Self-avoiding walks and real polymer chains

Abstract

The model of Domb and Joyce enables a continuous transition to be effected between a random and self-avoiding walk on a lattice. By combining a virial expansion with exact enumerations for this model, it has been possible to derive numerical estimates of the expansion factor alpha ²=(R_N²)/N for different values of N and w (the excluded volume parameter) for different three-dimensional lattices. The results have been used to test the two-parameter approximation, and the closed form expressions of Flory, Flory and Fisk, and Alexandrowicz and Kurata.