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.

A New Theory of Fluids: The 'Tunnel' Model

1960 ◽  
Vol 13 (2) ◽  
pp. 187 ◽  
Author(s):  
JA Barker
Keyword(s):  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Cell Model ◽  
New Method ◽  
Virial Expansion ◽  
Cell Theory ◽  
Hard Sphere Fluid ◽  
Tunnel Model

A new method for calculating the thermodynamic properties of liquids and compressed gases is proposed, based on a model in which lines of molecules move almost one-dimensionally in " tunnels ", the walls of the tunnels being formed by neighbouring lines of molecules. This picture is related to the " cell " model, but it is a disordered picture, as is appropriate in a model for fluids, and the problem of the " communal entropy " which besets the cell model, does not arise. The method is applied to the hard-sphere fluid and the calculated pressure/volume isotherm is in very much better agreement with the expected isotherm than either the cell theory or the superposition theory, and also in rather better agreement than the virial expansion truncated after five terms.

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.

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).

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