J.M. Haile

On the use of computer simulation to determine the excess free energy in fluid mixtures

Haile, J.M., 1986. On the use of computer simulation to determine the excess free energy in fluid mixtures. Fluid Phase Equilibria, 26: 103–127 This paper first reviews the use of Kirkwoods coupling parameter for determining residual chemical potentials, activity coefficients, and Henrys constants from Monte Carlo and molecular dynamics computer simulations. A new version of the method is then developed for obtaining the excess Gibbs free energy from isothermal-isobaric simulations. New expressions are also given for the excess volume and excess entropy. The revised method is demonstrated by computing excess free energies for 14 mixtures of repulsive soft spheres. Isothermal-isobaric molecular dynamics was used to generate the necessary simulation data. Although the excess free energies for these particular mixtures are small in magnitude (|GE/NkT| < 0.1), the simulation method generally gives GE within 5% of the values calculated by thermodynamic perturbation theory.

Computer simulation results for thermodynamic excess properties in fluid mixtures

This paper reports results from isothermal-isobaric molecular dynamics simulations of binary mixtures of Lennard-Jones fluids. The simulations were performed at several component size ratios in the range 1 ˇ- σ BB /σ AA ˇ- 2 and at three pressures. The principal results reported here are excess Gibbs free energies g E, excess volumes v E, and excess enthalpies h E. These new results do not coincide with previous Lennard-Jones simulations because of the extensive size and pressure ranges studied and because of the accuracy attained in the values for g E. The simulation data are used to test a recent revision of thermodynamic perturbation theory based on hard-sphere mixtures.

Computer simulation results for thermodynamic excess properties in fluid mixtures II. Effects of energy parameter differences in simple binary mixtures

This paper reports results from isothermal-isobaric molecular dynamics simulations of binary mixtures of Lennard-Jones fluids. The simulations were performed for size-parameter ratios in the range 1ˇ-σ BB /σ AA ˇ-1·5 and energy-parameter ratios 1ˇ-e BB /e AA ˇ-2. The principal results are excess Gibbs free energies, excess enthalpies, and excess volumes, which are used to test a first-order perturbation theory based on hard sphere mixtures.

Effect of molecular elongation on the quadrupolar free energy in diatomic fluids

This paper reports results obtained from computer simulations of pure fluids composed of two-centre Lennard-Jones plus point quadrupole molecules. Simulations were performed over a range of quadrupole moments 0 ⩽ Q 2 ⩽ 4 and a range of molecular elongations 0 ⩽ l ⩽ 0·793. The principal results reported are values of the quadrupolar contribution to the Helmholtz free energy AQ , which was computed via Kirkwoods coupling parameter method. We show how AQ responds to changes in both Q and l. Results are also presented for the configurational internal energy, the quadrupolar internal energy, and site-site pair distribution functions. The simulation results are used to test two forms of first-order perturbation theory; neither form of the theory satisfactorily predicts the simulation results when both the quadrupole moment and the molecular elongation are large.

Specific heat of simple liquids

Residual specific heats c v/* are calculated from a Weeks-Chandler-Andersen-type perturbation theory for Lennard-Jones (LJ) and two-centre-Lennard-Jones (2CLJ) liquids. For spherical molecules the theory predicts that as the density is increased up to slightly above three times the critical density (ρc), c v/* increases to 2R. Corresponding states considerations indicate that rotational degrees of freedom in 2CLJ fluids make no contributions to c v/*. Comparing with real liquids, the theoretical predictions of c v/* agree, within the accuracy of the experiments, with experimental data for liquid argon, methane, and oxygen, at densities ρ/ρc > 2·5. For ethane, the theoretical predictions of c v/*, assuming a 2CLJ fluid with elongation L = 0·67, are too low. This deficiency in the theory for long molecules is attributed to the neglect of the angle-dependence of the background correlation function. However, computer simulation results for c v/* in 2CLJ fluids of elongation L = 0·67 agree with the perturbatio...

On the isoenthalpic-isobaric ensemble in classical statistical mechanics

Generalized ensemble theory is used to develop several fundamental formulae which describe the isoenthalpic-isobaric ensemble of classical statistical mechanics. The isoenthalpic-isobaric partition function is related to thermodynamics and averages for properties in the ensemble are expressed in terms of averages in the microcanonical ensemble. Mean square volume fluctuations in the ensemble are found to be simply related to the adiabatic compressibility and mean square kinetic energy fluctuations are found to be related to the isobaric heat capacity.

Determination of excess gibbs free energy from computer simulation: multiple-parameter charging approach

Abstract We devise a general procedure for determining the excess Gibbs free energy from molecular-scale computer simulations of binary mixtures. The method is based upon Kirkwoods coupling-parameter interpretation of the chemical potential. We show that, by a suitable choice of integration path, coupling involving any number of parameters can be represented by a single independent parameter. Thus for (rigid-molecule) solutions made nonideal by differences among several potential parameters, the determination of the excess free energy generally requires little more effort than if all the differences reside in one potential parameter. The development here is an extension of the recent revision of the coupling-parameter approach that avoids the need for the pure component free energies in obtaining the excess free energy of the mixture.

The influence of unlike molecule interaction parameters on liquid mixture excess properties

Abstract The dependence of the liquid mixture excess properties g E , h E , and v E on an unlike molecule interaction parameter is considered. Firstly, the derivatives of the excess properties with respect to that parameter are expressed as averages in the isobaric-isothermal (NpT) ensemble which can be evaluated in computer simulations. As a special case the derivatives of the excess properties with respect to the unlike interaction parameters describing the deviations from the Lorentz-Berthelot combining rule for a mixture of n-center Lennard-Jones molecules are given. Then, a hypothetical mixture of equal Lennard-Jones molecules is considered in which case these derivatives can be expressed rigorously by thermodynamic quantities of the pure fluid. Finally, by using a WCA-type perturbation theory it is shown that these thermodynamic relations for the derivatives of the excess properties are also approximately valid for a certain class of mixtures including nonspherical molecules. Relevant conclusions are that the unlike energy parameter influences g E , h E , and v E , whereas the unlike size parameter practically influences only V E . The quantities g E and h E are strongly coupled to each other but not necessarily to v E .

Computer simulation of fluid mixtures

Abstract Molecular-scale computer simulations can contribute to the development of correlations for properties of fluid mixtures. This point is illustrated here by sample results from three problems: (1) determination of the excess Gibbs free energy for fluid mixtures, (2) determination of inter- and intramolecular structure in fluids of short-chain molecules, and (3) tests of the fundamental hypothesis of group contribution methods for correlating thermodynamic properties.

Representation of static three-body correlations in dense fluids

This paper reports upon new studies of the error involved in the superposition approximation to the triplet distribution function g 3 in atomic fluids. The analysis is performed by first expressing g 3 in spherical perimetric coordinates (ρ, θ, φ) in which the ‘size’ of a triangle, ρ, is measured independently of its ‘shape’ θ and φ. Then g 3 is expanded in spherical harmonics of the triangular shape parameters. The expansion coefficients were evaluated by analysing molecular dynamics simulation data for a Lennard-Jones fluid and the results were compared with the corresponding coefficients appearing in an explicit expansion of the superposition approximation. We show how these two sets of coefficients may be combined to give a precise representation of the difference between the simulation and the superposition correlation functions. This formulation is then tested by evaluating the Axilrod-Teller triple-dipole energy directly from simulation and from the superposition approximation plus correction terms.