Lattice-gas models have found widespread application in the study of gas adsorption and condensation in porous materials due to their ability to adequately capture the changes in thermodynamic properties brought about by fluid confinement while also being computationally inexpensive. The lattice-gas density functional model of Kierlik et al. [1,2] has found particular success in modeling condensation hysteresis in disordered porous materials [3] and gas adsorption in silica aerogels [4], among other applications. Ultimately, the model is most effective when applied to large length scale problems because the lattice spacing must be at least as large as the molecular dimension. This makes the model incompatible with sub-nanometer scale confinement. Alternatively, one could study such nano-confined fluids via the conventional and well-established density functional theory (DFT) for off-lattice fluids, though at significant computational cost when the confinement is asymmetric [5].

We report progress on a new lattice-gas DFT that retains elements of both the coarse-grained DFT of Kierlik et al. and off-lattice conventional DFT. Our approach is well-suited to the study of fluids in highly-disordered or asymmetric confinements and offers reductions in computational demand compared to off-lattice DFT even in ordered or symmetric confinements. We begin by presenting a new density functional for hard-spheres on a cubic lattice of arbitrary discretization based on the off-lattice 'weighted density approximation' of Tarazona [6], and demonstrate that it satisfactorily reproduces the structural properties obtained by simulation. Accordingly, our lattice DFT is not a 'local' density approximation, but imposes local order on the hard-sphere fluid through an estimation of the direct correlation function. Following, we demonstrate how a mean-field attractive perturbation (e.g., that of Weeks, Chandler, and Anderson [7]) may be applied to our hard-sphere lattice DFT and produce a coarse-grained representation of a fluid with a realistic intermolecular interaction.

As an initial application of this new lattice DFT, we study adsorption hysteresis of a lattice Lennard-Jones fluid in classic systems such as slit pores and cylindrical pores to demonstrate both its flexibility and reduced computational cost. We also investigate its use in the study of hydrogen adsorption in metal-organic frameworks and other complex structures. Finally, we discuss end-use applications such as screening experiments of adsorption or condensation in bicontinuous structures and materials with rough surfaces and three-dimensional reconstruction of mesoporous materials.

[1] Kierlik et al., Phys. Rev. Lett., 74, 4361 (1995)

[2] Kierlik et al., Mol. Phys., 95, 341 (1998)

[3] Kierlik et al., Phys. Rev. Lett., 87, 055701 (2001)

[4] Salazar and Gelb, Mol. Phys., 102, 1015 (2004)

[6] Frink and Salinger, J. Comp. Phys., 159, 407 (2000)

[7] Tarazona, Phys. Rev. A, 31, 2672 (1985)

[8] Weeks, Chandler, and Anderson, J. Chem. Phys., 54, 5237 (1971)