K.P. Shukla

Associating fluids with four bonding sites against a hard wall: density functional theory

We present two new perturbation density functional theories to investigate non-uniform fluids of associating molecules. Each fluid molecule is modelled as a spherical hard core with four highly anisotropic square well sites placed in tetrahedral symmetry on the hard core surface. In one theory we apply the weighting from Tarazonas hard sphere density functional theory to Wertheims bulk first-order perturbation theory. The other theory uses the inhomogeneous form of Wertheims theory as a perturbation to Tarazonas hard-sphere density functional theory. Each theory approaches Tarazonas theory in the limit of zero association. We compare results from theory and simulation for density profiles, fraction of monomers, and adsorption of an associating fluid against a hard, smooth wall over a range of temperatures and densities. The non-uniform fluid theory which uses Tarazonas weighting of Wertheims theory in the bulk is in good agreement with computer simulation results.

Phase equilibria and thermodynamic properties of hard core Yukawa fluids of variable range from simulations and an analytical theory

New Gibbs ensemble Monte Carlo (GEMC) simulation results for vapor/liquid phase equilibria and new Monte Carlo simulation results for structure and thermodynamic properties of the hard core Yukawa fluids of variable range (HCYF-VR) are presented. Using the inverse temperature expansion of the free energy of mean spherical approximation a new version of the analytical theory of HCYF-VR has been developed. GEMC results for 108, 216, and 500 particles show a significant system size dependence of the vapor/liquid phase diagram. Comparisons of theoretical predictions with simulation data show that the analytical theory is highly reliable in describing structure, thermodynamic properties and phase equilibrium of HCYF-VR over a range of the attraction parameter and thermodynamic conditions. Both simulation and theoretical results show that the range of vapor/liquid equilibrium temperature shrinks as the range of interaction decreases. Theoretical results for the critical point and triple point temperatures illus...

Conformal solutions: which model for which application?

Abstract Shukla, K.P., Luckas, M., Marquardt, H. and Lucas, K., 1986. Conformal solutions: which model for which application? Fluid phase Equilibria, 26: 129–147. Various forms of conformal solution theories are discussed and compared to computer simulations for Lennard-Jones mixtures under rather different conditions. It is found that the simple VDW1-theory is applicable when the ratio of the energy parameters is 1.5, and the ratio of the size parameters is 1.1. The same region of applicability is found for the Mean Density Approximation (MDA). Two models using explicitly known properties of the hard-sphere mixture, i.e., the Hard-Sphere Expansion theory (HSE) and a particular version of the Hard-Sphere Perturbation theory (WCA-LL-GH), have also been tested. The HSE is not complete unless a consistent method is found to calculate the hard-sphere diameter. The overall best results are found for WCA-LL-GH. While WCA-LL-GH turns out to be limited in applicability to size ratios smaller than 1.3 and appears to be inaccurate for particular cases, it is definitely the best model available today.

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.

Thermodynamic properties of simple fluid mixtures from perturbation theory

Thermodynamic properties for several binary mixtures of atomic fluids are predicted from perturbation theories using the hard-sphere reference. These calculations differ from previous studies in that the hard-sphere mixture properties are computed more accurately and a new criterion is proposed and tested for determining the hard-sphere diameters. Comparisons with computer simulation results and with experimental data show the theory to be highly accurate.

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.

Third virial coefficient of simple linear molecules

The third virial coefficient of nitrogen, oxygen and ethane is calculated from a potential which uses a site-site repulsive model and the usual contributions to the long range forces. The model contains three adjustable parameters, which are fitted to the second virial coefficient and the Joule-Thomson coefficient. Nonadditive three-body dispersion forces are derived. The numerical evaluations of the third virial coefficient is discussed in some detail. When account is taken of the non-additive dispersion forces, the third virial coefficients are considerably overestimated. However, a universal correlation of this contribution with the non-dimensional polarizability is proposed. This permits accurate predictions of the third virial coefficients.

Thermodynamics of the xenon+methyl chloride system

Abstract The total vapour pressure of the xenon + methyl chloride system has been measured as a function of composition at 175.44 and 182.32 K. The resulting data have been used to evaluate the excess Gibbs functions GE at the same temperatures. The excess enthalpy and excess molar volume have also been measured at 182.32 K. The system shows large positive deviations from Raoults law but negative volumes on mixing. These results are compared with theoretical predictions of a recent molecular theory and of standard engineering methods. The calculations show the superiority of the molecular theory over more empirical procedures such as those based on the Redlich-Kwong equation of state or the regular-solution model.

TPT2 and SAFTD equations of state for mixtures of hard chain copolymers

We present the second-order thermodynamic perturbation theory (TPT2) and the dimer statistical associating fluid theory (SAFTD) equations of state for mixtures consisting of hetero-nuclear hard chain molecules based on extensions of Wertheims theory for associating fluids. The second-order perturbation theory, TPT2, is based on the hard sphere mixture reference fluid. SAFTD is an extension of TPT1 (= SAFT) and is based on the non-spherical (hard disphere mixture) reference fluid. The TPT2 equation of state requires only the contact values of the hard sphere mixture site-site correlation functions, while the SAFTD equation of state requires the contact values of site-site correlation functions of both hard sphere and hard disphere mixtures. We test several approximations for site-site correlation functions of hard disphere mixtures and use these in the SAFTD equation of state to predict the compressibility factor of copolymers. Since simulation data are available only for a few pure copolymer systems, theoretical predictions are compared with molecular simulation results for the compressibility factor of pure hard chain copolymer systems. Our comparisons show a very good performance of TPT2, which is found to be more accurate than TPT1 (= SAFT). Using a modified Percus-Yevick site-site correlation function SAFTD is found to represent a significant improvement over SAFT and is slightly more accurate than TPT2. Comparison of SAFTD with generalized Flory dimer (GFD) theory shows that both are equivalent at intermediate to high densities for the compressibility factor of copolymer systems investigated here.

PHASE EQUILIBRIA AND THERMODYNAMIC PROPERTIES OF MOLECULAR FLUIDS FROM PERTURBATION THEORY. II: BINARY FLUID MIXTURES

Abstract The thermodynamic perturbation theory developed in Part I of this work is applied to describe phase equilibria and thermodynamic excess properties of binary fluid mixtures. The theory is based on the spherically symmetric reference system represented by the Lennard-Jones pair interactions, whereas the isotropic and anisotropic interactions arising from two-body electrostatic induction dispersion and repulsion forces and from three-body induction and dispersion forces, are treated as perturbations. These calculations differ from the previous perturbation theories based on the equation of state for argon as the reference system in two major respects. First the reference mixture properties are computed more accurately using a reliable form of the perturbation theory of simple fluid mixtures. Second unlike potential parameters are estimated adequately using a recently proposed set of combination rules. Comparisons of theoretical results with experimental data for phase equilibria and thermodynamic excess properties are presented for some selected fluid mixtures, namely argon + krypton xenon + ethylene, carbon dioxide + ethane, and xenon + hydrogen bromide. These comparisons show a very good performance of the perturbation theory, which offers a significant improvement over a similar form of the perturbation theory based on the equation of state for argon as the reference mixture.