Limits of the third virial coefficient at low and high temperatures for a Lennard-Jones potential

1963 ◽  
Vol 6 (1) ◽  
pp. 75-83 ◽  
Author(s):  
J.S. Rowlinson
Keyword(s):  
High Temperatures ◽  
Virial Coefficient ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
The Third ◽  
Lennard Jones ◽  
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.

Second virial coefficient of a generalized Lennard-Jones potential

2015 ◽  
Vol 142 (3) ◽  
pp. 034305 ◽  
Author(s):  
Alfredo González-Calderón ◽  
Adrián Rocha-Ichante
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones

scholarly journals The Third Virial Coefficient of a Lennard‐Jones Gas by Kihara's Method with Tables for the 6—9 Potential

1954 ◽  
Vol 22 (3) ◽  
pp. 464-468 ◽  
Author(s):  
Leo F. Epstein ◽  
Celesta J. Hibbert ◽  
Marion D. Powers ◽  
Glenn M. Roe
Keyword(s):  
Virial Coefficient ◽  
The Third ◽  
Lennard Jones ◽  
Third Virial Coefficient

Third-order WKBJ eigenvalues for Lennard-Jones and Varshni V potentials

1978 ◽  
Vol 56 (11) ◽  
pp. 1488-1493 ◽  
Author(s):  
R. N. Kesarwani ◽  
Y. P. Varshni
Keyword(s):  
Wave Equation ◽  
Numerical Integration ◽  
Error Estimates ◽  
Lennard Jones Potential ◽  
Third Order ◽  
Jones Potential ◽  
The Third ◽  
Lennard Jones ◽  
Equation Error ◽  
Special Case

The WKBJ method is applied to the third order for obtaining the eigenvalues for the fifth potential of Varshni, and the relevant integrals are analytically evaluated. Numerical results are obtained for the Lennard-Jones potential, which is a special case of the Varshni V potential, and are compared to the results of Harrison and Bernstein obtained by a numerical integration of the wave equation. Error estimates are made. It is shown that for diatomic potentials, the Langer correction is not needed if the WKBJ approximation is carried to second and higher orders.

scholarly journals Enhancing capabilities of Atomic Force Microscopy by tip motion harmonics analysis

2013 ◽  
Vol 61 (2) ◽  
pp. 535-539
Author(s):  
S. Babicz ◽  
J. Smulko ◽  
A. Zieliński
Keyword(s):  
Linear Response ◽  
General Framework ◽  
Lennard Jones Potential ◽  
Range Interaction ◽  
Jones Potential ◽  
Force Microscopy ◽  
The Third ◽  
Lennard Jones ◽  
Atomic Force ◽  
Long Range Interaction

Abstract Motion of a tip used in an atomic force microscope can be described by the Lennard-Jones potential, approximated by the van der Waals force in a long-range interaction. Here we present a general framework of approximation of the tip motion by adding three terms of Taylor series what results in non-zero harmonics in an output signal. We have worked out a measurement system which allows recording of an excitation tip signal and its non-linear response. The first studies of spectrum showed that presence of the second and the third harmonics in cantilever vibrations may be observed and used as a new method of the investigated samples characterization.

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.

GRÜNEISEN PARAMETER OF IONIC AND COVALENT CRYSTALS FOR LOW AND HIGH TEMPERATURES

2002 ◽  
Vol 13 (02) ◽  
pp. 209-216
Author(s):  
S. D. D. ROY ◽  
K. RAMACHANDRAN
Keyword(s):  
High Temperatures ◽  
Anisotropy Factor ◽  
Force Model ◽  
Lennard Jones Potential ◽  
Ionic Crystals ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter ◽  
Jones Potential ◽  
Lennard Jones

The Grüneisen parameter for covalent crystals is calculated by employing an angular force model with eight parameters and using a 6–12 potential [Lennard–Jones potential (L–J)] whereas for ionic crystals, it is calculated by employing the Daniel's method, which uses anisotropy factor tables f(s,t) of de Launay.

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