Statistical Mechanics of Crosslink Orientation in a Rubber Network

Abstract

Existing theories of the origin of the Mooney–Rivlin C 2 term in rubberelasticity theory are briefly reviewed. The James–Guth model for the deformation of a rubber network is generalized in a consistent manner to allow for the statistical mechanism of the re‐orientation of cross links. An explicit expression for the angular probability distribution of cross links is obtained for a somewhat simplified James–Guth model. The contribution of the re‐orientation of cross links to the elastic modulus is calculated and found to be insignificant.