Direct Evaluation of Vapour-Liquid Equilibria by Molecular Dynamics using Gibbs-Duhem Integration

Abstract

An application of the Gibbs-Duhem integration [D. A. Kofke, J. Chem. Phys., 98, 4149 (1993)] for the direct evaluation of vapour-liquid equilibria by molecular dynamics is presented. The Gibbs-Duhem integration combines the best elements of the Gibbs ensemble Monte Carlo technique and thermodynamic integration. Given conditions of coexistence at one coexistence point, simultaneous but independent NPT molecular dynamics simulations of each phase are carried out in succession along saturation lines. In each simulation, the saturated pressure is adjusted to satisfy the Clapeyron equation. The Clapeyron equation is a first-order nonlinear differential equation that prescribes how the pressure must change with the temperature to maintain coexistence. The Clapeyron equation is solved by the predictor-corrector method. Running averages of enthalpy and density of each phase are used to evaluate the right-hand side of the Clapeyron equation. The Gibbs-Duhem integration method is applied to a two-centre Lennard-Jones fluid of elongation 0.505. The starting coexistence point was taken from published data or was determined via the Widom test particle insertion method. Implementation of the Gibbs-Duhem integration with a thermodynamic model for the vapour phase is also presented.