Chemical potential, Helmholtz free energy and entropy of argon with kinetic Monte Carlo simulation

Abstract

We present a method, based on kinetic Monte Carlo (kMC), to determine the chemical potential, Helmholtz free energy and entropy of a fluid within the course of a simulation. The procedure requires no recourse to auxiliary methods to determine the chemical potential, such as the implementation of a Widom scheme in Metropolis Monte Carlo simulations, as it is determined within the course of the simulation. The equation for chemical potential is proved, for the first time in the literature, to have a direct connection with the inverse Widom potential theory in using the real molecules, rather than the ghost molecules. We illustrate this new procedure by several examples, including: fluid argon and adsorption of argon as a non-uniform fluid on a graphite surface and in slit pores.

On the consistency of NVT , NPT , μVT and Gibbs ensembles in the framework of kinetic Monte Carlo – Fluid phase equilibria and adsorption of pure component systems

“…The chemical potential thus determined is very accurate because all configurations generated are used in its calculation. As we have shown recently [20], this determination of the chemical potential with real molecules is the inverse of the Widom potential theory [26,27].…”

“…The kMC scheme does not suffer from this drawback and therefore, it enables reliable determination of pressure, density, and other thermodynamic properties, such as chemical potentials. In particular, the kMC scheme can determine the chemical potential very accurately because it uses the molecules in the actual system to sample the energy space, in contrast to the Widom method [20], in which ghost particles are inserted in a number of frozen configurations. The accuracy of this method depends critically on the number of insertions, and is therefore computationally intensive.…”

Development of kinetic Monte Carlo and Bin-Monte Carlo schemes for simulation of mixtures – vapor–liquid equilibria & adsorption

“…The Bin-MC scheme, recently introduced by Fan et al (2012), overcomes these difficulties by taking advantage of the grand canonical features built within a canonical ensemble, to provide effective sampling of both dense and rarefied regions. A second novel technique originating from this group Nguyen et al, 2012;Fan et al, 2013aFan et al, , 2013b, the kMC scheme, gives good results for phase equilibria and adsorption of pure components, because it offers a distinct advantage over other schemes in the direct determination of chemical potential. The statistical thermodynamic basis of the determination of the chemical potential in the kMC is established in our recent paper (Fan et al, 2013b).…”

“…A second novel technique originating from this group Nguyen et al, 2012;Fan et al, 2013aFan et al, , 2013b, the kMC scheme, gives good results for phase equilibria and adsorption of pure components, because it offers a distinct advantage over other schemes in the direct determination of chemical potential. The statistical thermodynamic basis of the determination of the chemical potential in the kMC is established in our recent paper (Fan et al, 2013b). These two new methods, Bin-MC and kMC, have advantages over the classical Gibbs ensemble MC (GEMC) because they can describe density profiles across the vapour-liquid interface and determine the surface tension which cannot be obtained by the Gibbs ensemble because of the absence of interface in GEMC.…”

Kinetic Monte Carlo simulation of mixtures: phase equilibria

“…In a canonical kMC simulation, the excess (configurational) chemical potential [10] of a component β is calculated as follows:…”