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

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. 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.

Applications of the augmented van der waals theory of fluids

1978 ◽  
Vol 75 ◽  
pp. 347-352 ◽  
Author(s):  
Aleksander Kreglewski ◽  
Stephen S. Chen
Keyword(s):  
Van Der Waals ◽  
Van Der Waals Theory
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