Monte Carlo study of polymers in equilibrium with random obstacles

Abstract

We have performed Monte Carlo calculations for two-dimensional freely jointed polymers with no excluded volume in equilibrium with a quenched random lattice of obstacles. In addition to the obstacle density, there are two microscopic parameters in the problem: the obstacle side length a and the polymer step length l. Our Monte Carlo calculations extend to N=50 000 monomer polymer units. The calculations begin to exhibit standard Flory–Lifshitz scaling only at extremely large values of N. For example, when l≊a, nonuniversal behavior is found for N<104. For some choices of parameters, this behavior includes a nonmonotonic mean-square end-to-end length R2 as a function of N. These calculations are made feasible by exploiting an equivalence between annealed and quenched disorder valid when the polymer may equilibrate to the quenched material.