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.

Generalized van der Waals theory. II. Quantum effects on the equation of state

1980 ◽  
Vol 33 (9) ◽  
pp. 2029 ◽  
Author(s):  
MA Hooper ◽  
S Nordholm
Keyword(s):  
Equation Of State ◽  
Vapour Pressure ◽  
Van Der Waals ◽  
Translational Motion ◽  
Quantum Effects ◽  
Corresponding States ◽  
Critical Parameters ◽  
Van Der Waals Model ◽  
Van Der Waals Theory ◽  
Law Of Corresponding States

The light gases deviate markedly from the Law of Corresponding States approximately obeyed by the heavier gases. This is due, at least in part, to the quantization of translational motion at higher densities. This effect has been studied within the framework of a generalized van der Waals model. Each particle is treated as moving within a cubic volume determined by the surrounding particles. Changes to the critical parameters and to the shapes of the coexistence and vapour pressure curves are calculated and compare well with experiment, considering the simplicity of our model.

MODEL EQUATION OF STATE OF LIQUID C60 BASED ON HARD SPHERE–YUKAWA POTENTIAL

2006 ◽  
Vol 20 (23) ◽  
pp. 3373-3382 ◽  
Author(s):  
M. BAHAA KHEDR
Keyword(s):  
Computer Simulation ◽  
Equation Of State ◽  
Hard Sphere ◽  
Yukawa Potential ◽  
Coexistence Curve ◽  
Critical Parameters ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
The Fourier Transform ◽  
New Equation

The series mean spherical approximation (SMSA) for the hard sphere–Yukawa (HSYK) fluid is applied to C 60. The energy and range parameters of HSYK potential have been reduced to one parameter by forcing the q→0 limit of the Fourier transform of the potential to be identical to that of the empirical potential of C 60. The new equation of state (EOS) allows us to investigate the liquid–vapor coexistence curve and calculate the thermodynamic properties of liquid C 60. The comparisons with computer simulation results suggest the importance of treating the attractive tail of the potential accurately. The estimated critical parameters Tc=1984.8 K , ρc=0.464 nm -3 and Pc=36.3 bar , which are in good agreement with NVT-Monte Carlo computer simulation predictions. The results are discussed by making reference to previous studies.

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.

Generalized van der Waals theory. I. Basic formulation and application to uniform fluids

1980 ◽  
Vol 33 (9) ◽  
pp. 2013 ◽  
Author(s):  
S Nordholm ◽  
ADJ Haymet
Keyword(s):  
Free Energy ◽  
Equation Of State ◽  
Particle Density ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Energy Functional ◽  
Coarse Grained ◽  
Uniform Structure ◽  
Free Energy Functional ◽  
Van Der Waals Theory

A generalized van der Waals theory is derived on the basis of simple physical and mathematical arguments. The derivation results in a free- energy functional wherein the independent variable is a coarse-grained particle density. It is assumed that a well defined particle density dominates the free energy and this density is to be obtained by minimizing the free energy functional. The variational theory so obtained can be applied to non-uniform fluids. In the present work the possibility of stable non-uniform structure is neglected and the theory is applied to uniform fluids. It then produces an equation of state identical in form to that proposed originally by van der Waals but the excluded volume is only about half as large in the three-dimensional case. Applications to several two- and three-dimensional systems indicate that the new equation of state is a distinct improvement over the traditional van der Waals theory when the full range of fluid densities is considered. The quantitative accuracy in the case of simple uniform fluids is sufficient to warrant further development and exploitation of the theory.

Sign in / Sign up

Export Citation Format

Share Document