Keith E. Gubbins

Phase separation in confined systems

We review the current state of knowledge of phase separation and phase equilibria in porous materials. Our emphasis is on fundamental studies of simple fluids (composed of small, neutral molecules) and well-characterized materials. While theoretical and molecular simulation studies are stressed, we also survey experimental investigations that are fundamental in nature. Following a brief survey of the most useful theoretical and simulation methods, we describe the nature of gas‐liquid (capillary condensation), layering, liquid‐liquid and freezing/melting transitions. In each case studies for simple pore geometries, and also more complex ones where available, are discussed. While a reasonably good understanding is available for phase equilibria of pure adsorbates in simple pore geometries, there is a need to extend the models to more complex pore geometries that include effects of chemical and geometrical heterogeneity and connectivity. In addition, with the exception of liquid‐liquid equilibria, little work has been done so far on phase separation for mixtures in porous media.

The Lennard-Jones equation of state revisited

We review the existing simulation data and equations of state for the Lennard-Jones (LJ) fluid, and present new simulation results for both the cut and shifted and the full LJ potential. New parameters for the modified Benedict-Webb-Rubin (MBWR) equation of state used by Nicolas, Gubbins, Streett and Tildesley are presented. In contrast to previous equations, the new equation is accurate for calculations of vapour-liquid equilibria. The equation also accurately correlates pressures and internal energies from the triple point to about 4·5 times the critical temperature over the entire fluid range. An equation of state for the cut and shifted LJ fluid is presented and compared with the simulation data of this work, and previously published Gibbs ensemble data. The MBWR equation of state can be extended to mixtures via the van der Waals one-fluid theory mixing rules. Calculations for binary fluid mixtures are found to be accurate when compared with Gibbs ensemble simulations.

SAFT: Equation-of-state solution model for associating fluids

An equation-of-state model has been developed for predicting phase equilibria, based on the Statistical Associating Fluid Theory (SAFT). The agreement with molecular simulation data has been found to be excellent at all the stages of model development; for associating spheres, mixtures of associating spheres, and non-associating chains. The model has been shown to reproduce experimental phase equilibrium data for a few selected real pure compounds.

Phase equilibria of associating fluids

As a continuation of our work on spherical associating molecules, we have derived expressions for changes in the thermodynamic properties due to association in mixtures of molecules with multiple bonding sites. The equations are written in terms of a hard-core reference whose pair distribution function is known. In practise, the hard-sphere reference mixture is the easiest to use. A reference system of homonuclear chains is examined in order to account for asymmetries in molecular shape; chains are constructed by bonding equal-sized spheres together. An equation of state for hard-sphere chains is obtained which is in good agreement with recent simulation data. Expressions for mixtures of homonuclear chains of different sizes are also presented. The approach is extended to examine associating chain molecules with multiple bonding sites. The phase equilibria of non-associating chains, and of associating chains with one or two bonding sites are determined. In this study, the separate effects of molecular ass...

Equation of state for the Lennard-Jones fluid

Molecular dynamics calculations of the pressure and configurational energy of a Lennard-Jones fluid are reported for 108 state conditions in the density range 0·35 ≦ ρ* ≦ 1·20 and temperature range 0·5 ≦ T* ≦ 6 (where ρ* = ρσ3, T* = kT/e). Particular attention is paid to the dense fluid region (ρ* ≧ 0·9), including state conditions in the subcooled liquid region. These new simulation results for P and U are combined with those of previous workers, together with low density values calculated from the virial series and values of the second virial coefficients themselves, to derive an equation of state for the Lennard-Jones fluid that is valid over a wide range of temperatures and densities. The equation of state used is a modified Benedict-Webb-Rubin equation having 33 constants. It fits the data well over the density range 0 ≦ ρ* ≦ 1·2 and for T* values ranging from 0·5 to 6·0 (the exact temperature range depending to some extent on the density considered). We also calculate for the same range of state con...

Phase equilibria of associating fluids : spherical molecules with multiple bonding sites

The effect of molecular associations on the phase coexistence properties of fluids with one or two directional, attractive centres is investigated. The individual molecules are represented by hard-sphere repulsive cores with off-centre, square-well attractive sites. Such a system’s thermodynamic properties can be calculated by using expressions based on a theory recently proposed by Wertheim. Isothermal-isobaric Monte Carlo simulations of hard-sphere fluids with one or two attractive sites are shown to be in good agreement with the results of the theory. In order to study the system’s phase equilibria using the theory, a simple van der Waals mean-field term is added to account for the dispersion forces. The critical points and phase equilibria of the associating fluids are determined for various values of the strength and range of the attractive site. Furthermore, results are presented for the degree of association in the gas and liquid phases along the vapour pressure curve. The theory can treat fluids with strong hydrogen-bonding associations such as those found in the carboxylic acids, the aliphatic alcohols, hydrogen fluoride, water etc.

Effects of confinement on freezing and melting

We present a review of experimental, theoretical, and molecular simulation studies of confinement effects on freezing and melting. We consider both simple and more complex adsorbates that are confined in various environments (slit or cylindrical pores and also disordered porous materials). The most commonly used molecular simulation, theoretical and experimental methods are first presented. We also provide a brief description of the most widely used porous materials. The current state of knowledge on the effects of confinement on structure and freezing temperature, and the appearance of new surface-driven and confinement-driven phases are then discussed. We also address how confinement affects the glass transition.

A molecular dynamics study of liquid drops

We report molecular dynamics studies of small liquid drops (41–2004 molecules) in which the atoms interact with a Lennard‐Jones intermolecular potential cutoff at 2.5σ and shifted by the potential at cutoff. We calculate the density profiles ρ(r) and the normal and tangential components of the pressure tensor pN(r) and pT(r), using both the Irving–Kirkwood and Harasima definitions of p. From these functions we calculate the surface thickness, the equimolar radius Re and surface of tension Rs, the surface tension γs referred to Rs, the length δ that appears in Tolman’s equation for γs, the pressure change across the drop, and the densities and pressures of the liquid at the drop center and of the gas. The variation of these properties with both surface curvature and temperature is studied, and the results are used to discuss the validity of Laplace’s equation for the pressure change, Tolman’s equation for the effect of curvature on surface tension, and Kelvin’s equation for the vapor pressure. We also make...

Water in porous carbons

Abstract We present an overview of progress in understanding the behavior of water in porous carbons at the molecular level. We survey experimental investigations, semi-empirical approaches, and simulation studies. Experimental work faces a number of challenges: the determination of the distribution of carbon microcrystal sizes, the densities and species of surface groups, the topological nature of the connected pore structure, and pore size distributions. The lack of experimental characterization, together with the uncertainty in the intermolecular potentials involved, has thwarted molecular simulation efforts thus far. A concerted approach that links experimental and simulation efforts appears promising in gaining a better understanding of the behavior of water in porous carbons. Experimental results could aid in the development of realistic carbon models and improve the intermolecular potentials used in the simulation studies. In a complementary fashion, molecular simulation could help improve characterization methods of both the carbon structure and the surface chemistry.

The chemical potential in dense fluids and fluid mixtures via computer simulation

We describe a new computer simulation technique to evaluate the chemical potential in dense fluids, where the usual test particle method fails. The method rests on the use of the well known Widom test particle equation in conjunction with another equation which is the inverse of the Widom equation. We show that the distribution functions (f and g, respectively) that describe the distribution of the test particle interaction energy u t for these two equations are exactly related (equation (10) below), and that g can be obtained accurately for the values of u t that are needed to calculate the chemical potential. This equation provides the basis for the method. We also propose a further refinement called ‘restricted umbrella sampling’, which improves the efficiency of placing the test particle in the fluid for a fixed configuration of real molecules. Detailed tests of the method are presented using the Monte Carlo technique, for both pure Lennard-Jones (LJ) fluids and LJ mixtures. We find that the method wo...