Statistical properties of a polymer chain in the two-parametor approximation

Abstract

The diagrammatic method developed in a previous paper is used to derive two terms of the virial expansion for the mean square distance from the origin, the mean square radius of gyration, and the probability of ring closure for a lattice model of a simple polymer chain. It is found that the logarithmic terms in the partition function cancel in the virial series for these universal quantities. The universality hypothesis is tested with the numerical data for self-avoiding walks (s.a.w.) for different lattices. The virial series is combined with the s.a.w. results to provide formulae for the expansion factor as a function of the excluded volume.