Direct calculation of liquid–vapor phase equilibria from transition matrix Monte Carlo simulation

Abstract

An approach for directly determining the liquid–vapor phase equilibrium of a model system at any temperature along the coexistence line is described. The method relies on transition matrix Monte Carlo ideas developed by Fitzgerald, Picard, and Silver [Europhys. Lett. 46, 282 (1999)]. During a Monte Carlo simulation attempted transitions between states along the Markov chain are monitored as opposed to tracking the number of times the chain visits a given state as is done in conventional simulations. Data collection is highly efficient and very precise results are obtained. The method is implemented in both the grand canonical and isothermal–isobaric ensemble. The main result from a simulation conducted at a given temperature is a density probability distribution for a range of densities that includes both liquid and vapor states. Vapor pressures and coexisting densities are calculated in a straightforward manner from the probability distribution. The approach is demonstrated with the Lennard-Jones fluid. Coexistence properties are directly calculated at temperatures spanning from the triple point to the critical point.

Vapor-liquid critical and interfacial properties of square-well fluids in slit pores

“…29,46 In this approach, MC simulations are conducted in a standard grand canonical ensemble where the volume ͑V͒, chemical potential ͑ ͒, and temperature ͑T͒ are held constant and the particle number N ͑or density͒ and energy ͑U͒ fluctuates. During a simulation, attempted transitions between states of different densities are monitored.…”

Critical points, phase transitions and water-like anomalies for an isotropic two length scale potential with increasing attractive well

“…The structural properties of the fluid were obtained by inspection of the behavior of the translation order parameter [13][14][15], defined as…”

“…While for normal liquids the system becomes more structured with the increase of the density, water shows a maximum. Such behavior can be characterized by translational order parameter t [13][14][15] that exhibits a region in which t decreases under compression. The entropy also shows a very peculiar behavior.…”

“…Studies have shown that Te [27], Ga, Bi [28], S [29,30], Ge 15 Te 85 [31], BeF 2 [16,[32][33][34], silica [13,16,32,35] and silicon [36] present water-like anomalies.…”

Direct determination of fluid-solid coexistence of square-well fluids confined in narrow cylindrical hard pores

“…Many results are available for vapor-liquid phase behaviors for the SW model. [1][2][3][4] There are several techniques to determine the vapor-liquid coexistence, such as Gibbs ensemble Monte Carlo ͑GEMC͒, 5 Gibbs-Duhem integration ͑GDI͒, 6,7 grandcanonical transition-matrix Monte Carlo, 2,8 but less is known about the fluid-solid behavior. Pagan and Gunton 9 used the free energy calculation and GDI to determine the fluid-solid coexistence and the metastable fluid-fluid coexistence for a short range SW model.…”