Chemistry Reference
In-Depth Information
4-12 An ideal rubber band is stretched to a length of 15.0 cm from its original
length of 6.00 cm. It is found that the stress at this length increases by an
increment of 1.5
10
5
Pa when the temperature is raised 5
C (from 27
C
up to 32
C). What modulus (E
3
) should we expect to measure at 1%
elongation at 27
C? Neglect any changes in volume with temperature. Do
all the calculations using the engineering tensile stress equation.
5σ
/
ε
4-13 About one out of every 150 chain carbon atoms is cross-linked in a typical
natural rubber (
cis
-polyisoprene) compound with good properties. The
density of such a vulcanizate is 0.97 g cm
2
3
at 25
C. The gas constant
10
7
ergs mol
K
2
1
1
.
987 cal mol
K
2
1
. Estimate the modulus of
R
5
8
.
3
3
5
the sample at low extensions.
4-14 The work done by an external force applied on a piece of ideal rubber con-
taining
ν
network chains is given by
r
2
5
ν
k
B
T
2
h
i
i
2
x
1Λ
2
y
1Λ
2
z
2
w
i
0
ðΛ
3
Þ
h
r
2
10
2
23
J/K);
r
2
r
2
where
k
B
is the Boltzmann constant (1.38
.
o
are the mean square end-to-end distances of the network chains in and out of
the network; and
3
,
.
i
and
,
Λ
z
are the extension ratios in the
x
,
y
,and
z
directions. A bar of ideal rubber with square in cross-section containing
6
Λ
x
,
Λ
y
,and
10
20
network chains is extended uniaxially at 20
C until its length is
double the initial
3
r
2
r
2
length. Assuming that
,
.
i
5
0.8
,
.
o
and
Λ
x
Λ
y
Λ
z
5
1,
(a) Calculate the heat gained or lost;
(b) Determine the entropy change of the process;
(c) Comment on the result you obtained in part (b).
4-15 The raw data from a tensile test are obtained in terms of force and correspond-
ing elongation for a test specimen of given dimensions. The area under such
a force
elongation curve can be equated to the impact strength of an isotro-
pic polymer specimen if the tensile test is performed at impact speeds. Show
that this area is proportional to the work necessary to rupture the sample.
4-16 The stress relaxation modulus for a polyisobutene sample at 0
Cis
2.5
10
5
N/m
2
. The stress here is measured 10 min after imposition of a
fixed deformation. Use the WLF equation (
Eq. 4-72
) to estimate the tem-
perature at which the relaxation modulus is 2
.
5
3
10
5
N/m
2
3
for a measur-
ing time of 1 min.
4-17 The stress relaxation behavior of a particular grade of polymer under con-
stant strain is given by the following expression:
γ
0
e
2t=λ
1 τ
0
τð
t
Þ 5
G
