Statistical Mechanics of Monatomic Systems in an External Periodic Potential Field. I. Introduction, Virial Expansion, and Classical Second Virial Coefficient

1961 ◽  
Vol 34 (5) ◽  
pp. 1538-1543 ◽  
Author(s):  
Terrell L. Hill ◽  
Samuel Greenschlag
Keyword(s):  
Statistical Mechanics ◽  
Potential Field ◽  
Virial Coefficient ◽  
Periodic Potential ◽  
Second Virial Coefficient ◽  
Virial Expansion

The application of the gas–solid virial expansion to argon absorbed on the (100) face of sodium chloride

1976 ◽  
Vol 348 (1654) ◽  
pp. 317-337 ◽  
Keyword(s):  
Sodium Chloride ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Expansion ◽  
Two Dimensional ◽  
Third Body ◽  
Translation Model ◽  
Dimensional Approximation ◽  
Limiting Parameters ◽  
The Ideal

The gas–solid virial expansion is developed for argon adsorbed on the (100) sodium chloride surface. Limiting parameters for the attractive components of the gas-ion interaction are suggested and the corresponding repulsive parameters for the Li + , Na + , K + , Rb + , Cs + , F – , Cl – , Br – and I – ions are determined from an analysis of alkali halide bulk crystal data. The second two dimensional virial coefficient for argon absorbed on (100) sodium chloride is determined over a range of temperatures by using the generalized ‘exponential-six’ equation for all interatomic interactions. The results indicate large changes from the ideal perfectly mobile two-dimensional second virial coefficient caused by the inclusion of perturbation terms that take account of the periodic structured surface. These changes are shown to be sensitive to the exact structure of the crystal at the interface as shown by adsorption of argon on the (100) sodium chloride surface which has been allowed to relax to its equilibrium conformation. The third body (surface) interactions at the interface are considered together with the applicability of the two dimensional approximation for the adsorbate self interactions. The zero coverage isosteric enthalpy and Henry’s law constants at 80 K are computed for each of the gas-ion potentials that are chosen. The results are found to agree with those obtained by using the hindered translation model and from a comparison with experimental data, suggest a larger attractive gas–crystal interaction than previously thought.

Interpretation of Preferential Adsorption Using Random Phase Approximation Theory

1995 ◽  
Vol 60 (10) ◽  
pp. 1641-1652 ◽  
Author(s):  
Henri C. Benoît ◽  
Claude Strazielle
Keyword(s):  
Approximation Theory ◽  
Random Phase Approximation ◽  
Virial Coefficient ◽  
Random Phase ◽  
Second Virial Coefficient ◽  
Solvent Mixture ◽  
Gyration Radius ◽  
Thermodynamic Quantities ◽  
Phase Approximation ◽  
Preferential Adsorption

It has been shown that in light scattering experiments with polymers replacement of a solvent by a solvent mixture causes problems due to preferential adsorption of one of the solvents. The present paper extends this theory to be applicable to any angle of observation and any concentration by using the random phase approximation theory proposed by de Gennes. The corresponding formulas provide expressions for molecular weight, gyration radius, and the second virial coefficient, which enables measurements of these quantities provided enough information on molecular and thermodynamic quantities is available.

Scattering of anyons with hard-disk repulsion and the second virial coefficient

1991 ◽  
Vol 44 (19) ◽  
pp. 10731-10735 ◽  
Author(s):  
Akira Suzuki ◽  
M. K. Srivastava ◽  
R. K. Bhaduri ◽  
J. Law
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Hard Disk

GENERAL FORMULA FOR THE SECOND VIRIAL COEFFICIENT

1961 ◽  
Vol 39 (11) ◽  
pp. 1563-1572 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Resolvent Operators ◽  
Simple Derivation ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Quantization Volume ◽  
Mechanical Expression ◽  
The Waves

A simple derivation is given of the quantum mechanical expression for the second virial coefficient in terms of the scattering phase shifts. The derivation does not require the introduction of a quantization volume and is based on the identity R(z)−R0(z) = R0(z)H1R(z), where R0(z) and R(z) are the resolvent operators corresponding to the unperturbed and total Hamiltonians H0 and H0 + H1 respectively. The derivation is valid in particular for a gas of excitons in a crystal for which the shape of the waves describing the relative motion of two excitons is not spherical, and, in general, varies with varying energy. The validity of the phase shift formula is demonstrated explicitly for this case by considering a quantization volume with a boundary the shape of which varies with the energy in such a way that for each energy the boundary is a surface of constant phase. The density of states prescribed by the phase shift formula is shown to result if the enclosed volume is required to be the same for all energies.

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