Dynamics of deterministic fractal polymer networks: Hydrodynamic interactions and the absence of scaling

Abstract

We numerically analyze the scaling behavior of experimentally accessible dynamical relaxation forms for networks modeled through finite Sierpinski-type lattices. Previous work has established unequivocally for such lattices that in the Rouse picture both the mechanical and the dielectric relaxation forms scale in frequency and in time. As we show here, in the Zimm model, based on the preaveraged Oseen tensor, the picture changes drastically; the introduction of the hydrodynamic interactions leads to relaxation patterns which do not scale. Our results show that the relaxation forms are very sensitive to the number of monomers in the network and to the strength of the hydrodynamic interaction parameter.