“Belt-loop” model of chain entanglement

Abstract

A simple model of an entangled chain is proposed. Statistical properties of the model are examined based on the partition function derived to include geometrical constraints imposed by entanglements. The model chain statistics results, for long chains, in a modified Gaussian function. The new statistics applied in the “affine network” theory yield stress-strain dependence, which qualitatively agrees with experimental data obtained for uniaxial extension and compression. Non-linear Mooney-Rivlin plots with a maximum appearing in the compression region are predicted for unswollen networks. With increasing swelling, non-linearity decreases. The proposed explanation of these phenomena is based on the restraints imposed on entangled chains, rather than on network junctions, unlike in the Flory-Erman theory. No arbitrary parameters are involved in the model.