TOPOLOGICAL INTERACTIONS IN STATISTICAL POLYMER THEORY (original) (raw)

A mean-field theory describing the effects of the topological interactions that occur in polymers on account of the mutual impenetrability of their chains is constructed by means of the replica formalism. On the basis of this theory for the description of a polymer with strongly entangled chains a physical model of a quasinetwork of effective hookings is proposed, the parameters of which are determined by the number N, % 1 of links along a chain between two quasi-cross-links. The free energies of a linear polymer and of a polymer gel network, subjected to a specified stretching and swelling, respectively, are calculated in the leading approximation in the small parameter E = l/Ns. It is shown that the deformation of such a network has both an affine component and a nonaffine component associated with the partial disentangling of the chains of the network as the network is stretched. The deformation dependence of a gel network with entangled chains, obtained by equilibrium linking of the chains via polyfunctional monomers both close to and far from the gel-formation point, is calculated. It is shown that this dependence is in agreement with the experimental data.

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