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.

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.

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.

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.

The statistical thermodynamics of solutions of non-spherical molecules. I. The thermodynamic functions

1955 ◽  
Vol 229 (1177) ◽  
pp. 271-280 ◽  
Keyword(s):  
Carbon Tetrachloride ◽  
Equation Of State ◽  
Thermodynamic Functions ◽  
Statistical Thermodynamics ◽  
Intermolecular Forces ◽  
Pure Component ◽  
Experimental Results ◽  
Thermodynamics Of Solutions ◽  
Theory And Experiment

The perturbation treatment of the orientational forces between non-spherical molecules proposed by Cook & Rowlinson (1953) is extended to mixtures by using the theory of solutions put forward by Longuet-Higgins (1951). The thermodynamic functions and the equation of state of such mixtures are expressed in terms of the intermolecular forces and the properties of one pure component. Expressions are derived for the excess (or non-ideal) thermodynamic functions which are compared with the experimental results on the four solutions, benzene+ cyclohexane , benzene+carbon tetrachloride, benzene + ethylene dychloride, and cyclohexane + carbon tetrachloride. The agreement between theory and experiment is improved by taking account of the orientational forces.

The virial coefficients of the carbon dioxide-ethylene system I. Pure gases

1964 ◽  
Vol 277 (1371) ◽  
pp. 448-467 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Direct Determination ◽  
Expansion Method ◽  
National Physical Laboratory ◽  
Intermolecular Potential ◽  
Gaseous Mixtures ◽  
Physical Laboratory ◽  
The Relationship

This paper describes the first part of an investigation of the thermodynamic properties of gases and gaseous mixtures undertaken a few years ago at the National Physical Laboratory, with the main object of providing data on the relationship between the properties of mixtures and those of the pure constituents. The virial coefficients of carbon dioxide and ethylene have been determined by the series-expansion method over the range —10 to 200 °C, and the representation of the results by several forms of intermolecular potential has been investigated. In the case of ethylene it appears that the second virial coefficient may be represented accurately in terms of a Lennard-Jones 6:12 potential, the parameters of which are determined. In the corresponding representation for carbon dioxide there is a small but systematic discrepancy and evidence is adduced that this may be rectified by the introduction of a quadrupole interaction term on the lines of the theory developed by Pople. The value of the quadrupole moment suggested by this calculation proves to be in fairly close agreement with a recent direct determination. Work on the virial coefficients of mixtures of the two gases will be described in a further paper.

Nematic virial coefficients of very long hard molecules and Onsager theory

1998 ◽  
Vol 94 (2) ◽  
pp. 335-339 ◽  
Author(s):  
E. VELASCO ◽  
P. PADILLA
Keyword(s):  
Virial Coefficients ◽  
Onsager Theory

Excluded volume effect for the nuclear matter equation of state

1991 ◽  
Vol 51 (3) ◽  
pp. 485-489 ◽  
Author(s):  
D. H. Rischke ◽  
M. I. Gorenstein ◽  
H. St�cker ◽  
W. Greiner
Keyword(s):  
Equation Of State ◽  
Nuclear Matter ◽  
Volume Effect ◽  
Excluded Volume ◽  
Excluded Volume Effect

scholarly journals Hadron resonance gas with van der Waals interactions

2020 ◽  
Vol 29 (05) ◽  
pp. 2040002 ◽  
Author(s):  
Volodymyr Vovchenko
Keyword(s):  
Equation Of State ◽  
Van Der Waals ◽  
Heavy Ion ◽  
Van Der Waals Interactions ◽  
Excluded Volume ◽  
Heavy Ion Collision ◽  
Lattice Quantum Chromodynamics ◽  
Qcd Critical Point ◽  
Lattice Quantum ◽  
Ion Collision

An overview of a hadron resonance gas (HRG) model that includes van der Waals (vdW) interactions between hadrons is presented. Applications of the excluded volume HRG model to heavy-ion collision data and lattice quantum chromodynamics (QCD) equation of state are discussed. A recently developed quantum vdW HRG model is covered as well. Applications of this model in the context of the QCD critical point are elaborated.

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