Loops in Polymer Networks

The classical theory suggests that phantom polymer networks have a treelike structure. In this study, we investigate the actual polymer networks, in which the polymer loops have a finite size and strongly overlap with each other. We show that the elastic modulus of such networks has two contributions: of elastically effective strands and of finite size loops shunting the network strands. The latter contribution substantially depends on the interaction of the network strand monomers at network preparation conditions. The result of calculations performed in the framework of the replica theory of polymer networks is interpreted using a generalized combined chain model. This model allows us to describe quantitatively the elasticity of the polymer network with finite size loops and the deformation of its individual strands. We also calculate the impact of primary loops and cyclic defects of arbitrary concentration on the elasticity of such a network.