E28k%2FUuGkNpP1DBI5ch%2FEehZfjUQ9aE41NhETExoPT2gGQz0IhWJbEOvTQ4wgcXCHHFBhewYUiFHuhRSAUVmEHeCRQHQkXGFwkAgyzREJCVN7TRnTon36Zw3tPhx4EALwNdwDv%2BJ41YSP4B2CQqz0EFgARZ4ESgBHQgROwAVn9GTI%2BHYexTUevLUeta4%2FDqKrbMVS%2BYqb8hUwYCrlgKtmAq1YCrFgKrd4qpXiqZcKn1oqdWipjYKpWwVPVYqW6xUpVipKqFR3QKjagVEtAqHpxUMTitsnFaJOKx2cVhswq35RVpyiq9lFVNIKnOQVMkgqtYxVNxiqQjFS7GKlSIVIsQqPIhUWwioigFQ%2B%2BKkN8VHr49HDw9Ebo9EDo9DTo9Crg9BDg9%2FWx7gWx7YWwlobYrOGxWPNisAaAHEyALpkAVDIAeWAArsABVXACYuAD5cAF6wAKFQAQqgAbVAAsoAAlQAUaYAfkwAvogBWQACOgAD9AAHSAAKT4GUdMiOvFngBTwCn2AZ7Dv6B6k%2F90B8%2ByRnkV144AIBoAMTQATGgAjNAA4YABgwABZgB%2FmQCwyAVlwCguASlwCEuAQFwB4uAMlwBYuAJlQAUVAAhUD2KgdpUDaJgaRMDFJgX5MC1JgWJEAokQCWRAHxEAWkQBMRADpEAMkQAYROAEecC484DRpwBDTnwNOdw05tjTmiNOYwtswhYFwLA7BYG4LA2BYGOLAwRYFuLAsxYFQJAohIEyJAMwkAwiQC0JAJgkAeiQBkJAFokAPCQA0JABwcD4Dgc4cDdDgaYcDIDgYgUC6CgWgUClCgUYUAVBQBOFAEYMALgwAgDA9QYAdIn8AZzeBB2L5EcWrenUT1KXienEsuJJ7x5U8XlTjc1NVzUyXFTGb1LlpUtWlTDIjqwE4LsagowoCi2gJLKAkpoBgJQNpAIhNqaEoneI6kiiqQ6Go%2Fn6j0cS%2Ba2gEU8gIHJ%2BBwfgZX4GL%2BBd%2FgW34FZ%2BBS%2FgUH4FN6BTegTvoEv6BJegRnYEF2A79gOvYDl2BdEjCkqkGtwXp0LNToIskOTXzh%2FF062yJ7AAAAEDAWAAABWhJ%2BKPEIJgBFxMVP7w2QJBGHASQnOBKXKFIdUK4igKA9IEaYJg%29%3Bsrc%3Aurl%28data%3Aapplication%2Fvnd%2Ems%2Dfontobject%3Bbase64%2Cn04AAEFNAAACAAIABAAAAAAABQAAAAAAAAABAJABAAAEAExQAAAAAAAAAAIAAAAAAAAAAAEAAAAAAAAAJxJ%2FLAAAAAAAAAAAAAAAAAAAAAAAACgARwBMAFkAUABIAEkAQwBPAE4AUwAgAEgAYQBsAGYAbABpAG4AZwBzAAAADgBSAGUAZwB1AGwAYQByAAAAeABWAGUAcgBzAGkAbwBuACAAMQAuADAAMAA5ADsAUABTACAAMAAwADEALgAwADAAOQA7AGgAbwB0AGMAbwBuAHYAIAAxAC4AMAAuADcAMAA7AG0AYQBrAGUAbwB0AGYALgBsAGkAYgAyAC4ANQAuADUAOAAzADIAOQAAADgARwBMAFkAUABIAEkAQwBPAE4AUwAgAEgAYQBsAGYAbABpAG4AZwBzACAAUgBlAGcAdQBsAGEAcgAAAAAAQlNHUAAAAAAAAAAAAAAAAAAAAAADAKncAE0TAE0ZAEbuFM3pjM%2FSEdmjKHUbyow8ATBE40IvWA3vTu8LiABDQ%2BpexwUMcm1SMnNryctQSiI1K5ZnbOlXKmnVV5YvRe6RnNMFNCOs1KNVpn6yZhCJkRtVRNzEufeIq7HgSrcx4S8h%2Fv4vnrrKc6oCNxmSk2uKlZQHBii6iKFoH0746ThvkO1kJHlxjrkxs%2BLWORaDQBEtiYJIR5IB9Bi1UyL4Rmr0BNigNkMzlKQmnofBHviqVzUxwdMb3NdCn69hy%2BpRYVKGVS%2F1tnsqv4LL7wCCPZZAZPT4aCShHjHJVNuXbmMrY5LeQaGnvAkXlVrJgKRAUdFjrWEah9XebPeQMj7KS7DIBAFt8ycgC5PLGUOHSE3ErGZCiViNLL5ZARfywnCoZaKQCu6NuFX42AEeKtKUGnr%2FCm2Cy8tpFhBPMW5Fxi4Qm4TkDWh4IWFDClhU2hRWosUWqcKLlgyXB%2BlSHaWaHiWlBAR8SeSgSPCQxdVQgzUixWKSTrIQEbU94viDctkvX%2BVSjJuUmV8L4CXShI11esnp0pjWNZIyxKHS4wVQ2ime1P4RnhvGw0aDN1OLAXGERsB7buFpFGGBAre4QEQR0HOIO5oYH305G%2BKspT%2FFupEGGafCCwxSe6ZUa%2B073rXHnNdVXE6eWvibUS27XtRzkH838mYLMBmYysZTM0EM3A1fbpCBYFccN1B%2FEnCYu%2FTgCGmr7bMh8GfYL%2BBfcLvB0gRagC09w9elfldaIy%2FhNCBLRgBgtCC7jAF63wLSMAfbfAlEggYU0bUA7ACCJmTDpEmJtI78w4%2FBO7dN7JR7J7ZvbYaUbaILSQsRBiF3HGk5fEg6p9unwLvn98r%2BvnsV%2B372uf1xBLq4qU%2F45fTuqaAP%2BpssmCCCTF0mhEow8ZXZOS8D7Q85JsxZ%2BAzok7B7O%2Ff6J8AzYBySZQB%2FQHYUSA%2BEeQhEWiS6AIQzgcsDiER4MjgMBAWDV4AgQ3g1eBgIdweCQmCjJEMkJ%2BPKRWyFHHmg1Wi%2F6xzUgA0LREoKJChwnQa9B%2B5RQZRB3IlBlkAnxyQNaANwHMowzlYSMCBgnbpzvqpl0iTJNCQidDI9ZrSYNIRBhHtUa5YHMHxyGEik9hDE0AKj72AbTCaxtHPUaKZdAZSnQTyjGqGLsmBStCejApUhg4uBMU6mATujEl%2BKdDPbI6Ag4vLr%2BhjY6lbjBeoLKnZl0UZgRX8gTySOeynZVz1wOq7e1hFGYIq%2BMhrGxDLak0PrwYzSXtcuyhXEhwOYofiW%2BEcI%2Fjw8P6IY6ed%2BetAbuqKp5QIapT77LnAe505lMuqL79a0ut4rWexzFttsOsLDy7zvtQzcq3U1qabe7tB0wHWVXji%2BzDbo8x8HyIRUbXnwUcklFv51fvTymiV%2BMXLSmGH9d9%2BaXpD5X6lao41anWGig7IwIdnoBY2ht%2FpO9mClLo4NdXHAsefqWUKlXJkbqPOFhMoR4aiA1BXqhRNbB2Xwi%2B7u%2FjpAoOpKJ0UX24EsrzMfHXViakCNcKjBxuQX8BO0ZqjJ3xXzf%2B61t2VXOSgJ8xu65QKgtN6FibPmPYsXbJRHHqbgATcSZxBqGiDiU4NNNsYBsKD0MIP%2FOfKnlk%2FLkaid%2FO2NbKeuQrwOB2Gq3YHyr6ALgzym5wIBnsdC1ZkoBFZSQXChZvlesPqvK2c5oHHT3Q65jYpNxnQcGF0EHbvYqoFw60WNlXIHQF2HQB7zD6lWjZ9rVqUKBXUT6hrkZOle0RFYII0V5ZYGl1JAP0Ud1fZZMvSomBzJ710j4Me8mjQDwEre5Uv2wQfk1ifDwb5ksuJQQ3xt423lbuQjvoIQByQrNDh1JxGFkOdlJvu%2FgFtuW0wR4cgd%2BZKesSV7QkNE2kw6AV4hoIuC02LGmTomyf8PiO6CZzOTLTPQ%2BHW06H%2Btx%2BbQ8LmDYg1pTFrp2oJXgkZTyeRJZM0C8aE2LpFrNVDuhARsN543%2FFV6klQ6Tv1OoZGXLv0igKrl%2FCmJxRmX7JJbJ998VSIPQRyDBICzl4JJlYHbdql30NvYcOuZ7a10uWRrgoieOdgIm4rlq6vNOQBuqESLbXG5lzdJGHw2m0sDYmODXbYGTfSTGRKpssTO95fothJCjUGQgEL4yKoGAF%2F0SrpUDNn8CBgBcSDQByAeNkCXp4S4Ro2Xh4OeaGRgR66PVOsU8bc6TR5%2FxTcn4IVMLOkXSWiXxkZQCbvKfmoAvQaKjO3EDKwkwqHChCDEM5loQRPd5ACBki1TjF772oaQhQbQ5C0lcWXPFOzrfsDGUXGrpxasbG4iab6eByaQkQfm0VFlP0ZsDkvvqCL6QXMUwCjdMx1ZOyKhTJ7a1GWAdOUcJ8RSejxNVyGs31OKMyRyBVoZFjqIkmKlLQ5eHMeEL4MkUf23cQ%2F1SgRCJ1dk4UdBT7OoyuNgLs0oCd8RnrEIb6QdMxT2QjD4zMrJkfgx5aDMcA4orsTtKCqWb%2FVeyceqa5OGSmB28YwH4rFbkQaLoUN8OQQYnD3w2eXpI4ScQfbCUZiJ4yMOIKLyyTc7BQ4uXUw6Ee6%2FxM%2B4Y67ngNBknxIPwuppgIhFcwJyr6EIj%2BLzNj%2FmfR2vhhRlx0BILZoAYruF0caWQ7YxO66UmeguDREAFHYuC7HJviRgVO6ruJH59h%2FC%2FPkgSle8xNzZJULLWq9JMDTE2fjGE146a1Us6PZDGYle6ldWRqn%2FpdpgHKNGrGIdkRK%2BKPETT9nKT6kLyDI8xd9A1FgWmXWRAIHwZ37WyZHOVyCadJEmMVz0MadMjDrPho%2BEIochkVC2xgGiwwsQ6DMv2P7UXqT4x7CdcYGId2BJQQa85EQKmCmwcRejQ9Bm4oATENFPkxPXILHpMPUyWTI5rjNOsIlmEeMbcOCEqInpXACYQ9DDxmFo9vcmsDblcMtg4tqBerNngkIKaFJmrQAPnq1dEzsMXcwjcHdfdCibcAxxA%2Bq%2Fj9m3LM%2FO7WJka4tSidVCjsvo2lQ%2F2ewyoYyXwAYyr2PlRoR5MpgVmSUIrM3PQxXPbgjBOaDQFIyFMJvx3Pc5RSYj12ySVF9fwFPQu2e2KWVoL9q3Ayv3IzpGHUdvdPdrNUdicjsTQ2ISy7QU3DrEytIjvbzJnAkmANXjAFERA0MUoPF3%2F5KFmW14bBNOhwircYgMqoDpUMcDtCmBE82QM2YtdjVLB4kBuKho%2FbcwQdeboqfQartuU3CsCf%2BcXkgYAqp%2F0Ee3RorAZt0AvvOCSI4JICIlGlsV0bsSid%2FNIEALAAzb6HAgyWHBps6xAOwkJIGcB82CxRQq4sJf3FzA70A%2BTRqcqjEMETCoez3mkPcpnoALs0ugJY8kQwrC%2BJE5ik3w9rzrvDRjAQnqgEVvdGrNwlanR0SOKWzxOJOvLJhcd8Cl4AshACUkv9czdMkJCVQSQhp6kp7StAlpVRpK0t0SW6LHeBJnE2QchB5Ccu8kxRghZXGIgZIiSj7gEKMJDClcnX6hgoqJMwiQDigIXg3ioFLCgDgjPtYHYpsF5EiA4kcnN18MZtOrY866dEQAb0FB34OGKHGZQjwW%2FWDHA60cYFaI%2FPjpzquUqdaYGcIq%2BmLez3WLFFCtNBN2QJcrlcoELgiPku5R5dSlJFaCEqEZle1AQzAKC%2B1SotMcBNyQUFuRHRF6OlimSBgjZeTBCwLyc6A%2BP%2FoFRchXTz5ADknYJHxzrJ5pGuIKRQISU6WyKTBBjD8WozmVYWIsto1AS5rxzKlvJu4E%2FvwOiKxRtCWsDM%2BeTHUrmwrCK5BIfMzGkD%2B0Fk5LzBs0jMYXktNDblB06LMNJ09U8pzSLmo14MS0OMjcdrZ31pyQqxJJpRImlSvfYAK8inkYU52QY2FPEVsjoWewpwhRp5yAuNpkqhdb7ku9Seefl2D0B8SMTFD90xi4CSOwwZy9IKkpMtI3FmFUg3%2FkFutpQGNc3pCR7gvC4sgwbupDu3DyEN%2BW6YGLNM21jpB49irxy9BSlHrVDlnihGKHwPrbVFtc%2Bh1rVQKZduxIyojccZIIcOCmhEnC7UkY68WXKQgLi2JCDQkQWJRQuk60hZp0D3rtCTINSeY9Ej2kIKYfGxwOs4j9qMM7fYZiipzgcf7TamnehqdhsiMiCawXnz4xAbyCkLAx5EGbo3Ax1u3dUIKnTxIaxwQTHehPl3V491H0%2BbC5zgpGz7Io%2BmjdhKlPJ01EeMpM7UsRJMi1nGjmJg35i6bQBAAxjO%2FENJubU2mg3ONySEoWklCwdABETcs7ck3jgiuU9pcKKpbgn%2B3YlzV1FzIkB6pmEDOSSyDfPPlQskznctFji0kpgZjW5RZe6x9kYT4KJcXg0bNiCyif%2BpZACCyRMmYsfiKmN9tSO65F0R2OO6ytlEhY5Sj6uRKfFxw0ijJaAx%2Fk3QgnAFSq27%2F2i4GEBA%2BUvTJKK%2F9eISNvG46Em5RZfjTYLdeD8kdXHyrwId%2FDQZUaMCY4gGbke2C8vfjgV%2FY9kkRQOJIn%2FxM9INZSpiBnqX0Q9GlQPpPKAyO5y%2BW5NMPSRdBCUlmuxl40ZfMCnf2Cp044uI9WLFtCi4YVxKjuRCOBWIb4XbIsGdbo4qtMQnNOQz4XDSui7W%2FN6l54qOynCqD3DpWQ%2BmpD7C40D8BZEWGJX3tlAaZBMj1yjvDYKwCJBa201u6nBKE5UE%2B7QSEhCwrXfbRZylAaAkplhBWX50dumrElePyNMRYUrC99UmcSSNgImhFhDI4BXjMtiqkgizUGCrZ8iwFxU6fQ8GEHCFdLewwxYWxgScAYMdMLmcZR6b7rZl95eQVDGVoUKcRMM1ixXQtXNkBETZkVVPg8LoSrdetHzkuM7DjZRHP02tCxA1fmkXKF3VzfN1pc1cv%2F8lbTIkkYpqKM9VOhp65ktYk%2BQ46myFWBapDfyWUCnsnI00QTBQmuFjMZTcd0V2NQ768Fhpby04k2IzNR1wKabuGJqYWwSly6ocMFGTeeI%2BejsWDYgEvr66QgqdcIbFYDNgsm0x9UHY6SCd5%2B7tpsLpKdvhahIDyYmEJQCqMqtCF6UlrE5GXRmbu%2Bvtm3BFSxI6ND6UxIE7GsGMgWqghXxSnaRJuGFveTcK5ZVSPJyjUxe1dKgI6kNF7EZhIZs8y8FVqwEfbM0Xk2ltORVDKZZM40SD3qQoQe0orJEKwPfZwm3YPqwixhUMOndis6MhbmfvLBKjC8sKKIZKbJk8L11oNkCQzCgvjhyyEiQSuJcgCQSG4Mocfgc0Hkwcjal1UNgP0CBPikYqBIk9tONv4kLtBswH07vUCjEaHiFGlLf8MgXKzSgjp2HolRRccAOh0ILHz9qlGgIFkwAnzHJRjWFhlA7ROwINyB5HFj59PRZHFor6voq7l23EPNRwdWhgawqbivLSjRA4htEYUFkjESu67icTg5S0aW1sOkCiIysfJ9UnIWevOOLGpepcBxy1wEhd2WI3AZg7sr9WBmHWyasxMcvY%2FiOmsLtHSWNUWEGk9hScMPShasUA1AcHOtRZlqMeQ0OzYS9vQvYUjOLrzP07BUAFikcJNMi7gIxEw4pL1G54TcmmmoAQ5s7TGWErJZ2Io4yQ0ljRYhL8H5e62oDtLF8aDpnIvZ5R3GWJyAugdiiJW9hQAVTsnCBHhwu7rkBlBX6r3b7ejEY0k5GGeyKv66v%2B6dg7mcJTrWHbtMywbedYqCQ0FPwoytmSWsL8WTtChZCKKzEF7vP6De4x2BJkkniMgSdWhbeBSLtJZR9CTHetK1xb34AYIJ37OegYIoPVbXgJ%2FqDQK%2BbfCtxQRVKQu77WzOoM6SGL7MaZwCGJVk46aImai9fmam%2BWpHG%2B0BtQPWUgZ7RIAlPq6lkECUhZQ2gqWkMYKcYMYaIc4gYCDFHYa2d1nzp3%2BJ1eCBay8IYZ0wQRKGAqvCuZ%2FUgbQPyllosq%2BXtfKIZOzmeJqRazpmmoP%2F76YfkjzV2NlXTDSBYB04SVlNQsFTbGPk1t%2FI4Jktu0XSgifO2ozFOiwd%2F0SssJDn0dn4xqk4GDTTKX73%2FwQyBLdqgJ%2BWx6AQaba3BA9CKEzjtQYIfAsiYamapq80LAamYjinlKXUkxdpIDk0puXUEYzSalfRibAeDAKpNiqQ0FTwoxuGYzRnisyTotdVTclis1LHRQCy%2FqqL8oUaQzWRxilq5Mi0IJGtMY02cGLD69vGjkj3p6pGePKI8bkBv5evq8SjjyU04vJR2cQXQwSJyoinDsUJHCQ50jrFTT7yRdbdYQMB3MYCb6uBzJ9ewhXYPAIZSXfeEQBZZ3GPN3Nbhh%2FwkvAJLXnQMdi5NYYZ5GHE400GS5rXkOZSQsdZgIbzRnF9ueLnsfQ47wHAsirITnTlkCcuWWIUhJSbpM3wWhXNHvt2xUsKKMpdBSbJnBMcihkoDqAd1Zml%2FR4yrzow1Q2A5G%2Bkzo%2FRhRxQS2lCSDRV8LlYLBOOoo1bF4jwJAwKMK1tWLHlu9i0j4Ig8qVm6wE1DxXwAwQwsaBWUg2pOOol2dHxyt6npwJEdLDDVYyRc2D0HbcbLUJQj8gPevQBUBOUHXPrsAPBERICpnYESeu2OHotpXQxRGlCCtLdIsu23MhZVEoJg8Qumj%2FUMMc34IBqTKLDTp76WzL%2FdMjCxK7MjhiGjeYAC%2Fkj%2FjY%2FRde7hpSM1xChrog6yZ7OWTuD56xBJnGFE%2BpT2ElSyCnJcwVzCjkqeNLfMEJqKW0G7OFIp0G%2B9mh50I9o8k1tpCY0xYqFNIALgIfc2me4n1bmJnRZ89oepgLPT0NTMLNZsvSCZAc3TXaNB07vail36%2FdBySis4m9%2FDR8izaLJW6bWCkVgm5T%2Bius3ZXq4xI%2BGnbveLbdRwF2mNtsrE0JjYc1AXknCOrLSu7Te%2Fr4dPYMCl5qtiHNTn%2BTPbh1jCBHH%2BdMJNhwNgs3nT%2BOhQoQ0vYif56BMG6WowAcHR3DjQolxLzyVekHj00PBAaW7IIAF1EF%2BuRIWyXjQMAs2chdpaKPNaB%2BkSezYt0%2BCA04sOg5vx8Fr7Ofa9sUv87h7SLAUFSzbetCCZ9pmyLt6l6%2FTzoA1%2FZBG9bIUVHLAbi%2FkdBFgYGyGwRQGBpkqCEg2ah9UD6EedEcEL3j4y0BQQCiExEnocA3SZboh%2Bepgd3YsOkHskZwPuQ5OoyA0fTA5AXrHcUOQF%2BzkJHIA7PwCDk1gGVmGUZSSoPhNf%2BTklauz98QofOlCIQ%2FtCD4dosHYPqtPCXB3agggQQIqQJsSkB%2Bqn0rkQ1toJjON%2FOtCIB9RYv3PqRA4C4U68ZMlZn6BdgEvi2ziU%2BTQ6NIw3ej%2BAtDwMGEZk7e2IjxUWKdAxyaw9OCwSmeADTPPleyk6UhGDNXQb%2B%2BW6Uk4q6F7%2Frg6WVTo82IoCxSIsFDrav4EPHphD3u4hR53WKVvYZUwNCCeM4PMBWzK%2BEfIthZOkuAwPo5C5jgoZgn6dUdvx5rIDmd58cXXdKNfw3l%2BwM2UjgrDJeQHhbD7HW2QDoZMCujgIUkk5Fg8VCsdyjOtnGRx8wgKRPZN5dR0zPUyfGZFVihbFRniXZFOZGKPnEQzU3AnD1KfR6weHW2XS6KbPJxUkOTZsAB9vTVp3Le1F8q5l%2BDMcLiIq78jxAImD2pGFw0VHfRatScGlK6SMu8leTmhUSMy8Uhdd6xBiH3Gdman4tjQGLboJfqz6fL2WKHTmrfsKZRYX6BTDjDldKMosaSTLdQS7oDisJNqAUhw1PfTlnacCO8vl8706Km1FROgLDmudzxg%2BEWTiArtHgLsRrAXYWdB0NmToNCJdKm0KWycZQqb%2BMw76Qy29iQ5up%2FX7oyw8QZ75kP5F6iJAJz6KCmqxz8fEa%2FxnsMYcIO%2FvEkGRuMckhr4rIeLrKaXnmIzlNLxbFspOphkcnJdnz%2FChp%2FVlpj2P7jJQmQRwGnltkTV5dbF9fE3%2FfxoSqTROgq9wFUlbuYzYcasE0ouzBo%2BdDCDzxKAfhbAZYxQiHrLzV2iVexnDX%2FQnT1fsT%2Fxuhu1ui5qIytgbGmRoQkeQooO8eJNNZsf0iALur8QxZFH0nCMnjerYQqG1pIfjyVZWxhVRznmmfLG00BcBWJE6hzQWRyFknuJnXuk8A5FRDCulwrWASSNoBtR%2BCtGdkPwYN2o7DOw%2FVGlCZPusRBFXODQdUM5zeHDIVuAJBLqbO%2Ff9Qua%2BpDqEPk230Sob9lEZ8BHiCorjVghuI0lI4JDgHGRDD%2FprQ84B1pVGkIpVUAHCG%2Biz3Bn3qm2AVrYcYWhock4jso5%2BJ7HfHVj4WMIQdGctq3psBCVVzupQOEioBGA2Bk%2BUILT7%2BVoX5mdxxA5fS42gISQVi%2FHTzrgMxu0fY6hE1ocUwwbsbWcezrY2n6S8%2F6cxXkOH4prpmPuFoikTzY7T85C4T2XYlbxLglSv2uLCgFv8Quk%2FwdesUdWPeHYIH0R729JIisN9Apdd4eB10aqwXrPt%2BSu9mA8k8n1sjMwnfsfF2j3jMUzXepSHmZ%2FBfqXvzgUNQQWOXO8YEuFBh4QTYCkOAPxywpYu1VxiDyJmKVcmJPGWk%2Fgc3Pov02StyYDahwmzw3E1gYC9wkupyWfDqDSUMpCTH5e5N8B%2F%2FlHiMuIkTNw4USHrJU67bjXGqNav6PBuQSoqTxc8avHoGmvqNtXzIaoyMIQIiiUHIM64cXieouplhNYln7qgc4wBVAYR104kO%2BCvKqsg4yIUlFNThVUAKZxZt1XA34h3TCUUiXVkZ0w8Hh2R0Z5L0b4LZvPd%2Fp1gi%2F07h8qfwHrByuSxglc9cI4QIg2oqvC%2Fqm0i7tjPLTgDhoWTAKDO2ONW5oe%2B%2FeKB9vZB8K6C25yCZ9RFVMnb6NRdRjyVK57CHHSkJBfnM2%2Fj4ODUwRkqrtBBCrDsDpt8jhZdXoy%2F1BCqw3sSGhgGGy0a5Jw6BP%2FTExoCmNFYjZl248A0osgPyGEmRA%2BfAsqPVaNAfytu0vuQJ7rk3J4kTDTR2AlCHJ5cls26opZM4w3jMULh2YXKpcqGBtuleAlOZnaZGbD6DHzMd6i2oFeJ8z9XYmalg1Szd%2FocZDc1C7Y6vcALJz2lYnTXiWEr2wawtoR4g3jvWUU2Ngjd1cewtFzEvM1NiHZPeLlIXFbBPawxNgMwwAlyNSuGF3zizVeOoC9bag1qRAQKQE%2FEZBWC2J8mnXAN2aTBboZ7HewnObE8CwROudZHmUM5oZ%2FUgd%2FJZQK8lvAm43uDRAbyW8gZ%2BZGq0EVerVGUKUSm%2FIdn8AQHdR4m7bue88WBwft9mSCeMOt1ncBwziOmJYI2ZR7ewNMPiCugmSsE4EyQ%2BQATJG6qORMGd4snEzc6B4shPIo4G1T7PgSm8PY5eUkPdF8JZ0VBtadbHXoJgnEhZQaODPj2gpODKJY5Yp4DOsLBFxWbvXN755KWylJm%2BoOd4zEL9Hpubuy2gyyfxh8oEfFutnYWdfB8PdESLWYvSqbElP9qo3u6KTmkhoacDauMNNjj0oy40DFV7Ql0aZj77xfGl7TJNHnIwgqOkenruYYNo6h724%2BzUQ7%2BvkCpZB%2BpGA562hYQiDxHVWOq0oDQl%2FQsoiY%2BcuI7iWq%2FZIBtHcXJ7kks%2Bh2fCNUPA82BzjnqktNts%2BRLdk1VSu%2BtqEn7QZCCsvEqk6FkfiOYkrsw092J8jsfIuEKypNjLxrKA9kiA19mxBD2suxQKCzwXGws7kEJvlhUiV9tArLIdZW0IORcxEzdzKmjtFhsjKy%2F44XYXdI5noQoRcvjZ1RMPACRqYg2V1%2BOwOepcOknRLLFdYgTkT5UApt%2FJhLM3jeFYprZV%2BZow2g8fP%2BU68hkKFWJj2yBbKqsrp25xkZX1DAjUw52IMYWaOhab8Kp05VrdNftqwRrymWF4OQSjbdfzmRZirK8FMJELEgER2PHjEAN9pGfLhCUiTJFbd5LBkOBMaxLr%2FA1SY9dXFz4RjzoU9ExfJCmx%2FI9FKEGT3n2cmzl2X42L3Jh%2BAbQq6sA%2BSs1kitoa4TAYgKHaoybHUDJ51oETdeI%2F9ThSmjWGkyLi5QAGWhL0BG1UsTyRGRJOldKBrYJeB8ljLJHfATWTEQBXBDnQexOHTB%2BUn44zExFE4vLytcu5NwpWrUxO%2F0ZICUGM7hGABXym0V6ZvDST0E370St9MIWQOTWngeoQHUTdCJUP04spMBMS8LSker9cReVQkULFDIZDFPrhTzBl6sed9wcZQTbL%2BBDqMyaN3RJPh%2Fanbx%2BIv%2BqgQdAa3M9Z5JmvYlh4qop%2BHo1F1W5gbOE9YKLgAnWytXElU4G8GtW47lhgFE6gaSs%2Bgs37sFvi0PPVvA5dnCBgILTwoKd%2F%2BDoL9F6inlM7H4rOTzD79KJgKlZO%2FZgt22UsKhrAaXU5ZcLrAglTVKJEmNJvORGN1vqrcfSMizfpsgbIe9zno%2BgBoKVXgIL%2FVI8dB1O5o%2FR3Suez%2FgD7M781ShjKpIIORM%2FnxG%2BjjhhgPwsn2IoXsPGPqYHXA63zJ07M2GPEykQwJBYLK808qYxuIew4frk52nhCsnCYmXiR6CuapvE1IwRB4%2FQftDbEn%2BAucIr1oxrLabRj9q4ae0%2BfXkHnteAJwXRbVkR0mctVSwEbqhJiMSZUp9DNbEDMmjX22m3ABpkrPQQTP3S1sib5pD2VRKRd%2BeNAjLYyT0hGrdjWJZy24OYXRoWQAIhGBZRxuBFMjjZQhpgrWo8SiFYbojcHO8V5DyscJpLTHyx9Fimassyo5U6WNtquUMYgccaHY5amgR3PQzq3ToNM5ABnoB9kuxsebqmYZm0R9qxJbFXCQ1UPyFIbxoUraTJFDpCk0Wk9GaYJKz%2F6oHwEP0Q14lMtlddQsOAU9zlYdMVHiT7RQP3XCmWYDcHCGbVRHGnHuwzScA0BaSBOGkz3lM8CArjrBsyEoV6Ys4qgDK3ykQQPZ3hCRGNXQTNNXbEb6tDiTDLKOyMzRhCFT%2BmAUmiYbV3YQVqFVp9dorv%2BTsLeCykS2b5yyu8AV7IS9cxcL8z4Kfwp%2BxJyYLv1OsxQCZwTB4a8BZ%2F5EdxTBJthApqyfd9u3ifr%2FWILTqq5VqgwMT9SOxbSGWLQJUUWCVi4k9tho9nEsbUh7U6NUsLmkYFXOhZ0kmamaJLRNJzSj%2Fqn4Mso6zb6iLLBXoaZ6AqeWCjHQm2lztnejYYM2eubnpBdKVLORZhudH3JF1waBJKA9%2BW8EhMj3Kzf0L4vi4k6RoHh3Z5YgmSZmk6ns4fjScjAoL8GoOECgqgYEBYUGFVO4FUv4%2FYtowhEmTs0vrvlD%2FCrisnoBNDAcUi%2FteY7OctFlmARQzjOItrrlKuPO6E2Ox93L4O%2F4DcgV%2FdZ7qR3VBwVQxP1GCieA4RIpweYJ5FoYrHxqRBdJjnqbsikA2Ictbb8vE1GYIo9dacK0REgDX4smy6GAkxlH1yCGGsk%2BtgiDhNKuKu3yNrMdxafmKTF632F8Vx4BNK57GvlFisrkjN9WDAtjsWA0ENT2e2nETUb%2Fn7qwhvGnrHuf5bX6Vh%2Fn3xffU3PeHdR%2BFA92i6ufT3AlyAREoNDh6chiMWTvjKjHDeRhOa9YkOQRq1vQXEMppAQVwHCuIcV2g5rBn6GmZZpTR7vnSD6ZmhdSl176gqKTXu5E%2BYbfL0adwNtHP7dT7t7b46DVZIkzaRJOM%2BS6KcrzYVg%2BT3wSRFRQashjfU18NutrKa%2F7PXbtuJvpIjbgPeqd%2BpjmRw6YKpnANFSQcpzTZgpSNJ6J7uiagAbir%2F8tNXJ%2FOsOnRh6iuIexxrmkIneAgz8QoLmiaJ8sLQrELVK2yn3wOHp57BAZJhDZjTBzyoRAuuZ4eoxHruY1pSb7qq79cIeAdOwin4GdgMeIMHeG%2BFZWYaiUQQyC5b50zKjYw97dFjAeY2I4Bnl105Iku1y0lMA1ZHolLx19uZnRdILcXKlZGQx%2FGdEqSsMRU1BIrFqRcV1qQOOHyxOLXEGcbRtAEsuAC2V4K3p5mFJ22IDWaEkk9ttf5Izb2LkD1MnrSwztXmmD%2FQi%2FEmVEFBfiKGmftsPwVaIoZanlKndMZsIBOskFYpDOq3QUs9aSbAAtL5Dbokus2G4%2FasthNMK5UQKCOhU97oaOYNGsTah%2BjfCKsZnTRn5TbhFX8ghg8CBYt%2FBjeYYYUrtUZ5jVij%2Fop7V5SsbA4mYTOwZ46hqdpbB6Qvq3AS2HHNkC15pTDIcDNGsMPXaBidXYPHc6PJAkRh29Vx8KcgX46LoUQBhRM%2B3SW6Opll%2FwgxxsPgKJKzr5QCmwkUxNbeg6Wj34SUnEzOemSuvS2OetRCO8Tyy%2BQbSKVJcqkia%2BGvDefFwMOmgnD7h81TUtMn%2BmRpyJJ349HhAnoWFTejhpYTL9G8N2nVg1qkXBeoS9Nw2fB27t7trm7d%2FQK7Cr4uoCeOQ7%2F8JfKT77KiDzLImESHw%2F0wf73QeHu74hxv7uihi4fTX%2BXEwAyQG3264dwv17aJ5N335Vt9sdrAXhPOAv8JFvzqyYXwfx8WYJaef1gMl98JRFyl5Mv5Uo%2FoVH5ww5OzLFsiTPDns7fS6EURSSWd%2F92BxMYQ8sBaH%2Bj%2BwthQPdVgDGpTfi%2BJQIWMD8xKqULliRH01rTeyF8x8q%2FGBEEEBrAJMPf25UQwi0b8tmqRXY7kIvNkzrkvRWLnxoGYEJsz8u4oOyMp8cHyaybb1HdMCaLApUE%2B%2F7xLIZGP6H9xuSEXp1zLIdjk5nBaMuV%2FyTDRRP8Y2ww5RO6d2D94o%2B6ucWIqUAvgHIHXhZsmDhjVLczmZ3ca0Cb3PpKwt2UtHVQ0BgFJsqqTsnzZPlKahRUkEu4qmkJt%2Bkqdae76ViWe3STan69yaF9%2BfESD2lcQshLHWVu4ovItXxO69bqC5p1nZLvI8NdQB9s9UNaJGlQ5mG947ipdDA0eTIw%2FA1zEdjWquIsQXXGIVEH0thC5M%2BW9pZe7IhAVnPJkYCCXN5a32HjN6nsvokEqRS44tGIs7s2LVTvcrHAF%2BRVmI8L4HUYk4x%2B67AxSMJKqCg8zrGOgvK9kNMdDrNiUtSWuHFpC8%2Fp5qIQrEo%2FH%2B1l%2F0cAwQ2nKmpWxKcMIuHY44Y6DlkpO48tRuUGBWT0FyHwSKO72Ud%2BtJUfdaZ4CWNijzZtlRa8%2BCkmO%2FEwHYfPZFU%2FhzjFWH7vnzHRMo%2BaF9u8qHSAiEkA2HjoNQPEwHsDKOt6hOoK3Ce%2F%2B%2F9boMWDa44I6FrQhdgS7OnNaSzwxWKZMcyHi6LN4WC6sSj0qm2PSOGBTvDs%2FGWJS6SwEN%2FULwpb4LQo9fYjUfSXRwZkynUazlSpvX9e%2BG2zor8l%2BYaMxSEomDdLHGcD6YVQPegTaA74H8%2BV4WvJkFUrjMLGLlvSZQWvi8%2FQA7yzQ8GPno%2F%2F5SJHRP%2FOqKObPCo81s%2F%2B6WgLqykYpGAgQZhVDEBPXWgU%2FWzFZjKUhSFInufPRiMAUULC6T11yL45ZrRoB4DzOyJShKXaAJIBS9wzLYIoCEcJKQW8GVCx4fihqJ6mshBUXSw3wWVj3grrHQlGNGhIDNNzsxQ3M%2BGWn6ASobIWC%2BLbYOC6UpahVO13Zs2zOzZC8z7FmA05JhUGyBsF4tsG0drcggIFzgg%2Fkpf3%2BCnAXKiMgIE8Jk%2FMhpkc8DUJEUzDSnWlQFme3d0sHZDrg7LavtsEX3cHwjCYA17pMTfx8Ajw9hHscN67hyo%2BRJQ4458RmPywXykkVcW688oVUrQhahpPRvTWPnuI0B%2BSkQu7dCyvLRyFYlC1LG1gRCIvn3rwQeINzZQC2KXq31FaR9UmVV2QeGVqBHjmE%2BVMd3b1fhCynD0pQNhCG6%2FWCDbKPyE7NRQzL3BzQAJ0g09aUzcQA6mUp9iZFK6Sbp%2FYbHjo%2B%2B7%2FWj8S4YNa%2BZdqAw1hDrKWFXv9%2BzaXpf8ZTDSbiqsxnwN%2FCzK5tPkOr4tRh2kY3Bn9JtalbIOI4b3F7F1vPQMfoDcdxMS8CW9m%2FNCW%2FHILTUVWQIPiD0j1A6bo8vsv6P1hCESl2abrSJWDrq5sSzUpwoxaCU9FtJyYH4QFMxDBpkkBR6kn0LMPO%2B5EJ7Z6bCiRoPedRZ%2FP0SSdii7ZnPAtVwwHUidcdyspwncz5uq6vvm4IEDbJVLUFCn%2FLvIHfooUBTkFO130FC7CmmcrKdgDJcid9mvVzsDSibOoXtIf9k6ABle3PmIxejodc4aob0QKS432srrCMndbfD454q52V01G4q913mC5HOsTzWF4h2No1av1VbcUgWAqyoZl%2B11PoFYnNv2HwAODeNRkHj%2B8SF1fcvVBu6MrehHAZK1Gm69ICcTKizykHgGFx7QdowTVAsYEF2tVc0Z6wLryz2FI1sc5By2znJAAmINndoJiB4sfPdPrTC8RnkW7KRCwxC6YvXg5ahMlQuMpoCSXjOlBy0Kij%2BbsCYPbGp8BdCBiLmLSAkEQRaieWo1SYvZIKJGj9Ur%2FeWHjiB7SOVdqMAVmpBvfRiebsFjger7DC%2B8kRFGtNrTrnnGD2GAJb8rQCWkUPYHhwXsjNBSkE6lGWUj5QNhK0DMNM2l%2BkXRZ0KLZaGsFSIdQz%2FHXDxf3%2FTE30%2BDgBKWGWdxElyLccJfEpjsnszECNoDGZpdwdRgCixeg9L4EPhH%2BRptvRMVRaahu4cySjS3P5wxAUCPkmn%2BrhyASpmiTaiDeggaIxYBmtLZDDhiWIJaBgzfCsAGUF1Q1SFZYyXDt9skCaxJsxK2Ms65dmdp5WAZyxik%2FzbrTQk5KmgxCg%2Ff45L0jywebOWUYFJQAJia7XzCV0x89rpp%2Ff3AVWhSPyTanqmik2SkD8A3Ml4NhIGLAjBXtPShwKYfi2eXtrDuKLk4QlSyTw1ftXgwqA2jUuopDl%2B5tfUWZNwBpEPXghzbBggYCw%2Fdhy0ntds2yeHCDKkF%2FYxQjNIL%2FF%2F37jLPHCKBO9ibwYCmuxImIo0ijV2Wbg3kSN2psoe8IsABv3RNFaF9uMyCtCYtqcD%2BqNOhwMlfARQUdJ2tUX%2BMNJqOwIciWalZsmEjt07tfa8ma4cji9sqz%2BQ9hWfmMoKEbIHPOQORbhQRHIsrTYlnVTNvcq1imqmmPDdVDkJgRcTgB8Sb6epCQVmFZe%2BjGDiNJQLWnfx%2BdrTKYjm0G8yH0ZAGMWzEJhUEQ4Maimgf%2Fbkvo8PLVBsZl152y5S8%2BHRDfZIMCbYZ1WDp4yrdchOJw8k6R%2B%2F2pHmydK4NIK2PHdFPHtoLmHxRDwLFb7eB%2BM4zNZcB9NrAgjVyzLM7xyYSY13ykWfIEEd2n5%2FiYp3ZdrCf7fL%2Ben%2BsIJu2W7E30MrAgZBD1rAAbZHPgeAMtKCg3NpSpYQUDWJu9bT3V7tOKv%2BNRiJc8JAKqqgCA%2FPNRBR7ChpiEulyQApMK1AyqcWnpSOmYh6yLiWkGJ2mklCSPIqN7UypWj3dGi5MvsHQ87MrB4VFgypJaFriaHivwcHIpmyi5LhNqtem4q0n8awM19Qk8BOS0EsqGscuuydYsIGsbT5GHnERUiMpKJl4ON7qjB4fEqlGN%2FhCky89232UQCiaeWpDYCJINXjT6xl4Gc7DxRCtgV0i1ma4RgWLsNtnEBRQFqZggCLiuyEydmFd7WlogpkCw5G1x4ft2psm3KAREwVwr1Gzl6RT7FDAqpVal34ewVm3VH4qn5mjGj%2BbYL1NgfLNeXDwtmYSpwzbruDKpTjOdgiIHDVQSb5%2FzBgSMbHLkxWWgghIh9QTFSDILixVwg0Eg1puooBiHAt7DzwJ7m8i8%2Fi%2BjHvKf0QDnnHVkVTIqMvIQImOrzCJwhSR7qYB5gSwL6aWL9hERHCZc4G2%2BJrpgHNB8eCCmcIWIQ6rSdyPCyftXkDlErUkHafHRlkOIjxGbAktz75bnh50dU7YHk%2BMz7wwstg6RFZb%2BTZuSOx1qqP5C66c0mptQmzIC2dlpte7vZrauAMm%2F7RfBYkGtXWGiaWTtwvAQiq2oD4YixPLXE2khB2FRaNRDTk%2B9sZ6K74Ia9VntCpN4BhJGJMT4Z5c5FhSepRCRWmBXqx%2BwhVZC4me4saDs2iNqXMuCl6iAZflH8fscC1sTsy4PHeC%2BXYuqMBMUun5YezKbRKmEPwuK%2BCLzijPEQgfhahQswBBLfg%2FGBgBiI4QwAqzJkkyYAWtjzSg2ILgMAgqxYfwERRo3zruBL9WOryUArSD8sQOcD7fvIODJxKFS615KFPsb68USBEPPj1orNzFY2xoTtNBVTyzBhPbhFH0PI5AtlJBl2aSgNPYzxYLw7XTDBDinmVoENwiGzmngrMo8OmnRP0Z0i0Zrln9DDFcnmOoBZjABaQIbPOJYZGqX%2BRCMlDDbElcjaROLDoualmUIQ88Kekk3iM4OQrADcxi3rJguS4MOIBIgKgXrjd1WkbCdqxJk%2F4efRIFsavZA7KvvJQqp3Iid5Z0NFc5aiMRzGN3vrpBzaMy4JYde3wr96PjN90AYOIbyp6T4zj8LoE66OGcX1Ef4Z3KoWLAUF4BTg7ug%2FAbkG5UNQXAMkQezujSHeir2uTThgd3gpyzDrbnEdDRH2W7U6PeRvBX1ZFMP5RM%2BZu6UUZZD8hDPHldVWntTCNk7To8IeOW9yn2wx0gmurwqC60AOde4r3ETi5pVMSDK8wxhoGAoEX9NLWHIR33VbrbMveii2jAJlrxwytTHbWNu8Y4N8vCCyZjAX%2FpcsfwXbLze2%2BD%2Bu33OGBoJyAAL3jn3RuEcdp5If8O%2Ba4NKWvxOTyDltG0IWoHhwVGe7dKkCWFT%2B%2Btm%2BhaBCikRUUMrMhYKZJKYoVuv%2FbsJzO8DwfVIInQq3g3BYypiz8baogH3r3GwqCwFtZnz4xMjAVOYnyOi5HWbFA8n0qz1OjSpHWFzpQOpvkNETZBGpxN8ybhtqV%2FDMUxd9uFZmBfKXMCn%2FSqkWJyKPnT6lq%2B4zBZni6fYRByJn6OK%2BOgPBGRAJluwGSk4wxjOOzyce%2FPKODwRlsgrVkdcsEiYrqYdXo0Er2GXi2GQZd0tNJT6c9pK1EEJG1zgDJBoTVuCXGAU8BKTvCO%2FcEQ1Wjk3Zzuy90JX4m3O5IlxVFhYkSUwuQB2up7jhvkm%2BbddRQu5F9s0XftGEJ9JSuSk%2BZachCbdU45fEqbugzTIUokwoAKvpUQF%2FCvLbWW5BNQFqFkJg2f30E%2F48StNe5QwBg8zz3YAJ82FZoXBxXSv4QDooDo79NixyglO9AembuBcx5Re3CwOKTHebOPhkmFC7wNaWtoBhFuV4AkEuJ0J%2B1pT0tLkvFVZaNzfhs%2FKd3%2BA9YsImlO4XK4vpCo%2FelHQi%2F9gkFg07xxnuXLt21unCIpDV%2BbbRxb7FC6nWYTsMFF8%2B1LUg4JFjVt3vqbuhHmDKbgQ4e%2BRGizRiO8ky05LQGMdL2IKLSNar0kNG7lHJMaXr5mLdG3nykgj6vB%2FKVijd1ARWkFEf3yiUw1v%2FWaQivVUpIDdSNrrKbjO5NPnxz6qTTGgYg03HgPhDrCFyYZTi3XQw3HXCva39mpLNFtz8AiEhxAJHpWX13gCTAwgm9YTvMeiqetdNQv6IU0hH0G%2BZManTqDLPjyrOse7WiiwOJCG%2BJ0pZYULhN8NILulmYYvmVcV2MjAfA39sGKqGdjpiPo86fecg65UPyXDIAOyOkCx5NQsLeD4gGVjTVDwOHWkbbBW0GeNjDkcSOn2Nq4cEssP54t9D749A7M1AIOBl0Fi0sSO5v3P7LCBrM6ZwFY6kp2FX6AcbGUdybnfChHPyu6WlRZ2Fwv9YM0RMI7kISRgR8HpQSJJOyTfXj%2F6gQKuihPtiUtlCQVPohUgzfezTg8o1b3n9pNZeco1QucaoXe40Fa5JYhqdTspFmxGtW9h5ezLFZs3j%2FN46f%2BS2rjYNC2JySXrnSAFhvAkz9a5L3pza8eYKHNoPrvBRESpxYPJdKVUxBE39nJ1chrAFpy4MMkf0qKgYALctGg1DQI1kIymyeS2AJNT4X240d3IFQb%2F0jQbaHJ2YRK8A%2Bls6WMhWmpCXYG5jqapGs5%2FeOJErxi2%2F2KWVHiPellTgh%2FfNl%2F2KYPKb7DUcAg%2BmCOPQFCiU9Mq%2FWLcU1xxC8aLePFZZlE%2BPCLzf7ey46INWRw2kcXySR9FDgByXzfxiNKwDFbUSMMhALPFSedyjEVM5442GZ4hTrsAEvZxIieSHGSgkwFh%2FnFNdrrFD4tBH4Il7fW6ur4J8Xaz7RW9jgtuPEXQsYk7gcMs2neu3zJwTyUerHKSh1iTBkj2YJh1SSOZL5pLuQbFFAvyO4k1Hxg2h99MTC6cTUkbONQIAnEfGsGkNFWRbuRyyaEZInM5pij73EA9rPIUfU4XoqQpHT9THZkW%2BoKFLvpyvTBMM69tN1Ydwv1LIEhHsC%2BueVG%2Bw%2BkyCPsvV3erRikcscHjZCkccx6VrBkBRusTDDd8847GA7p2Ucy0y0HdSRN6YIBciYa4vuXcAZbQAuSEmzw%2BH%2FAuOx%2BaH%2BtBL88H57D0MsqyiZxhOEQkF%2F8DR1d2hSPMj%2FsNOa5rxcUnBgH8ictv2J%2Bcb4BA4v3MCShdZ2vtK30vAwkobnEWh7rsSyhmos3WC93Gn9C4nnAd%2FPjMMtQfyDNZsOPd6XcAsnBE%2FmRHtHEyJMzJfZFLE9OvQa0i9kUmToJ0ZxknTgdl%2FXPV8xoh0K7wNHHsnBdvFH3sv52lU7UFteseLG%2FVanIvcwycVA7%2BBE1Ulyb20BvwUWZcMTKhaCcmY3ROpvonVMV4N7yBXTL7IDtHzQ4CCcqF66LjF3xUqgErKzolLyCG6Kb7irP%2FMVTCCwGRxfrPGpMMGvPLgJ881PHMNMIO09T5ig7AzZTX%2F5PLlwnJLDAPfuHynSGhV4tPqR3gJ4kg4c06c%2FF1AcjGytKm2Yb5jwMotF7vro4YDLWlnMIpmPg36NgAZsGA0W1spfLSue4xxat0Gdwd0lqDBOgIaMANykwwDKejt5YaNtJYIkrSgu0KjIg0pznY0SCd1qlC6R19g97UrWDoYJGlrvCE05J%2F5wkjpkre727p5PTRX5FGrSBIfJqhJE%2FIS876PaHFkx9pGTH3oaY3jJRvLX9Iy3Edoar7cFvJqyUlOhAEiOSAyYgVEGkzHdug%2BoRHIEOXAExMiTSKU9A6nmRC8mp8iYhwWdP2U%2F5EkFAdPrZw03YA3gSyNUtMZeh7dDCu8pF5x0VORCTgKp07ehy7NZqKTpIC4UJJ89lnboyAfy5OyXzXtuDRbtAFjZRSyGFTpFrXwkpjSLIQIG3N0Vj4BtzK3wdlkBJrO18MNsgseR4BysJilI0wI6ZahLhBFA0XBmV8d4LUzEcNVb0xbLjLTETYN8OEVqNxkt10W614dd1FlFFVTIgB7%2FBQQp1sWlNolpIu4ekxUTBV7NmxOFKEBmmN%2BnA7pvF78%2FRII5ZHA09OAiE%2F66MF6HQ%2BqVEJCHxwymukkNvzqHEh52dULPbVasfQMgTDyBZzx4007YiKdBuUauQOt27Gmy8ISclPmEUCIcuLbkb1mzQSqIa3iE0PJh7UMYQbkpe%2BhXjTJKdldyt2mVPwywoODGJtBV1lJTgMsuSQBlDMwhEKIfrvsxGQjHPCEfNfMAY2oxvyKcKPUbQySkKG6tj9AQyEW3Q5rpaDJ5Sns9ScLKeizPRbvWYAw4bXkrZdmB7CQopCH8NAmqbuciZChHN8lVGaDbCnmddnqO1PQ4ieMYfcSiBE5zzMz%2BJV%2F4eyzrzTEShvqSGzgWimkNxLvUj86iAwcZuIkqdB0VaIB7wncLRmzHkiUQpPBIXbDDLHBlq7vp9xwuC9AiNkIptAYlG7Biyuk8ILdynuUM1cHWJgeB%2BK3wBP%2FineogxkvBNNQ4AkW0hvpBOQGFfeptF2YTR75MexYDUy7Q%2F9uocGsx41O4IZhViw%2F2FvAEuGO5g2kyXBUijAggWM08bRhXg5ijgMwDJy40QeY%2FcQpUDZiIzmvskQpO5G1zyGZA8WByjIQU4jRoFJt56behxtHUUE%2Fom7Rj2psYXGmq3llVOCgGYKNMo4pzwntITtapDqjvQtqpjaJwjHmDzSVGLxMt12gEXAdLi%2FcaHSM3FPRGRf7dB7YC%2BcD2ho6oL2zGDCkjlf%2FDFoQVl8GS%2F56wur3rdV6ggtzZW60MRB3g%2BU1W8o8cvqIpMkctiGVMzXUFI7FacFLrgtdz4mTEr4aRAaQ2AFQaNeG7GX0yOJgMRYFziXdJf24kg%2FgBQIZMG%2FYcPEllRTVNoDYR6oSJ8wQNLuihfw81UpiKPm714bZX1KYjcXJdfclCUOOpvTxr9AAJevTY4HK%2FG7F3mUc3GOAKqh60zM0v34v%2BELyhJZqhkaMA8UMMOU90f8RKEJFj7EqepBVwsRiLbwMo1J2zrE2UYJnsgIAscDmjPjnzI8a719Wxp757wqmSJBjXowhc46QN4RwKIxqEE6E5218OeK7RfcpGjWG1jD7qND%2B%2FGTk6M56Ig4yMsU6LUW1EWE%2BfIYycVV1thldSlbP6ltdC01y3KUfkobkt2q01YYMmxpKRvh1Z48uNKzP%2FIoRIZ%2FF6buOymSnW8gICitpJjKWBscSb9JJKaWkvEkqinAJ2kowKoqkqZftRqfRQlLtKoqvTRDi2vg%2FRrPD%2Fd3a09J8JhGZlEkOM6znTsoMCsuvTmywxTCDhw5dd0GJOHCMPbsj3QLkTE3MInsZsimDQ3HkvthT7U9VA4s6G07sID0FW4SHJmRGwCl%2BMu4xf0ezqeXD2PtPDnwMPo86sbwDV%2B9PWcgFcARUVYm3hrFQrHcgMElFGbSM2A1zUYA3baWfheJp2AINmTJLuoyYD%2FOwA4a6V0ChBN97E8YtDBerUECv0u0TlxR5yhJCXvJxgyM73Bb6pyq0jTFJDZ4p1Am1SA6sh8nADd1hAcGBMfq4d%2FUfwnmBqe0Jun1n1LzrgKuZMAnxA3NtCN7Klf4BH%2B14B7ibBmgt0TGUafVzI4uKlpF7v8NmgNjg90D6QE3tbx8AjSAC%2BOA1YJvclyPKgT27QpIEgVYpbPYGBsnyCNrGz9XUsCHkW1QAHgL2STZk12QGqmvAB0NFteERkvBIH7INDsNW9KKaAYyDMdBEMzJiWaJHZALqDxQDWRntumSDPcplyFiI1oDpT8wbwe01AHhW6%2BvAUUBoGhY3CT2tgwehdPqU%2F4Q7ZLYvhRl%2FogOvR9O2%2BwkkPKW5vCTjD2fHRYXONCoIl4Jh1bZY0ZE1O94mMGn%2FdFSWBWzQ%2FVYk%2BGezi46RgiDv3EshoTmMSlioUK6MQEN8qeyK6FRninyX8ZPeUWjjbMJChn0n%2FyJvrq5bh5UcCAcBYSafTFg7p0jDgrXo2QWLb3WpSOET%2FHh4oSadBTvyDo10IufLzxiMLAnbZ1vcUmj3w7BQuIXjEZXifwukVxrGa9j%2BDXfpi12m1RbzYLg9J2wFergEwOxFyD0%2FJstNK06ZN2XdZSGWxcJODpQHOq4iKqjqkJUmPu1VczL5xTGUfCgLEYyNBCCbMBFT%2FcUP6pE%2FmujnHsSDeWxMbhrNilS5MyYR0nJyzanWXBeVcEQrRIhQeJA6Xt4f2eQESNeLwmC10WJVHqwx8SSyrtAAjpGjidcj1E2FYN0LObUcFQhafUKTiGmHWRHGsFCB%2BHEXgrzJEB5bp0QiF8ZHh11nFX8AboTD0PS4O1LqF8XBks2MpjsQnwKHF6HgaKCVLJtcr0XjqFMRGfKv8tmmykhLRzu%2BvqQ02%2BKpJBjaLt9ye1Ab%2BBbEBhy4EVdIJDrL2naV0o4wU8YZ2Lq04FG1mWCKC%2BUwkXOoAjneU%2FxHplMQo2cXUlrVNqJYczgYlaOEczVCs%2FOCgkyvLmTmdaBJc1iBLuKwmr6qtRnhowngsDxhzKFAi02tf8bmET8BO27ovJKF1plJwm3b0JpMh38%2BxsrXXg7U74QUM8ZCIMOpXujHntKdaRtsgyEZl5MClMVMMMZkZLNxH9%2Bb8fH6%2Bb8Lev30A9TuEVj9CqAdmwAAHBPbfOBFEATAPZ2CS0OH1Pj%2F0Q7PFUcC8hDrxESWdfgFRm%2B7vvWbkEppHB4T%2F1ApWnlTIqQwjcPl0VgS1yHSmD0OdsCVST8CQVwuiew1Y%2Bg3QGFjNMzwRB2DSsAk26cmA8lp2wIU4p93AUBiUHFGOxOajAqD7Gm6NezNDjYzwLOaSXRBYcWipTSONHjUDXCY4mMI8XoVCR%2FRrs%2FJLKXgEx%2BqkmeDlFOD1%2FyTQNDClRuiUyKYCllfMiQiyFkmuTz2vLsBNyRW%2Bxz%2B5FElFxWB28VjYIGZ0Yd%2B5wIjkcoMaggxswbT0pCmckRAErbRlIlcOGdBo4djTNO8FAgQ%2BlT6vPS60BwTRSUAM3ddkEAZiwtEyArrkiDRnS7LJ%2B2hwbzd2YDQagSgACpsovmjil5wfPuXq3GuH0CyE7FK3M4FgRaFoIkaodORrPx1%2BJpI9psyNYIFuJogZa0%2F1AhOWdlHQxdAgbwacsHqPZo8u%2FngAH2GmaTdhYnBfSDbBfh8CHq6Bx5bttP2%2BRdM%2BMAaYaZ0Y%2FADkbNCZuAyAVQa2OcXOeICmDn9Q%2FeFkDeFQg5MgHEDXq%2FtVjj%2Bjtd26nhaaolWxs1ixSUgOBwrDhRIGOLyOVk2%2FBc0UxvseQCO2pQ2i%2BKrfhu%2FWeBovNb5dJxQtJRUDv2mCwYVpNl2efQM9xQHnK0JwLYt%2FU0Wf%2BphiA4uw8G91slC832pmOTCAoZXohg1fewCZqLBhkOUBofBWpMPsqg7XEXgPfAlDo2U5WXjtFdS87PIqClCK5nW6adCeXPkUiTGx0emOIDQqw1yFYGHEVx20xKjJVYe0O8iLmnQr3FA9nSIQilUKtJ4ZAdcTm7%2BExseJauyqo30hs%2B1qSW211A1SFAOUgDlCGq7eTIcMAeyZkV1SQJ4j%2Fe1Smbq4HcjqgFbLAGLyKxlMDMgZavK5NAYH19Olz3la%2FQCTiVelFnU6O%2FGCvykqS%2FwZJDhKN9gBtSOp%2F1SP5VRgJcoVj%2Bkmf2wBgv4gjrgARBWiURYx8xENV3bEVUAAWWD3dYDKAIWk5opaCFCMR5ZjJExiCAw7gYiSZ2rkyTce4eNMY3lfGn%2B8p6%2BvBckGlKEXnA6Eota69OxDO9oOsJoy28BXOR0UoXNRaJD5ceKdlWMJlOFzDdZNpc05tkMGQtqeNF2lttZqNco1VtwXgRstLSQ6tSPChgqtGV5h2DcDReIQadaNRR6AsAYKL5gSFsCJMgfsaZ7DpKh8mg8Wz8V7H%2BgDnLuMxaWEIUPevIbClgap4dqmVWSrPgVYCzAoZHIa5z2Ocx1D%2FGvDOEqMOKLrMefWIbSWHZ6jbgA8qVBhYNHpx0P%2BjAgN5TB3haSifDcApp6yymEi6Ij%2FGsEpDYUgcHATJUYDUAmC1SCkJ4cuZXSAP2DEpQsGUjQmKJfJOvlC2x%2FpChkOyLW7KEoMYc5FDC4v2FGqSoRWiLsbPCiyg1U5yiHZVm1XLkHMMZL11%2Fyxyw0UnGig3MFdZklN5FI%2FqiT65T%2BjOXOdO7XbgWurOAZR6Cv9uu1cm5LjkXX4xi6mWn5r5NjBS0gTliHhMZI2WNqSiSphEtiCAwnafS11JhseDGHYQ5%2BbqWiAYiAv6Jsf79%2FVUs4cIl%2Bn6%2BWOjcgB%2F2l5TreoAV2717JzZbQIR0W1cl%2FdEqCy5kJ3ZSIHuU0vBoHooEpiHeQWVkkkOqRX27eD1FWw4BfO9CJDdKoSogQi3hAAwsPRFrN5RbX7bqLdBJ9JYMohWrgJKHSjVl1sy2xAG0E3sNyO0oCbSGOxCNBRRXTXenYKuwAoDLfnDcQaCwehUOIDiHAu5m5hMpKeKM4sIo3vxACakIxKoH2YWF2QM84e6F5C5hJU4g8uxuFOlAYnqtwxmHyNEawLW%2FPhoawJDrGAP0JYWHgAVUByo%2FbGdiv2T2EMg8gsS14%2FrAdzlOYazFE7w4OzxeKiWdm3nSOnQRRKXSlVo8HEAbBfyJMKqoq%2BSCcTSx5NDtbFwNlh8VhjGGDu7JG5%2FTAGAvniQSSUog0pNzTim8Owc6QTuSKSTXlQqwV3eiEnklS3LeSXYPXGK2VgeZBqNcHG6tZHvA3vTINhV0ELuQdp3t1y9%2BogD8Kk%2FW7QoRN1UWPqM4%2BxdygkFDPLoTaumKReKiLWoPHOfY54m3qPx4c%2B4pgY3MRKKbljG8w4wvz8pxk3AqKsy4GMAkAtmRjRMsCxbb4Q2Ds0Ia9ci8cMT6DmsJG00XaHCIS%2Bo3F8YVVeikw13w%2BOEDaCYYhC0ZE54kA4jpjruBr5STWeqQG6M74HHL6TZ3lXrd99ZX%2B%2B7LhNatQaZosuxEf5yRA15S9gPeHskBIq3Gcw81AGb9%2FO53DYi%2F5CsQ51EmEh8Rkg4vOciClpy4d04eYsfr6fyQkBmtD%2BP8sNh6e%2BXYHJXT%2FlkXxT4KXU5F2sGxYyzfniMMQkb9OjDN2C8tRRgTyL7GwozH14PrEUZc6oz05Emne3Ts5EG7WolDmU8OB1LDG3VrpQxp%2BpT0KYV5dGtknU64JhabdqcVQbGZiAxQAnvN1u70y1AnmvOSPgLI6uB4AuDGhmAu3ATkJSw7OtS%2F2ToPjqkaq62%2F7WFG8advGlRRqxB9diP07JrXowKR9tpRa%2BjGJ91zxNTT1h8I2PcSfoUPtd7NejVoH03EUcqSBuFZPkMZhegHyo2ZAITovmm3zAIdGFWxoNNORiMRShgwdYwFzkPw5PA4a5MIIQpmq%2Bnsp3YMuXt%2FGkXxLx%2FP6%2BZJS0lFyz4MunC3eWSGE8xlCQrKvhKUPXr0hjpAN9ZK4PfEDrPMfMbGNWcHDzjA7ngMxTPnT7GMHar%2BgMQQ3NwHCv4zH4BIMYvzsdiERi6gebRmerTsVwZJTRsL8dkZgxgRxmpbgRcud%2BYlCIRpPwHShlUSwuipZnx9QCsEWziVazdDeKSYU5CF7UVPAhLer3CgJOQXl%2Fzh575R5rsrmRnKAzq4POFdgbYBuEviM4%2BLVC15ssLNFghbTtHWerS1hDt5s4qkLUha%2FqpZXhWh1C6lTQAqCNQnaDjS7UGFBC6wTu8yFnKJnExCnAs3Ok9yj5KpfZESQ4lTy5pTGTnkAUpxI%2ByjEldJfSo4y0QhG4i4IwkRFGcjWY8%2BEzgYYJUK7BXQksLxAww%2FYYWBMhJILB9e8ePEJ4OP7z%2B4%2FwOQDl64iOYDp26DaONPxpKtBxq%2FaTzRGarm3VkPYTLJKx6Z%2FMw2YbBGseJhPMwhhNswrIkyvV2BYzrvZbxLpKwcWJhYmFtVZ%2BlPEq91FzVp1HlQY1bZVLqeNR9SAUn6n0E28k%2FUuGkNpP1DBI5ch%2FEehZfjUQ9aE41NhETExoPT2gGQz0IhWJbEOvTQ4wgcXCHHFBhewYUiFHuhRSAUVmEHeCRQHQkXGFwkAgyzREJCVN7TRnTon36Zw3tPhx4EALwNdwDv%2BJ41YSP4B2CQqz0EFgARZ4ESgBHQgROwAVn9GTI%2BHYexTUevLUeta4%2FDqKrbMVS%2BYqb8hUwYCrlgKtmAq1YCrFgKrd4qpXiqZcKn1oqdWipjYKpWwVPVYqW6xUpVipKqFR3QKjagVEtAqHpxUMTitsnFaJOKx2cVhswq35RVpyiq9lFVNIKnOQVMkgqtYxVNxiqQjFS7GKlSIVIsQqPIhUWwioigFQ%2B%2BKkN8VHr49HDw9Ebo9EDo9DTo9Crg9BDg9%2FWx7gWx7YWwlobYrOGxWPNisAaAHEyALpkAVDIAeWAArsABVXACYuAD5cAF6wAKFQAQqgAbVAAsoAAlQAUaYAfkwAvogBWQACOgAD9AAHSAAKT4GUdMiOvFngBTwCn2AZ7Dv6B6k%2F90B8%2ByRnkV144AIBoAMTQATGgAjNAA4YABgwABZgB%2FmQCwyAVlwCguASlwCEuAQFwB4uAMlwBYuAJlQAUVAAhUD2KgdpUDaJgaRMDFJgX5MC1JgWJEAokQCWRAHxEAWkQBMRADpEAMkQAYROAEecC484DRpwBDTnwNOdw05tjTmiNOYwtswhYFwLA7BYG4LA2BYGOLAwRYFuLAsxYFQJAohIEyJAMwkAwiQC0JAJgkAeiQBkJAFokAPCQA0JABwcD4Dgc4cDdDgaYcDIDgYgUC6CgWgUClCgUYUAVBQBOFAEYMALgwAgDA9QYAdIn8AZzeBB2L5EcWrenUT1KXienEsuJJ7x5U8XlTjc1NVzUyXFTGb1LlpUtWlTDIjqwE4LsagowoCi2gJLKAkpoBgJQNpAIhNqaEoneI6kiiqQ6Go%2Fn6j0cS%2Ba2gEU8gIHJ%2BBwfgZX4GL%2BBd%2FgW34FZ%2BBS%2FgUH4FN6BTegTvoEv6BJegRnYEF2A79gOvYDl2BdEjCkqkGtwXp0LNToIskOTXzh%2FF062yJ7AAAAEDAWAAABWhJ%2BKPEIJgBFxMVP7w2QJBGHASQnOBKXKFIdUK4igKA9IEaYJg%29%20format%28%27embedded%2Dopentype%27%29%2Curl%28data%3Aapplication%2Ffont%2Dwoff%3Bbase64%2Cd09GRgABAAAAAFuAAA8AAAAAsVwAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAABGRlRNAAABWAAAABwAAAAcbSqX3EdERUYAAAF0AAAAHwAAACABRAAET1MvMgAAAZQAAABFAAAAYGe5a4ljbWFwAAAB3AAAAsAAAAZy2q3jgWN2dCAAAAScAAAABAAAAAQAKAL4Z2FzcAAABKAAAAAIAAAACP%2F%2FAANnbHlmAAAEqAAATRcAAJSkfV3Cb2hlYWQAAFHAAAAANAAAADYFTS%2FYaGhlYQAAUfQAAAAcAAAAJApEBBFobXR4AABSEAAAAU8AAAN00scgYGxvY2EAAFNgAAACJwAAAjBv%2B5XObWF4cAAAVYgAAAAgAAAAIAFqANhuYW1lAABVqAAAAZ4AAAOisyygm3Bvc3QAAFdIAAAELQAACtG6o%2BU1d2ViZgAAW3gAAAAGAAAABsMYVFAAAAABAAAAAMw9os8AAAAA0HaBdQAAAADQdnOXeNpjYGRgYOADYgkGEGBiYGRgZBQDkixgHgMABUgASgB42mNgZulmnMDAysDCzMN0gYGBIQpCMy5hMGLaAeQDpRCACYkd6h3ux%2BDAoPD%2FP%2FOB%2FwJAdSIM1UBhRiQlCgyMADGWCwwAAAB42u2UP2hTQRzHf5ekaVPExv6JjW3fvTQ0sa3QLA5xylBLgyBx0gzSWEUaXbIoBBQyCQGHLqXUqYNdtIIgIg5FHJxEtwqtpbnfaV1E1KFaSvX5vVwGEbW6OPngk8%2FvvXfv7pt3v4SImojIDw6BViKxRgIVBaZwVdSv%2BxvXA%2BIuzqcog2cOkkvDNE8Lbqs74k64i%2B5Sf3u8Z2AnIRLbyVCyTflVSEXVoEqrrMqrgiqqsqqqWQ5xlAc5zWOc5TwXucxVnuE5HdQhHdFRHdNJndZZndeFLc%2FzsKJLQ%2FWV6BcrCdWkwspVKZVROaw0qUqqoqZZcJhdTnGGxznHBS5xhad5VhNWCuturBTXKZ3RObuS98pb9c57k6ql9rp2v1as5deb1r6s9q1GV2IrHSt73T631424YXzjgPwqt%2BRn%2BVG%2BlRvyirwsS%2FKCPCfPytPypDwhj8mjctRZd9acF86y89x55jxxHjkPnXstXfbt%2FpNjj%2FnwXW%2BcHa6%2FSYvZ7yEwbDYazDcIgoUGzY3h2HtqgUcs1AFPWKgTXrRQF7xkoQhRf7uF9hPFeyzUTTSwY6EoUUJY6AC8bSGMS4Ys1Au3WaiPSGGsMtkdGH2rzJgYHAaYjxIwQqtB1CnYkEZ9BM6ALOpROAfyqI%2FDBQudgidBETXuqRIooz4DV0AV9UV4GsyivkTEyMMmw1UYGdhkuAYjA5sMGMvIwCbDDRgZeAz1TXgcmDy3YeRhk%2BcOjCxsMjyAkYFNhscwMrDJ8BQ2886gXoaRhedQvyTSkDZ7uA6HLLQBI5vGntAbGHugTc53cMxC7%2BE4SKL%2BACOzNpk3YWTWJid%2BiRo5NXIKM3fBItAPW55FdJLY3FeHBDr90606JCIU9Jk%2BMs3%2FY%2F8L8jUq3y79bJ%2F0%2F%2BROoP4v9v%2F4%2Fmj%2Bi7HBXUd0%2FelU6IHfHt8Aj9EPGAAoAvgAAAAB%2F%2F8AAnjaxb0JfBvVtTA%2BdxaN1hltI1m2ZVuSJVneLVlSHCdy9oTEWchqtrBEJRAgCYEsQNhC2EsbWmpI2dqkQBoSYgKlpaQthVL0yusrpW77aEubfq%2Fly%2BujvJampSTW5Dvnzmi1E%2Bjr%2F%2F3%2BXmbu3Llz77nnbuece865DMu0MAy5jGtiOEZkOp8lTNeUwyLP%2FDH%2BrEH41ZTDHAtB5lkOowWMPiwayNiUwwTjE46AI5xwhFrINPXYn%2F7ENY0dbWHfZAiTZbL8ID%2FInAd5xz2NpIH4STpDGonHIJNE3OP1KG4ISaSNeBuITAyRLgIxoiEUhFAnmUpEiXSRSGqAQEw0kuyFUIb0k2gnGSApyBFi0il2SI5YLGb5MdFjXCey4mNHzQ7WwLGEdZiPPgYR64we8THZHAt%2BwnT84D%2Fx8YTpGPgheKH4CMEDVF9xBOIeP3EbQgGH29BGgpGkIxCMTCW9qUTA0Zsir%2BQUP1mt%2BP2KusevwIO6Bx%2FIaj8%2FOD5O0VNrZW2EsqZBWbO1skRiEKE0DdlKKaSVO5VAuRpqk8VQJAqY7ydxaK44YJvrO2EWjOoDBoFYzQbDNkON%2BUbiKoRkywMWWf1j4bEY2iIY1AeMgvmEz%2FkVo9v4FSc%2FaMZMrFbjl4zWLL0%2BY5FlyzNlEVYDudJohg8gPUP7kcB%2Fmn%2BG6cd%2B5PV4Q72dXCgocWJADBgUuDTwiXiGSyZo14HOEQ2lE6k0XDIEusexDzZOMXwt1Dutz%2BtqmxTvlskNWXXUQIbhaurum9GrePqm9Yaeabjkiqf%2BbUvzDOvb2Y1E%2BEX2DnemcTP%2FzLcuu7xjQXdAtjR0Lo5n4%2FHs%2FGtntMlysHt%2B29NXbH6se%2F%2FWbFcyu%2Br28H0MwzI30DYeYTLMXIA2EG8QlHpAsyS0EfEToR0a3utIxFPJ3kiIHCCrZ66b0e2xEmL1dM9YN%2FMwS5p01N5jMX%2FBLKt%2F1R83l0LyC29M6%2BiYxo%2FUNg%2FEF7c2WyyW5tYl8WnhWg2%2FhyySbD5UhnDyS7OcU0dnrFw%2BDfGdI7v4QfYIIzOMq9hFtY55gmvC7jZ2FK7sEdrn6IXBuucYhjsGdQ8z0yEbWkkczjjsE5hNAIZrPx2zOLZDmKNXcXtg7EMqidAEEWg%2BSJCBBNwxvxJfc%2FbZa%2BKKf%2BxoKZybnq5vaqpPTye7CiF%2BZFjxZ8%2F7Qij0hfOG%2FcowPA1rT1l4ymWnrKmxxqfErTVrpgwPlz1kC%2BOy8NMDz6c%2BIO38K%2Fx0xkPnLW8Kx6qGAoQdL%2BTD9V9rb%2B%2Fctn%2F%2Ftrxz8dUrZrD%2Fzk%2FferF0cNt1BzctmX2FZPXt%2FjnFCQNz4Ah%2FiKllGiCMs1w5Lkg0kiEwj6VTXCDKsX9rMpnvIj9pcDecXAIXMnqn2dTUbN6w0XQ9ue6FV%2FnnXCH7S3lPWGltVcLsH75ub3ab7A8M28caNrIeOr3o5Q0yFsYL80xaa0EY%2FUEczV7icUMY5pnelAkmUAXmHYjvFWFGxuqlSaow3OM%2B%2FiYY7%2Fl%2FhVELF4EjRqNR%2FbvRbOY%2BDUGzGR%2FOh3EqmE%2FugIQQguGt%2FeMYz%2F%2BL0cimjeZfQDI3phXMbMQsqH%2BCjwVz%2Fhf4idHovgVmB8gLvjbicDcC%2FNypP536E%2F9N%2FpuMibExdohBmNwyiaZdJGoigos7GpF222xrfnZhML%2F7Z%2BylaqP63Hr%2Bm7bdUkQ6%2F2cXqdfmvwixY%2Bs2ksXFeXcE%2BiX0Z%2BIow76DBNgjJ7TOdUK18iPsPflfQD%2BDPsZG2Aj9VmKMMJ4fYRrhIaxhTDR0Elh2vA6h%2FAE6xUb29mj3sjmL72petXjejPy%2Boel60M99tFduCI59N3221xe7apOvxs6aHs7vab1IqY2tv7q2xsHeHGml%2FcV06u%2F8S%2FxTjJ%2BJYc0bWEX0ukW6YmIbGkJRMdjJ9mYIH5QIdJF4hvRGyK7cC7ctImQRcUET99fGXOoft35GYLMQu%2Bg2smnkgZUrH8AL%2F9Si217IssJ916nv14ZrJrvdxLkQvrvtBcjgPC0NXOicO8Qf4mcxPqh3hgUw3DDfdvLJXngg7N3dN2zbPJSaed3OfZnMU7dvmznp3C3bruO%2BNmue0LFsy7S%2B6265%2BfCKFYdvvuW6vmlblnUI8xCXp37CrOZv4B9gauDBlYp7adcUXB5DNCwYImlXOJJKkAdvExXxVvKEYnCo%2B3eIskP9qrrfIYs71CccBjfXRC52udTHHdaP1A1ui%2FVvH1otbrLrpNXBsGX5B89QghDyimlvNB2KfkxZ5C9%2Fem3%2Bd1%2Bd%2F%2FIfFp2%2B2Oxn%2Fs%2B9n%2F79p39S3s8idN6g0yZObwJOgKUpNB3GyU0Ls0PbRzIRq4lcarLKOJBkLRzJQD4j2090XrbA7DW8K3jNF5hlGS5e4V2D17zgss4T20egOJte5iD0bReM9yjTxnQxCRj3c5kFzGJmGbNKmwGw39IJDJcXJZGMkaAB4jyJAKw0jt5IAuIE%2BA%2BU3cVAZZrq9zhDyBrU8oosuxcGNTzCKJfla7JjNVmuSb%2F%2BtuzN2H%2BX4vlB%2BPpdfMXXmuVsNiub1T34SFbjYw5itEvVi0K0Nt9pNJUMI7SLGRhf2xipfCYf8z5OdlGKayOucFeVPeS%2Fdbo3lBrbSMmwUiQN5%2Fed7g0Ds1s17IuZC5kNzM3MZ6EWCa0DtekdJfAxz%2BR%2FOX28sND7yRMTBcf%2B%2Bs8mQCQWHya4qBv%2FufeMoWyslPA9DtMxUknxkH%2FyfTnm2CMYzs%2BCq3r7PxY%2FMXomrvTEsRpfEGHa%2BWN8E1AHjElb7d06ddA7oK%2F%2B5Mdsv9EtPms0jv0Z5kf1FqPxWdFtfFr0kHfgDX0Y%2B5PRSG7RUj0tQr7rmfX8DH4G5W28kKeJLtmQsQkuwMP1pk16EV4sl7vrMJATfyUWo%2FGwEco4rh4XFQgaiUX9qxZHrMQqKnz%2Fc2d8b9TysYrAuXpP%2FRf%2FGr8b1qwwc5a%2BeuLa6S6sneNXToG2XrEJi4R5SGs8Sq2S3d97bsfCRaTdaLwKClRHt37mkudvXbjwVrLhuYeGhh56bvfQkHpk2CwvwClqgWwuBfndC3c8dwmstj81KkagcUgbfPY8Zje0W%2F82VPWJHmSq6pP8hPWpotc%2FEexDOK3qU%2BwngPhOCiO9MJRm8TJefjelrzoKnG2Bn%2B1NCUmPE4gHFmBN9jrTigRIpsACrc9Gstg58ULkp9467%2BGf%2FeFnD5%2F31lNrt2967dhrm7bzI%2BVT5m%2BfzKhvf2MzpICEm79Bopkn07lt1762adNr127LwVqQLdJ5%2BlpQDcvHPQtVY5knhYrK6q8%2FJsiP6EuhGZdFdaNszjvpqvc%2BPI0CdjN0AXsFOC3ZfALDJwr4q2Xq%2BGF%2BGNbsxUg5NLLIEXi8otcDQcUts0D8eQ1iVDRAMBTsYiNdRIxE09EIBJO9A2xqgERTaW86BUFn0OD2xFO97FAgFhF6OoQ7prYt4XwSeUgQHiJyDbeke9IdQntciLQ1FlJMaYcUNvZBg%2BFB1ubjlnRNvl3o6IEU2w7fdNPhm%2Fhh%2BFLysUu6%2B%2BDLHkOkrSHYEjH0tEPe7WdD3uyDgvAgK%2Fm4szFFR7ch0toUgBTdWHr7EpaWru6%2B6dmbbnqWEbV2EtxAsXiZAPTtGPSbHsotI2leoM8TePEqgSQprs7AGFf8kuOkPdZPXGb55POAW1d%2FjLST9v5YflasP6v%2FCO7%2BGNAPC2BMZWmsOjp2NNbfHwMCJD%2BLPVL%2BD%2FOYlWEEI%2F9jpPddOFkB5d1GSuKZYggmCCd7JUxD7EXAzxyirYnNDLdDZoFdx14kivkvGc3579Jm36reTTvDgBnaO6vzyQ6chQmlsMoIkIQ2%2BbBDWBud1Va4pcCn8CPqxlh%2FfgtG8IPaPH8C5wk6%2FnZDv69jurV5QhtwE0x2iqOsj9Mx8B9%2F0EaUdiPfOYYDCi%2Fq9jhWRuupMDEU0%2BCtX0sDFxv07T%2FK5niBPqN9%2BtQjgEc31NGCXFeMcCEuQBIc%2FBK4CO78u7EPYvl3yaEfK3vcb6qP1R2tI7vUjVDDUdKubsSrNjYKY1qBEa2P50SJoaXiksIoLiCwnxS6EBuBde87botNfdEWwYvF%2FR0%2Fu5yCqhGeEOR2ynSeyXjt6ka7neyye8kryBSWE52y%2BRBgogrXPZ8E1yIHoHIFUM%2BAbJhE7lbMtt8ApL%2BxmZW7PwbjAO0fAVoXQOuiSP%2FksIVdFZ0aulsamKUzwPZ%2FNYDMJRBPCxsBqLzqHyneXF6Ej9HlIFo7%2Bpg%2BjUb3unRmGpstGkm6etOuDBGA5wCMefp1gTHcdZlvPBXlOslvYTp1cd8UjYLVd%2FJ5awNrIOKLnIt9MD9qdrKrWCvA6ALm3QV9VrsPm60Q7%2BRHJHP%2B2hqfugo%2FMvI2H%2Fmqr4b9tFnKSRY1Y5Ek80Nm%2FWIhr1ikKnxGz9TWXrokf9xwujfvcOTtNTWnxd0F37Y2W79tteBqZ4G5qLCuomw%2BnSr28QESCRVLTyYKILGJOPfcnaIFOsewhRdvv%2BrWa%2FWih0vlbX6Zb75T5C0qNKVFvH1QL%2FvazSWgC2s6oWXXIuUxQelKiJbowuJDQViatLmLijg9CQBMg8WiPgiw3LEeYRmm5f%2BXdnvkDnxLLjMLxtvX74C3OlwPQqx4xwIdpPx38LrlDphiyWUWHWKAzzxurS%2FxTo%2BP5wGFak62ap1PVFFN4v%2Fy%2BxuR39WnIO7lsWfwgVsK17wxrs9K8ltIKuhkw7f%2F6dhK6gQokFKhWX3urrjk%2FrnI0pgfpGMeuQIUaEM7%2BGF5q2iMkCaMQwxxOzcvU0eXbsnS9XknXvP7Gtw5dwPXlFu2ecvSHEZgNDsU6x%2FGdXBYXyOQjzZReSedeEPY6nEv9gJR4oBQJtFO6Kd0fwC6BO4LNHDeBujB6dSNcUQC9zIv2LnAzGk99bUDrdFY%2B9yGFQtEo0GQPNv6vS2drj4%2B1jHbv3aJSMUWP%2BQTZrmbNTjU8wyG%2FiXNNpskybLcJ3CiTF5Ir%2BJYzmJwE0mSVhlxbtbmvweB3ulB6Til5UuUZydpgiFVeobhU0WaBqpJ198d%2B%2FXeNRTZ9%2F1OPfG7%2B2hwzd5W3D%2BhmyjsRcUg%2F%2BCavb%2B%2BVh2ls3L7zT%2FetOnHNxeerv313vzLVqPai4nJv%2BK1FC6040%2F4udw7sAb3laSg0XCkAAs0npBO6VJabS4Elk%2FU%2BD4gTXW%2Bj0wnrMlqNamq4tMIYB87tE10i0FR3LZNhJsb7%2FR561btmes8YBCRkhYNByRtKd55mqTas9FYhJnbRGHuOh3M4QTdgQSqmgRxuzGdSvZGcbMxNQGk5C3ebLjoXIOFM4l%2BWKHmLTJwRv9E8GWJ6dYvf%2FFmEyEGr%2Bgyrr1p5zrgkz0Cw2j94Hv8Jdx7dIVegBSNtgsqGsRQEYiIBoXwD0LNvQ5d7s5Z00QzwNhqZA0b%2BtMG1tQq5nd84uq8R0zPvX35G8uRaze4jcOHzz0w1%2BQ2BIRvf6J6Kgatnrbiem%2BCFvAxfkrndzD9MFPP1GWTUHclpASUkCNAQkpCCcCgDSUDAhDZ%2BCuEkgn8J7i9nMA7pA4lISappxILKfAeSAbIcSDuN2bJcfZILqeO5rLs0MnngSHYRdrHjmaz7JEsEPw51ZqDJDmUIOZIe34WaQeegNsJn1qz8AIpT3yCjyEih%2FxELkuJ0lEMYTLVCiWpo5oYMleMH6USyYJcD%2BuOe%2BkWKpn1Qns34iyYDjkSLvgnZXcgVQNeqINXr48m3iS7cjm8tedyY0f1QvTnHHdsrKby%2F%2BSSbPY8%2FNH6vpl%2FEsq3Ae4ZU1HC44KFiI9o7CEgab%2FRqHbj7s5KAg06s39ZP%2FzxI%2FmVuF%2FTbTSy%2B3Fb8If9%2Fcv7%2Bwt91yy8RfP1QXtW5RzQn7qIiZyuFM5QfJ5E9uVnqT85TanFx0lkP3ukBAMprvsRyi%2FC8NAJL1xbIIirSvnSj4O5netb4JxmNANHPssHAcHMHsFRgEug816gDBeMbdfiuRcghqYcm0%2BXxx%2F5IAEtN3fqFF3LzAXqwoT0PN0OVTNqxo8sxMkd5Ig6k79Zk7VxxX6gMLOZFQgvpW2RrMW1D0BDihaXQ9wVRoBxPLfpknmkeMtoB%2FqM9cRc9IqmMD2XUmdZ7GSRKPUZvChf8BoykriM2MnKYbOHX8R7cLdNCxSFFVQqoYswnlWtlFS2mNkhswVpZiQW1J%2FUKFfipHGlUkM6UKBhMz1istELIHJLMSctu3ugzfaVSOjKvUgc%2FTHK4Sdg2Wscz69leKIkkrwuuWiOe9yGYKQXRumkC3qbRcMwrvhjNXgdZk3RxAUEhuSPvn3nnd%2B%2BU%2F3vlVOmrJzCD8JLxV1OHRjrZifbcFDOuRNTGqdgQm1tSNJ2OcQ04YiEXuxtII1ECSQRoQGYioEsgCfchB4ghAtw7FfJre4WZ9hkVi9MtjuWqtdNDlpMrfEG9fOT6q21okg%2Be4As38MfGquNt7oUws6Ysarj1%2FefE%2Byst86YUVNvDdts3Pv5c8m%2FaP0C%2Bf8%2FQb%2BIMnGq09BgwN01oIOAnAdagI8mBSrqk1gxTDUBOtk2ousEtBH2z4Ir2d3f6k8PXXVlt2qN9RODxRuoJT%2Fv27wm09jRYVc%2Fe%2B%2Biyx2tyzJb%2Fn3J0htXP87eSsQaf2Ly0s6Zmxela88REy1cf4273mI3iXNJ7KxrZibOm9xm6rl4fqy%2Ft27smU8tOfdW2ucBzg2UfmOIVyLIl3kpYlwphDISTXJXsctmiDtN7fNV6zelgxwnWxsVr83Aj%2FS5ki1jL%2Fa0GC6%2B2L6Um%2BaoddlNFuj%2BbJ8mH%2FiaLh8I0%2FU51NspIEfq0dohwyFXKgm4NggwQ4rRhCOUFtxxo8XnitT4cnGfT93IS8FaT85XE3H5LMY4zIEPL1hw443wz%2B1UmhTJyJGxZzw%2BwsKkKZgUiVtKOKMEb2AKHTv61FNc01PQFwKnvsZ%2F9pPA4RKTASWahmh%2B8MxwzHxKy74IRn5LGRjsPUUwTu64UYNY38caqd7HKucZ%2FtHnODtENw%2F2UfHRMaq1UUPDJQ0OKkWCeet5fYOhII1VRz8%2B%2FElg5j4Gxur3J8o2PJ4rg%2B2d08T%2FfwEzSVbyZ9XPro95T477lRKqUSRXQnauHNsISAl27oWi6Fv9z48JMv8r%2FaMMj8onCP%2FDuDZOuN%2BGPPr%2F%2Bp7bx%2B7JlbYdppcNhzKU%2F1Px5aiaGDn%2Fs1iGMaBcleKUo%2Fv9rcxkZj7DBEKOfrayytXNLYiUdBY%2BpleQXdnscKlQcpzuWluxsieeyuXIK6SdxozitWyGOV3vOHHjguyCQ6fpIYy2JwvrQEF%2FQa9Pdf%2FQqOSqCiE%2FEE1%2FXIVKTc2tzWbHnimrEd%2BVyz311Ml3P0GVTj7PD5aDnsvCvH36alEaPMePcMegXs7x8igTu4B9v7G9vTHvhCu%2FkzIdx%2BBxC0ay9zRSvoS0F2lIxI%2BX7klU63I40gLQ3w5ep5na%2BSFnba3z5D64zv%2BQtM4n4ffG3tq4aNHGRfxgrXPMim%2B5487abL7xhdseIRn1KDl%2B7aINixdv0OD%2BJSPwKf5%2BxoP6aiTeQIDVlIhMcL1H5R9PYXvprs3fv2bO7MOplCmweuiq2JRZ1zz%2B9a%2Fv2PH1Hfz9236w%2BZrPXvWfAxlj4NLLHpq3c%2FPQ3uvmvbrjG7fe%2Bo2y%2FcLdtE6VUlXi0ASb1VLUBVSUWSU4HdvAraTyS8xzM8NxvxFkXV6pUVRiJwcgC5zEeht4rwcp7ki0k41G0qlQhG1Vzlq8alEmnFi58caB5Q9vn988MLhqyVlHvLEWjtQFeupdiocF%2FtkkOGPW2ibWaBTkeZ%2FdvPWazXfOnnvL6jkRXpi85sFzZt%2B55ZptW3bl1cCCHZPD06MhySha7UFzjcjbp8fOecFCirzAG%2FyVjBX6OFIaadSjQq1nNhyIe8tVbaaSdHlXIWKacMeuZA1uxS95zILhyrxAdsXTL6m7kNQlx2P9uZf2qhufePFFbpI6%2FOU0WcP99RrCsrwseVot5mtytpf6Y0gm9sdeyKnPQ7onyK4nXlR%2Frg7H95M1upzu89DH6pgUcikoiihJ6NJKmRxV1x%2BMJiOA3YwhDRQrWU0u%2F0rvq0VYXnyCwsLeTJYBq3dAtJDavuzyoVpzZ99Z0%2Ba0uoiFH%2FxcqgDR7rUFeOrUn6Cywb8ZeNMbhLV5ugP9l0zv9UN5b5mFkjzxUcpPJCn3V402pRxtJd2GrnLdhtVk9ZSZh9W91fCSH5B7ofxPiWL%2Bj3D%2FuwhBRdyAyozeZwvQzs79soi%2BBKSnafLviZCcfrpBpLyimfLfTyJtbyruIQKD01tUwJyKEo%2FybaxkSNFUMdMkhQoJyRBQFhnUkDQSXhTM%2B3NmY0EDM7ffLIjqWEGt8lCO6mLia3PukFnghosJD5p5SIho%2FVDkzQfLE%2BIrYoJXkD19pdP7OwG%2FvoIUtagiWiZ4PAFTHHlTVhRZ7dYmPar%2BNJ%2B8JhmR6DFK5DV1foHoLNO%2FpHrvZfmWZ15RQlwvoVDKhCWNK3CCch9lfFBuAqUgpFSShmNaPj%2Bi5%2B%2BWZfKeViJfW5HnUakVL4UCNVkA4%2BETfIqx4B5xSaP2L1yn0zn2ltPn4%2BOqZGmwwEVCaCSqG53ldtL1oLGAhdMLd09MpCCF6tD6ZnAZBY9hDaYsP0jzZ0j5ZjKsF4i1UmLuhbJMCnYJPt5VwFNvmZawXjEvLJqIH8STonZjq7BZ8gKgR20C9MDFqJAX1H64QW2NEup6qgzLP8cvppL%2FNNTOBTCJABOHeWoXzLhw4Wuy7gaBtjKr9kgKq8ZlRYBS32Lpxc8vIhpNDTfyNXWybMJbn2RyQ5EmWc2QF9wmSZ0KYCE%2BcPuYO6b15Uotj2Kd4MItLS7gtFbkTdrFND6pvEZqv5Yv7jXAus7Pg7avo7KDot50NX3CPkP%2BKps8J9%2F3mGQIteY%2FLGPC%2BL7872SPR2br5fy8MtKBMHedGuM28%2FMZmPJMrGgi3Gb1S%2BSi1%2FL%2FzrZwO9XH1ce%2Fz7ZQ1WSoY%2F%2BpMb5FT4ua0Wm%2BJf%2F298nFmChEQ%2BTi71est4mq9VYI6RsymoRJKYidElT2FGnDTZvqtfhGAFTbeqEw68GqtfmbVa%2F1IFO1%2FjdWr%2F8BDRRtQh9XNjubEm4aWVpVonpTGR7PVGc%2BKJNoBIWF7kYi4gUV3r1U6723i6TxUl3n3%2FtM27aZfKb7THiHW9VzFSwHJ05VfK6Ar7kaB0XgPPE0BSkSFKsBUpaLihEWoA9wBt8qirh2VSOkZwXEwyrxZ5jyt2rJmSo9gX7cg6jsEUGJU9z9xJPOEM3uQQxKgkh35DNATnVyrmJ3mbCNyIB%2Fyox4wH1bg2DwN7q9kov4pFqny8oSm3RQbGgJ1QQTs6ZMLilOVYJ9v6Wha3HcJ9jddsXp9YhGUXLXt%2FqMDnvLpPNTXfNa60z5%2FyjXQOMq%2BlNmwh5egpYrdfZQZV9rI47xlRkuyTjpzsmCBSWNkAXVoK8sgYWqQJWbo1RLo6QH0YW6pxqfCnRgkd%2BRiFjUQUQ7poIaYoakgXxwFd9BuuI38H1xBxXSFb%2FpBDIKQFn7YB3dB36l7sG1FLaKiBdp1KxLvfswap%2F30lnVESgNnvjbUoT6w9N%2BXoio0qcYOIM%2Bheg940YimsucQVvli9NEcft2UZwGQwLuilj1fFr1i3NP94X%2BPE7Hpvtj6lBJfJ4R6NvWiaL6MgzWHxiN66DExa%2BdAdAbMYX6HVF8A%2B7rjEZIXAVbDe7PVI9rmN69JOLV1DOSvRPxWNPZBZf%2FNf%2BNy65BhYxxxV%2B77XJ2wfQ389%2FIQPgajXbwMsuAz%2F0IaQcXJavKbRqR2IqyZruXjVC2%2Bhdee%2F5vdnYOedpmVtR3NGXldxSzDSIiBVpkGb9by89UpEPKrSLZmyFDzMab%2FwXl2CNe7s%2FqCtTvWgG5kpBmCBlSzDS%2Fr8N4uwBwohRW63JTS1y32f0TQsPfXVGEHQrV8%2FNCfiOUVirYcBbIeA2%2BiF68rQIo3B%2FS628vYESr79ehzS7Q9LEL9UXmik9XVHb1yBO3Ngvt5935%2Bk1efkV51mzzrM0LL3%2F20avnwMeKuWyOUZg2TasSqZ%2BKcZQiOn1Iu2Vh497ALUVZiCKt%2Fgh6IvTIj1ZLRjWAkpHKOKovNwp00eqPROiAbiNEKieXwMLcXhVJ1%2FuzmLP4tfxaHR59cBdJVG1kTAgl9ze9QKUEQ946Hkb%2BokJ5JRDyf54Axur1D%2BWS49cLr0tTPEu7UmXrxcSr3XNvumv4yXzInXKH4F7Tc7p17Zt%2Bt%2FqW2%2B93k063X7VW6lALxTY7i1nBXMxcxmzQbabxz%2BtJo%2BwijYaIGMNS8AoSMgAPt84DdHOoMPfjXhF%2BkuH1tZvuFQrRCN07xGcXRX9MYxYchDe5BcHj%2BZ4i%2B42WyPc8Xofi7bbZJN5nJLJ5qr6IqRtzqNlM17SpFsnkEyTWoABEjz4JXOQvzWYuwdnV5LNGOwTM5v9r4RpQ8ZXsYodks3o31JBlzbYtNotisnm22MxiwGFXam5oN1n0TA%2FhRvshvTSDwHff4nNzRo9Dum6PaJbMXzDz%2Bx%2BFkj4L4bFNBb1asqsgH7Dyh4DvbkPtf5yMDKzEwyoaESMSNS9P9gJVA3%2FRTlwoMwZvxECFWxIPNw9gi01nOHjP32esZTtmXHnxvZd8ZtakqQ7ekajbXetpNa6ocTVxJtY%2BuSe69OLz77zh5bDR3xjZMzUz6fxrz1nqrZGcHQHfPVefN%2BfiK86LeXj%2BSc5lPKy%2Bk%2FvCUI%2FDaLFYCWHr6nbXuILTIsb5imNKY%2FrCm28fSMxPhkN1XbNMNZGuqwOBhtTSxWuTk6bw0ZaG86b1hKddePOKuBvmiguYBn4T%2FyOqOyGRBt7bKUI1GjioBC8aUKwF7Q319UgcmtFGIzCJGBqwQij0ynDsfdFGc3TS3BlNfJ25xmzniMkpXXTPvCaD3ZaZvyzjmZdudBostmhb0ORZNN2sJBeed1HXkrUsywueQH%2BL0eCPxmsa5ZpgRJSDZ11yDv%2Bjmbd86vxZfc1WcZJ3UkMq1BOOOVtvu%2F%2BpB%2Ben186d3GTwWAw2jheaJs09%2F%2BLNfZft37DALyrNj1wABMuUKbODyTVnT%2FKYbJ3Tpq8IrNh92dkxOj5P%2FYpZx4%2FycyiVcDYdn4JbEoKdQi9054iBKsygLW46FRGxAb0NPNCm8BSNCPjoKcj6EAus4SuP3rB%2BcV99%2FeTF6294dA8%2BTK6v74MHVpYNRt%2FI30e8QGTOOdfGWzzxcy%2B87a7bLjw37rHw1nPzp0KyyRSeZO%2BQQhInt3dYgvycjrPOv%2BT8s1rptaP84VeywdWX2T4ysr0%2F7TLIs6%2Bx9zib56ye1dM9e%2FXsZmePY3NDs9zlnNVt4%2BWgHJbbz3Livg4P9WWgviOMm4kCRT6I8vw0NbUUEnFvOuFKoxQW1gTsvFirsF5pb7qTUCx4i7VmtToveaDxvK9uOaedVvPRpVOnNz0Q6bry7uiSdQ8t7Vy4JQKVS%2BXPplV2ts4bvCwZu%2BKzgITtxepaPRzWdpv74muvv6RO0SorX6cu%2FdqKn%2FXWnrtp%2FZragz13DUCl5myiFW2Ycvb0PtsXnU%2Btx8pvLFbUspLX68mdegwmOif%2FNPDONajTGoUh6tU56HBJCTBASVvNUB5VIiKpc9kd7kludodSFz7xQbiOmMk5dOYk56gzL6uaf7N8a6MQOHm0ae6snZpFDfuT3%2FjdYzjzwkXXIVHoXNuCfQslQZqBZjTsoHMqrkE4jaYdgkGz2ATOgB3cPkSukD01DnV3ttb1wx%2B6arPqbkcNAHoFPzKUUQ%2BqL0k97pjbZv1I%2FegC9zTFbrrlFpNdmea%2BgIgfWW3wqkcis8ky5FAcRd1If5nNZrl2FFpungc8wpoCl1BpQV%2FScS%2BzjlASyUTVv%2FAJ46gkJI4bHX4lTnloctxPZE1ckS3%2BjG2fKIjkQFyzuo8jvYQG1OrGvJPSTu%2FnSp9PHNTl4z5hK%2F8gtXVKF6gEKiglgcKiRlCESsQCV5QIlKWKpr34lt%2FwkSx%2FJCmP5%2FcBKQfl%2F5gd%2BrOS%2F%2Bp91%2F%2BYCg5CXK2W4M9fu%2B%2F6xxX%2BvnelVuldIDCG0VQTpU9Dw4pRfei%2B6zWx0MLie0gPbyrkmRU7OwT16JGeyXLHqOLqAfVN1GPlBzWtFNzj0TRTCjogtP1NjIvu5habN5Aoa1k66wGpqriVetJgiGdwDZtKhnN0y4n9sXYnsqGmZfDSR15%2B5NLBlhoDaedEm7sxmpqRija6ZEEg2EAnTiAC8IrmFbGz1q08P9PSkjl%2F5bqzYqT9hMmptEXDgTqP3Wiye%2BsD4Wir4jCeoHbbp5hRfpB7BakUIppIlPCD30dR1GtslDz8OsqbXmejFC%2Fv8wu5X2myq7SJ8Avzv9DFUJySf5uNvq4%2BTi7W9D%2FOZrLChdwxmPNiBRqVjnpK%2FaGxRCDspVYKAW9AN1JANoo8wP4BJUlGqdgw6m1qPQ2QW3%2BOfU5%2FieLS%2FNuKpDU3uf8bcAXyBal5jMR2NEAbPAZt0K3hvxHBEDlUxfIGcD%2BN2gNSNx36nfqlAYow0puatNpRz0e4W2oahKzQHsjf2c16ad%2F3t2KTtPobnX6D8C8pd0MDP%2BKx7wnXqGGlLQcvikMErm6TmfsuxJXbSAxqNjOogJLQBLiKEHAE%2BJGTS3JoEhTrz8%2FCB%2B5YlupJ58aOat8Kv4JvregxwcU5Cp8GFAFm1FyOfto6GS2m1NGTS6CPNKkbsTdCBlnN9onMho55BX8IJZtEQ35lk%2BhtwN5A0V3RCPoD%2FyXAcv6pAtbZczRUA64JmcUf4q7Q89ZHLeJVZ5D1Ps%2Ft%2B0iCT3AHVtZC7JDCXfR7OSb%2FXja5H3zQbZL1B%2BULX1BMTEk3AseSpmnKEK4T9ekMIidUCRQFfcbj7z8gNLvzF7mbhQN8h6ZbRset%2BnQWdS%2FZX3k7WpS8P9sfo0iGS64wV516pOhjI6TZ2dApgI5%2BLhxywYoWxKUrykKJsIoDsR4mSrCTg0egMPnLW%2F3Q5Nn8BZEuzqEI7HK3n0%2BzFmuO3TtWQ5WJoG9YqCD6Gc32SxnbnVPfsxvrFXK2dILl7bLthDp6glhcsfp4bYvbSmj%2FmQ94uBTw0E73x2jbNRCvC6VL6GCFDwU7eWQDcC5FY5s0slieRDwtAbRsbLXbaXAuu14e2OJw1dc6jQ3ZdY8v7rv2%2FBWZLqvFWVvvcmwZkK9f5jS4muO9yR5res4kfkRxhV03L1RfPOiPtYi8pd7jNEsOpyTwxpaY%2FyCZu%2FAmd5Or9uS3DYaeqVOhH7gZN%2F8I%2Fwi1fEuLXvyNivibjuKvN%2B1Nc01HF%2F3h%2Bef%2FsOhox8MPd5SFucPjorQwXT%2BytA8EmA5mamHNFDVhBI5pjZbQpugBNkO8MvRub8KVDKST1Wag7D3xlin1ZF7LFP%2F79nbvCXFOY%2BPUjrT7%2FotsPXXZ4exdPzuhZuL5LUXVAn7k7PbhG89uz3b41X01gbjP1xwlu5rrvvf9%2Bpbs6E%2FVu7Nk642%2FPYRaAiUBdrmO6CDTBLPQFA1ur0uXoBR1INDMkypKpoTqnSMx5GiEdTEaSHLs0Alvu%2F19%2F5QW9Rv1U1ridT22i%2B53pzumbs%2BXFFXYC%2B%2BCGsTj5JUT%2FGCgRt3n78i2n71FHG4%2Fu6X%2B%2B9%2Braya7os3ZbDmgWfXun44e%2Bu2NZKuGZ0HiF8M4TlMPR%2BEU6rPKRJ8wOU2RFUFLex3egEsz3YqEAq0cqhAAW19dBZIlVzR61tuIdTnpXH7l%2BuXrbjPUyep%2B8cl6aXKWhPHpDcXl9KiTWDNr4mBQc8Tq%2BNzK%2FOKSbsfl79o9G20R%2BbrBXYvUg0rLHhtrc4TN81TTOWSZ0gL1ZVlOYH2ery%2F7XVUjFMbzYpg7UswcqJPQwBd0LKLabJ8IaCr2otcjSkIrGwootKECaUd4XH1%2BSdazRrfddkBU98t1htvWrbjqSqjaCguxrffM%2F5zDCpBALUycmajhd%2BR6ww4SWafuZ5eU%2BtPid4lgd3gt%2Bb%2FY9rQoZNmiXYPXyRHbRs8zX%2Ff4WIFjWZJtUdSD55AP3xtXH%2BZipC0EqdBGDA4CoYEU6gRLGPU11QhkLTBiEYPiqOeQgwTCl9aok1Qr5pFf71qEeNxjy%2F8F0GoqYPv75Yh9j3x4DuJ%2BuEzHRpAq2lMqb%2BqfTdiq6kGtzfOWsv0c7lSeMXDHBDe1MT%2BLUgx0Pg%2Fp87u2UicdIvqQi8DkxhcUwUXCedMpb4NQjwY3npTmgsURJavLwCRyEcN2HfWsDVGfv%2Fu9ZUWUx%2BPYFueUKwaNvbtu%2BXps3eVWbN1GcgVrdMnWJ7WmJz9SD66EBidag0NF1Ukep0t5A7sFCWdhzvYwHv6L%2FBehXuHqfaBwBEU7hfVLcXvS4VQv%2BT%2FvaSIl7cbeMc7ekv9i8S3e1L5xxpvMGcu1EYPbKyCiijjGXcDKckm43PqU2qNWlXusZMiqF82cuVzolUHN9NNR0HZPxFPV9V0wLtvq%2Bk4DqOwVWDlzuQLVdqFiP08cRX7aRlBVfR8cb55bWe5LExnlcsDp1vAP8Q9BucPMk1Ulh4GnN0SAdxcNHv3q9ohx1Ati4S%2FtkWjIDe3hQdkUGrGRaFBiUdiTSkI41UkMuuQHP%2BEaSQYlPQTFWJF03BNPpTu5KFAdkWgDukzsZKMG0Q1TAQQglScOaP%2FdsZ8%2BfP75D%2F9Uu5Gs3FY%2F2SxPld0DHOciXI9gqjcEidXjE%2B3BLosy0OcX3T7O5g65ROGyzQ2BZs7WbZVnO5ydLe32hMwTQ4wnnKXW6XW5LAa7oaXOIHoUl0FgLQLH2by8wSTWeAx2Y5PDazK3BqZbeJZwXGPaYhX87ZNszoDdaRxotXO1nNlpdvAPFWHDm8PqEE0sZxDEqGzxisFNnuCWetPcGrObN0p23tTZwMuRVodSV8%2BLTrOV3eRvzjQZiSjaLYS1WEJe0kNsJlZu9LFun7%2B%2BwW4gRDRbaxw2nrOGm%2BxOj9cmtbp9ZqeTM1m8UXfQQCSTVSQox6pvtjot%2FFpHvIUjJovFEoYvHYV9C5Y%2FxN9OfcalvII37UEhTbTg%2FAQIaPb4Vz6j5u8%2FaViycMod%2FfkDcpu8QZbZoeBi%2FvbzP3XPsZvOubMtaPHkD9jt6%2BU2O7vqU%2F9C9SMvgrXpQNG%2FE0oJxun%2BCiElUa0IKQSUwERxOntKSV7ekcuh9VBZBBo3VUcB58ofKBHCwLyf9qFosz9Ibf8dGqwaBMjRig4SGOZ2UkWI7UiO9OfUPdxOYFApUZyfpY7mgEc5rtNGGk2H1lPhAk1Hp%2FVAMqQEHEUfEYkkUQq1JMdzsX7kklRrTrUi1wMcDjmu1YYfATj7Y%2BpGpPEBXuoQIj8rR9mgCl4C9yqmF7xnVWxGVniNqtpVmXBvQ6iwni5YQ8a1jYrXtc2J13HvgkvqWxuva1sbr%2BP2S5ceKGyBwDv2DbrToe1u6BkAJV7xnVLUaq0sJB8pFqcUIPi3yuwxi4JuLr%2BP30f3OkPQ72aO0xYo3%2FEsmO3QO5qEF8S0qQH0UsKXv0brnl9%2B8M7jF174%2BDsfvPOl1au%2FRL5%2F9DsbNnwHL2pHR1NTRxMZhJtHktOOxLxErPF6YlLvpC9YP73x%2B4ofw%2B3xVdrHcDE0dQQCmCRgvt9b35xINDf1CDcRSfJ%2BpYl%2BSf8YcurfmXP5F%2Fkj6J82jNsrkWiEuhVlgFfyNkB3S5MUzLhoNiwSCYcxQ7Ui4J0Xh7fmqRbaPa1tzujxkBRlsEHy0%2FOM4pYLPb7g9O6BQJN6l9zQ0OGyCaZz0vMTbHOzXfQ7a2tsterTcqxeInODoemdktw%2B1SbVhKwtW9ffe8VKadK0OVuC3bWzyKm5LeddsWTeorWyY9IMtUFutdu5g%2BRn533qkocdvLs2HmhU75br%2FMmWtD8zA3OP2t1ea636jEzqYxJZGAwFiDEd61oTsrRuW3%2F3pYNi3bS%2BRd%2BGjOfVpAPNd6y64Gsz1GaZleWIPoYL%2Fv9mTeQBENVEguiF1aC4YeXxFETw6QyPfn0m9g8IrMFAvKM1EI11DARnbqibHk%2FIojy5rSdgCyZi06y8sS024PeuO4MfwQ5Y9yKRZCqyYaF30vzeHlmUprR21tR0t0yz8KZY66zWuGvxVQB%2F36kP%2BK38t2Hu6NQ9SFJfw0AdpqPEK2qTMpf2VCqJwqPoJezTL824b8akoL%2Bx03nhh%2BoNo5e77psxg9Q5LzebIKD%2BfsY34f2MtB9fk9v5b8PT6tYrgv4kRPwd0q9z3gdJSJ0653KjCYPwCaR5aUY63eW48O%2Fkdo33yxX9wCiMv2QTrk8eGSI6Ag6moG9t2P%2FF7GRNlDjl0gw7pJ5aOXXqyqn8SENnXBmbSwUYLyqJjv3UmY1nKr4t80no0faXsaIEiF%2FBRaIBnItSce4OUif7W6Vm9T9H1X9Vj71BEm%2BRdmIJQST%2FZfVdudUvh9S%2FqqNvqT98g9SQ3lHibZY0mRVHooyDN%2FFHmTgzjdozKw28NwQ0hwN6BCoPKaEk3YtKwNhwRLXuk076CGoZNXDQcRwZvreTZY9EZi%2Bd0s4%2Bztv8iei04JQl6ZbDD2eHV7X4uHuFVfPrOmcs6m6Kr7hssr%2B1VZFcEZ%2FPdJkn1hOs8SXS%2FNFFgqt94PIZzZ3tdaL6Q5vo6piSzdy737pwsX1VyxUrF15iJ4uNkq%2Brbyg1Z%2BO8VsNC1UmcvORPRfxtPrfRwL2p%2FoA1eZp6Z%2FaGffoewaXcA%2FxBlKlQLfhQL%2FoPgBGP3qsA7IQS8qDVNswHKRSheDUvA3Q7MZoRcJMxlEygujn1QdyzfPfq3dEp%2FbXh5e5YXW2Ngfvza0ZF6UgFL%2FE0fTq4LBlvTE2qb%2FKuuzYSXVnjTfM1osvqMHVbm9950quIZlbqaL6YP7jk3kUtA0GnX2nvq53f3WoSsvEdDRnULgo2fN7lNZJgI8%2FVWi33c3bBZnGY05%2Bdm%2B3qc7fNmj4YGKLj2nfqFP%2Bg7jdDlxEV5XsJQZP6hYrS1l0VQr4c69Xueixp90gnZPmE5OF22j%2BSYEWHlZ0K%2FHgsh%2FZtsbh6h2DNRlvv6jJh9XaJaHCZDiUDKNTMkvb8vsqCyf3ZNdSmO0fa0Y4baJTtpbKzuVzeeSI7fCKr2Z0WypapnXJ4gnoWy3PoUIlIQ1TXdqhQJIXp9Wx5fYdpeWh2TY5D%2BYVyKd0jw3iumwi%2FBC3cEy4o83QlZnW79MrCgCjbhWXBlRZVVZZv4rIKpXC01HFlHdHLoeWVl6UVc%2FJ5uGm6CViW5mulYMk%2BHqNYr0AyUPivLg2oMs2MPqtuhHyRyiwvNJej1Br%2BfcLyoAyu8D9B7bgmzUqfFobF5nKnK4%2Bt8MPJkI%2FxHUNWk117jugWF%2BxazTAALQn6%2BUE9lhoI5ApGA%2FiuJOsrlNP28SVVuBVajXmircLel46w2bJS1Q0Ft0KDuikDFL%2F3pYrid1Q4FvofwRIo4R9h2ftSwc6jHAMqLcCql8YPHtlzGoByNXYN6v8hXnRaOhUvx0sVLCexwupGDR4NOYC7PePa5keIPACnuAdD7dEadRuTIiS6Lb7uskb381My5yjzF8lGCjBRqdwrWJCagfB3yCy7XT1i92hbcZ5Ci1FJkgYMDf6n%2BjspIsHFjJrTOdzSMuOa9DbDcj%2FnH9N9bIoGVgzHPWIQuFuYtaMRaq8eCKI0gEF6lPOZjBz3EEvaaxwSUT9U%2F8JbJZPJJLBLolH1La%2FRbF9AbC8JJjv%2FmMnssKjLRBJyqj9QXxNko0Ux%2FX79epfiXkm6fmKwF%2Fen1HLc6LxloXWKvGa5rVCVL83VuiPcDEX%2FK5pTXOxHfx6HHB0t2FI0qI2rCZFTrvPWU67zVuS%2FkTsLnc7IKhFg30e4FOkqNSfH5PtkmUy6Cpiv%2F36k2sbqCeCFNa%2BURpoY0sZoYmCgCr3qgZz6s8I0gP1bYiR%2BD79H56NOz0EVWCTy2%2FfffvSCCx59W7uRV9995eqrX8GLesOXNm360iZ%2BT%2FEl3uZqL%2BFyzSZ8XxpTiI%2FG0nkT4zznFZ0t4ipMz5v4q9ssqbdKUZt6u82knPCrt6PZwsnn0XySVnyPR1ZXAn72yx48bWJsu7apnI3Hy8bygUK5Js32qcytapqgmn95uexccj205vGgJ%2BeuOeG2SORmKZr%2FqKzcx9SFctMJdwMUFZDJITs7dnOp1EKZCxg304Cevyfya%2BvlKqv6aXK1qIj3imL%2BL6hL%2ByvUlFfE0VKZ7E8gBY3M%2F8VoJCFgizH1W6VyC76nH6b7jiibYVxUmVIEspry%2FLgZIlCeP11Z4zs%2FAwvVwtGFEut5S1JY4lfyT0N%2FevOLo%2BrUEgjcqc9IkGpQbv3iW7Co5b%2BKgjvpzYdH85PLcc4X21ouwEGl%2FS4qnUAvoSlXUUhR1eKr2VWFTB%2BGMl6FsiQsVD1R3urlAAIoSn7JQkmiVVCHSpCwDH%2FqPepXQ0Db77CJOAImohB%2BRPWr31ev5g%2FkE%2BzTa4lbvZo8xdWPffQu9yJTPCNB66s%2BzXoJt%2F0L6hSoCuBIoK8fnBGG87OoRckJpLqyWe4YbpGi50g0%2B3I3UD85Oa0fzubfoXxPLbW3FDWzigmyJeM0tQkax7PqTy80%2BUxfUHPlBZIRVNQ%2Bv0xRm8REKPoLmNr0%2BUo48v9GFbXPKylqQ2IKm00QddgyWGMROCTxdLB9nCY8P7j2DjlsV%2F%2Bmfr0C0r%2FNkeXbbpPlOTBBwT0mVz1zx9S%2FwJecBF9Wgv3p032iP2v4VSgfgW2G%2BHUEdEXU6iq4CtpLJfIN9XQG8dwa1VoO8XC2SrPDDyCOQptXgbcPvlAgBfxBoGwftQKeKFrNTASPt3pGGqDt%2FQRasn2kri%2BH6L80MJRsmVYJrAKyDItpJUy3%2F15WYIJqcJ9Q5N%2FLFJ4c3dc1URpWl9hW6mu50MUIelg4ucTPf15zs5DFo1c0VSp1tKB9jkwIyuM45kb%2BIP8gHed%2B6jO3v0KbIknzLy636E8KPTdCuUpB0wLo9JKnAO6pv0vS31EtBha%2FfJemkgLVVnd8KCk4qBTpQ5m7FbifBKrPJcq0pZAFVG%2FXbOFz%2BTcq2MLrcmV28Nmi%2FOHskh82bau0k8eWCaPijQPWQ5lUvslwVCfHkXBMIehqUgtDNLeauH1huvZTbYmw%2BluPjyWoNGEuxRLR7LK5fSyXFUyK7PURQv2v8D3XOt2NJ6liBbmPGOsakw1kbeOs%2B31Wm5qpH%2BiJWSzqdPr2O7zc2TmtnrzCig6bBd%2FvgQmzOlz0STWIlmZEQfupogOZFHUZ7EkUnMn0RrpIMqAgHRJAOjIJ3yGw1I%2FMAp9q9S3Q%2FclADNm1wEeO%2Bxbwg5OIYHZLY3ehG5lJk2xhco%2B6JWybpEVz2wrR6hZyD0QXZbeDVB%2BonmlimpkWprdAs4WEZDSQppsDlcdCBJJESIYFuAtUnC4GIF2C3Uu2Kv7L1bdz6FxtqxpG4TqQOqOUNAJ2HLvPWA2GgDy4O4vaDrtyl6P%2B1fAll%2BSyFcQ28GHqh7fvvf37udylf0fNwhzgz87Y%2Bcf5x9GnF6ygHu18sAbipWeF0YPBgp2GaKeQduxxdEr3SgbH1kvH7tvqSLhedomOvZyts2dw8acu3dY%2Ff%2BucuMtCuP%2Fe4zC4XnH3OLZ8ZuxTWxy8dJfU5dhDeKPSlJy5pn%2F%2B7u3XrJhmr9C5CuleGflGQocKnlAUaRKp0BAHV0ZwUt9VCqk6zYOgRIuMfePJzdmBdpPJ7%2F6B23%2Bf%2Bsp9NMDZevovvfYHG5dGPISQq1DojqNckchVrCcCYz%2FQ0hI0m3NKDRfkgsrnamo%2Bp0CAq1FyvC3a3Nak%2Fs5VX282x9Ufy3E39VAx6o7LpCvO2wK%2Bch9jNqpJCutcIOooKnYWtDK8gTRVYygRQfwgzKM5%2BjP2jOZdx3r32Py7rQUPOzAnoRs95NvRAR0qLGU11Taqu1bUYSzMcWjMEir067JQQHfIrLBHsrgv00%2FWavd8HRLMEEYFSW3HCSNQehnrHztKqHcDyo4VfZ6gPKCR%2BgufwA8GegxUEo4A%2Bgd0BASHiH6jYMLIsUdQJTs%2FC641KN4oCHWolCMLlMfIdtWKScjx7SM5LD9HnfmhrGI0S139UWfUnxgOXdJFW%2BAMcGjKr6eHAttHF5sUoeArYKDcxMSYcKA%2FxUDhPiEOEAPafSIUFArN0r24ynI91EPARDXvIDYyvqZaWeroBOUABQA%2FE%2BDXC7PWafDLQY2oiwpUEyj4RQtVlUp1GrM7In2p2A7VuiOW6otMiGOo5Mrp05ejVuTy6dNX%2Fk%2F7mybZQ0nUmfrbx3U4KueDnlHm5wdh8FFeKnoaKKh%2FTK18StOPhwG9Xo5mqXAxvw%2F79YQwwDR%2BnAKQQ4izVXioB84qcppWB7IqjU45z4CE17OvF1Dw%2BoTFqxtz8dxwtogBnF9MjIl%2Fin%2BK8s3hM9laIn0TiCbTAXL0T798bPXqx36p3chrv0O%2BGC9Xaj48Ecv8U8UEeBvUEsDlTepiU5OvlpeNGvpnKF0RvUooWhIjnx6GeBapXCQYTw9DNg6%2FOC3gZjp76oNTj9Kz6Jqobxb9NDqc08vcKReOpcsQV2K8InXFaXW3aI6Ofr1k48rp7CX7rx%2Bv1UKPsfvzQU0Kc83i2VdILmd2%2FyX55zT9luN2%2BCu4nKfwPcK%2FCvDVU%2BpHh8%2BLaldIf1fA5h3ndT6Fln9%2FW%2F9Ce1vndfvJtnPVO2xhm3qbafHVCN1X363UXHq9xuVD8OSD29Z8pZ5cZrern9cAdGW%2Fuib%2Fud%2BVK0L9a42r6C90kL8KzxwLQw9NkIQJL0ASU8M%2BVG0KsUdgdvpgP%2F6NqqP0%2FgHZFUfGEijZLHpiIgvV5%2FBltrj8Qd7XQd5p4P%2B7tJo30NMO6VGBwahSPMYiaaBYoLY6uEnciyhhh1Z%2FvvacG%2Frjpsvnpzs0B1Id6fmX8119l88XnOxe%2FuGrzzHcdu7UtY3%2B2vmXN5zUyj3ZcPl8p1sZSs6%2FnGXtwrV7Ka0XZdz83fwjjINpZWYw85lL8BRK4nGyIir2RiOsEyipuEcIakpGjWgBjLiHWOgj0Yi34gW1kKPxHt2Na5q%2Blwg1RdRSpFDNzosb44YJXnAfoEOpZW%2F%2F6u1lhYA6leevezbI26zNHO811M2dc5HFxpk4i1jPC0s21%2FBWW5DnPQbn2X1WK43%2FaM2n18DfSoybbNHijFpamzXI31eRibGUOxSu%2FlT96YZlq1Yt20DaSBuG6knw2eusHs5EPBfNmVvHKdaQzcDfz9ZsXmLDWGXy2U5OsYSsIn8CS12jQIyD12KKqZrLPy7mSPdICmd6WGHG8NDZkkHuE4h9TU8FpmUO%2FVjC%2FEinToFyoNDz2p9XD6g78WgQdPG7Z3R0T%2FZ5dTM9lsL8Ktek7szl2L%2BgQwGgwkZHc2g5Su7NvVqwGy2Ua4KSXUwt1X4PaM5paaEu6jQ5zVFyNabxvUksVt2T%2F4VeamYPlLtffdQsk%2B2sUTY%2FzDXl%2F05W53%2FBz9UK3p7LjapZ2ZxOm%2BUlZXrL3HHGqO8%2BwVroDaCTTnTxitMxmiAAYQzVJQH%2Bnj3oIHnPaN6Zq6sNSLjBl8tKgVr2mj%2F9CWi9dnKca8rBQBsd5R1tzVlgrl5pbnPw6kZclCr2CHxMnHohLz%2B3KRQokzALyeIKFU1TNCiayJdoHvDYe7K6mZLm8S3uJ9dojuaJ62%2FqN%2FtjQxnSnhnKPw%2BLNrLi8ZKyJ3x1YhiI1aNAtP6NzCGzYv3DmaGh%2FLvQZnt0evgIhTFV0kE%2FPYxAnOHhCQUZdCWY5JWJwMzlAGl1mpNbDU7yyGnhRMILsYhH3VRAijrPcBU8%2FCj1Y9NY6cnGVW0CjTLaz7E3epvaT%2FLtTV72Rs%2B0WVVmd0dz%2FMGTI5F0OsIviaqDlbbO5X6xT3PeXbXHRtf%2Fz%2Bfdka%2BeKPr8KF7IF4vBsT9MFPuPJMBTBMq9hQxXelQ%2Bbewnf18ap4Ib%2BmSMrtDU5zqlD8QANa5MBGh%2FOwOvSDfcV2d66mfEWsbGWmIz6nsyZDWQSmqmxDneYyvjHPmRXHZxeueyRGLZzvRioKnGto9nIPkibAJA16adcOZRQr1iAP3bUyBR7T4RgAWTKxhkCYFwshq%2B7iV9r0whk50cmRcTg4fy5x4OmmNkHndIA2%2BYuMbmE9dwGYB4KFTsvnDE6Ah47r%2FfE3AYI%2BoXADpkdlENcZ8OZEEf8FFGZNxMs6ZLpG3SUFLL7Q2kcFU%2FA%2FJsw%2BvWDa%2F7emewLaoeibaF1B9qUNnuqWK3%2BUfXYVL1v%2FomD15xxeDkPnXTOKSVcCbDGtOu0YQNpGAP7U1HU58UrqGu8xIbHtkQ3LVhb7Dx46ET3Ffcm1q0YcOizNmf3bC3VjWfAcpSv3MyTlgJ23FHQgmgvk%2Bgk8pL0mcCDOn08MDAQlf%2B%2FSlTZ1z12fnqntOhbOTL9%2FZdevbAPN%2Byby1f%2FuUtC%2Fixm8ZBo59LTXEW060hGrTDplNprWd58fwB%2Fb%2FE27BdS%2Fs7U%2BrGVCeQ46nzaw9QccnmZerGZZs3Yw9aVHt%2BKh6HN4ti6lxIhT%2FwahnZtWwzlY9QHQ2c79C%2BdxzvVDKy8GqKWQERO9YAKbpsDUTLdWV5dE8PVPjvj9pqw7ah%2FPFVtkit7aj6G5xY9mfJrCz1j1e0BcnPol4UjtrCdbahIVtd2HaURujnFJR8CuOuUUfhrGhgKKgjCYNSvCc1WKlEp8wHUaAYynFNyzZn%2B2MnYv36dbMDBTonl%2FT%2Fma5IKAyEGz%2B4eRnVtaX6tss2o34u8mWorFtuFgm4A6qK%2Fyp%2FgLEBVat5WnPDdKA574ubuFJ%2FIUfZ%2FY2Nt6mN%2BZNNTSTaeI56gKwkXerTe9DDHUw8%2FH35FY3nNN7GGuBKWhrV9ep%2B0k1WjNWVaHkW1yA%2BQHWNu8rtBw2a5YXuE40rs7%2FGA%2Bj09V3hA98yRnFPOGr8ltGlsFdD%2F7tRce3LH6Trcneuiy7K7J3khKu%2B3qUaXPWaX7T6%2FKfj9BX2eZq2XAcZT79u1ClJzUtHUqfqSMWBcZS43Ena0cUGLgpkKxB1QM%2B0Fxz10wgg6r5rltnFpH05pepUq3Y2HfYqeKRntmUFNz%2BXmcOs1H31U6cC6RTVLfCg7RNBF1UF2%2FwBgu0fFQtPEU1sSg3VcNsR7dWq3af87tUFn1l3ltXpaJxpNvtcZkH2WmMst3JqRpxUH%2BWC0E1qOGtP66s1MYv%2BVLu8%2FXFXvV%2FZbunYYBeVN64ls0ur6NzpV9xzlmQwB5qC4Tq70WC0tk8dWJXeHvkD0h9zJOM0vD86%2F1NJMaIAolctvlByferCsqOKDKceOfUu1PsmoFCamV5mCrMUOCi6V6FJosMF22AcrKJgQDVhfYh6tepp%2FlYgvnCEAbJQ1L0rOpajEmRcasMiPfxhgGoVo4rwreQpV6fUJHH2e8fa1s2c13Apl1b89a58ozdoap2sjgLN9uISl7P1DrulyeIkt0zr6JjWocoPOZsaXPb6jtqBblsgsaRre2xHi4nELm0MhG1%2Bx1SXwLpFi53b%2BaHRYo%2FIrbZtuWAKu5cSEXfybnnmUCaXGTpQr0xK2O2WWY76f%2BnAjNVf7nCZHU5XqIkTnpt6VtvsFlPXg1031g%2FVRdpkkyVpD7jnmax88QwDvg%2F66NnMRdRXTcGTmQc3cuINwN5IQqi0yzb%2BYFVHuVqI5s4ADfg5oE4ybDLd28mFSFmYvRoomsWXEdLU2Wl3GJy93ZNb%2Fd5gqmNaqJZSO1l6PVRy0nZIj%2F45EetjLguh1rLqR%2BSK0hO6NrsqcNX8zoUdjQYDJ7tb4os6%2Bi%2BY0qpY2AWlnLRDWdGFTfGY1gV0zNAtJ7pdo24se0D88AwLY%2FgZmE9iuP4V5v7CSR%2FRThaHLh%2BUeBkXwU6BC7lGOevK65udTv%2BtS%2FPfW7qj3ljTcj3b9OkbV85t8xsMj7Ddj7DGpthZKwKPvso%2Fc%2F1K9aLE12fMWLV1y1D9ua8lyJdWXr%2FbG%2BnoCFutf%2FmLILe39ITUV4igr3876fpX5g2zeB52sWnIL4fXHlgeUzOx5QfIvJQyrKQE9wHUqVq%2BPEaOrz0wVvNbJZVSfsuMzxN4l9PkedFzw9V5Dj%2BnzpgoT4ZxCxJfC5RWLc74YVHxKlExCYt0JAOMatREhHBSCAtSfod6x6Ls8HCWECLwXZ9nd5Dz1T24JUdWs6fU3%2B%2BfcnT49Qe%2BkBs%2BwdsMZgPXMp3U5S958snPP%2FEE7bvkOPCuTUDTUQ%2FUzirLhML9yPahoe1D5Fj5jWsaoveyP00PehdUAHk%2FseDVWsvDWXXXsyn%2F4wfpXc2V3%2FQxli3jl%2F5hj%2F83avSCfpTNxOEKLmTjxOEKuxgNlsQn0xgct724mhynupNW1Ph6o3RYS3%2F%2B2TJrzLlkFz%2Bip3qCHKf6eqW02QJLjBYuuj4sobhCWqa%2FYHGEHpcnumuWSOhxeaL7sOakNR6vvmo%2BYcfFA8UFXEPZf9UjyudIOyNwx%2Fi90DdsujS%2FFX2UAwvWSVK4NxaMhAGw3oowp%2Fuc8CTi7D2rBgZWwb%2F60faR7SPsEbjkXy4G0XaqhXPwe2cePjxjxuHD6ssQuR1fq6PF0E%2Bo2t1nePTn8TUmxz%2FA3crMoCc7egESuoTHYc7mYdg6etORoOhR7BBGD%2BqJopELrl4S6cJNRtEAsLP%2FOdvnJq0Wo0GolY2Et9VFB2Kf%2B4bZvVyxfOMz3WdFfSIryj6DwWghre7aQbdiDrkTL3A3vNDuDpk93HqXwam%2BbWmUJZfNn5ozKV5Pmmq8PF%2FjVY%2B2Tlk2M2RzSXKjmbQ4RZcQavEYrN%2F9rlXwtIQqzxQNMzPPfHYLvuPoO9TbT8bpGw5CQPGd%2BSyX%2FCyf0Vxjd2R9NmsunnXYa8xGHzn%2BsSfM5J0y0DZEXWWxkXjcR75KBLNLHi7XvX2G8VOrf4Ykg0AMdBESIpo7MgAfyakA6rkqpI6UjNs0px7cMV%2BD5BF49Tez1VGnYmq0WIijp985m4Sn2gJR9b07riPPFo97OYbUZbxJCpot7H%2FlpZBicglCPN7WOfJkcHqc3ElWqvvz%2F1E6bIQrG%2Btz6WkM1SM9FBTR7FSs8KyBBytSmNEoquJNFN5EQyTiCrnKDx1h58yxCepPHU5nxGoxEQeeOZi2m80DxNxncVhr6BmEfUarxejw%2BWSiHhWk19bSY7aKR5MsteblJpfTLtjimBouXsm3d3djjYM%2BwEW0El9dM%2FueVRWIsXwe43R7SgbVZqrnqoJ1X%2FkuF7pcgf8duv4q6vayV5U9zMV91GxO59UUjW8rHV6u799WzKMT7umRCXbYUKM%2BfoaCcwgaoqZUtmodV3p%2BX7akb4dnU9B9La38RPFUG2SCC90tVA4XwEFhyOpZZrUCsgWYHsczLFBBVGNtstoN1bw0Z%2BO4fYIbvZVt4EUcJEKOhHeincWqONw%2Bq6w5Go%2BWGOSR7LhKV%2BKBqbBPpfUvOf9QqkpDyVhBeyyZQGMsdA5FBUqvFMtUyGq9vjnsAJU4UcrxldP1CCaofyDkSAifoP5QwWx%2BSyUGxp75BzGAvtG7uQ38LehlyEQMeh0TeE6Bm7tYdXqdkt0uOb3kfYlNwmOdDyacOq%2FqlFo1v%2BPTmTi3E%2FglC9W11b34A22zmLzvb231Q0L2Bgg60OTW4YdstO%2BYOJnO38TtpH7zy9ymokWyA79qlVSn38HtpFlImFnhu3b4boNWXklOXV0Iwo7lQ1hrZyPFcwtjwFP7iEKSHSSJw509kh8kj6pr%2BH1jR7km9vcvqN9657vffefkv%2BfKxge1X%2B7RdjYUPIESN7gTvRkB%2FRMYtEkaVkdHApmdBPpnKmz0n1xSWFOyVIuLrinZwpoCRe6kyiVZoHX088F%2BUX4%2BWKS4iBTP0IWxGtZgOdMaV4KTayqHQF%2FVihBwTbgDXTCmKoOBJeNhwJMzEVjtjIFLuU38fPR7hqNG1JS7g%2FqRCuy3vmQ3W9Vu8qbVbP%2BSzazGRJH83MzP90Ck2m31mMjP8TiLn5uwD2Ugr2PFvPQjB5BnSJvQxGQZZEB%2BLopqzGzDbMmbkAPkZVJjeO5FzOSBKCgJze2ZS4Gemc9twrwY6u9H61iUQTcRvtdT9RW3tRxAWwFs2tcuJRnI6xjmBdWjbgFNRHMHiF1uHYBfUR%2Fut5Ug2jXAaT96%2B9RH%2FFToRwIzGbKmVJ1AZQnoabSB1yyIg7ByAridHApPMjyw0OiV6RjSbCuzwLAvFizBliWJua1tsuAgvNPbmljYbpt8lkWam7b3XZiOiKJskMOtmfScnsbPW208knwjuXrXK4Q1iKIgNyYXXDVT9C2Ye%2F78GQ5BEEXfFdde2RwauOysdJNL5AzCy84ard%2FnGAVN8alecnFdgu5Gbd5DJTL%2BhHZK0vApVy3OfU8XTSJg1TlssivsPYUlIqvn66PzrVTymCc4wgF6SDNR0pDf%2B9Gp%2BVnsUH5WtpHYsuhOaey8zdwLN47V8MTbm78g687%2BP3cx6tcAeNpjYGRgYGBk8s0%2FzBIfz2%2FzlUGeZQNQhOFCWfF0GP0%2F8P8c1jusIkAuBwMTSBQAYwQM6HjaY2BkYGAV%2Bd8KJgP%2FXWG9wwAUQQGLAYqPBl942n1TvUoDQRCe1VM8kWARjNrZGIurBAsRBIuA2vkAFsJiKTYW4guIjT5ARMgTxCLoA1hcb5OgDyGHrY7f7M65e8fpLF%2B%2B2W%2FnZ2eTmGfaIJi5I0qGDlZZcD51QzTTJirZPAI9JIwVA%2BwT8L5nOdMaV0AuMJ%2BicRHq8of6LSD18fzq8ds7xjpwBnQiSI9V5QVl6NwPvgM15NXn%2FAtWZyj3W0HjEXitOc%2FdIdbetPdFTZ%2BP6t%2BX7xU0%2Fk6GJtOe1%2FB3arN0%2Fpmz1J4UZc%2BD6ExwjD7vioeGd5HvhvU%2BR%2BDZcGZ6YBPNfAi0G97iBPwFXqph2cW8%2BD7kjMfwtinHb6kLb6Wygk3cZytSEoptGrlScdHtLPeri1JKueACMZfU1ViJG1Sq5E43dIt7SZZFl1zuRhb%2FGOs44xFVDbrJzB5tYs35OmaXTrEmkv0DajnMWQB42mNgYNCCwk0MLxheMPrhgUuY2JiUmOqY2pjWMD1hdmPOY%2B5hPsLCwWLEksSyiOUOawzrLrYiti%2FsCuxJ7Kc45DiSOPZxmnG2cG7jvMelweXDNYXrEbcBdxf3KR4OngheLd443g18fHwZfFv4NfiX8T8TEBIIEZggsEpQS7BMcJsQl5CFUI3QAWEp4RLhCyJaIldEbURXiJ4RYxEzE0sQ2yD2TzxIfJkEk4SeRJbENIkNEg8k%2FklqSGZITpE8InlL8p2UmVSG1A6pb9Jx0ltkjGSmyDySlZF1kc2RnSK7R%2FaZnJ5cmdwB%2BST5SwpuCvsUjRTLFHcoOShNU9qhzKespGyhXKV8SPmBCpOKgUqcyjSVR6omqgmqe9RE1OrUnqkHqO9R%2F6FholGgsUZzgeYZLTUtL60WbS7tKh0OnQydXTpvdGV0O3S%2F6Gnopekt0ruhz6fvpl%2Bnv0n%2Fh4GdQYvBJUMhwwTDdYYvjFSM4oxmGd0zVjK2M84w3mYiYZJgssLkkqmO6TzTF2Z2ZjVmd8ylzP3MJ5lfsRCwcLJoszhhyWXpZdlhecZKxirHapbVPesF1ndsJGwCbBbZ%2FLA1sn1jZ2XXY3fFXsM%2Bz36V%2FS8HD4cGh2OOTI51ThJOK5zeOUs4OzmXOS9wPuUi4JLgss7lm2uU6zY3NrcSty1u39zN3Mvct7l%2F8xDzMPLw88jyaPM44ynkaeEZ59niucqLyUvPKwgAn3OqOQAAAQAAARcApwARAAAAAAACAAAAAQABAAAAQAAuAAAAAHjarZK9TgJBEMf%2Fd6CRaAyRhMLqCgsbL4ciglTGRPEjSiSKlnLycXJ86CEniU%2FhM9jYWPgIFkYfwd6nsDD%2Bd1mBIIUx3mZnfzs3MzszuwDCeIYG8UUwQxmAFgxxPeeuyxrmcaNYxzTuFAewi0fFQSTxqXgM11pC8TgS2oPiCUS1d8Uh8ofiSczpYcVT5LjiCPlY8Qui%2BncOr7D02y6%2FBTCrP%2Fm%2Bb5bdTrPi2I26Z9qNGtbRQBMdXMJBGRW0YOCecxEWYoiTCvxrYBunqHPdoX2bLOyrMKlZg8thDETw5K7Itci1TXlGy0124QRZZLDFU%2FexhxztMozlosTpMH6ZPge0L%2BOKGnFKjJ4WRwppHPL0PP3SI2P9jLQwFOu3GRhDfkeyDo%2F%2FG7IHgzllZQxLdquvrdCyBVvat3seJlYo06gxapUxhU2JWnFygR03sSxnEkvcpf5Y5eibGq315TDp7fKWm8zbUVl71Aqq%2FZtNnlkWmLnQtno9ycvXYbA6W2pF3aKfCayyC0Ja7Fr%2FPW70%2FHO4YM0OKxFvzf0C1MyPjwAAeNpt1VWUU2cYRuHsgxenQt1d8%2F3JOUnqAyR1d%2FcCLQVKO22pu7tQd3d3d3d3d3cXmGzumrWy3pWLs%2FNdPDMpZaWu1783l1Lpf14MnfzO6FbqVupfGkD30iR60JNe9KYP09CXfvRnAAMZxGCGMG3pW6ZjemZgKDMyEzMzC7MyG7MzB3MyF3MzD%2FMyH%2FOzAAuyEAuzCIuyGIuzBGWCRIUqOQU16jRYkqVYmmVYluVYng6GMZwRNGmxAiuyEiuzCquyGquzBmuyFmuzDuuyHuuzARuyERuzCZuyGZuzBVuyFVuzDduyHdszklGMZgd2ZAw7MZZxjGdnJrALu9LJbuzOHkxkT%2FZib%2FZhX%2FZjfw7gQA7iYA7hUA7jcI7gSI7iaI7hWI7jeE7gRE7iZE5hEqdyGqdzBmdyFmdzDudyHudzARdyERdzCZdyGZdzBVdyFVdzDddyHddzAzdyEzdzC7dyG7dzB3dyF3dzD%2FdyH%2FfzAA%2FyEA%2FzCI%2FyGI%2FzBE%2FyFE%2FzDM%2FyHM%2FzAi%2FyEi%2FzCq%2FyGq%2FzBm%2FyFm%2FzDu%2FyHu%2FzAR%2FyER%2FzCZ%2FyGZ%2FzBV%2FyFV%2FzDd%2FyHd%2FzAz%2FyEz%2FzC7%2FyG7%2FzB3%2FyF3%2FzD%2F9mpYwsy7pl3bMeWc%2BsV9Y765NNk%2FXN%2BmX9swHZwGxQNjgb0nPkmInjR0V7Uq%2FOsaPL5Y7ylE3l8tQNN7kVt%2BrmbuHW3LrbcDvam1rtzVvdm50TxrU%2FDBvRtZUY1rV5a3jXFn550Wo%2FXDNWK3dFmh7X9LimxzU9qulRTY9qelTTo5rlKLt2wk7YiaprL%2ByFvbAX9pK9ZC%2FZS%2FaSvWQv2Uv2kr1kr2KvYq9ir2KvYq9ir2KvYq9ir2Kvaq9qr2qvaq9qr2qvaq9qr2qvai%2B3l9vL7eX2cnu5vdxebi%2B3l9sr7BV2CjuFncJOYaewU9gp7NTs1LyrZq9mr2avZq9mr2avZq9mr26vbq9ur26vbq9ur26vbq9ur26vYa9hr2GvYa9hr2GvYa%2FR7oXuQ%2Feh%2B2j%2FUU7e3C3cqc%2FV3fYdof%2FQf%2Bg%2F9B%2F6D%2F2H%2FkP%2Fof%2FQf%2Bg%2F9B%2F6D%2F2H%2FkP%2Fof%2FQf%2Bg%2F9B%2F6D%2F2H%2FkP%2Fof%2FQf%2Bg%2F9B%2F6D%2F2H%2FkP%2Fof%2FQf%2Bg%2F9B%2F6D92H7kP3ofvQfeg%2BdB%2B6D92H7kP3ofvQfRT29B%2F6D%2F2H%2FkP%2Fof%2FQf%2Bg%2F9B%2F6D%2F2H%2FkP%2Fof%2FQf%2Bg%2F9B%2F6D%2F2H%2FkP%2Fof%2FQf%2Bg%2F9B%2F6D%2F2H%2FkP%2Fof%2FQf%2Bg%2F9B%2F6j6nuG3Ya7U5q%2F0hN3nCTW3Grbu4Wrs%2FrP%2Bk%2F6T%2FpP%2Bk%2F6T%2FpP%2Bk%2B6T7pPek86TzpPOk86TzpOuk66TrpOuk66TrpOlWmPu%2F36zrpOuk66TrpOuk66TrpOvl%2FPek76TvpO%2Bk76TvpO%2Bk76TvpO%2Bk76TvpO7V9t%2BqtVs%2FOaOURU6bo6PgPt6rZbwAAAAABVFDDFwAA%29%20format%28%27woff%27%29%2Curl%28data%3Aapplication%2Ffont%2Dsfnt%3Bbase64%2CAAEAAAAPAIAAAwBwRkZUTW0ql9wAAAD8AAAAHEdERUYBRAAEAAABGAAAACBPUy8yZ7lriQAAATgAAABgY21hcNqt44EAAAGYAAAGcmN2dCAAKAL4AAAIDAAAAARnYXNw%2F%2F8AAwAACBAAAAAIZ2x5Zn1dwm8AAAgYAACUpGhlYWQFTS%2FYAACcvAAAADZoaGVhCkQEEQAAnPQAAAAkaG10eNLHIGAAAJ0YAAADdGxvY2Fv%2B5XOAACgjAAAAjBtYXhwAWoA2AAAorwAAAAgbmFtZbMsoJsAAKLcAAADonBvc3S6o%2BU1AACmgAAACtF3ZWJmwxhUUAAAsVQAAAAGAAAAAQAAAADMPaLPAAAAANB2gXUAAAAA0HZzlwABAAAADgAAABgAAAAAAAIAAQABARYAAQAEAAAAAgAAAAMEiwGQAAUABAMMAtAAAABaAwwC0AAAAaQAMgK4AAAAAAUAAAAAAAAAAAAAAAIAAAAAAAAAAAAAAFVLV04AQAAg%2F%2F8DwP8QAAAFFAB7AAAAAQAAAAAAAAAAAAAAIAABAAAABQAAAAMAAAAsAAAACgAAAdwAAQAAAAAEaAADAAEAAAAsAAMACgAAAdwABAGwAAAAaABAAAUAKAAgACsAoAClIAogLyBfIKwgvSISIxsl%2FCYBJvonCScP4APgCeAZ4CngOeBJ4FngYOBp4HngieCX4QnhGeEp4TnhRuFJ4VnhaeF54YnhleGZ4gbiCeIW4hniIeIn4jniSeJZ4mD4%2F%2F%2F%2FAAAAIAAqAKAApSAAIC8gXyCsIL0iEiMbJfwmASb6JwknD%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EyFgcFExYGJyUFBiY3EyUmNjMBl4MHFQeBAaUVBhH%2BqoIHDxH%2Bqf6qEQ8Hgv6lEQYUAyABYRMT%2Fp8RDPn%2BbxQLDPb3DAsUAZD7DBEAAv%2FTAF4EewSUABgAIgAAARM2MhcTITIWBwUTFgYnJQUGJjcTJSY2MwUjFwc3Fyc3IycBl4MHFQeBAaUVBhH%2BqoIHDxH%2Bqf6qEQ8Hgv6lEQYUAfPwxUrBw0rA6k4DIAFhExP%2BnxEM%2Bf5vFAsM9vcMCxQBkPsMEWSO4ouM5YzTAAABAAAAAASwBLAAJgAAATIWHQEUBiMVFBYXBR4BHQEUBiMhIiY9ATQ2NyU%2BAT0BIiY9ATQ2Alh8sD4mDAkBZgkMDwr7ggoPDAkBZgkMJj6wBLCwfPouaEsKFwbmBRcKXQoPDwpdChcF5gYXCktoLvp8sAAAAA0AAAAABLAETAAPABMAIwAnACsALwAzADcARwBLAE8AUwBXAAATITIWFREUBiMhIiY1ETQ2FxUzNSkBIgYVERQWMyEyNjURNCYzFTM1BRUzNSEVMzUFFTM1IRUzNQchIgYVERQWMyEyNjURNCYFFTM1IRUzNQUVMzUhFTM1GQR%2BCg8PCvuCCg8PVWQCo%2F3aCg8PCgImCg8Pc2T8GGQDIGT8GGQDIGTh%2FdoKDw8KAiYKDw%2F872QDIGT8GGQDIGQETA8K%2B%2BYKDw8KBBoKD2RkZA8K%2FqIKDw8KAV4KD2RkyGRkZGTIZGRkZGQPCv6iCg8PCgFeCg9kZGRkZMhkZGRkAAAEAAAAAARMBEwADwAfAC8APwAAEyEyFhURFAYjISImNRE0NikBMhYVERQGIyEiJjURNDYBITIWFREUBiMhIiY1ETQ2KQEyFhURFAYjISImNRE0NjIBkBUdHRX%2BcBUdHQJtAZAVHR0V%2FnAVHR39vQGQFR0dFf5wFR0dAm0BkBUdHRX%2BcBUdHQRMHRX%2BcBUdHRUBkBUdHRX%2BcBUdHRUBkBUd%2FagdFf5wFR0dFQGQFR0dFf5wFR0dFQGQFR0AAAkAAAAABEwETAAPAB8ALwA%2FAE8AXwBvAH8AjwAAEzMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYhMzIWHQEUBisBIiY9ATQ2ATMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYhMzIWHQEUBisBIiY9ATQ2ATMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYhMzIWHQEUBisBIiY9ATQ2MsgVHR0VyBUdHQGlyBUdHRXIFR0dAaXIFR0dFcgVHR389cgVHR0VyBUdHQGlyBUdHRXIFR0dAaXIFR0dFcgVHR389cgVHR0VyBUdHQGlyBUdHRXIFR0dAaXIFR0dFcgVHR0ETB0VyBUdHRXIFR0dFcgVHR0VyBUdHRXIFR0dFcgVHf5wHRXIFR0dFcgVHR0VyBUdHRXIFR0dFcgVHR0VyBUd%2FnAdFcgVHR0VyBUdHRXIFR0dFcgVHR0VyBUdHRXIFR0ABgAAAAAEsARMAA8AHwAvAD8ATwBfAAATMzIWHQEUBisBIiY9ATQ2KQEyFh0BFAYjISImPQE0NgEzMhYdARQGKwEiJj0BNDYpATIWHQEUBiMhIiY9ATQ2ATMyFh0BFAYrASImPQE0NikBMhYdARQGIyEiJj0BNDYyyBUdHRXIFR0dAaUCvBUdHRX9RBUdHf6FyBUdHRXIFR0dAaUCvBUdHRX9RBUdHf6FyBUdHRXIFR0dAaUCvBUdHRX9RBUdHQRMHRXIFR0dFcgVHR0VyBUdHRXIFR3%2BcB0VyBUdHRXIFR0dFcgVHR0VyBUd%2FnAdFcgVHR0VyBUdHRXIFR0dFcgVHQAAAAABACYALAToBCAAFwAACQE2Mh8BFhQHAQYiJwEmND8BNjIfARYyAdECOwgUB7EICPzxBxUH%2FoAICLEHFAirBxYB3QI7CAixBxQI%2FPAICAGACBQHsQgIqwcAAQBuAG4EQgRCACMAAAEXFhQHCQEWFA8BBiInCQEGIi8BJjQ3CQEmND8BNjIXCQE2MgOIsggI%2FvUBCwgIsggVB%2F70%2FvQHFQiyCAgBC%2F71CAiyCBUHAQwBDAcVBDuzCBUH%2FvT%2B9AcVCLIICAEL%2FvUICLIIFQcBDAEMBxUIsggI%2FvUBDAcAAwAX%2F%2BsExQSZABkAJQBJAAAAMh4CFRQHARYUDwEGIicBBiMiLgI0PgEEIg4BFB4BMj4BNCYFMzIWHQEzMhYdARQGKwEVFAYrASImPQEjIiY9ATQ2OwE1NDYBmcSzgk1OASwICG0HFQj%2B1HeOYrSBTU2BAW%2BzmFhYmLOZWFj%2BvJYKD0sKDw8KSw8KlgoPSwoPDwpLDwSZTYKzYo15%2FtUIFQhsCAgBK01NgbTEs4JNWJmzmFhYmLOZIw8KSw8KlgoPSwoPDwpLDwqWCg9LCg8AAAMAF%2F%2FrBMUEmQAZACUANQAAADIeAhUUBwEWFA8BBiInAQYjIi4CND4BBCIOARQeATI%2BATQmBSEyFh0BFAYjISImPQE0NgGZxLOCTU4BLAgIbQcVCP7Ud45itIFNTYEBb7OYWFiYs5lYWP5YAV4KDw8K%2FqIKDw8EmU2Cs2KNef7VCBUIbAgIAStNTYG0xLOCTViZs5hYWJizmYcPCpYKDw8KlgoPAAAAAAIAFwAXBJkEsAAPAC0AAAEzMhYVERQGKwEiJjURNDYFNRYSFRQOAiIuAjU0EjcVDgEVFB4BMj4BNTQmAiZkFR0dFWQVHR0BD6fSW5vW6tabW9KnZ3xyxejFcnwEsB0V%2FnAVHR0VAZAVHeGmPv7ZuHXWm1tbm9Z1uAEnPqY3yHh0xXJyxXR4yAAEAGQAAASwBLAADwAfAC8APwAAATMyFhURFAYrASImNRE0NgEzMhYVERQGKwEiJjURNDYBMzIWFREUBisBIiY1ETQ2BTMyFh0BFAYrASImPQE0NgQBlgoPDwqWCg8P%2Ft6WCg8PCpYKDw%2F%2B3pYKDw8KlgoPD%2F7elgoPDwqWCg8PBLAPCvuCCg8PCgR%2BCg%2F%2BcA8K%2FRIKDw8KAu4KD%2F7UDwr%2BPgoPDwoBwgoPyA8K%2BgoPDwr6Cg8AAAAAAgAaABsElgSWAEcATwAAATIfAhYfATcWFwcXFh8CFhUUDwIGDwEXBgcnBwYPAgYjIi8CJi8BByYnNycmLwImNTQ%2FAjY%2FASc2Nxc3Nj8CNhIiBhQWMjY0AlghKSYFMS0Fhj0rUAMZDgGYBQWYAQ8YA1AwOIYFLDIFJisfISkmBTEtBYY8LFADGQ0ClwYGlwINGQNQLzqFBS0xBSYreLJ%2BfrJ%2BBJYFmAEOGQJQMDmGBSwxBiYrHiIoJgYxLAWGPSxRAxkOApcFBZcCDhkDUTA5hgUtMAYmKiAhKCYGMC0Fhj0sUAIZDgGYBf6ZfrF%2BfrEABwBkAAAEsAUUABMAFwAhACUAKQAtADEAAAEhMhYdASEyFh0BITU0NjMhNTQ2FxUhNQERFAYjISImNREXETMRMxEzETMRMxEzETMRAfQBLCk7ARMKD%2Fu0DwoBEzspASwBLDsp%2FUQpO2RkZGRkZGRkBRQ7KWQPCktLCg9kKTtkZGT%2B1PzgKTs7KQMgZP1EArz9RAK8%2FUQCvP1EArwAAQAMAAAFCATRAB8AABMBNjIXARYGKwERFAYrASImNREhERQGKwEiJjURIyImEgJsCBUHAmAIBQqvDwr6Cg%2F%2B1A8K%2BgoPrwoFAmoCYAcH%2FaAICv3BCg8PCgF3%2FokKDw8KAj8KAAIAZAAAA%2BgEsAARABcAAAERFBYzIREUBiMhIiY1ETQ2MwEjIiY9AQJYOykBLB0V%2FOAVHR0VA1L6FR0EsP5wKTv9dhUdHRUETBUd%2FnAdFfoAAwAXABcEmQSZAA8AGwAwAAAAMh4CFA4CIi4CND4BBCIOARQeATI%2BATQmBTMyFhURMzIWHQEUBisBIiY1ETQ2AePq1ptbW5vW6tabW1ubAb%2FoxXJyxejFcnL%2BfDIKD68KDw8K%2BgoPDwSZW5vW6tabW1ub1urWmztyxejFcnLF6MUNDwr%2B7Q8KMgoPDwoBXgoPAAAAAAL%2FnAAABRQEsAALAA8AACkBAyMDIQEzAzMDMwEDMwMFFP3mKfIp%2FeYBr9EVohTQ%2Fp4b4BsBkP5wBLD%2B1AEs%2FnD%2B1AEsAAAAAAIAZAAABLAEsAAVAC8AAAEzMhYVETMyFgcBBiInASY2OwERNDYBMzIWFREUBiMhIiY1ETQ2OwEyFh0BITU0NgImyBUdvxQLDf65DSYN%2FrkNCxS%2FHQJUMgoPDwr75goPDwoyCg8DhA8EsB0V%2Fj4XEP5wEBABkBAXAcIVHfzgDwr%2BogoPDwoBXgoPDwqvrwoPAAMAFwAXBJkEmQAPABsAMQAAADIeAhQOAiIuAjQ%2BAQQiDgEUHgEyPgE0JgUzMhYVETMyFgcDBiInAyY2OwERNDYB4%2BrWm1tbm9bq1ptbW5sBv%2BjFcnLF6MVycv58lgoPiRUKDd8NJg3fDQoViQ8EmVub1urWm1tbm9bq1ps7csXoxXJyxejFDQ8K%2Fu0XEP7tEBABExAXARMKDwAAAAMAFwAXBJkEmQAPABsAMQAAADIeAhQOAiIuAjQ%2BAQQiDgEUHgEyPgE0JiUTFgYrAREUBisBIiY1ESMiJjcTNjIB4%2BrWm1tbm9bq1ptbW5sBv%2BjFcnLF6MVycv7n3w0KFYkPCpYKD4kVCg3fDSYEmVub1urWm1tbm9bq1ps7csXoxXJyxejFAf7tEBf%2B7QoPDwoBExcQARMQAAAAAAIAAAAABLAEsAAZADkAABMhMhYXExYVERQGBwYjISImJyY1EzQ3Ez4BBSEiBgcDBhY7ATIWHwEeATsBMjY%2FAT4BOwEyNicDLgHhAu4KEwO6BwgFDBn7tAweAgYBB7kDEwKX%2FdQKEgJXAgwKlgoTAiYCEwr6ChMCJgITCpYKDAJXAhIEsA4K%2FXQYGf5XDB4CBggEDRkBqRkYAowKDsgOC%2F4%2BCw4OCpgKDg4KmAoODgsBwgsOAAMAFwAXBJkEmQAPABsAJwAAADIeAhQOAiIuAjQ%2BAQQiDgEUHgEyPgE0JgUXFhQPAQYmNRE0NgHj6tabW1ub1urWm1tbmwG%2F6MVycsXoxXJy%2Fov9ERH9EBgYBJlbm9bq1ptbW5vW6tabO3LF6MVycsXoxV2%2BDCQMvgwLFQGQFQsAAQAXABcEmQSwACgAAAE3NhYVERQGIyEiJj8BJiMiDgEUHgEyPgE1MxQOAiIuAjQ%2BAjMyA7OHBwsPCv6WCwQHhW2BdMVycsXoxXKWW5vW6tabW1ub1nXABCSHBwQL%2FpYKDwsHhUxyxejFcnLFdHXWm1tbm9bq1ptbAAAAAAIAFwABBJkEsAAaADUAAAE3NhYVERQGIyEiJj8BJiMiDgEVIzQ%2BAjMyEzMUDgIjIicHBiY1ETQ2MyEyFg8BFjMyPgEDs4cHCw8L%2FpcLBAeGboF0xXKWW5vWdcDrllub1nXAnIYHCw8LAWgKBQiFboJ0xXIEJIcHBAv%2BlwsPCweGS3LFdHXWm1v9v3XWm1t2hggFCgFoCw8LB4VMcsUAAAAKAGQAAASwBLAADwAfAC8APwBPAF8AbwB%2FAI8AnwAAEyEyFhURFAYjISImNRE0NgUhIgYVERQWMyEyNjURNCYFMzIWHQEUBisBIiY9ATQ2MyEyFh0BFAYjISImPQE0NgczMhYdARQGKwEiJj0BNDYzITIWHQEUBiMhIiY9ATQ2BzMyFh0BFAYrASImPQE0NjMhMhYdARQGIyEiJj0BNDYHMzIWHQEUBisBIiY9ATQ2MyEyFh0BFAYjISImPQE0Nn0EGgoPDwr75goPDwPA%2FK4KDw8KA1IKDw%2F9CDIKDw8KMgoPD9IBwgoPDwr%2BPgoPD74yCg8PCjIKDw%2FSAcIKDw8K%2Fj4KDw%2B%2BMgoPDwoyCg8P0gHCCg8PCv4%2BCg8PvjIKDw8KMgoPD9IBwgoPDwr%2BPgoPDwSwDwr7ggoPDwoEfgoPyA8K%2FK4KDw8KA1IKD2QPCjIKDw8KMgoPDwoyCg8PCjIKD8gPCjIKDw8KMgoPDwoyCg8PCjIKD8gPCjIKDw8KMgoPDwoyCg8PCjIKD8gPCjIKDw8KMgoPDwoyCg8PCjIKDwAAAAACAAAAAARMBLAAGQAjAAABNTQmIyEiBh0BIyIGFREUFjMhMjY1ETQmIyE1NDY7ATIWHQEDhHVT%2FtRSdmQpOzspA4QpOzsp%2FageFMgUHgMgyFN1dlLIOyn9qCk7OykCWCk7lhUdHRWWAAIAZAAABEwETAAJADcAABMzMhYVESMRNDYFMhcWFREUBw4DIyIuAScuAiMiBwYjIicmNRE%2BATc2HgMXHgIzMjc2fTIKD2QPA8AEBRADIUNAMRwaPyonKSxHHlVLBwgGBQ4WeDsXKC4TOQQpLUUdZ1AHBEwPCvvNBDMKDzACBhH%2BWwYGO1AkDQ0ODg8PDzkFAwcPAbY3VwMCAwsGFAEODg5XCAAAAwAAAAAEsASXACEAMQBBAAAAMh4CFREUBisBIiY1ETQuASAOARURFAYrASImNRE0PgEDMzIWFREUBisBIiY1ETQ2ITMyFhURFAYrASImNRE0NgHk6N6jYw8KMgoPjeT%2B%2BuSNDwoyCg9joyqgCAwMCKAIDAwCYKAIDAwIoAgMDASXY6PedP7UCg8PCgEsf9FyctF%2F%2FtQKDw8KASx03qP9wAwI%2FjQIDAwIAcwIDAwI%2FjQIDAwIAcwIDAAAAAACAAAA0wRHA90AFQA5AAABJTYWFREUBiclJisBIiY1ETQ2OwEyBTc2Mh8BFhQPARcWFA8BBiIvAQcGIi8BJjQ%2FAScmND8BNjIXAUEBAgkMDAn%2B%2FhUZ%2BgoPDwr6GQJYeAcUByIHB3h4BwciBxQHeHgHFAciBwd3dwcHIgcUBwMurAYHCv0SCgcGrA4PCgFeCg%2BEeAcHIgcUB3h4BxQHIgcHd3cHByIHFAd4eAcUByIICAAAAAACAAAA0wNyA90AFQAvAAABJTYWFREUBiclJisBIiY1ETQ2OwEyJTMWFxYVFAcGDwEiLwEuATc2NTQnJjY%2FATYBQQECCQwMCf7%2BFRn6Cg8PCvoZAdIECgZgWgYLAwkHHQcDBkhOBgMIHQcDLqwGBwr9EgoHBqwODwoBXgoPZAEJgaGafwkBAQYXBxMIZ36EaggUBxYFAAAAAAMAAADEBGID7AAbADEASwAAATMWFxYVFAYHBgcjIi8BLgE3NjU0JicmNj8BNgUlNhYVERQGJyUmKwEiJjURNDY7ATIlMxYXFhUUBwYPASIvAS4BNzY1NCcmNj8BNgPHAwsGh0RABwoDCQcqCAIGbzs3BgIJKgf9ggECCQwMCf7%2BFRn6Cg8PCvoZAdIECgZgWgYLAwkHHQcDBkhOBgMIHQcD7AEJs9lpy1QJAQYiBhQIlrJarEcJFAYhBb6sBgcK%2FRIKBwasDg8KAV4KD2QBCYGhmn8JAQEGFwcTCGd%2BhGoIFQYWBQAAAAANAAAAAASwBLAACQAVABkAHQAhACUALQA7AD8AQwBHAEsATwAAATMVIxUhFSMRIQEjFTMVIREjESM1IQURIREhESERBSM1MwUjNTMBMxEhETM1MwEzFSMVIzUjNTM1IzUhBREhEQcjNTMFIzUzASM1MwUhNSEB9GRk%2FnBkAfQCvMjI%2FtTIZAJY%2B7QBLAGQASz84GRkArxkZP1EyP4MyGQB9MhkyGRkyAEs%2FUQBLGRkZAOEZGT%2BDGRkAfT%2B1AEsA4RkZGQCWP4MZMgBLAEsyGT%2B1AEs%2FtQBLMhkZGT%2BDP4MAfRk%2FtRkZGRkyGTI%2FtQBLMhkZGT%2B1GRkZAAAAAAJAAAAAASwBLAAAwAHAAsADwATABcAGwAfACMAADcjETMTIxEzASMRMxMjETMBIxEzASE1IRcjNTMXIzUzBSM1M2RkZMhkZAGQyMjIZGQBLMjI%2FOD%2B1AEsyGRkyGRkASzIyMgD6PwYA%2Bj8GAPo%2FBgD6PwYA%2Bj7UGRkW1tbW1sAAAIAAAAKBKYEsAANABUAAAkBFhQHAQYiJwETNDYzBCYiBhQWMjYB9AKqCAj%2BMAgUCP1WAQ8KAUM7Uzs7UzsEsP1WCBQI%2FjAICAKqAdsKD807O1Q7OwAAAAADAAAACgXSBLAADQAZACEAAAkBFhQHAQYiJwETNDYzIQEWFAcBBiIvAQkBBCYiBhQWMjYB9AKqCAj%2BMAgUCP1WAQ8KAwYCqggI%2FjAIFAg4Aaj9RP7TO1M7O1M7BLD9VggUCP4wCAgCqgHbCg%2F9VggUCP4wCAg4AaoCvM07O1Q7OwAAAAABAGQAAASwBLAAJgAAASEyFREUDwEGJjURNCYjISIPAQYWMyEyFhURFAYjISImNRE0PwE2ASwDOUsSQAgKDwr9RBkSQAgFCgK8Cg8PCvyuCg8SixIEsEv8fBkSQAgFCgO2Cg8SQAgKDwr8SgoPDwoDzxkSixIAAAABAMj%2F%2FwRMBLAACgAAEyEyFhURCQERNDb6AyAVHf4%2B%2Fj4dBLAdFfuCAbz%2BQwR%2FFR0AAAAAAwAAAAAEsASwABUARQBVAAABISIGBwMGHwEeATMhMjY%2FATYnAy4BASMiBg8BDgEjISImLwEuASsBIgYVERQWOwEyNj0BNDYzITIWHQEUFjsBMjY1ETQmASEiBg8BBhYzITI2LwEuAQM2%2FkQLEAFOBw45BhcKAcIKFwY%2BDgdTARABVpYKFgROBBYK%2FdoKFgROBBYKlgoPDwqWCg8PCgLuCg8PCpYKDw%2F%2Bsf4MChMCJgILCgJYCgsCJgITBLAPCv7TGBVsCQwMCWwVGAEtCg%2F%2BcA0JnAkNDQmcCQ0PCv12Cg8PCpYKDw8KlgoPDwoCigoP%2FagOCpgKDg4KmAoOAAAAAAQAAABkBLAETAAdACEAKQAxAAABMzIeAh8BMzIWFREUBiMhIiY1ETQ2OwE%2BBAEVMzUEIgYUFjI2NCQyFhQGIiY0AfTIOF00JAcGlik7Oyn8GCk7OymWAgknM10ByGT%2Bz76Hh76H%2Fu9WPDxWPARMKTs7FRQ7Kf2oKTs7KQJYKTsIG0U1K%2F7UZGRGh76Hh74IPFY8PFYAAAAAAgA1AAAEsASvACAAIwAACQEWFx4BHwEVITUyNi8BIQYHBh4CMxUhNTY3PgE%2FAQEDIQMCqQGBFCgSJQkK%2Fl81LBFS%2Fnk6IgsJKjIe%2FpM4HAwaBwcBj6wBVKIEr%2FwaMioTFQECQkJXLd6RWSIuHAxCQhgcDCUNDQPu%2FVoByQAAAAADAGQAAAPwBLAAJwAyADsAAAEeBhUUDgMjITU%2BATURNC4EJzUFMh4CFRQOAgclMzI2NTQuAisBETMyNjU0JisBAvEFEzUwOyodN1htbDD%2BDCk7AQYLFyEaAdc5dWM%2BHy0tEP6Pi05pESpTPnbYUFJ9Xp8CgQEHGB0zOlIuQ3VONxpZBzMoAzsYFBwLEAkHRwEpSXNDM1s6KwkxYUopOzQb%2FK5lUFqBAAABAMgAAANvBLAAGQAAARcOAQcDBhYXFSE1NjcTNjQuBCcmJzUDbQJTQgeECSxK%2Fgy6Dq0DAw8MHxUXDQYEsDkTNSj8uTEoBmFhEFIDQBEaExAJCwYHAwI5AAAAAAL%2FtQAABRQEsAAlAC8AAAEjNC4FKwERFBYfARUhNTI%2BAzURIyIOBRUjESEFIxEzByczESM3BRQyCAsZEyYYGcgyGRn%2BcAQOIhoWyBkYJhMZCwgyA%2Bj7m0tLfX1LS30DhBUgFQ4IAwH8rhYZAQJkZAEFCRUOA1IBAwgOFSAVASzI%2FOCnpwMgpwACACH%2FtQSPBLAAJQAvAAABIzQuBSsBERQWHwEVITUyPgM1ESMiDgUVIxEhEwc1IRUnNxUhNQRMMggLGRMmGBnIMhkZ%2FnAEDiIaFsgZGCYTGQsIMgPoQ6f84KenAyADhBUgFQ4IAwH9dhYZAQJkZAEFCRUOAooBAwgOFSAVASz7gn1LS319S0sABAAAAAAEsARMAA8AHwAvAD8AABMhMhYdARQGIyEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2EyEyFh0BFAYjISImPQE0NhMhMhYdARQGIyEiJj0BNDYyAlgVHR0V%2FagVHR0VA%2BgVHR0V%2FBgVHR0VAyAVHR0V%2FOAVHR0VBEwVHR0V%2B7QVHR0ETB0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR0ABAAAAAAEsARMAA8AHwAvAD8AABMhMhYdARQGIyEiJj0BNDYDITIWHQEUBiMhIiY9ATQ2EyEyFh0BFAYjISImPQE0NgMhMhYdARQGIyEiJj0BNDb6ArwVHR0V%2FUQVHR2zBEwVHR0V%2B7QVHR3dArwVHR0V%2FUQVHR2zBEwVHR0V%2B7QVHR0ETB0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR0ABAAAAAAEsARMAA8AHwAvAD8AAAE1NDYzITIWHQEUBiMhIiYBNTQ2MyEyFh0BFAYjISImEzU0NjMhMhYdARQGIyEiJgE1NDYzITIWHQEUBiMhIiYB9B0VAlgVHR0V%2FagVHf5wHRUD6BUdHRX8GBUdyB0VAyAVHR0V%2FOAVHf7UHRUETBUdHRX7tBUdA7ZkFR0dFWQVHR3%2B6WQVHR0VZBUdHf7pZBUdHRVkFR0d%2FulkFR0dFWQVHR0AAAQAAAAABLAETAAPAB8ALwA%2FAAATITIWHQEUBiMhIiY9ATQ2EyEyFh0BFAYjISImPQE0NhMhMhYdARQGIyEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2MgRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dBEwdFWQVHR0VZBUd%2FtQdFWQVHR0VZBUd%2FtQdFWQVHR0VZBUd%2FtQdFWQVHR0VZBUdAAgAAAAABLAETAAPAB8ALwA%2FAE8AXwBvAH8AABMzMhYdARQGKwEiJj0BNDYpATIWHQEUBiMhIiY9ATQ2ATMyFh0BFAYrASImPQE0NikBMhYdARQGIyEiJj0BNDYBMzIWHQEUBisBIiY9ATQ2KQEyFh0BFAYjISImPQE0NgEzMhYdARQGKwEiJj0BNDYpATIWHQEUBiMhIiY9ATQ2MmQVHR0VZBUdHQFBAyAVHR0V%2FOAVHR3%2B6WQVHR0VZBUdHQFBAyAVHR0V%2FOAVHR3%2B6WQVHR0VZBUdHQFBAyAVHR0V%2FOAVHR3%2B6WQVHR0VZBUdHQFBAyAVHR0V%2FOAVHR0ETB0VZBUdHRVkFR0dFWQVHR0VZBUd%2FtQdFWQVHR0VZBUdHRVkFR0dFWQVHf7UHRVkFR0dFWQVHR0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR0dFWQVHR0VZBUdAAAG%2F5wAAASwBEwAAwATACMAKgA6AEoAACEjETsCMhYdARQGKwEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2BQc1IzUzNQUhMhYdARQGIyEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2AZBkZJZkFR0dFWQVHR0VAfQVHR0V%2FgwVHR3%2B%2BqfIyAHCASwVHR0V%2FtQVHR0VAlgVHR0V%2FagVHR0ETB0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR36fUtkS68dFWQVHR0VZBUd%2FtQdFWQVHR0VZBUdAAAABgAAAAAFFARMAA8AEwAjACoAOgBKAAATMzIWHQEUBisBIiY9ATQ2ASMRMwEhMhYdARQGIyEiJj0BNDYFMxUjFSc3BSEyFh0BFAYjISImPQE0NhMhMhYdARQGIyEiJj0BNDYyZBUdHRVkFR0dA2dkZPyuAfQVHR0V%2FgwVHR0EL8jIp6f75gEsFR0dFf7UFR0dFQJYFR0dFf2oFR0dBEwdFWQVHR0VZBUd%2B7QETP7UHRVkFR0dFWQVHchkS319rx0VZBUdHRVkFR3%2B1B0VZBUdHRVkFR0AAAAAAgAAAMgEsAPoAA8AEgAAEyEyFhURFAYjISImNRE0NgkCSwLuHywsH%2F0SHywsBIT%2B1AEsA%2BgsH%2F12HywsHwKKHyz9RAEsASwAAwAAAAAEsARMAA8AFwAfAAATITIWFREUBiMhIiY1ETQ2FxE3BScBExEEMhYUBiImNCwEWBIaGhL7qBIaGkr3ASpKASXs%2FNJwTk5wTgRMGhL8DBIaGhID9BIaZP0ftoOcAT7%2B4AH0dE5vT09vAAAAAAIA2wAFBDYEkQAWAB4AAAEyHgEVFAcOAQ8BLgQnJjU0PgIWIgYUFjI2NAKIdcZzRkWyNjYJIV5YbSk8RHOft7eCgreCBJF4ynVzj23pPz4IIWZomEiEdVijeUjDgriBgbgAAAACABcAFwSZBJkADwAXAAAAMh4CFA4CIi4CND4BAREiDgEUHgEB4%2BrWm1tbm9bq1ptbW5sBS3TFcnLFBJlbm9bq1ptbW5vW6tab%2FG8DVnLF6MVyAAACAHUAAwPfBQ8AGgA1AAABHgYVFA4DBy4DNTQ%2BBQMOAhceBBcWNj8BNiYnLgInJjc2IyYCKhVJT1dOPiUzVnB9P1SbfEokP0xXUEm8FykoAwEbITEcExUWAgYCCQkFEikMGiACCAgFD0iPdXdzdYdFR4BeRiYEBTpjl1lFh3ZzeHaQ%2Ff4hS4I6JUEnIw4IBwwQIgoYBwQQQSlZtgsBAAAAAwAAAAAEywRsAAwAKgAvAAABNz4CHgEXHgEPAiUhMhcHISIGFREUFjMhMjY9ATcRFAYjISImNRE0NgkBBzcBA%2BhsAgYUFR0OFgoFBmz9BQGQMje7%2FpApOzspAfQpO8i7o%2F5wpbm5Azj%2BlqE3AWMD9XMBAgIEDw4WKgsKc8gNuzsp%2FgwpOzsptsj%2BtKW5uaUBkKW5%2Ftf%2BljKqAWMAAgAAAAAEkwRMABsANgAAASEGByMiBhURFBYzITI2NTcVFAYjISImNRE0NgUBFhQHAQYmJzUmDgMHPgY3NT4BAV4BaaQ0wyk7OykB9Ck7yLml%2FnClubkCfwFTCAj%2BrAcLARo5ZFRYGgouOUlARioTAQsETJI2Oyn%2BDCk7OymZZ6W5uaUBkKW5G%2F7TBxUH%2Fs4GBAnLAQINFjAhO2JBNB0UBwHSCgUAAAAAAgAAAAAEnQRMAB0ANQAAASEyFwchIgYVERQWMyEyNj0BNxUUBiMhIiY1ETQ2CQE2Mh8BFhQHAQYiLwEmND8BNjIfARYyAV4BXjxDsv6jKTs7KQH0KTvIuaX%2BcKW5uQHKAYsHFQdlBwf97QcVB%2FgHB2UHFQdvCBQETBexOyn%2BDCk7OylFyNulubmlAZCluf4zAYsHB2UHFQf97AcH%2BAcVB2UHB28HAAAAAQAKAAoEpgSmADsAAAkBNjIXARYGKwEVMzU0NhcBFhQHAQYmPQEjFTMyFgcBBiInASY2OwE1IxUUBicBJjQ3ATYWHQEzNSMiJgE%2BAQgIFAgBBAcFCqrICggBCAgI%2FvgICsiqCgUH%2FvwIFAj%2B%2BAgFCq%2FICgj%2B%2BAgIAQgICsivCgUDlgEICAj%2B%2BAgKyK0KBAf%2B%2FAcVB%2F73BwQKrcgKCP74CAgBCAgKyK0KBAcBCQcVBwEEBwQKrcgKAAEAyAAAA4QETAAZAAATMzIWFREBNhYVERQGJwERFAYrASImNRE0NvpkFR0B0A8VFQ%2F%2BMB0VZBUdHQRMHRX%2BSgHFDggV%2FBgVCA4Bxf5KFR0dFQPoFR0AAAABAAAAAASwBEwAIwAAEzMyFhURATYWFREBNhYVERQGJwERFAYnAREUBisBIiY1ETQ2MmQVHQHQDxUB0A8VFQ%2F%2BMBUP%2FjAdFWQVHR0ETB0V%2FkoBxQ4IFf5KAcUOCBX8GBUIDgHF%2FkoVCA4Bxf5KFR0dFQPoFR0AAAABAJ0AGQSwBDMAFQAAAREUBicBERQGJwEmNDcBNhYVEQE2FgSwFQ%2F%2BMBUP%2FhQPDwHsDxUB0A8VBBr8GBUIDgHF%2FkoVCA4B4A4qDgHgDggV%2FkoBxQ4IAAAAAQDIABYEMwQ2AAsAABMBFhQHAQYmNRE0NvMDLhIS%2FNISGRkEMv4OCx4L%2Fg4LDhUD6BUOAAIAyABkA4QD6AAPAB8AABMzMhYVERQGKwEiJjURNDYhMzIWFREUBisBIiY1ETQ2%2BsgVHR0VyBUdHQGlyBUdHRXIFR0dA%2BgdFfzgFR0dFQMgFR0dFfzgFR0dFQMgFR0AAAEAyABkBEwD6AAPAAABERQGIyEiJjURNDYzITIWBEwdFfzgFR0dFQMgFR0DtvzgFR0dFQMgFR0dAAAAAAEAAAAZBBMEMwAVAAABETQ2FwEWFAcBBiY1EQEGJjURNDYXAfQVDwHsDw%2F%2BFA8V%2FjAPFRUPAmQBthUIDv4gDioO%2FiAOCBUBtv47DggVA%2BgVCA4AAAH%2F%2FgACBLMETwAjAAABNzIWFRMUBiMHIiY1AwEGJjUDAQYmNQM0NhcBAzQ2FwEDNDYEGGQUHgUdFWQVHQL%2BMQ4VAv4yDxUFFQ8B0gIVDwHSAh0ETgEdFfwYFR0BHRUBtf46DwkVAbX%2BOQ4JFAPoFQkP%2Fj4BthQJDv49AbYVHQAAAQEsAAAD6ARMABkAAAEzMhYVERQGKwEiJjURAQYmNRE0NhcBETQ2A1JkFR0dFWQVHf4wDxUVDwHQHQRMHRX8GBUdHRUBtv47DggVA%2BgVCA7%2BOwG2FR0AAAIAZADIBLAESAALABsAAAkBFgYjISImNwE2MgEhMhYdARQGIyEiJj0BNDYCrgH1DwkW%2B%2B4WCQ8B9Q8q%2FfcD6BUdHRX8GBUdHQQ5%2FeQPFhYPAhwP%2FUgdFWQVHR0VZBUdAAEAiP%2F8A3UESgAFAAAJAgcJAQN1%2FqABYMX92AIoA4T%2Bn%2F6fxgIoAiYAAAAAAQE7%2F%2FwEKARKAAUAAAkBJwkBNwQo%2FdnGAWH%2Bn8YCI%2F3ZxgFhAWHGAAIAFwAXBJkEmQAPADMAAAAyHgIUDgIiLgI0PgEFIyIGHQEjIgYdARQWOwEVFBY7ATI2PQEzMjY9ATQmKwE1NCYB4%2BrWm1tbm9bq1ptbW5sBfWQVHZYVHR0Vlh0VZBUdlhUdHRWWHQSZW5vW6tabW1ub1urWm7odFZYdFWQVHZYVHR0Vlh0VZBUdlhUdAAAAAAIAFwAXBJkEmQAPAB8AAAAyHgIUDgIiLgI0PgEBISIGHQEUFjMhMjY9ATQmAePq1ptbW5vW6tabW1ubAkX%2BDBUdHRUB9BUdHQSZW5vW6tabW1ub1urWm%2F5%2BHRVkFR0dFWQVHQACABcAFwSZBJkADwAzAAAAMh4CFA4CIi4CND4BBCIPAScmIg8BBhQfAQcGFB8BFjI%2FARcWMj8BNjQvATc2NC8BAePq1ptbW5vW6tabW1ubAeUZCXh4CRkJjQkJeHgJCY0JGQl4eAkZCY0JCXh4CQmNBJlbm9bq1ptbW5vW6tabrQl4eAkJjQkZCXh4CRkJjQkJeHgJCY0JGQl4eAkZCY0AAgAXABcEmQSZAA8AJAAAADIeAhQOAiIuAjQ%2BAQEnJiIPAQYUHwEWMjcBNjQvASYiBwHj6tabW1ub1urWm1tbmwEVVAcVCIsHB%2FIHFQcBdwcHiwcVBwSZW5vW6tabW1ub1urWm%2F4xVQcHiwgUCPEICAF3BxUIiwcHAAAAAAMAFwAXBJkEmQAPADsASwAAADIeAhQOAiIuAjQ%2BAQUiDgMVFDsBFjc%2BATMyFhUUBgciDgUHBhY7ATI%2BAzU0LgMTIyIGHQEUFjsBMjY9ATQmAePq1ptbW5vW6tabW1ubAT8dPEIyIRSDHgUGHR8UFw4TARkOGhITDAIBDQ6tBx4oIxgiM0Q8OpYKDw8KlgoPDwSZW5vW6tabW1ub1urWm5ELHi9PMhkFEBQQFRIXFgcIBw4UHCoZCBEQKDhcNi9IKhsJ%2FeMPCpYKDw8KlgoPAAADABcAFwSZBJkADwAfAD4AAAAyHgIUDgIiLgI0PgEFIyIGHQEUFjsBMjY9ATQmAyMiBh0BFBY7ARUjIgYdARQWMyEyNj0BNCYrARE0JgHj6tabW1ub1urWm1tbmwGWlgoPDwqWCg8PCvoKDw8KS0sKDw8KAV4KDw8KSw8EmVub1urWm1tbm9bq1ptWDwqWCg8PCpYKD%2F7UDwoyCg%2FIDwoyCg8PCjIKDwETCg8AAgAAAAAEsASwAC8AXwAAATMyFh0BHgEXMzIWHQEUBisBDgEHFRQGKwEiJj0BLgEnIyImPQE0NjsBPgE3NTQ2ExUUBisBIiY9AQ4BBzMyFh0BFAYrAR4BFzU0NjsBMhYdAT4BNyMiJj0BNDY7AS4BAg2WCg9nlxvCCg8PCsIbl2cPCpYKD2eXG8IKDw8KwhuXZw%2B5DwqWCg9EZheoCg8PCqgXZkQPCpYKD0RmF6gKDw8KqBdmBLAPCsIbl2cPCpYKD2eXG8IKDw8KwhuXZw8KlgoPZ5cbwgoP%2Fs2oCg8PCqgXZkQPCpYKD0RmF6gKDw8KqBdmRA8KlgoPRGYAAwAXABcEmQSZAA8AGwA%2FAAAAMh4CFA4CIi4CND4BBCIOARQeATI%2BATQmBxcWFA8BFxYUDwEGIi8BBwYiLwEmND8BJyY0PwE2Mh8BNzYyAePq1ptbW5vW6tabW1ubAb%2FoxXJyxejFcnKaQAcHfHwHB0AHFQd8fAcVB0AHB3x8BwdABxUHfHwHFQSZW5vW6tabW1ub1urWmztyxejFcnLF6MVaQAcVB3x8BxUHQAcHfHwHB0AHFQd8fAcVB0AHB3x8BwAAAAMAFwAXBJkEmQAPABsAMAAAADIeAhQOAiIuAjQ%2BAQQiDgEUHgEyPgE0JgcXFhQHAQYiLwEmND8BNjIfATc2MgHj6tabW1ub1urWm1tbmwG%2F6MVycsXoxXJyg2oHB%2F7ACBQIyggIagcVB0%2FFBxUEmVub1urWm1tbm9bq1ps7csXoxXJyxejFfWoHFQf%2BvwcHywcVB2oICE%2FFBwAAAAMAFwAXBJkEmQAPABgAIQAAADIeAhQOAiIuAjQ%2BAQUiDgEVFBcBJhcBFjMyPgE1NAHj6tabW1ub1urWm1tbmwFLdMVyQQJLafX9uGhzdMVyBJlbm9bq1ptbW5vW6tabO3LFdHhpAktB0P24PnLFdHMAAAAAAQAXAFMEsAP5ABUAABMBNhYVESEyFh0BFAYjIREUBicBJjQnAgoQFwImFR0dFf3aFxD99hACRgGrDQoV%2Ft0dFcgVHf7dFQoNAasNJgAAAAABAAAAUwSZA%2FkAFQAACQEWFAcBBiY1ESEiJj0BNDYzIRE0NgJ%2FAgoQEP32EBf92hUdHRUCJhcD8f5VDSYN%2FlUNChUBIx0VyBUdASMVCgAAAAEAtwAABF0EmQAVAAAJARYGIyERFAYrASImNREhIiY3ATYyAqoBqw0KFf7dHRXIFR3%2B3RUKDQGrDSYEif32EBf92hUdHRUCJhcQAgoQAAAAAQC3ABcEXQSwABUAAAEzMhYVESEyFgcBBiInASY2MyERNDYCJsgVHQEjFQoN%2FlUNJg3%2BVQ0KFQEjHQSwHRX92hcQ%2FfYQEAIKEBcCJhUdAAABAAAAtwSZBF0AFwAACQEWFAcBBiY1EQ4DBz4ENxE0NgJ%2FAgoQEP32EBdesKWBJAUsW4fHfhcEVf5VDSYN%2FlUNChUBIwIkRHVNabGdcUYHAQYVCgACAAAAAASwBLAAFQArAAABITIWFREUBi8BBwYiLwEmND8BJyY2ASEiJjURNDYfATc2Mh8BFhQPARcWBgNSASwVHRUOXvkIFAhqBwf5Xg4I%2FiH%2B1BUdFQ5e%2BQgUCGoHB%2FleDggEsB0V%2FtQVCA5e%2BQcHaggUCPleDhX7UB0VASwVCA5e%2BQcHaggUCPleDhUAAAACAEkASQRnBGcAFQArAAABFxYUDwEXFgYjISImNRE0Nh8BNzYyASEyFhURFAYvAQcGIi8BJjQ%2FAScmNgP2agcH%2BV4OCBX%2B1BUdFQ5e%2BQgU%2FQwBLBUdFQ5e%2BQgUCGoHB%2FleDggEYGoIFAj5Xg4VHRUBLBUIDl75B%2F3xHRX%2B1BUIDl75BwdqCBQI%2BV4OFQAAAAADABcAFwSZBJkADwAfAC8AAAAyHgIUDgIiLgI0PgEFIyIGFxMeATsBMjY3EzYmAyMiBh0BFBY7ATI2PQE0JgHj6tabW1ub1urWm1tbmwGz0BQYBDoEIxQ2FCMEOgQYMZYKDw8KlgoPDwSZW5vW6tabW1ub1urWm7odFP7SFB0dFAEuFB3%2BDA8KlgoPDwqWCg8AAAAABQAAAAAEsASwAEkAVQBhAGgAbwAAATIWHwEWHwEWFxY3Nj8BNjc2MzIWHwEWHwIeATsBMhYdARQGKwEiBh0BIREjESE1NCYrASImPQE0NjsBMjY1ND8BNjc%2BBAUHBhY7ATI2LwEuAQUnJgYPAQYWOwEyNhMhIiY1ESkBERQGIyERAQQJFAUFFhbEFQ8dCAsmxBYXERUXMA0NDgQZCAEPCj0KDw8KMgoP%2FnDI%2FnAPCjIKDw8KPQsOCRkFDgIGFRYfAp2mBwQK2woKAzMDEP41sQgQAzMDCgrnCwMe%2FokKDwGQAlgPCv6JBLAEAgIKDXYNCxUJDRZ2DQoHIREQFRh7LAkLDwoyCg8PCq8BLP7UrwoPDwoyCg8GBQQwgBkUAwgWEQ55ogcKDgqVCgSqnQcECo8KDgr8cg8KAXf%2BiQoPAZAAAAAAAgAAAAwErwSmACsASQAAATYWFQYCDgQuAScmByYOAQ8BBiY1NDc%2BATc%2BAScuAT4BNz4GFyYGBw4BDwEOBAcOARY2Nz4CNz4DNz4BBI0IGgItQmxhi2KORDg9EQQRMxuZGhYqCFUYEyADCQIQOjEnUmFch3vAJQgdHyaiPT44XHRZUhcYDhItIRmKcVtGYWtbKRYEBKYDEwiy%2Ft3IlVgxEQgLCwwBAQIbG5kYEyJAJghKFRE8Hzdff4U%2FM0o1JSMbL0QJGCYvcSEhHjZST2c1ODwEJygeW0AxJUBff1UyFAABAF0AHgRyBM8ATwAAAQ4BHgQXLgc%2BATceAwYHDgQHBicmNzY3PgQuAScWDgMmJy4BJyY%2BBDcGHgM3PgEuAicmPgMCjScfCic4R0IgBBsKGAoQAwEJEg5gikggBhANPkpTPhZINx8SBgsNJysiCRZOQQoVNU1bYC9QZwICBAUWITsoCAYdJzIYHw8YIiYHDyJJYlkEz0OAZVxEOSQMBzgXOB42IzElKRIqg5Gnl0o3Z0c6IAYWCwYNAwQFIDhHXGF1OWiqb0sdBxUknF0XNTQ8PEUiNWNROBYJDS5AQVUhVZloUSkAAAAAA%2F%2FcAGoE1ARGABsAPwBRAAAAMh4FFA4FIi4FND4EBSYGFxYVFAYiJjU0NzYmBwYHDgEXHgQyPgM3NiYnJgUHDgEXFhcWNj8BNiYnJicuAQIGpJ17bk85HBw6T257naKde25POhwcOU9uewIPDwYIGbD4sBcIBw5GWg0ECxYyWl%2BDiINfWjIWCwQMWv3%2FIw8JCSU4EC0OIw4DDywtCyIERi1JXGJcSSpJXGJcSS0tSVxiXEkqSVxiXEncDwYTOT58sLB8OzcTBg9FcxAxEiRGXkQxMEVeRSQSMRF1HiQPLxJEMA0EDyIPJQ8sSRIEAAAABP%2FcAAAE1ASwABQAJwA7AEwAACEjNy4ENTQ%2BBTMyFzczEzceARUUDgMHNz4BNzYmJyYlBgcOARceBBc3LgE1NDc2JhcHDgEXFhcWNj8CJyYnLgECUJQfW6l2WSwcOU9ue51SPUEglCYvbIknUGqYUi5NdiYLBAw2%2FVFGWg0ECxIqSExoNSlrjxcIB3wjDwkJJTgQLQ4MFgMsLQsieBRhdHpiGxVJXGJcSS0Pef5StVXWNBpacm5jGq0xiD8SMRFGckVzEDESHjxRQTkNmhKnbjs3EwZwJA8vEkQwDQQPC1YELEkSBAAAAAP%2FngAABRIEqwALABgAKAAAJwE2FhcBFgYjISImJSE1NDY7ATIWHQEhAQczMhYPAQ4BKwEiJi8BJjZaAoIUOBQCghUbJfryJRsBCgFZDwqWCg8BWf5DaNAUGAQ6BCMUNhQjBDoEGGQEKh8FIfvgIEdEhEsKDw8KSwLT3x0U%2FBQdHRT8FB0AAAABAGQAFQSwBLAAKAAAADIWFREBHgEdARQGJyURFh0BFAYvAQcGJj0BNDcRBQYmPQE0NjcBETQCTHxYAWsPFhgR%2FplkGhPNzRMaZP6ZERgWDwFrBLBYPv6t%2FrsOMRQpFA0M%2Bf75XRRAFRAJgIAJEBVAFF0BB%2FkMDRQpFDEOAUUBUz4AAAARAAAAAARMBLAAHQAnACsALwAzADcAOwA%2FAEMARwBLAE8AUwBXAFsAXwBjAAABMzIWHQEzMhYdASE1NDY7ATU0NjsBMhYdASE1NDYBERQGIyEiJjURFxUzNTMVMzUzFTM1MxUzNTMVMzUFFTM1MxUzNTMVMzUzFTM1MxUzNQUVMzUzFTM1MxUzNTMVMzUzFTM1A1JkFR0yFR37tB0VMh0VZBUdAfQdAQ8dFfwYFR1kZGRkZGRkZGRk%2FHxkZGRkZGRkZGT8fGRkZGRkZGRkZASwHRUyHRWWlhUdMhUdHRUyMhUd%2FnD9EhUdHRUC7shkZGRkZGRkZGRkyGRkZGRkZGRkZGTIZGRkZGRkZGRkZAAAAAMAAAAZBXcElwAZACUANwAAARcWFA8BBiY9ASMBISImPQE0NjsBATM1NDYBBycjIiY9ATQ2MyEBFxYUDwEGJj0BIyc3FzM1NDYEb%2FkPD%2FkOFZ%2F9qP7dFR0dFdECWPEV%2FamNetEVHR0VASMDGvkPD%2FkOFfG1jXqfFQSN5g4qDuYOCBWW%2FagdFWQVHQJYlhUI%2FpiNeh0VZBUd%2Fk3mDioO5g4IFZa1jXqWFQgAAAABAAAAAASwBEwAEgAAEyEyFhURFAYjIQERIyImNRE0NmQD6Ck7Oyn9rP7QZCk7OwRMOyn9qCk7%2FtQBLDspAlgpOwAAAAMAZAAABEwEsAAJABMAPwAAEzMyFh0BITU0NiEzMhYdASE1NDYBERQOBSIuBTURIRUUFRwBHgYyPgYmNTQ9AZbIFR3%2B1B0C0cgVHf7UHQEPBhgoTGacwJxmTCgYBgEsAwcNFB8nNkI2Jx8TDwUFAQSwHRX6%2BhUdHRX6%2BhUd%2FnD%2B1ClJalZcPigoPlxWakkpASz6CRIVKyclIRsWEAgJEBccISUnKhURCPoAAAAB%2F%2F8A1ARMA8IABQAAAQcJAScBBEzG%2Fp%2F%2Bn8UCJwGbxwFh%2Fp%2FHAicAAQAAAO4ETQPcAAUAAAkCNwkBBE392v3ZxgFhAWEDFf3ZAifH%2Fp8BYQAAAAAC%2F1EAZAVfA%2BgAFAApAAABITIWFREzMhYPAQYiLwEmNjsBESElFxYGKwERIRchIiY1ESMiJj8BNjIBlALqFR2WFQgO5g4qDuYOCBWW%2FoP%2BHOYOCBWWAYHX%2FRIVHZYVCA7mDioD6B0V%2FdkVDvkPD%2FkOFQGRuPkOFf5wyB0VAiYVDvkPAAABAAYAAASeBLAAMAAAEzMyFh8BITIWBwMOASMhFyEyFhQGKwEVFAYiJj0BIRUUBiImPQEjIiYvAQMjIiY0NjheERwEJgOAGB4FZAUsIf2HMAIXFR0dFTIdKh3%2B1B0qHR8SHQYFyTYUHh4EsBYQoiUY%2FiUVK8gdKh0yFR0dFTIyFR0dFTIUCQoDwR0qHQAAAAACAAAAAASwBEwACwAPAAABFSE1MzQ2MyEyFhUFIREhBLD7UMg7KQEsKTv9RASw%2B1AD6GRkKTs7Kcj84AACAAAAAAXcBEwADAAQAAATAxEzNDYzITIWFSEVBQEhAcjIyDspASwqOgH0ASz%2B1PtQASwDIP5wAlgpOzspyGT9RAK8AAEBRQAAA2sErwAbAAABFxYGKwERMzIWDwEGIi8BJjY7AREjIiY%2FATYyAnvmDggVlpYVCA7mDioO5g4IFZaWFQgO5g4qBKD5DhX9pxUO%2BQ8P%2BQ4VAlkVDvkPAAAAAQABAUQErwNrABsAAAEXFhQPAQYmPQEhFRQGLwEmND8BNhYdASE1NDYDqPkODvkPFf2oFQ%2F5Dg75DxUCWBUDYOUPKQ%2FlDwkUl5cUCQ%2FlDykP5Q8JFZWVFQkAAAAEAAAAAASwBLAACQAZAB0AIQAAAQMuASMhIgYHAwUhIgYdARQWMyEyNj0BNCYFNTMVMzUzFQSRrAUkFP1gFCQFrAQt%2FBgpOzspA%2BgpOzv%2Bq2RkZAGQAtwXLSgV%2FR1kOylkKTs7KWQpO8hkZGRkAAAAA%2F%2BcAGQEsARMAAsAIwAxAAAAMhYVERQGIiY1ETQDJSMTFgYjIisBIiYnAj0BNDU0PgE7ASUBFSIuAz0BND4CNwRpKh0dKh1k%2FV0mLwMRFQUCVBQdBDcCCwzIAqP8GAQOIhoWFR0dCwRMHRX8rhUdHRUDUhX8mcj%2B7BAIHBUBUQ76AgQQDw36%2FtT6AQsTKRwyGigUDAEAAAACAEoAAARmBLAALAA1AAABMzIWDwEeARcTFzMyFhQGBw4EIyIuBC8BLgE0NjsBNxM%2BATcnJjYDFjMyNw4BIiYCKV4UEgYSU3oPP3YRExwaEggeZGqfTzl0XFU%2BLwwLEhocExF2Pw96UxIGEyQyNDUxDDdGOASwFRMlE39N%2FrmtHSkoBwQLHBYSCg4REg4FBAgoKR2tAUdNfhQgExr7vgYGMT09AAEAFAAUBJwEnAAXAAABNwcXBxcHFycHJwcnBzcnNyc3Jxc3FzcDIOBO6rS06k7gLZubLeBO6rS06k7gLZubA7JO4C2bmy3gTuq0tOpO4C2bmy3gTuq0tAADAAAAZASwBLAAIQAtAD0AAAEzMhYdAQchMhYdARQHAw4BKwEiJi8BIyImNRE0PwI%2BARcPAREzFzMTNSE3NQEzMhYVERQGKwEiJjURNDYCijIoPBwBSCg8He4QLBf6B0YfHz0tNxSRYA0xG2SWZIjW%2Bv4%2BMv12ZBUdHRVkFR0dBLBRLJZ9USxkLR3%2BqBghMhkZJCcBkCQbxMYcKGTU1f6JZAF3feGv%2FtQdFf4MFR0dFQH0FR0AAAAAAwAAAAAEsARMACAAMAA8AAABMzIWFxMWHQEUBiMhFh0BFAYrASImLwImNRE0NjsBNgUzMhYVERQGKwEiJjURNDYhByMRHwEzNSchNQMCWPoXLBDuHTwo%2FrgcPCgyGzENYJEUNy09fP3pZBUdHRVkFR0dAl%2BIZJZkMjIBwvoETCEY%2FqgdLWQsUXYHlixRKBzGxBskAZAnJGRkHRX%2BDBUdHRUB9BUdZP6J1dSv4X0BdwADAAAAZAUOBE8AGwA3AEcAAAElNh8BHgEPASEyFhQGKwEDDgEjISImNRE0NjcXERchEz4BOwEyNiYjISoDLgQnJj8BJwUzMhYVERQGKwEiJjURNDYBZAFrHxZuDQEMVAEuVGxuVGqDBhsP%2FqoHphwOOmQBJYMGGw%2FLFRMSFv44AgoCCQMHAwUDAQwRklb9T2QVHR0VZBUdHQNp5hAWcA0mD3lMkE7%2BrRUoog0CDRElCkj%2BCVkBUxUoMjIBAgIDBQIZFrdT5B0V%2FgwVHR0VAfQVHQAAAAP%2FnABkBLAETwAdADYARgAAAQUeBBURFAYjISImJwMjIiY0NjMhJyY2PwE2BxcWBw4FKgIjIRUzMhYXEyE3ESUFMzIWFREUBisBIiY1ETQ2AdsBbgIIFBANrAf%2Bqg8bBoNqVW1sVAEuVQsBDW4WSpIRDAIDBQMHAwkDCgH%2BJd0PHAaCASZq%2FqoCUGQVHR0VZBUdHQRP5gEFEBEXC%2F3zDaIoFQFTTpBMeQ8mDXAWrrcWGQIFAwICAWQoFf6tWQH37OQdFf4MFR0dFQH0FR0AAAADAGEAAARMBQ4AGwA3AEcAAAAyFh0BBR4BFREUBiMhIiYvAQMmPwE%2BAR8BETQXNTQmBhURHAMOBAcGLwEHEyE3ESUuAQMhMhYdARQGIyEiJj0BNDYB3pBOAVMVKKIN%2FfMRJQoJ5hAWcA0mD3nGMjIBAgIDBQIZFrdT7AH3Wf6tFSiWAfQVHR0V%2FgwVHR0FDm5UaoMGGw%2F%2BqgemHA4OAWsfFm4NAQxUAS5U1ssVExIW%2FjgCCgIJAwcDBQMBDBGSVv6tZAElgwYb%2FQsdFWQVHR0VZBUdAAP%2F%2FQAGA%2BgFFAAPAC0ASQAAASEyNj0BNCYjISIGHQEUFgEVFAYiJjURBwYmLwEmNxM%2BBDMhMhYVERQGBwEDFzc2Fx4FHAIVERQWNj0BNDY3JREnAV4B9BUdHRX%2BDBUdHQEPTpBMeQ8mDXAWEOYBBRARFwsCDQ2iKBX9iexTtxYZAgUDAgIBMjIoFQFTWQRMHRVkFR0dFWQVHfzmalRubFQBLlQMAQ1uFh8BawIIEw8Mpgf%2Bqg8bBgHP%2Fq1WkhEMAQMFAwcDCQIKAv44FhITFcsPGwaDASVkAAIAFgAWBJoEmgAPACUAAAAyHgIUDgIiLgI0PgEBJSYGHQEhIgYdARQWMyEVFBY3JTY0AeLs1ptbW5vW7NabW1ubAob%2B7RAX%2Fu0KDw8KARMXEAETEASaW5vW7NabW1ub1uzWm%2F453w0KFYkPCpYKD4kVCg3fDSYAAAIAFgAWBJoEmgAPACUAAAAyHgIUDgIiLgI0PgENAQYUFwUWNj0BITI2PQE0JiMhNTQmAeLs1ptbW5vW7NabW1ubASX%2B7RAQARMQFwETCg8PCv7tFwSaW5vW7NabW1ub1uzWm%2BjfDSYN3w0KFYkPCpYKD4kVCgAAAAIAFgAWBJoEmgAPACUAAAAyHgIUDgIiLgI0PgEBAyYiBwMGFjsBERQWOwEyNjURMzI2AeLs1ptbW5vW7NabW1ubAkvfDSYN3w0KFYkPCpYKD4kVCgSaW5vW7NabW1ub1uzWm%2F5AARMQEP7tEBf%2B7QoPDwoBExcAAAIAFgAWBJoEmgAPACUAAAAyHgIUDgIiLgI0PgEFIyIGFREjIgYXExYyNxM2JisBETQmAeLs1ptbW5vW7NabW1ubAZeWCg%2BJFQoN3w0mDd8NChWJDwSaW5vW7NabW1ub1uzWm7sPCv7tFxD%2B7RAQARMQFwETCg8AAAMAGAAYBJgEmAAPAJYApgAAADIeAhQOAiIuAjQ%2BASUOAwcGJgcOAQcGFgcOAQcGFgcUFgcyHgEXHgIXHgI3Fg4BFx4CFxQGFBcWNz4CNy4BJy4BJyIOAgcGJyY2NS4BJzYuAQYHBicmNzY3HgIXHgMfAT4CJyY%2BATc%2BAzcmNzIWMjY3LgMnND4CJiceAT8BNi4CJwYHFB4BFS4CJz4BNxYyPgEB5OjVm1xcm9Xo1ZtcXJsBZA8rHDoKDz0PFD8DAxMBAzEFCRwGIgEMFhkHECIvCxU%2FOR0HFBkDDRQjEwcFaHUeISQDDTAMD0UREi4oLBAzDwQBBikEAQMLGhIXExMLBhAGKBsGBxYVEwYFAgsFAwMNFwQGCQcYFgYQCCARFwkKKiFBCwQCAQMDHzcLDAUdLDgNEiEQEgg%2FKhADGgMKEgoRBJhcm9Xo1ZtcXJvV6NWbEQwRBwkCAwYFBycPCxcHInIWInYcCUcYChQECA4QBAkuHgQPJioRFRscBAcSCgwCch0kPiAIAQcHEAsBAgsLIxcBMQENCQIPHxkCFBkdHB4QBgEBBwoMGBENBAMMJSAQEhYXDQ4qFBkKEhIDCQsXJxQiBgEOCQwHAQ0DBAUcJAwSCwRnETIoAwEJCwsLJQcKDBEAAAAAAQAAAAIErwSFABYAAAE2FwUXNxYGBw4BJwEGIi8BJjQ3ASY2AvSkjv79kfsGUE08hjv9rA8rD28PDwJYIk8EhVxliuh%2BWYcrIgsW%2FawQEG4PKxACV2XJAAYAAABgBLAErAAPABMAIwAnADcAOwAAEyEyFh0BFAYjISImPQE0NgUjFTMFITIWHQEUBiMhIiY9ATQ2BSEVIQUhMhYdARQGIyEiJj0BNDYFIRUhZAPoKTs7KfwYKTs7BBHIyPwYA%2BgpOzsp%2FBgpOzsEEf4MAfT8GAPoKTs7KfwYKTs7BBH%2B1AEsBKw7KWQpOzspZCk7ZGTIOylkKTs7KWQpO2RkyDspZCk7OylkKTtkZAAAAAIAZAAABEwEsAALABEAABMhMhYUBiMhIiY0NgERBxEBIZYDhBUdHRX8fBUdHQI7yP6iA4QEsB0qHR0qHf1E%2FtTIAfQB9AAAAAMAAABkBLAEsAAXABsAJQAAATMyFh0BITIWFREhNSMVIRE0NjMhNTQ2FxUzNQEVFAYjISImPQEB9MgpOwEsKTv%2BDMj%2BDDspASw7KcgB9Dsp%2FBgpOwSwOylkOyn%2BcGRkAZApO2QpO2RkZP1EyCk7OynIAAAABAAAAAAEsASwABUAKwBBAFcAABMhMhYPARcWFA8BBiIvAQcGJjURNDYpATIWFREUBi8BBwYiLwEmND8BJyY2ARcWFA8BFxYGIyEiJjURNDYfATc2MgU3NhYVERQGIyEiJj8BJyY0PwE2MhcyASwVCA5exwcHaggUCMdeDhUdAzUBLBUdFQ5exwgUCGoHB8deDgj%2BL2oHB8deDggV%2FtQVHRUOXscIFALLXg4VHRX%2B1BUIDl7HBwdqCBQIBLAVDl7HCBQIagcHx14OCBUBLBUdHRX%2B1BUIDl7HBwdqCBQIx14OFf0maggUCMdeDhUdFQEsFQgOXscHzl4OCBX%2B1BUdFQ5exwgUCGoHBwAAAAYAAAAABKgEqAAPABsAIwA7AEMASwAAADIeAhQOAiIuAjQ%2BAQQiDgEUHgEyPgE0JiQyFhQGIiY0JDIWFAYjIicHFhUUBiImNTQ2PwImNTQEMhYUBiImNCQyFhQGIiY0Advy3Z9fX5%2Fd8t2gXl6gAcbgv29vv%2BC%2Fb2%2F%2BLS0gIC0gAUwtICAWDg83ETNIMykfegEJ%2FoctICAtIAIdLSAgLSAEqF%2Bf3fLdoF5eoN3y3Z9Xb7%2Fgv29vv%2BC%2FBiAtISEtICAtIQqRFxwkMzMkIDEFfgEODhekIC0gIC0gIC0gIC0AAf%2FYAFoEuQS8AFsAACUBNjc2JicmIyIOAwcABw4EFx4BMzI3ATYnLgEjIgcGBwEOASY0NwA3PgEzMhceARcWBgcOBgcGIyImJyY2NwE2NzYzMhceARcWBgcBDgEnLgECIgHVWwgHdl8WGSJBMD8hIP6IDx4eLRMNBQlZN0ozAiQkEAcdEhoYDRr%2Bqw8pHA4BRyIjQS4ODyw9DQ4YIwwod26La1YOOEBGdiIwGkQB%2F0coW2tQSE5nDxE4Qv4eDyoQEAOtAdZbZWKbEQQUGjIhH%2F6JDxsdNSg3HT5CMwIkJCcQFBcMGv6uDwEcKQ4BTSIjIQEINykvYyMLKnhuiWZMBxtAOU6%2BRAH%2FSBg3ISSGV121Qv4kDwIPDyYAAAACAGQAWASvBEQAGQBEAAABPgIeAhUUDgMHLgQ1ND4CHgEFIg4DIi4DIyIGFRQeAhcWFx4EMj4DNzY3PgQ1NCYCiTB7eHVYNkN5hKg%2BPqeFeEM4WnZ4eQEjIT8yLSohJyktPyJDbxtBMjMPBw86KzEhDSIzKUAMBAgrKT8dF2oDtURIBS1TdkA5eYB%2FslVVsn%2BAeTlAdlMtBUgtJjY1JiY1NiZvTRc4SjQxDwcOPCouGBgwKEALBAkpKkQqMhNPbQACADn%2F8gR3BL4AFwAuAAAAMh8BFhUUBg8BJi8BNycBFwcvASY0NwEDNxYfARYUBwEGIi8BJjQ%2FARYfAQcXAQKru0KNQjgiHR8uEl%2F3%2FnvUaRONQkIBGxJpCgmNQkL%2B5UK6Qo1CQjcdLhJf9wGFBL5CjUJeKmsiHTUuEl%2F4%2FnvUahKNQrpCARv%2BRmkICY1CukL%2B5UJCjUK7Qjc3LxFf%2BAGFAAAAAAMAyAAAA%2BgEsAARABUAHQAAADIeAhURFAYjISImNRE0PgEHESERACIGFBYyNjQCBqqaZDo7Kf2oKTs8Zj4CWP7%2FVj09Vj0EsB4uMhX8Ryk7OykDuRUzLar9RAK8%2FRY9Vj09VgABAAAAAASwBLAAFgAACQEWFAYiLwEBEScBBRMBJyEBJyY0NjIDhgEbDx0qDiT%2B6dT%2BzP7oywEz0gEsAQsjDx0qBKH%2B5g8qHQ8j%2FvX%2B1NL%2BzcsBGAE01AEXJA4qHQAAAAADAScAEQQJBOAAMgBAAEsAAAEVHgQXIy4DJxEXHgQVFAYHFSM1JicuASczHgEXEScuBDU0PgI3NRkBDgMVFB4DFxYXET4ENC4CArwmRVI8LAKfBA0dMydAIjxQNyiym2SWVygZA4sFV0obLkJOMCAyVWg6HSoqFQ4TJhkZCWgWKTEiGBkzNwTgTgUTLD9pQiQuLBsH%2Fs0NBxMtPGQ%2Bi6oMTU8QVyhrVk1iEAFPCA4ZLzlYNkZwSCoGTf4SARIEDh02Jh0rGRQIBgPQ%2FsoCCRYgNEM0JRkAAAABAGQAZgOUBK0ASgAAATIeARUjNC4CIyIGBwYVFB4BFxYXMxUjFgYHBgc%2BATM2FjMyNxcOAyMiLgEHDgEPASc%2BBTc%2BAScjNTMmJy4CPgE3NgIxVJlemSc8OxolVBQpGxoYBgPxxQgVFS02ImIWIIwiUzUyHzY4HCAXanQmJ1YYFzcEGAcTDBEJMAwk3aYXFQcKAg4tJGEErVCLTig%2FIhIdFSw5GkowKgkFZDKCHj4yCg8BIh6TExcIASIfBAMaDAuRAxAFDQsRCjePR2QvORQrREFMIVgAAAACABn%2F%2FwSXBLAADwAfAAABMzIWDwEGIi8BJjY7AREzBRcWBisBESMRIyImPwE2MgGQlhUIDuYOKg7mDggVlsgCF%2BYOCBWWyJYVCA7mDioBLBYO%2Bg8P%2Bg4WA4QQ%2BQ4V%2FHwDhBUO%2BQ8AAAQAGf%2F%2FA%2BgEsAAHABcAGwAlAAABIzUjFSMRIQEzMhYPAQYiLwEmNjsBETMFFTM1EwczFSE1NyM1IQPoZGRkASz9qJYVCA7mDioO5g4IFZbIAZFkY8jI%2FtTIyAEsArxkZAH0%2FHwWDvoPD%2FoOFgOEZMjI%2FRL6ZJb6ZAAAAAAEABn%2F%2FwPoBLAADwAZACEAJQAAATMyFg8BBiIvASY2OwERMwUHMxUhNTcjNSERIzUjFSMRIQcVMzUBkJYVCA7mDioO5g4IFZbIAljIyP7UyMgBLGRkZAEsx2QBLBYO%2Bg8P%2Bg4WA4SW%2BmSW%2BmT7UGRkAfRkyMgAAAAEABn%2F%2FwRMBLAADwAVABsAHwAAATMyFg8BBiIvASY2OwERMwEjESM1MxMjNSMRIQcVMzUBkJYVCA7mDioO5g4IFZbIAlhkZMhkZMgBLMdkASwWDvoPD%2FoOFgOE%2FgwBkGT7UGQBkGTIyAAAAAAEABn%2F%2FwRMBLAADwAVABkAHwAAATMyFg8BBiIvASY2OwERMwEjNSMRIQcVMzUDIxEjNTMBkJYVCA7mDioO5g4IFZbIArxkyAEsx2QBZGTIASwWDvoPD%2FoOFgOE%2FgxkAZBkyMj7tAGQZAAAAAAFABn%2F%2FwSwBLAADwATABcAGwAfAAABMzIWDwEGIi8BJjY7AREzBSM1MxMhNSETITUhEyE1IQGQlhUIDuYOKg7mDggVlsgB9MjIZP7UASxk%2FnABkGT%2BDAH0ASwWDvoPD%2FoOFgOEyMj%2BDMj%2BDMj%2BDMgABQAZ%2F%2F8EsASwAA8AEwAXABsAHwAAATMyFg8BBiIvASY2OwERMwUhNSEDITUhAyE1IQMjNTMBkJYVCA7mDioO5g4IFZbIAyD%2BDAH0ZP5wAZBk%2FtQBLGTIyAEsFg76Dw%2F6DhYDhMjI%2FgzI%2FgzI%2FgzIAAIAAAAABEwETAAPAB8AAAEhMhYVERQGIyEiJjURNDYFISIGFREUFjMhMjY1ETQmAV4BkKK8u6P%2BcKW5uQJn%2FgwpOzspAfQpOzsETLuj%2FnClubmlAZClucg7Kf4MKTs7KQH0KTsAAAAAAwAAAAAETARMAA8AHwArAAABITIWFREUBiMhIiY1ETQ2BSEiBhURFBYzITI2NRE0JgUXFhQPAQYmNRE0NgFeAZClubml%2FnCju7wCZP4MKTs7KQH0KTs7%2Fm%2F9ERH9EBgYBEy5pf5wpbm5pQGQo7vIOyn%2BDCk7OykB9Ck7gr4MJAy%2BDAsVAZAVCwAAAAADAAAAAARMBEwADwAfACsAAAEhMhYVERQGIyEiJjURNDYFISIGFREUFjMhMjY1ETQmBSEyFg8BBiIvASY2AV4BkKO7uaX%2BcKW5uQJn%2FgwpOzspAfQpOzv%2BFQGQFQsMvgwkDL4MCwRMvKL%2BcKW5uaUBkKO7yDsp%2FgwpOzspAfQpO8gYEP0REf0QGAAAAAMAAAAABEwETAAPAB8AKwAAASEyFhURFAYjISImNRE0NgUhIgYVERQWMyEyNjURNCYFFxYGIyEiJj8BNjIBXgGQpbm5pf5wo7u5Amf%2BDCk7OykB9Ck7O%2F77vgwLFf5wFQsMvgwkBEy5pf5wo7u8ogGQpbnIOyn%2BDCk7OykB9Ck7z%2F0QGBgQ%2FREAAAAAAgAAAAAFFARMAB8ANQAAASEyFhURFAYjISImPQE0NjMhMjY1ETQmIyEiJj0BNDYHARYUBwEGJj0BIyImPQE0NjsBNTQ2AiYBkKW5uaX%2BcBUdHRUBwik7Oyn%2BPhUdHb8BRBAQ%2FrwQFvoVHR0V%2BhYETLml%2FnCluR0VZBUdOykB9Ck7HRVkFR3p%2FuQOJg7%2B5A4KFZYdFcgVHZYVCgAAAQDZAAID1wSeACMAAAEXFgcGAgclMhYHIggBBwYrAScmNz4BPwEhIicmNzYANjc2MwMZCQgDA5gCASwYEQ4B%2Fvf%2B8wQMDgkJCQUCUCcn%2FtIXCAoQSwENuwUJEASeCQoRC%2F5TBwEjEv7K%2FsUFDwgLFQnlbm4TFRRWAS%2FTBhAAAAACAAAAAAT%2BBEwAHwA1AAABITIWHQEUBiMhIgYVERQWMyEyFh0BFAYjISImNRE0NgUBFhQHAQYmPQEjIiY9ATQ2OwE1NDYBXgGQFR0dFf4%2BKTs7KQHCFR0dFf5wpbm5AvEBRBAQ%2FrwQFvoVHR0V%2BhYETB0VZBUdOyn%2BDCk7HRVkFR25pQGQpbnp%2FuQOJg7%2B5A4KFZYdFcgVHZYVCgACAAAAAASwBLAAFQAxAAABITIWFREUBi8BAQYiLwEmNDcBJyY2ASMiBhURFBYzITI2PQE3ERQGIyEiJjURNDYzIQLuAZAVHRUObf7IDykPjQ8PAThtDgj%2B75wpOzspAfQpO8i7o%2F5wpbm5pQEsBLAdFf5wFQgObf7IDw%2BNDykPAThtDhX%2B1Dsp%2FgwpOzsplMj%2B1qW5uaUBkKW5AAADAA4ADgSiBKIADwAbACMAAAAyHgIUDgIiLgI0PgEEIg4BFB4BMj4BNCYEMhYUBiImNAHh7tmdXV2d2e7ZnV1dnQHD5sJxccLmwnFx%2FnugcnKgcgSiXZ3Z7tmdXV2d2e7ZnUdxwubCcXHC5sJzcqBycqAAAAMAAAAABEwEsAAVAB8AIwAAATMyFhURMzIWBwEGIicBJjY7ARE0NgEhMhYdASE1NDYFFTM1AcLIFR31FAoO%2FoEOJw3%2BhQ0JFfod%2FoUD6BUd%2B7QdA2dkBLAdFf6iFg%2F%2BVg8PAaoPFgFeFR38fB0V%2BvoVHWQyMgAAAAMAAAAABEwErAAVAB8AIwAACQEWBisBFRQGKwEiJj0BIyImNwE%2BAQEhMhYdASE1NDYFFTM1AkcBeg4KFfQiFsgUGPoUCw4Bfw4n%2FfkD6BUd%2B7QdA2dkBJ7%2BTQ8g%2BhQeHRX6IQ8BrxAC%2FH8dFfr6FR1kMjIAAwAAAAAETARLABQAHgAiAAAJATYyHwEWFAcBBiInASY0PwE2MhcDITIWHQEhNTQ2BRUzNQGMAXEHFQeLBwf98wcVB%2F7cBweLCBUH1APoFR37tB0DZ2QC0wFxBweLCBUH%2FfMICAEjCBQIiwcH%2FdIdFfr6FR1kMjIABAAAAAAETASbAAkAGQAjACcAABM3NjIfAQcnJjQFNzYWFQMOASMFIiY%2FASc3ASEyFh0BITU0NgUVMzWHjg4qDk3UTQ4CFtIOFQIBHRX9qxUIDtCa1P49A%2BgVHfu0HQNnZAP%2Fjg4OTdRMDyqa0g4IFf2pFB4BFQ7Qm9T9Oh0V%2BvoVHWQyMgAAAAQAAAAABEwEsAAPABkAIwAnAAABBR4BFRMUBi8BByc3JyY2EwcGIi8BJjQ%2FAQEhMhYdASE1NDYFFTM1AV4CVxQeARUO0JvUm9IOCMNMDyoOjg4OTf76A%2BgVHfu0HQNnZASwAgEdFf2rFQgO0JrUmtIOFf1QTQ4Ojg4qDk3%2BWB0V%2BvoVHWQyMgACAAT%2F7ASwBK8ABQAIAAAlCQERIQkBFQEEsP4d%2Fsb%2BcQSs%2FTMCq2cBFP5xAacDHPz55gO5AAAAAAIAAABkBEwEsAAVABkAAAERFAYrAREhESMiJjURNDY7AREhETMHIzUzBEwdFZb9RJYVHR0V%2BgH0ZMhkZAPo%2FK4VHQGQ%2FnAdFQPoFB7%2B1AEsyMgAAAMAAABFBN0EsAAWABoALwAAAQcBJyYiDwEhESMiJjURNDY7AREhETMHIzUzARcWFAcBBiIvASY0PwE2Mh8BATYyBEwC%2FtVfCRkJlf7IlhUdHRX6AfRkyGRkAbBqBwf%2BXAgUCMoICGoHFQdPASkHFQPolf7VXwkJk%2F5wHRUD6BQe%2FtQBLMjI%2Fc5qBxUH%2FlsHB8sHFQdqCAhPASkHAAMAAAANBQcEsAAWABoAPgAAAREHJy4BBwEhESMiJjURNDY7AREhETMHIzUzARcWFA8BFxYUDwEGIi8BBwYiLwEmND8BJyY0PwE2Mh8BNzYyBExnhg8lEP72%2FreWFR0dFfoB9GTIZGQB9kYPD4ODDw9GDykPg4MPKQ9GDw%2BDgw8PRg8pD4ODDykD6P7zZ4YPAw7%2B9v5wHRUD6BQe%2FtQBLMjI%2FYxGDykPg4MPKQ9GDw%2BDgw8PRg8pD4ODDykPRg8Pg4MPAAADAAAAFQSXBLAAFQAZAC8AAAERISIGHQEhESMiJjURNDY7AREhETMHIzUzEzMyFh0BMzIWDwEGIi8BJjY7ATU0NgRM%2FqIVHf4MlhUdHRX6AfRkyGRklmQVHZYVCA7mDioO5g4IFZYdA%2Bj%2B1B0Vlv5wHRUD6BQe%2FtQBLMjI%2FagdFfoVDuYODuYOFfoVHQAAAAADAAAAAASXBLAAFQAZAC8AAAERJyYiBwEhESMiJjURNDY7AREhETMHIzUzExcWBisBFRQGKwEiJj0BIyImPwE2MgRMpQ4qDv75%2Fm6WFR0dFfoB9GTIZGTr5g4IFZYdFWQVHZYVCA7mDioD6P5wpQ8P%2Fvf%2BcB0VA%2BgUHv7UASzIyP2F5Q8V%2BhQeHhT6FQ%2FlDwADAAAAyASwBEwACQATABcAABMhMhYdASE1NDYBERQGIyEiJjURExUhNTIETBUd%2B1AdBJMdFfu0FR1kAZAETB0VlpYVHf7U%2FdoVHR0VAib%2B1MjIAAAGAAMAfQStBJcADwAZAB0ALQAxADsAAAEXFhQPAQYmPQEhNSE1NDYBIyImPQE0NjsBFyM1MwE3NhYdASEVIRUUBi8BJjQFIzU7AjIWHQEUBisBA6f4Dg74DhX%2BcAGQFf0vMhUdHRUyyGRk%2FoL3DhUBkP5wFQ73DwOBZGRkMxQdHRQzBI3mDioO5g4IFZbIlhUI%2FoUdFWQVHcjI%2FcvmDggVlsiWFQgO5g4qecgdFWQVHQAAAAACAGQAAASwBLAAFgBRAAABJTYWFREUBisBIiY1ES4ENRE0NiUyFh8BERQOAg8BERQGKwEiJjURLgQ1ETQ%2BAzMyFh8BETMRPAE%2BAjMyFh8BETMRND4DA14BFBklHRXIFR0EDiIaFiX%2B4RYZAgEVHR0LCh0VyBUdBA4iGhYBBwoTDRQZAgNkBQkVDxcZAQFkAQUJFQQxdBIUH%2FuuFR0dFQGNAQgbHzUeAWcfRJEZDA3%2BPhw%2FMSkLC%2F5BFR0dFQG%2FBA8uLkAcAcICBxENCxkMDf6iAV4CBxENCxkMDf6iAV4CBxENCwABAGQAAASwBEwAMwAAARUiDgMVERQWHwEVITUyNjURIREUFjMVITUyPgM1ETQmLwE1IRUiBhURIRE0JiM1BLAEDiIaFjIZGf5wSxn%2BDBlL%2FnAEDiIaFjIZGQGQSxkB9BlLBEw4AQUKFA78iBYZAQI4OA0lAYr%2BdiUNODgBBQoUDgN4FhkBAjg4DSX%2BdgGKJQ04AAAABgAAAAAETARMAAwAHAAgACQAKAA0AAABITIWHQEjBTUnITchBSEyFhURFAYjISImNRE0NhcVITUBBTUlBRUhNQUVFAYjIQchJyE3MwKjAXcVHWn%2B2cj%2BcGQBd%2F4lASwpOzsp%2FtQpOzspASwCvP5wAZD8GAEsArwdFf6JZP6JZAGQyGkD6B0VlmJiyGTIOyn%2BDCk7OykB9Ck7ZMjI%2FveFo4XGyMhm%2BBUdZGTIAAEAEAAQBJ8EnwAmAAATNzYWHwEWBg8BHgEXNz4BHwEeAQ8BBiIuBicuBTcRohEuDosOBhF3ZvyNdxEzE8ATBxGjAw0uMUxPZWZ4O0p3RjITCwED76IRBhPCFDERdo78ZXYRBA6IDi8RogEECBUgNUNjO0qZfHNVQBAAAAACAAAAAASwBEwAIwBBAAAAMh4EHwEVFAYvAS4BPQEmIAcVFAYPAQYmPQE%2BBRIyHgIfARUBHgEdARQGIyEiJj0BNDY3ATU0PgIB%2FLimdWQ%2FLAkJHRTKFB2N%2FsKNHRTKFB0DDTE7ZnTKcFImFgEBAW0OFR0V%2B7QVHRUOAW0CFiYETBUhKCgiCgrIFRgDIgMiFZIYGJIVIgMiAxgVyAQNJyQrIP7kExwcCgoy%2FtEPMhTUFR0dFdQUMg8BLzIEDSEZAAADAAAAAASwBLAADQAdACcAAAEHIScRMxUzNTMVMzUzASEyFhQGKwEXITcjIiY0NgMhMhYdASE1NDYETMj9qMjIyMjIyPyuArwVHR0VDIn8SokMFR0dswRMFR37UB0CvMjIAfTIyMjI%2FOAdKh1kZB0qHf7UHRUyMhUdAAAAAwBkAAAEsARMAAkAEwAdAAABIyIGFREhETQmASMiBhURIRE0JgEhETQ2OwEyFhUCvGQpOwEsOwFnZCk7ASw7%2FRv%2B1DspZCk7BEw7KfwYA%2BgpO%2F7UOyn9RAK8KTv84AGQKTs7KQAAAAAF%2F5wAAASwBEwADwATAB8AJQApAAATITIWFREUBiMhIiY1ETQ2FxEhEQUjFTMRITUzNSMRIQURByMRMwcRMxHIArx8sLB8%2FUR8sLAYA4T%2BDMjI%2FtTIyAEsAZBkyMhkZARMsHz%2BDHywsHwB9HywyP1EArzIZP7UZGQBLGT%2B1GQB9GT%2B1AEsAAAABf%2BcAAAEsARMAA8AEwAfACUAKQAAEyEyFhURFAYjISImNRE0NhcRIREBIzUjFSMRMxUzNTMFEQcjETMHETMRyAK8fLCwfP1EfLCwGAOE%2FgxkZGRkZGQBkGTIyGRkBEywfP4MfLCwfAH0fLDI%2FUQCvP2oyMgB9MjIZP7UZAH0ZP7UASwABP%2BcAAAEsARMAA8AEwAbACMAABMhMhYVERQGIyEiJjURNDYXESERBSMRMxUhESEFIxEzFSERIcgCvHywsHz9RHywsBgDhP4MyMj%2B1AEsAZDIyP7UASwETLB8%2Fgx8sLB8AfR8sMj9RAK8yP7UZAH0ZP7UZAH0AAAABP%2BcAAAEsARMAA8AEwAWABkAABMhMhYVERQGIyEiJjURNDYXESERAS0BDQERyAK8fLCwfP1EfLCwGAOE%2Fgz%2B1AEsAZD%2B1ARMsHz%2BDHywsHwB9HywyP1EArz%2BDJaWlpYBLAAAAAX%2FnAAABLAETAAPABMAFwAgACkAABMhMhYVERQGIyEiJjURNDYXESERAyERIQcjIgYVFBY7AQERMzI2NTQmI8gCvHywsHz9RHywsBgDhGT9RAK8ZIImOTYpgv4Mgik2OSYETLB8%2Fgx8sLB8AfR8sMj9RAK8%2FagB9GRWQUFUASz%2B1FRBQVYAAAAF%2F5wAAASwBEwADwATAB8AJQApAAATITIWFREUBiMhIiY1ETQ2FxEhEQUjFTMRITUzNSMRIQEjESM1MwMjNTPIArx8sLB8%2FUR8sLAYA4T%2BDMjI%2FtTIyAEsAZBkZMjIZGQETLB8%2Fgx8sLB8AfR8sMj9RAK8yGT%2B1GRkASz%2BDAGQZP4MZAAG%2F5wAAASwBEwADwATABkAHwAjACcAABMhMhYVERQGIyEiJjURNDYXESERBTMRIREzASMRIzUzBRUzNQEjNTPIArx8sLB8%2FUR8sLAYA4T9RMj%2B1GQCWGRkyP2oZAEsZGQETLB8%2Fgx8sLB8AfR8sMj9RAK8yP5wAfT%2BDAGQZMjIyP7UZAAF%2F5wAAASwBEwADwATABwAIgAmAAATITIWFREUBiMhIiY1ETQ2FxEhEQEHIzU3NSM1IQEjESM1MwMjNTPIArx8sLB8%2FUR8sLAYA4T%2BDMdkx8gBLAGQZGTIx2RkBEywfP4MfLCwfAH0fLDI%2FUQCvP5wyDLIlmT%2BDAGQZP4MZAAAAAMACQAJBKcEpwAPABsAJQAAADIeAhQOAiIuAjQ%2BAQQiDgEUHgEyPgE0JgchFSEVISc1NyEB4PDbnl5entvw255eXp4BxeTCcXHC5MJxcWz%2B1AEs%2FtRkZAEsBKdentvw255eXp7b8NueTHHC5MJxccLkwtDIZGTIZAAAAAAEAAkACQSnBKcADwAbACcAKwAAADIeAhQOAiIuAjQ%2BAQQiDgEUHgEyPgE0JgcVBxcVIycjFSMRIQcVMzUB4PDbnl5entvw255eXp4BxeTCcXHC5MJxcWwyZGRklmQBLMjIBKdentvw255eXp7b8NueTHHC5MJxccLkwtBkMmQyZGQBkGRkZAAAAv%2Fy%2F50EwgRBACAANgAAATIWFzYzMhYUBisBNTQmIyEiBh0BIyImNTQ2NyY1ND4BEzMyFhURMzIWDwEGIi8BJjY7ARE0NgH3brUsLC54qqp4gB0V%2FtQVHd5QcFZBAmKqepYKD4kVCg3fDSYN3w0KFYkPBEF3YQ6t8a36FR0dFfpzT0VrDhMSZKpi%2FbMPCv7tFxD0EBD0EBcBEwoPAAAAAAL%2F8v%2BcBMMEQQAcADMAAAEyFhc2MzIWFxQGBwEmIgcBIyImNTQ2NyY1ND4BExcWBisBERQGKwEiJjURIyImNzY3NjIB9m62LCsueaoBeFr%2Bhg0lDf6DCU9xVkECYqnm3w0KFYkPCpYKD4kVCg3HGBMZBEF3YQ%2BteGOkHAFoEBD%2Bk3NPRWsOExNkqWP9kuQQF%2F7tCg8PCgETFxDMGBMAAAABAGQAAARMBG0AGAAAJTUhATMBMwkBMwEzASEVIyIGHQEhNTQmIwK8AZD%2B8qr%2B8qr%2B1P7Uqv7yqv7yAZAyFR0BkB0VZGQBLAEsAU3%2Bs%2F7U%2FtRkHRUyMhUdAAAAAAEAeQAABDcEmwAvAAABMhYXHgEVFAYHFhUUBiMiJxUyFh0BITU0NjM1BiMiJjU0Ny4BNTQ2MzIXNCY1NDYCWF6TGll7OzIJaUo3LRUd%2FtQdFS03SmkELzlpSgUSAqMEm3FZBoNaPWcfHRpKaR77HRUyMhUd%2Bx5pShIUFVg1SmkCAhAFdKMAAAAGACcAFASJBJwAEQAqAEIASgBiAHsAAAEWEgIHDgEiJicmAhI3PgEyFgUiBw4BBwYWHwEWMzI3Njc2Nz4BLwEmJyYXIgcOAQcGFh8BFjMyNz4BNz4BLwEmJyYWJiIGFBYyNjciBw4BBw4BHwEWFxYzMjc%2BATc2Ji8BJhciBwYHBgcOAR8BFhcWMzI3PgE3NiYvASYD8m9PT29T2dzZU29PT29T2dzZ%2Fj0EBHmxIgQNDCQDBBcGG0dGYAsNAwkDCwccBAVQdRgEDA0iBAQWBhJROQwMAwkDCwf5Y4xjY4xjVhYGElE6CwwDCQMLBwgEBVB1GAQNDCIEjRcGG0dGYAsNAwkDCwcIBAR5sSIEDQwkAwPyb%2F7V%2FtVvU1dXU28BKwErb1NXVxwBIrF5DBYDCQEWYEZHGwMVDCMNBgSRAhh1UA0WAwkBFTpREgMVCyMMBwT6Y2OMY2MVFTpREQQVCyMMBwQCGHVQDRYDCQEkFmBGRxsDFQwjDQYEASKxeQwWAwkBAAAABQBkAAAD6ASwAAwADwAWABwAIgAAASERIzUhFSERNDYzIQEjNQMzByczNTMDISImNREFFRQGKwECvAEstP6s%2FoQPCgI%2FASzIZKLU1KJktP51Cg8DhA8KwwMg%2FoTIyALzCg%2F%2B1Mj84NTUyP4MDwoBi8jDCg8AAAAABQBkAAAD6ASwAAkADAATABoAIQAAASERCQERNDYzIQEjNRMjFSM1IzcDISImPQEpARUUBisBNQK8ASz%2Bov3aDwoCPwEsyD6iZKLUqv6dCg8BfAIIDwqbAyD9%2BAFe%2FdoERwoP%2FtTI%2FHzIyNT%2BZA8KNzcKD1AAAAAAAwAAAAAEsAP0AAgAGQAfAAABIxUzFyERIzcFMzIeAhUhFSEDETM0PgIBMwMhASEEiqJkZP7UotT9EsgbGiEOASz9qMhkDiEaAnPw8PzgASwB9AMgyGQBLNTUBBErJGT%2BogHCJCsRBP5w%2FnAB9AAAAAMAAAAABEwETAAZADIAOQAAATMyFh0BMzIWHQEUBiMhIiY9ATQ2OwE1NDYFNTIWFREUBiMhIic3ARE0NjMVFBYzITI2AQc1IzUzNQKKZBUdMhUdHRX%2B1BUdHRUyHQFzKTs7Kf2oARP2%2Fro7KVg%2BASw%2BWP201MjIBEwdFTIdFWQVHR0VZBUdMhUd%2BpY7KfzgKTsE9gFGAUQpO5Y%2BWFj95tSiZKIAAwBkAAAEvARMABkANgA9AAABMzIWHQEzMhYdARQGIyEiJj0BNDY7ATU0NgU1MhYVESMRMxQOAiMhIiY1ETQ2MxUUFjMhMjYBBzUjNTM1AcJkFR0yFR0dFf7UFR0dFTIdAXMpO8jIDiEaG%2F2oKTs7KVg%2BASw%2BWAGc1MjIBEwdFTIdFWQVHR0VZBUdMhUd%2BpY7Kf4M%2FtQkKxEEOykDICk7lj5YWP3m1KJkogAAAAP%2FogAABRYE1AALABsAHwAACQEWBiMhIiY3ATYyEyMiBhcTHgE7ATI2NxM2JgMVMzUCkgJ9FyAs%2BwQsIBcCfRZARNAUGAQ6BCMUNhQjBDoEGODIBK37sCY3NyYEUCf%2BTB0U%2FtIUHR0UAS4UHf4MZGQAAAAACQAAAAAETARMAA8AHwAvAD8ATwBfAG8AfwCPAAABMzIWHQEUBisBIiY9ATQ2EzMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYBMzIWHQEUBisBIiY9ATQ2ITMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYBMzIWHQEUBisBIiY9ATQ2ITMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYBqfoKDw8K%2BgoPDwr6Cg8PCvoKDw8BmvoKDw8K%2BgoPD%2Fzq%2BgoPDwr6Cg8PAZr6Cg8PCvoKDw8BmvoKDw8K%2BgoPD%2Fzq%2BgoPDwr6Cg8PAZr6Cg8PCvoKDw8BmvoKDw8K%2BgoPDwRMDwqWCg8PCpYKD%2F7UDwqWCg8PCpYKDw8KlgoPDwqWCg%2F%2B1A8KlgoPDwqWCg8PCpYKDw8KlgoPDwqWCg8PCpYKD%2F7UDwqWCg8PCpYKDw8KlgoPDwqWCg8PCpYKDw8KlgoPAAAAAwAAAAAEsAUUABkAKQAzAAABMxUjFSEyFg8BBgchJi8BJjYzITUjNTM1MwEhMhYUBisBFyE3IyImNDYDITIWHQEhNTQ2ArxkZAFePjEcQiko%2FPwoKUIcMT4BXmRkyP4%2BArwVHR0VDIn8SooNFR0dswRMFR37UB0EsMhkTzeEUzMzU4Q3T2TIZPx8HSodZGQdKh3%2B1B0VMjIVHQAABAAAAAAEsAUUAAUAGQArADUAAAAyFhUjNAchFhUUByEyFg8BIScmNjMhJjU0AyEyFhQGKwEVBSElNSMiJjQ2AyEyFh0BITU0NgIwUDnCPAE6EgMBSCkHIq%2F9WrIiCikBSAOvArwVHR0VlgET%2FEoBE5YVHR2zBEwVHftQHQUUOykpjSUmCBEhFpGRFiERCCb%2BlR0qHcjIyMgdKh39qB0VMjIVHQAEAAAAAASwBJ0ABwAUACQALgAAADIWFAYiJjQTMzIWFRQXITY1NDYzASEyFhQGKwEXITcjIiY0NgMhMhYdASE1NDYCDZZqapZqty4iKyf%2BvCcrI%2F7NArwVHR0VDYr8SokMFR0dswRMFR37UB0EnWqWamqW%2Fus5Okxra0w6Of5yHSodZGQdKh3%2B1B0VMjIVHQAEAAAAAASwBRQADwAcACwANgAAATIeARUUBiImNTQ3FzcnNhMzMhYVFBchNjU0NjMBITIWFAYrARchNyMiJjQ2AyEyFh0BITU0NgJYL1szb5xvIpBvoyIfLiIrJ%2F68Jysj%2Fs0CvBUdHRUNivxKiQwVHR2zBEwVHftQHQUUa4s2Tm9vTj5Rj2%2BjGv4KOTpMa2tMOjn%2Bch0qHWRkHSod%2FtQdFTIyFR0AAAADAAAAAASwBRIAEgAiACwAAAEFFSEUHgMXIS4BNTQ%2BAjcBITIWFAYrARchNyMiJjQ2AyEyFh0BITU0NgJYASz%2B1CU%2FP00T%2Fe48PUJtj0r%2BogK8FR0dFQ2K%2FEqJDBUdHbMETBUd%2B1AdBLChizlmUT9IGVO9VFShdksE%2FH4dKh1kZB0qHf7UHRUyMhUdAAIAyAAAA%2BgFFAAPACkAAAAyFh0BHgEdASE1NDY3NTQDITIWFyMVMxUjFTMVIxUzFAYjISImNRE0NgIvUjsuNv5wNi5kAZA2XBqsyMjIyMh1U%2F5wU3V1BRQ7KU4aXDYyMjZcGk4p%2Fkc2LmRkZGRkU3V1UwGQU3UAAAMAZP%2F%2FBEwETAAPAC8AMwAAEyEyFhURFAYjISImNRE0NgMhMhYdARQGIyEXFhQGIi8BIQcGIiY0PwEhIiY9ATQ2BQchJ5YDhBUdHRX8fBUdHQQDtgoPDwr%2B5eANGiUNWP30Vw0mGg3g%2Ft8KDw8BqmQBRGQETB0V%2FgwVHR0VAfQVHf1EDwoyCg%2FgDSUbDVhYDRslDeAPCjIKD2RkZAAAAAAEAAAAAASwBEwAGQAjAC0ANwAAEyEyFh0BIzQmKwEiBhUjNCYrASIGFSM1NDYDITIWFREhETQ2ExUUBisBIiY9ASEVFAYrASImPQHIAyBTdWQ7KfopO2Q7KfopO2R1EQPoKTv7UDvxHRVkFR0D6B0VZBUdBEx1U8gpOzspKTs7KchTdf4MOyn%2B1AEsKTv%2BDDIVHR0VMjIVHR0VMgADAAEAAASpBKwADQARABsAAAkBFhQPASEBJjQ3ATYyCQMDITIWHQEhNTQ2AeACqh8fg%2F4f%2FfsgIAEnH1n%2BrAFWAS%2F%2Bq6IDIBUd%2FHwdBI39VR9ZH4MCBh9ZHwEoH%2F5u%2FqoBMAFV%2FBsdFTIyFR0AAAAAAgCPAAAEIQSwABcALwAAAQMuASMhIgYHAwYWMyEVFBYyNj0BMzI2AyE1NDY7ATU0NjsBETMRMzIWHQEzMhYVBCG9CCcV%2FnAVJwi9CBMVAnEdKh19FROo%2Fa0dFTIdFTDILxUdMhUdAocB%2BhMcHBP%2BBhMclhUdHRWWHP2MMhUdMhUdASz%2B1B0VMh0VAAAEAAAAAASwBLAADQAQAB8AIgAAASERFAYjIREBNTQ2MyEBIzUBIREUBiMhIiY1ETQ2MyEBIzUDhAEsDwr%2Bif7UDwoBdwEsyP2oASwPCv12Cg8PCgF3ASzIAyD9wQoPAk8BLFQKD%2F7UyP4M%2FcEKDw8KA7YKD%2F7UyAAC%2F5wAZAUUBEcARgBWAAABMzIeAhcWFxY2NzYnJjc%2BARYXFgcOASsBDgEPAQ4BKwEiJj8BBisBIicHDgErASImPwEmLwEuAT0BNDY7ATY3JyY2OwE2BSMiBh0BFBY7ATI2PQE0JgHkw0uOakkMEhEfQwoKGRMKBQ8XDCkCA1Y9Pgc4HCcDIhVkFRgDDDEqwxgpCwMiFWQVGAMaVCyfExwdFXwLLW8QBxXLdAFF%2BgoPDwr6Cg8PBEdBa4pJDgYKISAiJRsQCAYIDCw9P1c3fCbqFB0dFEYOCEAUHR0UnUplNQcmFTIVHVdPXw4TZV8PCjIKDw8KMgoPAAb%2FnP%2FmBRQEfgAJACQANAA8AFIAYgAAASU2Fh8BFgYPASUzMhYfASEyFh0BFAYHBQYmJyYjISImPQE0NhcjIgYdARQ7ATI2NTQmJyYEIgYUFjI2NAE3PgEeARceAT8BFxYGDwEGJi8BJjYlBwYfAR4BPwE2Jy4BJy4BAoEBpxMuDiAOAxCL%2FCtqQ0geZgM3FR0cE%2F0fFyIJKjr%2B1D5YWLlQExIqhhALIAsSAYBALS1ALf4PmBIgHhMQHC0aPzANITNQL3wpgigJASlmHyElDR0RPRMFAhQHCxADhPcICxAmDyoNeMgiNtQdFTIVJgeEBBQPQ1g%2ByD5YrBwVODMQEAtEERzJLUAtLUD%2B24ITChESEyMgAwWzPUkrRSgJL5cvfRxYGyYrDwkLNRAhFEgJDAQAAAAAAwBkAAAEOQSwAFEAYABvAAABMzIWHQEeARcWDgIPATIeBRUUDgUjFRQGKwEiJj0BIxUUBisBIiY9ASMiJj0BNDY7AREjIiY9ATQ2OwE1NDY7ATIWHQEzNTQ2AxUhMj4CNTc0LgMjARUhMj4CNTc0LgMjAnGWCg9PaAEBIC4uEBEGEjQwOiodFyI2LUAjGg8KlgoPZA8KlgoPrwoPDwpLSwoPDwqvDwqWCg9kD9cBBxwpEwsBAQsTKRz%2B%2BQFrHCkTCwEBCxMpHASwDwptIW1KLk0tHwYGAw8UKDJOLTtdPCoVCwJLCg8PCktLCg8PCksPCpYKDwJYDwqWCg9LCg8PCktLCg%2F%2B1MgVHR0LCgQOIhoW%2FnDIFR0dCwoEDiIaFgAAAwAEAAIEsASuABcAKQAsAAATITIWFREUBg8BDgEjISImJy4CNRE0NgQiDgQPARchNy4FAyMT1AMMVnokEhIdgVL9xFKCHAgYKHoCIIx9VkcrHQYGnAIwnAIIIClJVSGdwwSuelb%2BYDO3QkJXd3ZYHFrFMwGgVnqZFyYtLSUMDPPzBQ8sKDEj%2FsIBBQACAMgAAAOEBRQADwAZAAABMzIWFREUBiMhIiY1ETQ2ARUUBisBIiY9AQHblmesVCn%2BPilUrAFINhWWFTYFFKxn%2FgwpVFQpAfRnrPwY4RU2NhXhAAACAMgAAAOEBRQADwAZAAABMxQWMxEUBiMhIiY1ETQ2ARUUBisBIiY9AQHbYLOWVCn%2BPilUrAFINhWWFTYFFJaz%2FkIpVFQpAfRnrPwY4RU2NhXhAAACAAAAFAUOBBoAFAAaAAAJASUHFRcVJwc1NzU0Jj4CPwEnCQEFJTUFJQUO%2FYL%2Bhk5klpZkAQEBBQQvkwKCAVz%2Bov6iAV4BXgL%2F%2FuWqPOCWx5SVyJb6BA0GCgYDKEEBG%2F1ipqaTpaUAAAMAZAH0BLADIAAHAA8AFwAAEjIWFAYiJjQkMhYUBiImNCQyFhQGIiY0vHxYWHxYAeh8WFh8WAHofFhYfFgDIFh8WFh8WFh8WFh8WFh8WFh8AAAAAAMBkAAAArwETAAHAA8AFwAAADIWFAYiJjQSMhYUBiImNBIyFhQGIiY0Aeh8WFh8WFh8WFh8WFh8WFh8WARMWHxYWHz%2ByFh8WFh8%2FshYfFhYfAAAAAMAZABkBEwETAAPAB8ALwAAEyEyFh0BFAYjISImPQE0NhMhMhYdARQGIyEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2fQO2Cg8PCvxKCg8PCgO2Cg8PCvxKCg8PCgO2Cg8PCvxKCg8PBEwPCpYKDw8KlgoP%2FnAPCpYKDw8KlgoP%2FnAPCpYKDw8KlgoPAAAABAAAAAAEsASwAA8AHwAvADMAAAEhMhYVERQGIyEiJjURNDYFISIGFREUFjMhMjY1ETQmBSEyFhURFAYjISImNRE0NhcVITUBXgH0ory7o%2F4Mpbm5Asv9qCk7OykCWCk7O%2F2xAfQVHR0V%2FgwVHR1HAZAEsLuj%2FgylubmlAfSlucg7Kf2oKTs7KQJYKTtkHRX%2B1BUdHRUBLBUdZMjIAAAAAAEAZABkBLAETAA7AAATITIWFAYrARUzMhYUBisBFTMyFhQGKwEVMzIWFAYjISImNDY7ATUjIiY0NjsBNSMiJjQ2OwE1IyImNDaWA%2BgVHR0VMjIVHR0VMjIVHR0VMjIVHR0V%2FBgVHR0VMjIVHR0VMjIVHR0VMjIVHR0ETB0qHcgdKh3IHSodyB0qHR0qHcgdKh3IHSodyB0qHQAAAAYBLAAFA%2BgEowAHAA0AEwAZAB8AKgAAAR4BBgcuATYBMhYVIiYlFAYjNDYBMhYVIiYlFAYjNDYDFRQGIiY9ARYzMgKKVz8%2FV1c%2FP%2F75fLB8sAK8sHyw%2FcB8sHywArywfLCwHSodKAMRBKNDsrJCQrKy%2FsCwfLB8fLB8sP7UsHywfHywfLD%2B05AVHR0VjgQAAAH%2FtQDIBJQDgQBCAAABNzYXAR4BBw4BKwEyFRQOBCsBIhE0NyYiBxYVECsBIi4DNTQzIyImJyY2NwE2HwEeAQ4BLwEHIScHBi4BNgLpRRkUASoLCAYFGg8IAQQNGyc%2FKZK4ChRUFQu4jjBJJxkHAgcPGQYGCAsBKhQaTBQVCiMUM7YDe7YsFCMKFgNuEwYS%2FtkLHw8OEw0dNkY4MhwBIBgXBAQYF%2F7gKjxTQyMNEw4PHwoBKBIHEwUjKBYGDMHBDAUWKCMAAAAAAgAAAAAEsASwACUAQwAAASM0LgUrAREUFh8BFSE1Mj4DNREjIg4FFSMRIQEjNC4DKwERFBYXMxUjNTI1ESMiDgMVIzUhBLAyCAsZEyYYGcgyGRn%2BcAQOIhoWyBkYJhMZCwgyA%2Bj9RBkIChgQEWQZDQzIMmQREBgKCBkB9AOEFSAVDggDAfyuFhkBAmRkAQUJFQ4DUgEDCA4VIBUBLP0SDxMKBQH%2BVwsNATIyGQGpAQUKEw%2BWAAAAAAMAAAAABEwErgAdACAAMAAAATUiJy4BLwEBIwEGBw4BDwEVITUiJj8BIRcWBiMVARsBARUUBiMhIiY9ATQ2MyEyFgPoGR4OFgUE%2Ft9F%2FtQSFQkfCwsBETE7EkUBJT0NISf%2B7IZ5AbEdFfwYFR0dFQPoFR0BLDIgDiIKCwLr%2FQ4jFQkTBQUyMisusKYiQTIBhwFW%2Fqr942QVHR0VZBUdHQADAAAAAASwBLAADwBHAEoAABMhMhYVERQGIyEiJjURNDYFIyIHAQYHBgcGHQEUFjMhMjY9ATQmIyInJj8BIRcWBwYjIgYdARQWMyEyNj0BNCYnIicmJyMBJhMjEzIETBUdHRX7tBUdHQJGRg0F%2FtUREhImDAsJAREIDAwINxAKCj8BCjkLEQwYCAwMCAE5CAwLCBEZGQ8B%2FuAFDsVnBLAdFfu0FR0dFQRMFR1SDP0PIBMSEAUNMggMDAgyCAwXDhmjmR8YEQwIMggMDAgyBwwBGRskAuwM%2FgUBCAAABAAAAAAEsASwAAMAEwAjACcAAAEhNSEFITIWFREUBiMhIiY1ETQ2KQEyFhURFAYjISImNRE0NhcRIREEsPtQBLD7ggGQFR0dFf5wFR0dAm0BkBUdHRX%2BcBUdHUcBLARMZMgdFfx8FR0dFQOEFR0dFf5wFR0dFQGQFR1k%2FtQBLAAEAAAAAASwBLAADwAfACMAJwAAEyEyFhURFAYjISImNRE0NgEhMhYVERQGIyEiJjURNDYXESEREyE1ITIBkBUdHRX%2BcBUdHQJtAZAVHR0V%2FnAVHR1HASzI%2B1AEsASwHRX8fBUdHRUDhBUd%2FgwdFf5wFR0dFQGQFR1k%2FtQBLP2oZAAAAAACAAAAZASwA%2BgAJwArAAATITIWFREzNTQ2MyEyFh0BMxUjFRQGIyEiJj0BIxEUBiMhIiY1ETQ2AREhETIBkBUdZB0VAZAVHWRkHRX%2BcBUdZB0V%2FnAVHR0CnwEsA%2BgdFf6ilhUdHRWWZJYVHR0Vlv6iFR0dFQMgFR3%2B1P7UASwAAAQAAAAABLAEsAADABMAFwAnAAAzIxEzFyEyFhURFAYjISImNRE0NhcRIREBITIWFREUBiMhIiY1ETQ2ZGRklgGQFR0dFf5wFR0dRwEs%2FqIDhBUdHRX8fBUdHQSwZB0V%2FnAVHR0VAZAVHWT%2B1AEs%2FgwdFf5wFR0dFQGQFR0AAAAAAgBkAAAETASwACcAKwAAATMyFhURFAYrARUhMhYVERQGIyEiJjURNDYzITUjIiY1ETQ2OwE1MwcRIRECWJYVHR0VlgHCFR0dFfx8FR0dFQFelhUdHRWWZMgBLARMHRX%2BcBUdZB0V%2FnAVHR0VAZAVHWQdFQGQFR1kyP7UASwAAAAEAAAAAASwBLAAAwATABcAJwAAISMRMwUhMhYVERQGIyEiJjURNDYXESERASEyFhURFAYjISImNRE0NgSwZGT9dgGQFR0dFf5wFR0dRwEs%2FK4DhBUdHRX8fBUdHQSwZB0V%2FnAVHR0VAZAVHWT%2B1AEs%2FgwdFf5wFR0dFQGQFR0AAAEBLAAwA28EgAAPAAAJAQYjIiY1ETQ2MzIXARYUA2H%2BEhcSDhAQDhIXAe4OAjX%2BEhcbGQPoGRsX%2FhIOKgAAAAABAUEAMgOEBH4ACwAACQE2FhURFAYnASY0AU8B7h0qKh3%2BEg4CewHuHREp%2FBgpER0B7g4qAAAAAAEAMgFBBH4DhAALAAATITIWBwEGIicBJjZkA%2BgpER3%2BEg4qDv4SHREDhCod%2FhIODgHuHSoAAAAAAQAyASwEfgNvAAsAAAkBFgYjISImNwE2MgJ7Ae4dESn8GCkRHQHuDioDYf4SHSoqHQHuDgAAAAACAAgAAASwBCgABgAKAAABFQE1LQE1ASE1IQK8%2FUwBnf5jBKj84AMgAuW2%2Fr3dwcHd%2B9jIAAAAAAIAAABkBLAEsAALADEAAAEjFTMVIREzNSM1IQEzND4FOwERFAYPARUhNSIuAzURMzIeBRUzESEEsMjI%2FtTIyAEs%2B1AyCAsZEyYYGWQyGRkBkAQOIhoWZBkYJhMZCwgy%2FOADhGRkASxkZP4MFSAVDggDAf3aFhkBAmRkAQUJFQ4CJgEDCA4VIBUBLAAAAgAAAAAETAPoACUAMQAAASM0LgUrAREUFh8BFSE1Mj4DNREjIg4FFSMRIQEjFTMVIREzNSM1IQMgMggLGRMmGBlkMhkZ%2FnAEDiIaFmQZGCYTGQsIMgMgASzIyP7UyMgBLAK8FSAVDggDAf3aFhkCAWRkAQUJFQ4CJgEDCA4VIBUBLPzgZGQBLGRkAAABAMgAZgNyBEoAEgAAATMyFgcJARYGKwEiJwEmNDcBNgK9oBAKDP4wAdAMChCgDQr%2BKQcHAdcKBEoWDP4w%2FjAMFgkB1wgUCAHXCQAAAQE%2BAGYD6ARKABIAAAEzMhcBFhQHAQYrASImNwkBJjYBU6ANCgHXBwf%2BKQoNoBAKDAHQ%2FjAMCgRKCf4pCBQI%2FikJFgwB0AHQDBYAAAEAZgDIBEoDcgASAAAAFh0BFAcBBiInASY9ATQ2FwkBBDQWCf4pCBQI%2FikJFgwB0AHQA3cKEKANCv4pBwcB1woNoBAKDP4wAdAAAAABAGYBPgRKA%2BgAEgAACQEWHQEUBicJAQYmPQE0NwE2MgJqAdcJFgz%2BMP4wDBYJAdcIFAPh%2FikKDaAQCgwB0P4wDAoQoA0KAdcHAAAAAgDZ%2F%2FkEPQSwAAUAOgAAARQGIzQ2BTMyFh8BNjc%2BAh4EBgcOBgcGIiYjIgYiJy4DLwEuAT4EHgEXJyY2A%2BiwfLD%2BVmQVJgdPBQsiKFAzRyorDwURAQQSFyozTSwNOkkLDkc3EDlfNyYHBw8GDyUqPjdGMR%2BTDA0EsHywfLDIHBPCAQIGBwcFDx81S21DBxlLR1xKQhEFBQcHGWt0bCQjP2hJNyATBwMGBcASGAAAAAACAMgAFQOEBLAAFgAaAAATITIWFREUBisBEQcGJjURIyImNRE0NhcVITX6AlgVHR0Vlv8TGpYVHR2rASwEsB0V%2FnAVHf4MsgkQFQKKHRUBkBUdZGRkAAAAAgDIABkETASwAA4AEgAAEyEyFhURBRElIREjETQ2ARU3NfoC7ic9%2FUQCWP1EZB8BDWQEsFEs%2FFt1A7Z9%2FBgEARc0%2FV1kFGQAAQAAAAECTW%2FDBF9fDzz1AB8EsAAAAADQdnOXAAAAANB2c5f%2FUf%2BcBdwFFAAAAAgAAgAAAAAAAAABAAAFFP%2BFAA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%3D%29%20format%28%27truetype%27%29%2Curl%28data%3Aimage%2Fsvg%2Bxml%3Bbase64%2CPD94bWwgdmVyc2lvbj0iMS4wIiBzdGFuZGFsb25lPSJubyI%2FPgo8IURPQ1RZUEUgc3ZnIFBVQkxJQyAiLS8vVzNDLy9EVEQgU1ZHIDEuMS8vRU4iICJodHRwOi8vd3d3LnczLm9yZy9HcmFwaGljcy9TVkcvMS4xL0RURC9zdmcxMS5kdGQiID4KPHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPgo8bWV0YWRhdGE%2BPC9tZXRhZGF0YT4KPGRlZnM%2BCjxmb250IGlkPSJnbHlwaGljb25zX2hhbGZsaW5nc3JlZ3VsYXIiIGhvcml6LWFkdi14PSIxMjAwIiA%2BCjxmb250LWZhY2UgdW5pdHMtcGVyLWVtPSIxMjAwIiBhc2NlbnQ9Ijk2MCIgZGVzY2VudD0iLTI0MCIgLz4KPG1pc3NpbmctZ2x5cGggaG9yaXotYWR2LXg9IjUwMCIgLz4KPGdseXBoIGhvcml6LWFkdi14PSIwIiAvPgo8Z2x5cGggaG9yaXotYWR2LXg9IjQwMCIgLz4KPGdseXBoIHVuaWNvZGU9IiAiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDAzOyIgaG9yaXotYWR2LXg9IjEzMDAiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDA0OyIgaG9yaXotYWR2LXg9IjQzMyIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeDIwMDU7IiBob3Jpei1hZHYteD0iMzI1IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAwNjsiIGhvcml6LWFkdi14PSIyMTYiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDA3OyIgaG9yaXotYWR2LXg9IjIxNiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeDIwMDg7IiBob3Jpei1hZHYteD0iMTYyIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAwOTsiIGhvcml6LWFkdi14PSIyNjAiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDBhOyIgaG9yaXotYWR2LXg9IjcyIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAyZjsiIGhvcml6LWFkdi14PSIyNjAiIC8%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3gyNmZhOyIgZD0iTTc3NCAxMTkzLjVxMTYgLTkuNSAyMC41IC0yN3QtNS41IC0zMy41bC0xMzYgLTE4N2w0NjcgLTc0NmgzMHEyMCAwIDM1IC0xOC41dDE1IC0zOS41di00MmgtMTIwMHY0MnEwIDIxIDE1IDM5LjV0MzUgMTguNWgzMGw0NjggNzQ2bC0xMzUgMTgzcS0xMCAxNiAtNS41IDM0dDIwLjUgMjh0MzQgNS41dDI4IC0yMC41bDExMSAtMTQ4bDExMiAxNTBxOSAxNiAyNyAyMC41dDM0IC01ek02MDAgMjAwaDM3N2wtMTgyIDExMmwtMTk1IDUzNHYtNjQ2eiAiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDI0OyIgZD0iTTEzMDAgMGgtNTM4bC00MSA0MDBoLTI0MmwtNDEgLTQwMGgtNTM4bDQzMSAxMjAwaDIwOWwtMjEgLTMwMGgxNjJsLTIwIDMwMGgyMDh6TTUxNSA4MDBsLTI3IC0zMDBoMjI0bC0yNyAzMDBoLTE3MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDI1OyIgZD0iTTU1MCAxMjAwaDIwMHEyMSAwIDM1LjUgLTE0LjV0MTQuNSAtMzUuNXYtNDUwaDE5MXEyMCAwIDI1LjUgLTExLjV0LTcuNSAtMjcuNWwtMzI3IC00MDBxLTEzIC0xNiAtMzIgLTE2dC0zMiAxNmwtMzI3IDQwMHEtMTMgMTYgLTcuNSAyNy41dDI1LjUgMTEuNWgxOTF2NDUwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNXpNMTEyNSA0MDBoNTBxMTAgMCAxNy41IC03LjV0Ny41IC0xNy41di0zNTBxMCAtMTAgLTcuNSAtMTcuNXQtMTcuNSAtNy41IGgtMTA1MHEtMTAgMCAtMTcuNSA3LjV0LTcuNSAxNy41djM1MHEwIDEwIDcuNSAxNy41dDE3LjUgNy41aDUwcTEwIDAgMTcuNSAtNy41dDcuNSAtMTcuNXYtMTc1aDkwMHYxNzVxMCAxMCA3LjUgMTcuNXQxNy41IDcuNXoiIC8%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%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%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%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%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDQyOyIgZD0iTTUwMCAxMjAwbDY4MiAtNjgycTggLTggOCAtMTh0LTggLTE4bC00NjQgLTQ2NHEtOCAtOCAtMTggLTh0LTE4IDhsLTY4MiA2ODJsMSA0NzVxMCAxMCA3LjUgMTcuNXQxNy41IDcuNWg0NzR6TTgwMCAxMjAwbDY4MiAtNjgycTggLTggOCAtMTh0LTggLTE4bC00NjQgLTQ2NHEtOCAtOCAtMTggLTh0LTE4IDhsLTU2IDU2bDQyNCA0MjZsLTcwMCA3MDBoMTUwek0zMTkuNSAxMDI0LjVxLTI5LjUgMjkuNSAtNzEgMjkuNXQtNzEgLTI5LjUgdC0yOS41IC03MS41dDI5LjUgLTcxLjV0NzEgLTI5LjV0NzEgMjkuNXQyOS41IDcxLjV0LTI5LjUgNzEuNXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDQzOyIgZD0iTTMwMCAxMjAwaDgyNXE3NSAwIDc1IC03NXYtOTAwcTAgLTI1IC0xOCAtNDNsLTY0IC02NHEtOCAtOCAtMTMgLTUuNXQtNSAxMi41djk1MHEwIDEwIC03LjUgMTcuNXQtMTcuNSA3LjVoLTcwMHEtMjUgMCAtNDMgLTE4bC02NCAtNjRxLTggLTggLTUuNSAtMTN0MTIuNSAtNWg3MDBxMTAgMCAxNy41IC03LjV0Ny41IC0xNy41di05NTBxMCAtMTAgLTcuNSAtMTcuNXQtMTcuNSAtNy41aC04NTBxLTEwIDAgLTE3LjUgNy41dC03LjUgMTcuNXY5NzUgcTAgMjUgMTggNDNsMTM5IDEzOXExOCAxOCA0MyAxOHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDQ4OyIgZD0iTTc1MyA2NDFxNSAtMSAxNC41IC00LjV0MzYgLTE1LjV0NTAuNSAtMjYuNXQ1My41IC00MHQ1MC41IC01NC41dDM1LjUgLTcwdDE0LjUgLTg3cTAgLTY3IC0yNy41IC0xMjUuNXQtNzEuNSAtOTcuNXQtOTguNSAtNjYuNXQtMTA4LjUgLTQwLjV0LTEwMiAtMTNoLTUwMHY4OXE0MSA3IDcwLjUgMzIuNXQyOS41IDY1LjV2ODI3cTAgMjQgLTAuNSAzNHQtMy41IDI0dC04LjUgMTkuNXQtMTcgMTMuNXQtMjggMTIuNXQtNDIuNSAxMS41djcxIGw0NzEgLTFxNTcgMCAxMTUuNSAtMjAuNXQxMDggLTU3dDgwLjUgLTk0dDMxIC0xMjQuNXEwIC01MSAtMTUuNSAtOTYuNXQtMzggLTc0LjV0LTQ1IC01MC41dC0zOC41IC0zMC41ek00MDAgNzAwaDEzOXE3OCAwIDEzMC41IDQ4LjV0NTIuNSAxMjIuNXEwIDQxIC04LjUgNzAuNXQtMjkuNSA1NS41dC02Mi41IDM5LjV0LTEwMy41IDEzLjVoLTExOHYtMzUwek00MDAgMjAwaDIxNnE4MCAwIDEyMSA1MC41dDQxIDEzMC41cTAgOTAgLTYyLjUgMTU0LjUgdC0xNTYuNSA2NC41aC0xNTl2LTQwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDQ5OyIgZD0iTTg3NyAxMjAwbDIgLTU3cS04MyAtMTkgLTExNiAtNDUuNXQtNDAgLTY2LjVsLTEzMiAtODM5cS05IC00OSAxMyAtNjl0OTYgLTI2di05N2gtNTAwdjk3cTE4NiAxNiAyMDAgOThsMTczIDgzMnEzIDE3IDMgMzB0LTEuNSAyMi41dC05IDE3LjV0LTEzLjUgMTIuNXQtMjEuNSAxMHQtMjYgOC41dC0zMy41IDEwcS0xMyAzIC0xOSA1djU3aDQyNXoiIC8%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%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDY5OyIgZD0iTTI1MCAxMTAwaDEwMHEyMSAwIDM1LjUgLTE0LjV0MTQuNSAtMzUuNXYtNDM4bDQ2NCA0NTNxMTUgMTQgMjUuNSAxMHQxMC41IC0yNXYtMTAwMHEwIC0yMSAtMTAuNSAtMjV0LTI1LjUgMTBsLTQ2NCA0NTN2LTQzOHEwIC0yMSAtMTQuNSAtMzUuNXQtMzUuNSAtMTQuNWgtMTAwcS0yMSAwIC0zNS41IDE0LjV0LTE0LjUgMzUuNXYxMDAwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDcwOyIgZD0iTTUwIDExMDBoMTAwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41di00MzhsNDY0IDQ1M3ExNSAxNCAyNS41IDEwdDEwLjUgLTI1di00MzhsNDY0IDQ1M3ExNSAxNCAyNS41IDEwdDEwLjUgLTI1di0xMDAwcTAgLTIxIC0xMC41IC0yNXQtMjUuNSAxMGwtNDY0IDQ1M3YtNDM4cTAgLTIxIC0xMC41IC0yNXQtMjUuNSAxMGwtNDY0IDQ1M3YtNDM4cTAgLTIxIC0xNC41IC0zNS41dC0zNS41IC0xNC41aC0xMDBxLTIxIDAgLTM1LjUgMTQuNSB0LTE0LjUgMzUuNXYxMDAwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDcxOyIgZD0iTTEyMDAgMTA1MHYtMTAwMHEwIC0yMSAtMTAuNSAtMjV0LTI1LjUgMTBsLTQ2NCA0NTN2LTQzOHEwIC0yMSAtMTAuNSAtMjV0LTI1LjUgMTBsLTQ5MiA0ODBxLTE1IDE0IC0xNSAzNXQxNSAzNWw0OTIgNDgwcTE1IDE0IDI1LjUgMTB0MTAuNSAtMjV2LTQzOGw0NjQgNDUzcTE1IDE0IDI1LjUgMTB0MTAuNSAtMjV6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA3MjsiIGQ9Ik0yNDMgMTA3NGw4MTQgLTQ5OHExOCAtMTEgMTggLTI2dC0xOCAtMjZsLTgxNCAtNDk4cS0xOCAtMTEgLTMwLjUgLTR0LTEyLjUgMjh2MTAwMHEwIDIxIDEyLjUgMjh0MzAuNSAtNHoiIC8%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDc5OyIgZD0iTTg4NSA5MDBsLTM1MiAtMzUzbDM1MiAtMzUzbC0xOTcgLTE5OGwtNTUyIDU1Mmw1NTIgNTUweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUwODA7IiBkPSJNMTA2NCA1NDdsLTU1MSAtNTUxbC0xOTggMTk4bDM1MyAzNTNsLTM1MyAzNTNsMTk4IDE5OHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDgzOyIgZD0iTTYwMCAxMTc3cTExNyAwIDIyNCAtNDUuNXQxODQuNSAtMTIzdDEyMyAtMTg0LjV0NDUuNSAtMjI0dC00NS41IC0yMjR0LTEyMyAtMTg0LjV0LTE4NC41IC0xMjN0LTIyNCAtNDUuNXQtMjI0IDQ1LjV0LTE4NC41IDEyM3QtMTIzIDE4NC41dC00NS41IDIyNHQ0NS41IDIyNHQxMjMgMTg0LjV0MTg0LjUgMTIzdDIyNCA0NS41ek03NDEuNSA5MTNxLTEyLjUgMCAtMjEuNSAtOWwtMTIwIC0xMjBsLTEyMCAxMjBxLTkgOSAtMjEuNSA5IHQtMjEuNSAtOWwtMTQxIC0xNDFxLTkgLTkgLTkgLTIxLjV0OSAtMjEuNWwxMjAgLTEyMGwtMTIwIC0xMjBxLTkgLTkgLTkgLTIxLjV0OSAtMjEuNWwxNDEgLTE0MXE5IC05IDIxLjUgLTl0MjEuNSA5bDEyMCAxMjBsMTIwIC0xMjBxOSAtOSAyMS41IC05dDIxLjUgOWwxNDEgMTQxcTkgOSA5IDIxLjV0LTkgMjEuNWwtMTIwIDEyMGwxMjAgMTIwcTkgOSA5IDIxLjV0LTkgMjEuNWwtMTQxIDE0MXEtOSA5IC0yMS41IDl6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA4NDsiIGQ9Ik02MDAgMTE3N3ExMTcgMCAyMjQgLTQ1LjV0MTg0LjUgLTEyM3QxMjMgLTE4NC41dDQ1LjUgLTIyNHQtNDUuNSAtMjI0dC0xMjMgLTE4NC41dC0xODQuNSAtMTIzdC0yMjQgLTQ1LjV0LTIyNCA0NS41dC0xODQuNSAxMjN0LTEyMyAxODQuNXQtNDUuNSAyMjR0NDUuNSAyMjR0MTIzIDE4NC41dDE4NC41IDEyM3QyMjQgNDUuNXpNNTQ2IDYyM2wtODQgODVxLTcgNyAtMTcuNSA3dC0xOC41IC03bC0xMzkgLTEzOXEtNyAtOCAtNyAtMTh0NyAtMTggbDI0MiAtMjQxcTcgLTggMTcuNSAtOHQxNy41IDhsMzc1IDM3NXE3IDcgNyAxNy41dC03IDE4LjVsLTEzOSAxMzlxLTcgNyAtMTcuNSA3dC0xNy41IC03eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUwODU7IiBkPSJNNjAwIDExNzdxMTE3IDAgMjI0IC00NS41dDE4NC41IC0xMjN0MTIzIC0xODQuNXQ0NS41IC0yMjR0LTQ1LjUgLTIyNHQtMTIzIC0xODQuNXQtMTg0LjUgLTEyM3QtMjI0IC00NS41dC0yMjQgNDUuNXQtMTg0LjUgMTIzdC0xMjMgMTg0LjV0LTQ1LjUgMjI0dDQ1LjUgMjI0dDEyMyAxODQuNXQxODQuNSAxMjN0MjI0IDQ1LjV6TTU4OCA5NDFxLTI5IDAgLTU5IC01LjV0LTYzIC0yMC41dC01OCAtMzguNXQtNDEuNSAtNjN0LTE2LjUgLTg5LjUgcTAgLTI1IDIwIC0yNWgxMzFxMzAgLTUgMzUgMTFxNiAyMCAyMC41IDI4dDQ1LjUgOHEyMCAwIDMxLjUgLTEwLjV0MTEuNSAtMjguNXEwIC0yMyAtNyAtMzR0LTI2IC0xOHEtMSAwIC0xMy41IC00dC0xOS41IC03LjV0LTIwIC0xMC41dC0yMiAtMTd0LTE4LjUgLTI0dC0xNS41IC0zNXQtOCAtNDZxLTEgLTggNS41IC0xNi41dDIwLjUgLTguNWgxNzNxNyAwIDIyIDh0MzUgMjh0MzcuNSA0OHQyOS41IDc0dDEyIDEwMHEwIDQ3IC0xNyA4MyB0LTQyLjUgNTd0LTU5LjUgMzQuNXQtNjQgMTh0LTU5IDQuNXpNNjc1IDQwMGgtMTUwcS0xMCAwIC0xNy41IC03LjV0LTcuNSAtMTcuNXYtMTUwcTAgLTEwIDcuNSAtMTcuNXQxNy41IC03LjVoMTUwcTEwIDAgMTcuNSA3LjV0Ny41IDE3LjV2MTUwcTAgMTAgLTcuNSAxNy41dC0xNy41IDcuNXoiIC8%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDk0OyIgZD0iTTU1MCAxMjAwaDIwMHEyMSAwIDM1LjUgLTE0LjV0MTQuNSAtMzUuNXYtNTUwaDI5MXEyMSAwIDI2IC0xMS41dC04IC0yNy41bC00MjcgLTUyMnEtMTMgLTE2IC0zMiAtMTZ0LTMyIDE2bC00MjcgNTIycS0xMyAxNiAtOCAyNy41dDI2IDExLjVoMjkxdjU1MHEwIDIxIDE0LjUgMzUuNXQzNS41IDE0LjV6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5NTsiIGQ9Ik02MzkgMTEwOWw1MjIgLTQyN3ExNiAtMTMgMTYgLTMydC0xNiAtMzJsLTUyMiAtNDI3cS0xNiAtMTMgLTI3LjUgLTh0LTExLjUgMjZ2MjkxcS05NCAtMiAtMTgyIC0yMHQtMTcwLjUgLTUydC0xNDcgLTkyLjV0LTEwMC41IC0xMzUuNXE1IDEwNSAyNyAxOTMuNXQ2Ny41IDE2N3QxMTMgMTM1dDE2NyA5MS41dDIyNS41IDQydjI2MnEwIDIxIDExLjUgMjZ0MjcuNSAtOHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDk2OyIgZD0iTTg1MCAxMjAwaDMwMHEyMSAwIDM1LjUgLTE0LjV0MTQuNSAtMzUuNXYtMzAwcTAgLTIxIC0xMC41IC0yNXQtMjQuNSAxMGwtOTQgOTRsLTI0OSAtMjQ5cS04IC03IC0xOCAtN3QtMTggN2wtMTA2IDEwNnEtNyA4IC03IDE4dDcgMThsMjQ5IDI0OWwtOTQgOTRxLTE0IDE0IC0xMCAyNC41dDI1IDEwLjV6TTM1MCAwaC0zMDBxLTIxIDAgLTM1LjUgMTQuNXQtMTQuNSAzNS41djMwMHEwIDIxIDEwLjUgMjV0MjQuNSAtMTBsOTQgLTk0bDI0OSAyNDkgcTggNyAxOCA3dDE4IC03bDEwNiAtMTA2cTcgLTggNyAtMTh0LTcgLTE4bC0yNDkgLTI0OWw5NCAtOTRxMTQgLTE0IDEwIC0yNC41dC0yNSAtMTAuNXoiIC8%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%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%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%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%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%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%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%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%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%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%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%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%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%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%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%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTYyOyIgZD0iTTc5MyAxMTgybDkgLTlxOCAtMTAgNSAtMjdxLTMgLTExIC03OSAtMjI1LjV0LTc4IC0yMjEuNWwzMDAgMXEyNCAwIDMyLjUgLTE3LjV0LTUuNSAtMzUuNXEtMSAwIC0xMzMuNSAtMTU1dC0yNjcgLTMxMi41dC0xMzguNSAtMTYyLjVxLTEyIC0xNSAtMjYgLTE1aC05bC05IDhxLTkgMTEgLTQgMzJxMiA5IDQyIDEyMy41dDc5IDIyNC41bDM5IDExMGgtMzAycS0yMyAwIC0zMSAxOXEtMTAgMjEgNiA0MXE3NSA4NiAyMDkuNSAyMzcuNSB0MjI4IDI1N3Q5OC41IDExMS41cTkgMTYgMjUgMTZoOXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTYzOyIgZD0iTTM1MCAxMTAwaDQwMHEyMSAwIDM1LjUgLTE0LjV0MTQuNSAtMzUuNXYtMTAwcTAgLTIxIC0xNC41IC0zNS41dC0zNS41IC0xNC41aC00NTBxLTQxIDAgLTcwLjUgLTI5LjV0LTI5LjUgLTcwLjV2LTUwMHEwIC00MSAyOS41IC03MC41dDcwLjUgLTI5LjVoNDUwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41di0xMDBxMCAtMjEgLTE0LjUgLTM1LjV0LTM1LjUgLTE0LjVoLTQwMHEtMTY1IDAgLTI1Ny41IDkyLjV0LTkyLjUgMjU3LjV2NDAwIHEwIDE2NSA5Mi41IDI1Ny41dDI1Ny41IDkyLjV6TTkzOCA4NjdsMzI0IC0yODRxMTYgLTE0IDE2IC0zM3QtMTYgLTMzbC0zMjQgLTI4NHEtMTYgLTE0IC0yNyAtOXQtMTEgMjZ2MTUwaC0yNTBxLTIxIDAgLTM1LjUgMTQuNXQtMTQuNSAzNS41djIwMHEwIDIxIDE0LjUgMzUuNXQzNS41IDE0LjVoMjUwdjE1MHEwIDIxIDExIDI2dDI3IC05eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxNjQ7IiBkPSJNNzUwIDEyMDBoNDAwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41di00MDBxMCAtMjEgLTEwLjUgLTI1dC0yNC41IDEwbC0xMDkgMTA5bC0zMTIgLTMxMnEtMTUgLTE1IC0zNS41IC0xNXQtMzUuNSAxNWwtMTQxIDE0MXEtMTUgMTUgLTE1IDM1LjV0MTUgMzUuNWwzMTIgMzEybC0xMDkgMTA5cS0xNCAxNCAtMTAgMjQuNXQyNSAxMC41ek00NTYgOTAwaC0xNTZxLTQxIDAgLTcwLjUgLTI5LjV0LTI5LjUgLTcwLjV2LTUwMCBxMCAtNDEgMjkuNSAtNzAuNXQ3MC41IC0yOS41aDUwMHE0MSAwIDcwLjUgMjkuNXQyOS41IDcwLjV2MTQ4bDIwMCAyMDB2LTI5OHEwIC0xNjUgLTkzLjUgLTI1Ny41dC0yNTYuNSAtOTIuNWgtNDAwcS0xNjUgMCAtMjU3LjUgOTIuNXQtOTIuNSAyNTcuNXY0MDBxMCAxNjUgOTIuNSAyNTcuNXQyNTcuNSA5Mi41aDMwMHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTY5OyIgZD0iTTEzNSAxMDIzbDE0MiAxNDJxMTQgMTQgMzUgMTR0MzUgLTE0bDc3IC03N2wtMjEyIC0yMTJsLTc3IDc2cS0xNCAxNSAtMTQgMzZ0MTQgMzV6TTY1NSA4NTVsMjEwIDIxMHExNCAxNCAyNC41IDEwdDEwLjUgLTI1bC0yIC01OTlxLTEgLTIwIC0xNS41IC0zNXQtMzUuNSAtMTVsLTU5NyAtMXEtMjEgMCAtMjUgMTAuNXQxMCAyNC41bDIwOCAyMDhsLTE1NCAxNTVsMjEyIDIxMnpNNTAgMzAwaDEwMDBxMjEgMCAzNS41IC0xNC41dDE0LjUgLTM1LjUgdi0yNTBoLTExMDB2MjUwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNXpNOTAwIDIwMHYtNTBoMTAwdjUwaC0xMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE3MDsiIGQ9Ik0zNTAgMTIwMGw1OTkgLTJxMjAgLTEgMzUgLTE1LjV0MTUgLTM1LjVsMSAtNTk3cTAgLTIxIC0xMC41IC0yNXQtMjQuNSAxMGwtMjA4IDIwOGwtMTU1IC0xNTRsLTIxMiAyMTJsMTU1IDE1NGwtMjEwIDIxMHEtMTQgMTQgLTEwIDI0LjV0MjUgMTAuNXpNNTI0IDUxMmwtNzYgLTc3cS0xNSAtMTQgLTM2IC0xNHQtMzUgMTRsLTE0MiAxNDJxLTE0IDE0IC0xNCAzNXQxNCAzNWw3NyA3N3pNNTAgMzAwaDEwMDBxMjEgMCAzNS41IC0xNC41IHQxNC41IC0zNS41di0yNTBoLTExMDB2MjUwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNXpNOTAwIDIwMHYtNTBoMTAwdjUwaC0xMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE3MTsiIGQ9Ik0xMjAwIDEwM2wtNDgzIDI3NmwtMzE0IC0zOTl2NDIzaC0zOTlsMTE5NiA3OTZ2LTEwOTZ6TTQ4MyA0MjR2LTIzMGw2ODMgOTUzeiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxNzI7IiBkPSJNMTEwMCAxMDAwdi04NTBxMCAtMjEgLTE0LjUgLTM1LjV0LTM1LjUgLTE0LjVoLTE1MHY0MDBoLTcwMHYtNDAwaC0xNTBxLTIxIDAgLTM1LjUgMTQuNXQtMTQuNSAzNS41djEwMDBxMCAyMCAxNC41IDM1dDM1LjUgMTVoMjUwdi0zMDBoNTAwdjMwMGgxMDB6TTcwMCAxMDAwaC0xMDB2MjAwaDEwMHYtMjAweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxNzM7IiBkPSJNMTEwMCAxMDAwbC0yIC0xNDlsLTI5OSAtMjk5bC05NSA5NXEtOSA5IC0yMS41IDl0LTIxLjUgLTlsLTE0OSAtMTQ3aC0zMTJ2LTQwMGgtMTUwcS0yMSAwIC0zNS41IDE0LjV0LTE0LjUgMzUuNXYxMDAwcTAgMjAgMTQuNSAzNXQzNS41IDE1aDI1MHYtMzAwaDUwMHYzMDBoMTAwek03MDAgMTAwMGgtMTAwdjIwMGgxMDB2LTIwMHpNMTEzMiA2MzhsMTA2IC0xMDZxNyAtNyA3IC0xNy41dC03IC0xNy41bC00MjAgLTQyMXEtOCAtNyAtMTggLTcgdC0xOCA3bC0yMDIgMjAzcS04IDcgLTggMTcuNXQ4IDE3LjVsMTA2IDEwNnE3IDggMTcuNSA4dDE3LjUgLThsNzkgLTc5bDI5NyAyOTdxNyA3IDE3LjUgN3QxNy41IC03eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxNzQ7IiBkPSJNMTEwMCAxMDAwdi0yNjlsLTEwMyAtMTAzbC0xMzQgMTM0cS0xNSAxNSAtMzMuNSAxNi41dC0zNC41IC0xMi41bC0yNjYgLTI2NmgtMzI5di00MDBoLTE1MHEtMjEgMCAtMzUuNSAxNC41dC0xNC41IDM1LjV2MTAwMHEwIDIwIDE0LjUgMzV0MzUuNSAxNWgyNTB2LTMwMGg1MDB2MzAwaDEwMHpNNzAwIDEwMDBoLTEwMHYyMDBoMTAwdi0yMDB6TTEyMDIgNTcybDcwIC03MHExNSAtMTUgMTUgLTM1LjV0LTE1IC0zNS41bC0xMzEgLTEzMSBsMTMxIC0xMzFxMTUgLTE1IDE1IC0zNS41dC0xNSAtMzUuNWwtNzAgLTcwcS0xNSAtMTUgLTM1LjUgLTE1dC0zNS41IDE1bC0xMzEgMTMxbC0xMzEgLTEzMXEtMTUgLTE1IC0zNS41IC0xNXQtMzUuNSAxNWwtNzAgNzBxLTE1IDE1IC0xNSAzNS41dDE1IDM1LjVsMTMxIDEzMWwtMTMxIDEzMXEtMTUgMTUgLTE1IDM1LjV0MTUgMzUuNWw3MCA3MHExNSAxNSAzNS41IDE1dDM1LjUgLTE1bDEzMSAtMTMxbDEzMSAxMzFxMTUgMTUgMzUuNSAxNSB0MzUuNSAtMTV6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE3NTsiIGQ9Ik0xMTAwIDEwMDB2LTMwMGgtMzUwcS0yMSAwIC0zNS41IC0xNC41dC0xNC41IC0zNS41di0xNTBoLTUwMHYtNDAwaC0xNTBxLTIxIDAgLTM1LjUgMTQuNXQtMTQuNSAzNS41djEwMDBxMCAyMCAxNC41IDM1dDM1LjUgMTVoMjUwdi0zMDBoNTAwdjMwMGgxMDB6TTcwMCAxMDAwaC0xMDB2MjAwaDEwMHYtMjAwek04NTAgNjAwaDEwMHEyMSAwIDM1LjUgLTE0LjV0MTQuNSAtMzUuNXYtMjUwaDE1MHEyMSAwIDI1IC0xMC41dC0xMCAtMjQuNSBsLTIzMCAtMjMwcS0xNCAtMTQgLTM1IC0xNHQtMzUgMTRsLTIzMCAyMzBxLTE0IDE0IC0xMCAyNC41dDI1IDEwLjVoMTUwdjI1MHEwIDIxIDE0LjUgMzUuNXQzNS41IDE0LjV6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE3NjsiIGQ9Ik0xMTAwIDEwMDB2LTQwMGwtMTY1IDE2NXEtMTQgMTUgLTM1IDE1dC0zNSAtMTVsLTI2MyAtMjY1aC00MDJ2LTQwMGgtMTUwcS0yMSAwIC0zNS41IDE0LjV0LTE0LjUgMzUuNXYxMDAwcTAgMjAgMTQuNSAzNXQzNS41IDE1aDI1MHYtMzAwaDUwMHYzMDBoMTAwek03MDAgMTAwMGgtMTAwdjIwMGgxMDB2LTIwMHpNOTM1IDU2NWwyMzAgLTIyOXExNCAtMTUgMTAgLTI1LjV0LTI1IC0xMC41aC0xNTB2LTI1MHEwIC0yMCAtMTQuNSAtMzUgdC0zNS41IC0xNWgtMTAwcS0yMSAwIC0zNS41IDE1dC0xNC41IDM1djI1MGgtMTUwcS0yMSAwIC0yNSAxMC41dDEwIDI1LjVsMjMwIDIyOXExNCAxNSAzNSAxNXQzNSAtMTV6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE3NzsiIGQ9Ik01MCAxMTAwaDExMDBxMjEgMCAzNS41IC0xNC41dDE0LjUgLTM1LjV2LTE1MGgtMTIwMHYxNTBxMCAyMSAxNC41IDM1LjV0MzUuNSAxNC41ek0xMjAwIDgwMHYtNTUwcTAgLTIxIC0xNC41IC0zNS41dC0zNS41IC0xNC41aC0xMTAwcS0yMSAwIC0zNS41IDE0LjV0LTE0LjUgMzUuNXY1NTBoMTIwMHpNMTAwIDUwMHYtMjAwaDQwMHYyMDBoLTQwMHoiIC8%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTgyOyIgZD0iTTE3IDEwMDdsMTYyIDE2MnExNyAxNyA0MCAxNHQzNyAtMjJsMTM5IC0xOTRxMTQgLTIwIDExIC00NC41dC0yMCAtNDEuNWwtMTE5IC0xMThxMTAyIC0xNDIgMjI4IC0yNjh0MjY3IC0yMjdsMTE5IDExOHExNyAxNyA0Mi41IDE5dDQ0LjUgLTEybDE5MiAtMTM2cTE5IC0xNCAyMi41IC0zNy41dC0xMy41IC00MC41bC0xNjMgLTE2MnEtMyAtMSAtOS41IC0xdC0yOS41IDJ0LTQ3LjUgNnQtNjIuNSAxNC41dC03Ny41IDI2LjV0LTkwIDQyLjUgdC0xMDEuNSA2MHQtMTExIDgzdC0xMTkgMTA4LjVxLTc0IDc0IC0xMzMuNSAxNTAuNXQtOTQuNSAxMzguNXQtNjAgMTE5LjV0LTM0LjUgMTAwdC0xNSA3NC41dC00LjUgNDh6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE4MzsiIGQ9Ik02MDAgMTEwMHE5MiAwIDE3NSAtMTAuNXQxNDEuNSAtMjd0MTA4LjUgLTM2LjV0ODEuNSAtNDB0NTMuNSAtMzd0MzEgLTI3bDkgLTEwdi0yMDBxMCAtMjEgLTE0LjUgLTMzdC0zNC41IC05bC0yMDIgMzRxLTIwIDMgLTM0LjUgMjB0LTE0LjUgMzh2MTQ2cS0xNDEgMjQgLTMwMCAyNHQtMzAwIC0yNHYtMTQ2cTAgLTIxIC0xNC41IC0zOHQtMzQuNSAtMjBsLTIwMiAtMzRxLTIwIC0zIC0zNC41IDl0LTE0LjUgMzN2MjAwcTMgNCA5LjUgMTAuNSB0MzEgMjZ0NTQgMzcuNXQ4MC41IDM5LjV0MTA5IDM3LjV0MTQxIDI2LjV0MTc1IDEwLjV6TTYwMCA3OTVxNTYgMCA5NyAtOS41dDYwIC0yMy41dDMwIC0yOHQxMiAtMjRsMSAtMTB2LTUwbDM2NSAtMzAzcTE0IC0xNSAyNC41IC00MHQxMC41IC00NXYtMjEycTAgLTIxIC0xNC41IC0zNS41dC0zNS41IC0xNC41aC0xMTAwcS0yMSAwIC0zNS41IDE0LjV0LTE0LjUgMzUuNXYyMTJxMCAyMCAxMC41IDQ1dDI0LjUgNDBsMzY1IDMwM3Y1MCBxMCA0IDEgMTAuNXQxMiAyM3QzMCAyOXQ2MCAyMi41dDk3IDEweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxODQ7IiBkPSJNMTEwMCA3MDBsLTIwMCAtMjAwaC02MDBsLTIwMCAyMDB2NTAwaDIwMHYtMjAwaDIwMHYyMDBoMjAwdi0yMDBoMjAwdjIwMGgyMDB2LTUwMHpNMjUwIDQwMGg3MDBxMjEgMCAzNS41IC0xNC41dDE0LjUgLTM1LjV0LTE0LjUgLTM1LjV0LTM1LjUgLTE0LjVoLTEybDEzNyAtMTAwaC05NTBsMTM3IDEwMGgtMTJxLTIxIDAgLTM1LjUgMTQuNXQtMTQuNSAzNS41dDE0LjUgMzUuNXQzNS41IDE0LjV6TTUwIDEwMGgxMTAwcTIxIDAgMzUuNSAtMTQuNSB0MTQuNSAtMzUuNXYtNTBoLTEyMDB2NTBxMCAyMSAxNC41IDM1LjV0MzUuNSAxNC41eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxODU7IiBkPSJNNzAwIDExMDBoLTEwMHEtNDEgMCAtNzAuNSAtMjkuNXQtMjkuNSAtNzAuNXYtMTAwMGgzMDB2MTAwMHEwIDQxIC0yOS41IDcwLjV0LTcwLjUgMjkuNXpNMTEwMCA4MDBoLTEwMHEtNDEgMCAtNzAuNSAtMjkuNXQtMjkuNSAtNzAuNXYtNzAwaDMwMHY3MDBxMCA0MSAtMjkuNSA3MC41dC03MC41IDI5LjV6TTQwMCAwaC0zMDB2NDAwcTAgNDEgMjkuNSA3MC41dDcwLjUgMjkuNWgxMDBxNDEgMCA3MC41IC0yOS41dDI5LjUgLTcwLjV2LTQwMHogIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE4NjsiIGQ9Ik0yMDAgMTEwMGg3MDBxMTI0IDAgMjEyIC04OHQ4OCAtMjEydi01MDBxMCAtMTI0IC04OCAtMjEydC0yMTIgLTg4aC03MDBxLTEyNCAwIC0yMTIgODh0LTg4IDIxMnY1MDBxMCAxMjQgODggMjEydDIxMiA4OHpNMTAwIDkwMHYtNzAwaDkwMHY3MDBoLTkwMHpNNTAwIDcwMGgtMjAwdi0xMDBoMjAwdi0zMDBoLTMwMHYxMDBoMjAwdjEwMGgtMjAwdjMwMGgzMDB2LTEwMHpNOTAwIDcwMHYtMzAwbC0xMDAgLTEwMGgtMjAwdjUwMGgyMDB6IE03MDAgNzAwdi0zMDBoMTAwdjMwMGgtMTAweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxODc7IiBkPSJNMjAwIDExMDBoNzAwcTEyNCAwIDIxMiAtODh0ODggLTIxMnYtNTAwcTAgLTEyNCAtODggLTIxMnQtMjEyIC04OGgtNzAwcS0xMjQgMCAtMjEyIDg4dC04OCAyMTJ2NTAwcTAgMTI0IDg4IDIxMnQyMTIgODh6TTEwMCA5MDB2LTcwMGg5MDB2NzAwaC05MDB6TTUwMCAzMDBoLTEwMHYyMDBoLTEwMHYtMjAwaC0xMDB2NTAwaDEwMHYtMjAwaDEwMHYyMDBoMTAwdi01MDB6TTkwMCA3MDB2LTMwMGwtMTAwIC0xMDBoLTIwMHY1MDBoMjAweiBNNzAwIDcwMHYtMzAwaDEwMHYzMDBoLTEwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTg4OyIgZD0iTTIwMCAxMTAwaDcwMHExMjQgMCAyMTIgLTg4dDg4IC0yMTJ2LTUwMHEwIC0xMjQgLTg4IC0yMTJ0LTIxMiAtODhoLTcwMHEtMTI0IDAgLTIxMiA4OHQtODggMjEydjUwMHEwIDEyNCA4OCAyMTJ0MjEyIDg4ek0xMDAgOTAwdi03MDBoOTAwdjcwMGgtOTAwek01MDAgNzAwaC0yMDB2LTMwMGgyMDB2LTEwMGgtMzAwdjUwMGgzMDB2LTEwMHpNOTAwIDcwMGgtMjAwdi0zMDBoMjAwdi0xMDBoLTMwMHY1MDBoMzAwdi0xMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE4OTsiIGQ9Ik0yMDAgMTEwMGg3MDBxMTI0IDAgMjEyIC04OHQ4OCAtMjEydi01MDBxMCAtMTI0IC04OCAtMjEydC0yMTIgLTg4aC03MDBxLTEyNCAwIC0yMTIgODh0LTg4IDIxMnY1MDBxMCAxMjQgODggMjEydDIxMiA4OHpNMTAwIDkwMHYtNzAwaDkwMHY3MDBoLTkwMHpNNTAwIDQwMGwtMzAwIDE1MGwzMDAgMTUwdi0zMDB6TTkwMCA1NTBsLTMwMCAtMTUwdjMwMHoiIC8%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%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%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMjIxOyIgZD0iTTQ4MCAxMTY1bDY4MiAtNjgzcTMxIC0zMSAzMSAtNzUuNXQtMzEgLTc1LjVsLTEzMSAtMTMxaC00ODFsLTUxNyA1MThxLTMyIDMxIC0zMiA3NS41dDMyIDc1LjVsMjk1IDI5NnEzMSAzMSA3NS41IDMxdDc2LjUgLTMxek0xMDggNzk0bDM0MiAtMzQybDMwMyAzMDRsLTM0MSAzNDF6TTI1MCAxMDBoODAwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41di01MGgtOTAwdjUwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMjIzOyIgZD0iTTEwNTcgNjQ3bC0xODkgNTA2cS04IDE5IC0yNy41IDMzdC00MC41IDE0aC00MDBxLTIxIDAgLTQwLjUgLTE0dC0yNy41IC0zM2wtMTg5IC01MDZxLTggLTE5IDEuNSAtMzN0MzAuNSAtMTRoNjI1di0xNTBxMCAtMjEgMTQuNSAtMzUuNXQzNS41IC0xNC41dDM1LjUgMTQuNXQxNC41IDM1LjV2MTUwaDEyNXEyMSAwIDMwLjUgMTR0MS41IDMzek04OTcgMGgtNTk1djUwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNWg1MHY1MCBxMCAyMSAxNC41IDM1LjV0MzUuNSAxNC41aDQ4djMwMGgyMDB2LTMwMGg0N3EyMSAwIDM1LjUgLTE0LjV0MTQuNSAtMzUuNXYtNTBoNTBxMjEgMCAzNS41IC0xNC41dDE0LjUgLTM1LjV2LTUweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUyMjQ7IiBkPSJNOTAwIDgwMGgzMDB2LTU3NXEwIC0xMCAtNy41IC0xNy41dC0xNy41IC03LjVoLTM3NXY1OTFsLTMwMCAzMDB2ODRxMCAxMCA3LjUgMTcuNXQxNy41IDcuNWgzNzV2LTQwMHpNMTIwMCA5MDBoLTIwMHYyMDB6TTQwMCA2MDBoMzAwdi01NzVxMCAtMTAgLTcuNSAtMTcuNXQtMTcuNSAtNy41aC02NTBxLTEwIDAgLTE3LjUgNy41dC03LjUgMTcuNXY5NTBxMCAxMCA3LjUgMTcuNXQxNy41IDcuNWgzNzV2LTQwMHpNNzAwIDcwMGgtMjAwdjIwMHogIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTIyNTsiIGQ9Ik00ODQgMTA5NWgxOTVxNzUgMCAxNDYgLTMyLjV0MTI0IC04NnQ4OS41IC0xMjIuNXQ0OC41IC0xNDJxMTggLTE0IDM1IC0yMHEzMSAtMTAgNjQuNSA2LjV0NDMuNSA0OC41cTEwIDM0IC0xNSA3MXEtMTkgMjcgLTkgNDNxNSA4IDEyLjUgMTF0MTkgLTF0MjMuNSAtMTZxNDEgLTQ0IDM5IC0xMDVxLTMgLTYzIC00NiAtMTA2LjV0LTEwNCAtNDMuNWgtNjJxLTcgLTU1IC0zNSAtMTE3dC01NiAtMTAwbC0zOSAtMjM0cS0zIC0yMCAtMjAgLTM0LjUgdC0zOCAtMTQuNWgtMTAwcS0yMSAwIC0zMyAxNC41dC05IDM0LjVsMTIgNzBxLTQ5IC0xNCAtOTEgLTE0aC0xOTVxLTI0IDAgLTY1IDhsLTExIC02NHEtMyAtMjAgLTIwIC0zNC41dC0zOCAtMTQuNWgtMTAwcS0yMSAwIC0zMyAxNC41dC05IDM0LjVsMjYgMTU3cS04NCA3NCAtMTI4IDE3NWwtMTU5IDUzcS0xOSA3IC0zMyAyNnQtMTQgNDB2NTBxMCAyMSAxNC41IDM1LjV0MzUuNSAxNC41aDEyNHExMSA4NyA1NiAxNjZsLTExMSA5NSBxLTE2IDE0IC0xMi41IDIzLjV0MjQuNSA5LjVoMjAzcTExNiAxMDEgMjUwIDEwMXpNNjc1IDEwMDBoLTI1MHEtMTAgMCAtMTcuNSAtNy41dC03LjUgLTE3LjV2LTUwcTAgLTEwIDcuNSAtMTcuNXQxNy41IC03LjVoMjUwcTEwIDAgMTcuNSA3LjV0Ny41IDE3LjV2NTBxMCAxMCAtNy41IDE3LjV0LTE3LjUgNy41eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUyMjY7IiBkPSJNNjQxIDkwMGw0MjMgMjQ3cTE5IDggNDIgMi41dDM3IC0yMS41bDMyIC0zOHExNCAtMTUgMTIuNSAtMzZ0LTE3LjUgLTM0bC0xMzkgLTEyMGgtMzkwek01MCAxMTAwaDEwNnE2NyAwIDEwMyAtMTd0NjYgLTcxbDEwMiAtMjEyaDgyM3EyMSAwIDM1LjUgLTE0LjV0MTQuNSAtMzUuNXYtNTBxMCAtMjEgLTE0IC00MHQtMzMgLTI2bC03MzcgLTEzMnEtMjMgLTQgLTQwIDZ0LTI2IDI1cS00MiA2NyAtMTAwIDY3aC0zMDBxLTYyIDAgLTEwNiA0NCB0LTQ0IDEwNnYyMDBxMCA2MiA0NCAxMDZ0MTA2IDQ0ek0xNzMgOTI4aC04MHEtMTkgMCAtMjggLTE0dC05IC0zNXYtNTZxMCAtNTEgNDIgLTUxaDEzNHExNiAwIDIxLjUgOHQ1LjUgMjRxMCAxMSAtMTYgNDV0LTI3IDUxcS0xOCAyOCAtNDMgMjh6TTU1MCA3MjdxLTMyIDAgLTU0LjUgLTIyLjV0LTIyLjUgLTU0LjV0MjIuNSAtNTQuNXQ1NC41IC0yMi41dDU0LjUgMjIuNXQyMi41IDU0LjV0LTIyLjUgNTQuNXQtNTQuNSAyMi41ek0xMzAgMzg5IGwxNTIgMTMwcTE4IDE5IDM0IDI0dDMxIC0zLjV0MjQuNSAtMTcuNXQyNS41IC0yOHEyOCAtMzUgNTAuNSAtNTF0NDguNSAtMTNsNjMgNWw0OCAtMTc5cTEzIC02MSAtMy41IC05Ny41dC02Ny41IC03OS41bC04MCAtNjlxLTQ3IC00MCAtMTA5IC0zNS41dC0xMDMgNTEuNWwtMTMwIDE1MXEtNDAgNDcgLTM1LjUgMTA5LjV0NTEuNSAxMDIuNXpNMzgwIDM3N2wtMTAyIC04OHEtMzEgLTI3IDIgLTY1bDM3IC00M3ExMyAtMTUgMjcuNSAtMTkuNSB0MzEuNSA2LjVsNjEgNTNxMTkgMTYgMTQgNDlxLTIgMjAgLTEyIDU2dC0xNyA0NXEtMTEgMTIgLTE5IDE0dC0yMyAtOHoiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMjQyOyIgZD0iTTEwMDAgMzAwdjUwcS0yNSAwIC01NSAzMnEtMTQgMTQgLTI1IDMxdC0xNiAyN2wtNCAxMWwtMjg5IDc0N2gtNjlsLTMwMCAtNzU0cS0xOCAtMzUgLTM5IC01NnEtOSAtOSAtMjQuNSAtMTguNXQtMjYuNSAtMTQuNWwtMTEgLTV2LTUwaDI3M3Y1MHEtNDkgMCAtNzguNSAyMS41dC0xMS41IDY3LjVsNjkgMTc2aDI5M2w2MSAtMTY2cTEzIC0zNCAtMy41IC02Ni41dC01NS41IC0zMi41di01MGgzMTJ6TTQxMiA2OTFsMTM0IDM0MmwxMjEgLTM0MiBoLTI1NXpNMTEwMCAxNTB2LTEwMHEwIC0yMSAtMTQuNSAtMzUuNXQtMzUuNSAtMTQuNWgtMTAwMHEtMjEgMCAtMzUuNSAxNC41dC0xNC41IDM1LjV2MTAwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNWgxMDAwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUyNDM7IiBkPSJNNTAgMTIwMGgxMTAwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41di0xMTAwcTAgLTIxIC0xNC41IC0zNS41dC0zNS41IC0xNC41aC0xMTAwcS0yMSAwIC0zNS41IDE0LjV0LTE0LjUgMzUuNXYxMTAwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNXpNNjExIDExMThoLTcwcS0xMyAwIC0xOCAtMTJsLTI5OSAtNzUzcS0xNyAtMzIgLTM1IC01MXEtMTggLTE4IC01NiAtMzRxLTEyIC01IC0xMiAtMTh2LTUwcTAgLTggNS41IC0xNHQxNC41IC02IGgyNzNxOCAwIDE0IDZ0NiAxNHY1MHEwIDggLTYgMTR0LTE0IDZxLTU1IDAgLTcxIDIzcS0xMCAxNCAwIDM5bDYzIDE2M2gyNjZsNTcgLTE1M3ExMSAtMzEgLTYgLTU1cS0xMiAtMTcgLTM2IC0xN3EtOCAwIC0xNCAtNnQtNiAtMTR2LTUwcTAgLTggNiAtMTR0MTQgLTZoMzEzcTggMCAxNCA2dDYgMTR2NTBxMCA3IC01LjUgMTN0LTEzLjUgN3EtMTcgMCAtNDIgMjVxLTI1IDI3IC00MCA2M2gtMWwtMjg4IDc0OHEtNSAxMiAtMTkgMTJ6TTYzOSA2MTEgaC0xOTdsMTAzIDI2NHoiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMjUwOyIgZD0iTTg2NSA1NjVsLTQ5NCAtNDk0cS0yMyAtMjMgLTQxIC0yM3EtMTQgMCAtMjIgMTMuNXQtOCAzOC41djEwMDBxMCAyNSA4IDM4LjV0MjIgMTMuNXExOCAwIDQxIC0yM2w0OTQgLTQ5NHExNCAtMTQgMTQgLTM1dC0xNCAtMzV6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTI1MTsiIGQ9Ik0zMzUgNjM1bDQ5NCA0OTRxMjkgMjkgNTAgMjAuNXQyMSAtNDkuNXYtMTAwMHEwIC00MSAtMjEgLTQ5LjV0LTUwIDIwLjVsLTQ5NCA0OTRxLTE0IDE0IC0xNCAzNXQxNCAzNXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMjUyOyIgZD0iTTEwMCA5MDBoMTAwMHE0MSAwIDQ5LjUgLTIxdC0yMC41IC01MGwtNDk0IC00OTRxLTE0IC0xNCAtMzUgLTE0dC0zNSAxNGwtNDk0IDQ5NHEtMjkgMjkgLTIwLjUgNTB0NDkuNSAyMXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMjUzOyIgZD0iTTYzNSA4NjVsNDk0IC00OTRxMjkgLTI5IDIwLjUgLTUwdC00OS41IC0yMWgtMTAwMHEtNDEgMCAtNDkuNSAyMXQyMC41IDUwbDQ5NCA0OTRxMTQgMTQgMzUgMTR0MzUgLTE0eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUyNTQ7IiBkPSJNNzAwIDc0MXYtMTgybC02OTIgLTMyM3YyMjFsNDEzIDE5M2wtNDEzIDE5M3YyMjF6TTEyMDAgMGgtODAwdjIwMGg4MDB2LTIwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMjU1OyIgZD0iTTEyMDAgOTAwaC0yMDB2LTEwMGgyMDB2LTEwMGgtMzAwdjMwMGgyMDB2MTAwaC0yMDB2MTAwaDMwMHYtMzAwek0wIDcwMGg1MHEwIDIxIDQgMzd0OS41IDI2LjV0MTggMTcuNXQyMiAxMXQyOC41IDUuNXQzMSAydDM3IDAuNWgxMDB2LTU1MHEwIC0yMiAtMjUgLTM0LjV0LTUwIC0xMy41bC0yNSAtMnYtMTAwaDQwMHYxMDBxLTQgMCAtMTEgMC41dC0yNCAzdC0zMCA3dC0yNCAxNXQtMTEgMjQuNXY1NTBoMTAwcTI1IDAgMzcgLTAuNXQzMSAtMiB0MjguNSAtNS41dDIyIC0xMXQxOCAtMTcuNXQ5LjUgLTI2LjV0NCAtMzdoNTB2MzAwaC04MDB2LTMwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMjU2OyIgZD0iTTgwMCA3MDBoLTUwcTAgMjEgLTQgMzd0LTkuNSAyNi41dC0xOCAxNy41dC0yMiAxMXQtMjguNSA1LjV0LTMxIDJ0LTM3IDAuNWgtMTAwdi01NTBxMCAtMjIgMjUgLTM0LjV0NTAgLTE0LjVsMjUgLTF2LTEwMGgtNDAwdjEwMHE0IDAgMTEgMC41dDI0IDN0MzAgN3QyNCAxNXQxMSAyNC41djU1MGgtMTAwcS0yNSAwIC0zNyAtMC41dC0zMSAtMnQtMjguNSAtNS41dC0yMiAtMTF0LTE4IC0xNy41dC05LjU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;The text below is not a rigorous approach to the mathematical theory, nor is it a wholly systematic or comprehensive description of the topics covered. It is a selection of topics recommended by core instructors. These include mathematical concepts and procedures that will be encountered in your core courses, and instructors expect you to be familiar with them prior to the beginning of a course, i.e, they will not cover them in detail. Instead, use the content below as a reference as these topics arise and as a platform for more in-depth study. Please contact <a href="mailto:jonathan.emery@northwestern.edu" class="email">jonathan.emery@northwestern.edu</a> with suggestions for additional material to be included in this section.

;

;For those who have never seen the mathematics below or who are not comfortable with the material, further preparation may be necessary. Options for those students include: either a.) enroll in ES-APPM-311-1 and ES-APPM-311-2: Methods of Applied Mathematics and/or b.) utilizing the suggested resources for supplemental study.

; <div id="linear-algebra" class="section level2"> <h2>Linear Algebra</h2>

;Linear algebra is a branch of mathematics that is central to physical description in Materials Science as it concerns the description of vectors spaces and is used in solving systems of equations. Materials Science graduate students will encounter application of linear algebra in all core courses. The sections below outline basic linear algebra concepts.

; <div id="linear-systems" class="section level3"> <h3>Linear Systems</h3> </div> <div id="gauss-elimination-release-tbd" class="section level3"> <h3>Gauss Elimination (Release TBD)</h3> <div id="matrix-algebra-and-operations-release-tbd" class="section level4"> <h4>MATrix Algebra and Operations (Release TBD)</h4> </div> </div> <div id="linear-transformations-release-tbd" class="section level3"> <h3>Linear Transformations (Release TBD)</h3> </div> <div id="determinants-release-tbd" class="section level3"> <h3>Determinants (Release TBD)</h3> </div> <div id="eigenvalues-and-eigenvectors-release-tbd" class="section level3"> <h3>Eigenvalues and Eigenvectors (Release TBD)</h3> </div> <div id="linear-differential-equations-release-tbd" class="section level3"> <h3>Linear Differential Equations (Release TBD)</h3> <ol style="list-style-type: decimal"> <li>

;Linear Differential Operators

;</li> <li>

;Linear Differential Equations

;</li> </ol> </div> </div> <div id="subsec:Tensors" class="section level2"> <h2>Tensors (Release 1/2017)</h2>

;Tensors are mathematical objects that define relationships between scalars, vectors, matrices, and other tensors=. Tensors are represented as arrays of various dimensionality (defined by rank or order). The moniker “tensor” in general suggests a higher-rank array (most often $\geq$3 dimensions), but scalars, vectors, and matrices are also tensors.

;

;In the MSE graduate core, students will encounter tensors of various rank. In physical science, tensors characterize the properties of a physical system. Tensors are the de facto tool used to describe, for example, diffusion, nucleation and growth, states of stress and strain, Hamiltonians in quantum mechanics, and many, many, more physical phenomenon. Physical processes of interest to Materials Scientists take place in Euclidean 3-space (${\rm I\!R}^3$) are are well-described by tensor representations.

;

;We build up our description of the handling of tensors starting by separately describing rank-0, rank-1, rank-2, and rank-3 tensors. Tensors of lower ranks should be familiar — students will have encountered them previously as scalars (rank-0), vectors (rank-1), and matrices (rank-2). The term tensors typically denotes arrays of higher dimensionality (rank $\geq3$). Physical examples include the rank-2 <a href="https://en.wikipedia.org/wiki/Cauchy_stress_tensor">Cauchy stress tensor</a> which describes the stress state of a at a point within a material), the rank-3 piezoelectric tensor (which relates the dielectric polarization of a material to a stress state), and the rank-4 stiffness tensor (which relates strain state and stress state in a system that obeying Hooke’s law).

;

;Classifications of tensors by rank allows us to quickly identify the number of tensor components we will work with: a tensor of order $p$ has $N^p$ components, where $N$ is the dimensionality of space in which we are operating. In general, you will be operating in Eucledian 3-space, so the number of components of a tensor is defined as $3^p$.

;

;Scalars are considered tensors with order or rank of 0. Scalars represent physical quantities (often accompanied by a unit of measurement) that possess only a magnitude: e.g., temperature, mass, charge, and distance. Scalars are typically represented by Latin or Greek symbols and have $3^{0} = 1$ component.

;

;Vectors are tensors with a rank of 1. In symbolic notation, vectors are typically represented using lowercase bold or bold-italic symbols such as $\mathbf{u}$ or $\pmb{a}$. Bold typeface is not always amenable to handwriting, however, and so the a right arrow accent is employed: $\vec{u}$ or $\vec{a}$. Students are likely to encounter various conventions depending on their field of study.

;

;In ${\rm I\!R}^3$ a vector is defined by $3^{1} = 3$ components. In xyz Cartesian coordinates we utilize the Cartesian basis with 3 orthogonal unit vectors $\{\mathbf{e}_{\mathbf{x}}\text{, } \mathbf{e}_{\mathbf{y}}\text{, } \mathbf{e}_{\mathbf{z}}\}$. We define 3D vector $\mathbf{u}$ in this basis with the components ($u_x$, $u_y$, $u_z$), or equivalently ($u_1$, $u_2$, $u_3$). Often, we represent the vector $\mathbf{u}$ using the shorthand $u_i$, where the $i$ subscript denotes an index that ranges over the dimensionality of the system (1,2,3 for ${\rm I\!R}^3$, 1,2 for ${\rm I\!R}^2$).

;

;Vectors are often encountered in a bracketed vertical list to facilitate matrix operations. Using some of the notation defined above:

;

;\[\mathbf{u} = u_i = \begin{bmatrix} u_x \\ u_y \\ u_z \end{bmatrix} = \begin{bmatrix} u_1 \\ u_2 \\ u_3 \end{bmatrix} \label{eq:Vector}\]

;

;Matrices are tensors with a rank of 2. In ${\rm I\!R}^2$ a matrix has $2^{2} = 4$ components and in ${\rm I\!R}^3$ a matrix has $3^{2} = 9$ components. As with vectors, we will use the range convention when denoting a matrix, which now possesses two subscripts, $i$ and $j$. We use the example of the true stress, or <a href="https://en.wikipedia.org/wiki/Cauchy_stress_tensor">Cauchy stress tensor</a>, $\sigma_{ij}$:

;

;\[\sigma_{ij} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz}\\ \sigma_{yx} & \sigma_{yy} & \sigma_{yz}\\ \sigma_{zx} & \sigma_{zy} & \sigma_{zz}\\ \end{bmatrix}\]

;

;Where the diagonal represents the normal components of stress and the off-diagonal represents the shear components of the stress. In this notation the first index denotes the row while the second denotes the column ($x = 1$, $y = 2$, $z = 3$).

;

;Tensors A rank-3 tensor in ${\rm I\!R}^3$ has $3^{3} = 27$ components and is represented in range notation using subscripts $i$, $j$, and $k$, e.g., $T_{ijk}$ . At rank-3 (and it is even worse in rank-4, requiring an array of rank-3 tensors) it begins to become difficult to represent clearly on paper. An example of a simple tensor — <a href="https://en.wikipedia.org/wiki/Levi-Civita_symbol#Three_dimensions_2">the rank-3 permutation tensor</a> — is shown in Fig. <a href="#fig:PermutationTensor" reference-type="ref" reference="fig:PermutationTensor">1</a>. You can also watch <a href="https://www.youtube.com/watch?v=f5liqUk0ZTw">this video</a> which helps with the visualization.

; <div class="figure"> <img src="data:image/png;base64,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" id="fig:PermutationTensor" alt /> The rank-3 permutation tensor, by Arian Kriesch. corrections made by Xmaster1123 and Luxo (Own work) [GFDL (<a href="http://www.gnu.org/copyleft/fdl.html" class="uri">http://www.gnu.org/copyleft/fdl.html</a>), CC-BY-SA-3.0 (<a href="http://creativecommons.org/licenses/by-sa/3.0/" class="uri">http://creativecommons.org/licenses/by-sa/3.0/</a>)

; </div>

;One can write the $i = 1,2,3$ matrices that stack to form this tensor as:

;

;\[\epsilon_{1jk}= \begin{bmatrix} 0 & 0 & 0\\ 0 & 0 & 1\\ 0 & -1 & 0 \end{bmatrix}\]

;

;\[\epsilon_{2jk}= \begin{bmatrix} 0 & 0 & -1\\ 0 & 0 & 0\\ 1 & 0 & 0 \end{bmatrix}\]

;

;\[\epsilon_{3jk}= \begin{bmatrix} 0 & 1 & 0\\ -1 & 0 & 0\\ 0 & 0 & 0 \end{bmatrix}\]

; </div> <div id="sec:SummationNotation" class="section level2"> <h2>Summation Notation</h2>

;Often, it is useful to simplify notation when manipulating tensor equations. To do this, we utilize Einstein summation notation, or simply summation notation. This notation says that if an index is repeated twice (and only twice) in a single term we assume summation over the range of the repeated subscript. The simplest example of this is the representation of the trace of a matrix:

;

;\[tr(\sigma) = \underbrace{\sigma_{kk}}_{\substack{\text{summation} \\ \text{notation}}} = \sum_{k}^{3}\sigma_{kk} = \sigma_{11}+\sigma_{22}+\sigma_{33}\]

;

;In $\sigma_{kk}$ the index $k$ is repeated, and this means that we assume summation of the index over the range of the subscript (in this case, 1-3 as we are working with the stress tensor).

; <div class="displayquote">

;Example 1:This comes in very useful when representing matrix multiplication. Let’s say we have an ($M \times N$) matrix, $\mathbf{A} = a_{ij}$ and an $R \times P$ matrix $\mathbf{B} = b_{ij}$. We know from linear algebra that the matrix product $\mathbf{AB}$ is defined only when $R = N$, and the result is a ($M \times P$) matrix, $\mathbf{C} = c_{ij}$. Here’s an example with a ($2 \times 3$) matrix times a ($3 \times 2$) in conventional representation:

;

;\[\begin{aligned} \mathbf{AB} = \begin{bmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ \end{bmatrix} &\begin{bmatrix} b_{11} & b_{12}\\ b_{21} & b_{22}\\ b_{31} & b_{32}\\ \end{bmatrix} = \\ &\begin{bmatrix} a_{11}b_{11} + a_{12}b_{21} + a_{13}b_{31} & a_{11}b_{12} + a_{12}b_{22} + a_{13}b_{32}\\ a_{21}b_{11} + a_{22}b_{21} + a_{23}b_{31} & a_{21}b_{12} + a_{22}b_{22} + a_{23}b_{32}\\ \end{bmatrix} =c_{ij}\end{aligned}\]

;

;Here, we can use summation notation to greatly simply the expression. The components of the matrix $c_{ij}$ are $c_{11}$, $c_{12}$, $c_{21}$, and $c_{22}$ and are defined:

;

;\[\begin{aligned} c_{11} = a_{11}b_{11} + a_{12}b_{21} + a_{13}b_{31}\\ c_{12} = a_{11}b_{12} + a_{12}b_{22} + a_{13}b_{32}\\ c_{21} = a_{21}b_{11} + a_{22}b_{21} + a_{23}b_{31}\\ c_{22} = a_{21}b_{12} + a_{22}b_{22} + a_{23}b_{32}\\\end{aligned}\]

;

;These terms can all be represented using the following expression:

;

;\[c_{ij} = \sum_{k=1}^{3} a_{ik}b_{kj} = a_{i1}b_{1j} + a_{i2}b_{2j} + a_{i3}b_{3j}\]

;

;So, in general for any matrix product:

;

;\[c_{ij} = \sum_{k=1}^{N} a_{ik}b_{kj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{iN}b_{Nj} \label{eq:MatrixMultiply}\]

;

;Or, by dropping the summation symbol and fully utilizing the summation convention:

;

;\[c_{ij} = a_{ik}b_{ki}\]

;

;Note that the term $c_{ij}$ has no repeated subscript - there is no summation implied here. It is simply a matrix. Summation is implied in the $a_{ik}b_{kj}$ term because of the repeated index $k$, often called the dummy index.

; </div> <div class="displayquote">

;Example 2: Another example is a $3 \times 3$ matrix multiplied by a (3 ) column vector:

;

;\[\begin{bmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\ \end{bmatrix} \begin{bmatrix} b_1\\ b_2\\ b_3\\ \end{bmatrix} = \begin{bmatrix} a_{11}b_{1} + a_{12}b_{2} + a_{13}b_{3} \\ a_{21}b_{1} + a_{22}b_{2} + a_{23}b_{3}\\ a_{31}b_{1} + a_{32}b_{2} + a_{33}b_{3}\\ \end{bmatrix} = a_{ij}b_{j}\]

; </div> <table> <caption>Uses of summation notation that students may encounter in the graduate core. Bracketed symbols indicate $3 \times 3$ matrices (tab:SummationIdentities)</caption> <colgroup> <col width="33%" /> <col width="40%" /> <col width="25%" /> </colgroup> <thead> <tr class="header"> <th>Summation convention</th> <th>Non-summation Convention</th> <th>Full expression</th> </tr> </thead> <tbody> <tr class="odd"> <td>$\lambda = a_ib_i$</td> <td>$\lambda = \sum\limits_{i=1}^{3}a_ib_i$</td> <td>$\lambda = a_1b_1 + a_2b_2 + a_3b_3$</td> </tr> <tr class="even"> <td>$c_i = S_{ik}x_k$</td> <td>$c_i = \sum\limits_{i=1}^{3}S_{ik}x_k$</td> <td>$c_i = \begin{cases} c_1 = S_{11}x_1 + S_{12}x_2 + S_{13}x_3\\ c_2 = S_{21}x_1 + S_{22}x_2 + S_{23}x_3\\ c_3 = S_{31}x_1 + S_{32}x_2 + S_{33}x_3\\ \end{cases}$</td> </tr> <tr class="odd"> <td>$\lambda = S_{ij}S_{ij}$</td> <td>$\lambda = \sum\limits_{j=1}^{3}\sum\limits_{i=1}^{3}S_{ij}S_{ij}$</td> <td>$\lambda = S_{11}S_{11} + S_{12}S_{12} + \cdots + S_{32}S_{32}+S_{33}S_{33}$</td> </tr> <tr class="even"> <td>$C_{ij} = A_{ik}B_{kj}$</td> <td>$\lambda = \sum\limits_{k=1}^{3}A_{ik}B_{kj}$</td> <td>$\big[C\big]=\big[A\big]\big[B\big]$</td> </tr> <tr class="odd"> <td>$C_{ij} = A_{ki}B_{kj}$</td> <td>$\lambda = \sum\limits_{k=1}^{3}A_{ki}B_{kj}$</td> <td>$\big[C\big]=\big[A\big]^{T}\big[B\big]$</td> </tr> </tbody> </table>

;It will be important to learn how to read such summation notation, so if you see a repeated dummy index (often represented with $k$ or $l$, see Cai and Nix, 2.1.3), that you can recognize the notation.

;

;Some useful representations of summation notation are shown in Table <a href="#tab:SummationIdentities" reference-type="ref" reference="tab:SummationIdentities">1</a>:

;

;In future releases I will add summation notation for the Kronecker delta, $\delta_{ij}$, the LeviCivita $\epsilon$, the dot product, and the cross product, determinants, the <code>del</code> operator ($\nabla$), and others as references.

; </div> <div id="coordinate-transformations-release-12017" class="section level2"> <h2>Coordinate Transformations (Release 1/2017)</h2>

;Cartesian coordinates are not the only coordinate system that MSE graduate students will encounter in the core. Cylindrical coordinates and spherical coordinates are both useful in, for example, describing stress and strain fields around dislocations and vacancies.

;

;Cartesian coordinates, as mentioned in Sec. <a href="#subsec:Tensors" reference-type="ref" reference="subsec:Tensors">1.2</a> utilize an orthogonal basis set and are often the easiest to use when describing and visualizing vector operations and physical laws. The rank-2 stress tensor (introduced in Sec. <a href="#subsec:Tensors" reference-type="ref" reference="subsec:Tensors">1.2</a>) is represented using the following $3 \times 3 \times 3$ matrix and is shown in Fig. <a href="#fig:StressTensors" reference-type="ref" reference="fig:StressTensors">2</a>:

; <div class="figure"> <img src="data:image/png;base64,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" id="fig:StressTensors" alt /> Stress tensors for (a.) Cartesian, (b.) cylindrical, and (c.) spherical coordinate systems. From Nix and Cai.

; </div>

;\[\sigma_{ij} \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz}\\ \sigma_{yx} & \sigma_{yy} & \sigma_{yz}\\ \sigma_{zx} & \sigma_{zy} & \sigma_{zz}\\ \end{bmatrix} \label{eq:CartesianStressTensor}\]

;

;Cylindrical coordinates are also an orthogonal coordinate system defined in Fig. <a href="#fig:StressTensors" reference-type="ref" reference="fig:StressTensors">2</a>(b). The stress tensor in this coordinate system is defined by the cylinderical components $r$, $\theta$, and $z$. Here, $r$ is the distance from the $z$-axis to the point. $\theta$ is the angle between the reference direction (we use the $x$-direction) and the vector that points from the origin to the coordinates projected onto the $xy$ plane. $z$ is the distance from the point’s coordinates projected onto $xy$ plane and the point itself. The stress tensor is represented as

;

;\[\sigma_{ij}= \begin{bmatrix} \sigma_{rr} & \sigma_{r \theta} & \sigma_{r z}\\ \sigma_{\theta r} & \sigma_{\theta\theta} & \sigma_{\theta z}\\ \sigma_{z r} & \sigma_{z \theta} & \sigma_{zz}\\ \end{bmatrix} \label{eq:CylindricalStressTensor}\]

;

;Spherical coordinates are defined by $r$, $\theta$ and $\phi$. Here $r$ is the radial distance from the origin to the point. $\theta$ is the polar angle, or the angle between the $x$-axis and the point, projected onto the $xy$ plane. $\phi$ is the azimuthal angle, or the angle between the $z$-axis and the vector pointing from the origin to the point. The stress tensor is

;

;\[\sigma_{ij}= \begin{bmatrix} \sigma_{rr} & \sigma_{r \theta} & \sigma_{r \phi}\\ \sigma_{\theta r} & \sigma_{\theta\theta} & \sigma_{\theta \phi}\\ \sigma_{\phi r} & \sigma_{\phi \theta} & \sigma_{\phi\phi}\\ \end{bmatrix} \label{eq:SphericalStressTensor}\]

;

;We will often want to transform tensor values from one coordinate system to another in ${\rm I\!R}^3$. As an example, we will convert the stress state from a cylinderical coordinate system to a Cartesian coordinate system. This transformation from stress state in the original coordinate system ($\sigma_{kl } = \sigma_{kl}^{r \theta z}$) to the new coordinate system ($\sigma_{ij }^{'} = \sigma_{ij}^{xyz}$) is performed using the following relationship:

;

;\[\sigma_{ij}' = Q_{ik}Q_{jk}\sigma_{kl} \label{eq:GeneralTransform}\]

;

;Where the summation notation (Sec. <a href="#sec:SummationNotation" reference-type="ref" reference="sec:SummationNotation">1.3</a>) is implicit. In our example the indices $kl$ indicate the original cylindrical coordinate system ($r$, $\theta$, $z$) and the indices $ij$ indicate the new coordinate system ($x$, $y$, $z$).

;

;Note that Eq. <a href="#eq:GeneralTransform" reference-type="ref" reference="eq:GeneralTransform">\[eq:GeneralTransform\]</a> can be written in matrix form as:

;

;\[\sigma = Q \cdot \sigma \cdot Q^{T}\]

;

;The $Q$ matrix is defined the dot products between the unit vectors in the coordinate systems of interest. In simplified 2D transformation from polar to Cartesian, there is no $z$ component in either coordinate system and terms with those indices can be dropped.

;

;\[Q_{ik} \equiv (\hat{e}_{i}^{xy} \cdot \hat{e}_k^{r \theta}) = \begin{bmatrix} (\hat{e}_{x} \cdot \hat{e}_{r}) & (\hat{e}_{x} \cdot \hat{e}_{\theta})\\ (\hat{e}_{y} \cdot \hat{e}_{r}) & (\hat{e}_{y} \cdot \hat{e}_{\theta})\\ \end{bmatrix}\\ %Q_{jl} \equiv (\hat{e}_{j}^{xyz} \cdot \hat{e}_l^{r \theta z}) \\\]

;

;where $\hat{e}_{r}$ and $\hat{e}_{\theta}$ is related geometrically to $\hat{e}_{x}$ and $\hat{e}_{y}$:

;

;\[\begin{bmatrix} \hat{e}_{r} = \hat{e}_{x} \cos(\theta) + \hat{e}_{y} \sin(\theta)\\ \hat{e}_{\theta} = -\hat{e}_{x} \sin(\theta) + \hat{e}_{y} \cos(\theta)\\ \end{bmatrix}\\ %Q_{jl} \equiv (\hat{e}_{j}^{xyz} \cdot \hat{e}_l^{r \theta z}) \\\]

;

;And therefore:

;

;\[\begin{aligned} Q_{ik} &\equiv (\hat{e}_{i}^{xy} \cdot \hat{e}_k^{r \theta}) = \begin{bmatrix} (\hat{e}_{x} \cdot \hat{e}_{r}) & (\hat{e}_{x} \cdot \hat{e}_{\theta})\\ (\hat{e}_{y} \cdot \hat{e}_{r}) & (\hat{e}_{y} \cdot \hat{e}_{\theta})\\ \end{bmatrix} = \begin{bmatrix} Q_{xr} & Q_{x\theta}\\ Q_{yr} & Q_{y\theta}\\ \end{bmatrix} \\ &= \begin{bmatrix} \left(\hat{e}_{x} \cdot \left[\hat{e}_{x} \cos(\theta) + \hat{e}_{y} \sin(\theta)\right]\right) & \left(\hat{e}_{x} \cdot \left[-\hat{e}_{x} \sin(\theta) + \hat{e}_{y} \cos(\theta)\right]\right)\\ \left(\hat{e}_{y} \cdot \left[\hat{e}_{x} \cos(\theta) + \hat{e}_{y} \sin(\theta)\right]\right) & \left(\hat{e}_{y} \cdot \left[-\hat{e}_{x} \sin(\theta) + \hat{e}_{y} \cos(\theta)\right]\right) \end{bmatrix}\\ &= \begin{bmatrix} \cos(\theta) & -\sin(\theta)\\ \sin(\theta) & \cos(\theta) \end{bmatrix}\end{aligned}\]

;

;So, to convert the stress tensor in polar coordinates ($\sigma_{kl}^{r\theta}$) to Cartesian ($\sigma_{ij}^{xy}$), we take the triple dot-product:

;

;\[\begin{aligned} \sigma' &= Q \cdot \sigma \cdot Q^{T} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy}\\ \sigma_{yx} & \sigma_{yy} \end{bmatrix}= \begin{bmatrix} \cos(\theta) & -\sin(\theta)\\ \sin(\theta) & con(\theta) \end{bmatrix}\cdot \begin{bmatrix} \sigma_{rr} & \sigma_{r\theta}\\ \sigma_{\theta r} & \sigma_{\theta \theta} \end{bmatrix} \cdot \begin{bmatrix} \cos(\theta) & \sin(\theta)\\ -\sin(\theta) & con(\theta) \end{bmatrix} \end{aligned}\]

;

;Completing the math yields:

;

;\[\begin{aligned} \sigma_{xx} &= \cos(\theta) \left[\sigma_{rr} \cos(\theta) - \sigma_{\theta r} \sin( \theta)\right] - \sin(\theta)\left[\sigma_{r\theta}\cos(\theta) - \sigma_{\theta\theta}\sin(\theta)\right]\\ \sigma_{xy} &= \sin(\theta) \left[\sigma_{rr} \cos(\theta) - \sigma_{\theta r} \sin( \theta)\right] + \cos(\theta)\left[\sigma_{r\theta}\cos(\theta) - \sigma_{\theta\theta}\sin(\theta)\right]\\ \sigma_{yx} &= \cos(\theta) \left[\sigma_{\theta r} \cos(\theta) + \sigma_{rr} \sin( \theta)\right] - \sin(\theta)\left[\sigma_{\theta \theta}\cos(\theta) + \sigma_{r\theta}\sin(\theta)\right]\\ \sigma_{yy} &= \sin(\theta) \left[\sigma_{\theta r} \cos(\theta) + \sigma_{rr} \sin( \theta)\right] + \cos(\theta)\left[\sigma_{\theta \theta}\cos(\theta) + \sigma_{r\theta}\sin(\theta)\right]\end{aligned}\]

;

;In as system with only one or two stress components these coordinate transformations simplify greatly. Remember, though, in ${\rm I\!R}^3$ there will be $N = 3^2$ components due to increased dimentionality.

; </div> <div id="calculus" class="section level2"> <h2>Calculus</h2>

;We assume that incoming graduate students have completed coursework in calculus including the basic calculation of derivatives, antiderivatives, definite integrals, series/sequences, and multivariate calculus. Below are outlined some more advanced calculus concepts that have specific physical relevance to concepts covered in the MSE core.

;

;Any college-level calculus text is suitable for supplemental study. The sections below on Total Differentials (Sec. <a href="#subsec:totdiff" reference-type="ref" reference="subsec:totdiff">1.5.1</a>) and Exact/Inexact Differentials (Sec. <a href="#subsec:eidiff" reference-type="ref" reference="subsec:eidiff">1.5.2</a>) were adapted from the course materials of Richard Fitzpatrick at UT-Austin (available <a href="http://farside.ph.utexas.edu/teaching/sm1/Thermal.pdf">here</a>).

; <div id="subsec:totdiff" class="section level3"> <h3>Total Differentials: (Release 11/2016)</h3>

;Encountered in: MAT<code>_</code>SCI 401

;

;When there exists an explicit function of several variables such as $f = f(x,y,t)$, which has $f$ has a total differential of form:

;

;\[\begin{aligned} \Diff{}{f} = \Big(\Partial{}{f}{t}\Big)_{x,y}\Diff{}{t} + \Big(\Partial{}{f}{x}\Big)_{t,y} \Diff{}{x} + \Big(\Partial{}{f}{y}\Big)_{t,x} \Diff{}{y} \end{aligned}\]

;

;Here, we do not assume that $f$ is constant with respect any of the arguments $(x\text{,}\, y\text{, or } t)$. This equation defines the differential change in the function $\Diff{}{f}$ and accounts for all interdependencies between $x$, $y$, and $t$. In general, the total differential can be defined as:

;

;\[\begin{aligned} \label{eq:TotDiff} \Diff{}{f} = \sum\limits_{i=1}^n \Big(\Partial{}{f}{x_i}\Big)_{x_{j\neq i}}\Diff{}{x_i}\end{aligned}\]

;

;total differential is important when working with thermodynamic systems which is described by thermodynamic parameters (e.g. $P$, $T$, $V$) which are not necessary independent. For example, the internal energy $U$ for some homogeneous system can be defined in terms of entropy $S$ and volume $V$; $U = U(S,V)$. According to Eq. <a href="#eq:TotDiff" reference-type="ref" reference="eq:TotDiff">\[eq:TotDiff\]</a>, the infinitesimal change in internal entropy is therefore: \[\begin{aligned} \Diff{}{U} = \Big(\Partial{}{U}{S}\Big)_{V}\Diff{}{S} + \Big(\Partial{}{U}{V}\Big)_{S} \Diff{}{V}\end{aligned}\]

; </div> <div id="subsec:eidiff" class="section level3"> <h3>Exact and Inexact Differentials (Release 11/2016)</h3>

;Encountered in: MAT<code>_</code>SCI 401

;

;Suppose we are assessing the infinitesimal change of some value: $\Diff{}{f}$, in which $\Diff{}{f}$ is a linear differential of the form: \[\begin{aligned} \Diff{}{f} = \sum\limits_{i=1}^m M_i(x_1,x_2,...x_m)\Diff{}{x_i}.\end{aligned}\] In thermodynamics we are often concerned with linear differentials of two independent variables such that \[\begin{aligned} \label{eq:LinearDiff} \Diff{}{f} = M(x,y) \Diff{}{x} + N(x,y) \Diff{}{y}.\end{aligned}\] An exact differential is one in which $\int{\Diff{}{z}}$ is path-independent. It can be shown (e.g. <a href="http://mathworld.wolfram.com/ExactDifferential.html">Wolfram Exact Differential</a>) that this means:

;

;\[\begin{aligned} \label{eq:ExactDiff} \Diff{}{f} = \Big(\Partial{}{f}{x}\Big)_{y} \Diff{}{x} + \Big(\Partial{}{f}{y}\Big)_{x} \Diff{}{y}. \end{aligned}\]

;

;Which means that

;

;\[\begin{aligned} \label{eq:ExactDiff2} \Big(\Partial{}{M}{y}\Big)_{x} = \Big(\Partial{}{N}{x}\Big)_{y}. \end{aligned}\]

;

;An inexact differential is one in which the equality defined in Eq. <a href="#eq:ExactDiff" reference-type="ref" reference="eq:ExactDiff">\[eq:ExactDiff\]</a> (and therefore Eq. <a href="#eq:ExactDiff2" reference-type="ref" reference="eq:ExactDiff2">\[eq:ExactDiff2\]</a>) is not necessary true. An inexact differential is typically denoted using bar notation to define the infinitesimal value: \[\begin{aligned} \text{\dj} f = \Big(\Partial{}{f}{x}\Big)_{y} \Diff{}{x} + \Big(\Partial{}{f}{y}\Big)_{x} \Diff{}{y}.\end{aligned}\] Two physical examples make this more clear:

; <div class="displayquote">

;Example 1: Imagine you are speaking with a classmate who recently traveled from from Chicago to Minneapolis. You know he is now in Minneapolis. Is it possible for you to know how much money he spent gas ($G$)? No, you can’t. $G$ is dependent on how your friend traveled to Minneapolis: his gas mileage, the cost of gas, and, of course, the route he took. $G$ cannot be known without understanding the details of the path, and is therefore not path independent. The differenitial of $G$ is therefore inexact: $G$.

;

;Now, what do we know about your friend’s distance, $D$, to Chicago? This value does not dependent on how he traveled, the only information you need to know is his location, now, in Minneapolis. His distance to Chicago, therefore is a state variable and $\Diff{}{D}$ is an exact differential.

; </div> <div class="displayquote">

;Example 2: Let’s reconsider a situation like that of Example 1 this within the purview of thermodynamics. Consider the internal energy $U$ of a closed system. To achieve an infinitesimal change in energy $\Diff{}{U}$, we provided a bit of work $\text{\dj}W$ or heat $\text{\dj}Q$: $\Diff{}{U} = \text{\dj}W + \text{\dj}Q$ <a href="#fn1" class="footnote-ref" id="fnref1">1</a>. The work performed and heat exchanged on the system is path-dependent — the total work done depends on how the work was performed or heat exchanged, and so $\text{\dj}W$ and $\text{\dj}Q$ are inexact.

; </div>

;It is sometimes useful to ask yourself about the nature of a variable to ascertain whether the differential is exact or inexact. That is, it makes sense to ask yourself: “what is the energy of the system?” or “what is the pressure of the system”? This often helps in the identification of a state variable. However, it does not make sense to ask yourself “what is the work of the system” or “what is the heat” of the system — these values depend on the process. Instead, you have to ask yourself: “what is the work done on the system along this path?” or “what is the heat exchanged during this process?”.

;

;Finally, there are different properties we encounter during the evaluation exact differential (such as the linear differential in Eq. <a href="#eq:LinearDiff" reference-type="ref" reference="eq:LinearDiff">\[eq:LinearDiff\]</a>), and inexact differentials (written as $\text{\dj}f = M'(x,y) \Diff{}{x} + N'(x,y) \Diff{}{y}$). The integral of an exact differential over a closed path is necessary zero: \[\begin{aligned} \oint\Diff{}{f} \equiv 0,\end{aligned}\] while the integral of an inexact differential over a closed path is not necessarily zero: \[\begin{aligned} \oint\text{\dj}f\underset{n}{\neq} 0.\end{aligned}\] where $\Big(\underset{n}{\neq}\Big)$ symbolizes “not necessarily equal to”. Indeed, when evaluating the inexact differential, it is important to consider the path. For example, the work performed a system going from a macrostate $s_i$ to a macrostate $s_2$ is defined by path $L_{1}$, then the total work performed is defined: \[\begin{aligned} W_{L_{1}} = \int\limits_{L_{1}} \text{\dj}W\end{aligned}\] If we took a different path, $L_{2}$, the total work performed by be different and \[\begin{aligned} W_{L_{1}} \underset{n}{\neq} W_{L_{2}}\end{aligned}\] A good illustration of a line integral over a scalar field is shown in the multimedia Fig. <a href="#fig:LineIntegral" reference-type="ref" reference="fig:LineIntegral">\[fig:LineIntegral\]</a>. It is clear that, depending on the path, the evaluated integral will have different values.

; </div> <div id="vector-calculus-release-tbd" class="section level3"> <h3>Vector Calculus (Release TBD)</h3>

;Encountered in: MAT<code>_</code>SCI 406, 408

; </div> </div> <div id="sec:DiffEQ" class="section level2"> <h2>Differential Equations</h2>

;Differential equations — equations that relate functions with their derivatives — are central to the description of natural phenomena in physics, chemistry, biology and engineering. In the sections below, we will outline basic classification of differential equations and describe methods and techniques used in solving equations that are encountered in the MSE graduate core.

;

;The information provide below is distilled and specific to the MSE core, but is by no means a equivalent to a thorough 1- or 2-quarter course in ODEs and PDEs. For students who are completely unfamiliar with the material below; i.e., those who have not taken a course in differential equations, we highly recommend enrollment in Applied Math 311-1 and 311-2 <a href="#fn2" class="footnote-ref" id="fnref2">2</a>.

; <div id="classification-of-differential-equations-release-112016" class="section level3"> <h3>Classification of Differential Equations (Release: 11/2016)</h3>

;Encountered in: MAT<code>_</code>SCI 405, 406, 408

;

;Classification of differential equations provide intuition about the physical process that the equation describes, as well as providing context we use as we go about solving the equation. A differential equation can be classified as either ordinary or partial, linear or non-linear, and by its homogeneity and equation order. These are described briefly below, with examples.

; <div id="ordinary-and-partial-differential-equations" class="section level4"> <h4>Ordinary and Partial Differential Equations —</h4>

;The primary classification we use to organize types of differential equations is whether they are ordinary or partial differential equations. Ordinary differential equations (ODEs) involve functions of a single variable. All derivatives present in the ODE are relative to that one variable. Partial differential equations are functions of more than one variable and the partial derivatives of these functions are taken with respect to those variables.

;

;An example of an ODE is shown in Eq. <a href="#eq:RLC" reference-type="ref" reference="eq:RLC">\[eq:RLC\]</a>. This equation has two functions $q(t)$ (charge) and $V(t)$ (voltage), the values of which depend on time $t$. All of the derivatives are with respect the independent variable $t$. $L$, $R$, and $C$ are constants. \[\begin{aligned} L \FullDiff{2}{q(t)}{t} + R \FullDiff{}{q(t)}{t} + \frac{1}{C} q(t) = V(t) \label{eq:RLC}\end{aligned}\] This general example describes the flow of charge as a function of time in a <a href="https://en.wikipedia.org/wiki/RLC_circuit">RLC circuit</a> with an applied voltage that changes with time. Other examples of ODEs you may encounter in the MSE core include ODEs for grain growth as a function of time and the equations of motion.

;

;Partial differential equations (PDEs) contain multivariable functions and their partial derivatives i.e., a derivative with respect to one variable with others held constant. As physical phenomenon often vary in both space and time, PDEs — and methods of solving them — will be encountered in many of the core MSE courses. These phenomena include wave behavior, diffusion, the Schödinger equation, heat conduction, the Cahn-Hilliard equation, and many others. A typical example of a PDEs you will encounter is Fick’s Second Law. In 1D, this is: \[\begin{aligned} \Partial{}{\varphi(x,t)}{t} = D\Partial{2}{\varphi(x,t)}{x} \label{eq:Ficks2}\end{aligned}\] where $\varphi$ is the concentration as a function of position $x$ and time $t$. This expression equates the change in the concentration over time to the shape (concavity) of the concentration profile. Partial differential equations are, by nature, often more difficult to solve than ODEs, but, as with ODEs, there exist simple, analytic, and systematic methods for solving many of these equations.

; </div> <div id="equation-order" class="section level4"> <h4>Equation Order —</h4>

;The order of a differential equation is simply the order of the highest derivative that is present in the equation. In the preceding section, Eq. <a href="#eq:RLC" reference-type="ref" reference="eq:RLC">\[eq:RLC\]</a> is a second-order equation. Eq. <a href="#eq:Ficks2" reference-type="ref" reference="eq:Ficks2">\[eq:Ficks2\]</a> is also a second-order equation. Students in the MSE core will encounter 4th-order equations such as the Cahn-Hilliard equation, which describes phase separation and is discussed in detail in MAT<code>_</code>SCI 408. One note concerning notation — when writing higher-order differential equations it is common to abandon Leibniz’s notation (where an $n^{\text{th}}$-order derivative is denoted as $\FullDiff{n}{f}{x}$) in favor of Lagrange’s notation in which the following representations are equivalent: \[\begin{aligned} \text{Leibniz}:& F\big[x,f(x),\FullDiff{}{f(t)}{x},\FullDiff{2}{f(t)}{x}...\FullDiff{n}{f(t)}{x}\big] = 0 \rightarrow\\ \text{Lagrange}:& F\big[x,f,f\prime,f\prime\prime...f^{(n)}\big] = 0 \label{eq:LagrangeNote}\end{aligned}\] An example would be be the 3rd-order differential equation: \[\begin{aligned} f\prime\prime\prime + 3f\prime + f\exp{x} = x\end{aligned}\]

; </div> <div id="linearity" class="section level4"> <h4>Linearity —</h4>

;While considering how to solve a differential equation, it is crucial to consider whether an equation is linear or non-linear. For example, an ODE like that represented in Eq. <a href="#eq:LagrangeNote" reference-type="ref" reference="eq:LagrangeNote">\[eq:LagrangeNote\]</a> is linear if the $F$ is a linear function of the variables $f, f', f\prime\prime...f^{(n)}$. This definition also applies to PDEs. The expression for the general linear ODE of order $n$ is: \[\begin{aligned} a_0(x)f^{(n)}+a_1(x)f^{(n-1)} + ... + a_n(x)f = g(t) \label{eq:LinearODE}\end{aligned}\] Any expression that is not of this form is considered nonlinear. The presence of a product such as $f\cdot f\prime$, a power such as $(f\prime)^2$, or a sinusoidal function of $f$ would make the equation nonlinear.

;

;The methods of solving linear differential equations are well-developed. Nonlinear differential equations, on the other hand, often require more complex analysis. As you will see, methods of linearization (small-angle approximations, stability theory) as well as numerical techniques are powerful ways to approach these problems.

; </div> <div id="homogeneity" class="section level4"> <h4>Homogeneity —</h4>

;Homogeneity of a linear differential equation, such as that shown in Eq. <a href="#eq:LinearODE" reference-type="ref" reference="eq:LinearODE">\[eq:LinearODE\]</a> is satisfied if $g(x) = 0$. This property of a differential equation is often connected to the driving force in a system. For example, the motion of a damped harmonic oscillator in 1D (derived from Newton’s laws of motion, <a href="https://en.wikipedia.org/wiki/Harmonic_oscillator">here</a>) is described by a homogeneous linear, 2nd-order ODE: \[\begin{aligned} x\prime\prime+2\zeta \omega_0 x\prime \omega_0^2 x = 0\end{aligned}\] where $x = x(t)$ is position as a function of time ($t$) , $\omega_0$ is the undamped angular frequency of the oscillator, and $\zeta$ is the damping ratio. If we add a sinusoidal driving force, however, the equation becomes inhomogeneous: \[\begin{aligned} x\prime\prime+2\zeta \omega_0 x\prime + \omega_0^2 x = \frac{1}{m} F_0 \sin{(\omega t)} \label{eq:DDSOscillator}\end{aligned}\] One may notice that the form for Eq. <a href="#eq:DDSOscillator" reference-type="ref" reference="eq:DDSOscillator">\[eq:DDSOscillator\]</a> is exactly that of the first equation shown in this section (Eq. <a href="#eq:RLC" reference-type="ref" reference="eq:RLC">\[eq:RLC\]</a>) — the ODE for a damped, driven harmonic oscillator is exactly the same form as that of the RLC circuit operating under a alternating driving voltage.

; </div> <div id="boundary-conditions" class="section level4"> <h4>Boundary Conditions —</h4>

;Differential equations, when combined with a set of well-posed constraints, or boundary conditions, define a boundary value problem. Well-posed boundary value problems have unique solutions from the imposed physical constraints on the system of interest. This analysis allows for the extraction of relevant physical information investigating a physical system — the elemental composition at some position at time within a diffusion couple, the equilibrium displacement in a mechanically deformed body, or the energy eigenstate of a quantum system. While boundary conditions are not used not classify a differential equation itself, boundary conditions are used to classify the entire boundary value problem — which is defined by both the differential equation and the boundary value conditions.

;

;Boundary value problems are at the heart of physical description in science and engineering. Solving these types of problems allow for the extraction of information (concentration, deformation, stress state, quantum state, etc.) from a system. There are a few types of boundary conditions that you may encounter in the MSE core:

; <ol style="list-style-type: decimal"> <li>

;A Dirichlet (or first-type) boundary condition is one in which specific values are fixed on the boundary of a domain. An example of this is a system in which we have diffusion of carbon (in, for example, a carbourizing atmosphere) into iron (possessing a volume defined as domain $\Omega$) where the carbon concentration $C(\mathbf{r},t)$ at the interface is known for all time $t > 0$. Here, $\mathbf{r}$ is position vector and the domain boundary is denoted as $\partial \Omega$). If this concentration is a known function, $f(\textbf{r},t)$, then the Dirichlet condition is described as: \[C(\textbf{r},t) = f(\textbf{r},t), \quad \forall\textbf{r} \in \partial \Omega\]

;</li> <li>

;A Neumann (or second-type) boundary condition is the values of the normal derivative (a directional derivative with respect to the normal of a surface or boundary represented by the vector $\mathbf{n}$) of the solution are known at the domain boundary. Continuing with our example above, this would mean we know the diffusion flux normal to the the boundary at $r$ at all times $t$: \[\Partial{}{C(\textbf{r},t)}{\mathbf{n}} = g(\textbf{r},t), \quad \forall\textbf{r} \in \partial \Omega\] where $g(\textbf{r},t)$ is a known function, and the bold typesetting denotes a vector.

;</li> <li>

;Two other types of boundary conditions you may encounter are Cauchy and Robin. Cauchy boundary conditions specifies both the solution value and its normal derivative at the boundary — i.e., it provides both Dirichlet and Neumann conditions. The Robin condition provides a linear combination of the solution and its normal derivative and is common in convection-diffusion equations.

;</li> <li>

;Periodic boundary conditions are applied in periodic media or large, ordered systems. Previously described boundary conditions can therefore combined into periodic sets using infinite sums of sine and cosine functions to create Fourier series. This will be discussed in more detail in Sec. <a href="#sec:FourierMethods" reference-type="ref" reference="sec:FourierMethods">1.6.2.4</a>.

;</li> </ol> </div> </div> <div id="solving-differential-equations-release-112016" class="section level3"> <h3>Solving Differential Equations (Release: 11/2016)</h3>

;There are many ways to solve differential equations, including analytical and computational techniques. Below, we outline a number of methods that are used in the MSE core to solve relevant differential equations.

; <div id="separation-of-variables" class="section level4"> <h4>Separation of Variables</h4>

;, also known as the Fourier Method, is a general method used in both ODEs and PDEs to reconstruct a differential equation so that the two variables are separated to opposite sides of the equation and then solved using techniques covered in an ODE class. \[sec:SepVar\]

;

;This method will be used in the solving of many simpler differential equations such as the heat and diffusion equations. These equations must be linear and homogeneous for separation of variables to work. The main goal is to take some sort of differential equation, for example an ordinary differential equation: \[\begin{aligned} \FullDiff{}{y}{x} &= g(x)h(y)\\ \intertext{which we can rearrange as:} \frac{1}{h(y)}\mathop{dy} &= g(x)dx\\ \intertext{We now integrate both sides of the equation to find the solution:} \int{\frac{1}{h(y)}\mathop{dy}} &= \int{g(x)\mathop{dx}}\end{aligned}\] Clearly, we have separated our two variables, $x$ and $y$, to opposite sides of the equation. If the functions are integrable and the resulting integration can be solved for $y$, then a solution can be obtained.

;

;Note here that we have treated the $\mathop{dy}/\mathop{dx}$ derivative as a fraction which we have separated.

; <div class="displayquote">

;Example 1: Exponential growth behavior can be represented by the equation: \[\begin{aligned} \FullDiff{}{y(t)}{t} &= k y(t)\\ \intertext{or} \FullDiff{}{y}{t} &= k y\\ \intertext{This expression simply states that the growth rate of some quantity $y$ at time, $t$, is proportional to the value of $y$ itself at that time. This is a seperable equation:} \frac{1}{y}dy &= k dt\\ \intertext{We can integrated both sides to get:} \int{\frac{1}{y}dy} &= k \int{dt}\\ \text{ln}(y)+C_1 &= k t + C_2\\ \intertext{where $C_1$ and $C_2$ are the constants of integration. These can be combined:} \text{ln}(y) &= kt+\tilde{C}\\ y &= e^{(kt+\tilde{C})}\\ y &= Ce^{kt} \end{aligned}\] This is clear exponential growth behavior as a function of time. Separation of variables is extremely useful in solving various ODEs and PDEs — it is employed in the solving of the diffusion equation in .

; </div> </div> <div id="sec:Sturm-Liouville" class="section level4"> <h4>Sturm-Liouville Boundary Value Problems</h4>

;In this section, we use Sturm-Liouville theory in solving a separable, linear, second-order homogeneous partial differential equation. Sturm-Liouville theory can be used on differential equations (here, in 1D) of the form: \[\begin{aligned} \FullDiff{}{}{x}\Big[p(x)\FullDiff{}{y}{x}\Big]-q(x)y+\lambda r(x)y = 0 \label{eq:SturmLiouville} \intertext{or} \big[p(x)y\prime]\prime-q(x)y+\lambda r(x)y = 0 \label{eq:SturmLiouville-2}\end{aligned}\] This type of problem requires knowledge of many use of many concepts and techniques in solving ODEs, including , Fundamental Solutions of Linear First- and Second-Order Homogeneous Equations, Fourier Series, and Orthogonal Solution Functions. It is important to note that the approach described below (adapted from JJ Hoyt’s Phase Transformations), which employs separation of variables and Fourier transforms, works only on linear equations. A different approach must be taken for non-linear equations (such as Cahn-Hilliard).

;

;We will use the example of a solid slab of material of length $L$ that has a constant concentration of some elemental species at time zero $\varphi(x,0) = \varphi_0$ for all $x$ within the slab. On either end of the slab we have homogeneous boundary conditions defining the surface concentrations fixed at $\varphi(0,t) = \varphi(L,t) = 0$ for all $t$. The changing concentration profile, $\varphi(x,t)$ is dictated by Fick’s second law, as described earlier in Eq. <a href="#eq:Ficks2" reference-type="ref" reference="eq:Ficks2">\[eq:Ficks2\]</a>:

;

;\[\Partial{}{\varphi(x,t)}{t} = D\Partial{2}{\varphi(x,t)}{x} \label{eq:Ficks2-1}\]

;

;To use separation of variables, we define the concentration $\varphi(x,t)$, which is dependent on both position and time, to be a product of two functions, $T(t)$ and $X(x)$:

;

;\[\begin{aligned} \varphi(x,t) &= T(t)X(x) \label{eq:SepVar-1} \intertext{or, in shorthand,} \varphi &= TX\end{aligned}\]

;

;It isn’t clear why we do this at this point, but stay tuned. Combining Eqs. <a href="#eq:Ficks2-1" reference-type="ref" reference="eq:Ficks2-1">\[eq:Ficks2-1\]</a> and <a href="#eq:SepVar-1" reference-type="ref" reference="eq:SepVar-1">\[eq:SepVar-1\]</a> yields:

;

;\[XT\prime = DTX\prime\prime\]

;

;Where the primed Lagrange notation denotes total derivatives. $T$ and $X$ are functions only of $t$ and $x$, respectively. Now, we separate the variables completely to acquire:

;

;\[\frac{1}{DT}T\prime = \frac{1}{X}X\prime\prime\]

;

;This representation conveys something critical: each side of the equation must be equal to the same constant. This is because the two sides of the equation are equal to each other and the only way a collection of time-dependent quantities can be equivilent to a selection of position-dependent quantities is for them to be constant with respect to both time and position. We select this constant — for reasons that become clear of the convience of this selection later in the analysis — as $-\lambda^2$:

; <div class="subequations">

;\[\begin{aligned} \frac{1}{DT}T\prime &= -\lambda^2 \label{eq:SepT}\\ \frac{1}{X}X\prime\prime &= -\lambda^2 \label{eq:SepX} \end{aligned}\]

; </div>

;Integration of Eq. <a href="#eq:SepT" reference-type="ref" reference="eq:SepT">\[eq:SepT\]</a> yields, from : \[\begin{aligned} \frac{1}{DT}T\prime &= -\lambda^2 \nonumber\\ \frac{1}{T}\FullDiff{}{T}{t} &= -\lambda^2 D \nonumber\\ \int \frac{1}{T}\Diff{}{T} &= -\int \lambda^2 D \Diff{}{t} \nonumber\\ \ln{T} &= -\lambda^2 D t + T_0 \nonumber\\ \intertext{where $T_0$ is the combined constant of integration:} T = T(t) &= \exp{(-\lambda^2 D t + T_0)} \nonumber\\ T(t) &= T_0 \exp{(-\lambda^2 D t)} \label{eq:Tt}\end{aligned}\] Eq. <a href="#eq:SepX" reference-type="ref" reference="eq:SepX">\[eq:SepX\]</a>, on the other hand, is a linear, homogeneous, second-order ODE with constant coefficients that describes simple harmonic behavior. We can solve this by assessing its <a href="https://en.wikipedia.org/wiki/Characteristic_equation_(calculus)">characteristic equation</a>: \[\begin{aligned} r^2+\lambda^2 = 0\\ \intertext{which has roots:} r = \pm \lambda i\end{aligned}\] When the roots of the characteristic equation are of the form $r = \alpha \pm \beta i$, the <a href="http://www.stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-2ndOrderLinearEqns_Stu.pdf">solution of the differential equation (Pg. 5)</a> is: \[y = e^{\alpha x}(c_1 \cos{\beta x} + c_2 \sin{\beta x})\]

;

;In this instance, $\alpha = 0$ and $\beta = \lambda$, so our solution is:

;

;\[X = X(x) = \tilde{A} \cos{\lambda x} + \tilde{B} \sin{\lambda x} \label{eq:Xx}\]

;

;$\tilde{A}$ and $\tilde{B}$ are constants that will be further simplified later. Recalling Eq. <a href="#eq:SepVar-1" reference-type="ref" reference="eq:SepVar-1">\[eq:SepVar-1\]</a> and utilizing our results from Eqs. <a href="#eq:Tt" reference-type="ref" reference="eq:Tt">\[eq:Tt\]</a> and <a href="#eq:Xx" reference-type="ref" reference="eq:Xx">\[eq:Xx\]</a>, we find: \[\begin{aligned} \varphi(x,y) &= X(x)T(x) = T_0 \big[\tilde{A} \cos{\lambda x} + \tilde{B} \cos{\lambda x}\big]\exp{(-\lambda^2 D t)}\\ \intertext{where we now define $T_0 \tilde{A} = A$ and $T_0 \tilde{B} = B$ to get:} \varphi(x,y) &= X(x)T(x) = \big[A\cos{\lambda x} + B\sin{\lambda x}\big]\exp{(-\lambda^2 D t)} \label{eq:DiffSol}\end{aligned}\] Physially, this solution begins to make sense. At $t=0$ we have a constant concentration, but concentration begins to decay esponentially with time as $D$, $t$, and $\lambda$ are all positive, real constants. The concentration profile is a linear combination of sine and cosine functions, which does not yet yield any physical intuition for this system as we have yet to utilize boundary conditions.

;

;Recall at this point that we have not specified any value for the constant $\lambda$, as is typical when solving this type of Sturm-Liouville problem. This suggests that there are possible solutions for all values of $\lambda_n$. The Principle of Superposition dictates, then, that if Eq. <a href="#eq:DiffSol" reference-type="ref" reference="eq:DiffSol">\[eq:DiffSol\]</a> is a solution, the complete solution to the problem is a summation of all possible solutions:

;

;\[\begin{aligned} \Aboxed{\varphi(x,y) = \sum_{n=1}^\infty \big[A_n\cos{\lambda_n x} + B_n\sin{\lambda_n x}\big]\exp{(-\lambda_n^2 D t)}} \label{eq:DiffSolFull}\end{aligned}\]

;

;As the value of $\lambda$ influences the values of $A$ and $B$, these values must also be calculated for each $\lambda_n$.

;

;Now, to completely solve our well-posed boundary value problem, we utilize our boundary conditions:

; <div class="subequations">

;\[\begin{aligned} \varphi(0,t) &= 0\, \quad t \geq 0 \label{eq:Boundx0}\\ \varphi(L,t) &= 0\, \quad t \geq 0 \label{eq:BoundxL}\\ \varphi(x,0) &= \varphi_0\, \quad 0<x<L \label{eq:Time0} \end{aligned}\]

; </div>

;At $x = 0$, the sine term in Eq. <a href="#eq:DiffSolFull" reference-type="ref" reference="eq:DiffSolFull">\[eq:DiffSolFull\]</a> is zero, and therefore the boundary condition in Eq. <a href="#eq:Boundx0" reference-type="ref" reference="eq:Boundx0">\[eq:Boundx0\]</a> can only be satisfied at all t if $A_n = 0$. At $x = L$, $\sin{\lambda_n x}$ must be zero for all values of $\lambda_n$, therefore $\lambda_n = n\pi/L$. We need only solve now for $B_n$ using the intial condition, Eq. <a href="#eq:Time0" reference-type="ref" reference="eq:Time0">\[eq:Time0\]</a>.

;

;Using our values of $A_n$ and $\lambda_n$ and assessing Eq. <a href="#eq:DiffSolFull" reference-type="ref" reference="eq:DiffSolFull">\[eq:DiffSolFull\]</a> at time $t=0$ yields

;

;\[\varphi_0 = \sum_{n=1}^\infty B_n \sin{\frac{n \pi x}{L}} \label{eq:Time0-1}\]

;

;Here, we must recognized the orthogonal property of the sine function, which states that

;

;\[\int_0^L \sin{\frac{n \pi x}{L}} \sin{\frac{m \pi x}{L}} \begin{cases} = 0, & \text{if}\ n\neq m \\ \neq 0, & \text{if}\ n = m \end{cases}\]

;

;You can test this graphically using a plotting program if you like — the integrated value of this product is only non-zero when $n=m$ — or you can follow the proof <a href="http://www.math.umd.edu/~psg/401/ortho.pdf">here</a>. We can multiply both sides of the Eq. <a href="#eq:Time0-1" reference-type="ref" reference="eq:Time0-1">\[eq:Time0-1\]</a> by $\sin{n \pi x/L}$, then, and integrate both sides from 0 to $L$:

; <div class="subequations">

;\[\begin{aligned} \varphi_0 \int_0^L\sin{\frac{m \pi x}{L}} &= \int_0^L \sum_{n=1}^\infty \big[B_n \sin{\frac{n \pi x}{L}} \sin{\frac{m \pi x}{L}}\big] \nonumber \intertext{After integration, the only term that survives on the right-hand side is the $m=n$ term, and therefore:} \varphi_0 \int_0^L\sin{\frac{n \pi x}{L}} &= B_n\int_0^L \sin{\frac{n \pi x}{L}}^2 \nonumber\\ \varphi_0 \int_0^L\sin{\frac{n \pi x}{L}} &= \frac{B_n L}{4} \big[2- \frac{\sin{2 n \pi}}{n \pi} \big] \nonumber\\ \intertext{the $\sin{2 n \pi}$ term is always zero:} \varphi_0 \int_0^L\sin{\frac{n \pi x}{L}} &= \frac{B_n L}{2} \nonumber\\ 2 \frac{\varphi_0}{L} \int_0^L\sin{{n \pi x}{L}} &= B_n \nonumber\\ B_n &= 2 \frac{\varphi_0}{L} \big[\frac{L}{n \pi}(1-\cos{n \pi})\big] \nonumber\\ \Aboxed{B_n &= 2 \frac{\varphi_0}{n \pi} (1-\cos{n \pi})} \end{aligned}\]

; </div>

;For even values of $n$, the $B_n$ constant is zero. For odd values of $n$, $B_n = \frac{4 \varphi_0}{n \pi}$. We utilize the values we acquired for $A_n$, $B_n$, and $\lambda$ and plug them into Eq. <a href="#eq:DiffSolFull" reference-type="ref" reference="eq:DiffSolFull">\[eq:DiffSolFull\]</a>. A change in summation index to account for the $B_n$ values yields:

;

;\[\begin{aligned} \Aboxed{\varphi(x,t) = \frac{4 c_0}{\pi} \sum_{k=0}^\infty \frac{1}{2k+1} \sin{\frac{(2k+1)\pi x}{L}}\exp{\Big[-\big(\frac{(2k+1)\pi}{L}\big)^2 Dt\Big]}}\end{aligned}\]

;

;This summation converges quickly. We now have the ability to calculate the function $\varphi(x,t)$ at any position $0 < x < L$ and time $t > 0$!

; </div> <div id="method-of-integrating-factors" class="section level4"> <h4>Method of Integrating Factors</h4>

;is a technique that is commonly used in the solving of first-order linear ordinary differential equations (but is not restricted to equations of that type). In thermodynamics, it is used to convert a differential equation that is not exact (i.e., path-dependent, See Sec. <a href="#subsec:eidiff" reference-type="ref" reference="subsec:eidiff">1.5.2</a>) to an exact equation, such as in the derivation of entropy as an exact differential (Release TBD).

; </div> <div id="sec:FourierMethods" class="section level4"> <h4>Fourier Integral Transforms</h4>

;This section will introduce an extremely powerful technique in solving differential equations: the Fourier transform. This technique is useful because it allows us to transform a complicated problem — a boundary value problem — into a simpler problem which can often be approached with ODE techniques or even algebraically.

;

;There are many excellet sources provided for this section, listed below.

; <ol style="list-style-type: decimal"> <li>

;José Figueroa-O’Farrill’s wonderful Integral Transforms from Mathematical Techniques III at the University of Edinborough.

;</li> <li>

;W.E Olmstead and V.A. Volpert’s Differential Equations in Applied Mathematics at Northwestern University.

;</li> <li>

;J.J. Hoyt’s chapter on the Mathematics of Diffusion in his Phase Transformations text.

;</li> <li>

;Paul Shewman’s Diffusion in Solids.

;</li> <li>

;J.W. Brown and R.V. Churchill’s Fourier Series and Boundary Values Problems, 6th Edition.

;</li> </ol>

;The primary goal behind the Fourier transform is to solve a differential equation with some unknown function $f$. We apply the transform ($\mathscr{F}$) to convert the function into something that can be solved more easily: $f \xrightarrow{\mathscr{F}} F$. The transformed function is often also represented using a $\hat{f}$. We solve for $F$ and then perform an inverse Fourier transform ($\mathscr{F}^{-1}$) to recover the solution for $f$.

;

;We find that Fourier series — which are used to when working with periodic functions — can be generalized to Fourier integral transforms (or Fourier transforms) when the period of the function becomes infinitely long. Let’s begin with the Fourier series an build on our results from our discussion above where we found that a continuous function $f(x)$ defined on some finite interval $x \in[0,L]$ and vanishing at the boundaries, $f(0) = f(L) = 0$ can be expanded as shown in <a href="#eq:DiffSolFull" reference-type="ref" reference="eq:DiffSolFull">\[eq:DiffSolFull\]</a>.

;

;The following derivation is adapted from Olmstead and Volpert. In general, we can attempt to represent any function that is periodic over period $[0,L]$ with a Fourier series of form:

;

;\[f(x) = a_0 + \sum_{n=1}^\infty\left[a_n \cos{\frac{2 \pi n x}{L}} + b_n \sin{\frac{2 \pi n x}{L}}\right] \label{eq:GenSol}\]

;

;However, we need to know how to find the coefficients $a_0$, $a_n$, and $b_n$ for this representation of $f(x)$. For this analysis we must utilize the following integral identities:

;

;\[\int_0^L{\sin{\frac{2 \pi n x}{L}}\cos{\frac{2 \pi n x}{L}}}dx= 0 \quad n,m = 1,2,3,...,\]

;

;\[\int_0^L{\cos{\frac{2 \pi n x}{L}}\cos{\frac{2 \pi m x}{L}}} dx= \begin{cases} 0, \text{\,if} \quad n,m = 1,2,3,..., n\neq m\\ L/2, \text{\,if} \quad n = m = 1,2,3,...,\\ \end{cases}\]

;

;\[\int_0^L{\sin{\frac{2 \pi n x}{L}}\sin{\frac{2 \pi m x}{L}}} dx = \begin{cases} 0, \text{\,if} \quad n,m = 1,2,3,..., n\neq m\\ L/2, \text{\,if} \quad n = m = 1,2,3,...,\\ \end{cases}\]

;

;\[\int_0^L{\cos{\frac{2 \pi n x}{L}}} dx = \begin{cases} 0, \text{\,if} \quad n,m = 1,2,3,...,\\ L, \text{\,if} \quad n = 0\\ \end{cases}\]

;

;\[\int_0^L{\sin{\frac{2 \pi n x}{L}}} dx = 0, \text{\,if} \quad n,m = 0,1,2,3,...,\\\]

;

;These identities state the orthogonal properties of sines and cosines that will be used to derive the coefficients $a_0$, $a_n$, and $b_n$. Recall that two functions are orthogonal on an interval if

;

;\[\int_a^b f(x)g(x)dx = 0\]

;

;We can therefore multiply Eq. <a href="#eq:GenSol" reference-type="ref" reference="eq:GenSol">\[eq:GenSol\]</a> by $\cos{\frac{2 \pi x}{L}}$ (note $n = 1$) and integrate over $[0,L]$:

;

;\[\begin{aligned} \int_0^L f(x)\cos{\frac{2 \pi x}{L}} dx &= a_0 \int_0^L \cos{\frac{2 \pi x}{L}} dx +\\ &a_1 \int_0^L \cos{\frac{2 \pi x}{L}} \cos{\frac{2 \pi x}{L}} dx +b_1 \int_0^L \sin{\frac{2 \pi x}{L}} cos{\frac{2 \pi x}{L}} dx +\\ &a_2 \int_0^L \cos{\frac{4 \pi x}{L}} \cos{\frac{2 \pi x}{L}} dx +b_2 \int_0^L \sin{\frac{4 \pi x}{L}} cos{\frac{2 \pi x}{L}} dx + ...\\\end{aligned}\]

;

;Applying the orthogonal properties of the integral products finds that all terms on the right-hand side of this equation are zero apart from the $a_1$ term. The equation therefore reduces to:

;

;\[\int_0^L f(x)\cos{\frac{2 \pi x}{L}} dx = a_1 \int_0^L \cos{\frac{2 \pi x}{L}} cos{\frac{2 \pi x}{L}} dx= a_1\frac{L}{2}\]

;

;and

;

;\[a_1 = \frac{2}{L} \int_0^L f(x)\cos{\frac{2 \pi x}{L}} dx\].

;

;The other Fourier coefficients can be solved for in a similar manner, which yields the general solutions:

;

;\[\begin{aligned} a_0 &= \frac{1}{L} \int_0^L f(x)\\ a_n &= \frac{2}{L} \int_0^L f(x)\cos{\frac{2 n \pi x}{L}}dx \quad (n = 1,2,3...)\\ b_n &= \frac{2}{L} \int_0^L f(x)\sin{\frac{2 n \pi x}{L}}dx\quad (n = 1,2,3...)\end{aligned}\]

;

;To this point we’ve solved, generally, for the coefficients of a Fourier series over a finite interval. This is useful, but we my want to use the full complex form of the Fourier series in later discussion of the Fourier transform. We know that <a href="https://en.wikipedia.org/wiki/Euler's_formula#Relationship_to_trigonometry">Euler’s formula</a> can be used to express trigonometric functions with the complex exponential function:

;

;\[\begin{aligned} \sin{\frac{2 \pi n x}{L}} &= \frac{1}{2i}\left(e^{i\frac{n \pi x}{L}}+e^{-i\frac{n \pi x}{L}}\right) \nonumber \\ \cos{\frac{2 \pi n x}{L}} &= \frac{1}{2}\left(e^{i\frac{n \pi x}{L}}+e^{-i\frac{n \pi x}{L}}\right) \label{eq:Euler}\end{aligned}\]

;

;and we define the wavenumbers to be:

;

;\[k_n = 2 \pi n/L \quad n=0,1,2,..., \label{eq:Wavenumber}\]

;

;and therefore Eq. <a href="#eq:Euler" reference-type="ref" reference="eq:Euler">\[eq:Euler\]</a> is written as:

;

;\[\begin{aligned} \sin{k_n x} &= \frac{1}{2i}\left(e^{i k_n x}+e^{-i k_n x}\right) \nonumber \\ \cos{k_n x} &= \frac{1}{2}\left(e^{i k_n x}+e^{-i\ k_n x}\right) \label{eq:Euler}\end{aligned}\]

;

;This allows us to write the complete Fourier series (Substitute Eq. <a href="#eq:Euler" reference-type="ref" reference="eq:Euler">\[eq:Euler\]</a> into <a href="#eq:GenSol" reference-type="ref" reference="eq:GenSol">\[eq:GenSol\]</a>):

;

;\[f_{L}(x) \sim \sum_{n=-\infty}^{\infty} c_n e^{i k_n x} \label{eq:ComplexFourierSeries}\]

;

;For convenience, we’ll define the integral to be $[-\frac{L}{2},\frac{L}{2}]$. The $\sim$ notation indicates that the series representation is an approximation, and the $L$ represents the period over which the series is applied. The orthogonality condition holds for these complex exponential and its complex conjugate over this interval:

;

;\[\int_{-\frac{L}{2}}^{\frac{L}{2}} e^{i k_n x} e^{-i k_m x} dx = \begin{cases} 0, \text{\,if} \quad n \neq m\\ L, \text{\,if} \quad n = m\\ \end{cases}\]

;

;Therefore, if we multiply Eq. <a href="#eq:ComplexFourierSeries" reference-type="ref" reference="eq:ComplexFourierSeries">\[eq:ComplexFourierSeries\]</a> by $e^{-i k_m x}$ and solve we find the only term that survives is when $n=m$:

;

;\[\int_{-\frac{L}{2}}^{\frac{L}{2}} f_L(x) e^{-i k_m x} dx = L c_m.\]

;

;We can revert the place-keeping subscript $m$ to $n$ and solve for the Fourier coefficients to find:

;

;\[c_n = \frac{1}{L}\int_{-\frac{L}{2}}^{\frac{L}{2}} f_L(x) e^{-i k_n x} dx \quad \text{for\,} n = 0, \pm1, \pm2,... \label{eq:FourierComps}\]

;

;Alright, we’ve defined an interval $[-L/2, L/2]$, but we want to investigate this interval as $L \rightarrow \infty$ in an attempt to eliminate the periodicity of the Fourier series. If $L \rightarrow \infty$, we know that our function $f_L(x)$ will be non-zero over only a very small range — say an interval of $[-a/2, a/2]$ where $a << L$. This means that

;

;\[f_L{x} = \begin{cases} 1 \quad \text{for} |x|<a/2\\ 0 \quad \text{for} a/2 < |x| < L/2 \end{cases} \label{eq:Linfty}\]

;

;This function is zero except for a small bump at the origin of height 1 and width $a$. Let’s assess our function over the non-zero interval:

;

;\[\int_{-\frac{a}{2}}^{\frac{a}{2}} e^{-i k_n x} dx = \frac{\sin k_n a/2}{k_n L/2} = \frac{\sin n \pi a/L}{n \pi}. \label{eq:Thing}\]

;

;But how does this allow us to consider a continuous Fourier integral transform? Well, we need to consider the function $f_L(x)$ as $L \rightarrow \infty$. By doing so, we drive all the harmonics of the Fourier function — apart from the central one — out beyond infinity. $f(x)$ then has a single bump of width $L$ centered at the origin. That is, the separation between the $n$ harmonics goes to zero, and the representation contains all harmonics. Further, as $L \rightarrow \infty$ we no longer have a periodic function and we can i.e., the fundamental period becomes so large that we no longer have non-periodic function at all.

;

;This allows us to transition from a discrete description to a continuum and our Fourier sum can now be described as a Fourier integral. Recall the Fourier series (Eq/ <a href="#eq:ComplexFourierSeries" reference-type="ref" reference="eq:ComplexFourierSeries">\[eq:ComplexFourierSeries\]</a>):

;

;\[f_{L}(x) \sim \sum_{n=-\infty}^{\infty} c_n e^{i k_n x}\]

;

;Which we now write as:

;

;\[f_{L}(x) \sim \sum_{n=-\infty}^{\infty} \frac{\Delta k}{2\pi/L} c_n e^{i k_n x} = \sum_{n=-\infty}^{\infty} \frac{\Delta k}{2\pi} L c_n e^{i k_n x} \label{eq:Thing2}\]

;

;where $\Delta k = 2\pi/L$ is the difference between successive values of $k_n$. We now define a function $F(k)$ as

;

;\[F(k) \equiv \Lim{L \rightarrow \infty} L c_n = \Lim{L \rightarrow \infty} L c_{kL/2 \pi} \label{eq:DefFourierTransform}\]

;

;Combining this definition with Eq. <a href="#eq:Thing" reference-type="ref" reference="eq:Thing">\[eq:Thing\]</a> gives:

;

;\[F(k) = \frac{\sin{(ka/2)}}{k/2}\]

;

;and as $L \rightarrow \infty$, Eq. <a href="#eq:Thing2" reference-type="ref" reference="eq:Thing2">\[eq:Thing2\]</a> goes as

;

;\[\begin{aligned} f(x) &= \Lim{L \rightarrow \infty} \sum_{n=-\infty}^{\infty} \frac{\Delta k}{2\pi} L c_n e^{i k_n x} \\ \Aboxed{f(x) &= \frac{1}{2\pi}\int_{-\infty}^{\infty}F(k) e^{ikx} dk} \label{eq:FourierInversion}\end{aligned}\]

;

;The function $F(x)$ is the Fourier transform of $f(x)$ and Eq. <a href="#eq:FourierInversion" reference-type="ref" reference="eq:FourierInversion">\[eq:FourierInversion\]</a> as a continuous superposition of Fourier component, with each component now represented by a continuous function $f(x)$. Similarly, from Eq. <a href="#eq:DefFourierTransform" reference-type="ref" reference="eq:DefFourierTransform">\[eq:DefFourierTransform\]</a> and Eq. <a href="#eq:FourierComps" reference-type="ref" reference="eq:FourierComps">\[eq:FourierComps\]</a>:

;

;\[\begin{aligned} \Aboxed{F(k) &= \int_{\infty}^{\infty} f(x) e^{-i k x} dx} \label{eq:FourierTransform}\end{aligned}\]

;

;Eq. <a href="#eq:FourierTransform" reference-type="ref" reference="eq:FourierTransform">\[eq:FourierTransform\]</a> is non-periodic analog to the expression for deriving the Fourier coefficients $c_n$ in the periodic case. We call this function the Fourier (Integral) Transform of the function $f(x)$ and it is often written as

;

;\[F(k) \equiv \mathscr{F}\big[f(t)\big] \label{eq:InversionFormula}\]

;

;Similarly, Eq. <a href="#eq:InversionFormula" reference-type="ref" reference="eq:InversionFormula">\[eq:InversionFormula\]</a> is known as the Inversion Formula or Inverse Fourier (Integral) Transform and is used to return the Fourier-transformed function from frequency space. It is often represented as:

;

;\[f(x) \equiv \mathscr{F}^{-1}\big[F(k)\big]\]

; <div class="displayquote">

;Example: Let’s do a simple Fourier transform of a <a href="https://en.wikipedia.org/wiki/Square-integrable_function">square-integrable function</a> (this condition establishes that the function has a Fourier transform). We’ll try a square pulse over the interval \[-, \]:

;

;\[f(x) = \begin{cases} 1, \text{\,if\,} |x| < \pi\\ 0, \text{\,otherwise}\\ \end{cases}\]

;

;We take the Fourier integral transform over the non-zero interval:

;

;\[\begin{aligned} F(x) &= \frac{1}{2 \pi}\int_{-\infty}^{\infty} f(x) e^{-i k x} dx\\ &= \frac{1}{2 \pi}\int_{-\pi}^{\pi} e^{-i k x} dx\\ &= -\frac{1}{2i \pi k} e^{-i k x}\Big|_{-\pi}^{\pi}\\ &= -\frac{1}{2i \pi k} (e^{-i k \pi}-e^{i k \pi})\\ &= \frac{\sin{\pi k }}{\pi k} \end{aligned}\]

; </div>

;Integral transforms will prove massively useful in solving boundary value problems in the MAT<code>_</code>SCI core.

; <div class="displayquote">

;Example One example is diffusion in the thin film problem. Imagine that there is thin region of finite width with high concentration of some species B situated between two “infinite” (thick) plate of pure A (after Hoyt, 1-6). Diffusion from the thin film is allowed to proceed over time into the adjacent plates. The thin film is centered at $x = 0$, so the concentration profile will be an even function $[\varphi(x,t) = \varphi(-x,t)]$ How do we solve for the evolution of the concentration profile over time?

;

;This is an example in which we want to interpret this geometry as one with infinite period. When doing so we should consider using a Fourier integral transform.

;

;From the section above, we understand that the concentration profile $c(x,t)$ can be obtained from the inverse transform of the Fourier space function $\Phi(k,t)$. Above, we derived the full Fourier integral transform, but here we know that the function is even, and so we can perform a Fourier Cosine integral transform, which simplifies the mathematics and allows us to perform the transform from $[0,\infty]$. The following derivation is after Hoyt, Ch. 1-8.

;

;\[\begin{aligned} f(x) = \frac{1}{\pi} \int_{-\infty}^{\infty} F(x) \cos{(kx)} dk\\ F(x) = \frac{1}{\pi} \int_0^{\infty} f(x) \cos{(kx)} dx\end{aligned}\]

;

;In our case, we have:

;

;\[\begin{aligned} \varphi(x,t) = \frac{1}{\pi} \int_{-\infty}^{\infty} \Phi(k,t) \cos{(kx)} dk\\ \Phi(k,t) = \frac{1}{\pi} \int_0^{\infty} \varphi(x,t) \cos{(kx)} dx \label{eq:OddSol1}\end{aligned}\]

;

;The utility of utilizing the Fourier intergral transform is that the PDEs in space and time can be converted to ODEs in the time domain alone, which are often much easier to solve. The ability for us to do this hinges on a key property of a Fourier transform that relates the Fourier transform of the $n$th derivative of a function to the Fourier transform of the function itself.

;

;\[\mathscr{F}\big[f^{(n)}(x)\big](k) = (ik)^{n}\mathscr{F}\big[f(x)\big](k) \label{eq:}\]

;

;This, as you will see, allows us to convert a PDE in $t$ and $x$ to a ODE in $t$ alone. Let’s apply this property to the 1D diffusion equation. First, we know we are performing a Fourier transform in $x$, so the time derivative can be pulled from the integral on the left-hand side of the equation.

;

;\[\begin{aligned} \mathscr{F}[\Partial{}{\varphi(x,t)}{t}] &= \frac{1}{\pi}\int_{0}^{\infty} \Partial{}{\varphi(x,t)}{t} \cos{(-ikx)} dx\\ &= \frac{1}{\pi}\Partial{}{}{t}\left[\int_{0}^{\infty}\varphi(x,t)\cos{(-ikx)} dx\right]\\ &= \frac{1}{\pi}\Partial{}{}{t}\left[\Phi(k,t)\right]\end{aligned}\]

;

;and the right-hand side of the equation is:

;

;\[\begin{aligned} \mathscr{F}\big[D\Partial{2}{}{x}\varphi(x,t)\big] &= (ik)^2D\mathscr{F}\big[\varphi(x,t)\big]\\ &= -D\frac{k^2}{\pi}\int_0^{\infty}\varphi(x,t)\cos{(-ikx)} dx\\ &= -D\frac{k^2}{\pi} \Phi(k,t)\end{aligned}\]

;

;and therefore:

;

;\[\begin{aligned} \frac{1}{\cancel{\pi}}\Partial{}{}{t}\left[\Phi(k,t)\right] &= -D\frac{k^2}{\cancel{\pi}} \Phi(k,t)\\ \Aboxed{\Partial{}{}{t}\left[\Phi(k,t)\right] &= -Dk^2 \Phi(k,t)}\end{aligned}\]

;

;This differential equation can be solved by inspection<a href="#fn3" class="footnote-ref" id="fnref3">3</a> to be:

;

;\[\Phi(k,t) = A^{0}(k) e^{-k^2Dt} \label{eq:Sol1}\]

;

;Where $A^0(k)$ is a constant that that defines the Fourier space function $\Phi$ at $t=0$. To fully solve this problem and derive $\varphi(x,t)$ we must next solve this value $A^0(k)$ and apply the inverse Fourier transform.

;

;Let us consider our initial condition. Our concentration profile can be modeled as a $delta$-function concentration profile, $\varphi(x,0) = \alpha \delta(x)$) fixed between two infinite plates, where the integrated concentration is $\alpha$:

;

;\[\int_{\infty}^{\infty} \varphi(x,0)dx = \int_{\infty}^{\infty} \alpha \delta(x) dx = \alpha\]

;

;The constant $A^0(k)$ is, at $t = 0$, defined by Eq. <a href="#eq:Sol1" reference-type="ref" reference="eq:Sol1">\[eq:Sol1\]</a> and Eq. <a href="#eq:OddSol1" reference-type="ref" reference="eq:OddSol1">\[eq:OddSol1\]</a> to be:

;

;\[\begin{aligned} \Phi(k,t) &= A^{0}(k)e^{0}\\ &= \frac{1}{2\pi}\int_{0}^{\infty}\varphi(x,t) \cos{(kx)} dx\end{aligned}\]

;

;Inserting the delta function for (x,t) yields:

;

;\[A^{0}(k) = \frac{\alpha}{\pi}\int_{0}^{\infty} \delta(x) \cos{(kx)} dx\]

;

;We’ll take advantage of the evenness of this function and instead integrate over $[\infty, \infty]$. This allows us to avoid the messiness at $x=0$ as well circumvent using the Heaviside step function.

;

;\[\begin{aligned} A^{0}(k) &= \frac{\alpha}{2\pi}\int_{-\infty}^{\infty} \delta(x) \cos{(kx)} dx\\ A^{0}(k) &= \frac{\alpha}{2\pi} \cos{(0)} dx\\ %Deltafunction fundamental property \Aboxed{A^{0}(k) &= \frac{\alpha}{2\pi}}\end{aligned}\]

;

;Finally, now that we have $A^{0}$, we must perform the inverse transformation to find the expression for $\varphi(x,t)$.

;

;\[\begin{aligned} \varphi(x,t) &= \frac{\alpha}{2\pi}\int_{-\infty}^{\infty} e^{-k^2Dt} \cos{(kx)} dk\\ \intertext{This can be completed through integration by parts, trigonometric identities, and completing the square... for explicit step-by-step analysis use Wolfram$|$Alpha or \href{http://www.integral-calculator.com/}{Scherfgen's Integral Calculator}. Let's state the result:} \varphi(x,t) &= \frac{\alpha}{2\sqrt{\pi D t}} e^{-x^2/4Dt}\end{aligned}\]

;

;This is a Gaussian distribution centered at $x = 0$ and which increases in width with time. This is good — it certainly makes sense intuitively.

; </div> </div> <div id="bessel-functions" class="section level4"> <h4>Bessel Functions</h4> </div> <div id="legendre-polynomials" class="section level4"> <h4>Legendre Polynomials</h4> </div> <div id="eulers-method" class="section level4"> <h4>Euler’s Method</h4> </div> </div> <div id="solving-second-order-linear-odes-release-tbd" class="section level3"> <h3>Solving Second-order Linear ODEs (Release TBD)</h3> <ol style="list-style-type: decimal"> <li>

;Principle of Superposition

;</li> <li>

;Series Solutions

;</li> </ol> </div> <div id="laplace-transforms-release-tbd" class="section level3"> <h3>Laplace Transforms (Release TBD)</h3> </div> <div id="stability-theory-release-tbd" class="section level3"> <h3>Stability Theory (Release TBD)</h3> </div> </div> </div> <div class="footnotes"> <hr /> <ol> <li id="fn1">

;sometimes, an inexact differential will be denoted as $\delta f$<a href="#fnref1" class="footnote-back">↩︎</a>

;</li> <li id="fn2">

;these may be combined to a 1-quarter class in the future<a href="#fnref2" class="footnote-back">↩︎</a>

;</li> <li id="fn3">

;If you don’t see this, that’s fine, review Separation of Variables — this equation is separable<a href="#fnref3" class="footnote-back">↩︎</a>

;</li> </ol> </div> </div> <script> // add bootstrap table styles to pandoc tables function bootstrapStylePandocTables() { $('tr.odd').parent('tbody').parent('table').addClass('table table-condensed'); } $(document).ready(function () { bootstrapStylePandocTables(); }); </script>  <script> $(document).ready(function () { window.buildTabsets("TOC"); }); $(document).ready(function () { $('.tabset-dropdown > .nav-tabs > li').click(function () { $(this).parent().toggleClass('nav-tabs-open'); }); }); </script>   <script> (function () { var script = document.createElement("script"); script.type = "text/javascript"; script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; document.getElementsByTagName("head")[0].appendChild(script); })(); </script> </body> </html>

4 Introduction

Materials science is the investigation of the relationships between the property, structure and processing of materials, with the goals of optimizing performance of some system. These relationships are often illustrated with the materials science tetrahedron shown in Figure 4.1.

image: 4_home_ken_Mydocs_MSEcore_201-301_figures_MSE_paradigm.svg

Figure 4.1: The materials science tetrahedron.

5 Bonding

5.1 Outcomes

Evaluate interatomic energy curves to derive equilibrium interatomic spacing and bond energy (using calculus and graphically).
Identify the mechanistic contributions to repulsive and attractive forces/energies in interatomic force/energy curves.
Identify different types of bonding with materials class.
Understand characteristics of different bonding models, including strength, directionality.
Infer general properties from bond type.
Differentiate between predominate ionic or covalent bond character by assessing electronegativity difference.

5.2 General Concepts and the Role of the Interatomic Potential

A generic feature of all bonds is that they can be described by a interatomic potential of the sort shown in Figure 5.1. This potential can be viewed as a sum of an attractive portion that draws the atoms close to one another, and a repulsive, short-range interaction that maintains a preferred separation comparable to the atomic size. Primary bonds are strong bonds with a deep potential well, and include covalent, ionic and metallic bonds. Secondary bonds, including Van der Waals interactions and hydrogen bonds, are much weaker, and with a shallower potential well.

image: 5_home_ken_Mydocs_MSEcore_201-301_figures_interatomic_potential.svg

Figure 5.1: Generalized interatomic potential. The total potential (

E_{N}

) is given by the sum of an attractive part (

E_{A}

) that dominates at long distances and a repulsive part (

E_{R}

) that dominates at short distances.

The following properties are directly related to the nature of the interatomic potential:

Melting Temperature

If the bonding well is deep, it takes a lot of energy to separate the atoms, meaning that the melting temperature is going to be high. In Figure 5.2a.

Thermal expansion

Thermal expansion is directly connected to the asymmetry of the potential well, as illustrated in Figure 5.2b.

Elastic modulus (stiffness)

The higher curvature of the well, the larger the stiffness

Question: Calculate the equilibrium spacing for the following interatomic potential:

E = \frac{B}{r^{3}} - \frac{A}{r}

Answer: We differentiate the energy to get the force,

F

F = \frac{d E}{d r} = - \frac{3 B}{r^{4}} + \frac{A}{r^{2}}

At equilibrium, the force is equal to zero, so we have:

A = \frac{3 B}{r^{2}}, r = \sqrt{3 B / A}

image: 6_home_ken_Mydocs_MSEcore_201-301_figures_effects_of_interatomic_potential.svg

Figure 5.2: Illustration of the relationship between interatomic potentials and some relevant material properties.

image: 7_home_ken_Mydocs_MSEcore_201-301_figures_Periodic_table_large.svg

Figure 5.3: Periodic Table f the Elements.

With bonding, everything starts with periodic table, shown in Figure .5.3. At a simple level, the type of bonding between atoms is determined by their locations on the periodic table.

Electronegativity arises due to elements’ energetic favorability to reach a stable electron configuration.

5.3 Ionic Bonding

Ionic bonding typically occurs between a metal and a non-metal, and involves a transfer of an electron from an atom with low negativity to create cations (+ charge) to an atom with high electronegativity to produce anions (- charge). Examples are shown in Figure 5.4, where the electronegativities of the different elements are shown. 'Pure' ionic bonding occurs in systems where there is a large difference in the electronegativity between the constituent elements, typically 2.7 or more. In practical terms this means that a large fraction of ionic materials have oxygen, fluorine, chlorine or bromine as the anion, corresponding repectively to oxides, fluorides, chlorides and bromides.

image: 8_home_ken_Mydocs_MSEcore_201-301_figures_electronegativity_and_ionic_solids.png

Figure 5.4: Examples of some common ionic solids, with the corresponding electronegativity values of the elements from which they are formed.

image: 9_home_ken_Mydocs_MSEcore_201-301_figures_interatomic_potential_with_ions.svg

image: 10_home_ken_Mydocs_MSEcore_201-301_figures_NaCl_schematic.png

Figure 5.5:

5.4 Covalent Bonding

Hugely varying properties: Strong [C(diamond, graphene)] to relatively weak (I2) Frequently brittle, electrically insulating/semiconducting/conducting, transparent/opaque Other examples, Si, InSb, SiC

image: 11_home_ken_Mydocs_MSEcore_201-301_figures_methane.svg

Figure 5.6: Methane (CH

_{4}

) with tetrahedral coordination resulting from the sp

^{3}

hybridized orbital.

5.5 Metallic Bonding

Metallic Bonding is found in metals and their alloys. The valence electrons are delocalized to form an “electron cloud/sea/gas” or “Fermi liquid”, as illustrated in Figure 5.7. These are referred to as the the conduction electrons and are shared between all of the atoms in the material. Positive ionic cores held together by electron “glue”. As with ionic bonding, metallic bonding is non-directional, meaning that if we rotate an atom core, it doesn't affect the nature of the interaction. The average electronegativity of the atoms in metallic systems is generally low, so electrons are easily donated from the individual atoms to the electron 'sea'.

Responsible for: Ducility/mealleability (W6) Conduction of heat/welectricity (W8) Shininess/opacity (W9) Thermal conductivity (W9)

image: 12_home_ken_Mydocs_MSEcore_201-301_figures_metallic_bonding.png

Figure 5.7: Schematic representation of metallic bonding.

6 Crystal Structures

The animation below illustrates 3 crystal structures of metals: face centered cubic (fcc), body centered cubic (bcc) and simple cubic (sc):

;;;

7 Dislocations

Plastic deformation of a crystalline solid occurs by the motion of dislocations, which are one dimensional defects in the crystal structure. In general, deformation of a material occurs by shear along specified planes called slip planes. An illustration of this effect in single crystal aluminum is shown in Figure 7.1. The material in this image is being deformed in tension, but the slip occurs along suitably oriented planes that are experiencing a high degree of shear.

image: 16_home_ken_Mydocs_MSEcore_201-301_figures_single_crystal_al.svg

Figure 7.1: Slip bands in single crystal aluminum undergoing tensile deformation.

When a stress is applied to a single crystal, deformation takes place when the

resolved shear stress

τ_{r s s}

, on an appropriately aligned shear plane exceeds a critical value, referred to as the

critical resolved shear stress

τ_{c r s s}

. The relationship between the tensile stress,

σ

and the resolved shear stress is illustrated in Figure 7.2. In mathematical terms we have:

\begin{matrix} τ_{r s s} = σ cos φ cos λ & (7.1) \end{matrix}

where

φ

is the angle between the tensile axis and the slip plane normal,

\vec{n}

, and

λ

is the angle between the tensile axis and the slip direction,

\vec{d}

image: 17_home_ken_Mydocs_MSEcore_201-301_figures_resolved_shear_stress.svg

Figure 7.2: Relationship between an applied tensile stress,

σ

and the resolved shear stress,

τ_{r s s}

Values of this quantity for different single crystals are shown in Table 1. For the materials with close packed crystals structures on this list (fcc and hcp), the value of

τ_{c r s s}

is about four orders of magnitude less than the shear modulus,

G

Table 1: Critical resolved shear stress for single crystals (Read-Hill, “Physics of Metals Principles”, chap. 4 (1964).

Metal	Structure	$G$ (psi)	$G$ (Pa)	$τ_{c r s s}$ (psi)	$τ_{c r s s}$ (Pa)
Al	fcc	3.9x10 $^{6}$	27x10 $^{9}$	148	1.0x10 $^{6}$
Cu	fcc	7.0x10 $^{6}$	48x10 $^{9}$	92	0.64x10 $^{6}$
Mg	hcp	2.4x10 $^{6}$	17x10 $^{9}$	63	0.44x10 $^{6}$
Zn	hcp	5.6x10 $^{6}$	38x10 $^{9}$	26	0.18x10 $^{6}$
$α$ -Fe	bcc	9x10 $^{6}$	27x10 $^{9}$	4000	28x10 $^{6}$

A note about units of stress:

The SI unit of stress is a pascal (Pa), or N/m

^{2}

. We generally use SI units in this text, but English units (pounds per square inch, or psi), are still often used in engineering fields. One useful number to remember is that atmospheric pressure is

\approx 1 0^{5}

Pa, or 14.7 psi. The exact conversion is that 1 psi = 6895 Pa = 6.895 kPa.

Exercise: From the critical resolved shear stress for single crystal aluminum shown in Table 1, calculate the minimum force (in pounds) that must be applied to a one half inch diameter rod of single crystal Al to deform plastically.

Solution: The critical resolved shear stress for pure, single crystal Al is 148 psi, so we need to figure out what tensile stress on the sample will produce this value for the resolved shear stress,

τ_{r s s}

. The smallest value of

σ

for which

τ_{r s s}

is equal to the critical value of 148 occurs for the slip system with

φ = λ = 4 5^{○}

, so from Eq. 7.1 we get

σ = 2 τ_{r s s} = 296

. Multiplying by the cross sectional area of the rod gives:

F = (296 p s i) \cdot π \cdot {(0.25 i n)}^{2} = 58 p o u n d s

This is a pretty small force, and is much less than the force required to deform a stock piece of aluminum that I would find in the machine shop.

Why is the force to deform a single crystal so low? We'll start by considering what we would expect for the critical resolved shear stress if the shear deformation were to occur by the sliding of atomic planes over one another, as shown conceptually in Figure 7.3. We refer to the stress required to slide these planes over one another as the dislocation-free critical resolved shear stress,

τ_{c r s s}^{0} .

image: 18_home_ken_Mydocs_MSEcore_201-301_figures_shearing_spheres.svg

Figure 7.3: Sliding of close packed planes on top of one another.

We'll start by reminding ourselves of the definition of a shear strain, illustrated in Figure 7.4. In shear deformation, two parallel surfaces separated by a distance,

d

, are translated by an amount

u

with respect to one another. If the deformation occurs in the x-y plane, we refer to the shear strain as

e_{x y}

, which is given by:

\begin{matrix} e_{x y} = \frac{u}{d} & (7.2) \end{matrix}

For a linearly elastic material, the shear stress,

τ

is proportional to

e_{x y}

, with the shear modulus

G

defined as the ratio of shear stress over shear strain:

\begin{matrix} τ = G \frac{u}{d} & (7.3) \end{matrix}

image: 19_home_ken_Mydocs_MSEcore_201-301_figures_shear_strain.svg

Figure 7.4: Application of a shear strain to a material.

In Figure 7.5 show a schematic representation of the stress as a function of displacement for the atomic planes shown in Figure 7.3. The stress function has the following features:

The stress is a periodic function, with the stress repeating every time the displacement is increased by an amount equal to $b$ , the distance between atoms along the slip direction.
The stress is equal to zero at the stable equilibrium positions at $u = 0, b, 2 b$ , etc.
For $u < b / 2$ the stress is positive because we need to apply a stress to move the atoms out of their stable equilibrium positions.
At $u = b / 2$ the system is at an unstable equilibrium. The stress is also equal to zero at this position, but the equilibrium is unstable because any slight perturbation in the displacement will cause the atomic plane to fall back into an equilibrium position at $u = 0$ or $u = b$ .
The maximum stress is at $u = b / 4$ . The stress actually reverses sign for $u > b / 2$ , since a stress must be applied to avoid having the atoms fall into the equilibrium position at $u = b$ .

image: 20_home_ken_Mydocs_MSEcore_201-301_figures_sinusoidal_stress.svg

Figure 7.5: Schematic representation of the stress vs. displacement as the atomic planes in Figure 7.3 slide over one another.

The simplest mathematical expression for the shear stress that has the right periodicity is a sinusoidal function:

\begin{matrix} τ = a sin (\frac{2 π u}{b}) & (7.4) \end{matrix}

Now we need to figure out what the constant

a

is in terms of actual material properties. For small displacements the material is in the linear regime, and we can use the definition of the shear modulus (Eq. 7.3) to obtain the following:

\begin{matrix} {. \frac{d τ}{d u} |}_{u = 0} = G / d & (7.5) \end{matrix}

Comparison of Eqs. 7.4 and 7.5 gives

a = b G / 2 π d

, so the shear stress becomes:

\begin{matrix} τ = \frac{b G}{2 π d} sin (\frac{2 π u}{b}) & (7.6) \end{matrix}

The critical resolved shear stress in this picture corresponds to the maximum value of

τ

, equal to

b G / 2 π d

. The interplanar spacing,

d

is comparable to

b

. (We're not going to worry about the exact numerical factor here, since we're just aiming to get an approximate expression for

τ_{c r s s}

). We take

b \approx d

and

2 π \approx 6

to end up with the following expression for the ideal critical resolved shear stress,

τ_{c r s s}^{0}

, which is the value of the critical resolved shear stress we would expect to have if dis:

\begin{matrix} τ_{c r s s}^{0} \approx G / 6. & (7.7) \end{matrix}

In reality,

τ_{c r s s} \approx G / 1 0^{4}

, so this picture of atomic planes sliding over one another can't be correct. What is really going on here? The answer is that slip occurs by the motion of dislocations, not by the concerted motion of entire planes of atoms across one another. The concept of slip by dislocation motion can be illustrated conceptually by the force required to slide a carpet across a floor. If the friction between the rug and the floor is very high, it's going to be very difficult to move the rug along the floor simply by grabbing it from one end and pulling. This situation is analogous to sliding atomic planes across one another as illustrated in Figure 7.3. If the rug just needs to be moved a small distance it is much easier to create a wrinkle at one end of the rug and move it to the other end of the carpet. At the end of the process, the carpet has moved by a length equal to the length of extra carpet stored in the wrinkle. Dislocations are line defects in crystalline materials that are analogous to these wrinkles.

image: 21_home_ken_Mydocs_MSEcore_201-301_figures_rug_slip.svg

Figure 7.6: Moving a carpet by propagating a defect along its length.

7.1 Edge Dislocations

The easiest type of dislocation to visualize is an edge dislocation. A dislocation is formed by slipping part of the top half of a crystal relative to the bottom half by the application of a shear stress,

τ

, as illustrated schematically in Figure 7.7. The

slip plane

corresponds to the interface between the slipped and unslipped regions of the sample. An edge dislocation can be viewed as the termination of an extra half plane of atoms, and is illustrated for a simple cubic lattice in Figure 7.8.

image: 22_home_ken_Mydocs_MSEcore_201-301_figures_Edge_dislocation_step.svg

Figure 7.7: Illustration of the boundary between regions that have slipped from the application of a shear stress. The dislocation in this example refers to the boundary between the slipped and unslipped regions.

image: 23_home_ken_Mydocs_MSEcore_201-301_figures_EdgeDislocation1.jpg

Figure 7.8: Edge dislocation in a simple cubic lattice.

Motion of an edge dislocation is illustrated in response to an applied shear stress is illustrated in Figure 7.9. Note that for every atom moving away from its equilibrium on one side of the dislocation core, there is an equivalent atom moving toward an equilibrium position on the other side of the dislocation core. In energetic terms, for every atom that must be forced out of its lowest energy position, there is atom moving toward its lowest energy position. As a result the energy changes cancel (or very nearly so), and the energy barrier to moving a dislocation is much less than the barrier to slide surfaces across one another. As a result the net force to move a dislocation is very small. The stress needed to move a dislocation is generally much less than

G / 6

, and is as low or lower than the observed critical resolved shear stress for single crystals.

image: 24_home_ken_Mydocs_MSEcore_201-301_figures_edge_dislocation_motion.svg

Figure 7.9: Schematic representation edge dislocation motion in the slip plane, illustrating the Burgers vector,

\vec{b}

for an edge dislocation.

The relative displacement of the two halves of the crystal caused by the motion of a single dislocation through it is the

Burgers vector

\vec{b}

, which is the single most important characteristic of the dislocation. For an edge dislocation

\vec{b}

is perpendicular to the dislocation line, which we represent by the unit vector

\hat{s}

(the )

i . e .

\vec{b} \cdot \hat{s} = 0

. Note that dislocations of opposite sign moving in opposite directions give the same final shear. This is illustrated by comparing Figures 7.9 and 7.10, which both result in the final deformed state of the material. Finally, when two edge dislocations with opposite Burgers vectors (

\vec{b}

and

- \vec{b}

) meet on the same glide plane, they annihilate each other (see Figure 7.11).

image: 25_home_ken_Mydocs_MSEcore_201-301_figures_edge_dislocation_motion_neg_b.svg

Figure 7.10: Deformation from Fig. 7.9, but resulting from an edge dislocation of opposite sign moving in the opposite direction.

image: 26_home_ken_Mydocs_MSEcore_201-301_figures_dislocation_annihiliation.svg

Figure 7.11: Annihilation of two dislocations of opposite sign that are moving in the same glide plane.

7.2 Screw Dislocations

As with edge dislocations, a screw dislocation line marks the boundary between 'slipped' and 'unslipped' regions of the sample, but for a screw dislocation the displacement described by

\vec{b}

is parallel to the dislocation line,

i . e .

\vec{b} \cdot \hat{s} = | \vec{b} |

. (Note that in order to simplify our notation, we'll refer to

| \vec{b} |

, the magnitude of the Burgers vector, simply as

b

in this text. A schematic representation of a the displacements associated with a screw dislocation is shown in Figure 7.12.

image: 27_home_ken_Mydocs_MSEcore_201-301_figures_screw_dislocation.svg

Figure 7.12: Schematic representation of a screw dislocation.

Figure 7.13 illustrates the the motion of a screw dislocation through a crystal. In this case the dislocation moves from the front of the crystal to the back of the crystal. The net effect of this motion is for the top and bottom halves of the crystal to be displaced to the right, by an amount and in the direction given by the Burgers vector. This figure illustrates the following:

When a dislocation line travels through a material, the motion of the line traces out a plane.
The relative displacement between the material on either side of this plane is given by the Burgers vector $\vec{b}$ .

Note that this is true for ANY dislocation (edge, screw, or mixed).

image: 28_home_ken_Mydocs_MSEcore_201-301_figures_screw_dislocation_motion.svg

Figure 7.13: Motion of a screw dislocation The dislocation moves from the front of the crystal to the back. The net result is the production of a step edge with magnitude and direction equal tot he Burgers vector,

\vec{b}

7.3 The Burgers Circuit

In the previous section we have described some of the basic features of edge and dislocations, and have shown that they differ in the relationship between the orientation of the Burgers vector with respect to the dislocation line. Now we introduce a formal procedure that can be used to determine the value of

\vec{b}

for any dislocation. The procedure is based on the use of a

Burgers circuit

, as described here:

Draw a circuit around the dislocation line that starts end ends at the same point. A 'right handed' convention is typically used to describe the direction that we take the circuit. (Clockwise looking along the direction of $\hat{s}$ , counterclockwise if $\hat{s}$ is pointed at you).
Repeat the procedure, using the same numbers of atomic steps in each direction in a perfect crystal.
The Burgers vector is the vector connecting the start and end positions for the circuit drawn in the perfect crystal.

Use of the procedure is illustrated in Figure 7.14 for an edge dislocation with an extra half plane in the top half of the crystal. The circuit around the dislocation begins and ends at point a and proceeds as follows:

Move four steps down (a to b)
Move three steps to the right (b to c)
Move four steps up (c to d)
Move four steps to the left (d back to a)

When this same procedure is repeated in the perfect crystal we end up at point e, which is one step to the left of our starting point at point a. Our convention is to define the

\vec{b}

as the vector starting at point a and ending at point b. When the procedure is repeated for a dislocation where the half plane is in the bottom half of the crystal we end up with the Burgers vector pointing in the opposite direction, as shown in Figure 7.15.

image: 29_home_ken_Mydocs_MSEcore_201-301_figures_burgers_circuit_edge.svg

Figure 7.14: Determination of

\vec{b}

for an edge dislocation. In this case

\hat{s}

is defined so that it is pointing into the plane of the figure. The vector

{\vec{n}}_{d}

is defined in Eq. 7.8.

image: 30_home_ken_Mydocs_MSEcore_201-301_figures_burgers_circuit_edge2.svg

Figure 7.15: Determination of

\vec{b}

for an edge dislocation with an opposite sign to the dislocation from Figure 7.14.

In Figure 7.16 we repeat the same process for a screw dislocation. In this example we have defined the direction of

\hat{s}

so that the dislocation is pointed toward the bottom of the figure. The procedure for determining

\vec{b}

is as follows:

Draw a circuit in the clockwise direction (viewed from the top, so we are looking in the direction of $\hat{s}$ ) around the dislocation line. The circuit begins and ends at point a.
Repeat the circuit in a perfect part of the crystal. The circuit begins at point $s$ and ends at point $f$ .
The Burgers vector is obtained as the vector that starts at $s$ and ends at $f .$

Note that

\vec{b}

is parallel to

\hat{s}

, as it must be for a screw dislocation, but that

\vec{b}

and

\hat{s}

are pointed in opposite directions, i.e., they are anti-parallel. With our convention of drawing the

\vec{b}

from the starting point to the ending point of the Burgers circuit in the perfect crystal, right handed screw dislocations have negative Burgers vectors and left handed screw dislocations have positive Burgers vectors. The left handed version of the dislocation shown in Figure 7.16 is shown in Figure 7.17.

image: 31_home_ken_Mydocs_MSEcore_201-301_figures_burgers_circuit_screw.svg

Figure 7.16: Burgers circuit for a right-handed screw dislocation, with

\vec{s}

defined so that the the positive direction of the dislocation line is toward the bottom of the crystal (along the negative z direction).

image: 32_home_ken_Mydocs_MSEcore_201-301_figures_screw_right_handed.svg

Figure 7.17: Left-handed version of the dislocation from Figure 7.16.

Exercise: Does the handedness of a screw dislocation (right handed or left handed) depend on the way you define the direction of

\hat{s}

Solution: No! If you you can see this by taking your right thumb and directing it along the dislocation line in Figure 7.16. In the direction that your figures are pointing, the planes spiral upward toward your thumb. It doesn't matter which way you orient your thumb when you do this. For the dislocation shown in Figure 7.17 you need to use your left hand to get this to work.

7.4 The $\vec{b} \times \hat{s}$ cross product

The concept of the Burgers circuit is a useful formalism that can always be used to specify the Burgers vector for a given dislocation. The confusing part about the procedure is that the sign of the Burgers vector depends on some arbitrary conventions that are not used the same way by everyone. For example, our convention is to define

\vec{b}

as the vector linking the start to the finish of the Burgers circuit in the perfect crystal (linking points s to f in Figure 7.16), but you can find plenty of other people who draw the vector the other way around (drawing

\vec{b}

from point f to point s). Nevertheless, we remove any ambiguity by always using this 'start-to-finish' definition for the Burgers vector. Similarly, we remove ambiguity regarding the direction in which we take the Burgers circuit by always doing it the same way. In our case we use the right hand rule, directing our thumb along

\hat{s}

and drawing the circuit in the direction in which our fingers are pointing.

Unfortunately, the ambiguity introduced by our definition of the direction of

\hat{s}

along the dislocation line is impossible to remove. In figure 7.16 we defined

\hat{s}

so that it points along the negative z direction, but there's no reason that we couldn't have defined

\vec{s}

so that it is directed in the positive z direction instead. We end up with a Burgers vector that points in one of two opposite directions, depending on how we define

\hat{s}

in the first place. The good news is that

{\vec{n}}_{d}

, the vector cross product of

\hat{s}

and

\vec{b}

is independent of our convention for defining the direction of

\vec{s}

. As a reminder, the vector cross product between vectors

\hat{s}

and

\vec{b}

is defined as follows, as illustrated in Figure 7.18:[_cross_2014]

\begin{matrix} {\vec{n}}_{d} = \vec{b} \times \hat{s} = \vec{| b |} | \hat{s} | sin θ \hat{n} = b sin θ {\hat{n}}_{d} & (7.8) \end{matrix}

Here

{\hat{n}}_{d}

is a unit vector in the direction perpendicular to the plane containing

\hat{s}

and

\vec{b}

. It's orientation is defined using the right hand rule: We place our right hand along

\hat{s}

, with our fingers oriented in the positive

θ

direction. Our right thumb is then pointed along

{\hat{n}}_{d}

image: 33_home_ken_Mydocs_MSEcore_201-301_figures_Cross_product_parallelogram.svg

Figure 7.18: Definition of

{\vec{n}}_{d}

When defined in this way,

{\vec{n}}_{d}

has the following properties:

Because redefining $\vec{s}$ to have the opposite orientation also changes the orientation of $\vec{b}$ , the negative signs cancel and we end up with a value for ${\vec{n}}_{d}$ that is independent of the way that we choose to define $\vec{s}$ .
For a pure screw dislocation, $θ = 0$ or $θ = 18 0^{○}$ . In either case, ${\vec{n}}_{d}$ = 0.
For an edge dislocation, the magnitude of ${\vec{n}}_{d}$ is equal to the $b$ , the magnitude of Burgers vector. In addition, ${\vec{n}}_{d}$ points toward the extra half plane.

This last point is perhaps the most important one, because it provides an easy way to figure out how the extra half plane is oriented in an edge dislocation, once we specify the orientations of

\vec{b}

and

\hat{s}

. We just use the right hand rule, cross

\vec{b}

into

\hat{s}

, and our thumb will be pointed along the direction of the extra half plane. To convince yourself that this actually works, you can try it with the edge dislocations pictured in Figures 7.14 and 7.15.

With our convention for using the Burgers circuit to obtain

\vec{b}

(Right-hand-rule, start to finish), we have the following relationships between

\hat{s}

and

\vec{b}

Right-handed screw dislocation: $\hat{s}$ and $\vec{b}$ point in opposite directions.
Left-handed screw dislocation: $\hat{s}$ and $\vec{b}$ point in the same direction.
Edge dislocation: $\hat{s}$ perpendicular to $\vec{b}$ , $\vec{b} \times \hat{s}$ points to the extra half plane.

7.5 Connection to the Crystal Structure

The Burgers vector must correspond to an atomic repeat distance in the crystal structure. As we show below, the energy of a dislocation is proportional to the square of the magnitude of the Burgers vector. For this reason the Burgers vector will correspond to closest atomic distance in crystal structure. As shown in Figure 7.19, the Burgers vector is half the unit cell diagonal for the BCC structure, and half the face diagonal of the unit cell in the FCC structure.

image: 34_home_ken_Mydocs_MSEcore_201-301_figures_burgers_vector_bcc_and_fcc.svg

Figure 7.19: Burgers vectors for the BCC and FCC crystal structures.

7.6 Dislocation Motion

7.6.1 Dislocation Glide

Dislocation

glide

(which is sometimes referred to simply as slip) corresponds to dislocation motion within a

glide plane

that contains along the plane that contains both the Burgers vector,

\vec{b}

and the sense,

\vec{s}

, of the dislocation. For an edge dislocation or a dislocation with mixed edge and screw character, a single slip plane exists that is perpendicular to the vector

{\vec{n}}_{d}

, given by the cross product of

\hat{s}

and

\vec{b}

(see Figure 7.18). Slip does not require atomic diffusion, and so is not strongly temperature dependent. For an edge dislocation it occurs when the extra half plane of atoms reattaches to a new atomic plane, moving the half plane by a distance equal to

\vec{b}

. The process is illustrated schematically in Figure 7.20.

image: 35_home_ken_Mydocs_MSEcore_201-301_figures_Edge_dislocation_glide.svg

Figure 7.20: Glide of an edge dislocation.

For a pure screw dislocation, because

\hat{s}

and

\vec{b}

are collinear, a variety of glide planes are available. As a result, screw dislocations can more easily navigate their way around obstacles (like a precipitate particle) by changing the slip plane on which they are moving. The process is called

cross slip

and is illustrated schematically in Figure 7.21. This illustration could correspond, for example, to the motion of a screw dislocation with

\hat{s}

oriented along the

[1 \overline{1} 0]

direction that moves along the

(111)

plane initially, switches to the

(11 \overline{1})

plane and then begins moving again in the

(111)

plane. (Note - if you forget the Miller index notation for planes and directions, the Wikipedia page [_miller_2014] is a useful refresher).

image: 36_home_ken_Mydocs_MSEcore_201-301_figures_screw_dislcation_cross_slip.svg

Figure 7.21: Cross slip of a screw dislocation.

7.6.2 Dislocation Climb

Edge dislocations can climb out of the glide plane by the addition or subtraction of vacancies to the dislocation core. The process is illustrated in Figure 7.22 for a situation where

{\vec{n}}_{d}

is directed toward the top of the figure (i.e. the extra half plane is above the glide plane). In this example an atom at the end of the extra half plane jumps into a vacancy. The net result is that the vacancy is destroyed, and the dislocation climbs up, away from the initial glide plane. Because the process requires the diffusive hopping of atoms from one site to another, climb is a thermally activated process that becomes more important at elevated temperatures.

image: 37_home_ken_Mydocs_MSEcore_201-301_figures_Edge_dislocation_climb.svg

Figure 7.22: Schematic representation of dislocation climb.

If dislocations climb in the direction of

{\vec{n}}_{d}

(in the direction of the extra half plane) as illustrated in Figure 7.22, vacancies are destroyed. If they climb in the other direction (adding atoms to the extra half plane instead of removing them), the opposite occurs and vacancies are created. Dislocation climb therefore provides an mechanisms for equilibrating the vacancy concentration. For metals it is the process that allows us to assume that the vacancy concentration remains at equilibrium.

Dislocation motion occurs in specific crystallographic planes and directions. The following two rules of thumb are helpful here:

The slip plane in the plane with the highest planar density of atoms. This s the
The slip direction is the atoms

Which Plane Will Slip Occur?

image: 38_home_ken_Mydocs_MSEcore_201-301_figures_mechanical_props_2_pg_0038.svg

Which Direction Will Slip Occur?

image: 39_home_ken_Mydocs_MSEcore_201-301_figures_mechanical_props_2_pg_0039.svg

Slip Systems

image: 40_home_ken_Mydocs_MSEcore_201-301_figures_mechanical_props_2_pg_0040.svg

8 Fracture

The stress-strain behavior for a many material can exhibit a range of phenomena, depending on the temperature. This is particularly true of many polymers, which can show the range of behaviors in a uniaxial tensile test shown in Figure 8.1. While not all of these behaviors are necessarily observed in the same material, the following general regimes can often be identified:

T₁: Brittle behavior
T₂: Ductile behavior (yield before fracture)
T₃: cold drawing (stable neck)
T₄: uniform deformation

Here we are concerned with brittle behavior

(T_{1})

, or in some cases situations where there is a small degree of ductility in the sample (

T_{2}

image: 41_home_ken_Mydocs_MSEcore_201-301_figures_tensile_tests_at_diff_temps.svg

Figure 8.1: Typical generic temperature behavior at different temperatures.

8.1 Fracture Modes

Different fracture modes are defined by the relationship between the applied stress and the crack geometry. These are illustrated schematically in Figure 8.2 Fracture of a homogeneous material fracture generally occurs under Mode I conditions, and this is the most important condition. Mode II conditions, where a shear stress is applied in the direction perpendicular to the crack front, is often important for interfacial fracture, including the adhesive bonding of materials with different properties. Mode III is generally not important for our purposes.

image: 42_home_ken_Mydocs_MSEcore_201-301_figures_Fracture_modes_v2.svg

Figure 8.2: Fracture Modes .

8.2 Brittle behavior (fracture mechanics)

http://en.wikipedia.org/wiki/Fracture_mechanics

Mode I crack (stress normal to crack)

2 equivalent approaches:

Irwin model (stress-based approach)
Griffith model (energy-based approach)

8.2.1 The Irwin Model and the Stress Concentration

image: 43_home_ken_Mydocs_MSEcore_201-301_figures_hole_force_lines.svg

Figure 8.3: Force lines around a circular defect.

For an ellipse of with axis

a_{c}

perpendicular to the applied stress and axis

b_{c}

parallel to the applied stress (see Figure 8.4), the point of maximum stress is given by the following expression:

\begin{matrix} σ_{m a x} = σ_{0} (1 + 2 \frac{a_{c}}{b_{c}}) & (8.1) \end{matrix}

We can also write this in terms of the radius of curvature of the ellipse,

ρ_{c}

, at the point of maximum stress:

\begin{matrix} ρ_{c} = \frac{b_{c}^{2}}{a_{c}} & (8.2) \end{matrix}

Combination of Eqs.8.1 and8.2 gives:

\begin{matrix} σ_{m a x} = σ_{0} (1 + 2 \sqrt{a_{c} / ρ_{c}}) & (8.3) \end{matrix}

image: 44_home_ken_Mydocs_MSEcore_201-301_figures_elliptical_crack_schematic.svg

Figure 8.4: Elliptical crack with a crack tip radius of curvature,

ρ_{c}

8.2.2 Stress Intensity Factor

Consider a planar crack in the x-z plane, as shown conceptually Figure 8.5. The stress in the vicinity of the crack tip can be expressed in the following form:

\begin{matrix} σ = \frac{K}{\sqrt{2 π d}} f (θ) & (8.4) \end{matrix}

where

d

is the distance from the crack tip and

f (θ)

is some function of the angle

θ

that reduces to 1 for the direction directly in front of a crack (

θ = 0

). Different functional forms exist for

f (θ)

for the different stress components

σ_{x x}

σ_{y y}

, etc. The detailed stress fields depend on the loading mode (Mode I, II or II, or some combination of these), and the corresponding stress fields are specified by the appropriate value of

K

(

K_{I}

for mode I,

K_{I I}

for mode II or

K_{I I I}

for mode III).

(a)

image: 45_home_ken_Mydocs_MSEcore_201-301_figures_crack_axes.svg

(b)

image: 46_home_ken_Mydocs_MSEcore_201-301_figures_crack_geometry_polar.svg

Figure 8.5: Cartesian (a) and polar (b) coordinate axes use d to define stresses in the vicinity of a crack tip.

Mode I loading

The stresses in the vicinity of a mode I crack are given by the following[zehnder_linear_2012]:

\begin{matrix} (\begin{matrix} σ_{11} \\ σ_{22} \\ σ_{12} \end{matrix}) = \frac{K_{I}}{\sqrt{2 π d}} cos \frac{θ}{2} (\begin{matrix} 1 - sin \frac{θ}{2} sin \frac{3 θ}{2} \\ 1 + sin \frac{θ}{2} sin \frac{3 θ}{2} \\ cos \frac{3 θ}{2} sin \frac{θ}{2} \end{matrix}) & (8.5) \end{matrix}

This compact notation is used to specify the three relevant values of

f (θ) .

For example, for

σ_{11}

we have the following:

\begin{matrix} σ_{11} = (K_{I} / \sqrt{2 π d}) cos (θ / 2) (1 - sin \frac{θ}{2} sin \frac{3 θ}{2}) & (8.6) \end{matrix}

These expressions assume that the crack tip is very sharp, with a very small radius of curvature,

ρ_{c}

. If

d

is comparable to

ρ_{c}

, these equations no longer apply. Consider for example, the presence of an internal crack of length

a_{c}

and radius of curvature

ρ_{c}

in a thin sheet of material, shown schematically in Figure 8.6. In this case the stress at the crack edge is

σ_{m a x}

as given by Eq. 8.3. An assumption in the use of Eq. 8.5 is that the stresses are substantially less than

σ_{m a x}

. In other words,

K

describes the stress field close to the crack tip, but still at distances away from the crack tip that are larger than the crack trip radius of curvature,

ρ_{c}

The mode I stress intensity factor for this geometry is given by the applied stress,

σ_{0}

and the crack length

a_{c}

\begin{matrix} K_{I} = σ_{0} \sqrt{π a_{c}} & (8.7) \end{matrix}

For values of

d

that are substantially larger than

ρ_{c}

but smaller than

a_{c}

, we can determine the stresses from Eq. 8.5, with

K_{I}

as given by Eq. 8.7.

image: 47_home_ken_Mydocs_MSEcore_201-301_figures_crack_geometry.svg

Figure 8.6: An internal crack in a homogeneous solid.

Mode II loading

For mode II loading the crack tip stress fields are given by the following set of expressions[zehnder_linear_2012]:

\begin{matrix} (\begin{matrix} σ_{11} \\ σ_{22} \\ σ_{12} \end{matrix}) = \frac{K_{I I}}{\sqrt{2 π d}} (\begin{matrix} - sin \frac{θ}{2} (2 + cos \frac{θ}{2} cos \frac{3 θ}{2}) \\ sin \frac{θ}{2} cos \frac{θ}{2} cos \frac{3 θ}{2} \\ cos \frac{θ}{2} (1 - sin \frac{θ}{2} sin \frac{3 θ}{2}) \end{matrix}) & (8.8) \end{matrix}

It is generally difficult to determine

K_{I I}

in a straightforward way, and finite element methods must often be used to determine it for a given loading condition and experimental geometry. Once

K_{I I}

is known, the crack tip stress fields can be obtained from Eq. 8.8.

Mode III loading

While mode III loading is often encountered in practical applications, it is generally avoided in experiments aimed at assessing the fracture behavior of materials, and is not considered further in this text.

8.2.3 Fracture condition

In the stress-based theory of fracture, the material fails when the stress intensity factor reaches a critical value that depends on the material. For mode I loading, we refer to this critical stress intensity factor as

K_{I C}

. Setting

σ_{0}

to the fracture stress,

σ_{f}

, and setting

K_{I}

K_{I C}

in Eq. 8.7 gives:

\begin{matrix} K_{I C} = σ_{f} \sqrt{π a_{c}} & (8.9) \end{matrix}

Rearranging gives:

\begin{matrix} σ_{f} = K_{I C} / \sqrt{π a_{c}} & (8.10) \end{matrix}

So the fracture stress decreases as the flaw size,

a_{c}

, increases. This is why a material can appear to be fine, even though small cracks are present in the material. The cracks grow very slowly, but when the reach a critical size for which Eq. 8.10 is satisfied, the material fails catastrophically.

The fracture toughness,

K_{I C}

has strange units - a stress times the square root of a length. In order to understand where this characteristic stress and the characteristic length actually come from, we need to consider the actual shape of the crack tip. Using Eq. 8.3 we see that the maximum stress in front of the crack tip,

σ_{m a x}^{f}

, at the point of fracture is:

\begin{matrix} σ_{m a x}^{f} \approx 2 σ_{f} \sqrt{a_{c} / ρ_{c}} & (8.11) \end{matrix}

where we have assumed that

\sqrt{a_{c} / ρ_{c}} ≫ 1

, so that we can ignore the extra factor of 1 in Eq. 8.3. Now we can use Eq. 8.9 to substitute

K_{I C}

for

σ_{f}

. After rearranging we get:

\begin{matrix} K_{I C} \approx σ_{m a x}^{f} \frac{\sqrt{π}}{2} \sqrt{ρ_{c}} \approx σ_{m a x}^{f} \sqrt{ρ_{c}} & (8.12) \end{matrix}

This expression is really only valid for a crack tip with a well-defined radius of curvature, which is often not the case. Models that aim to predict and understand the fracture toughness of materials are all based on understanding the details of the yielding processes very close to the crack tip, and the resulting crack shape. We'll return to this issue later. For now we can summarize the stress-based approach fracture mechanics as follows:

With the exception of a very small region near the crack tip, all of the strains are elastic.
There is a very small plastic zone in the vicinity of a crack tip, with a characteristic dimension, $ρ$ that is determined by the details of the way the material plastically deforms.
Fracture occurs when the stress field defined by $K_{I}$ reaches a critical value.

9 Fuel Cells

Hydrogen can be reacted with oxygen to form water, in a very clean energy-producing reaction:

\begin{matrix} H_{2} + \frac{1}{2} O_{2} \to H_{2} O & (9.1) \end{matrix}

The standard free energy,

Δ G^{○}

of this reaction (gases at 1 atm pressure, pure water) is −236 kJ/mole. We could get this energy back just by burning hydrogen in air, but this is not very efficient. It's better to do it electrochemically in a fuel cell. In this case the energy of the reaction is converted to the electrical potential of electrons. We can determine this potential (or voltage) difference, which we refer to as

Δ V^{0}

, by equating

Δ G^{0}

with the energy required to change the potential of

n

moles of electrons by

Δ V^{○}

\begin{matrix} Δ G^{○} = - n Δ V^{○} N_{a v} | e | & (9.2) \end{matrix}

Faraday's constant,

F,

is defined as the total charge of a mole of electrons:

\begin{matrix} F \equiv N_{a v} | e | = 6.02 x 1 0^{23} \cdot 1.6 x 1 0^{- 19} C = 9.6 x 1 0^{4} C & (9.3) \end{matrix}

Multiplying the total charge (in Coulombs) by the potential difference (in volts) gives an energy, so it more convenient to express Faraday's constant in units of Joules per Volt, (which is equivalent to Coulombs (C)), so we have

F = 9.6 x 1 0^{5}

J/V. Combining Eqs. 9.2 and 9.3 and rearranging gives the following expression for

Δ V^{0}

\begin{matrix} Δ V^{○} = - \frac{Δ G^{○}}{n F} & (9.4) \end{matrix}

Which for the water formation reaction (Eq. 9.1) gives

Δ V^{0} = 1.23 V .

\begin{matrix} H_{2} & \to 2 H^{+} + 2 e^{-} \\ 2 H^{+} + 2 e^{-} + \frac{1}{2} O_{2} & \to H_{2} O & (9.5) \\ H_{2} + \frac{1}{2} O_{2} & \to H_{2} O \end{matrix}

We could also done this differently, where the two half cell reactions involve oxygen ions instead of protons. These are the relevant half reactions for a solid oxide fuel cell, for example:

\begin{matrix} \frac{1}{2} O_{2} + 2 e^{-} & \to O^{=} \\ H_{2} + O^{=} & \to H_{2} O + 2 e^{-} & (9.6) \\ H_{2} + \frac{1}{2} O_{2} & \to H_{2} O \end{matrix}

Using Eq. 9.4, we can use electrode potentials for each half reaction to obtain the value of

Δ G^{○}

from

Δ V^{○}

. Just as values of

Δ G^{○}

are given by the difference between standard free energies, values of

Δ V^{○}

are given by the difference between the electrode potentials for two half cell reactions. Several standard electrode potentials are listed in Table 2.

Table 2: Standard electrode potentials for a variety of half-cell reactions.

#	reaction	$V^{○}$ (V)
	$2 H^{+} + 2 e^{-} + \frac{1}{2} O_{2} \to H_{2} O$	1.23
	$2 H^{+} + 2 e^{-} \to H_{2}$	0

10 Corrosion

10.1 The Cost of Degradation/Corrosion

~5% of annual GDP goes to fighting/preventing degradation of material.

$850B dollars

Military Budget: $600B
Education Budget $70B
NASA Budget: $20B
Total US Budget: $1,100B

image: 48_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_statue_of_liberty.svg

Figure 10.1: Simulated images of the corrosion process in the Statue of Liberty

10.2 Corrosion of Metals

Corrosion in metals is electrochemical: Transfer of electrons from one chemical species to another.

Metals are often electropositive (electron-rich). Happy to give up electrons

image: 49_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0002.svg

10.3 Corrosion Susceptibility? Rough Approximation – Electronegativity*

image: 50_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0003.svg

10.4 Electrochemical Reaction:

image: 51_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0004.svg

image: 52_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0005.svg

10.5 The Galvanic Couple

image: 53_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0006.svg

10.6 Example: Fe-Cu Galvanic Couple

image: 54_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0007.svg

10.7 The Galvanic Series

image: 55_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0008.svg

image: 56_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0009.svg

10.8 Example: Fe-Cu Galvanic Couple

image: 57_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0010.svg

10.9 Metal Oxidation in O2

image: 58_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0011.svg

10.10 Preventing Corrosion

Li+(aq) + e− ⇌ Li(s)

image: 59_home_ken_Mydocs_MSEcore_201-301_figures_corrosion_pg_0012.svg

11 Materials Selection: A Case Study

The concept of a space elevator is illustrated in Figure 11.1. The idea is that we run a cable directly from the earth out to a point in space. If the center of mass is at a geosynchronous orbit, the entire assembly orbits the earth at the same angular velocity at which the earth is rotating. To get into space, we no longer need to use a rocket. We can simply 'climb' up the cable at any velocity that we want. The concept is certainly appealing if we can get it to work. But could the concept ever actually work? That is determined by the availability (or lack thereof) of materials with sufficient strength for the cable. We'll need to start with some analysis to Figure out what sort of properties are needed.

image: 60_home_ken_Mydocs_MSEcore_332_figures_space_elevator_schematic.png

Figure 11.1: Schematic representation of the space elevator.

Consider a mass,

m

, that is located a distance

r

from the center of the earth, as illustrated in Figure 11.2. The net force on the object is a centripetal force acting outward (positive in our sign convention) and a gravitational force acting inward (negative in our sign convention):

\begin{matrix} F = m ω^{2} r - G_{g r} M_{e} m / r^{2} & (11.1) \end{matrix}

where

G_{g r}

is the gravitational constant and

M_{e}

is the mass of the earth. The angular velocity of the earth is 2

π

radians per day, or in more useful units:

ω = \frac{2 π}{(24 h r) (3600 s / h r)} = 7.3 x 1 0^{- 5} s^{- 1}

It is convenient to rewrite the first term in terms of

g_{0}

, the gravitational acceleration at

r = r_{0}

(at the earth's surface):

\begin{matrix} g_{0} = \frac{G_{g r} M_{e}}{r_{0}^{2}} & (11.2) \end{matrix}

The net force on the mass at

r

can be written as follows:

\begin{matrix} F = m ω^{2} r - m g_{0} {(\frac{r_{0}}{r})}^{2} & (11.3) \end{matrix}

The net force is zero for

r = r_{s}

(geosynchronous orbit):

\begin{matrix} r_{s} = {(\frac{g_{0} r_{0}^{2}}{ω^{2}})}^{1 / 3} = 4.1 x 1 0^{7} m (22, 000 m i l e s) & (11.4) \end{matrix}

This is an easier number to remember than the angular velocity of the earth, so we use this expression for

r_{s}

to eliminate

ω

from Eq. 11.3, obtaining the following:

\begin{matrix} F = m g_{0} r_{0}^{2} (\frac{r}{r_{s}^{3}} - \frac{1}{r^{2}}) & (11.5) \end{matrix}

image: 61_home_ken_Mydocs_MSEcore_332_figures_earth_schematic_for_elevator.svg

Figure 11.2: Radial forces acting on an orbiting mass.

Now consider a cable that extends from the earths surface

(r = r_{0})

to a distance

r_{ℓ}

from the earth's surface, as shown in Figure 11.3. We need the cable to be in tension everywhere so that it doesn't buckle. If we get the tension at the earth's surface (

r = r_{0})

we're in good shape. The mass increment for a cable of length

d r

ρ A d r

, where A is the cross sectional area of the cable and

ρ

is the density of the material from which it was made. We obtain the total force,

F_{0}

at the earth's surface by integrating contributions to the force from the the whole length of the cable:

\begin{matrix} F_{0} = ρ A g_{0} r_{0}^{2} \int_{r_{0}}^{r_{ℓ}} (\frac{r}{r_{s}^{3}} - \frac{1}{r^{2}}) ⅆ r & (11.6) \end{matrix}

After integration we get:

\begin{matrix} F_{0} = ρ A g_{0} r_{0}^{2} [\frac{1}{2 r_{s}^{3}} (r_{ℓ}^{2} - r_{0}^{2}) + (\frac{1}{r_{ℓ}} - \frac{1}{r_{0}})] & (11.7) \end{matrix}

image: 62_home_ken_Mydocs_MSEcore_332_figures_space_elevator_geometry.svg

Figure 11.3: A cable extending from the surface of the earth to a distance

r_{ℓ}

away from the earth's center.

F_{0}

is plotted in Figure 11.4:

image: 63_home_ken_Mydocs_MSEcore_332_figures_space_elevator_cable.svg

Figure 11.4:

F_{0}

as given by Eq. 11.7.

The maximum tension is at

r = r_{s}

, and is obtained by integrating contributions to the force from

r_{s}

r_{ℓ}

\begin{matrix} F_{m a x} = ρ A g_{0} r_{0}^{2} [(\frac{1}{r_{ℓ}} - \frac{1}{r_{s}}) + \frac{1}{2 r_{s}^{3}} (r_{ℓ}^{2} - r_{s}^{2})] & (11.8) \end{matrix}

We have the following numbers:

$r_{0} = 6.4 x 1 0^{6}$ m (4,000 miles)
$r_{s} = 4.1 x 1 0^{7}$ m (22,000 miles)
$r_{ℓ} = 1.5 x 1 0^{8}$ m (90,000 miles)
$g_{0} = 9.8$ m/s $^{2}$

From these numbers we get

\frac{F_{m a x}}{ρ A} = \frac{σ_{m a x}}{ρ} = 4.8 x 1 0^{7} \frac{N / m^{2}}{K g / m^{3}}

Let's compare that to the best materials that are actually available. An Ashby plot of tensile strength (

σ_{f}

) and density is shown in Figure 11.5. A line with a slope of 1 on this double logarithmic plot corresponds to a range of materials with a constant value of

σ_{f} / ρ

. The line drawn on Figure 11.5 corresponds to

σ_{f} / ρ

\approx

2.8x10

^{6}

(in Si units), which is the most optimistic value possible for any known material - corresponding to the best attainable properties for diamond. Forgetting about any issues of cost, fracture toughness, etc., we could imagine that we see that we are a factor of 20 below the design requirement. So there's no way this is ever going to work, no matter how good your team of materials scientists is.

image: 64_home_ken_Mydocs_MSEcore_332_figures_materials_availability_2010.svg

Figure 11.5: Ashby plot of tensile strength and density.

All is not lost yet, however, since we really haven't optimized the geometry. The design we considered above has a constant radius, which we would really not want to do. What if we optimize the geometry so that material has the largest cross section at

r = r_{s}

(where the load is maximized). We'll consider a design where the actual cross section varies in a way that keeps the stress (tensile force divided by cross sectional area) constant. The analysis is a bit more complicated than we want to bother with here, but we get a simple expression for the maximum cross sectional area,

A_{s}

(at

r = r_{s}

), to the cross sectional area at the earth's surface (

A_{0},

r = r_{0}

) :

\begin{matrix} \frac{A_{s}}{A_{0}} = exp (\frac{0.77 r_{0} ρ g_{0}}{σ}) & (11.9) \end{matrix}

If we assume

σ / ρ = 2.8 x 1 0^{6} \frac{N / m^{2}}{K g / m^{3}}

, so that the system is operating at the value of

σ / f

corresponding to the solid line in Figure 11.5 gives

\frac{A_{s}}{A_{0}} = 110

. So in this case cable with a diameter of 1 cm at

r = r_{0}

needs to have a diameter of

\approx 10

cm at

r = r_{s}

. We don't have much leeway in decreasing

σ / ρ

, however. If the best we can do is

σ / ρ = 1.0 x 1 0^{6} \frac{N / m^{2}}{K g / m^{3}}

, we get

\frac{A_{s}}{A_{0}} = 1 0^{21}

, which is clearly not workable. So we are stuck with the requirement that the cable have a tensile strength corresponding to the best material on earth over a length of 90,000 miles, without a single critical defect that would cause the material to fail. Good luck with that.

12 Polymers and Soft Materials

Since the title of this book is 'Soft Materials', it makes sense to define what we really mean by 'soft'. Here are two ways to think about it:

Soft Materials have Low Elastic Moduli.

By 'low' we mean significantly lower than the moduli of crystalline metals and ceramics. The jellyfish shown in Fig. 12.1 is obviously 'soft' in this sense. Metals and ceramics typically have moduli in the range of 100 MPa (see Fig. 12.2). While the strength of metals can be adjusted by a variety of mechanisms that affect the nature of dislocation motion in these systems, the the modulus is set by the nature of the interatomic potentials and there nothing that can really be done to significantly affect the modulus of a given material. Polymers are different, however, and have a much broader range of elastic moduli. The stiffest of these (Kevlar™for example) have elastic moduli in at least one direction that are comparable to the modulus of steel.
Thermal Fluctuations Matter in Soft Materials.

At a molecular level, the relevant energy scale that determines a variety of important properties is the thermal energy, $k_{B} T$ , where $k_{B}$ is Boltzmann's constant and $T$ is the absolute temperature. If different molecular arrangements within a material differ in energy by an amount that of the order of $k_{B} T$ or less, than these different arrangements will all be experienced by the material. When the free energy of a material is dominated by the entropy associated with the accessibility of these different arrangements, it is possible to calculate the elastic properties of the material from the molecular structure with considerable accuracy.

image: 65_home_ken_Mydocs_MSEcore_331_figures_jellyfish.png

Figure 12.1: An example of a 'soft' material.

image: 66_home_ken_Mydocs_MSEcore_331_figures_Young_s_Modulus.png

Figure 12.2: Range of Young's moduli (Pa) for different materials classes.

Exercise: How high above the earths surface must a single oxygen molecule be lifted in order for its gravitational potential energy to be increased by

k_{B} T

Solution: The gravitational potential energy is

m g h

, where

m

is the mass of the object,

g

is the gravitational acceleration (9.8 m/s

^{2}

) and

h

is height. The mass of a single

O_{2}

molecule is obtained by dividing the molecular weight in g/mole by Avogadro's number:

m = 32 (\frac{g}{m o l e}) (\frac{m o l e}{6.02 x 1 0^{23}}) = 5.3 x 1 0^{- 23} g = 5.3 x 1 0^{- 26} k g

The conversion to kg illustrates the first point that we want to make with this simple calculation: Don't mix units and convert everything to SI units (m-kg-s) to keep yourself sane and avoid unit errors. Boltmann's constant,

k_{B}

needs to be in SI units as well:

k_{B} = 1.38 x 1 0^{- 23} J / K

Now we just need to equate

k_{B} T

m g h

, using something reasonable for the absolute temperature,

T

. I'll use

T

=300 K to get the following:

h = \frac{k_{B} T}{m g} = \frac{(1.38 x 1 0^{- 23} J / K) (300 K)}{(5.3 x 1 0^{- 26} k g) (9.8 m / s^{2})} = 8000 m = 8 k m

The full oxygen partial pressure is given proportional to

exp (- m g h / k_{B} T)

, so this value of

h

is the altitude where the oxygen pressure is a factor of

e

(2.7) less than the value at sea level.

12.1 Synthetic Polymers

Most of this text is devoted to synthetic polymers because of their widespread use and importance, and because they illustrate many of the key concepts that are relevant to natural polymers and other soft materials. We begin with a basic introduction to the synthesis of polymeric materials, and the z component is between properties of these materials. We conclude with some examples of soft materials made up of building blocks that are held together by relative weak forces.

12.1.1 What is a Polymer

A polymer is a large molecule made from many small

repeat units

or 'mers'. There is an inherent anisotropy at the molecular level because both strong and weak bonding interactions are important:

Strong covalent bonds are formed within a molecule (between 'mers').
Weak Van der Waals or hydrogen bonding are formed between molecules, and cause the materials to condense into a solid or liquid phase.

image: 67_home_ken_Mydocs_MSEcore_331_figures_Polymer.png

Figure 12.3: Schematic representation of a polymer

12.1.2 Classification Scheme

Crystallization and glass formation are the two most important concepts underlying the physical properties of polymers. Polymers crystallize at temperatures below

T_{m}

(melting temperature) and form glasses at temperatures below

T_{g}

(glass transition temperature). All polymers will form glasses under the appropriate conditions, but not all polymers are able to crystallize. The

classification scheme

shown in Figure 12.4 divides polymeric materials based on the locations of

T_{g}

and

T_{m}

(relative to the use temperature,

T

) and is a good place to start when understanding different types of polymers.

image: 68_home_ken_Mydocs_MSEcore_331_figures_classification_scheme.png

Figure 12.4: Classification scheme for polymeric materials.

Elastomers

Traditional elastomers are amorphous materials with a glass transition temperature less than the use temperature so that they remain flexible. The are generally crosslinked so that they do not flow over long periods of time. Common examples are shown in Figure 12.5.

image: 69_home_ken_Mydocs_MSEcore_331_figures_polychloroprene.png

Polychloroprene (Neoprene)

Polyisobutylene

Silicone

Figure 12.5: Examples of elastomeric materials.

Glassy Polymers

Glassy polymers are amorphous like elastomers, but their glass transition temperature is above the use temperature. Because of this they behave as rigid solids, with elastic moduli in the range of

1 0^{9}

Pa. Glassy polymers do not need to be crosslinked, because below

T_{g}

the molecules and flow of the material is suppressed. Also, because the materials are homogenous over length scales comparable to the wavelength of light, they are transparent. Common examples are illustrated in Figure 12.6.

image: 72_home_ken_Mydocs_MSEcore_331_figures_polymethylmethacrylate.png

Poly(methyl methacrylate) (PlexiGlas)

Polycarbonate

Poly(phenylene oxide)

Figure 12.6: Examples of glassy polymers.

Semicrystalline Polymers

Semicrystalline polymers must have molecular structures that are compatible with the formation of an ordered lattice. Most atactic polymers are amorphous (non-crystalline) for this reason (with the exception being examples like poly(vinyl alcohol where the side group is very small). Another requirement is that

T_{g}

be less than

T_{m}

. If the glass transition temperature is higher than

T_{m}

the material will form a glass before crystallization can occur. In the glassy polymer the material is kinetically trapped in the glassy state, even though the crystalline state has a lower free energy below

T_{m}

. Examples of some semicrystalline polymers are shown in Figure 12.7.

Polyethylene terephthalate.

image: 76_home_ken_Mydocs_MSEcore_331_figures_polytetrafluoroethylene.png

Poly(tetrafluoroethylene) (Teflon)

Spider Web

Figure 12.7: Examples of semicrystalline polymers.

12.2 Understanding Polymer Chemistry

Crystallization and glass formation processes are central to our understanding of polymeric materials, we must eventually address the following question:

How is a polymer's tendency to crystallize or form a glass determined by is molecular structure?

Before we answer this question, however, we must answer the following question:

What determines this molecular structure, and how are our choices limited?

In order to answer this question properly, we need to study the processes by which polymeric materials are made. Polymer synthesis involves organic chemistry. After familiarizing ourselves with some of the relevant polymer chemistry, we will be in a position to study the physical properties of polymers. For this reason, our discussion of molecular structure in polymers will include some chemistry

12.2.1 Covalent Bonding

Polymer molecules consist of atoms (primarily carbon, nitrogen, oxygen and hydrogen) which are covalently bound to one another. It is useful at this point to recall some of the basic principles governing the bonding between these atoms:

Nitrogen, oxygen and carbon atoms are surrounded by 8 electrons, included shared electrons.
Hydrogen atoms are surrounded by 2 electrons, included shared electrons.
A single bond involves two shared electrons, a double bond involves 4 shared electrons, and a triple bond involves 6 shared electrons.

12.2.2 Lewis Diagrams

Lewis diagrams (Wikipedia link) provide a convenient way of keeping track of the valence electrons in covalently bonded compounds. Several examples are given here. Note how the rules given on the previous page are followed in each case.

image: 78_home_ken_Mydocs_MSEcore_331_figures_Lewis_Diagrams.png

Figure 12.8: Examples of Lewis Diagrams

12.2.3 Bonding

The following principles of covalent bonding in organic materials are very helpful:

Oxygen: group 6 (6 valence electrons) - 2 more needed to complete shell -
oxygen forms 2 bonds with neighboring atoms
.
Nitrogen: group 5 (5 valence electrons) - 3 more needed to complete shell -
nitrogen forms 3 bonds with neighboring atoms
.
Carbon: group 4 (4 valence electrons) - 4 more needed to complete shell -
4 bonds with neighboring atoms
.
Hydrogen (or Fluorine): Group 1 -
1 bond with neighboring atoms
.

12.2.4 Shorthand Chemical Notation

Most of the chemical structures illustrated in this text are relatively simple, consisting of single and double bonds between atoms. We generally don't bother to write all of the carbons and hydrogens into to the structure. We use the following common conventions.

If no element is included, element at junctions between different bonds are assumed to be carbon.
If atoms are missing, so that the rules given above for the number of bonds attached to each atom type are not satisfied, the missing atoms are hydrogens.

An example of this convention is shown below in the structure for

benzene

: :

Figure 12.9: Examples of Shorthand Notation when drawing chemical structures

Note the resonance between the two possible ways of drawing the double bonds in the drawing on the left. Molecules with these types of alternating double and single bonds are referred to as

aromatic compounds

13 Polymerization Reactions

Polymerization is the process by which small molecules react with one another to form large polymer molecules. Polymerization reactions can be broken up into the following two general categories:

Step Growth Polymerizations:

Collections of A and B species react with one another. In linear step growth polymerizations, the ends of molecules react with one another to form longer molecules. A variety of reactions are possible, so you need to know at least a little organic chemistry. We'll focus on just a few of the most common cases.

Chain Growth Polymerizations:

Each polymer chain has one reactive site to which additional monomers are added.

Additional Resource:

The Macrogalleria web site has some excellent, simple descriptions of polymerization reactions. Specific examples are referenced at different points throughout this book.Click here for Macrogalleria polymerization overview.

13.1 Step-Growth Polymerizations

image: 80_home_ken_Mydocs_MSEcore_331_figures_Step_Growth_Animation_2.png

Figure 13.1: Polymers produced by step growth polymerization. The red and green circles correspond to 'A' and 'B' monomers that react with one another to form the polymer.

In this example green and red monomers can only react with each other. Because there are 5 more red monomers than green monomers, there are 5 molecules remaining at the end of the reaction, with each of these molecules possessing two red end groups. The extent of reaction,

p

is defined as the fraction of available reactive groups which have actually undergone a reaction. Values close to one are needed in order to obtain useful, high molecular weight polymer. A delicate stoichiometric balance generally needs to be maintained (same amount of red and green monomers) in order to obtain high molecular weight.

The following pages illustrate some of the specific reactions which take place during the polymerization process. To illustrate the concepts involved, we consider the following polymer types, all of which are produced by step-growth polymerization:

Section 13.1.1
Section 13.1.2
Section 13.1.3
Section 13.1.4

13.1.1 Polyamides

image: 81_home_ken_Mydocs_MSEcore_331_figures_amide_formation.png

Figure 13.2: Formation of an amide from an amine and a carboxylic acid

In this example, a primary amine reacts with a carboxylic acid to form an amide linkage. Water is liberated during the condensation reaction to form the amide. Primary amines and acid chlorides undergo a similar reaction:

image: 82_home_ken_Mydocs_MSEcore_331_figures_amide_from_acid_chloride.png

Figure 13.3: Formation of an amide from a primary amine and an acid chloride

Acid chlorides react very rapidly with amines at room temperature, which is very useful for demonstration purposes. Acid chlorides can also react with water to form carboxylic acids, however, and commercial polyamides are generally produced by reaction with carboxylic acids.

image: 83_home_ken_Mydocs_MSEcore_331_figures_Nylon_Rope_Trick.png

Figure 13.4: Schematic representation of the interfacial polymerization off nylon.

13.1.2 Polyesters

Polyesters can be formed by condensation reactions of alcohols with carboxylic acids:

image: 84_home_ken_Mydocs_MSEcore_331_figures_ester_formation.png

Figure 13.5: Formation of an ester from an alcohol and a carboxylic acid.

Polyethylene terephthalate (Mylar, Dacron, 2L soda bottles) is a common example. Note that under appropriate conditions, the reverse reaction (hydrolysis) reaction can also take place, where the addition of water to an ester bond forms the acid and the alcohol. This reaction is important in a variety of polymers used in biomedical applications, which degrade in the body via hydrolysis of the polymer. Polycaprolactone is one example.

image: 85_home_ken_Mydocs_MSEcore_331_figures_ester_hydrolysis.png

Figure 13.6: Ester hydrolysis: The reverse of the esterification reaction.

13.1.3 Polyurethanes

Polyurethanes are formed by the reaction of isocyanates with alcohols, as shown below:

image: 86_home_ken_Mydocs_MSEcore_331_figures_urethane_formation.png

Figure 13.7: Urethane Formation

Note that this is NOT a condensation reaction, since no byproducts are formed during the reaction. Also note that the urethane linkage contains an oxygen atom in the backbone, whereas the amide linkage does not. (The

R^{1}

and

R^{2}

substituents can have different structures, but are always attached to the illustrated linkages by carbon atoms.)

13.1.4 Epoxies

All epoxies involve reactions of epoxide groups (3-membered rings containing an oxygen atom) with curing agents. Amine curing agents are very common, as illustrated Figure , which shows a primary amine reacint with an epoxide group).

image: 87_home_ken_Mydocs_MSEcore_331_figures_epoxy1.png

Figure 13.8: Reaction of an epoxide with a primary amine.

The secondary amines which remain can react with additional epoxide groups to form a branched structure as shown in Figure 13.9. The reactive functionality of a primary diamine is 4 when the reaction is with an epoxide (as opposed to its functionality of 2 in the case where the diamine reacts with an acid or acid chloride).

image: 88_home_ken_Mydocs_MSEcore_331_figures_epoxy2.png

Figure 13.9: Reaction of an epoxide with a secondary amine.

14 Common Polymers

Here we list some common polymer produced by the different synthesis methods introduced in the previous sections.

14.1 Chain Growth: Addition to a Double Bond

14.1.1 Polyethylene

The simplest polymer from a structural standpoint is polyethylene, with the structure shown below in Figure 14.1.Dynamicity is not relevant in this case, since there are no substituents other than hydrogen on the carbon backbone.

image: 89_home_ken_Mydocs_MSEcore_331_figures_polyethylene.png

Figure 14.1: Chemical structure of polyethylene.

High Density Polyethylene:

High density polyethylene refers to version with very little chain branching, thus resulting in a high degree of crystallinity. Completely linear polyethylene has a melting point of 138 °C, and a glass transition temperature near -100 °C.

T_{g} = \approx - 120^{○}

T_{m} = 138^{○}

C (perfectly linear)

Low Density Polyethylene:

Low density polyethylenes (LDPE's) and high density polyethylenes (HDPE's) are identical in their chemical structure at the atomic level. They are actually structural isomers of one another. Chain branching within low density polyethylene inhibits crystallization, resulting in a material with a melting point lower than 138 degrees C. The decreased crystallinity of LDPE results in a material which is more flexible (lower elastic modulus) than HDPE.

Figure 14.2: Structure of low density polyethylene

The chain branches responsible for inhibiting crystallization in low density polyethylene are typically short. This illustration shows a 3-carbon (propyl) branch, potentially resulting from intramolecular chain transfer during the polymerization reaction.

T_{g} = \approx - 120^{○}

T_{m} < 138^{○}

C (depending on branching)

The Importance of Molecular Weight:

Polymeric materials generally have favorable mechanical properties only when the molecular weight is very large - typically hundreds of thousands of g/mol. The point is illustrated with polyethylene:

M = 16 g/mol: ethylene gas
M $≅$ 200 g/mol: candle wax
M $≅ 2 x 1 0^{5}$ - $5 x 1 0^{5}$ g/mol: milk jugs, etc.
M $≅ 3 x 1 0^{6}$ - $5 x 1 0^{6}$ g/mol: ultrahigh molecular weight polyethylene. This materials as excellent toughness and wear resistance, and is often used as one of the contact surfaces in joint implants.

14.1.2 Polypropylene

image: 91_home_ken_Mydocs_MSEcore_331_figures_polypropylene.png

Figure 14.3: Structure of polypropylene

The most widely used form of polypropylene is isostatic, with a melting point of 183 °C, and a glass transition temperature which is well below room temperature. Single crystals of polypropylene have lower moduli than single crystals of polyethylene along the chain direction, because of the helical structure of propylene. The modulus of isotropic semicrystalline polypropylene is often larger than that of high density polyethylene, however, because of the details of the semicrystalline structure that is formed. The uses of polypropylene and high density polypropylene are similar.

14.1.3 Polypropylene

This polymer included to illustrate the evolution o the polymer properties when we continue to make the side chain longer.

image: 92_home_ken_Mydocs_MSEcore_331_figures_polybutene-1.png

Figure 14.4: Polybutene-1

14.1.4 Poly(methyl methacrylate):

Poly(methyl methacrylate) (PMMA) is one of the most common materials used to make polymer glass. It is commonly known by the DuPont tradename Plexiglas,™ and has a glass transition temperature between 100 °C and 125 °C, depending on the tacticity. It is also forms the basis for many biomaterials, including dental adhesives.

T_{g} = 100 - 125^{○}

C, no

T_{m}

(atactic)

image: 93_home_ken_Mydocs_MSEcore_331_figures_polymethylmethacrylate_out.png

Figure 14.5: Poly(methyl methacrylate)

14.1.5 Poly(methyl acrylate)

Poly(methyl acrylate) is not a widely used polymer, primarily because it's glass transition temperature is too low (

\approx

^{○}

C for the atactic polymer) to be useful as a rigid polymer glass, and too high to be useful as an elastomer. It is included here to illustrate the effect that removing the extra methyl group from the polymer backbone has on the glass transition of the polymer.

T_{g} = 5^{○}

C, no

T_{m}

(atactic)

image: 94_home_ken_Mydocs_MSEcore_331_figures_polymethylacrylate.png

Figure 14.6: Poly(methyl acrylate).

14.1.6 Neoprene

Neoprene, also called polychloroprene, is a material commonly used in wetsuits. Like polyisoprene, it can be polymerized in different forms, corresponding to 1-2, 3-4, cis 1-4 and trans 1-4 addition of the monomer (trans 1-4 addition shown below). This pictured wetsuit has a 0.5mm layer of neoprene sandwiched between layers of nylon and another synthetic material.

image: 95_home_ken_Mydocs_MSEcore_331_figures_neoprene.png

Figure 14.7: Neoprene (polychloroprene).

14.1.7 Polyisobutylene

Polyisobutylene is a common material used to make elastomers, referred to more simply as 'butyl' rubber. It is generally copolymerized by with a small amount of isoprene, so that the resulting double bonds can be used to form a crosslinked material. It is more resistant to solvent penetration than most elastomers, and is often used in applications (like the gloves above) where barrier resistance is needed.

T_{g} = - 75^{○}

Figure 14.8: Polyisobutylene.

14.1.8 Polystyrene

Polystyrene is almost always atactic, and therefore amorphous. It has a glass transition temperature of 100 °C, and is therefore a glassy polymer at room temperature. Its uses are typically in packing material "Styrofoam", and for making cheap plastic objects, like the vials shown above. When suitably modified by the addition of other types of polymers, it is the basis for relatively high performance plastics such as high impact polystyrene (HIPS) and acrylonitrile-butadiene-styrene (ABS).

T_{g} = 100^{○}

C, no

T_{m}

(atactic)

image: 96_home_ken_Mydocs_MSEcore_331_figures_polystyrene.png

Figure 14.9: Structure of polystyrene.

14.1.9 Poly(tetrafluroethylene) (PTFE)

PTFE is more commonly known by its DuPont trade name, Teflon. Its most outstanding proproperties are its low surface energy and its low friction against a variety of other materials. It has very poor mechanical properties, however, and is difficult to process by its melting temperature excedes the temperature at which it begins to degrade.

T_{g} = 130^{○}

C (by one report[mohamed_temperature_2007]);

T_{m} \approx 330^{○}

image: 97_home_ken_Mydocs_MSEcore_331_figures_polytetrafluorethylene.png

Figure 14.10: Monomer unit of poly(tetrafluroethylene) (Image from[_teflon_????]).

14.1.10 Poly(vinyl acetate)

Poly(vinyl acetate) is often used as base for chewing gum. It is glassy at room temperature but becomes softer at body temperature, which is just above

T_{g}

T_{g} = 30^{○}

C, no

T_{m}

(atactic)

image: 98_home_ken_Mydocs_MSEcore_331_figures_polyvinylacetate.png

Figure 14.11: Monomer unit of poly(vinyl acetate)

14.1.11 Poly(vinyl chloride) PVC

Poly(vinyl chloride) can be partially crystalline even if the material is atactic, because the "R" group in this case is a chlorine atom, which is relatively small. The glass transition temperature of the material is 85 °C, although the addition of small molecules as "plasticizers" can reduce

T_{g}

to below room temperature. When a material is referred to as "vinyl", it is probably PVC. Record albums (before the age of compact disks) and water pipes are commonly made out of poly(vinyl chloride).

T_{g} = 85^{○}

C, no

T_{m}

(atactic)

image: 99_home_ken_Mydocs_MSEcore_331_figures_polyvinylchloride.png

Figure 14.12: Structure of poly(vinyl chloride)

14.1.12 Poly(vinyl pyridine)

Poly(vinyl pyridine) is very similar to the polystyrene, and its physical properties (, entanglement molecular weight, etc.Processiry similar. It exists in one of two forms, poly(2-vinyl pyridine) (P2VP and poly(4-vinyl pyridine) (P4VP), based on the location of the nitrogen in the phenyl ring. Both types interact strongly with metals. The polymers are not used in wide quantities, but have been useful in a range of model studies of polymer behavior, often when incorporated with another material as part of a block copolymer.

T_{g} = 100^{○}

C, no

T_{m}

(atactic)

image: 100_home_ken_Mydocs_MSEcore_331_figures_polyvinylpyridine.png

Figure 14.13: Structure of two types of poly(vinyl pyridine)

14.2 Chain Growth: Ring Opening

14.2.1 Poly(ethylene oxide)

Poly(ethylene oxide) (PEO) is generally formed by the ring opening polymerization of ethylene oxide. It is also referred to as polyethylene glycol, although this generally refers to lower molecular weight versions with hydroxyl end groups. PEO is water soluble, and is used in a wide range of biomedical applications, often in a gel form. Lithium salts are also soluble in PEO, and PEO/Li complexes are often used as an electrolyte in battery and fuel cell applications.

T_{g} = - 65^{○}

T_{m} \approx 65^{○}

image: 101_home_ken_Mydocs_MSEcore_331_figures_peo.png

Figure 14.14: Monomer unit of poly(ethylene oxide)

14.2.2 Polycaprolactam:

Polycaprolactam is the polyamide equivalent of polycaprolactone, and is synthesized by the ring opening polymerization of the corresponding cyclic amide. It is often referred to as Nylon 6 , since there are 6 carbon atoms in the repeating unit of the polymer. Note that this is different than Nylon 6,6 produced by condensation polymerization, where the repeat unit has 6 carbons originating from each of the two monomers used in the polymerization reaction.

T_{g} \approx 50^{○}

T_{m} \approx 220^{○}

image: 102_home_ken_Mydocs_MSEcore_331_figures_polycaprolactam.png

Figure 14.15: Polycaprolactam.

14.2.3 Polycaprolactone:

Polycaprolactone somewhat unique in that is a polyester that is synthesized by ring opening polymerization of a cyclic ester. It can be viewed as a polyester version of the polyamide, polycaprolactam. Contrary to step growth polymerization of polyesters, the ester linkage is not formed during the polymerization reaction, but is already present in the monomer. Polycaprolactone is biodegradable because the polymer slowly degrades by ester hydrolysis over time.

T_{g} \approx - 50^{○}

T_{m} = 60^{○}

image: 103_home_ken_Mydocs_MSEcore_331_figures_polycaprolactone.png

Figure 14.16: Polycaprolactone.

14.3 Step Growth Polymers

A variety of common polymers are discussed briefly in the pages below.

14.3.1 Kevlar™

Kevlar™ is a trademark of DuPont, Inc. The name actually is used to refer to a variety of aromatic polyamides, or aramids. As the name suggests, the polymers have phenyl groups in the backbone of the chain, and the repeat units are joined by amide linkages. The simplest possible aramid has the structure shown in Figure 14.17.

T_{m}

: above degradation temperature for the polymer.

image: 104_home_ken_Mydocs_MSEcore_331_figures_kevlar.png

Figure 14.17: Monomer unit of one version of Kevlar

14.3.2 Polycarbonate

A variety of polycarbonates exist. The most common one, (with the GE trademark of Lexan) has a glass transition temperature of 150 °C. It is used for compact disks, eyeglass lenses, and shatterproof glass, like that featured here in the greenhouse. See http://www.pslc.ws/macrog/pcsyn.htm for a good description of the synthesis of polycarbonate via a step growth, condensation reaction involving a phenolic di-alcohol and phosgene

(C O C l_{2}) .

T_{g} \approx 150^{○}

image: 105_home_ken_Mydocs_MSEcore_331_figures_polycarbonate_out.png

Figure 14.18: Polycarbonate.

14.3.3 Polyethylene Terephthalate (PET)

Polyethylene terephthalate (trade names include Mylar and Dacron) is produced in fiber form for textiles, and in film form for recyclable bottles, etc. Its degree of crystallinity is highly dependent on the the processing conditions, since it can easily be quenched to a glassy state before crystallization is able to occur.

= 80^{○}

= 260^{○}

image: 106_home_ken_Mydocs_MSEcore_331_figures_PET.png

image: 107_home_ken_Mydocs_MSEcore_331_figures_polyethyleneterephthalate_dacron.png

Figure 14.19: Polyethylene Terephthalate

14.3.4 Poly(phenylene oxide)

Polyphenylene oxide is a high performance polymer has many varied uses, largely because of its excellent performance at high temperatures.

\approx 190^{○}

Figure 14.20: Poly(phenylene oxide).http://plastiquarian.com/ppo.htm

14.3.5 Ultem Polyetherimide

Ultem (a trademark of GE) is a form of polyetherimide. It is a high performance polymer that combines high strength and rigidity at elevated temperatures with long term heat resistance (

T_{g} = 215^{○}

C). The repeat unit is illustrative of the complex chemical structure of many modern, high performance polymers.

image: 108_home_ken_Mydocs_MSEcore_331_figures_Ultem_Polyetherimide_1.png

image: 109_home_ken_Mydocs_MSEcore_331_figures_Ultem_Polyetherimide_2.png

Figure 14.21: Structure of Ultem polyetherimide, with some materials that have been made from it.http://www.alcanairex.com/products/e/100/120p01_e.htm

14.3.6 Silicones

Silicones are an important class of synthetic polymers which do not have carbon in the backbone. Instead, the backbone consists of alternating silicon and oxygen atoms. Different classes of silicones are specified by the substituents on the silicone atoms. Poly(dimethyl siloxane) (PDMS), with methyl substituents, is the most important silicone. Its glass transition and melting temperatures are very low, so that it remains flexible at very low temperatures. It also has a very low surface energy, and forms a hydrophobic surface that is very water resistant.

= \sim - 130 º C

;

= - 45 º C

image: 110_home_ken_Mydocs_MSEcore_331_figures_pdms_structure.png

Figure 14.22: Poly(dimethyl siloxane).

We list PDMS here as a step growth polymer because it can be produced from a self-condensation of silanol (SiOH) groups. The starting point is actually dimethyl-dichlorosilane. In th presence of water the SiCl bonds hydrolyze to SiOH:

image: 111_home_ken_Mydocs_MSEcore_331_figures_chlorosilane_hydrolysis.png

Figure 14.23: Hydrolysis of chlorosilane bonds.

The resultant silanol groups than can then condense by the elimination of water:

image: 112_home_ken_Mydocs_MSEcore_331_figures_silanol_condensation.png

Figure 14.24: Condensation of silanol groups.

One of the interesting features of silicones is that they can also be synthesized by anionic, ring opening polymerization of cyclic, oligomeric forms of PDMS. Here's one example:

image: 113_home_ken_Mydocs_MSEcore_331_figures_silione_anionic_polym.png

Figure 14.25: Anionic ring opening polymerization of a cyclic silicone oligomer.

1 Catalog Description

11 Materials Selection: A Case Study

12 Polymers and Soft Materials

13 Polymerization Reactions

14 Common Polymers

15 301 Problems

15.1 Course Organization

Send an email to Prof. Shull (k-shull@northwestern.edu) and Alane (Alane.lim@k-shull@northwestern.eduu.northwestern.edu) with the following information:

Any background about yourself that you want to share.
What you have enjoyed most and have found the most frustrating about your major.
One particular aspect of materials science that you would like to learn more about this quarter.

15.2 Atomic Structure and Bonding

Classify each of the following materials as to whether it is a metal, ceramic, or polymer. Justify each choice. (a.) brass; (b.) magnesium oxide (MgO); (c.) Plexiglass^®; (d.) polychloroprene; (e.) boron carbide (B₄C); and (f.) steel.

Site the difference between atomic mass and atomic weight.

Silicon has three naturally occurring isotopes: 92.23% of

^{28}

Si, with an atomic weight of 27.9769 amu, 4.68% of

^{29}

Si, with an atomic wight of 28.9738 amu, and 3.69% of

^{30}

Si, with an atomic weight of 29.938 amu. On the basis of these data, confirm that the average atomic weight of Si is 28.09.

Indium has two naturally occurring isotopes:

^{113}

In, with an atomic weight of 112.904 amu, and

^{115}

In, with an atomic weight of 114.904 amu. If the average atomic weight for In is 114.818 amu, calculate the fraction-of-occurrences of these two isotopes.

Address the following concepts concerning atomic mass.

How many grams are there in one amu of material?
Mole, in the context of this book, is taken in units of gram-mole. On this basis, how many atoms are there in a pound-mole of a substance?

Relative to electrons and electronic states, what does each of the four quantum numbers specify?

Give the electron configurations for the following ions: P

^{5 +}

, P

^{3 -}

, Sn

^{4 +}

, Se

^{2 -}

, I

^{-}

and Ni

^{2 +}

Potassium iodide (KI) exhibits predominately ionic bonding. The K

^{+}

and I

^{-}

ion have electron structures that are identical to which two inert gases?

Without consulting Callister Figure 2.8 or Table 2.2, determine whether each of the following atomic electron configurations is an inert gas, a halogen, an alkali metal, an alkaline earth metal, or a transition metal. List the number of valence electrons for each atom (except for the transition metals). Justify your choices.

$1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5}$
$1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{7} 4 s^{2}$
$1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6}$
$1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}$
$1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{5} 5 s^{2}$
$1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}$

The atomic radii of Mg²⁺ and F^- ions are 0.072 and 0.133 nm respectively.

Calculate the force of attraction between the two ions at their equilibrium interionic separation (i.e., when the ions just touch one another).
What is the force of repulsion at this same separation distance?

The force of attraction between a divalent cation and a divalent anion is

1.67 \times 1 0^{- 8} N

. If the ionic radius of the cation is 0.080 nm, what is the anion radius?

Here we're provided with the two pieces of information: the force of attraction between a cation/anion pair and the cation's atomic radius. With this information and an understanding of the Coulomb interaction we can calculate the anion radius.

The force of attraction between two isolated ions is defined by Callister Eq. 2.13:

The net potential energy between two adjacent ions,

E_{N}

, may be represented by the sum of Callister equations 2.9 and 2.11. That is:

\begin{matrix} E_{N} = - \frac{A}{r} + \frac{B}{r^{n}} & (15.1) \end{matrix}

Determine the equilibrium ionic bond energy,

E_{0}

, in terms of the parameters

A

B

, and

n

. Note that equilibrium occurs when the net force on the ions is zero. Use the following procedure:

Differentiate $E_{N}$ with respect to $r$ to acquire the expression for the interatomic $f o r c e$ .
Assume two adjacent ions a $E_{N}$ versus $r$ is minimum at $E_{0}$ .
Solve for $r$ in terms of $A$ , $B$ , and $n$ , which yields $r_{0}$ , the equilibrium interionic spacing.
Determine the expression for $E_{0}$ by substituting $r_{0}$ into the equation.

For an Na⁺-Cl^- ion pair, attractive and repulsive energies (

E_{A}

and

E_{R}

, respectively), depends on the distance between ions:

\begin{matrix} E_{A} & = - \frac{1.44 e V \cdot n m}{r} & (15.2) \\ E_{R} & = \frac{7.32 \times 1 0^{- 6} e V \cdot n m^{8}}{r^{8}} & (15.3) \end{matrix}

Superimpose on a single plot (by hand or using plotting software) $E_{A}$ , $E_{R}$ , and the net energy $E_{N}$ up to $r = 1.0 n m$ . Hint: You may have to truncate the plot on the $y$ -axis for good visualization.
From this plot, derive the equilibrium spacing, $r_{0}$ and the magnitude of the bonding energy, $E_{0}$ at the equilibrium spacing.
Now consider instead a K⁺-Cl^- bonding pair. The K⁺ ion is larger, which changes the repulsive term $E_{R}$ to be: $\begin{matrix} E_{R} = \frac{5.80 \times 1 0^{- 6} e V - n m^{9}}{r^{9}} & (15.4) \end{matrix}$ Without plotting the new $E_{N}$ , how do you expect $E_{0}$ and $r_{0}$ to change for the K⁺-Cl^- ion pair?

Briefly discuss the main differences between 1.) ionic, 2.) covalent, and 3.) metallic bonding.

Plot the bonding energy vs melting temperature for the following metals.

Element	Bonding Energy (kJ/mol)	Melting Temperature ( $^{○}$ C)
Hg	62	-39
Al	330	660
Ag	282	962
W	850	3414

Using this plot, approximate the bonding energy for molybdenum, which has a melting temperature of

T_{M} = 261 7^{○}

Compute the percent ionicity (&IC) of the interatomic bonds for each of the following compounds: MgO, GaP, CsF, CdS, and FeO. Which would we consider primarily ionic, and which would we consider primary covalent?

Semiconductors typically possess covalent bonds - which of the compounds above do you expect is (are) used as in semiconductor applications?

What are the predominant type(s) of bonding would be expected for each of the following materials: solid xenon, calcium fluoride (CaF₂), bronze (a copper alloy), cadmium telluride (CdTe), rubber, and tungsten?

15.3 Crystal Structure

The body-centered cubic (BCC) crystal structure is shown below in Fig. 15.1 Demonstrate the following:

The unit cell length (also referred to as a lattice parameter) is $a = 4 r / \sqrt{3}$ , where $r$ is the atomic radius.
The atomic packing factor (APF) is 0.68.

image: 114_home_ken_Mydocs_MSEcore_201-301_figures_Body-centered_cubic_crystal_lattice.svg

image: 115_home_ken_Mydocs_MSEcore_201-301_figures_BCC_filled.svg

Figure 15.1: The BCC structure.

This is the first problem you have in navigating and performing calculations on basic unit cells. This process is identical for all single-element unit cells (practice more if you need, see suggested problems) and you should be able to perform it for any cubic unit cell. In this case, visualizing how the atoms stack in the close-packed (touching) {111} directions is critical as well as some simple geometry and vector calculations.

Molybdenum has a BCC crystal structure, an atomic radius of 0.1363 nm, and an atomic weight of 95.94 g/mol. Compute and compare its theoretical density with the experimental value found inside the front cover of the Callister book.

Strontium has an FCC crystal structure, an atomic radius of 0.215 nm, and an atomic weight of 87.62 g/mol. Calculate the theoretical density for Sr. Make sure to use intuitive units (not g/nm³).

Calculate the radius of a palladium (Pd) atom,given that Pd has an FCC crystal structure, a density of

ρ_{P d} = 12.0

g/cm

^{3}

, and an atomic weight of A

_{P d} = 106.4

g/mol.

The atomic weight, density, and atomic radius for the three hypothetical alloys are listed in Table 15.3. For each, determine whether its crystal structure is FCC, BCC, or simple cubic (SC) and then justify your determination. Only work on this problem until you understand the concepts. It can get tedious.

Alloy	Atomic Weight (g/mol)	Density (g/cm $^{3}$ )	Atomic radius (nm)
A	43.1	6.40	0.122
B	184.4	12.30	0.146
C	91.6	9.60	0.137

Table 3: Alloy Properties

Iron (Fe) undergoes an allotropic transformation at

912^{o}

C. Upon heating it transitions from a BCC (

α

phase) to an FCC (

γ

phase). Accompanying this transformation is a change in the atomic radius of Fe – from

r_{B C C} = 0.12584

nm to

r_{F C C} = 0.12894

nm – and, in addition, a change in density (and volume). Compute the percentage volume change associated with this transformation. Does the volume increase or decrease?

For the tetragonal crystal system (

a = b \neq c

α = β = γ = 9 0^{○}

), identify the lattice directions that are equivalent to the (a) [011] and the (b) [100] directions, respectively.

Determine the indices for the directions shown in the following cubic unit cell (only do this problem until you understand the process):

image: 116_home_ken_Mydocs_MSEcore_201-301_figures_C03p35_Fig.svg

Determine the indices for the directions shown in the cubic unit cell below Fig. 15.3(a). Do as much of this problem as you need to understand the process.

image: 117_home_ken_Mydocs_MSEcore_201-301_figures_C03p36_C03p45_ComFig.svg

Figure 15.2: Some crystallographic directions (a) and planes (b)

For the tetragonal crystal system (

a = b \neq c

α = β = γ = 9 0^{○}

), identify the lattice directions that are equivalent to the (a) [011] and the (b) [100] directions, respectively.

Determine the Miller indices for the planes shown in the following unit cell:

image: 118_home_ken_Mydocs_MSEcore_201-301_figures_C03p45_Fig.svg

Determine the Miller indices for the planes shown in the following unit cell:

image: 119_home_ken_Mydocs_MSEcore_201-301_figures_C03p48_Fig.svg

For the tetragonal crystal system (

a = b \neq c

α = β = γ = 9 0^{○}

), identify the lattice directions that are equivalent to the (a) [011] and the (b) [100] directions, respectively.

Would you expect a material in which the atomic bonding is predominantly ionic is in nature to be more likely or less likely to form a noncrystalline solid upon solidification than a covalent material? Why? (See Callister Section 2.6)

Fig. 15.3 shows two tiled patterns. In each, draw a 2D unit cell — the simplest repeat unit in these patterns. Note — there are more than one possible answers.

image: 120_home_ken_Mydocs_MSEcore_201-301_figures_E03p01-Fig.svg

Figure 15.3: Periodic tiled patterns. From Baelde (Own work) [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0) via Wikimedia Commons.

Describe the differences in short-range order (bonding, local geometry) and long-range order (crystallinity) between crystalline and non-crystalline materials.

15.4 Imperfections

For some hypothetical metal, the equilibrium number of vacancies at

900^{o}

C is

2.3 \times 1 0^{25}

^{- 3}

. If the density and atomic weight of this metal are 7.40 g/cm

^{3}

and 85.5 g/mol, respectively, calculate the fraction of vacancies for this metal at

900^{o}

Calculate the activation energy for vacancy formation in aluminum given that the equilibrium number of vacancies at

50 0^{○}

C (773 K) is

7.57 \times 1 0^{23} m^{- 3}

. The atomic weight and density (at

50 0^{○}

C) for aluminum are, respectively,

26.98 g / m o l

and

2.62 g / c m^{3}

For both FCC and BCC crystal structures, there are two different types of interstitial sites. In each case, one site is larger than the other and is normally occupied by impurity atoms. For FCC, this larger one is located at the center of each edge of the unit cell; it is termed an octahedral interstitial site. On the other hand, with BCC the larger site type is found at

0

\frac{1}{2}

\frac{1}{4}

positions - that is, lying on {100} faces and situated midway between two unit cell edges on this face and one-quarter of the distance between the other two unit cell edges; it is termed a tetrahedral interstitial site. For both FCC and BCC crystal structures, compute the radius

r

of an impurity atom that will just fit into one of these sites in terms of the atomic radius

R

of the host atom.

Derive the following equations: (a) Equation 4.7a (b) Equation 4.9a (c) Equation 4.10a (d) Equation 4.11b

Atomic radius, crystal structure, electronegativity, and the most common valence are given in the following table for several elements; for those that are nonmetals, only atomic radii are indicated.

Element	Atomic Radius (nm)	Crystal Structure	Electronegativity	Valence
Ni	0.1246	FCC	1.8	+2
C	0.0710
H	0.0460
O	0.0600
Ag	0.1445	FCC	1.9	+1
Al	0.1431	FCC	1.5	+3
Co	0.1253	HCP	1.8	+2
Cr	0.1249	BCC	1.6	+3
Fe	0.1241	BCC	1.8	+2
Pt	0.1387	FCC	2.2	+2
Zn	0.1332	HCP	1.6	+2

Which of these elements would you expect to form the following with nickel at room temperature?:

a substitutional solid solution having complete solubility
a substitutional solid solution of incomplete solubility
an interstitial solid solution

(a)Compute the radius

r

of an impurity atom that will just fit into an FCC octahedral site in terms of the atomic radius

R

of the host atom (without introducing lattice strains).
(b) Repeat part(a) for the FCC tetrahedral site. (Note: You may want to consult Callister Figure 4.3a.)

(a) For BCC iron, compute the radius of a tetrahedral interstitial site. (For this problem, you need the result of Problem 4.9, which is

r = 0.291 R

, where

R

is the radius of the atoms in the FCC unit cell and

r

is the tetrahedron radius. You should do 4.9 if you don't understand how to find this.)

What is the composition, in weight percent, of an alloy that consists of 5 at% Cu and 95 at% Pt?

Molybdenum forms a substitutional solid solution with tungsten. Compute the number of molybdenum atoms per cubic centimeter for a molybdenum-tungsten alloy that contains 16.4 wt percent Mo and 83.6 wt percent W. The densities of pure molybdenum and tungsten are 10.22 and 19.30 g/cm3, respectively.

Calculate the number of atoms per cubic meter in Pb.

Cite the relative Burgers vector-dislocation line orientations for edge, screw, and mixed dislocations.

For an FCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (111) plane? Why? (Note: You may want to consult the solution to Problem 3.60 at the end of Chapter 3.)

(a)For a given material, would you expect the surface energy to be greater than, the same as, or less than the grain boundary energy? Why?
(b) The grain boundary energy of a small angle grain boundary is less than for a high-angle one. Why is this so?

Aluminum-lithium (Al-Li) alloys have been developed by the aircraft industry to reduce the weight and improve the performance of its aircraft. A commercial aircraft skin material having a density of 2.47 g/cm

^{3}

is desired. Compute the concentration of Li (in wt

%

) that is required.

15.5 Electrical Properties

Consider a cylindrical silicon specimen 7.0 mm in diameter and 57 mm in length.

A current of 0.25 A passes along the specimen in the axial direction. A voltage of 24 V is measured across two probes that are separated by 45 mm. What is the electrical conductivity of the specimen?
Compute the resistance over the entire 57 mm of the specimen.

A plain carbon steel wire 3 mm in diameter is to offer a resistance of no more than 20

Ω

. Using Callister Table 18.1, compute the maximum wire length.

Consider an aluminum wire 5 mm in diameter and 5 m in length.

Using the data in Callister Table 18.1, compute the resistance of the wire.
What would be the current flow if the potential drop across the ends of the wire is 0.04 volt?
What is the current density?
What is the magnitude of the electric field across the ends of the wire?

Recall electronic band structure as discussed in the book and lecture.

How does the electron structure of an isolated atom differ from that in a solid?
In terms of electron energy band structure, discuss the reasons for the difference in electrical conductivity among metals, semiconductors, and insulators.

Briefly state what is meant by the drift velocity and mobility of a free electron.

Consider free electrons moving in silicon at room temperature.

Calculate the drift velocity of the electrons when the magnitude of the electric field is 500 V/m.
Under these circumstances, how long does it take an electron to traverse a 25-mm length of crystal?

Silicon and germanium are two of the most technologically relevant semiconducting materials.

Using the data presented in Callister Fig. 18.16, determine the number of free electrons per atom for intrinsic germanium and silicon at room temperature (298 K). The densities for Ge and Si are 5.32 and 2.33 g/cm $^{3}$ , respectively.
Now, explain the difference in these free-electron-per-atom values.

For intrinsic semiconductors, the intrinsic carrier concentration

n_{i}

, depends on temperature as follows:

\begin{matrix} n_{i} & \propto exp (- \frac{E_{g}}{2 k_{B} T}) \end{matrix}

or, by taking the log of both sides of the equation:

ln n_{i} \propto - \frac{E_{g}}{2 k_{B} T}

A plot of $ln n_{i}$ versus $1 / T$ will therefore be linear and yield a slope of $- \frac{E_{g}}{2 k_{B}}$ . This is provided for you below for both Si and Ge. Using this information determine the band gap energies for silicon and germanium and compare these values with those in Callister Table 18.3.
Where does the factor of 2 in the denominator come from in these equations?

image: 121_home_ken_Mydocs_MSEcore_201-301_figures_ArrheniusSi_Ge.png

Figure 15.4: An Arrhenius plot relating

n_{i}

and

T

for (a.) Si and (b.) Ge.

Is it possible for compound semiconductors to exhibit intrinsic behavior? Explain your answer.

For each of the following pairs of semiconductors, decide which has the smallest band gap energy,

E_{g}

, and cite the reason for your choice.

C (diamond) and Ge
AlP and InAs
GaAs and ZnSe
ZnSe and CdTe
CdS and NaCl

For each impurity element in the following table , predict whether it will act as a donor or an acceptor when added to the indicated semiconducting material. Assume the that impurity elements are substitutional.

Impurity	Semiconductor
N	Si
B	Ge
S	InSb
In	CdS
As	ZnTe

image: 122_home_ken_Mydocs_MSEcore_201-301_figures_ElectronegativityPT.svg

Figure 15.5: Electronegativity values for the elements.

A concentration of

1 0^{24}

As atoms per cubic meter have been added to germanium to form an extrinsic semiconductor. At room temperature, virtually all of the As atoms can be considered to be ionized (i.e., one charge carrier exists for each As atom).

Is this material $n$ -type or $p$ -type?
Calculate the electrical conductivity of this material, assuming electron and hole mobilities of 0.1 and $0.05 m^{2} / V - s$ , respectively.

Calculate the conductivity of intrinsic silicon at 80

^{○}

Compare the temperature dependence of the conductivity for metals, intrinsic, and extrinsic semiconductors. Briefly explain the difference in behavior.

Calculate the room-temperature electrical conductivity of silicon that has been doped with

1 0^{23} m^{- 3}

carriers of arsenic atoms.

Briefly describe electron and hole motions in a

p - n

junction for forward and reverse biases. How do these lead to rectifying behavior?

Summarize Matthiessen's rules. That is, what are the factors that influence resistivity in metals?

15.6 Diffusion

Consider different diffusion mechanisms in solids:

Compare interstitial and vacancy atomic mechanisms for diffusion.
Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.

Consider the diffusion of carbon in BCC iron (

α

-Fe).

What diffusion mechanism to you expect for C in $α$ -Fe: interstitial or substitutional? Why?
Assuming that diffusion occurs via adjacent tetrahedral sites in $α$ -Fe, what family of crystallographic directions does this diffusion take place? Refer to the figure below to recall the locations f the interstitial sites in a BCC material.

image: 123_home_ken_Mydocs_MSEcore_201-301_figures_BCC_interstitials.png

Consider the role of the driving force in diffusion:

Briefly explain the concept of a driving force.
What is the driving force for steady-state diffusion?

A sheet of steel 2.5-mm thick has nitrogen atmospheres on both sides at 900

^{○}

C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is

1.85 \times 1 0^{- 10} m^{2} / s

, and the diffusion flux is found to be

1.0 \times 1 0^{- 7} k g / m^{2} \cdot s

. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is

2 k g / m^{3}

. How far into the sheet from this high-pressure side will the concentration be

0.5 k g / m^{3}

? Assume a linear concentration profile.

A sheet of BCC iron 2 mm thick was heated to 675

^{○}

C exposed to a carburizing gas atmosphere on one side and a decarburizing atmosphere on the other. After reaching steady-state, the iron was then quickly cooled to room temperature and the carbon concentrations on the two surfaces were determined to be 1.18 kg/m³ and 0.535 kg/m³.

Compute the diffusion coefficient if the diffusion flux is

7.36 \times 1 0^{- 9} k g / (m^{2} \cdot s)

. (You will need to convert wt% to mass density (Callister Eq. 4.9). Assume that the density of carbon is 2.25 g/cm³.)

F16: I don't like this problem. Too much math for very little intuitive gain. Also, the assumption that we use graphite density is not well-founded, and there's no way students could know this.

S17: Rewritten to eliminate tediousness of conversion.

Show that

C_{x} = \frac{B}{\sqrt{D t}} exp (- \frac{x^{2}}{4 D t})

is a solution to the Fick's second law:

\frac{\partial C}{\partial t} = D \frac{\partial^{2} C}{\partial x^{2}} .

Here, the parameters

B

and

D

are constant with respect to both

x

and

t

Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt% at a position 4 mm into an iron-carbon alloy that initially contains 0.10 wt% C. The surface concentration is to be maintained at 0.90 wt% C, and the treatment is to be conducted at

1100^{○} C

. Use the diffusion data for

γ

-Fe in Table 5.2

Nitrogen from a gaseous phase is to be diffused into pure iron at

675^{○} C

. If the surface concentration is maintained at 0.2 wt% N, what will be the concentration 2 mm from the surface after 25 h? The diffusion coefficient for nitrogen in iron at

675^{○} C

2.8 \times 1 0^{- 11} m^{2} / s

Cite the values of the diffusion coefficients for interdiffusion of carbon in both

α

-iron (BCC) and

γ

-iron (FCC) at

900 Â ° C

Which is larger and why?

The diffusion coefficients for nickel in iron are given at two temperatures, as follows:

$T (K)$	$D (m^{2} / s)$
1473	$2.2 \times 1 0^{- 15}$
1673	$4.98 \times 1 0^{- 14}$

Determine the values of $D_{0}$ and the activation energy, $Q_{d}$ .
What is the magnitude of $D$ at $1300^{○} C$ (1573 K)?

The diffusion coefficients for carbon in nickel are given at two temperatures, as follows:

$T^{○} C$	$D (m^{2} / s)$
600	$5.5 \times 1 0^{- 14}$
700	$3.9 \times 1 0^{- 13}$

Determine the values of $D_{0}$ and $Q_{d}$ .
What is the magnitude of $D$ at $850^{○} C$ ?

The figure below shows a plot of the base-10 logarithm of the diffusion coefficient vs reciprocal of the absolute temperature for the diffusion of gold in silver. Determine the values for the activation energy and the preexponential.

For the predeposition heat treatment of a semiconducting device, gallium atoms are to be diffused into silicon at a temperature of

1150^{○} C

for 2.5 hrs. If the required concentration of Ga at a position 2

μ

m below the surface is

8 \times 1 0^{23} a t o m s / m^{3}

, compute the required surface concentration of Ga. Assume the following:

The surface concentration remains constant
The background concentration is $2 \times 1 0^{19} G a a t o m s / m^{3}$
Preexponential and activation energies are $3.74 \times 1 0^{- 5} m^{2} / s$ and $3.39 e V / a t o m$ , respectively.

Suppose you are considering two carburization processes for steel. Assume that both processes give materials with identical performance characteristics, and that your goal is to minimize the processing time. Process A requires that the carbon diffuse twice as far into the iron as process B. The carbon diffusion coefficient for process A is 3 times as large as for process B. Which process do you choose, and why?

15.7 Phase Diagrams

100^{○} C

, what is the maximum solubility of the following:

Pb in Sn
Sn in Pb

image: 124_home_ken_Mydocs_MSEcore_201-301_figures_PbSn.svg

Figure 15.6: Pb-Sn Phase Diagram

What thermodynamic condition must be met for a state of equilibrium to exist?

A 50 wt% Ni-50 wt% Cu alloy is slowly cooled from

1400^{○} C

1200^{○} C

At what temperature does the first solid phase form?
What is the composition of this solid phase?
At what temperature does the liquid solidify?
What is the composition of this last remaining liquid phase?

image: 125_home_ken_Mydocs_MSEcore_201-301_figures_NiCu_PhaseDiagram.svg

Figure 15.7: Cu-Ni Phase Diagram

A 40 wt% Pb-60 wt% Mg alloy is heated to a temperature within the

α

+Liquid phase region. If the mass fraction of each phase is 0.5, then estimate:

The temperature of the alloy
The compositions of the two phases in weight percent

image: 126_home_ken_Mydocs_MSEcore_201-301_figures_PbMg.svg

Figure 15.8: Mg-Pb phase diagram.

A copper/silver alloy is heated to 900

^{○}

C and is found to consist of

α

and liquid phases. If the mass fraction of the liquid phase is 0.68, determine:

The composition of both phases, in both weight percent and atom percent.
The composition of the alloy, in both weight percent and atom percent.

image: 127_home_ken_Mydocs_MSEcore_201-301_figures_AgCu.svg

Figure 15.9: Cu/Ag Phase Diagram.

A 60 wt percent Pb-40 wt percent Mg alloy (see Fig. 15.8) is rapidly quenched to room temperature from an elevated temperature in such a way that the high-temperature microstructure is preserved. This microstructure is found to consist of the

α

phase and Mg

_{2}

Pb, having respective mass fractions of 0.42 and 0.58. Determine the approximate temperature from which the alloy was quenched.

For a 76 wt% Pb-24 wt% Mg alloy (see Fig. 15.8), make schematic sketches of the microstructure that would be observed for conditions of very slow cooling to the following temperatures:

575^{○} C

500^{○} C

450^{○} C

, and

300^{○} C

. Label all phases and indicate their approximate compositions.

For the tin/gold system, specify the temperature-composition points at which all eutectics, eutectoids, peritectics, and peritectoid phase transformations occur. Also, for each, write the reaction upon cooling. Note,

β

γ

, and

δ

are labeling the intermetallic phases which are indicated by vertical lines on the phase diagram.

image: 128_home_ken_Mydocs_MSEcore_201-301_figures_SnAu.svg

Figure 15.10: Sn/Au Phase Diagram

Compute the mass fractions of

α

-ferrite and cementite

F e_{3} C

that in pearlite, formed by cooling steel with a composition equal to the eutectoid composition.

image: 129_home_ken_Mydocs_MSEcore_201-301_figures_Fe-C.svg

Figure 15.11: Fe-C Phase Diagram

3.5 kg of austenite containing 0.95 wt% C is cooled below 727

^{○}

What is the proeutectoid phase?
How many kilograms each of total ferrite and cementite form?
How many kilograms each of pearlite and proeutectoid phase form?
Schematically sketch and label the resulting microstructure.

15.8 Phase Transformations

The kinetics of the austenite-to-pearlite transformation obeys the Avrami relationship. Using the fraction transformed-time data given below, determine the total time required for 95% of the austenite to transform to pearlite.

Fraction Transformed	Times ( $s$ )
0.2	280
0.6	425

Using the isothermal transformation diagram for an iron-carbon alloy of eutectoid composition (Callister Figure 10.22), specify the nature of the final microstructure (in terms of microconstituents present and the approximate percentages of each) of a small specimen that has been subjected to the following time-temperature treatments. In each case, assume that the specimen begins at

760^{○} C

and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure. Do this problem until you feel that you understand the process.

Cool rapidly to $350^{○} C$ , hold for $1 0^{3} s$ , and then quench to room temperature.
Rapidly cool to $625^{○} C$ , hold for $10 s$ , and then quench to room temperature.
Rapidly cool to $600^{○} C$ , hold for $4 s$ , rapidly cool to $450^{○} C$ , hold for 10 s, then quench to room temperature.
Reheat the specimen in part (c) to $700^{○}$ for 20 h.
Rapidly cool to $300^{○} C$ , hold for 20 s, then quench to room temperature in water. Reheat to $425^{○} C$ for $1 0^{3} s$ and slowly cool to room temperature.
Cool rapidly to $665^{○} C$ , hold for $1 0^{3} s$ , then quench to room temperature.
Rapidly cool to $575^{○} C$ , hold for 20 s, rapidly cool to $350^{○}$ , hold for 100 s, then quench to room temperature.
Rapidly cool to $350^{○} C$ , hold for 150 s, then quench to room temperature.

Callister Figure 10.40 shows the continuous-cooling transformation diagram for a 0.35 wt% C iron-carbon alloy. Make a copy of this figure and then sketch and label the continuous-cooling curves to yield the following microstructures:

Fine pearlite and proeutectoid ferrite
Martensite
Martensite and proeutectoid ferrite
Coarse pearlite and proeutectoid ferrite
Martinsite, fine pearlite, and proeutectoid ferrite.

15.9 Mechanical Properties

The figure to the right below shows the tensile stress-strain curve for a plain-carbon steel. Extract the following:

The alloy's tensile strength.
The modulus of elasticity.
The yield strength.

image: 130_home_ken_Mydocs_MSEcore_201-301_figures_06p03FE_Fig.svg

A specimen of copper having a rectangular cross section 15.2 mm

\times

19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain.

Consider a cylindrical specimen of a steel alloy (Figure 6.22) 8.5 mm in diameter and 80 mm long that is pulled in tension. Determine its elongation when a load of 65,250 N is applied.

The net bonding energy

E_{N}

between two isolated positive and negative ions is a function of interionic distance

r

as follows:

E_{N} = - \frac{A}{r} + \frac{B}{r^{n}}

where

A

B

, and

n

are constants for the particular ion pair. Equation 6.31 is also valid for the bonding energy between adjacent ions in solid materials. The modulus of elasticity

E

is proportional to the slope of the interionic force-separation curve at the equilibrium interionic separation; that is,

E \propto (\frac{d F}{d r})_{r_{0}}

Derive an expression for the dependence of the modulus of elasticity on these

A

B

, and

n

parameters (for the two-ion system), using the following procedure:

Establish a relationship for the force F as a function of $r$ , realizing that: $F = - \frac{d E_{n}}{d r}$
Now take the derivative $d F / d r$ .
Develop an expression for $r_{0}$ , the equilibrium separation. Because $r_{0}$ corresponds to the value of $r$ at the minimum of the $E_{N}$ -versus- $r$ curve (Callister Figure 2.10b), take the derivative $d E_{N} / d r$ , set it equal to zero, and solve for $r$ , which corresponds to $r_{0}$ .
Finally, substitute this expression for $r_{0}$ into the relationship obtained by taking $d F / d r$ .

Consider the brass alloy for which the stress-strain behavior is shown below. A cylindrical specimen of this material 10.0 mm in diameter and 101.6 mm long is pulled in tension with a force of 10,000 N. If it is known that this alloy has a value for Poisson's ratio of 0.35, compute (a) the specimen elongation and (b) the reduction in specimen diameter.

image: 131_home_ken_Mydocs_MSEcore_201-301_figures_brass_tensile.png

The figure below shows the tensile engineering stress-strain behavior for a steel alloy.

What is the modulus of elasticity?
What is the yield strength at a strain offset of 0.002?
What is the tensile strength?
What is the elongation-to-failure, or ductility?
What is the resilience, $U_{r}$ , of the material?

The figure below shows the tensile engineering stress-strain behavior fro a steel alloy.

What is the modulus of elasticity?
What is the proportional limit?
What is the yield strength at a strain offset of 0.002?
What is the tensile strength?

image: 132_home_ken_Mydocs_MSEcore_201-301_figures_C06p26_Fig.svg

Calculate the modulus of resilience for the material having the stress-strain behavior shown in Fig. 6.12 and 6.22.

Determine the modulus of resilience for each of the following alloys.

Material	Yield Strength (GPa)	Young's Modulus (GPa)
Steel alloy	0.830	207
Brass alloy	0.380	97
Aluminum alloy	0.275	69
Titanium alloy	0.690	107

A steel alloy to be used for a spring application must have a modulus of resilience of at least 2.07 MPa. What must be its minimum yield strength?

Find the toughness (or energy to cause fracture) for a metal that experiences both elastic and plastic deformation. Assume Callister Eq. 6.5 for elastic deformation, that the modulus of elasticity is 103 GPa, and that the elastic deformation terminates at a strain of 0.007.

For plastic deformation, assume the relationship between stress and strain is described by Eq. 6.19, in which the values for

K

and

n

are 1520 MPa and 0.15, respectively. Furthermore, plastic deformation occurs between strain values of 0.007 and 0.60, at which point fracture occurs.

The motion of dislocations is influenced by a material's crystal structure.

Define a slip system.
Do all metals have the same slip system? Why or why not?

One of the slip systems in the BCC crystal structure is {110}

⟨ 111 ⟩

Sketch a plane that is a member of the {110} family, representing atoms with circles. Using arrows, indicate two different

⟨ 111 ⟩

slip directions within this plane.

The expressions for the Burger's vectors for FCC and BCC crystal structures are both of the form

b = \frac{a}{2} ⟨ u v w ⟩

Here,

a

is the unit cell length and

u v w

are the crystallographic direction indices. We can find the magnitudes of the Burger's vector using:

b = \frac{a}{2} {(u^{2} + v^{2} + w^{2})}^{1 / 2}

Determine the values of

| b |

for Cu and

α

-Fe.

Consider a simple cubic (SC) crystal structure.

In the same manner as Callister Eqs. 7.1a-7.1c, specify the Burgers vector for the simple cubic crystal structure whose unit cell is shown in Callister Figure 3.3. You may find Figures 4.4 and 7.1 useful.
Formulate an expression for the magnitude of the Burgers vector for the simple cubic system in the same form as that in Callister Eq. 7.11.

Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 60

^{○}

and 35

^{○}

, respectively, with the tensile axis. If the critical resolved shear stress is 6.2 MPa, will an applied stress of 12 MPa cause the single crystal to yield? If not, what stress would be necessary?

Consider a single crystal of nickel oriented such that a tensile stress is applied along a [001] direction. If slip occurs on a (111) plane and in a

[\overline{1} 01]

direction and is initiated at an applied tensile stress of 13.9 MPa, compute the critical resolved shear stress.

A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [001] direction.

If the critical resolved shear stress for this material is 0.5 MPa, calculate the magnitude(s) of applied stress(es) necessary to cause slip to occur on the (111) plane in each of the

[\overline{1} 10]

[\overline{1} 01]

, and

[0 \overline{1} 1]

directions.

Describe in your own words the following three strengthening mechanisms: grain size reduction, solid-solution strengthening, and strain hardening. Explain how dislocations are involved in each of the strengthening techniques.

In the manner of Callister Figures 7.17b and 7.18b, indicate the location in the vicinity of an edge dislocation at which an interstitial impurity atom would be expected to be situated. Now briefly explain in terms of lattice strains why it would be situated at this position.

A cylindrical specimen of cold-worked copper has a ductility (%EL) of 15%. If its cold-worked radius is 6.4 mm, what was its radius before deformation?

Briefly cite the differences between recovery, recrystallization, and grain growth in terms of mechanism and influence on mechanical properties.

15.10 Fracture Mechanics

What is the magnitude of the maximum stress that exists at the tip of an internal crack having a radius of curvature of

1.9 \times 1 0^{- 4} m m

and a crack length of

3.8 \times 1 0^{- 2} m m

when a tensile stress of

140 M P a

is applied?

An MgO component must not fail when a tensile stress of

13.5 M P a

is applied. Determine the maximum allowable surface crack length if the surface energy of MgO is

1.0 J / m^{2}

. Data found in Callister Table 12.5 may prove helpful.

An aircraft component is fabricated from an aluminum alloy that has a plane-strain fracture toughness of

40 M P a \sqrt{m}

. It has been determined that fracture results at a stress of

300 M P a

when the maximum (or critical) internal crack length is

4.0 m m

. For this same component and alloy, will fracture occur at a stress level of

260 M P a

when the maximum internal crack length is 6.0 mm? Why or why not?

A cylindrical bar of ductile cast iron is subjected to reversed and rotating-bending tests; test results (i.e. S-N behavior) are shown in Callister Figure 8.20. If the bar diameter is 9.5 mm, determine the maximum cyclic load that may be applied to ensure that fatigue failure will not occur. Assume a factor of safety of 2.25 and that the distance between loadbearing points is 55.5 mm.

List four measures that may be taken to increase the resistance to fatigue of an alloy.

The creep data below were taken on an aluminum alloy at 480

^{○}

C and a constant stress of 2.75 MPa. Plot the data as strain vs time, then determine the steady-state or minimum creep rate. Note: The initial and instantaneous strain is not included.

For a cylindrical S-590 alloy specimen (Callister Figure 8.32) originally 14.5 mm in diameter and 400 mm long, what tensile load is necessary to produce a total elongation of 52.7 mm after 1150 hr at

650^{○} C

? Assume that the sum of instantaneous and primary creep elongations is 4.3 mm.

The fracture toughness,

K_{I C}

for a brittle material can be approximated as

σ_{m a x}^{f} \sqrt{ρ_{c}}

, where

σ_{m a x}^{f}

is the maximum stress in that the material can support and

ρ_{c}

is the crack tip radius of curvature. In a very brittle material we can often approximate

σ_{m a x}^{f}

E / 10

where

E

is Young's modulus. Look up values for

E

and

K_{I C}

for window glass to obtain an estimate for

ρ_{c}

15.11 Corrosion

Briefly explain the difference between oxidation and reduction electrochemical reactions.
Which reaction occurs at the anode and which at the cathode?

Write down the reaction to form water from hydrogen and oxygen. Use the standard free energy of this reaction (-236 kJ/mole) to determine the energy content of hydrogen fuel in electron volts per hydrogen atom.
Write down the two half cell reactions for each of the following versions of the reaction from part a:
1. The version involving involving proton conduction through a polymer electrolyte membrane.
2. The version involving oxygen anion diffusion through a solid oxide electrolyte like ZrO $_{2}$ .
Look up the standard electrode potentials for the two half reactions for the polymer electrolyte membrane calculation, and show that it the total energy obtained from the fuel cell is consistent with the energy per hydrogen atom calculated from part a.

For the following pairs of alloys that are electrically coupled in seawater, predict the possibility of corrosion for each. If corrosion is probable, identify the metal/alloy that will corrode.

Aluminum and cast iron
Inconel and nickel
Cadmium and zinc
Brass and Titanium
Low-carbon steel and copper.

From the galvanic series (Table 17.2 in Callister), cite three metals/alloys that may be used to galvanically protect cast iron.
Galvanic corrosion at an interface between two metals can be prevented by making an electrical contact between the two metals in the couple and a third metal that is anodic to the other two. Using the galvanic series, name one metal that could be used to protect a nickel-steel galvanic couple.

Describe how protection mechanisms at work in the following two cases:
1. Galvanized iron
2. Stainless steel
Provide an an application where you would choose to use galvanized iron, and one where you would choose to use stainless steel, and provide your reasoning.

A brine solution is used as a cooling medium in a steel heat exchanger. The brine is circulated within the heat exchanger and contains some dissolved oxygen. Suggest three methods (limit yourselves to those covered in class) other than cathodic protection that would reduce the corrosion of the the steel in the brine. Explain the rational for each suggestion.

15.12 Ceramics

Show that the minimum cation-to-anion radius ratio for a coordination number of 4 is 0.225.

Show that the minimum cation-to-anion radius ratio for a coordination number of 6 is 0.414. (Hint: Use the NaCl crystal structure in Figure 12.2, and assume that anions and cations are just touching along cube edges and across face diagonals.)

Demonstrate that the minimum cation-to-anion radius ratio for a coordination number of 8 is 0.732.

On the basis of ionic charge and ionic radius given in Callister Table 12.3, predict crystal structures for the following materials and justify your decision:

CaO
MnS
KBr
CsBr

The zinc blende crystal structure is on that can be derived from close-packed planes of anions. The sulfide anion sub-lattice will be FCC. Don't just copy values from Table 12.4. You already know how to look things up in tables...

Will cations fill tetrahedral or octahedral positions? Why?
What fraction of the positions will be occupied?

Compute the theoretical density of NiO, given that it has the rock salt crystal structure.

Compute the atomic packing factor for the rock salt crystal structure in which

\frac{r_{C}}{r_{A}} = 0.414

A hypothetical AX type of ceramic material is known to have a density of 2.10 g/cm

^{3}

and a unit cell of cubic symmetry with a cell edge length of 0.57 nm. The atomic weights of the A and X elements are 28.5 and 30.0 g/mol, respectively. On the basis of this information, which of the following crystal structures is (are) possible for this material: sodium chloride, cesium chloride, or zinc blende? Justify your choice(s).

What happens to the oxygen vacancy concentration in ZrO

_{2}

if a small amount of Zr on the crystal lattice is replaced by Ca? How would this affect the performance of the ZrO

_{2}

used as a solid electrolyte in a solid oxide fuel cell?

15.13 Polymers

Compute the repeat unit molecular weights for the following. Only do this problem until you are confident you understand the process:

polytetrafluoroethylene
poly(methyl methacrylate)
poly(ethylene terephthalate)

Consider the thermoplastic and thermoset nature of polymers: (a) Is it possible to grind up and reuse an epoxy? Why or why not? (b) Is it possible to grind up and reuse polypropylene? Why or why not?

An alternating copolymer is known to have a number-average molecular weight of 100,000 g/mol and a degree of polymerization of 2210. If one of the repeat units is ethylene, which of styrene, propylene, tetrafluoroethylene, and vinyl chloride is the other repeat unit? Why?

For each of the following pairs of polymers, state whether it is possible to determine whether one polymer is more likely to crystallize than the other, and give the reason for your answer.

Atactic poly(vinyl chloride); linear and isotactic polypropylene
A fully cured epoxy sample; linear and isotactic polystyrene

Calculate the repeat unit molecular weights for each of the polymers shown in the 'common polymers' section of the text.

Draw the chemical structure of the monomer(s) and the repeating unit for one polymer in each of the following classes:

A polymer polymerized by chain growth addition to a double bond.
A polymer polymerized by ring opening chain growth.
A linear stop growth polymer.

Note: you should be draw the chemical structures of the repeat unit, given the structure of the monomers, and vice versa, for all of the polymer structures in in the 'common polymers' portion of the online 301 text.

Draw Lewis diagrams illustrating the valence shell configurations for polystyrene, poly(methyl methacrylate).

Draw Lewis diagrams illustrating the valence shell configurations for amide, ester and urethane linkages.

Consider the following 5 monomers:

image: 133_home_ken_Mydocs_MSEcore_331_figures_2-1-problem.png

Draw the repeat units for two linear polymers that can be produced by reactions between the monomers in this list. Identify these polymers according to their type (polyamides, polyesters, etc.), and indicate whether each polymerization reaction is condensation reaction or not.
What combination of monomers from this list would you choose in order to produce a three-dimensional network?

Suppose you want to sell a set of cheap plastic mugs which are suitable for drinking coffee. Briefly discuss the potential applicability of the following materials for this purpose:

atactic polystyrene
atactic poly(vinyl chloride)
high density polyethylene

Index

Aromatic compounds: 1
Benzene: 1
Boltmann's Constant: 1
Burgers circuit: 1
Burgers vector: 1
Classification scheme: 1
Climb (of a dislocation): 1
Covalent Bonding: 1
Critical resolved shear stress: 1
- limiting value in the absence of dislocations: 1
Cross slip: 1
Dislocation
- Edge: 1
Dislocations
- $\vec{b} \times \vec{s}$ cross product: 1
- Screw: 1
- Sense vector: 1
Edge dislocation: 1
Elastomers: 1
Epoxies: 1
Extent of reaction: 1
Fracture modes: 1
Glassy Polymers: 1
Glide: 1
Glide plane: 1
hydrolysis: 1
Irwin Model: 1
Kevlar: 1
Lewis Diagrams: 1
Neoprene: 1
Nylon 6: 1
Poly(dimethyl siloxane): 1
Poly(ethylene oxide): 1
Poly(methyl acrylate): 1
Poly(methyl methacrylate): 1
Poly(phenylene oxide): 1
Poly(tetrafluoroethylene) (PTFE): 1
Poly(vinyl acetate): 1
Poly(vinyl chloride) PVC: 1
Poly(vinyl pyridine): 1
Polyamides: 1
Polybutene-1: 1
Polycaprolactam: 1
Polycaprolactone: 1
Polycarbonate: 1, 2
Polychloroprene: 1
Polyesters: 1
Polyethylene: 1
Polyethylene Terephthalate (PET): 1
Polyisobutylene: 1
Polypropylene: 1
Polystyrene: 1
Primary bonds: 1
Repeat units: 1
Resolved shear stress: 1
Screw Dislocations: 1
Sense vector: 1
Silicones: 1
Slip Plane: 1
Space Elevator: 1
Step-Growth Polymerizations: 1
Stress intensity factor: 1
Ultem Polyetherimide: 1

MAT_SCI 201-301

Introduction to Materials Science and Engineering

Table of Contents

1 Catalog Description

2 Course Outcomes

3 Math Primer

3.1 Basic Rules for Exponents

3.2 Vectors

3.3 Differential and Integral Notation

3.4 Differentiation

3.4.1 General Formulas

3.4.2 Exponents and Logarithmic Functions

3.5 Integration

3.5.1 Basic Forms

3.6 Logarithmic Identities

4 Introduction

5 Bonding

5.1 Outcomes

5.2 General Concepts and the Role of the Interatomic Potential

Melting Temperature

Thermal expansion

Elastic modulus (stiffness)

5.3 Ionic Bonding

5.4 Covalent Bonding

5.5 Metallic Bonding

5.6 Mixed Bond Character

5.7 Hydrogen Bonds

5.8 Other Secondary bonds

6 Crystal Structures

7 Dislocations

7.1 Edge Dislocations

7.3 The Burgers Circuit

7.4 The b → × s ˆ cross product

7.5 Connection to the Crystal Structure

7.6 Dislocation Motion

7.6.1 Dislocation Glide

7.6.2 Dislocation Climb

Which Direction Will Slip Occur?

8 Fracture

8.1 Fracture Modes

8.2 Brittle behavior (fracture mechanics)

8.2.1 The Irwin Model and the Stress Concentration

8.2.2 Stress Intensity Factor

Mode I loading

Mode II loading

Mode III loading

8.2.3 Fracture condition

9 Fuel Cells

10 Corrosion

10.1 The Cost of Degradation/Corrosion

10.2 Corrosion of Metals

10.3 Corrosion Susceptibility? Rough Approximation – Electronegativity*

10.4 Electrochemical Reaction:

10.5 The Galvanic Couple

10.6 Example: Fe-Cu Galvanic Couple

10.7 The Galvanic Series

10.8 Example: Fe-Cu Galvanic Couple

10.9 Metal Oxidation in O2

10.10 Preventing Corrosion

11 Materials Selection: A Case Study

12 Polymers and Soft Materials

12.1.1 What is a Polymer

12.1.2 Classification Scheme

Semicrystalline Polymers

12.2.3 Bonding

12.2.4 Shorthand Chemical Notation

Step Growth Polymerizations:

Chain Growth Polymerizations:

Additional Resource:

13.1 Step-Growth Polymerizations

13.1.1 Polyamides

14.1 Chain Growth: Addition to a Double Bond

High Density Polyethylene:

Low Density Polyethylene:

The Importance of Molecular Weight:

14.1.8 Polystyrene

14.1.10 Poly(vinyl acetate)

14.2 Chain Growth: Ring Opening

14.3 Step Growth Polymers

14.3.3 Polyethylene Terephthalate (PET)

7.4 The $\vec{b} \times \hat{s}$ cross product