Elasticity of c*-Gels

(Received 13 June 1995, received in final form 27 June 1995, accepted 7 July 1995)

Abstract
A junction affine network model is solved for chains following a Redner-des Cloizeaux distribution. In a gel at c^* the network strands behave as isolated chains. In a good solvent their elastic properties cannot be obtained from Gaussian statistics as in the classical models of rubber elasticity. Instead the Redner-des Cloizeaux distribution is employed, which is known to be an excellent approximation to the end-to-end distance distribution of flexible polymer chains in a good solvent. The implications of using non-linear entropic springs, the role of fluctuations and the quality of the affine approximation are worked out for a Flory-Rehner model. The applicability to swollen networks and the elasticity of two dimensional c^*-gels are briefly discussed.