Dynamics and scaling of polymer networks: Vicsek fractals and hydrodynamic interactions

Abstract

In previous works we have analysed the scaling behavior of model fractal polymers both in the presence of hydrodynamic interactions (HI, Zimm-model) as well as when such interactions are missing (Rouse-model). While in Rouse-type approaches scaling holds both for very high and very low frequencies, as well as in the intermediate domain, for Sierpinski-type lattices scaling does not hold in the Zimm-case in the intermediate frequency regime. In this paper we consider Vicsek-fractals which are tree-like (belonging, as the dendrimers, to hyperbranched structures), and we analyse their dynamics, both under Rouse- and under Zimm-conditions. By this we get additional insight into the problem, since the Vicsek fractals are (distinct from Sierpinski-type networks) devoid of loops. Remarkably we find that Vicsek fractals scale rather well, even when taking HI into account. We perform our analysis based on quite large Vicsek-fractals, especially in the Rouse case, where we can determine their eigenvalues through a very efficient iterative procedure.