The scaling behavior of the second virial coefficient of linear and ring polymer

The scaling behavior of the second virial coefficient of ring polymers at the theta temperature of the corresponding linear polymer（θL） is investigated by off-lattice Monte Carlo simulations. The effects of the solvents are modeled by pairwise interaction between polymer monomers in this approach. Using the umbrella sampling, we calculate the effective potential U（r） between two ring polymers as well as the second virial coefficient A2 of ring polymers at θL, which results from a combination of 3-body interactions and topological constraints. The trend in the strength of the effective potential with respect to chain length shows a non-monotonic behavior, differently from that caused only by topological constraints. Our simulation suggests that there are three regimes about the scaling behavior of A2 of ring polymers at θL: 3-body interactions dominating regime, the crossover regime, and the topological constraints dominating regime.