Statistics of self-avoiding ring polymers

Some important statistical properties of the self-avoiding freely jointed ring-polymer model are studied. Using dynamic Monte Carlo techniques, which yield proper ring configurations, the probability distribution function Pn(r) of intrachain distances, the bond correlation function 〈u0u0+n〉 and related quantities as mean-square intrachain distances 〈R2n〉, mean-square radius of gyration 〈S2N〉, and structure function SN(q) are calculated. These quantities are analyzed using scaling assumptions and are compared to the same quantities of the corresponding linear polymer model. Closed analytical expressions for Pn(r) and 〈u0u0+n〉 are proposed. From the latter quantity, 〈R2n〉 and 〈S2N〉 are calculated and compared with Monte Carlo estimates. We show that all these quantities are governed asymptotically by exponents which have been found for linear polymers; but in contrast, the analytical expressions are rather different. The experimental relevance of these results is briefly discussed.