Contribution to a Liquid-Like Theory of Rubber Elasticity

Abstract

The contribution to the configurational entropy of a rubber arising from the competition of chain segments for space is evaluated and the associated entropy force is derived. This is done by expressing the orientation-dependent packing entropy as a function of the number of bonds (vector lengths between segments) in each of the permitted directions and then expressing the number of bonds in each direction as a function of the stretch ratios, λi. To make the calculations tractable, the three-chain model of a rubber is used and in addition only three mutually perpendicular orientations of the bonds are allowed. The predicted stress-strain curves are compared with the experimental situation. It is found that, for a dry rubber, the correction term has the same behavior at small and moderate elongations as the difference between the experimentally observed curve and the curve predicted by the uncorrected statistical theory. However, the magnitude of the correction term is from 1/10 to ½ the magnitude of the observed difference. It is concluded that one must go outside the equilibrium statistical mechanics to explain the magnitude of the observed deviation, but it is argued that the molecular basis of the deviation is the orientation-dependent packing problem.