Monte Carlo study of polymerization on a lattice: Two dimensions

Monte Carlo methods were used to study a two-dimensional lattice model for equilibrium polymerization, incorporating activation energy, stiffness, monomer-monomer binding energy, and excluded volume (bifunctionality). For stiff monomers we found a low-temperature orientationally ordered phase separated from the disordered state by first-order and Ising second-order boundaries. The transition to the ordered phase is coupled with an increase (but no apparent singularity) in average polymer weight. The ordered state portion of the phase diagram shrinks as monomer stiffness is reduced, until for flexible activated monomers it disappears and the ground-state entropy is proportional to the number of sites. The number of polymers of size s decreases exponentially with s wherever finite-lattice effects can be ignored. The average square of the radius of gyration for flexible polymers was found to be proportional to the average polymer length s, as would be the case in a monodisperse polymer melt.