Using Monte Carlo Simulation to Compute Liquid–Vapor Saturation Properties of Ionic Liquids

Abstract

We discuss Monte Carlo (MC) simulation methods for calculating liquid-vapor saturation properties of ionic liquids. We first describe how various simulation tools, including reservoir grand canonical MC, growth-expanded ensemble MC, distance-biasing, and aggregation-volume-biasing, are used to address challenges commonly encountered in simulating realistic models of ionic liquids. We then indicate how these techniques are combined with histogram-based schemes for determining saturation properties. Both direct methods, which enable one to locate saturation points at a given temperature, and temperature expanded ensemble methods, which provide a means to trace saturation lines to low temperature, are discussed. We study the liquid-vapor phase behavior of the restricted primitive model (RPM) and a realistic model for 1,3-dimethylimidazolium tetrafluoroborate ([C1mim][BF4]). Results are presented to show the dependence of saturation properties of the RPM and [C1mim][BF4] on the size of the simulation box and the boundary condition used for the Ewald summation. For [C1mim][BF4] we also demonstrate the ability of our strategy to sample ion clusters that form in the vapor phase. Finally, we provide the liquid-vapor saturation properties of these models over a wide range of temperature. Overall, we observe that the choice of system size and boundary condition have a non-negligible effect on the calculated properties, especially at high temperature. Also, we find that the combination of grand canonical MC simulation and isothermal-isobaric temperature expanded ensemble MC simulation provides a computationally efficient means to calculate liquid-vapor saturation properties of ionic liquids.

Liquid–vapor equilibrium and critical parameters of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate from molecular dynamics simulations

“…In addition to the results specific to [bmim][PF 6 ], the corresponding-states properties are of interest because they seem to be rather generic for room temperature ionic liquids (RTILs) and do not depend too sensitively on the chemical identity of the RTIL. In good agreement with the data reported by Rai and Maginn [16,17] and by Rane and Errington [18,19] for other ionic liquids (see below), the critical compressibility factor Z c of 0.03-0.05 is found to be markedly smaller than for non-ionic fluids (Z c ≈ 0.3 for simple fluids), but not far from the estimate of Z c = 0.029 for the simplest generic model of ionic fluids, the restricted primitive model (RPM), which consists of equisized charged hard spheres [18,47]. Guggenheim's ratio, relating the apparent enthalpy of vaporization (obtained as the supposedly constant slope of a plot of lnP vs. 1/T) to the critical temperature, Δ vap H app /(RT c ), is about 10, significantly larger than the value of 5-6 found for simple fluids, and it thus turns out to be in the range estimated for ionic liquids from experimental data and for the generic ionic fluid model RPM from simulations [15].…”

“…Guggenheim's ratio measures the apparent enthalpy of vaporization in relation to the critical temperature, Δ vap H app /(RT c ). For simple fluids, this ratio is typically 5-6; the value of 9.9 ± 0.5 obtained here is significantly larger, but in the range encompassed for RTILs (9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) based on experimental data [15].…”

“…The findings of Rai and Maginn [16,17] and of Rane and Errington [18,19], however, differ in the temperature-dependent behavior of the vapor pressure, which is best seen in a plot of lnP vs. 1/T. Both groups find the graph of this function to be curved, but while Rai and Maginn observe this function to be convex, implying that the effective/local enthalpy of vaporization Δ vap H eff (T) increases with increasing temperature, Rane and Errington find the opposite, a concave function, implying that Δ vap H eff (T) decreases with increasing temperature.…”

“…The vapor pressure of RTILs was studied by means of different variants of Monte Carlo (MC) simulations by Rai and Maginn [16,17] using direct Gibbs ensemble MC (GEMC) and by Rane and Errington [18,19] using temperature expanded ensemble (TEE) MC techniques allowing them to obtain data also at low and intermediate temperatures. (To the best of our knowledge, there have been no attempts to obtain vapor pressures directly from MD simulations, perhaps because this approach is restricted to very high temperatures for RTILs.)…”

“…Furthermore, we estimate the correlation length from the thickness of the liquid-vapor interface. Subsequently, we calculate several corresponding-states properties and compare them to those of generic ionic and non-ionic model fluids [15] and to the results for molecular models of RTILs evaluated by means of Monte Carlo simulation [16][17][18][19] to test the applicability of different methodologies.…”