Multipolar third-order non-pairwise additivity of intermolecular forces: Effects on crystal properties and third virial coefficients

1971 ◽  
Vol 24 (11) ◽  
pp. 2205 ◽  
Author(s):  
CHJ Johnson ◽  
TH Spurling
Keyword(s):  
Cohesive Energy ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Higher Order ◽  
The Third ◽  
Dipole Term ◽  
Third Virial Coefficient ◽  
Three Body ◽  
Body Potential

In this paper we give the results of computing the third virial coefficient and the cohesive energy of the crystal for argon taking into account the higher-order multipole terms in the long-range three- body interaction as recently calculated by Bell. The Barker-Pompe potential has been used as the two-body potential function. We find that the third virial coefficient values for argon computed with this more complete non-additive energy function agree very much better with the experimental values than when only the triple-dipole term is used. This is particularly true at lower temperatures. The results also show that better agreement would be obtained if some form of repulsive non- addivity were included in the computation. For the cohesive energy of the crystal we find that the dipole-dipole-quadrupole energy is one-third as large as the triple-dipole energy and so cannot be neglected in these lattice computations. Furthermore, we find that these higher- order three-body forces do not stabilize the face-centred-cubic lattice for argon, the hexagonal-close-packed lattice having a slightly lower energy.

Non-additivity of intermolecular forces: effects on the fourth virial coefficient

1974 ◽  
Vol 27 (2) ◽  
pp. 241 ◽  
Author(s):  
CHJ Johnson ◽  
TH Spurling
Keyword(s):  
Perturbation Theory ◽  
Long Range ◽  
Fourth Order ◽  
Virial Coefficient ◽  
Intermolecular Forces ◽  
The Third ◽  
Lennard Jones ◽  
Dipole Term ◽  
Third Virial Coefficient ◽  
Reduced Temperature

In this paper we give the results of computing the effect of non-additivity of long range forces on the fourth virial coefficient of a Lennard-Jones 12-6 gas. We have considered only dipolar effects but have included all terms up to the fourth order of perturbation theory. We have also calculated the effect of the fourth-order triple-dipole term on the third virial coefficient. For the fourth virial coefficient we find that the dispersion non-additivity, while being positive at low reduced temperatures, goes through a negative minimum at a reduced temperature of about 1.25 before becoming small and positive at high temperatures. This is in contradistinction to the behaviour of the third virial co-efficient where the dispersion non-additivity is always positive.

scholarly journals Nonadditivity of Intermolecular Forces: Effects on the Third Virial Coefficient

1966 ◽  
Vol 44 (8) ◽  
pp. 2984-2994 ◽  
Author(s):  
A. E. Sherwood ◽  
Andrew G. De Rocco ◽  
E. A. Mason
Keyword(s):  
Virial Coefficient ◽  
Intermolecular Forces ◽  
The Third ◽  
Third Virial Coefficient

scholarly journals Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters

2020 ◽  
Vol 65 (6) ◽  
pp. 500
Author(s):  
O. M. Chubai ◽  
A. A. Rovenchak
Keyword(s):  
Virial Coefficient ◽  
Space Dimension ◽  
Virial Coefficients ◽  
Bose Gas ◽  
Bose Gases ◽  
Second Virial Coefficients ◽  
The Third ◽  
Deformation Parameters ◽  
Third Virial Coefficient ◽  
The Ideal

Two approaches to the construction of thermodynamics in the framework of the q- and м-formalisms, which correspond to certain deformations of the algebra of the creation–annihilation operators, have been considered. By comparing the obtained results, an approximate, independent of the space dimension, correspondence was revealed between the second virial coefficients for the ideal q- and м-deformed Bose gases. The corresponding discrepancy arises only at the level of the third virial coefficient. A method for emulating the м-deformed Bose gas up to the third virial coefficient inclusive by means of the two-parametric nonadditive Polychronakos statistics is demonstrated.

Approximate method for calculating the third virial coefficient of a gaseous mixture

1967 ◽  
Vol 45 (4) ◽  
pp. 373-378 ◽  
Author(s):  
M. Orentlicher ◽  
J. M. Prausnitz
Keyword(s):  
Experimental Data ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Gaseous Mixture ◽  
Pure Component ◽  
Spherically Symmetric ◽  
Experimental Uncertainty ◽  
Symmetric Potential ◽  
The Third ◽  
Third Virial Coefficient

An approximation is suggested for calculating the third virial cross-coefficient Cijk from available generalized tables for pure-component third virial coefficients Ciii which are based on any one of several, spherically symmetric potential functions. A comparison of calculated results with the very limited experimental data now available indicates that the suggested approximation can reproduce the experimental results essentially within the probable (large) experimental uncertainty.

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.

The third virial coefficient of hard discs of different sizes

1987 ◽  
Vol 61 (2) ◽  
pp. 525-528 ◽  
Author(s):  
John S. Rowlinson ◽  
Donald A. McQuarrie
Keyword(s):  
Virial Coefficient ◽  
The Third ◽  
Third Virial Coefficient

Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

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