Strange kinetics of polymeric networks modelled by finite fractals

Abstract

Abstract Branched and crosslinked polymers in solution display many dynamical aspects related to anomalous diffusion. Now, distinct from situations such as charge transfer in photoconductivity, where the moving charges do not have internal degrees of freedom, here the anomalous aspects are due to the internal modes of the polymers, and less to the disorder of the medium. These internal modes are revealed by the stretching of the structures under external forces as well as by their response to external mechanical and electrical fields. We focus on models based on Sierpinski-type fractals, the advantage being that the eigenfrequencies of such fractals can be readily computed to very high accuracy using recursion formulas. This fact dispenses us from having to diagonalize very large matrices. In particular, we calculate G′(ω) and G″(ω) for a large class of fractal structures and we compare the results to our recent measurements on long chain branched polypropylene.