THE NUMBER OF CONTACTS IN A SELF-AVOIDING WALK OF VARIABLE RADIUS OF GYRATION IN 2 AND 3 DIMENSIONS

A simple scaling law is proposed for the dependence of the number of c ontacts on the radius of gyration of a self-avoiding walk (SAW). We te st our proposal on SAWs generated by a Monte Carlo simulation on squar e and cubic lattices. The distribution of the number of contacts is th en combined with the distribution of configurations previously derived to deduce the free energy of a polymer chain for low values of the in teraction parameter chi. As compared to the free energy of Flory, the new expression takes a much better account of the spatial correlations between distant monomers of the chain.