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.

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).

EQUATION OF STATE AND FREEZING OF GMSA HARD SPHERES

2003 ◽  
Vol 17 (31n32) ◽  
pp. 6057-6065 ◽  
Author(s):  
M. MORADI ◽  
H. SHAHRI
Keyword(s):  
Equation Of State ◽  
Hard Sphere ◽  
Density Functional ◽  
Hard Spheres ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Direct Correlation Function ◽  
Generalized Mean ◽  
Simulation Results ◽  
Good Agreement

The modified-weighted-density-functional approximation (MWDA) proposed by Denton and Ashcroft, is applied to study the equation of sate and freezing of the hard spheres using the generalized mean spherical approximation (GMSA) direct correlation function (DCF). Because of the attractive tail in the DCF, the perturbation method similar to that introduced by Yoon and Kim is applied. The free energy, freezing parameters and the equation of state of the hard sphere FCC crystal are obtained. The results are compared with some other previous theories and Monte Carlo simulation. Our results are in good agreement with the simulation results.

An optical method for measuring PVT data, critical constants, virial coefficients, and molecular parameters of GeH4

1983 ◽  
Vol 61 (7) ◽  
pp. 1060-1063
Author(s):  
D. Balzarini ◽  
A. Rosenberg ◽  
P. Palffy-Muhoray
Keyword(s):  
Refractive Index ◽  
Equation Of State ◽  
Optical Method ◽  
Virial Coefficients ◽  
Virial Equation ◽  
Density Range ◽  
Lennard Jones ◽  
Pvt Data ◽  
Virial Equation Of State ◽  
Critical Constants

An optical method has been developed for measuring PVT data for a fluid. The method consists of measuring the refractive index as a function of density and temperature and, separately, as a function of pressure and temperature. The results are combined to yield PVT data. Germane has been studied. Isotherms have been measured in the temperature range 293 to 323 K and the density range 0.07 to 0.7 g cm−3. The data in the critical region are analyzed to obtain the critical constants Pc = 48.8 atm, ρc = 0.522 g cm−3, and Tc = 38.97 C ± 0.2. The data at lower densities are fitted to a virial equation of state to obtain the second and third coefficients. The values at 312.15 K are B = −2.37 cm3 g−1 and C = 1.99 cm6 g−2. The data are analyzed to yield the Lennard–Jones parameters ε/K = 230 ± 15 deg and σ = 4.6 ± 0.2 Å.

Phase instabilities in charged hard‐sphere mixtures. I. Binary mixtures of salt and hard spheres

1995 ◽  
Vol 103 (18) ◽  
pp. 8098-8110 ◽  
Author(s):  
Paresh U. Kenkare ◽  
Carol K. Hall ◽  
C. Caccamo
Keyword(s):  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Phase Instabilities

Virial coefficients of the additive hard-sphere binary mixtures up to the eighth

2016 ◽  
Vol 115 (9-12) ◽  
pp. 1051-1056 ◽  
Author(s):  
Stanislav Labík ◽  
Anatol Malijevský ◽  
Jiří Kolafa
Keyword(s):  
Binary Mixtures ◽  
Hard Sphere ◽  
Virial Coefficients
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