Perturbation Calculations for a Triangular Well Potential at Low Densities

1972 ◽  
Vol 50 (13) ◽  
pp. 1419-1426 ◽  
Author(s):  
Damon N. Card ◽  
John Walkley
Keyword(s):  
Perturbation Theory ◽  
Equation Of State ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Perturbation Equation ◽  
Inverse Temperature ◽  
Temperature Expansion ◽  
Good Convergence ◽  
Virial Series ◽  
Triangular Well Potential

The perturbation theory of Barker and Henderson is applied to a triangular well potential. Virial coefficients are evaluated using the local compressibility and macroscopic compressibility approximations as well as superposition theory. For a two-term inverse temperature expansion, the local compressibility approximation gives best agreement with exact virial coefficient data. The convergence of a five-term virial series is examined. At high temperatures good convergence to the (perturbation) equation of state is found.

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.

The Bender Equation of State and Virial Coefficients

2000 ◽  
Vol 65 (9) ◽  
pp. 1464-1470 ◽  
Author(s):  
Anatol Malijevský ◽  
Tomáš Hujo
Keyword(s):  
Equation Of State ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Low Density ◽  
Second Virial Coefficients ◽  
The Third ◽  
Temperature Dependences ◽  
Experimental Values

The second and third virial coefficients calculated from the Bender equation of state (BEOS) are tested against experimental virial coefficient data. It is shown that the temperature dependences of the second and third virial coefficients as predicted by the BEOS are sufficiently accurate. We conclude that experimental second virial coefficients should be used to determine independently five of twenty constants of the Bender equation. This would improve the performance of the equation in a region of low-density gas, and also suppress correlations among the BEOS constants, which is even more important. The third virial coefficients cannot be used for the same purpose because of large uncertainties in their experimental values.

Parameters of the Bender Equation of State for Chloro Derivatives of Methane and Chlorobenzene

2001 ◽  
Vol 66 (6) ◽  
pp. 833-854 ◽  
Author(s):  
Ivan Cibulka ◽  
Lubomír Hnědkovský ◽  
Květoslav Růžička
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Liquid Equilibrium ◽  
Second Virial Coefficients ◽  
Equilibrium Data ◽  
State Behaviour ◽  
Derivatives Of

Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.

The exact fourth and fifth virial coefficients of an inverse-6 potential

1979 ◽  
Vol 57 (12) ◽  
pp. 2194-2195
Author(s):  
Donald S. Hall
Keyword(s):  
Equation Of State ◽  
Cluster Expansion ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients

Numerical values are calculated for all of the four- and five-particle diagrams in the Mayer cluster expansion of the equation of state for an inverse-6 potential. These diagrams are then summed with the appropriate weightings to give accurate values for the fourth and fifth virial coefficients, which are found to be B4 = 0.02820(B2)3 and B5 = −0.0104(B2)4, where B2 is the second virial coefficient.

Equation of state for the hard tetrahedron fluid at stable state

2019 ◽  
Vol 33 (14) ◽  
pp. 1950136
Author(s):  
Jianxiang Tian ◽  
Hua Jiang
Keyword(s):  
Equation Of State ◽  
Virial Coefficient ◽  
Factor Versus ◽  
Stable State ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Packing Fraction ◽  
Chem Phys ◽  
Simulation Data ◽  
New Equation

Based on the previous works [J. X. Tian, Y. X. Gui and A. Mulero, J. Phys. Chem. B 114, 13399 (2010); Phys. Chem. Chem. Phys. 12, 13597 (2010)], we constructed a new equation of state for the hard tetrahedron (HTH) fluid at stable state by using the recently published Monte Carlo simulation data [J. Kolafa and S. Labík, Mol. Phys. 113, 1119 (2015)]. It can reproduce the correct virial coefficients upto nine, which is the known highest order of virial coefficient for HTH fluid. It also describes the simulation data of the compressibility factor versus the packing fraction at stable state with high accuracy.

Some Explicit Results for the Mean Spherical Approximation for Mixtures of Yukawa Fluids

2008 ◽  
Vol 73 (3) ◽  
pp. 424-438 ◽  
Author(s):  
Douglas J. Henderson ◽  
Osvaldo H. Scalise
Keyword(s):  
Integral Equation ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Inverse Temperature ◽  
Temperature Expansion ◽  
Yukawa Fluid ◽  
The Mean ◽  
Full Solution ◽  
Insight Into ◽  
Reasonable Model

The mean spherical approximation (MSA) is of interest because it produces an integral equation that yields useful analytical results for a number of fluids. One such case is the Yukawa fluid, which is a reasonable model for a simple fluid. The original MSA solution for this fluid, due to Waisman, is analytic but not explicit. Ginoza has simplified this solution. However, Ginoza's result is not quite explicit. Some years ago, Henderson, Blum, and Noworyta obtained explicit results for the thermodynamic functions of a single-component Yukawa fluid that have proven useful. They expanded Ginoza's result in an inverse-temperature expansion. Even when this expansion is truncated at fifth, or even lower, order, this expansion is nearly as accurate as the full solution and provides insight into the form of the higher-order coefficients in this expansion. In this paper Ginoza's implicit result for the case of a rather special mixture of Yukawa fluids is considered. Explicit results are obtained, again using an inverse-temperature expansion. Numerical results are given for the coefficients in this expansion. Some thoughts concerning the generalization of these results to a general mixture of Yukawa fluids are presented.

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

scholarly journals On the determination of molecular fields. —II. From the equation of state of a gas

1924 ◽  
Vol 106 (738) ◽  
pp. 463-477 ◽  
Keyword(s):  
Equation Of State ◽  
Molecular Model ◽  
Virial Coefficients ◽  
Preceding Paper ◽  
Molecular Field ◽  
Inverse Power ◽  
Theoretical Expression ◽  
Inverse Power Law ◽  
Special Cases ◽  
Molecular Fields

The investigation of a preceding paper has shown that the temperature variation of viscosity, as determined experimentally, can be satisfactorily explained in many gases on the assumption that the repulsive and attractive parts of the molecular field are each according to an inverse power of the distance. In some cases, in argon, for example, it was further shown that the experimental facts can be explained by more than one molecular model, from which we inferred that viscosity results alone are insufficient to determine precisely the nature of molecular fields. The object of the present paper is to ascertain whether a molecular model of the same type will also explain available experimental data concerning the equation of state of a gas, and if so, whether the results so obtained, when taken in conjunction with those obtained from viscosity, will definitely fix the molecular field. Such an investigation is made possible by the elaborate analysis by Kamerlingh Onnes of the observational material. He has expressed the results in the form of an empirical equation of state of the type pv = A + B/ v + C/ v 2 + D/ v 4 + E/ v 6 + F/ v 8 , where the coefficients A ... F, called by him virial coefficients , are determined as functions of the temperature to fit the observations. Now it is possible by various methods to obtain a theoretical expression for B as a function of the temperature and a strict comparison can then be made between theory and experiment. Unfortunately the solution for B, although applicable to any molecular model of spherical symmetry, is purely formal and contains an integral which can be evaluated only in special cases. This has been done up to now for only two simple models, viz., a van der Waals molecule, and a molecule repelling according to an inverse power law (without attraction), but it is shown in this paper that it can also be evaluated in the case of the model, which was successful in explaining viscosity results. As the two other models just mentioned are particular cases of this, the appropriate formulæ for B are easily deduced from the general one given here.

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