(757e) Fourier Space Based Approach to Classical Density Functional Theory

Multidimensional density functional theory approach for square-well and Lennard-Jones chain and simple fluids in various confinement geometries was implemented. The approach uses Fast Fourier Transform (FFT) to integrate the convolution-like integrals appearing during calculation of the weighted densities and contribution of the attractive interactions. The latter are taken into account using the Fourier transform of the direct correlation function (DCF), derived by means of first-order mean spherical approximation (FMSA) theory [1,2,3,4]. It is demonstrated that the Fourier transforms of the FMSA DCFs are much simpler than their real-space counterparts and the use of FFT significantly increases computing performance, allowing the two-dimensional calculations to be performed on a single-processor machine.

The approach is tested against Monte-Carlo simulation data for model fluids confined in few geometries, including narrow slit and cylindrical pores. The latter case, because of the strong confinement of the fluid, constitutes a challenge for the usual theories based on the expansion of the thermodynamics around the bulk density. The overcome the difficulty we proposed a variant of the reference fluid density functional theory of Gillespie et al [5], but with the reference density functional kept constant over the pore volume. The approach shows improvements in the predictions of the density profiles and adsorption isotherms when compared to the results of the usual theories. Additionally a functional based on the energy route of FMSA thermodynamics is implemented and tested. It appears to be the most accurate for the models studied.

Several different approaches were tested for confined chain molecules. Inclusion of the contact value contribution of the attractive potential improves the prediction of density profiles at low densities, while at high densities, where the structure is dominated by hard-sphere repulsions, the inaccuracies seems to be mainly due to the simplifications in the inhomogeneous contact value of the monomer radial distribution function, and due to the ideal chain approximation, adopted for the description of chain conformations.

References

[1] Y. Tang, J Chem. Phys. 127, 164504 (2007).

[2] S. Hlushak, A. Trokhymchuk, S. Sokolowski, J Chem. Phys. 130, 234511 (2009).

[3] Y. Tang, and B. C.-Y. Lu, . Chem. Phys., 99, 9828 (1993).

[4] Y. Tang and B. C.-Y. Lu J. Chem. Phys., 100, 6665 (1994).

[5] D. Gillespie, W. Nonner, R. S. Eisenberg, Phys. Rev. E, 68, 031503 (2003).