scholarly journals Analysis of a First-order Perturbation Theory for the Direct Correlation Function of Dense Fluids

1972 ◽  
Vol 50 (19) ◽  
pp. 3135-3143
Author(s):  
S. W. Brelvi ◽  
J. P. O'Connell
Keyword(s):  
Correlation Function ◽  
Hard Sphere ◽  
Isothermal Compressibility ◽  
Critical Density ◽  
Pair Potential ◽  
Distribution Functions ◽  
Scattering Data ◽  
Intermolecular Potential ◽  
Sphere Diameter ◽  
Direct Correlation Function

An approximate expression for the direct correlation function of a real fluid in terms of its intermolecular potential and hard-sphere distribution functions is examined. Calculations for argon using the Percus–Yevick hard-sphere distribution functions are compared with molecular correlation functions from X-ray scattering data and the macroscopic integral of the correlation function related to the isothermal compressibility. The results are not satisfactory for any pair potential unless the parameters are made state dependent. However, since partial compensation occurs on integration, fairly good correlation of the isothermal compressibility can be obtained up to twice the critical density (except near the critical point itself) using Lennard–Jones (6–12) potential parameters obtained from second virial coefficient data and the Barker–Henderson hard-sphere diameter.

The gas-liquid surface of the penetrable sphere model. II

1978 ◽  
Vol 358 (1694) ◽  
pp. 267-280 ◽  
Keyword(s):  
Surface Tension ◽  
Correlation Function ◽  
Liquid Surface ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Direct Correlation Function ◽  
Sphere Model ◽  
One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

The Specific Heat of Liquid Metals

1991 ◽  
Vol 46 (5) ◽  
pp. 416-418
Author(s):  
K. N. Khanna ◽  
Abdul Quayoum
Keyword(s):  
Correlation Function ◽  
Specific Heat ◽  
Reference System ◽  
Hard Sphere ◽  
Random Phase Approximation ◽  
Liquid Metals ◽  
Random Phase ◽  
Direct Correlation Function ◽  
Phase Approximation ◽  
Semi Empirical

AbstractThe specific heat of liquid metals is calculated using a fluid of Percus-Yevick plus tail as a reference system together with the Cumming potential in a random-phase approximation. It is shown that the improved semi-empirical hard sphere direct correlation function proposed by Colot et al. leads to a drastic improvement of Cp values over the HS model

Solvation force in a hard-sphere fluid

1999 ◽  
Vol 77 (8) ◽  
pp. 585-590 ◽  
Author(s):  
M Moradi ◽  
M Kavosh Tehrani
Keyword(s):  
Correlation Function ◽  
Hard Sphere ◽  
Hard Core ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Direct Correlation Function ◽  
Functional Theory ◽  
Hard Sphere Fluid ◽  
Generalized Mean ◽  
Simulation Results

The solvation force in a hard-sphere fluid is obtained by the denisty functional theory proposed by Rickayzen and Augousti. The direct correlation function (DCF) with the tail introduced by Tang and Lu is used. This DCF (hereafter TL DCF ) is postulated to hold the Yukawa form outside the hard core; and the generalized mean spherical approximation (GMSA) approach has been applied. The results are compared with those obtained by using the Percus-Yevick (PY) DCF. These results are also compared with those of Monte Carlo simulations. At low densities and fairly high densities the results are in agreement. But at high densities there is more oscillation in the solvation force obtained by using TL DCF in comparison with the PY DCF. There are no simulation results at high densities to be compared with these results.PACS No. 61.20

Optimised Cluster Theory for the Triangular Well Potential

1980 ◽  
Vol 35 (4) ◽  
pp. 412-414
Author(s):  
K. N. Swamy ◽  
P. C. Wankhede
Keyword(s):  
Monte Carlo ◽  
Radial Distribution ◽  
Hard Sphere ◽  
Distribution Functions ◽  
Radial Distribution Functions ◽  
Sphere Diameter ◽  
Cluster Theory ◽  
Monte Carlo Calculations ◽  
Triangular Well Potential

Abstract The optimised cluster theory of Andersen and Chandler has been applied to calculate the radial distribution functions of a triangular well fluid with the width a the hard sphere diameter The results agree well with Monte Carlo Calculations of Card and Walkley.

The direct correlation function in hard sphere fluids

1987 ◽  
Vol 87 (4) ◽  
pp. 2263-2270 ◽  
Author(s):  
R. D. Groot ◽  
J. P. van der Eerden ◽  
N. M. Faber
Keyword(s):  
Correlation Function ◽  
Hard Sphere ◽  
Direct Correlation Function

Direct correlation function: Hard sphere fluid

1975 ◽  
Vol 63 (2) ◽  
pp. 601-607 ◽  
Author(s):  
Douglas Henderson ◽  
E. W. Grundke
Keyword(s):  
Correlation Function ◽  
Hard Sphere ◽  
Direct Correlation Function ◽  
Hard Sphere Fluid

scholarly journals Entropy of mixing of NaCd and AlMg molten alloys

1970 ◽  
Vol 9 (9) ◽  
pp. 25-28
Author(s):  
SK Chatterjee ◽  
LC Prasad ◽  
A Bhattarai
Keyword(s):  
Complex Formation ◽  
Hard Sphere ◽  
Pair Potential ◽  
Liquid Alloys ◽  
Sphere Diameter ◽  
Nearest Neighbour ◽  
Formation Model ◽  
Pseudopotential Theory ◽  
Entropy Of Mixing ◽  
Theory And Experiment

The complex formation model is used to explain the anomalous behaviour of entropy of mixing of NaCd and AlMg liquid alloys as a function of concentration.The interionic pair potential Φij(r) evaluated within the framework of pseudopotential theory which in turn is used to obtain the values of hard-sphere diameter of NaCd and AlMg liquid alloys. The hard-sphere diameter is used to evaluate the concentration dependent anamoly in entropy of mixing which occurs due to preferential ordering of unlike atoms as nearest neighbour on NaCd and AlMg liquid alloys, which could be simultaneously understood with the help of complex formation model. The computed value of Entropy of mixing (SM) from pseudopotential theory is positive at all concentration range except 0.8≤Ccd≤0.9 in NaCd liquid alloys. The disagreement between theory and experiment might be due to parameterisation of hard- sphere diameter of the complex (σ3) and Ψcomp. Key Words: Entropy of mixing; Pseudopotential theory; Hard-sphere diameter; Pair-Potential. DOI: http://dx.doi.org/10.3126/sw.v9i9.5513 SW 2011; 9(9): 25-28

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.

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