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.

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.

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).

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.

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.

INVESTIGATION OF THE PERTURBED VIRIAL EQUATIONS WITH ARBITRARY TEMPERATURE-DEPENDENT SECOND AND THIRD VIRIAL COEFFICIENTS

2011 ◽  
Vol 25 (19) ◽  
pp. 2593-2600 ◽  
Author(s):  
JIANXIANG TIAN
Keyword(s):  
Virial Coefficient ◽  
Equations Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Critical Properties ◽  
Temperature Dependent ◽  
Packing Factor ◽  
Third Virial Coefficient ◽  
Real Fluids

In this paper, the perturbed virial equations of state with temperature-dependent virial coefficients are constructed using the Carnahan–Starling (CS) hard sphere equation as reference. Considering the second virial coefficient, some critical properties are interaction-independent and the critical packing factor is in the range of that of real fluids. But the critical compressibility factor and the liquid–vapor equilibrium properties disagree with experiments. When both the second and the third virial coefficient are considered, the critical properties are interaction-dependent but are out of the range of experimental results of real fluids. As a conclusion, the fourth virial coefficients are required for further consideration.

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.

Sign in / Sign up

Export Citation Format

Share Document