Molecular theory of rubber elasticity

Abstract

Rubber elasticity, identified as the capacity to sustain very large deformations followed by complete recovery, is exhibited exclusively by polymeric substances consisting predominantly of long molecular chains. Moreover, it is manifested under suitable conditions by virtually all polymers so constituted. The molecular theory of rubber elasticity rests on the premise, now fully validated by experiments, that alterations of the configurations of the chains comprising the network account for the elastic free energy and for the stress arising from deformation. Early theories of rubber elasticity were propounded on the assumption that displacements of the junctions are affine in the macroscopic strain. James and Guth, avoiding this assumption, treated a phantom network consisting of Gaussian chains having otherwise no material properties. They showed (i) that the mean positions of the junctions in this hypothetical network are affine in the strain, and (ii) that fluctuations about these positions are invariant under strain. The corollary that the instantaneous distribution of the chain vectors cannot be affine in the strain escaped notice for many years. The copious interpenetration of chains that characterizes polymer networks should be expected to restrain the fluctuations of junctions embedded therein, but not to suppress them altogether. Moreover, the restraints on fluctuations should depend on the state of strain. Departures from phantom behavior consequently occur to a degree that depends on the strain. Formulation of a self-consistent theory based on this idea required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions led to a theory that accounts for the observed relationship of stress to strain virtually throughout the ranges accessible to measurement. The theory establishes connections between network structure and elastic properties. All essential parameters are determined by the connectivity of the network, the number and functionality of its junctions, and inherent characteristics of the molecular chains comprising the network. © 1985 The Society of Polymer Science, Japan. All Rights Reserved.