A method for calculating the nonequilibrium entropy of a flowing polymer melt via atomistic simulation

Nonequilibrium thermodynamics as applied to polymeric liquids is limited by the inability to quantify the configurational entropy. There is no known experimental method to determine it rigorously. Theoretically, entropy is based entirely on the configurational microstate of the material, but for polymer liquids, the number of available configurations is immense and covers long length scales associated with the chain-like nature of the constituent molecules. In principle, however, it should be possible to calculate the entropy from a realistic molecular dynamics simulation that contains positional data for each atomic unit making up the polymer macromolecules. However, there are two challenges in calculating the entropy from an atomistic simulation: it is necessary to relate atomic positions to configurational mesostates, depending on the degree of coarse-graining assumed (if any), and then to entropy, and considerable computational resources are required to determine the three-dimensional probability distribution functions of the configurational mesostates. In this study, a method was developed to calculate nonequilibrium entropy using 3d probability distributions for a linear, entangled polyethylene melt undergoing steady-state shear and elongational flow. An approximate equation expressed in terms of second moments of the 3d distributions was also examined, which turned out to provide almost identical values of entropy as the fully 3d distributions at the mesoscopic level associated with the end-to-end vector of the polymer chains.