End-bridging Monte Carlo: A fast algorithm for atomistic simulation of condensed phases of long polymer chains

The recently introduced end-bridging (EB) Monte Carlo move is revisited, an d a thorough analysis of its geometric formulation and numerical implementa tion is given. Detailed results are presented from applying the move, along with concerted rotation, in atomistic simulations of polyethylene (PE) mel t systems with mean molecular lengths ranging from C-78 up to C-500, flat m olecular weight distributions, and polydispersity indices I ranging from 1. 02 to 1.12. To avoid finite system-size effects, most simulations are execu ted in a superbox containing up to 5000 mers and special neighbor list stra tegies are implemented. For all chain lengths considered, excellent equilib ration is observed of the thermodynamic and conformational properties of th e melt at all length scales, from the level of the bond length to the level of the chain end-to-end vector. In sharp contrast, if no end bridging is a llowed among the Monte Carlo moves, no equilibration is achieved, even for the C-78 system. The polydispersity index I is found to have no effect on t he equilibrium properties of the melt. To quantify the efficiency of the EB Monte Carlo move, the CPU time to required for the chain center of mass to travel a distance equal to the root-mean-square end-to-end distance is est imated by simple analytical arguments. It is found that to should scale as n/((X) over bar Delta(2.5)), where n is the total number of mers in the sys tem, (X) over bar is the average chain length, and Delta similar or equal t o [3(I - 1)](1/2) is the reduced width of the chain-length distribution fun ction. This means that, if the size of the model system and the shape of th e chain-length distribution are kept constant, systems of larger average mo lecular weight equilibrate faster, a remarkable attribute of the EB Monte C arlo method. The simulation results obey the estimated scaling of t(0) with (X) over bar, n, and Delta remarkably well in the range of chain lengths a nd polydispersities for which the premises of the analysis are not violated (mean chain lengths greater than C-156 and polydispersity indices above ab out 1.07). Results for volumetric behavior, structure, and chain conformati on at temperature T = 450 K and pressure P ranging from 1 to 800 atm are pr esented, using three different PE united atom models proposed in the recent literature. All three models are shown to overestimate the density by ca. 4% and also overestimate the stiffness of chains. The Yoon et al. model is in best agreement with experimental characteristic ratios. Simulation predi ctions for the structure factor and for the chain-length dependence of the density are in excellent agreement with experiment.