Upper and lower bounds on the chemical potential of a hard-sphere fluid and other inequalities from scaled particle theory

1981 ◽  
Vol 85 (22) ◽  
pp. 3313-3322 ◽  
Author(s):  
Howard Reiss ◽  
George A. Merry
Keyword(s):  
Lower Bounds ◽  
Hard Sphere ◽  
Chemical Potential ◽  
Upper And Lower Bounds ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Hard Sphere Fluid

Fluids in random porous media: Scaled particle theory

2012 ◽  
Vol 85 (1) ◽  
pp. 115-133 ◽  
Author(s):  
Myroslav Holovko ◽  
Taras Patsahan ◽  
Wei Dong
Keyword(s):  
Porous Media ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Chemical Potential ◽  
Critical Density ◽  
Critical Parameters ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Confined Fluid ◽  
Random Porous Media

The scaled particle theory (SPT) is applied to describe thermodynamic properties of a hard sphere (HS) fluid in random porous media. To this purpose, we extended the SPT2 approach, which has been developed previously. The analytical expressions for the chemical potential of an HS fluid in HS and overlapping hard sphere (OPH) matrices, sponge matrix, and hard convex body (HCB) matrix are obtained and analyzed. A series of new approximations for SPT2 are proposed. The grand canonical Monte Carlo (GGMC) simulations are performed to verify an accuracy of the SPT2 approach combined with the new approximations. A possibility of mapping between thermodynamic properties of an HS fluid in random porous media of different types is discussed. It is shown that thermodynamic properties of a fluid in the different matrices tend to be equal if the probe particle porosities and the specific surface pore areas of considered matrices are identical. The obtained results for an HS fluid in random porous media as reference systems are used to extend the van der Waals equation of state to the case of a simple fluid in random porous media. It is observed that a decrease of matrix porosity leads to lowering of the critical temperature and the critical density of a confined fluid, while an increase of a size of matrix particles causes an increase of these critical parameters.

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.

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).

scholarly journals Scaled particle theory for hard sphere pairs. II. Numerical analysis

2006 ◽  
Vol 125 (20) ◽  
pp. 204505 ◽  
Author(s):  
Swaroop Chatterjee ◽  
Pablo G. Debenedetti ◽  
Frank H. Stillinger
Keyword(s):  
Numerical Analysis ◽  
Hard Sphere ◽  
Scaled Particle Theory ◽  
Particle Theory

Solubility of non-polar gases in cyclohexanone between 273.15 and 303.15 K at 101.32 kPa partial pressure of gas

1987 ◽  
Vol 65 (9) ◽  
pp. 2198-2202 ◽  
Author(s):  
María Asunción Gallardo ◽  
José María Melendo ◽  
José Santiago Urieta ◽  
Celso Gutierrez Losa
Keyword(s):  
Gibbs Energy ◽  
Partial Pressure ◽  
Temperature Dependence ◽  
Hard Sphere ◽  
Scaled Particle Theory ◽  
Sphere Diameter ◽  
Particle Theory ◽  
Enthalpy And Entropy

Solubility measurements of several non-polar gases (He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, C2H4, C2H6, CF4, SF6, andCO2) in cyclohexanone at 273.15 to 303.15 K and a partial pressure of gas of 101.32 kPa, are reported. Gibbs energy, enthalpy, and entropy of solution at 298.15 K and 101.32 kPa partial pressure of gas were evaluated. Effective hard-sphere diameter temperature dependence has been studied and its effect on the calculated SPT (Scaled Particle Theory) solubilities, and enthalpies and entropies of solution was also examined.

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