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Homework10 Solutions

# Homework10 Solutions - CHE/CHEM 178 Fall 2008 Homework#10...

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CHE/CHEM 178 Fall 2008 Homework #10 Solutions 1. Batch 1 of nearly monodisperse flexible polymer A has a molecular weight of 25 kg/mol, a statistical segment length of 0.7 nm and a monomer molecular weight of 125 g/mol. Batch 2 of the same, nearly monodisperse polymer has a molecular weight of 400 kg/mol. Polymer A has a density ρ of 900 kg/m 3 . a.) Compute the radius of gyration of a chain of batch 1 of polymer A in the melt. <r 2 >=Na 2 =200*.7 2 R g 2 =<r 2 >/6 R g =4.04nm b.) A single chain of batch 2 of molten polymer A is stretched. The Helmholtz free energy A(r) = U(r) - TS(r) where r is the distance between the ends of the chain. The force f(r) on the ends of the chain is given by: f (r ) = U r T,V - T S r T,V Which of the terms, U/ r or S/ r, is more significant in the expression for f(r) above? Why? S/ r is more significant because the number of chain conformations available decreases greatly as you stretch out the chain (increase r), and since entropy is defined as S=-kln , it is extremely dependent on r. Internal energy, U, is not particularly dependent on r because while the chain is stretched bond lengths and bond angles do not change significantly.

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Homework10 Solutions - CHE/CHEM 178 Fall 2008 Homework#10...

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