A Monte Carlo study of the second virial coefficient of semiflexible ring polymers

A Monte Carlo (MC) study was made of the second virial coefficient A(2) of the ideal Kratky-Porod (KP) worm-like ring using a model composed of infinitely thin bonds with harmonic bending energy between successive bonds. Two kinds of statistical ensembles were generated: one composed of configurations of all kinds of knots with the Boltzmann weight, called the mixed ensemble, and the other composed of only those of the trivial knot, called the trivial-knot ensemble. The effective volume VE excluded to one ring by the presence of another, resulting only from a topological interaction, and also the mean-square radius of gyration < S-2 > were evaluated for each ensemble. The dimensionless quantity lambda V-E/L-2 proportional to A2 was found to be a function only of the reduced total contour length lambda L, as in the case of lambda < S-2 >/L, where lambda(-1) is the stiffness parameter of the KP ring and L is its total contour length. The quantity lambda V-E/L-2 first increased and then decreased after passing through a maximum at lambda L similar or equal to 5, as lambda L was increased. A comparison with literature data for ring atactic polystyrene in cyclohexane at H shows that the present MC results may qualitatively explain the behavior of the data. Polymer Journal (2010) 42, 735-744; doi:10.1038/pj.2010.61; published online 21 July 2010