Equation of State Coupled with Scaled Particle Theory for Surface Tensions of Liquid Mixtures

2007 ◽  
Vol 46 (22) ◽  
pp. 7267-7274 ◽  
Author(s):  
Jinlong Li ◽  
Jun Ma ◽  
Changjun Peng ◽  
Honglai Liu ◽  
Ying Hu ◽  
...  
Keyword(s):  
Equation Of State ◽  
Liquid Mixtures ◽  
Scaled Particle Theory ◽  
Surface Tensions ◽  
Particle Theory

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.

scholarly journals Use of scaled-particle theory in the assessment of the Ph4As+/Ph4B− assumption for single ions

1979 ◽  
Vol 57 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Michael H. Abraham ◽  
Asadollah Nasehzadeh
Keyword(s):  
Free Energy ◽  
Recent Work ◽  
Scaled Particle Theory ◽  
Cavity Formation ◽  
Energy Term ◽  
Free Energies ◽  
Particle Theory ◽  
Novel Method ◽  
Energy Of Interaction ◽  
Solvent Molecules

A novel method for the assessment of the Ph4As+/Ph4B− assumption for free energies of transfer of single ions has recently been suggested by Treiner, and used by him to deduce that the assumption is not valid for transfers between water, propylene carbonate, sulpholane, dimethylsulphoxide, N-methyl-2-pyrrolidone, and perhaps also dimethylformamide. The basis of the method is the estimation of the free energy of cavity formation by scaled-particle theory, together with the hypothesis that the free energy of interaction of Ph4As+ (or Ph4B−) with solvent molecules is the same in all solvents, ΔGt0(int) = 0. It is shown in the present paper that (a) whether or not the Ph4As+/Ph4B− assumption applies to transfer to a given solvent depends on which other solvent is taken as the reference solvent in Treiner's method, (b) the calculation of the cavity free energy term by scaled-particle theory and by the theory of Sinanoglu – Reisse – Moura Ramos (SRMR) yields values so different that the method cannot be considered reliable, (c) the calculation of cavity enthalpies and entropies for Ph4As+ or Ph4B− by scaled-particle theory yields results that are chemically not reasonable, (d) the hypothesis that ΔGt0(int) = 0 conflicts with SRMR theory, and (e) the conclusions reached by Treiner are not in accord with recent work that in general supports the Ph4As+/Ph4B− assumption for solvents that are rejected by Treiner.

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