End-Bridging Monte Carlo:  A Fast Algorithm for Atomistic Simulation of Condensed Phases of Long Polymer Chains

Abstract

The recently introduced end-bridging (EB) Monte Carlo move is revisited, and a thorough analysis of its geometric formulation and numerical implementation is given. Detailed results are presented from applying the move, along with concerted rotation, in atomistic simulations of polyethylene (PE) melt systems with mean molecular lengths ranging from C78 up to C500, flat molecular weight distributions, and polydispersity indices I ranging from 1.02 to 1.12. To avoid finite system-size effects, most simulations are executed in a superbox containing up to 5000 mers and special neighbor list strategies are implemented. For all chain lengths considered, excellent equilibration is observed of the thermodynamic and conformational properties of the 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 allowed among the Monte Carlo moves, no equilibration is achieved, even for the C78 system. The polydispersity index I is found to have no effect on the equilibrium properties of the melt. To quantify the efficiency of the EB Monte Carlo move, the CPU time t 0 required for the chain center of mass to travel a distance equal to the root-mean-square end-to-end distance is estimated by simple analytical arguments. It is found that t 0 should scale as n/(X̄Δ2.5), where n is the total number of mers in the system, X̄ is the average chain length, and Δ ≃ [3(I − 1)]1/2 is the reduced width of the chain-length distribution function. This means that, if the size of the model system and the shape of the chain-length distribution are kept constant, systems of larger average molecular weight equilibrate faster, a remarkable attribute of the EB Monte Carlo method. The simulation results obey the estimated scaling of t 0 with X̄, n, and Δ remarkably well in the range of chain lengths and polydispersities for which the premises of the analysis are not violated (mean chain lengths greater than C156 and polydispersity indices above about 1.07). Results for volumetric behavior, structure, and chain conformation at temperature T = 450 K and pressure P ranging from 1 to 800 atm are presented, 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 predictions for the structure factor and for the chain-length dependence of the density are in excellent agreement with experiment.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

“…For example in atomistic simulations such localized moves include, among others, the configurational bias (CB) (de Pablo et al, 1992a(de Pablo et al, , 1992bLaso et al, 1992;Siepmann and Frenkel, 1992) and the concerted rotation (ConRot) (Dodd et al, 1993) algorithms. Full-scale, robust equilibration even for very long chains is ensured through the application of advanced, chain-connectivity-altering moves: the end-bridging (EB) (Mavrantzas et al, 1999;Pant and Theodorou, 1995) and the double-bridging (DB) (Karayiannis et al, 2002a(Karayiannis et al, , 2002b. These proceed by removing and re-constructing a properly selected trimer (EB) or pair of trimers (DB) between two different chains producing two new chains whose contours are distinctly different from the original ones.…”

“…These proceed by removing and re-constructing a properly selected trimer (EB) or pair of trimers (DB) between two different chains producing two new chains whose contours are distinctly different from the original ones. EB and DB have been proven very successful in the simulation of atomistic polymers, with the full-scale of polyethylene-like (PE) systems with chains of up to thousands of monomers being achieved in modest computational time, far exceeding any alternative method (Karayiannis et al, 2002b;Mavrantzas et al, 1999). Such chain-connectivityaltering moves can be further performed in parallel pattern allowing the simulation of well-entangled, industrially-relevant polymer systems (Uhlherr et al, 2002).…”

Improving the sampling efficiency of Monte Carlo molecular simulations: an evolutionary approach

“…Sum of lacunarity criteria for scales R ¼ 6; 7; 8 4 In both cases the IEA brings an improvement even if in the case of the long chains (A64) the curves are more oscillating, even when considering the weighted fitness scores. We clearly notice on the A32 fitness curves, the exploration/exploitation transition at generation 40, where the fitness jumps because only the best individual is used.…”

“…The ECFs show that the reptation is still favoured with regard to this criterion, but still with a non-negligible contribution of other MC moves and in the case of B64 there are 'hesitations' between rotation and reptation. It reveals a fact outlined in [4]: if we want the reptation to have a significant effect, it is necessary to include MC moves that change end monomer environments. Once a reptation succeeds, it leaves a hole at the former position of the displaced monomer.…”

“…We chose to work with the well-studied linear polyethylene model described in [4], with the same constants:…”