John A. Zollweg

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.

A critical study of the simulation of the liquid-vapour interface of a Lennard-Jones fluid

Despite the fact that the surface tension for a Lennard-Jones fluid has been simulated many times in the past, there is some considerable disagreement between the results. This paper calculates the surface tension and density profiles for the liquid-vapour interface of a Lennard-Jones fluid using molecular dynamics (MD) simulation techniques for a variety of system sizes, film thicknesses, interfacial areas, interatomic potential cut-offs, and temperatures. The results are compared with previous work in order to resolve some of the discrepancies of the past work. Combining this work with some reliable results from the past, the minimum system size, film thickness, and equilibration time necessary for the accurate description of the surface tension was determined. Using simulation results calculated for computationally-economic values of the potential cut-off, the surface tension was extrapolated to the full potential value using a tail correction and the results compared to simulations performed with long...

Tail corrections to the surface tension of a Lennard-Jones liquid-vapour interface

The Kirkwood-Buff formula for surface tension is used to derive an expression for the tail correction to the surface tension. This expression reduces to the expression for the tail correction, given by Chapela, G. A., Saville, G., Thompson, G., and Rowlinson, J. S. (1977, J. chem. Soc. Faraday Trans II, 8, 1133), when the interface is sharp but differs from it near the critical point. The difference appears to be the result of a mistake in the algebra by Chapela et al. In an example we show that, for a comparison with the surface tension of real fluids, both the tail correction to the surface tension, and the influence of the cut-off radius on the phase diagram are important.

Solubilities of fatty acids, fatty acid esters, triglycerides, and fats and oils in supercritical carbon dioxide

Using supercritical carbon dioxide (SC-CO2) as the solvent, the solubility of methyl esters, ethyl esters, fatty acids, triglycerides, and fats and oils were studied over a range of temperature and pressures. Equilibrium data from the literature were correlated using the Peng-Robinson equation of state. With the van der Waals (VDW) and Panagiotopoulos and Reid (PR) mixing rules. The data were also correlated using statistical methods and the solubilities predicted by various models were compared with experimental solubilities at the temperature and pressure conditions studied. The equation of state method provided good agreement of theory with experiment for the solubilities of fatty acids and their esters, but less so for the triglycerides, fats and oils. The statistical methods on the other hand, not only predicted the solubilities of fatty acids and fatty acid esters well, but also gave good agreement with the solubilities of triglycerides, fats and oils. Chain length, degree of unsaturation, and functional groups in compounds are known to affect the vapor pressures of these compounds which in turn influence their solubilities in SCCO2. As expected solubilities decreased in going from fatty acid esters, to fatty acids, to triglycerides.

Vapor-liquid equilibrium thermodynamics of N2 + CH4: Model and Titan applications

Calculations of the vapor-liquid equilibrium thermodynamics of the N2 + CH4 system show that the tropospheric clouds of Titan are not pure CH4, but solutions of CH4 containing substantial quantities of N2. The conditions for saturation, latent heat of condensation, and droplet composition all depend on this equilibrium. We present a thermodynamic model for vapor-liquid equilibrium in the N2 + CH4 system which, by its structure, places strong constraints on the consistency of experimental equilibrium data, and confidently embodies temperature effects by also including enthalpy (heat of mixing) data. Selected equilibrium and enthalpy data are used in a maximum likehood determination of model parameters. The model can be readily evaluated to compute the saturation criteria, composition of condensate, and latent heat in Titans atmosphere for a given pressure-temperature (p-T) profile. For a nominal p-T profile, the partial pressure of CH4 required for formation of CH4 + N2 condensate is ∼20% lower than that required to saturate pure CH4, and ∼25% higher than that which would be computed by Raoults law. N2 constitutes 16–30% of the cloud condensate, and higher altitude clouds are generally more N2-rich. The N2 content of condensate is ∼1/2 of that computed from Raoults law and about 30% greater than that computed from Henrys law. Heats of condensation are ∼10% lower than for pure CH4. Above 14 km altitude, the liquid solution becomes metastable with respect to a solid solution containing less N2: freezing of liquid droplets will be accompanied by the exsolution of about 30% of the dissolved N2, probably leading to an underdense, porous texture. The refractive index, single-scattering albedo, and density of CH4 + N2 cloud droplets of the appropriate composition and phase should be used in modeling and spacecraft planning studies for Titan. Cassini investigations with sufficient altitude resolution (primarily Huygens probe experiments) can potentially detect vertical motion of particles by determining whether condensate and gas are in local thermodynamic equilibrium.

Phase equilibria of oleic acid, methyl oleate, and anhydrous milk fat in supercritical carbon dioxide

Abstract A static recirculation method was developed and used to measure phase equilibria of binary, ternary, and multicomponent systems in supercritical carbon dioxide (SC-CO 2 ). Binary fluid-liquid equilibria of oleic acid + SCCO 2 were experimentally determined at 313.15 and 333.15 K and at pressures between 3 and 31 MPa. Fluid-liquid equilibria of the binary system methyl oleate + SCCO 2 were also measured at 313.15 and 333.15 K and at pressures between 2 and 14 MPa. Finally, the phase equilibria of anhydrous milk fat (AMF) in SC-CO 2 were determined at 313.15 and 333.15 K and at pressures between 2 and 31 MPa. The data were correlated using the Peng-Robinson equation-of-state with the Panagiotopoulos and Reid mixing rule.

Fluid-Liquid phase equilibria of fatty acids and fatty acid methyl esters in supercritical carbon dioxide

Abstract Fluid-liquid equilibrium data of fatty acids and fatty acid methyl esters in supercritical carbon dioxide at temperatures of 40 °C and 60 °C and pressures up to 300 bar were experimentally determined. The effect of temperature and pressure on solubility in four binary systems was studied. The Redlich-Kwong equation-of-state with a non-quadratic mixing rule was used for data correlation with successful results.

Adsorption, isosteric heat and commensurate-incommensurate transition of methane on graphite

We report a molecular simulation study of methane adsorption and phase transitions on a graphite substrate. Grand canonical Monte Carlo simulations have been carried out to study the adsorption isotherm and heat of adsorption at 77·5 K, using a uniform 10–4–3 substrate potential. Good agreement with experiment is found. Several layering transitions are observed at this temperature. Freezing transitions in the monolayer are found in the simulations, and are in qualitative agreement with experiment. Canonical Monte Carlo simulations have been used to study the commensurate-incommensurate transition of methane on a graphite substrate at conditions near the complete monolayer at 40·0 K, using a periodically varying adsorbate-adsorbent potential. The results are in qualitative agreement with experiments. A new method has been proposed to make a more realistic choice of the dimensions of the simulation cell. The effect of varying the corrugation of the fluid-wall potential on the commensurate and incommensurate...

Shape of the Coexistence Curve near a Plait Point in a Three‐Component System

The degree, d, of the coexistence curve near the plait point in the system ethanol–water–chloroform has been determined from measurements of the volumes of coexisting phases in sealed samples. The result, d = 2.67 ± 0.12, shows the deviation from the mean‐field d = 2 and shows also the renormalization d = (1 − α′) / β that is predicted by current theories. (1 / β is the degree of the temperature‐density coexistence curve in a pure fluid and α′ is the index of its constant‐volume specific heat singularity.)

Thermodynamic and structural properties of methanol-water mixtures: experiment, theory, and molecular simulation

Abstract We report a combined experimental, theoretical and molecular simulation study of the thermodynamics and structure of water-methanol mixtures. FTTR spectroscopic measurements in both the fundamental and overtone regions of the O-H stretch have been made over a wide range of concentration and temperature to obtain information on the energy of hydrogen-bonding and the concentrations of monomeric OH species. Theoretical work has been based on an extension of the cluster expansion theory of Wertheim. The FTIR measurements aid in determining the necessary intermolecular force parameters. The theory is used to predict the thermodynamic properties of both pure and mixed fluids, with particular emphasis on the excess properties of the mixture. Comparisons with experiment show moderately good agreement for this complex mixture. We also report Monte Carlo simulations for this mixture, using OPLS potentials for methanol-methanol and methanol-water interactions and several different potentials for the water-water interaction. We find that the resulting excess properties are sensitive to the water-water potential chosen. The CC potential for water gives quite good agreement with the experimental data.