Theory of elasticity of polymer networks. II. The effect of geometric constraints on junctions

Abstract

The effects of junction–chain interactions in a real network are analyzed in terms of a model in which the entanglements restricting fluctuations of the junctions are represented by vertical-wall potential domains. Within these domains the junctions are allowed to fluctuate freely. The domains are assumed to transform linearly with macroscopic strain. The additional stress that arises due to the restrictions on the fluctuations of junction points accounts for the principal departures of experimental stress–strain curves from phantom-network theory. The size of the entanglement domain, which is the only arbitrary parameter introduced, measures the deviations of the real network from phantom network theory. Calculations based on this model show the reduced force to be approximately independent of strain in the compression region (α<1) and to decrease approximately linearly with the reciprocal of the elongation α in tension (α≳1) over the range accessible to experiment.