Thermodynamics of a Fluid of Hard D-dimensional Spheres: Percus-Yevick and Carnahan-Starling-like Results for D = 4 and 5

Abstract

The equations of state (EOS) of four and five dimensional hyperspheres have been calculated using Leutheusser's ansatz. In five dimensions these, and the correlation functions, are compared with the results obtained from the analytic solution of the Percus—Yevick (PY) approximation. It is shown that the ansatz reproduces extremely well the PY results. However, in both approximations neither the virial, Z_v , nor the compressibility, Z_c , EOS reproduce well the available molecular dynamics (MD) results. Yet a linear combination of Z_v and Z_c , following the Carnahan—Starling EOS for hard spheres, are in excellent agreement with the MD results in four and five dimensions.     

Interpretation of Light Scattering Spectra of Dispersions – A Hybrid Approach to Account for Interparticle Interactions

The problem of extracting quantitative information on individual particle properties from spectroscopic measurements conducted at concentrations where particle interactions become significant is of great industrial and theoretical importance. For dispersions of charged particles, this can happen at fairly low concentrations. The effect of the fluid (slurry) structure has to be taken into account to interpret the light scattering spectra of such dispersions. In this paper, a hybrid method that addresses the effect of the fluid structure is proposed. The hybrid approach describes the fluid structure by relating the “effective” Percus‐Yevick hard‐sphere parameters to the system parameters using empirical models. The feasibility of this approach is examined through a theoretical study with data generated by Monte Carlo simulations of a monodisperse dispersion of charged spherical particles using realistic interaction potentials under single scattering conditions.     

A non-primitive model for the electrode electrolyte interface based on the Percus–Yevick theory. Analysis of the different molecular sizes, ion valences and electrolyte concentrations

The electrode electrolyte interface is modelled by a mixture of charged and dipolar hard spheres against a planar, charged hard wall. A mean field theory is used to describe the coulombic interactions while steric effects are given by the Percus–Yevick theory. The underlying Percus–Yevick theory for three uncharged species against a planar wall is derived by using the standard method developed by Henderson et al. (D. Henderson, F.F. Abraham, J.A. Barker, Mol. Phys., 31 (1976) 1291) and compared with Monte-Carlo simulations. Although the Percus–Yevick theory has shortcomings, the theory provides an estimate of how the high density of the solvent influences the structural and thermodynamic properties. Consideration of the solvent molecules introduces oscillations in the density distribution of the ions and solvent while the different molecular sizes and ion valences lead to an asymmetry in the differential capacitance.     

Sound Velocity in Liquid Binary Alloys as Calculated via the Percus-Yevick Liquid Phonon Dispersion Relation

Abstract

In this note, we utilize the recently calculatd long wavelength limit of the “liquid virtual crystal” model of binary alloy liquid structure factor at the melting temperature, ST_M ^AB (0), to estimate the long-volume binary liquid alloys. We compare the calculate sound velocities to the available experimental sound velocities in these liquid binary alloys and find reasonable agreement.     

Structure of the square-shoulder fluid

The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical steps, requiring only the numerical solution of a single transcendental equation. The comparison with available simulation data and with numerical solutions of the Percus–Yevick and hypernetted-chain integral equations shows that the present approximation represents an improvement over the Percus–Yevick theory for this system and a reasonable compromise between accuracy and simplicity.     

Investigation of structure factors in dense colloidal suspensions using frequency domain photon migration: polydisperse systems

Frequency domain photon migration (FDPM) technique was employed to investigate the structure factors of dense, polydisperse colloidal suspensions. The angle-integrated structure factors, [S(q)], extracted from FDPM measurements of scattering properties at volume fractions ranging from 0.05 to 0.4, were compared with the values predicted from the polydisperse hard sphere Percus-Yevick (HSPY) model, as well as decoupling approximation (DA) and local monodisperse approximation (LMA) models that incorporated independently measured particle size information. Results show that the polydisperse HSPY model is the most suitable for accounting for particle interactions which predominantly arise from volume exclusion effects. Furthermore, the influence of size polydispersity upon [S(q)] is most significant at high volume fractions. The static structure factors at small wave vector q, S(0), were also assessed from dual wavelength FDPM measurements by using the small wave number approximation as well as the local monodisperse approximation. The measured S(0) agrees well with the values predicted by the polydisperse HSPY model.     

Cavity correlation and bridge functions at high density and near the critical point: a test of second-order Percus–Yevick theory

ABSTRACT

Cavity correlation functions, pair correlation functions, and bridge functions for the Lennard-Jones fluid are calculated from first Percus–Yevick (PY) theory and second-order Percus– Yevick (PY2) theory, molecular dynamics, and grand canonical Monte Carlo techniques. We find that the PY2 theory is significantly more accurate than the PY theory, especially at high density and near the critical point. The pair correlation function near the critical point has the expected slowly decaying long-range behaviour. However, we do not observe any long-range behaviour in the bridge function for the state points near the critical point we have simulated. However, we do note that the bridge function, which is usually negative near r = 0, becomes positive as r → 0. This behaviour is seen for the bridge functions computed from both PY2 and molecular dynamics, but not from PY.     

Single-Ion Contributions to Activity Coefficient Derivatives, Second Moment Coefficients, and the Liquid Junction Potential

We discuss several interrelated single-ion thermodynamic properties required to calculate the liquid junction potential between two solutions of the same binary electrolyte. According to a previously reported molecular theory of nonuniform electrolyte solutions in nonequilibrium, is determined by the transport numbers of the ions, and by the second moment coefficients H ⁽²⁾ of the charge densities around the ions. The latter may be viewed as the single-ion contributors to the second moment condition of Stillinger and Lovett. For a solution of a single binary electrolyte, we relate the H ⁽²⁾ (R) to the derivatives of the single-ion activity coefficients with respect to the ionic strength. In the light of these results, we examine, in some detail, the role played by the specific short-range interionic interactions in determining . We investigate this matter by means of integral equation calculations for realistic models of LiCl and NaCl aqueous solutions in the 0–1 mol-dm^–3 range. In addition to the hypernetted-chain (HNC) relation, we perform calculations under a new integral equation closure that is a hybrid between the HNC and Percus–Yevick closures. Like the HNC approximation, the new closure satisfies the Stillinger and Lovett condition. However, for the models considered in this study, the two closures predict different dependence of the H ⁽²⁾ and of on the specific part of the interionic interactions.     

Dynamic effective properties of matrix composite materials with high volume concentrations of particles

A new approach is proposed to investigate the propagation of a plane compressional wave in matrix composite materials with high volume concentrations of particles. The theory of quasicrystalline approximation and Waterman’s T matrix formalism are employed to treat the multiple scattering resulting from the particles in composites. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The Percus–Yevick correlation function widely applied in the molecular theory of liquids is employed to analyze the interaction of the densely distributed particles. The analytical expression for the Percus–Yevick correlation function is also given. The closed form solution for the effective propagation constant is obtained in the low frequency limit. Only numerical solutions are obtained at higher frequencies. Numerical examples show that the phase velocities in the composite materials with low volume concentration are in good agreement with those in previous literatures. The effects of the incident wave number, the volume fraction and the material properties of the particles and matrix on the phase velocity are also examined.