Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions

Abstract

Simulations are performed for long hard-sphere polymer chains using a recently developed binary-tree based Monte Carlo method. Systems in two to five dimensions with free and periodic boundary conditions and up to 10⁷ repeat units are considered. The analysis is focused on scaling properties of the end-to-end distance and the entropy and their dependence on the sphere diameter. To this end new methods for measuring entropy and its derivatives are introduced. By determining the Flory exponent ν and the weakly universal amplitude ratio of end-to-end distance to radius of gyration we find that the system generally reproduces the behavior of self-avoiding lattice walks in strong support of universality.