Fourier space approach to the classical density functional theory for multi-Yukawa and square-well fluids

Abstract

We present a Fourier space density functional approach for hard particles with attractive interactions, which is based on a previously developed two-dimensional approach [S. Hlushak, W. Rżysko, and S. Sokołowski, J. Chem. Phys. 131, 094904 (2009)] for hard-sphere chains. The interactions are incorporated by means of a three-dimensional Fourier image of the direct correlation function that is obtained from the first-order mean-spherical approximation. In order to improve the computational efficiency, we make extensive use of fast Fourier transforms for calculating density convolution integrals. A two-dimensional implementation of the new density functional approach, based on the expansion of the functional around the bulk fluid density, is used to study structure and adsorption of two model fluids in narrow cylindrical pores. We also investigate two methods that improve the accuracy of the theory as compared to the conventional DFT approach, which expands the free energy functional around the bulk fluid density: One a variant of the reference fluid density functional theory used by Gillespie et al. [Phys. Rev. E 68, 031503 (2003)], and the second a weighted density approach with energy route thermodynamics. Results from these two methods are compared to the conventional approach and also to the results of Monte Carlo simulations. We find that the method of Gillespie et al. and the weighted density approach with energy route thermodynamics yield significant improvement over the conventional approach.

Exponential approximation for one-component Yukawa plasma

“…28,29 Nonetheless, the FMSA theory is only slightly less accurate than the full MSA theory, and in contrast to the latter is "solvable" at any thermodynamic conditions. 30 Its simplicity and robustness makes it useful for application in the inverse design approaches, 31 formulation of density functional theories, [32][33][34][35][36][37] and various other advanced approximations of the liquid-state theory. [38][39][40][41][42] In this contribution a new theory based on the exponential approximation 44 will be proposed for the description of the OCYP systems.…”

A hybrid perturbed-chain SAFT density functional theory for representing fluid behavior in nanopores

“…The weighting functions have been studied extensively, [32][33][34][35] and a comprehensive introduction of the weighted density approximation can be found in the review of Zhou. 36 A common normalized mean field weighting function is defined as w disp (r) = u attr (r)/ d ru attr (r), where u attr (r) is the attractive potential.…”