Translational diffusion in Monte Carlo simulations of polymer melts: center of mass displacement vs. integrated velocity autocorrelation function

Translational diffusion has been simulated in monodisperse melts of four linear alkanes, C_2xH_4x+2, x=6,30,50,158, and two cyclic alkanes, C_2xH_4x, x=30,50, at 473 K. The alkanes are expressed in a coarse-grained representation using x beads on a high coordination lattice, one bead for every two carbon atoms. Short-range intramolecular interactions are controlled by an adaptation of the rotational isomeric state model for unperturbed polyethylene, and the long-range interactions are controlled by a step-wise three-shell potential energy function derived from a continuous Lennard-Jones potential energy function. Acceptance of trial moves, each of which changes the coordinates of a single bead only, is governed by the Metropolis rule. Translational diffusion coefficients, D, are estimated from the mean square displacement of the center of mass and the integral of the velocity autocorrelation function. Both approaches yield the same value for D, which demonstrates that the velocity has been defined in a reasonable manner in the Monte Carlo simulation. A method is proposed for the estimation of D when the trajectory is not quite long enough to have achieved the behavior characteristic of the limit as time approaches infinity.