Monte Carlo simulation in the semi-grand canonical ensemble as a ‘thermodynamic’ reverseMonte Carlo technique, with application to a polymer melt

Abstract

We describe the use of Monte Carlo simulation in the semi-grand canonical ensemble(SGMC) to analyse and interpret experimental data for non-equilibrium states of mattersuch as glasses and many processed polymer melts. Experiments that provide informationabout atomic-level ordering are amenable to this approach. Closure of the inverse problemof determining the structural detail from limited data is achieved by selecting thelowest-free-energy ensemble of configurations that reproduces the experimental data. Thefree energy is calculated using the thermodynamic potential of the appropriatesemi-grand canonical ensemble defined by the experimental data. To illustrate themethod we examine uniaxially oriented polyethylene melts of average chain lengthC78. The simulation results are analysed for features not explicitly measured, such as thedensity, torsion angle distribution, and free energy, to understand more fully the underlyingfeatures of these non-equilibrium states.