Configurational entropy of a hard sphere system using modified density functional approximation (MWDA)

2019 ◽  
Author(s):  
Arijit Mondal ◽  
Leishangthem Premkumar ◽  
Shankar P. Das
Keyword(s):  
Hard Sphere ◽  
Density Functional ◽  
Configurational Entropy ◽  
Functional Approximation

Density profiles of fluids in some special symmetries

1995 ◽  
Vol 73 (7-8) ◽  
pp. 432-439 ◽  
Author(s):  
Seong-Chan Lee ◽  
Zi-Hong Yoon ◽  
Soon-Chul Kim
Keyword(s):  
Free Energy ◽  
Computer Simulations ◽  
Hard Sphere ◽  
Density Functional ◽  
Energy Functional ◽  
Empirical Method ◽  
Density Profiles ◽  
Functional Approximation ◽  
Free Energy Functional ◽  
Lennard Jones

A free-energy-functional approximation based on a semi-empirical method is proposed. The main advantage of the free-energy-functional approximation is its accuracy compared with other models and its relative simplicity compared with other well-known weighted-density approximations. The free-energy-functional approximation is applied to predict the density profiles of the hard-sphere fluids and the Lennard–Jones fluids in some special symmetries. For the density profiles near a hard flat wall, the results reproduced the hard-sphere oscillatory structures qualitatively and quantitatively. For the density profiles of hard-sphere fluids confined in a spherical cage, the results are also in a fair agreement with the computer simulations. For Lennard–Jones fluids, two kinds of density-functional perturbation theories, the density-functional mean-field theory (DFMFT) and the density-functional perturbation theory (DFPT), examined. The results show that at higher temperature the DFPT compares well with computer simulations. However, the agreement deteriorates slightly as the temperature of the Lennard–Jones fluids is reduced. These results demonstrate that both the free-energy-functional approximation and the DFPT succesfully describe the inhomogeneous properties of classical fluids.

DENSITY FUNCTIONAL APPROXIMATION FOR NON-HARD SPHERE FLUIDS SUBJECTED TO EXTERNAL FIELDS

2006 ◽  
Vol 20 (04) ◽  
pp. 469-493 ◽  
Author(s):  
SHIQI ZHOU
Keyword(s):  
Density Profile ◽  
Hard Sphere ◽  
Density Functional ◽  
Hard Core ◽  
External Fields ◽  
Functional Theory ◽  
Functional Approximation ◽  
Theoretical Predictions ◽  
Present Formalism ◽  
Square Well

A theoretical way is proposed, by which any hard sphere density functional approximation (DFA) can be applied to non-hard sphere fluids for the calculation of density profile in the framework of density functional theory (DFT). Used as examples, the present formalism is combined respectively with two recently proposed hard sphere DFAs to predict the density profile of Lennard–Jones (LJ) fluid, hard core square well (SW) fluid and penetrable potenial fluid subjected to diverse external fields. Extensive comparison between theoretical predictions and corresponding simulation results shows that the present theoretical way, when combined with an accurate hard sphere DFA, can perform well for calculating the density profile of the non-uniform fluids of the above mentioned potentials. Concretely speaking, for LJ and hard core SW fluid, even a less accurate FEDFA is sufficient, while for extreme potential such as the penetrable potenial, a more accurate adjustable parameter free version of LTDFA is needed to combine with the present theoretical way to predict density profile satisfactorily. The advantage of the proposed theoretical way is that the resultant DFA is applicable to both subcritical and supercritical temperature cases, thereby overcoming the disadvantages of previous two categories of DFT approach.

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