Density functional theory of size-dependent surface tension of Lennard-Jones fluid droplets using a double well type Helmholtz free energy functional

2011 ◽  
Vol 135 (12) ◽  
pp. 124710 ◽  
Author(s):  
Satinath Ghosh ◽  
Swapan K. Ghosh
Keyword(s):  
Density Functional Theory ◽  
Surface Tension ◽  
Free Energy ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Energy Functional ◽  
Functional Theory ◽  
Size Dependent ◽  
Free Energy Functional ◽  
Lennard Jones

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.

scholarly journals Modelling inelastic Granular Media Using Dynamical Density Functional Theory

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
B. D. Goddard ◽  
T. D. Hurst ◽  
R. Ocone
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Granular Media ◽  
Helmholtz Free Energy ◽  
Pair Correlation ◽  
Collision Operator ◽  
Energy Functional ◽  
Interparticle Interactions ◽  
Functional Theory ◽  
Closure Relations

AbstractWe construct a new mesoscopic model for granular media using Dynamical Density Functional Theory (DDFT). The model includes both a collision operator to incorporate inelasticity and the Helmholtz free energy functional to account for external potentials, interparticle interactions and volume exclusion. We use statistical data from event-driven microscopic simulations to determine the parameters not given analytically by the closure relations used to derive the DDFT. We numerically demonstrate the crucial effects of each term and approximations in the DDFT, and the importance of including an accurately parametrised pair correlation function.

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