Spatial correlations in a self-repelling ring polymer

Abstract

The scattering structure function S N (q) of a large flexible ringpolymer with Nmonomers in a good solvent is calculated as a universal expansion in the variable q 2<R G 2≳, where <R G 2≳ denotes the mean square radius of gyration of the ring. To solve the interacting polymer problem, the methods of renormalized field theory are applied directly to Fixman’s cluster expansion. The results are obtained using the approximation of expanding in ε≡4−(dimension of space) and indicate that the self‐repulsion has a greater influence on the large distance behavior of a ringpolymer when compared with a linear polymer. In particular, we find that the radius of gyration ratio <R G 2≳ring/<R G 2≳ line is a universal quantity and to first order in ε is equal to 0.568. For ideal polymers, the ratio is known to be 0.5.