Thermodynamic properties of a hard sphere fluid with temperature dependent effective hard sphere diameter

1974 ◽  
Vol 60 (10) ◽  
pp. 3896-3900 ◽  
Author(s):  
Emmerich Wilhelm
Keyword(s):  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Sphere Diameter ◽  
Temperature Dependent ◽  
Hard Sphere Fluid

Statistical Geometry and Cavity Correlations in the Hard Sphere Fluid

2008 ◽  
Vol 73 (3) ◽  
pp. 344-357 ◽  
Author(s):  
Robin J. Speedy ◽  
Richard K. Bowles
Keyword(s):  
Computer Simulation ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Sphere Diameter ◽  
Statistical Geometry ◽  
Empirical Expression ◽  
Hard Sphere Fluid ◽  
A Site ◽  
Exact Relations

The statistical geometry of a system of hard spheres is discussed in terms of the volumes Vj that lie with a sphere diameter, σ, of exactly j sphere centres. A site that has no sphere centre within σ is called a cavity site. We focus on the probability n00(r) that two sites separated by r are both cavity sites. n00(0), n00(σ), and the limiting slope (d ln n00(r)/dr)r=0, are all known in terms of the thermodynamic properties. The Vj and n00(r) are measured by computer simulation and an empirical expression, which satisfies the known exact relations, is shown to represent n00(r) precisely in the range 0 ≤ r ≤ σ.

A New Theory of Fluids: The 'Tunnel' Model

1960 ◽  
Vol 13 (2) ◽  
pp. 187 ◽  
Author(s):  
JA Barker
Keyword(s):  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Cell Model ◽  
New Method ◽  
Virial Expansion ◽  
Cell Theory ◽  
Hard Sphere Fluid ◽  
Tunnel Model

A new method for calculating the thermodynamic properties of liquids and compressed gases is proposed, based on a model in which lines of molecules move almost one-dimensionally in " tunnels ", the walls of the tunnels being formed by neighbouring lines of molecules. This picture is related to the " cell " model, but it is a disordered picture, as is appropriate in a model for fluids, and the problem of the " communal entropy " which besets the cell model, does not arise. The method is applied to the hard-sphere fluid and the calculated pressure/volume isotherm is in very much better agreement with the expected isotherm than either the cell theory or the superposition theory, and also in rather better agreement than the virial expansion truncated after five terms.

Temperature Dependent Structural Properties of Liquid Ga

2016 ◽  
Vol 1141 ◽  
pp. 29-33 ◽  
Author(s):  
Amit B. Patel ◽  
Nisarg K. Bhatt ◽  
Brijmohan Y. Thakore
Keyword(s):  
Structural Properties ◽  
Structure Factor ◽  
Hard Sphere ◽  
Pair Correlation ◽  
Pair Potential ◽  
Delta Function ◽  
Packing Fraction ◽  
Sphere Diameter ◽  
Temperature Dependent ◽  
Effective Pair

We present the calculation of structural properties for liquid Ga at different temperatures using pseudopotential theory. The temperature dependence of structure factor has been determined using the hard-sphere Percus-Yevick approximation which is characterized by single parameter hard sphere diameter or equivalently packing fraction. The temperature dependent hard-sphere diameter σ (T) is estimated using criterion from the calculated effective pair potential. The modified empty-core pseudopotential due to Hasegawa et al. (J. Non-Cryst. Solids. 117/118 (1990) 300), which is valid for all electrons and contains the repulsive delta function to achieve the necessary s-pseudisation is used for electron–ion interaction. The temperature effects have been studied via dimensionless damping term and potential parameter in the pair potential. Finally, the predicted results for structure factor, pair correlation function and coordination numbers have been compared with recent available data, and a good agreement has been achieved.

Thermodynamic properties and liquid-gas phase diagram of the dipolar hard-sphere fluid

2007 ◽  
Vol 80 (5) ◽  
pp. 56002 ◽  
Author(s):  
Y. V. Kalyuzhnyi ◽  
I. A. Protsykevytch ◽  
P. T. Cummings
Keyword(s):  
Phase Diagram ◽  
Thermodynamic Properties ◽  
Gas Phase ◽  
Hard Sphere ◽  
Hard Sphere Fluid

Scaled particle theory of gas solubility — inclusion of the temperature dependent hard sphere term

1982 ◽  
Vol 60 (14) ◽  
pp. 1896-1900 ◽  
Author(s):  
Bruce A. Cosgrove ◽  
John Walkley
Keyword(s):  
Temperature Dependence ◽  
Hard Sphere ◽  
Inert Gases ◽  
Scaled Particle Theory ◽  
Sphere Diameter ◽  
Gas Solubility ◽  
Particle Theory ◽  
Temperature Dependent ◽  
Limiting Behaviour ◽  
Self Consistency

The limiting behaviour of the scaled particle theory (spt) of gas solubility has been examined for the inert gases in a range of solvents. The hard sphere limit is shown to exhibit thermodynamic self-consistency only with the inclusion of an effective hard sphere diameter temperature dependence whereas the original spt (exclusion of a temperature dependence) fails to extrapolate to the correct hard sphere limit. Furthermore, inclusion of the temperature dependence yields correct thermodynamic properties for gases of small atomic diameter (and well depth potential) as would be expected from a hard sphere based theory.

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