An advanced Gibbs-Duhem integration method: Theory and applications

Abstract

The conventional Gibbs-Duhem integration method is very convenient for the prediction of phase equilibria of both pure components and mixtures. However, it turns out to be inefficient. The method requires a number of lengthy simulations to predict the state conditions at which phase coexistence occurs. This number is not known from the outset of the numerical integration process. Furthermore, the molecular configurations generated during the simulations are merely used to predict the coexistence condition and not the liquid-and vapor-phase densities and mole fractions at coexistence. In this publication, an advanced Gibbs-Duhem integration method is presented that overcomes above-mentioned disadvantage and inefficiency. The advanced method is a combination of Gibbs-Duhem integration and multiple-histogram reweighting. Application of multiple-histogram reweighting enables the substitution of the unknown number of simulations by a fixed and predetermined number. The advanced method has a retroactive nature; a current simulation improves the predictions of previously computed coexistence points as well. The advanced Gibbs-Duhem integration method has been applied for the prediction of vapor-liquid equilibria of a number of binary mixtures. The method turned out to be very convenient, much faster than the conventional method, and provided smooth simulation results. As the employed force fields perfectly predict pure-component vapor-liquid equilibria, the binary simulations were very well suitable for testing the performance of different sets of combining rules. Employing Lorentz-Hudson-McCoubrey combining rules for interactions between unlike molecules, as opposed to Lorentz-Berthelot combining rules for all interactions, considerably improved the agreement between experimental and simulated data.

Using reweighting and free energy surface interpolation to predict solid-solid phase diagrams

“…to one simulation volume, is not observed in one of the volumes 27 . It is also not useful for solid crystalline systems because of the particle insertion Monte Carlo step, which is not favorable in crystalline systems.…”

“…This process can be seen in Figure 1. The sources of error in this method include the accuracy of the initial coexistence point, the integration method used, the temperature step size 22 and the distance from the initial coexistence point 27 .…”

Multicomponent gauge cell method

“…As of now, free energies of multicomponent systems as well as the phase equilibria were studied using Widom insertion technique, 25,26 thermodynamic integration of GCMC adsorption isotherms 27 and Gibbs-Duhem integration, [28][29][30][31][32] GEMC ͑e.g., Refs. 33-36͒, umbrella sampling, 37-39 histogram reweighting, [40][41][42][43][44] and, recently, Wang-Landau technique.…”

The third industrial fluid properties simulation challenge

“…Accuracy is determined by the realism of the inter-atomic interactions (the functional form and parameters of the forcefield) [22], and by the strategies for creating and manipulating the model to provide property predictions (the molecular simulations methods used). Typical molecular simulations approaches that have been used for VLE prediction of mixtures include configurational-bias Monte Carlo simulations (Gibbs ensemble and the combination of GrandCanonical Monte Carlo and histogram reweighting) [23][24][25][26][27], the Gibbs-Duhem integration method [28][29][30], the NPT dynamics plus test particle method (Widom's insertion method) [31,32], the bubble point pseudo-ensemble method [33], and the Grand Equilibrium method [34].…”