Monte Carlo study of ring polymers

Abstract

Nonintersecting ring polymers of step number (chain length) 6–118 have been produced by the Monte Carlo method on a tetrahedral lattice. The mean square radius of gyration and its standard deviation for each sample have been determined. A log-log plot of the mean square radius of gyration 〈S2〉 vs N, the number of steps, gives the usual straight line with a slope of 1.218. The deviation of this exponent from reported values for the mean square end to end distance of linear polymers (1.200) lies within the margin of error and is unlikely to be due to the ring geometry of the polymer. The data are also compared with similar results on linear polymers; in particular, the ratio of the two radii of gyration 〈S2〉lin/〈S2〉ring in the presence of excluded volume is discussed, and its asymptotic value is compared with the value predicted from existing theory.