Generalized Vicsek Fractals:  Regular Hyperbranched Polymers

Abstract

We focus on Vicsek fractals (VF), which are regular hyperbranched macromolecules. As such, they belong to the same family as the dendrimers, without suffering from the growth problems of the latter. We compute the mechanical and dielectric properties of VF in dilute solutions. The evaluation of the static and dynamical properties of VF in the framework of generalized Gaussian structures (GGS) reveals that they, distinct from the dendrimers, obey scaling. Theoretically speaking, VF are probably the most natural extension of GGS from linear chains to nontrivial loopless fractal objects. We encourage the synthesis and experimental characterization of the properties of this class of hyperbranched macromolecules.