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

TL;DR

This paper uses advanced Monte Carlo simulations to study the scaling behavior of long hard-sphere polymer chains across multiple dimensions, revealing universal properties consistent with self-avoiding walks.

Contribution

It introduces new entropy measurement methods and applies a binary-tree Monte Carlo approach to analyze long polymer chains in various dimensions.

Findings

Reproduces self-avoiding walk behavior across dimensions

Determines Flory exponent and universal amplitude ratios

Provides insights into entropy and scaling properties

Abstract

We perform simulations 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 $10^7$ repeat units are considered. We focus on the scaling properties of the end-to-end distance and on 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 $\nu$ 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.