Statistics of selfhyphen;avoiding ring polymers

摘要

Some important statistical properties of the selfhyphen;avoiding freely jointed ringhyphen;polymer model are studied. Using dynamic Monte Carlo techniques, which yield proper ring configurations, the probability distribution functionPn(r) of intrachain distances, the bond correlation function lang;u0u0+nrang; and related quantities as meanhyphen;square intrachain distances lang;R2nrang;, meanhyphen;square radius of gyration lang;S2Nrang;, and structure functionSN(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 forPn(r) and lang;u0u0+nrang; are proposed. From the latter quantity, lang;R2nrang; and lang;S2Nrang; 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.