A DIFFUSED-CONSTRAINT THEORY FOR THE ELASTICITY OF AMORPHOUS POLYMER NETWORKS .1. FUNDAMENTALS AND STRESS-STRAIN ISOTHERMS IN ELONGATION

The theory proposed is an extension of the constrained-junction theory of Flory and Erman and the subsequent constrained-chain theory of Erm an and Monnerie. As in these earlier theories, the elastic free energy Delta A(el) is calculated as the sum Delta A(el) = Delta A(ph) + Delt a A(c), where Delta A(ph) is the contribution for a phantom network, a nd the additional term Delta A(c) is due to the effects of constraints on fluctuations. Instead of allowing the constraints to affect the fl uctuations of only the junctions or the centers of mass of the network chains, however, the constraints are now applied continuously along t he chains. The results of illustrative calculations on this ''diffused -constraint'' model are compared with the corresponding results from t he earlier theories.