Response of disordered polymer networks to external fields: Regular lattices built from complex subunits

Based on recent experiments, inhomogeneous polymer networks can be viewed as densely cross-linked regions embedded in more dilute surroundings. Here we put forward systems that model such situations, namely regular lattices built from complex subunits. The model takes into account both the disorder inside the subunits (cross-link agglomerations) and the connectivity between them. Combining analytical and numerical methods, we propose a general approach for determining the Rouse dynamics of such systems. Exemplarily, we apply this approach to two-dimensional lattices built from small-world Rouse networks and evaluate the model's mechanical and dielectric response to external fields. We find that the networks show interesting relaxation features and an unusual "plateau-type" behavior in the intermediate frequency (time) domain, which lies between the modes of the disordered subunits and those of the regular lattice. This behavior is directly related to the disorder inside the cross-link agglomerations and may be readily detected through appropriate mechanical and dielectric experiments.