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
Ω
, 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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 Fall '08
 SEGALMAN
 Energy, Mass, Entropy, Kilogram, Natural rubber

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