K. Urayama et al., Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 2. Experimental tests of molecular entanglement models of rubber elasticity, MACROMOLEC, 34(23), 2001, pp. 8261-8269
Five molecular models of rubber elasticity which employ different treatment
s of entanglement effects (the Kloczkowski-Mark-Erman diffused-constraint m
odel, the Edwards-Vilgis (E-V) slip-link model, the tube models of Gaylord-
Douglas (G-D), Kaliske-Heinrich, Rubinstein-Panyukov versions) are assessed
using biaxial deformation data for an entanglement-dominated network of en
d-linked poly(dimethylsiloxane) (PDMS) in which trapped entanglements are d
ominant in number relative to chemical cross-links. The theoretical stress-
strain relations were calculated from the elastic free energy (M of each mo
del. Using the reduced stress (the nominal stress divided by equilibrium mo
dulus G(o)), the strain-dependent predictions of each model were tested fro
m two different viewpoints, i.e., the dependence of the reduced stresses on
the principal ratio and the I-i dependence of (partial derivativeW/partial
derivativeI(j))/G(o) (i,j = 1,2), where I-1 and I-2 are the first and seco
nd invariants of deformation tensor (the Rivlin-Saunders method). The diffu
sed-constraint model is relatively successful in reproducing the reduced st
ress-strain data over a wide range of deformations, but the model definitel
y underestimates the magnitude of G because it does not consider trapped en
tanglements as additional cross-links contributing to G., in contrast to th
e tube models and the slip-link models. The G-D tube model is more successf
ul in reproducing the experimental data relative to the other two versions
of the tube model, but the G-D model obviously underestimates the stresses
at large deformations. Among the five molecular theories tested here, the E
-V slip-link model shows the most successful reproducibility over large por
tions of the experimental results. The agreements in reduced stress-strain
relations are satisfactory over the entire deformation range, although cons
iderable disagreement is recognized in the I-i dependence of partial deriva
tiveW/partial derivativeI(2). Also, the fitted parameter values in the E-V
slip-link model are fairly well explained using the molecular consideration
s based on the structural characteristics of the network sample employed he
re.