Dynamics of inhomogeneous cross-linked polymers consisting of domains of different sizes

The theoretical approach is developed to describe the dynamics of inhomogeneous cross-linked polymers consisting of cross-link agglomerations. An inhomogeneous polymer is treated as an ensemble of noninteracting cross-linked regions (domains) of different sizes. We model an internal architecture of the domains in a rather regular way and assume a power law decay of the relaxation modulus inside the domains, a decay usual for a broad class of cross-linked materials on microscopic scales. Assuming a broad size distribution of the domains in cross-linked polymers due to a random character of cross linking, we demonstrate a stretched exponential time behavior of the relaxation modulus on scales larger than the average size of inhomogeneities in the polymer. We apply this general approach to some special cases of cross-linked polymers, namely to polydisperse polymer networks, to inhomogeneous meshlike networks, and to inhomogeneously cross-linked polymeric gels. (C) 2001 American Institute of Physics.