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We consider application to the hard sphere (HS) model of the mapped-averaging framework for generating alternative ensemble averages for thermodynamic properties. Specifically, we develop a...

Analytical solution of the first-order Ornstein–Zernike equation known as the first-order mean spherical approximation (FMSA) theory due to Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] is used to write down a closed equation for the static structure factor of the hard-sphere fluid with a short-range Yukawa attraction. Calculations are performed for a Yukawa decay exponent that corresponds to a range of attraction that does not exceed the first coordination shell of Lennard-Jones-like simple fluids. By comparison with Monte Carlo simulation data it is shown that the analytical FMSA equation for the static structure factor is of the same or even of superior accuracy as that within the seminumerical mean spherical approximation theory.

The vapour–liquid phase diagram of long-range Yukawa fluids with the decay parameter zσ ≤ 1 is calculated by means of an augmented van der Waals theory based on the reference system that includes both the repulsive and short-range attractive interaction. Comparison with Monte Carlo simulation data, as well as with the traditional van der Waals approach based on a purely repulsive hard-sphere reference system and other semi-analytical theoretical approaches, is made.

The Henderson and Chan (HC) formulae for the contact values of the radial distribution functions (RDFs) of a highly asymmetric hard sphere mixture are reconsidered in light of a recent formula of Roth, Evans and Dietrich for the RDF of a pair of exceedingly large spheres at zero concentration in a solvent of small hard spheres. Two modifications of the HC formulae using this result give a large sphere–large sphere contact value that is considerably smaller than that of the original formulation. These new HC results are compared with the molecular dynamics simulations of Lue and Woodcock, for a diameter ratio of 1:10, supplemented by a few new results that are reported here. The new HC formulae are in much better agreement with the MD results than is the popular Boublik–Mansoori–Carnahan–Starling–Leland formula. Also, some simulation results for the RDFs as functions of separation are reported.

Analytic expressions for the Laplace transform of the interaction energy and force between two exceedingly large hard spheres at infinite dilution in a polydisperse hard-sphere suspending fluid are presented. The equations are based on the Percus–Yevick approximation for the many-component suspending fluid, supplemented by the hypernetted chain approximation for the correlation function of the suspended spheres. By applying the Derjaguin approximation, the energy and force results for two spheres are related to the energy per unit area and the disjoining pressure between two flat walls suspended in a polydisperse fluid. Numerical results for the representative Schultz distributions of the diameters of the species comprising the suspending fluid are presented and discussed.

The structure of a starlike molecule (SLM) fluid with four arms of different length is studied by applying the associative Percus–Yevick integral equation (IE) theory and canonical Monte Carlo (MC) simulations. In the IE study the SLM fluid is modelled by a fluid of hard spheres with four associative sites on each sphere while the MC has been performed for a freely-joined tangent hard sphere fluid. The total radial distribution functions have been calculated in both approaches for different volume fraction regimes and different arm lengths. It is shown that the associative IE theory predicts the structure of SLM fluid best for relatively long arms and at high densities. Additionally, the dependence of the SLM centre–centre correlations on the functionality and fluid particle density has been analysed using the MC results.

We have studied the structure and adsorption of a hard sphere fluid in a rigidly fixed array of permeable matrix species. The surface of each matrix particle is represented by a barrier of finite height and width, such that the entire model describes partitioning of a fluid in a set of permeable membranes. We have applied the grand canonical Monte Carlo (GCMC) simulations and replica Ornstein—Zernike (ROZ) equations for partly quenched systems complemented by the Percus—Yevick (PY) closure as our theoretical tools. The pair distribution functions of species and the adsorption isotherms are discussed dependent on the parameters of the model. It is shown that the theory provides adequate description of the behaviour of fluid species in the interior of the matrix particles, inside the barriers, and close to the interface. On the other hand, the coordination numbers for a fluid in the matrix interior and the adsorption isotherms from the ROZ-PY theory are in excellent agreement with computer simulation data.

The adsorption isotherms for diatomic fluids in disordered porous media have been obtained from grand canonical Monte Carlo computer simulation. A disordered porous medium, or matrix, is prepared by quenching an equilibrium configuration of spherical hard core molecules. In addition, canonical Monte Carlo simulations have been performed for equilibrium binary mixtures that represent counterparts of quenched-annealed systems in question. For the same chemical potential of diatomic molecules at a fixed density of matrix species, the structure and the density of the diatomic fluid in the binary mixture and in the quenched medium are very similar. This behaviour holds also for systems with attractive interactions in the region of high temperatures. Observed similarity of the structural and thermodynamic properties of the mixture and the corresponding annealed fluid-quenched matrix system permits the use of the thermodynamics of the mixture to evaluate some properties of quenched-annealed fluids. Calculations ...

Canonical ensemble Monte Carlo simulations and the non-uniform Percus–Yevick (NPY) equation for the local density are used to study the influence of surface mediated thirdorder interactions on the adsorption of associating hard spheres on a hard wall. A comparison of the NPY density profiles with the computer simulations data indicates that this approximation predicts the fluid structure reasonably well.

The associative replica Ornstein-Zernike equations, supplemented by the associative hypernetted chain approximation are used to describe the Smith-Nezbeda model for an associating fluid adsorbed in a disordered hard sphere matrix. These equations have been developed by combining the replica Ornstein-Zernike equations with the Wertheim theory of association in fluids. The pair distribution functions and fraction of unbonded species are calculated. Also investigated is the influence of the association on the equation of state and the chemical potential of the absorbed fluid.

Monte Carlo simulations are reported for the distribution functions, the fraction of unbonded and bonded particles, and the pressure of a chemically associating fluid of hard discs of a circularly symmetric attractive square well. Depending on the choice of the bonding length, dimers or chain molecules of different length can be formed. The dependence of the structural properties of the model on the fluid density and association energy is discussed.

The density profiles of a dimerizing fluid near a crystalline surface are investigated. The model of the bulk fluid is that proposed by Stell and Zhou, which is a generalization of Wertheim's model for dimerization. The formation of dimers results from the interaction between the intracore attractive sites. The fluid–solid interaction consists of two terms. The non-associative term is that proposed by Steele. The directional associative fluid–solid atom interaction is chosen to have a Gaussian form. This provides bonding of the bulk fluid particles with the solid atoms. The solid substrate is assumed to be the graphite basal plane. The density profiles are studied by using the associative singlet Percus–Yevick approximation. When the distance from the surface is greater than the dimer length, the effect of crystalline symmetry is not apparent. The second adlayer tends to disappear when association is present. The relative importance of various positions in the surface unit cell tends to be less when the s...

An investigation is begun into the structure of a chemically reacting or associating hard core Yukawa fluid near a hard wall by using Monte Carlo simulations. The model of the interparticle potential is an extension of that introduced by Cummings and Stell for an overlappping hard sphere fluid. This investigation studies the changes in the structure of this chemically reacting fluid at the wall, introduced by the presence of long-range attractive forces acting between atoms. The long-range attractive forces cause a lowering of the total number of particles in the vicinity of the wall and weaken the orientational ordering of the dimers formed by the effect of the chemical interactions. Also the singlet integral equation approach is applied to calculate the density profiles. A comparison of the theoretical predictions with the Monte Carlo data indicates that, in contrast to systems without long-range attractive forces, the singlet theory is insufficient, especially when the chemical interactions increase.

Density profiles of a double square-well model of a chemically associating fluid near a hard wall are studied using integral equations and computer simulation techniques. The model of the bulk fluid is a two-component system of ‘hard’ spheres which, if of different species, are able to overlap and form dimers. This kind of transformation represents a chemical reaction between monomeric units and is generated by an interparticle interaction in the form of an intracore attractive double square well. The dimers which consist of the same species, but differ in the bonding length, are treated as isomers of the product of the reaction of dimerization. Peculiarities in the behaviour of the bulk fluid influence the density profiles and the absorption of particles at a hard wall. The effects of chemical reaction, the bulk density, and energetic characteristics of each of the attractive wells on the density profiles are investigated. The theory is compared with Monte Carlo computer simulation data.

The radial distribution functions for a central force model of water, derived from a combination of computer simulation and integral equation techniques, are used to calculate the density-density and charge-charge structure factors. These quantities are compared with neutron scattering measurements of light and heavy water. From the behaviour of the density-density and charge-charge structure factors in the thermodynamic limit of small wavenumbers, the extent of density and charge fluctuations is estimated. In particular, the density fluctuations in water are found to extend to longer distances than charge fluctuates. The relations between the charge fluctuations and the behaviour of the static dielectric function as well as some dynamical properties are discussed.

A model of a chemically reacting fluid in a slit-like pore is studied. The density profiles of the fluid particles inside the pore, the adsorption isotherms, and the solvation force acting between the walls of the pore are investigated within the integral equation method. The Percus-Yevick and hypernetted chain approximations for the fluid particle-pore correlations are used. The model for the bulk chemically reacting fluid is that proposed by Cummings and Stell for a mixture of overlapping hard spheres. The investigations are performed for pores of different width, at different densities of the bulk fluid which is in an equilibrium with the confined fluid and for different degrees of bulk fluid association. The bulk fluid is described by using the Percus-Yevick approximation. A wide range of thermodynamic states and different bonding lengths between the reactants are investigated. It is shown that the effect of a chemical reaction in the bulk fluid produces qualitative changes in the behaviour of the den...

The mean spherical approximation integral equation is solved for a pair of large charged hard spheres in an ion-dipole mixture. In this work, the effect of the molecular nature of the solvent is taken into account approximately. Extra terms, not included in the DLVO theory, are found and are significant. The effect of dipole alignment near the macroions is repulsive at large separation but can be attractive at short separations.