The Extrapolation of Vapour–liquid Equilibrium Curves of Pure Fluids in Alternative Gibbs Ensemble Monte Carlo Implementations

Abstract

Extrapolation schemes based on Taylor series expansion to determine the vapour–liquid equilibrium (VLE) curves of pure molecular fluids are presented for the NpH and μVL versions of the Gibbs ensemble Monte Carlo (GEMC) simulations. The coexistence curves of the various configurational quantities can be expressed as Taylor series around the simulated equilibrium point as a function of pressure in the NpH version and chemical potential in the μVL version. The coefficients of the Taylor series are calculated from single GEMC simulations using Clapeyron-like equations and fluctuation formulas. A Padè approximant is used to widen the range where the extrapolation is accurate. These methods are demonstrated on atomic Lennard-Jones fluid. The procedure is found to be an accurate and useful tool to calculate wide sections of the VLE curves. With this procedure the saturation heat capacity can be directly determined using the calculated derivatives.

Keywords:

• Taylor series expansion
• NpH ensemble
• μVL ensemble
• Vapour–liquid equilibria

Acknowledgements

This work has been partially supported by the Hungarian National Research Fund (OTKA-TO38239).