The potential function for double square-well model and its application to calculation of the second virial coefficient

1993 ◽  
Vol 2 (3) ◽  
pp. 165-169
Author(s):  
Jingshan Tong ◽  
Guanghua Gao ◽  
Yongqi Chen
Keyword(s):  
Potential Function ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Well Model ◽  
Square Well

The analytical evaluation of the first-order density cluster integral in the radial distribution function

1970 ◽  
Vol 320 (1542) ◽  
pp. 323-348 ◽  
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Scattering Data ◽  
X Ray ◽  
Lennard Jones ◽  
X Ray Scattering ◽  
Cluster Integrals ◽  
Square Well ◽  
Three Body

It is shown how to evaluate the two-body, and three-body cluster integrals, ɳ 3 , ɳ * 3 , β 3 , β * 3 (equations (1.1) to (1.4)) for the hard-sphere, square-well and Lennard-Jones ( v :½ v ) potentials; the three-body potential used is the dipole-dipole-dipole potential of Axilrod & Teller. Explicit expressions are presented for the integrals ɳ * 3 , β * 3 using the above potentials; in the case of the first integral, its values for both small and large values of the separation distance are also given, for the Lennard-Jones ( v :½ v ) potential. Similar considerations have been carried out for ɳ 3 and β 3 , except that explicit expressions for the hard-sphere, and square-well potentials are not given, since these had been done before by other authors. The intermediate expressions for the four cluster integrals, are in terms of single integrals, and such expressions are valid for any continuous potential. Numerical results based on some of the expressions in this paper are compared with the results of numerical evaluation of the above integrals by other authors, and the agreement is seen to be good. Making use of the Mikolaj-Pings relation, the above results are used to obtain relationships between the second virial coefficient, and X-ray scattering data, as well as a means of deducing the pair potential at large separations, directly from a knowledge of X-ray scattering data, and the second virial coefficient.

Second Virial Coefficient Calculations for Square-Well Chain Molecules

1994 ◽  
Vol 27 (10) ◽  
pp. 2744-2756 ◽  
Author(s):  
John M. Wichert ◽  
Carol K. Hall
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Chain Molecules ◽  
Square Well

A POTENTIAL FUNCTION FOR LIQUID HELIUM AT 0°K.

1954 ◽  
Vol 32 (12) ◽  
pp. 759-763 ◽  
Author(s):  
C. F. A. Beaumont
Keyword(s):  
Liquid Helium ◽  
Potential Function ◽  
High Temperatures ◽  
Radial Distribution ◽  
Isothermal Compressibility ◽  
Virial Coefficient ◽  
Distribution Curve ◽  
Second Virial Coefficient ◽  
Fair Agreement ◽  
Radial Distribution Curve

A new potential function for liquid helium is obtained by modifying the Margenau potential function and summing over a suggested structure for the liquid. The new potential function leads to fair agreement with the first peak of the radial distribution curve for liquid helium, with the isothermal compressibility, and with second virial coefficient data at high temperatures.

STICKY SPHERES IN QUANTUM MECHANICS

1994 ◽  
Vol 06 (05a) ◽  
pp. 947-975 ◽  
Author(s):  
M. D. PENROSE ◽  
O. PENROSE ◽  
G. STELL
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Gaseous Phase ◽  
Virial Coefficient ◽  
Hard Spheres ◽  
Second Virial Coefficient ◽  
Dimensional System ◽  
3 Dimensional ◽  
Fermi Statistics ◽  
Square Well

For a 3-dimensional system of hard spheres of diameter D and mass m with an added attractive square-well two-body interaction of width a and depth ε, let BD, a denote the quantum second virial coefficient. Let BD denote the quantum second virial coefficient for hard spheres of diameter D without the added attractive interaction. We show that in the limit a → 0 at constant α: = ℰma2/(2ħ2) with α < π2/8, [Formula: see text] The result is true equally for Boltzmann, Bose and Fermi statistics. The method of proof uses the mathematics of Brownian motion. For α > π2/8, we argue that the gaseous phase disappears in the limit a → 0, so that the second virial coefficient becomes irrelevant.

Pairwise additive third virial coefficients for multipolar molecules : Application to water vapour

1971 ◽  
Vol 24 (8) ◽  
pp. 1567 ◽  
Author(s):  
CHJ Johnson ◽  
TH Spurling
Keyword(s):  
Water Vapour ◽  
Potential Function ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Axially Symmetric ◽  
Multidimensional Integration ◽  
Third Virial Coefficient ◽  
Qualitative Effect ◽  
Experimental Values

Pairwise additive third virial coefficients for axially symmetric multipolar molecules have been calculated using a non-product multidimensional integration formula. Results for the Stockmayer potential agree with the corrected results of Rowlinson. It is found that the inclusion of the dipole-quadrupole and quadrupole-quadrupole terms in the potential function has a marked qualitative effect on the shape of the C-T curve. Values of the third virial coefficient for water vapour calculated using a potential function derived from gaseous viscosity and second virial coefficient data are in good agreement with the experimental values.

scholarly journals Modified Lennard-Jones Potentials with a Reduced Temperature-Correction Parameter for Calculating Thermodynamic and Transport Properties: Noble Gases and Their Mixtures (He, Ne, Ar, Kr, and Xe)

2013 ◽  
Vol 2013 ◽  
pp. 1-29 ◽  
Author(s):  
Seung-Kyo Oh
Keyword(s):  
Transport Properties ◽  
Potential Function ◽  
Virial Coefficient ◽  
Noble Gases ◽  
Second Virial Coefficient ◽  
Temperature Correction ◽  
Viscosity Data ◽  
Lennard Jones ◽  
Thermodynamic And Transport Properties ◽  
Reduced Temperature

The three-parameter Lennard-Jones (12-6) potential function is proposed to calculate thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases (He, Ne, Ar, Kr, and Xe) and their mixtures at low density. Empirical modification is made by introducing a reduced temperature-correction parameter τ to the Lennard-Jones potential function for this purpose. Potential parameters (σ, ε, and τ) are determined individually for each species when the second virial coefficient and viscosity data are fitted together within the experimental uncertainties. Calculated thermodynamic and transport properties are compared with experimental data by using a single set of parameters. The present study yields parameter sets that have more physical significance than those of second virial coefficient methods and is more discriminative than the existing transport property methods in most cases of pure gases and of gas mixtures. In particular, the proposed model is proved with better results than those of the two-parameter Lennard-Jones (12-6) potential, Kihara Potential with group contribution concepts, and other existing methods.

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