Contribution to the study of self-avoiding random walks (SARW) confined to strips and capillaries

✍ Scribed by Lautout-Magat, Marguerite

• Book ID: 105334024
• Publisher: John Wiley and Sons
• Year: 1982
• Weight: 390 KB
• Volume: 20
• Category: Article
• ISSN: 0360-6376
• DOI: 10.1002/pol.1982.170200928

✦ Synopsis

Abstract

A flexible chain that can assume all possible positions on a lattice without intersection of segments (self‐avoiding random walk, SARW) has been used for a long time as a model of polymers in highly dilute solution, taking into account the excluded volume. In this article, we extend to a SARW subject to spatial constraints an analytical accurate method we have established for a SARW on an unbounded lattice. We now consider a square or cubic lattice extending without limit in the x direction but confined to D layers in the other directions. This is a model for the study of constrained macromolecules the behavior of which is important for instance in connection with the properties of thin polymeric films or fibers, or with the solubility of biopolymers in lipid bilayer membranes. We give recurrence relationships for calculating C~n~, the total number of configurations, and x~n~, the mean x projection of the end‐to‐end separation, for a chain length n. Our method, being analytical, allows a considerable economy of computational time with respect to other methods such as Monte Carlo calculations. It enables us to investigate the asymptotic behavior of x~n~ and to write the partition function of the system.