Diffusion of a Test Chain in a Quenched Background of Semidilute Polymers

TL;DR

This paper studies the diffusion of a long polymer in a quenched semidilute polymer medium using renormalization group theory, revealing new dynamic power laws that interpolate between Rouse and reptation behaviors.

Contribution

It introduces a systematic RG approach to analyze polymer diffusion in correlated disordered media, deriving novel dynamic exponents in the semidilute limit.

Findings

Identification of an attractive RG fixed point for correlated disorder

Derivation of new power-law exponents for polymer dynamics

Explicit one-loop calculation for center of mass motion

Abstract

Based on a recently established formalism (U. Ebert, J. Stat. Phys. 82, 183 (1996)) we analyze the diffusive motion of a long polymer in a quenched random medium. The medium is modeled by a frozen semidilute polymer system. In the framework of standard renormalization group (RG) theory we present a systematic perturbative approach to handle such a many chain system. In contrast to the work of Ebert we here deal with long range correlated disorder and find an attractive RG fixed point. Unlike in polymer statics the semidilute limit here yields new nontrivial power laws for dynamic quantities. The exponents are intermediate between the Rouse and reptation results. An explicit one loop calculation for the center of mass motion is given.