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Ch1b09Lecture25

Ch1b09Lecture25 - Lecture 25 March 9 2009 Summary of last...

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Summary of last lecture: •polymers •rubber elasticity Preview of coming attractions: •rubber elasticity •biopolymers: proteins Lecture 25 March 9, 2009 Reminders •PS9 is optional, due Weds, 11:59 pm •Final review, Thursday 7:30 pm, Baxter 1
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Final exam will be quasi-cumulative, but will emphasize material in lectures 16-26 •chemical equilibrium •kinetics •organic chemistry and reaction mechanisms •polymers and biopolymers •material from the entire course may be incorporated into problems review session Thursday, 7:30 pm Baxter Hall can e-mail questions in advance 2 same policies as midterm/Quiz
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Thermodynamics of rubber elasticity: summary Hooke s law: f = kx First law of thermodynamics: dE = TdS + fdx " E " x # $ % & ( T = T " S " x # $ % & ( T + f for a rubber band dE/dx ~ 0 (ideal gas-like), or T " S " x # $ % & ( T = ) f when a rubber band is stretched, f > 0 and dS/dx < 0 dE = dq + fdx ~ 0, giving dq = -fdx a rubber band gives off heat when stretched stretching is exothermic 3
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For this model, we can calculate the entropy change in extending a chain from the origin to a conformation with an end-to-end length = x: " S = S x ( ) # S 0 ( ) = # k B 2 Nl 2 x 2 4 The entropy of an idealized 1-D chain may be evaluated from the Boltzmann entropy expression and a Gaussian end-to-end length distribution S x ( ) = k B ln " x ( ) " x ( ) = 2 N P x ( ) = 2 N 2 # Nl 2 ( ) 1/ 2 e $ x 2 /(2 Nl 2 ) ( ) S x ( ) = $ k B 2 Nl 2 x 2 + constant
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Recall that the restoring force f is related to the change in entropy with extension: f = " T # S # x $ % & ( ) T , V
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