Andrij Trokhymchuk

Hard-sphere radial distribution function again

A theoretically based closed-form analytical equation for the radial distribution function, g(r), of a fluid of hard spheres is presented and used to obtain an accurate analytic representation. The method makes use of an analytic expression for the short- and long-range behaviors of g(r), both obtained from the Percus-Yevick equation, in combination with the thermodynamic consistency constraint. Physical arguments then leave only three parameters in the equation of g(r) that are to be solved numerically, whereas all remaining ones are taken from the analytical solution of the Percus-Yevick equation.

Direct correlation function of the square-well fluid with attractive well width up to two particle diameters

Analytical expression for direct correlation function of the square-well fluid with an attractive well width up to two particle diameters (2 < lambda < or = 3) is reported. This result is obtained within the first-order mean-spherical approximation (FMSA) and represents the nontrivial extension of the recent study due to Tang [J. Chem. Phys. 127, 164504 (2007)], where the width of square-well attraction was limited by one particle diameter (1 < lambda < or = 2). Prediction of the FMSA theory is validated by direct comparison against Monte Carlo simulation data. Additionally, an impact of the increase in the range of attraction on the parameters of the critical point of the square-well fluid is discussed using the compressibility route to thermodynamics.

Simulation and approximate formulae for the radial distribution functions of highly asymmetric hard sphere mixtures

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.

Attraction-driven disorder in a hard-core colloidal monolayer.

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of repulsive and attractive states in dense colloidal systems is discussed.

Effective interaction between large spheres immersed into a multicomponent hard-sphere fluid

An approach to study the effective interaction between two extremely large spheres, infinitely dilute, in a multicomponent hard-sphere fluid is presented. The proposed approach is an approximation that guarantees at least qualitative consistency with the experimental results for the interaction between two large solutes that is mediated by a background medium. The approach is developed to study the complex colloidal systems, i.e., extremely large (micronsized) spherical particles immersed in suspensions of the smaller (nanosized) colloid particles that are dissolved in a molecular solvents. Numerical results for the effective energy and force between two extremely large spheres in a one-component hard-sphere fluid (when only colloid particles are considered explicitly) and a two-component hard-sphere fluid (when both “solvent” particles and colloid particles are considered explicitly), are presented. The role of the discrete nature of the solvent on the interaction between two extremely large spheres imme...

Effective interaction between two giant spheres suspended in a size polydisperse hard-sphere fluid

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.

Non-hydrodynamic transverse collective excitations in hard-sphere fluids

Collective excitations in hard-sphere fluids were studied in a wide range of wave numbers and packing fractions η by means of molecular dynamics simulations. We report the observation of non-hydrodynamic transverse excitations for packing fractions η≥0.395 in the shape of transverse current spectral functions. Dispersion of longitudinal excitations in the whole range of packing fractions shows a negative deviation from the linear hydrodynamic law with increasing wave numbers even for dense hard-sphere fluids where the transverse excitations were observed. These results do not support a recent proposal within the Frenkel line approach that the positive sound dispersion in liquids is defined by transverse excitations. We report calculations of the cutoff Frenkel frequencies for transverse excitations in hard-sphere fluids and discuss their consistency with the estimated dispersions of shear waves.

Mean-spherical approximation for the Lennard-Jones-like two Yukawa model: Comparison against Monte Carlo data

Monte Carlo simulation studies are performed for the Lennard-Jones-like two Yukawa (LJ2Y) potential to show how properties of this model fluid depend on the replacement of soft repulsion by hard-core repulsion. Different distances for the positioning of hard-core have been explored. We have found that for temperatures slightly lower and slightly higher than the critical point temperature for the Lennard-Jones fluid, the placement of the hard-core at distances shorter than zero-potential energy is well justified by thermodynamic properties that are practically the same as in the original LJ2Y model without hard-core. However, going to extreme conditions with the high temperature one should be careful since the presence of the hard-core provokes changes in the properties of the system. The later is extremely important when the mean-spherical approximation (MSA) theory is applied to the treatment of the Lennard-Jones-like fluid.

Improved first order mean-spherical approximation for simple fluids

A perturbation approach based on the first-order mean spherical approximation (FMSA) is proposed. It consists in adopting a hard-sphere plus short-range attractive Yukawa fluid as the novel reference system, over which the perturbative solution of the Ornstein-Zernike equation is performed. A choice of the optimal range of the reference attraction is discussed. The results are compared against conventional FMSA/HS theory and Monte-Carlo simulation data for compressibility factor and vapor-liquid phase diagrams of the medium-ranged Yukawa fluid. Proposed theory keeps the same level of simplicity and transparency, as the conventional FMSA/HS approach does, but shows to be more accurate.

Erratum: "Hard sphere radial distribution function again" †J. Chem. Phys. 123, 024501 "2005…‡

− 1+2 . 30The calculations have been performed using correct equations and all results reported are not affected by these misprints.The authors thank Monte Pettitt, Marcelo Marucho, Sorin Bastea, and Andreas Santos for their interest in the applicationof our equation that led to the discovery of the above misprints.