Theory of relaxation spectra for two identical interpenetrating polymer networks

Abstract

Viscoelastic models for the description of the relaxation characteristics of two identical swollen interpenetrating polymer networks with different topologies moving against the background of an external viscous medium are considered. Two dynamic models that differ in the character of mutual interaction between network junctions are proposed. According to the first model, viscoelastic interaction is assumed to be constant and provided by the entanglements between a junction of one network with eight symmetrically arranged junctions of the other network. The second model involves (i) the predominant interaction between multiple-network junctions most closely located owing to entanglements and (ii) a weaker interaction with more distant junctions of neighboring cells. For the systems composed of two interpenetrating networks, relaxation-time spectra and average inverse relaxation-time spectra are compared with the corresponding spectra and characteristic times for individual noninteracting regular networks. Both models can involve two branches of the relaxation spectrum. One branch is a collective branch corresponding to the motion of the double network, whose parameters are controlled by the constants of elasticity of each of the interacting networks as well as by the effective mutual viscoelastic interactions between networks. This low-frequency branch is characterized by a broad spectrum of relaxation times. The second branch is a high-frequency branch that is primarily provided by mutual local motions of two interacting networks. This branch is characterized by a comparatively narrow relaxation spectrum and depends on quasielastic constants, which describe network entanglements, and on the characteristic elasticity of each network. The second branch does not involve any infinitely long relaxation times for infinitely continuous networks.