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).

About the Usage of Scaling Parameters in the Scaled Particle Theory of Mixtures of Non-Additive Hard Spheres

1993 ◽  
Vol 48 (8-9) ◽  
pp. 899-905 ◽  
Author(s):  
H. M. Schaink
Keyword(s):  
Equation Of State ◽  
Hard Spheres ◽  
Present Theory ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Scaling Parameters ◽  
Third Virial Coefficient ◽  
Theory Of Mixtures ◽  
The One ◽  
Compressibility Factors

Abstract A new simple equation of state is derived for symmetric and asymmetric mixtures of non-additive hard spheres. The derivation of the equation of state is reminiscent of the scaled particle theory. However, this method uses two scaling parameters, which depend on the composition of the mixture. As a result, the equation of state presented here approaches in a natural way the limit of the one component fluid. This feature of the present theory stands in sharp contrast to common scaled particle theories for non-additive hard spheres, where the one component limit has an unphysical dependence on the non-additivity. The equation of state can be used for mixtures of particles that differ in size and has a second and a third virial coefficient which are exact up to first order in the non-additivity. The compressibility factors and the demixing densities predicted by the present equation of state are in fairly good agreement which available MC data.

Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

2010 ◽  
Vol 75 (3) ◽  
pp. 359-369 ◽  
Author(s):  
Mariano López De Haro ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Virial Series ◽  
Consolute Point ◽  
Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

COMPUTER ALGEBRA REEXAMINATION OF THE SCALED PARTICLE THEORY FOR HARD-SPHERE AND LENNARD-JONES FLUIDS

2008 ◽  
Vol 22 (26) ◽  
pp. 2601-2615 ◽  
Author(s):  
S. B. KHASARE
Keyword(s):  
Real Number ◽  
Computer Algebra ◽  
Hard Sphere ◽  
Physical Property ◽  
Arbitrary Real Number ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Hard Sphere Fluid ◽  
Lennard Jones ◽  
Good Agreement

In the present work, an extension of the scaled particle theory (ESPT) for fluid using computer algebra is developed to obtain an equation of state (EOS), for Lennard-Jones fluid. A suitable functional form for surface tension S(r,d,∊) is assumed with intermolecular separation r as a variable, given below: [Formula: see text] where m is arbitrary real number, and d and ∊ are related to physical property such as average or suitable molecular diameter and the binding energy of the molecule respectively. It is found that, for hard sphere fluid ∊ = 0, the above assumption when introduced in scaled particle theory (SPT) frame and choosing arbitrary real number, m = 1/3, the corresponding EOS is in good agreement with the computer simulation of molecular dynamics (MD) result. Furthermore, for the value of m = -1 it gives a Percus–Yevick (pressure), and for the value of m = 1, it corresponds Percus–Yevick (compressibility) EOS.

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.

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