Theory of rubberlike elasticity modified to allow for the deformation-induced rearrangement of topological constraints in polymer networks

An assumption that topological constraints may rearrange during deformation of polymer networks leads to the appearance of additional components in expressions for the free energy and the restoring force. The contribution of these components depends on the ''efficiency'' of topological constraints, that is, on the magnitude of fluctuations of intermediate points of the chain in the direction normal to the chain contour. The calculation is restricted to the case of a single topological constraint per chain, which is the first approximation of the theory. A satisfactory agreement of the theory with experiment is observed only when fluctuations in the normal direction at intermediate points of the chain are sufficiently small, which can be treated as indication of small ''tube diameter'' in real polymer networks.