Monte Carlo Generation of a Restricted Random Walk and the Excluded-Volume Problem

Abstract

A Monte Carlo procedure was used to simulate non self‐intersecting random walks on a high‐speed digital computer. The specific model considered hard cores of 3½ units and different rotational angles. The mean‐square end‐to‐end distance and the mean‐square radius of gyration were fitted to an equation of the form 〈J _N²〉 = aN^b. It was found that the results obtained by considering nonlattice systems are not consistent with walks constrained to a lattice. This discrepancy is discussed in terms of intrinsic excluded volume and excess excluded volume. It is suggestive that the ratio 〈S _N²〉/〈R _N²〉 may be a more general parameter in discussing these systems.