Relaxation modulus of heterogeneous polymer networks with the domain structure

A dynamic model for the viscoelastic properties of inhomogeneous polymer ne tworks is proposed. A polymer network is modeled as an assembly of noninter acting crosslinked regions (domains) of various sizes. Network domains are represented as regular cubic networks of finite dimensions made of crosslin ked multisegmental Gaussian chains. The domains differ from one another in the number of networks cells. For averaging over all network domains, an ex ponential distribution function of the number of polymer segments in domain s is used, which was earlier proposed by one of the authors within the fram ework of the aggregate model. The time dependence of the relaxation modulus of the polymer network with domain-type heterogeneity was shown to follow a stretched exponent law, In contrast, the theory predicts a power-law depe ndence of the relaxation modulus for infinite regular polymer networks. Thi s conclusion can be extended to other exponential functions for the distrib ution of segments in network domains; i.e., to a rather wide range of heter ogeneous network systems.