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

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 matter such as glasses and many processed polymer melts. Experiments that provide information about atomic-level ordering are amenable to this approach. Closure of the inverse problem of determining the structural detail from limited data is achieved by selecting the lowest-free-energy ensemble of configurations that reproduces the experimental data. The free energy is calculated using the thermodynamic potential of the appropriate semi-grand canonical ensemble defined by the experimental data. To illustrate the method we examine uniaxially oriented polyethylene melts of average chain length C78. The simulation results are analysed for features not explicitly measured, such as the density, torsion angle distribution, and free energy, to understand more fully the underlying features of these non-equilibrium states