Polymers in disordered environments

TL;DR

This paper reviews recent research on the scaling behavior of polymers in disordered environments, focusing on a model with self-avoiding walks in critical percolation clusters, using simulations and enumeration methods.

Contribution

It introduces a comprehensive analysis combining numerical simulations and enumeration techniques to study polymer scaling in disordered media.

Findings

Determined critical exponents $b3$ and $$ for polymers in disordered environments.

Compared simulation results with exact enumeration to validate scaling behavior.

Provided insights into how disorder affects polymer conformations and spatial extent.

Abstract

A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by (interacting) self-avoiding walks and the disordered environment by critical percolation clusters. The scaling behaviour of the number of conformations and their average spatial extent as a function of the number of monomers and the associated critical exponents $\gamma$ and $\nu$ are examined with two complementary approaches: numerical chain-growth computer simulations using the PERM algorithm and complete enumerations of all possible polymer conformations employing a recently developed very efficient exact counting method.