Studies in Molecular Dynamics. VII. Hard‐Sphere Distribution Functions and an Augmented van der Waals Theory

1969 ◽  
Vol 50 (5) ◽  
pp. 2032-2037 ◽  
Author(s):  
B. J. Alder ◽  
C. E. Hecht
Keyword(s):  
Molecular Dynamics ◽  
Hard Sphere ◽  
Van Der Waals ◽  
Distribution Functions ◽  
Van Der Waals Theory

Generalized van der Waals theory. III. The prediction of hard sphere structure

1980 ◽  
Vol 33 (10) ◽  
pp. 2139 ◽  
Author(s):  
S Nordholm ◽  
M Johnson ◽  
BC Freasier
Keyword(s):  
Hard Sphere ◽  
Van Der Waals ◽  
Hard Core ◽  
Coarse Graining ◽  
Distribution Functions ◽  
Core Diameter ◽  
Fine Grained ◽  
Entropy Functional ◽  
Van Der Waals Theory ◽  
Non Local

This article is devoted to further development of the generalized van der Waals theory and its application to non-uniform hard sphere fluids. A coarse-graining assumption included in the original derivation is replaced by a weaker assumption recognizing the non-zero range of hard core interactions. The new fine-grained theory thus contains a non-local entropy functional and allows fluid structure on a length scale shorter than the hard core diameter to be resolved. Moreover, it contains a simplified representation of the mechanism leading to hard sphere structure due essentially to geometrical packing constraints. This is shown by application of the theory to hard sphere adsorption profiles in the case of a hard wall and to radial distribution functions of a hard sphere fluid. The amount of structure is underestimated partly due to the use of a density-independent excluded volume. It is shown that this flaw can be remedied by use of a hard- sphere entropy functional which successfully interpolates between the original high density estimate and the known behaviour in the low density limit.

Generalized van der Waals theory. IV. Variational determination of the hard-sphere diameter

1981 ◽  
Vol 34 (9) ◽  
pp. 1809 ◽  
Author(s):  
MA Hooper ◽  
S Nordholm
Keyword(s):  
Equation Of State ◽  
Hard Sphere ◽  
Pair Correlation ◽  
Van Der Waals ◽  
Critical Parameters ◽  
Variational Parameter ◽  
Sphere Diameter ◽  
Entropy Functional ◽  
Van Der Waals Theory

The generalized van der Waals theory is here extended by incorporating the hard-sphere diameter as a variational parameter. Moreover, the entropy functional has been chosen so as to accurately reflect the density dependence of the excluded volume revealed by the hard-sphere equation of state. The combined effect of these two improvements yields a theory capable of describing the equation of state of the Lennard- Jones model of classical fluids to an accuracy comparable to that of the pair correlation theories. The results presented here include critical parameters and coexistence and vapour pressure curves.

Generalized van der Waals theory. IX. Excess properties of simple fluid mixtures

1982 ◽  
Vol 35 (2) ◽  
pp. 247 ◽  
Author(s):  
S Nordholm ◽  
PR Harrowell ◽  
K Cheung
Keyword(s):  
Hard Spheres ◽  
Van Der Waals ◽  
Pair Potential ◽  
Distribution Functions ◽  
Single Component ◽  
Excess Properties ◽  
Fluid Mixtures ◽  
Simple Fluid ◽  
Wide Range ◽  
Van Der Waals Theory

The generalized van der Waals theory, recently developed and applied to a wide range of problems involving simple single component fluids, is here extended to uniform simple fluid mixtures. Binary mixtures of hard spheres or particles interacting by Lennard-Jones pair potentials are considered, the Lorentz-Berthelot rules being used to generate the between-species pair-potential. The basic theory is very simple, combining features of cell and mean field theories. Yet it differs considerably from the presently favoured theories of mixtures. The new GvdW theory is implemented at four levels of sophistication but the calculations remain very simple by present standards even for the most accurate form of the theory wherein the effective hard-sphere diameters are determined variationally. The results obtained for the equation of state and thermodynamic excess properties indicate that the very favourable accuracy relative to the simplicity of the theory observed for single component fluids is retained for mixtures. In the case of excess properties calculations for a wide range of equimolar mixtures suggest that the GvdW accuracy is substantially better than that obtained by random mixture or average potential theories but not as good as that obtained by the best theories based on the estimation of the radial distribution functions of the fluid.

Generalized van der Waals theory of hard sphere oscillatory structure

1989 ◽  
Vol 90 (10) ◽  
pp. 5657-5663 ◽  
Author(s):  
B. C. Freasier ◽  
C. E. Woodward ◽  
Sture Nordholm
Keyword(s):  
Hard Sphere ◽  
Van Der Waals ◽  
Oscillatory Structure ◽  
Van Der Waals Theory
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