Hard-sphere Fluid Mixture Research Articles

Analytical representation of the higher virial coefficients of binary mixtures of additive hard spheres

Approximate expressions for the fourth and fifth virial coefficients of binary hard-sphere fluid mixtures are derived. The procedure used to obtain these expressions is based on that previously proposed by Wheatley [J. chem. Phys., 111, 5455 (1999)], but slightly modified. Wheatley's procedure starts from a prescribed general analytical form of the virial coefficients, from which the particular expression for each virial coefficient is obtained by imposing to the general form a number of limiting conditions. Here, we propose an alternative general expression of the virial coefficients and derive one more condition. This condition is satisfied when the fourth and fifth virial coefficients are expressed in the form we propose, but not when they are expressed in Wheatley's form. The agreement of the proposed analytical expressions with exact numerical data is excellent. The procedure can be extended to higher virial coefficients, although the lack of exact numerical data prevents any comparison.

Structure of nonuniform three-component fluid mixtures: A density-functional approach

The structure of nonuniform three-component fluid mixtures is studied using a self-consistent density-functional approach as well as a simple weighted density approximation and also by computer simulation. The second-order direct correlation function and the bridge function of the corresponding uniform fluid mixture required as input in the self-consistent theory are obtained from integral equation theory using an accurate closure relation, whereas the available analytic expressions of second-order correlation function within the Percus–Yevick approximation is used in the simple weighted density approximation. This new approach is employed to predict the structure of ternary hard sphere fluid mixtures near a hard wall as well as the structure of ternary uniform hard sphere mixtures. The calculated density and concentration profiles of the nonuniform fluid mixtures as well as the radial distribution function profiles of the uniform fluid mixtures are shown to compare well with the computer simulation results performed in the present work.

Scaled hard-sphere equations of state for linear fused hard-sphere pure fluids and fluid mixtures

The performance of a theoretically based equation of state, previously developed for hard molecular fluids, is analysed on the basis of computer-simulation data which have recently become available for fluids of linear fused hard-sphere molecules with up to eight monomers. The equation allows one to obtain the excess compressibility factor of hard-body fluids by scaling the excess compressibility factor of an equivalent hard-sphere fluid by means of a parameter which can be obtained from the geometry of the molecules. The agreement between theory and simulation was found to be excellent. The extension of the equation of state to fluid mixtures of hard molecules expresses the excess compressibility factor of the mixture as a scaling of the excess compressibility factor of an equivalent hard-sphere fluid mixture. The scaling parameter is again obtained from the geometry of the molecules involved in the mixture. The equation of state obtained in this way is compared with NPT Monte Carlo simulations for several fluid mixtures of linear fused hard-sphere molecules which are also reported.

Equation of State for Repulsive Models of n-Alkane Pure Fluids and Mixtures

Theoretically-based equations of state previously developed for hard models of molecular pure fluids and mixtures are extended in this paper to repulsive models of pure n-alkane fluids and mixtures. For pure fluids, the compressibility factor is expressed in terms of a scaling of the excess compressibility factor of a hard-sphere fluid with a packing fraction equal to the effective packing fraction of the true fluid. For mixtures, the excess compressibility factor is expressed as a similar scaling of the excess compressibility factor of a hard-sphere fluid mixture. The theory requires two parameters, namely the scaling factor and the effective (averaged) molecular volume of the fluid (mixture), which can be determined from the molecular geometry. Results are in generally good agreement with available simulation data.

Structure of ternary additive hard-sphere fluid mixtures.

Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. López de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact.

Structure of nonuniform fluid mixtures: A self-consistent density-functional approach

A self-consistent density-functional approach is developed for the structure of nonuniform fluid mixtures, where the second-order direct correlation function and the bridge function of the corresponding uniform fluid mixture are used as the input. These two quantities are obtained through integral equation theory using an accurate closure relation. The present theory uses the concept of universality of the free energy density functional to obtain the first-order direct correlation function of the nonuniform system from that of the corresponding uniform system. This new approach is employed to predict the structure of binary hard-sphere fluid mixtures near a hard wall. The calculated density and concentration profiles are shown to compare well with available computer simulation results.

Simulations of binary hard-sphere crystal-melt interfaces: Interface between a one-component fcc crystal and a binary fluid mixture

The crystal-melt interfaces of a binary hard-sphere fluid mixture in coexistence with a single-component hard-sphere crystal is investigated using molecular-dynamics simulation. In the system under study, the fluid phase consists of a two-component mixture of hard spheres of differing size, with a size ratio α=0.414. At low pressures this fluid coexists with a pure fcc crystal of the larger particles in which the small particles are immiscible. For two interfacial orientations, [100] and [111], the structure and dynamics within the interfacial region is studied and compared with previous simulations on single component hard-sphere interfaces. Among a variety of novel properties, it is observed that as the interface is traversed from fluid to crystal the diffusion constant of the larger particle vanishes before that of the small particle, defining a region of the interface where the large particles are frozen in their crystal lattice, but the small particles exhibit significant mobility. This behavior was not seen in previous binary hard-sphere interface simulations with less asymmetric diameters.

Excess Gibbs' energy of binary mixtures of hard sphere fluids

Hard sphere model of Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) with Labowitz and Zomick's non-additivity corrections has been utilized to calculate excess Gibbs' energy (G E ) for toluene-cyclohexane and toluene-n-heptane systems over the entire compositions. The results are in excellent agreement with the experimental one.

Structure of a two-component mixture of sticky hard-sphere fluids in a planar gap

The structural properties of nonuniform, binary, sticky hard-sphere (SHS) fluid mixture (the particular components being denoted by SHS1 and SHS2) within a planar pore, maintaining the equilibrium with the bulk phase, were investigated. The wall–SHS1 and wall–SHS2 correlations of the SHS mixture confined in the pore, and its distribution between the pore and the bulk phase were studied on the basis of the solution to the Percus–Yevick/Ornstein–Zernike equation, obtained by using the analytic results for the direct correlation functions of the bulk SHS mixture. The density profiles of particular components with the hard core diameters σ1 and σ2 revealed distinct layering, a characteristic feature being the discontinuities in the slopes of the profiles at the distances n⋅σ1+m⋅σ2 (n=0,1,…;m=0,1,…) from the wall–SHS1 and wall–SHS2 contact planes. It was shown that narrowing of the pore considerably affects the partitioning of both components between the bulk phase and the interior of the pore, the effects being more pronounced in the case of a more adhesive component. As the individual components of the binary mixture are selectively partitioned between the bulk phase and narrow pore, the porous material, i.e., a network of narrow pores, makes possible a partial separation of both components from the bulk SHS mixture.

Binary associating fluid mixtures against a hard wall: density functional theory and simulation

We present an extension of our perturbation density functional (DF) theory [Segura, C. J., Chapman, W. G. and Shukla, K. P., 1997, Molec. Phys., 90, 759], which applies the weighting from Tarazona's hard sphere density functional theory to Wertheim's bulk first-order perturbation theory, to form a perturbation density functional theory for binary associating hard sphere fluid mixtures. Monte Carlo simulation results of a binary mixture of equal-sized hard spheres with one component having four associating sites placed in the Bol [1982, Molec. Phys., 45, 605] fashion are presented to compare with the theory. Comparison of theory and molecular simulation for the separation factor, component density profiles and fraction of monomers (associating component) show good agreement. Good to excellent accuracy are obtained for the densities and temperatures studied.

Consistency conditions and equation of state for additive hard-sphere fluid mixtures

A number of consistency conditions for the contact values gij(σij) of the pair correlation function of species i and j in an additive hard-sphere fluid mixture are discussed. It is shown that most of the theoretically-based expressions, as well as other more empirical in character, existing for these functions, fail to satisfy at least one of the conditions. It is suggested that one could improve the performance of the expressions for gij(σij) and the equation of state by using the consistency conditions. This is illustrated by modifying the Boublı́k–Mansoori–Carnahan–Starling–Leland expressions for gij(σij), which results in better predictions for these functions as well as for the compressibility factor and the fourth and fifth virial coefficients.

Inhomogeneous mixture system: A density functional formalism based on the universality of the free energy density functional

A density functional theory is proposed for an inhomogeneous mixture system, which is based on the universality of the free energy density functional. The present formalism requires as input only the second-order direct correlation function and bridge function of the corresponding uniform fluid mixture. Applicability of the density functional theory was verified by applying the formalism to study on the structure of binary hard-sphere fluid mixture near a hard-planar wall; the predictions of the theory compare well with the corresponding computer simulation results.

A new analytical equation of state for additive hard sphere fluid mixtures

A study has been made of the relation between the equation of state of additive binary hard sphere fluid mixtures and the equation of state of a pure hard sphere fluid for the same packing fraction. An analysis of the existing simulation data for a wide variety of compositions of the mixture and diameter ratios up to 1/0.2 makes it possible to conclude that the ratio of the excess compressibility factor of the mixture to that of the pure fluid is, to a very good approximation, a linear function of the packing fraction. This suggests the possibility of deriving the equation of state of the mixture from that of the pure fluid by using the second and third virial coefficients of the mixture, which are known analytically, to reproduce the linear relation mentioned above. When a suitable equation of state is chosen for the pure fluid, the results from the equation of state of the mixture thus obtained are in excellent agreement with simulation data. The predictions for the fourth and fifth virial coefficients also are very accurate compared with known numerical data.

A new analytical equation of state for additive hard sphere fluid mixtures

A new analytical equation of state for additive hard sphere fluid mixtures

Equation of state for fluid mixtures of hard spheres and heteronuclear hard dumbbells

A theoretically founded equation of state is developed for mixtures of hard spheres with heteronuclear hard dumbbells. It is based on a model previously developed for hard-convex-body fluid mixtures, and further extended to fluid mixtures of homonuclear hard dumbbells. The equation scales the excess compressibility factor for an equivalent hard-sphere fluid mixture to obtain that corresponding to the true mixture. The equivalent mixture is one in which the averaged volume of a sphere is the same as the effective molecular volume of a molecule in the real mixture. Thus, the theory requires two parameters, namely the averaged effective molecular volume of the molecules in the mixture and the scaling factor, which is the effective nonsphericity parameter. Expressions to determine these parameters are derived in terms of the geometrical characteristics of the molecules that form the mixture. The overall results are in closer agreement with simulation data than those obtained with other theories developed for these kinds of mixtures.

Equation of state for fused-hard-sphere fluid mixtures

This paper develops a theoretically-based equation of state for fused-hard-sphere fluid mixtures on the basis of an equation of state previously derived for hard-convex-body fluid mixtures. The equation uses as a reference the equation of state for an equivalent hard-sphere fluid mixture in which each component has the same molecular volume as the effective molecular volume of one of the components of the fused-hard-sphere mixture. The two parameters required by the theory, namely the averaged effective molecular volume of the molecules in the mixture and the corresponding effective non-sphericity parameter, are obtained from the geometrical characteristics of the molecules that form the mixture. The results are, on the whole, in closer agreement with simulation data than those obtained with other theories developed for this kind of mixture.

Demixing vs freezing of binary hard-sphere mixtures

The absence of demixing in the Percus–Yevick theory of fluid mixtures of additive hard-spheres is related to the fact that this theory predicts incorrect virial coefficients Bn for n>3. Incorporation of the exact Bn for 1⩽n⩽5 into a rescaled virial expansion is shown instead to lead to demixing for any size asymmetry between the spheres. This demixing is however thermodynamically metastable relative to freezing of the mixture into a partially ordered solid phase. This conclusion is reached on the basis of a density functional estimate of the free-energy of a nonuniform phase in which the large spheres form a face-centered cubic lattice whereas the small spheres remain disordered.

Equation of state for fluid mixtures of hard spheres and linear homonuclear fused hard spheres

This paper develops a theoretically based equation of state for fluid mixtures consisting of hard spheres and linear homonuclear fused hard spheres. The procedure is based on the equation of state previously developed for monocomponent athermal fluids. The equation of state only requires two parameters, namely the averaged effective molecular volume of the molecules in the mixture and the corresponding effective nonsphericity parameter. These parameters can be obtained from the geometry of the molecules forming the mixture. The results are in excellent agreement with simulation data and compare favorably with those obtained from other theories for athermal fluid mixtures.

Fundamental-measure free-energy density functional for hard spheres: Dimensional crossover and freezing

A geometrically based fundamental-measure free-energy density functional unified the scaled-particle and Percus-Yevick theories for the hard-sphere fluid mixture. It has been successfully applied to the description of simple (``atomic'') three-dimensional (3D) fluids in the bulk and in slitlike pores, and has been extended to molecular fluids. However, this functional was unsuitable for fluids in narrow cylindrical pores, and was inadequate for describing the solid. In this work we analyze the reason for these deficiencies, and show that, in fact, the fundamental-measure geometrically based theory provides a free-energy functional for 3D hard spheres with the correct properties of dimensional crossover and freezing. After a simple modification of the functional, as we propose, it retains all the favorable D=3 properties of the original functional, yet gives reliable results even for situations of extreme confinements that reduce the effective dimensionality D drastically. The modified functional is accurate for hard spheres between narrow plates (D=2), and inside narrow cylindrical pores (D=1), and it gives the exact excess free energy in the D=0 limit (a cavity that cannot hold more than one particle). It predicts the (vanishingly small) vacancy concentration of the solid, provides the fcc hard-sphere solid equation of state from closest packing to melting, and predicts the hard-sphere fluid-solid transition, all in excellent agreement with the simulations.

Excess gibbs free energy of mixing

Narayanan, K.V. and Ananth, M.S., 1993. Excess Gibbs free energy of mixing. Fluid Phase Equilibria, 91: 77-86. The statistical mechanical approach to developing excess Gibbs free energy models for liquids using lattice theories in the Canonical ensemble is reexamined numerically in the light of the fundamental observations of Sandler et al. (S.I. Sandler et al., 1989. Fluid Phase Equilibria, 45: 251-265). Calculations are carried out for mixtures of hard sphere fluids and model mixtures of Lennard-Jones (LJ) molecules to find the effect of varying the relative size of the hard sphere molecules and the unlike interaction parameters for LJ mixtures on the difference between the excess Gibbs free energy at constant pressure and the excess Helmholtz free energy under different mixing constraints. It is shown that for engineering purposes lattice theories can only provide mathematical expressions that fit mixture data accurately provided these expressions contain one or two adjustable parameters. Further, for fitting excess Gibbs free energy data it is shown that expressions for the excess Helmholtz free energy under any of the constraints (“Scatchard mixing”, mixing under constant number density or constant reduced density) are equally useful.