Polymer diffusion in quenched disorder: A renormalization group approach

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second moment v and the excluded-volume interaction u of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating Functional and the general structure of its perturbation expansion in It and v are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG now of the parameters are discussed. Universal results can be found for the effective static interaction w:=u-v greater than or equal to 0 and for small effective disorder coupling v(l) on the intermediate length scale l. As a first physical, prediction from our analysis, we determine the general nonlinear scaling form oi the chain diffusion constant and evaluate it explicityly as D proportional to N(l)(-1) D(v(l) N(l)(alpha)) for v(l) much less than 1.