Elasticity of highly cross-linked random networks

Abstract

Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Landau-Wilson free energy S for arbitrary cross-link densities. Considering pure shear deformations, S takes the form of the elastic energy of an isotropic amorphous solid state, from which the shear modulus can be identified. It is found to be a universal quantity, not depending on any microscopic length-scales of the model.