Statistical Computation of Configuration and Free Volume of a Polymer Molecule with Solvent Interaction

Abstract

A lattice model of a polymer molecule with excluded nearest-neighbor contacts is of particular interest since it can serve as a model for polymer systems in which the interactions between the polymer and its environment are incorporated. These interactions result in the partial overlapping of polymer segments, and consequently the volume fraction of detached polymer segments exceeds the volume fraction of connected polymer segments. It is found that the contraction in volume per segment is independent of the number of polymer segments n. The mean-square end-to-end distance is found to be approximately proportional to nγ for sufficiently large n, where γ is the mean-square polymer index, in agreement with Wall et al. The value of γ is shown to be considerably lower than the previous estimates of this parameter for a three-dimensional lattice with excluded nearest-neighbor contacts. The decrease in the value of γ from previous estimates is due to the cloverlike structures which result from the addition of a single step to a permissible configuration.