CONDUCTIVITY FLUCTUATIONS IN POLYMERS NETWORKS

A Polymer network is treated as an anisotropic fractal with fractional dimensionality D = 1 + epsilon close to one. Percolation model on suc h a fractal is studied. Using real space renormalization group approac h of Migdal and Kadanoff, we find the threshold value and all the crit ical exponents in the percolation model to be strongly nonanalytic fun ctions of epsilon, e.g. the critical exponent of the conductivity was obtained to be epsilon(-2)exp(-1-1/epsilon). The main part of the fini te-size conductivities distribution function at the threshold was foun d to be universal if expressed in terms of the fluctuating variable wh ich is proportional to a large power of the conductivity, but with eps ilon-dependent low-conductivity cut-off. Its reduced central momenta a re of the order of e(-1/epsilon) up to a very high order. (C) 1998 Els evier Science B.V. All rights reserved.