A hard sphere fluid model for superionic conductors

We develop a theory for the mobile constituent of a superionic conductor using the Ornstein-Zernike integral equation for the pair correlation function of an inhomogeneous fluid. We solve this equation in the Percus-Yevick approximation using a simple decoupling procedure and hard core potentials. Comparison is made with molecular dynamics calculations on α-AgI.     

Effects of polydispersity in quenched-annealed fluids: An integral equation approach

An extension of the replica Ornstein-Zernike (ROZ) equations for partly quenched polydisperse systems is presented. Explicit calculations have been performed for a monodisperse hard sphere fluid confined by a polydisperse hard sphere disordered matrix by using Percus-Yevick and hypernetted chain (HNC) approximations. The chemical potential of adsorbed fluid species has been evaluated. A numerical solution of the ROZ equations makes use of the orthonormal polynomials with the weight function corresponding to the distribution function of the diameters of matrix species. We have also compared the results of theoretical predictions with Monte Carlo simulation in a canonical ensemble. The result of this comparison suggests that the HNC approximation performs slightly better in predicting the structural properties of the system.     

Analytical expressions for the correlation function of a hard sphere dimer fluid

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.     

Ion-ion Correlations in Dense Plasma Derived from a Quasimolecular Thomas-Fermi Model

Ion-ion correlation functions of shock-compressed, strongly coupled aluminum plasma with 1–5 times solid density and 1–20 eV temperature are calculated by using a quasimolecular Thomas-Fermi model to determine the interaction potential between ions and by solving the Ornstein-Zernike equation together with the Percus-Yevick and, alternatively, the hypernetted chain aproximation. The results are checked by Monte-Carlo simulations and are compared with other independent calculations taken from the literature.     

Zusammenhang zwischen Paarkorrelationsfunktion und Paarpotential für flüssiges Aluminium

We solved the Percus-Yevick and the hypernetted chain equation for liquid aluminium using a pair potential given byHarrison and investigated how the radial distribution functiong(r) is affected by changing the shape of the potential. It was also tried to calculate a pair potential from experimentalg(r) and structure factor data by the PY and the HNC approximation.     

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered matrix of hard spheres: attractive wall-hard sphere interaction

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered hard sphere matrix is studied using the inhomogeneous Ornstein-Zernike equation with hypernetted chain closure. In contrast to previous studies, an attractive wall-hard sphere interaction is considered. The adsorption is affected by the attractive interaction both directly by the fluid-wall interaction and indirectly by the change in the structure of the matrix. Density profiles and pair distribution functions are reported. For comparison, grand canonical Monte Carlo simulation data are obtained. The agreement of the theoretical and simulation results is satisfactory but somewhat less pleasing than for the purely repulsive case.     

Transient coherent emission from a dressed molecule

Exact fourth virial coeficients have been computed for inverse power potentials over the full range of powers which allow thermodynamic stability. Values are given for the exact virial coefficient, together with those from the Percus-Yevick, hypernetted chain and thermodynamically self-consistent approximations. Comparisons show that the thermodynamically self-consistent approximation gives a good account of the variation of the fourth virial coefficient over the full range of inverse powers. A new consistency condition is defined using the pair and triplet direct correlation function, and is shown to be well satisfied by the thermodynamically self-consistent approximation.     

A new,accurate, statistical mechanical theory for simple fluids

A new integral equation in which the hypernetted chain and Percus-Yevick approximations are “mixed” as a function of interparticle separation is described. Calculations with fluids varying from hard spheres to the one-component plasma show good agreement with Monte Carlo calculations.     

Das Paarpotential für flüssiges Aluminium dicht oberhalb der Schmelztemperatur

The pseudopotential formalism is used to calculate the pair potential for liquid aluminium at 670 °C. All contributing terms are calculated in a rigorously self-consistent manner, valence-valence exchange is included in an approximation proposed by Kleinman, valence-core exchange is treated carefully. The resulting potential seems to be realistic as is shown by solving the hypernetted chain integral equation.     

The structure of Lennard-Jones dimerizing spheres near a hard wall from the nonuniform wertheim Ornstein-Zernike equation

A dimerizing model of Lennard-Jones particles near a hard wall is studied using the inhomogeneous or second order Wertheim Ornstein-Zernike equation and the inhomogeneous associative Percus-Yevick closure. We investigate the influence of the degree of dimerization on the shape of the density profiles and on inhomogeneous pair correlation functions. This work was supported in parts by KBN of Poland (the Grant No. 3T09A 06210) and by Cray Research, Inc., of Mexico under its University Research and Development Grant Program. Garcia.     

Phase Separation of Penetrable Core Mixtures

A two-component system of penetrable particles interacting via a gaussian core potential is considered, which may serve as a crude model for binary polymer solutions. The pair structure and thermodynamic properties are calculated within the random phase approximation (RPA) and the hypernetted chain (HNC) integral equation. The analytical RPA predictions are in semi-quantitative agreement with the numerical solutions of the HNC approximation, which itself is very accurate for gaussian core systems. A fluid-fluid phase separation is predicted to occur for a broad range of potential parameters. The pair structure exhibits a nontrivial clustering behaviour of the minority component. Similiar conclusions hold for the related model of parabolic core mixtures, which is frequently used in dissipative particle dynamics (DPD) simulations.     

The effective interactions between colloidal hard spheres in microporous media: Hypernetted chain approximation for replica Ornstein-Zernike equations

In this work, the effective interaction between hard sphere colloidal particles in the presence of a hard sphere solvent, both dispersed either in a disordered quenched matrix of hard spheres or in the random matrix of freely overlapping obstacles is analyzed, using the replica Ornstein-Zernike (ROZ) integral equations. The ROZ equations are supplemented by the hypernetted chain closure. The presence of either disordered or random matrix is manifested in the attractive minima of the colloid-colloid potential of mean force (PMF), in addition to a set of minima due to the presence of solvent species. The effects of matrix microporosity and solvent density on the PMF and the intercolloidal forces are investigated. This project has been supported in part by the National Council for Science and Technology of Mexico (CONACyT) under Grant 25301-E.     

Pair correlation functions in nematics: Free-energy functional and isotropic-nematic transition

We develop a free-energy functional for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function. These correlation functions are found by solving the Ornstein-Zernike equation with the Percus-Yevick closure relation. The method developed here gives the pair correlation functions in the ordered phase with features that agree well with the results found by computer simulations. The theory predicts accurately the isotropic-nematic transition in a system of anisotropic molecules and can be extended to study other ordered phases such as smectics and crystalline solids.     

Solution of the Ornstein-Zernike equation for a softcore Yukawa fluid. II. Numerical results

Numerical calculations are reported for the simplest case of the soft-core Yukawa fluid introduced in an earlier paper. Attention is given to the thermodynamic behavior, the correlation functions, and the interparticle potentials found by inverting the structural information using Percus-Yevick and hypernetted chain integration equation approximations.Supported by ARGC grant No. B7715646R.     

A Global Investigation About Hard Core Attractive Yukawa Approximation and Adhesive Hard Sphere Approximation for Structure of Colloidal Dispersion Systems

The accuracy of hard core attractive Yukawa (HCAY) potential and adhesive hard sphere (AH) potential in representing the structure factor of short range square well potential and Asakura and Oosawa (AO) depletion potential is examined by comparing theoretical predictions with the existing simulation data and the present numerical results from the non-linear optimized random phase approximation closure for Ornstein-Zernike equation. For the case of square-well (SW) potential, it is shown that the structure factor of HCAY potential based on a recently proposed semi-analytical expression for the radial distribution function can describe the structure factor of SW potential with reduced well width λ≤2 only if the reduced contact potential βε_SW≤0.25, while the analytical expression for the structure factor of AH potential under Percus-Yevick (PY) approximation completely fails for the case of λ>1.2. For the case of AO depletion potential, the domain of validity of both HCAY potential and AH potential is complementary. With the above analysis and considering the solid-liquid transition of the AH potential with an adhesive parameter τ below 1.31 cannot be predicted by modified weighted density approximation, the role played by the HCAY potential about the mapping manipulation should not be ignored.     

The structure of two-dimensional dimerizing fluids from Wertheim’s Ornstein-Zernike equation

A dimerizing fluid of hard discs is studied using two-dimensional (2D) Wertheim’s Ornstein-Zernike (WOZ) equation and associative Percus-Yevick (APY) closure. Dimerization takes place due to site-site associative interactions. The dependences of the association constant on disc density at different association energies are obtained. We calculate the compressibility and the virial equations of state (EOS) using the solution of the WOZ equation. Theoretical structure and thermodynamics is compared with Monte Carlo computer simulation data. Extension of our solution for polymerizing models is of special interest for the development of EOS for 2D chain fluids. This work was supported in part by Cray Research of Mexico under University Research and Development grant program and by KBN of Poland under the Grant No. 3T09A06210.     

Computer simulation and replica Ornstein—Zernike integral equation studies of a hard-sphere dipolar fluid adsorbed into disordered porous media

By means of extensive grand canonical Monte Carlo simulations and replica Ornstein-Zernike integral equation calculations, we explore the thermodynamics and dielectric behaviour of a dipolar fluid confined in disordered matrices. Different matrix topologies are modelled using, on the one hand, quenched hard-sphere configurations and, on the other, randomly positioned spheres. This illustrates the influence of the pore size and shape on the properties of the adsorbed fluid. For the same purpose, various sizes of the matrix particles have been considered. The integral equation calculations in the hypernetted chain approximation agree quantitatively with the simulation results. As in other studies on quenched disorder, one observes that the effect of confinement when considering hard-sphere matrices is rather limited, exhibiting however a tendency to facilitate the transition to ferroelectric states, as well as favouring the gas-liquid transition. Additionally, one observes that the sensitivity of the fluid properties to changes in the size of the matrix particles is considerably larger when these are randomly positioned.     

An Integral Equation Theory for the Widom–Rowlinson Mixture

The Widom–Rowlinson mixture is a two-component fluid in which like species do not interact and unlike species interact via a hard-core repulsion. As the density is increased, this fluid phase separates. Standard integral equation approaches, such as the Percus–Yevick or hypernetted chain, or thermodynamically self-consistent hybirds of these two, make very inaccurate predictions for the location of this critical point in the three-dimensional model. In this article we suggest a family of new approximations for this model that rely on incorporating terms in the density expansion of the direct correlation function into the closure approximation. We show that the simplest of these closures is significantly more accurate than previous theories for the structure and thermodynamics of the fluid.     

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

Binary fluid mixture of hard ellipses: Integral equation and weighted density functional theory

We study a two-dimensional (2D) classical fluid mixture of hard convex shapes. The components of the mixture are two kinds of hard ellipses with different aspect ratios. Two different approaches are used to calculate the direct, pair and total correlation functions of this fluid and results are compared. We first use a formalism based on the weighted density functional theory (WDFT), introduced by Chamoux and Perera [Phys. Rev. E 58 (1998) 1933]. Second, in general the Percus-Yevick (PY) and the hypernetted chain (HNC) integral equations are solved numerically for the 2D fluid mixtures of hard noncircular particles. Explicit results are obtained for the fluid mixtures of hard ellipses and comparisons are made by the two approaches. Also, the results are compared with the recent Monte Carlo simulation for the one-component fluids of hard ellipses. Finally we obtained the equation of state of hard ellipses for the aspect ratio sufficiently close to 1 and compared our results with the simulations of the fluid mixtures of hard disks.