Chemistry Reference
In-Depth Information
7.1.3 Some Elastomeric Quantities
The majority of studies of mechanical properties of elastomers have been
carried out in elongation because of the simplicity of this type of deforma-
tion.
71,
121-123
Results are typically expressed in terms of the nominal or
engineering stress
f
* =
f/A
*, which, in the simplest molecular theories, is
given by
(1)
=−
−
2
f
*
vkT
(
αα
)
where ν is the number density of network chains,
k
is the Boltzmann
constant,
T
is the absolute temperature, and α is the elongation or
relative length of the stretched elastomer. The modulus or reduced
stress is
(2)
−
2
[*]
f
≡−=
f
* /(
αα
)
vkT
[
f
*] is often fitted to the Mooney-Rivlin semi-empirical formula [
f
*] ≡ 2
C
1
+ 2
C
2
α
-1
, where
C
1
and
C
2
are constants independent of deformation α.
123,
124
The simplest model assumes affine deformations, in which the cross
links move in parallel with the macroscopic dimensions. This approach
has been revisited recently.
125
There are a fewer studies using other types
of deformation such as biaxial extension or compression, shear, and
torsion.
Swelling is a nonmechanical property that is frequently used to char-
acterize elastomeric materials.
71,
124,
126,
127
Swelling is an unusual defor-
mation in that volume changes are of central importance, rather than
being negligible. Swelling is a three-dimensional dilation in which the
network absorbs solvent, reaching an equilibrium degree of swelling at
which the free energy decrease due to the mixing of the solvent with the
network chains is balanced by the free energy increase accompanying
the stretching of the chains. The network is typically placed into an
excess of solvent, which it imbibes until the dilational stretching of the
chains prevents further absorption. The degree of cross linking can be
determined from equilibrium extent of swelling, provided the polymer-
solvent interaction parameter χ is known.
126
Conversely, if the degree of
cross linking is known from an independent experiment, then the in-
teraction parameter can be determined. The equilibrium degree of
swelling and its dependence on various parameters are important tests
of t heor y.
71,
96
A number of specialized elastomeric quantities have also been investi-
gated. PDMS networks have been particularly useful in investigating the
“Mullins Effect,” in which filler-reinforced elastomers exhibit a reduction
