MODELING OF ADSORPTION IN PORES BY MEANS OF THIRD ORDER + SECOND ORDER PERTURBATION DENSITY FUNCTIONAL THEORY AND MONTE CARLO SIMULATION

2007 ◽  
Vol 21 (20) ◽  
pp. 3601-3619 ◽  
Author(s):  
A. JAMNIK ◽  
F. LUO
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Density Functional ◽  
Hard Core ◽  
Second Order ◽  
Order Perturbation ◽  
Spherical Approximation ◽  
Third Order ◽  
Simulation Data ◽  
Physical Solution

Results for the inhomogeneous structure of the hard-core repulsive Yukawa (HCRY) fluid and of the hard-core attractive Yukawa (HCAY) fluid in planar and in spherical micropores are presented. The density profiles are obtained by the recently proposed third order + second order perturbation density functional approximation (DFA) and compared with the results of open ensemble Monte Carlo simulation. As known from other recent studies, the reliability of the DFA theory considered in this work is very sensitive to the accuracy of the required bulk direct correlation function (DCF) obtained by the solution of the Ornstein–Zernike (OZ) equation combined by a suitable closure relation. Comparison between the DFA results and simulation data shows that for the HCRY fluid, the DFA theory utilizing the DCF obtained by the OZ equation supplemented by Malijevsky–Labik approximation satisfies the required accuracy for a broad range of conditions. The results for the nonuniform HCAY fluid obtained in our previous work via the mean spherical approximation (MSA)/OZ DCF showed larger disagreement in some cases. In addition, the MSA/OZ equation for the HCAY model failed to have a physical solution at subcritical temperatures when approaching the vapor–liquid coexistence curve. For this reason, an improved version of the theory incorporating nonlinear optimized random phase approximation (ORPA) in the OZ equation for the RDF calculation of the HCAY fluid is applied. This leads to much better agreement of the DFA predictions with the simulation data. In addition, the calculations can also be performed at the conditions at which the MSA/OZ equation has no physical solution.

STRINGENT VERIFICATION OF THIRD ORDER + SECOND ORDER PERTURBATION DENSITY FUNCTION THEORY: BASED ON SHORT-RANGE SQUARE WELL POTENTIAL

2010 ◽  
Vol 24 (32) ◽  
pp. 6291-6306
Author(s):  
YUANTAO XIANG ◽  
A. JAMNIK
Keyword(s):  
Short Range ◽  
Density Functional ◽  
Perturbation Expansion ◽  
Second Order ◽  
Order Perturbation ◽  
Perturbation Scheme ◽  
Third Order ◽  
Density Profiles ◽  
Ensemble Monte Carlo ◽  
Square Well

A recently proposed third order + second order perturbation density functional theory (DFT) approach is made self-contained by using a virial pressure from the Ornstein–Zernike integral equation theory as input to determine the numerical value of an associated physical parameter. An exacting examination is formulated by applying the self-contained perturbation DFT approach to a short-range square well fluid of low temperatures subject to various external fields and comparing the theoretical results for density profiles to the corresponding grand canonical ensemble Monte Carlo simulation results. The comparison seems favorable for the third order + second order perturbation DFT approach as a self-contained and accurate predictive approach. It is surprisingly found that this self-contained third order + second order perturbation DFT approach is displayed outstandingly even if a deep SW perturbation term is being accounted for by a second order perturbation expansion. A discussion is presented about potential opportunity for this perturbation scheme.

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