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27,28&29- Coil Entropy.docx

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CHEM 204
Christopher Barrett

CHEM 204 03/20/2013 Lecture 27&28&29 Martin M. PHGY Tutor Coil Entropy 1. To see how random walks of diffusion apply to polymers a. Can be described well as random walks. 2. To learn how to define the entropy of a random walk coil a. With an entropy description defined by the usual Gaussian function 3. To learn the difference between a random walk and a self avoiding walk, and the size of real polymer chains a. SAWs are longer than random walks and can't cross over paths Polymer behaviour is mostly entropic. Polymers behave differently than molecules, and all our impressive features like skin, bone, muscle, DNA are ALL polymers. Same with out plastics and stuff. The larger the polymer, the more shapes. A simple model for polymers is N segments of size "a". The total length = . N is extremely variable but "a" is usually 3-10 Angstroms. The end-to-end coil length is √ Overall, Coil Entropy ΔS =-3/2 [ r /R2 02 + R /0 ] 2  r= the raduis we want to know the entropy of  R0= most likely random walk of radius a √ First term: energy penalty for stretching Second term: energy penalty for compression Using the √ rule doesn't give us the perfect length, real coils are actually longer. Diffusion theory works well for gas molecules, but polymer coils can't be in the same space at different times. No crossing over is allowed; it is a self avoiding walk. SAWs are much longer than random walks. Experimentally, the highest entropy is actually: A balance between entropy and enthalpy is the base of ALL self-organizing material. Folded polymers are held by enthalpic bonds (hydrogen, ionic bonds, and hydrophobic bonds). DNA is simple and well known, folding only due to H bonds and coil entropy.  AT enthalpy: 21kJ/mol (MP~82)  CG enthalpy: 29kL/mol (MP~96) At a critical T, enthalpy wins out. DNA doesn't melt at one temperature but depends on the bonds. DNA origami: A computer program can make ANY shape you want by feeding different sequen
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