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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. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present a theoretical study of polymer networks, formed by connecting dendritic building blocks (DBB’s). We concentrate on the Rouse dynamics of such networks and perform our study in two steps, considering first single generalized dendrimers (GD’s) and then networks formed by such DBB’s. In GD’s the functionality f of the inner branching points may differ from the functionality f[sub c] of the core. The GD’s cover wide classes of macromolecules, such as the “classical” dendrimers (f[sub c]=f ), the dendritic wedges (f[sub c]=f-1), and the macromolecular stars (f[sub c]>2, f=2). Here we present a systematic, analytic way which allows us to treat the dynamics of individual GD’s. Then, using a general approach based on regular lattices formed by identical cells (meshes) we study the dynamics of GD-based polymer networks. Using analytical and numerical methods we determine the storage and loss moduli, G[sup ′](ω) and G[sup ″](ω). In this way we find that the intradendrimer relaxation domain of G[sup ′](ω) becomes narrower when M[sub cr], the number of connections between the neighboring DBB’s, increases. This effect may be understood due to the exclusion of the longest DBB relaxation times from the spectrum of the network, given that the additional connections hinder the mobility of the peripheral DBB branches. We expect that such effects may be readily observed through appropriate mechanical experiments. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]