An accurate analytical representation of the bridge function of hard spheres and a question of existence of a general closure to the Ornstein–Zernike equation

2010 ◽  
Vol 76 (1) ◽  
pp. 51-64 ◽  
Author(s):  
Magda Francová ◽  
Anatol Malijevský ◽  
Stanislav Labík ◽  
Jiří Kolafa
Keyword(s):  
Hard Sphere ◽  
Pair Distribution Function ◽  
Hard Spheres ◽  
Interparticle Distance ◽  
Analytical Representation ◽  
Simulation Data ◽  
Bridge Function ◽  
Hard Sphere Fluid ◽  
Computer Simulation Data ◽  
The One

The bridge function of hard spheres is accurately calculated from computer simulation data on the pair distribution function via the inverted Ornstein–Zernike equation at reduced densities ρ* ≡ Nσ3/V ranging from 0.2 to 1.02, i.e. from low densities through densities in a vicinity of the phase transition to crystal to densities of metastable fluid region. The data are used to propose an analytical representation of the bridge function as a function of the interparticle distance and density. They are further used to construct the so-called Duh– Haymet plot. It is demonstrated that a “general closure” to the Ornstein–Zernike equation in the form B(r) = f[γ(r)], where γ is the indirect (or series) correlation function, does not match the data. Nor does an extended closure B(r) = f[γ(r),ρ*] even in the simplest case of the one component hard sphere fluid. A relative success of literature closures to the Ornstein–Zernike equation is discussed.

The bridge function of hard spheres by direct inversion of computer simulation data

2002 ◽  
Vol 100 (16) ◽  
pp. 2629-2640 ◽  
Author(s):  
JIŘÍ KOLAFA ◽  
STANISLAV LABÍK ◽  
ANATOL MALIJEVSKÝ
Keyword(s):  
Computer Simulation ◽  
Hard Spheres ◽  
Simulation Data ◽  
Bridge Function ◽  
Direct Inversion ◽  
Computer Simulation Data

scholarly journals Statistical mechanics of hard spheres: the scaled particle theory of the hard sphere fluid revisited

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Bruno Baeyens
Keyword(s):  
Equation Of State ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Simulation Data ◽  
Hard Sphere Fluid ◽  
Two Parameters ◽  
Compressibility Factors

The aim of this paper is to exhaust the possibilities offered by the scaled particle theory as far as possible and to confirm the reliability of the virial coefficients found in the literature, especially the estimated ones: B i for i > 11. In a previous article (J.Math.Phys.36,201,1995) a theoretical equation of state for the hard sphere fluid was derived making use of the ideas of the so called scaled particle theory which has been developed by Reiss et al.(J.Chem.Phys.31,369,1959). It contains two parameters which could be calculated. The equation of state agrees with the simulation data up to high densities, where the fluid is metastable. The derivation was besed on a generalized series expansion. The virial coefficients B 2 , B 3 and B 4 are exactly reproduced and B 5 , B 6 and B 7 to within small deviations, but the higher ones up to B 18 are systematically and significantly smaller than the values found in the literature. The scaled particle theory yields a number of equations of which only four were used. In this paper we make use of seven equations to calculate the compressibility factors of the fluid. They agree with the simulation data slightly better than those yielded by the old equation. Moreover, the differences between the calculated virial coefficients B i and those found in the literature up to B 18 are very small (less than 4 percent).

Evaluation of bridge function for hard sphere fluid confined in a narrow slit-pore via TMMC Mayer-sampling

2010 ◽  
Vol 108 (11) ◽  
pp. 1531-1537 ◽  
Author(s):  
Wen Wen Chen ◽  
Huan Cong Huang ◽  
Sang Kyu Kwak
Keyword(s):  
Hard Sphere ◽  
Narrow Slit ◽  
Bridge Function ◽  
Hard Sphere Fluid ◽  
Slit Pore

Structure of hard body fluids. A critical compilation of selected computer simulation data

1989 ◽  
Vol 54 (5) ◽  
pp. 1137-1202 ◽  
Author(s):  
Ivo Nezbeda ◽  
Stanislav Labík ◽  
Anatol Malijevský
Keyword(s):  
Computer Simulation ◽  
Correlation Function ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Body Fluids ◽  
Simulation Data ◽  
Computer Simulation Data ◽  
Expansion Coefficients ◽  
Triplet Correlation ◽  
Triplet Correlation Function

Computer simulation data on structural properties [spherical harmonic expansion coefficients of the full pair correlation function g(1,2), radial slices through g(1,2), the background correlation function y(1,2), and the triplet correlation function (for hard spheres), various angle averages of g(1,2) and, for hard spheres, also the direct correlation and bridge functions] of pure hard body fluids known to date have been critically assessed and tables of selected data are presented. In addition to the tables, parametrizations of the data are also given whenever they have been available. The molecular models considered include both convex body models (spheres and prolate spherocylinders) and interaction -site models (homo- and heteronuclear diatomics, linear and nonlinear symmetric triatomics, and tetrahedral penta-atomics).

scholarly journals BEHAVIOR OF THE CONFINED HARD-SPHERE FLUID WITHIN NANOSLITS: A FUNDAMENTAL-MEASURE DENSITY-FUNCTIONAL THEORY STUDY

2008 ◽  
Vol 07 (04n05) ◽  
pp. 245-253 ◽  
Author(s):  
MOHAMMAD KAMALVAND ◽  
TAHMINEH (EZZAT) KESHAVARZI ◽  
G. ALI MANSOORI
Keyword(s):  
Density Functional Theory ◽  
Density Profile ◽  
Hard Sphere ◽  
Density Functional ◽  
Hard Spheres ◽  
Calculated Data ◽  
Computational Procedure ◽  
Functional Theory ◽  
Hard Sphere Fluid ◽  
Wide Range

A property of central interest for theoretical study of nanoconfined fluids is the density distribution of molecules. The density profile of the hard-sphere fluids confined within nanoslit pores is a key quantity for understanding the configurational behavior of confined real molecules. In this report, we produce the density profile of the hard-sphere fluid confined within nanoslit pores using the fundamental-measure density-functional theory (FM-DFT). FM-DFT is a powerful approach to studying the structure and the phase behavior of nanoconfined fluids. We report the computational procedure and the calculated data for nanoslits with different widths and for a wide range of hard-sphere fluid densities. The high accuracy of the resulting density profiles and optimum grid-size values in numerical integration are verified. The data reveal a number of interesting features of hard spheres in nanoslits, which are different from the bulk hard-sphere systems. These data are also useful for a variety of purposes, including obtaining the shear stress, thermal conductivity, adsorption, solvation forces, free volume and prediction of phase transitions.

Statistical Geometry and Cavity Correlations in the Hard Sphere Fluid

2008 ◽  
Vol 73 (3) ◽  
pp. 344-357 ◽  
Author(s):  
Robin J. Speedy ◽  
Richard K. Bowles
Keyword(s):  
Computer Simulation ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Sphere Diameter ◽  
Statistical Geometry ◽  
Empirical Expression ◽  
Hard Sphere Fluid ◽  
A Site ◽  
Exact Relations

The statistical geometry of a system of hard spheres is discussed in terms of the volumes Vj that lie with a sphere diameter, σ, of exactly j sphere centres. A site that has no sphere centre within σ is called a cavity site. We focus on the probability n00(r) that two sites separated by r are both cavity sites. n00(0), n00(σ), and the limiting slope (d ln n00(r)/dr)r=0, are all known in terms of the thermodynamic properties. The Vj and n00(r) are measured by computer simulation and an empirical expression, which satisfies the known exact relations, is shown to represent n00(r) precisely in the range 0 ≤ r ≤ σ.

scholarly journals The Divergence of the Viscosity of a Fluid of Hard Spheres as an Indicator for the Fluid-Solid Phase Transition

1987 ◽  
Vol 42 (3) ◽  
pp. 231-235
Author(s):  
Hyearn-Maw Koo ◽  
Siegfried Hess
Keyword(s):  
Hard Sphere ◽  
Solid Phase ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Transition Density ◽  
Colloidal Dispersions ◽  
Number Density ◽  
Relative Pair ◽  
Hard Sphere Fluid ◽  
Solid Phase Transition

Solution of the Kirkwood-Smoluchowski equation for a hard sphere fluid yields an expression for the viscosity which shows a dramatic pretransitional increase and a divergence at a number density close to that one observed in computer simulations and in colloidal dispersions. The value for the transition density stems from a boundary condition at the surface of the hard sphere in the configurational relative pair-space and makes use of the density dependence of the pair-correlation function and of its derivative at the point of contact.

Wetting of a Smooth Substrate by Crystal

1991 ◽  
Vol 237 ◽  
Author(s):  
David J. Courtemanche ◽  
Frank van Swol
Keyword(s):  
Molecular Dynamics ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Phase System ◽  
Hard Wall ◽  
Direct Simulation ◽  
Two Phase ◽  
Complete Wetting ◽  
Hard Sphere Fluid ◽  
Partial Wetting

AbstractWe report on a molecular dynamics (MD) study of the wetting state of a system of hard spheres near a smooth planar hard wall. A direct simulation at the melting point of a two-phase system between two walls develops all the way from complete wetting by fluid (cos(θ) = 0) via partial wetting state to a final arrangement of complete wetting by crystal (cos(θ) = 1). This implies that a hard sphere fluid spontaneously crystallizes at a smooth hard wall, contrary to existing beliefs.

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