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

Abstract

A Monte Carlo (MC) study was made of the second virial coefficient A2 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 〈S2〉 were evaluated for each ensemble. The dimensionless quantity λVE/L2 proportional to A2 was found to be a function only of the reduced total contour length λL, as in the case of λ〈S2〉/L, where λ−1 is the stiffness parameter of the KP ring and L is its total contour length. The quantity λVE/L2 first increased and then decreased after passing through a maximum at λL≃5, as λL was increased. A comparison with literature data for ring atactic polystyrene in cyclohexane at Θ shows that the present MC results may qualitatively explain the behavior of the data. The effective volume VE excluded to a Kratky–Porod (KP) worm-like ring by the presence of another, resulting only from a topological interaction, was evaluated by Monte Carlo simulations. The quantity λVE/L2 proportional to the second virial coefficient A2 was shown to be a function only of λL with λ−1 the stiffness parameter of the KP ring and L its total contour length.