Chemistry Reference
In-Depth Information
(b) Given that
C
1
5
17.4 and
C
2
5
51.6, determine the activation energy
(kJ/mol) at
T
g
for
T
g
5
200 K.
is around 10
13
the polymer at
T
g
(c) If
the viscosity of
poise (10
poise
5
1Pa
s), estimate the shift factor and viscosity (poise) 50
C
above
T
g
.
4-9
If we consider a polymer to be made of only chain ends and chain mid-
dles, show that
the following equation may be obtained from the
T
g
N
2
Flory
Fox equation (
T
g
5
u/M
n
):
uw
e
M
e
T
g
5T
g
2
where
w
e
is the mass fraction of the chain ends and
M
e
is the mass of
chain ends per mole of chains. One of the equations used to predict glass
transition temperature depression due to the incorporation of a small
amount of solvent in a polymer is
T
g
5
T
g;p
w
p
1
T
g;s
w
s
1
Kw
p
w
s
where subscripts
p
and
s
refer to the polymer and the solvent, respectively,
and
K
is a constant. Rearrange the above equation into the following form
by considering chain ends as solvent
uw
e
M
e
T
g
5
T
g;p
2
where
M
e
is the mass of the polymer per mole of the polymer solution.
Note that
u
here and
u
that appeared in the Flory
Fox equation and in the
equation that relates
T
g
and the mass fraction of chain ends are not the
same constant.
4-10 A rubber has a shear modulus of 10
7
dyn/cm
2
and a Poisson's ratio of 0.49
at room temperature. A load of 5 kg is applied to a strip of this material
which is 10 cm long, 0.5 cm wide, and 0.25 cm thick. How much will the
specimen elongate?
4-11
If a bar of elastic material is held at constant length
L
while temperature
T
is raised, show that the force changes at the rate given by
L
52
@
@
f
S
@
T
@
L
T
where
S
is the entropy of the bar, if it is assumed that the stress-free length
is independent of temperature (i.e., free thermal expansion is ignored). In
practice, when this experiment is conducted on polymers in the rubbery
state, it is found that (
T
)
L
is negative at small extensions but is positive
at large extensions. Explain this.
@
f/
@
