Chemistry Reference
In-Depth Information
weaker than are the primary valence forces in the longitudinal direction. Greater amplitudes of
motion also take place perpendicular to the chains rather than in the direction of the chains. These
increased motions in the perpendicular direction result in repulsive forces between extended or
parallel chains. Such forces cause them to draw together after stretching. So, the stretched rubber
molecules retract due to longitudinal tension until the irregular arrangement of molecules is achieved
again. This more random conformation is actually a higher entropy state.
When unstretched rubber is heated it increases in dimension with an increase in the temperature, as
one might expect. At higher temperatures, however, rubbers, upon elongation, have a higher tendency
to contract. This can be written as follows:
retractive force,
f ¼Tð@
S
=@LÞ
Tv
ð@f =@TÞ
adiabatic
¼ð@L=@TÞT=C
p
In summary, polymeric materials exhibit rubber elasticity if they satisfy three requirements: (a) the
polymer must be composed of long-chain molecules, (b) the secondary bond forces between
molecules must be weak, and (c) there must be some occasional interlocking of the molecules
along the chain lengths to form three-dimensional networks. Should the interlocking arrangements
be absent, then elastomers lack memory, or have a fading memory and are not capable of completely
reversible elastic deformations.
2.2.2.1 Thermodynamics of Elasticity
Stretching an elastomer reduces its entropy and changes its free energy. The retractive force in an
elastomer is primarily the result of its tendency to increase the entropy towards the maximum value it
had in the original deformed state Current explanations of rubber-like elasticity are based on several
assumption [
20
]. The first one is that rubber-like elasticity is entirely intramolecular in origin. The
second one is that the free energy of the network is separable into two parts, an elastic one and a liquid
one. The liquid one is presumably not dependent on deformation. When an elastomer is stretched, the
free energy is changed, because it is subjected to work. If we consider the stretching in one direction
only, the work done
W
el
is equal to
f
∂
l
, where
f
is the retractive force and
∂
l
is the change in length.
The retractive force is then [
19
-
21
].
f ¼ð@F=@LÞ
T
;
p
¼ð@H=@LÞ
T
;
p
Tð@S=@LÞ
T
;
p
where
F
is the free energy,
H
is the enthalpy, and
S
is the entropy of the system. An ideal elastomer can
be defined as one where (
)
T,p
. The negative sign is due to the fact
that work has to be done to stretch and increase the length of the elastomer. This description of an ideal
elastomer is based, therefore, on the understanding that its retractive force is due to a decrease in
entropy upon extension. In other words, the
entropy of elasticity
is the distortion of the polymer chains
from their most probable random conformations in the unstretched condition. The probability that one
chain end in a unit volume of space coordinates,
∂
H
/
∂
L
)
T,p
¼
0 and
f ¼T
(
∂
S
/
∂
L
x
,
y
,
z
is at a distance
r
from the other end is [
21
,
22
]:
3
2
2
0
:
5
e
b
r
Wðx; y; zÞ¼ðb=p
Þ
2
2
. The number of links is
where
. The entropy of the system is
proportional to the logarithm of the number of configurations. Billmeyer expresses it as follows [
7
]:
b
¼
3/2
xL
x
and the length is
L
2
2
S ¼ð
constant
Þkb
r
