Pivot-coupled grand canonical Monte Carlo method for ring simulations

A new method is presented for the simulation of an ensemble of polymer rings of variable size at fixed monomer chemical potential. Called pivot-coupled grand canonical Monte Carlo ~PC-GCMC!, it is based on the directed addition or removal of a monomer to or from a ring, coupled to the pivot of a section of the ring to maintain the ring’s continuity. Application of PC-GCMC to single, isolated rings yields the free energy of the ring polymer as a function of number of monomers, information useful in determining equilibrium constants for polymer cyclization. Ring closure probabilities ~‘‘J-factors’’! for flexible and semiflexible polymers, both ideal and self-avoiding, in two and three dimensions are obtained in close agreement with available results from theory and other simulation methods. New results are obtained for two-dimensional semiflexible polygons. Potential applications of the method to simulations of ring-forming equilibrium polymers, disklike micelles, and self-assembling polymer loops are discussed. © 2002 American Institute of Physics. @DOI: 10.1063/1.1461359#