Density Functional Theory for Studies of Multiple States of Inhomogeneous Fluids at Solid Surfaces and in Pores
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and P.I. RAVIKOVITCH A.V. NEIMARKn' 1 TRI/Princeton, 601 Prospect Av., Princeton, NJ, 08542-0625, [email protected] 2 Chemical Engineering/Yale University, New Haven, CT, 06520-8286 ABSTRACT Two new versions of the density functional theory (DFT), which correspond to the canonical ensemble and the Gibbs ensemble respectively, are applied to study multiple equilibrium states and associated hysteresis on examples of capillary condensation of argon in nanopores of MCM-41 mesoporous molecular sieves and Kr adsorption on carbon. The canonical ensemble DFT (CEDFT) allows us to trace not only the stable and the metastable states along the hysteresis loop, but also the unstable states inside the hysteresis loop. The Gibbs ensemble DFT (GEDFT) allows us to determine precisely the points of equilibrium phase transitions in confined fluids. INTRODUCTION Multiple states of confined inhomogeneous fluids are well documented in surface science. They manifest themselves in step-wise phase transitions and hysteresis behavior, which are inherent to thin films between colloidal particles, soap films, wetting and adsorption films on solid surfaces, fluids in pores, etc. Some of the prominent examples are the capillary condensation phenomena in nanopores and the adsorption-desorption transitions in mono- and multilayers. Better understanding of the specifics of confined fluid transformations is needed in a variety of practical applications such as stability of colloids, fabrication of nanostructures, separations, lubrication, fluid flow and sorption in porous media. The density functional theory (DFT) has been used by many authors for analyses of inhomogeneous fluids at solid surfaces and in pores (for a comprehensive review, see [I]). In particular in our earlier papers [2-5], we employed the non-local density approximation due to Tarazona [6] to model hysteresis phenomena such as capillary condensation/evaporation in MCM-41 mesoporous molecular sieves and phase transitions in adsorption multilayers on carbon. Conventional versions of the DFT imply minimization of the grand thermodynamic potential with respect to the fluid density within fixed solid boundaries at the given temperature T and chemical potential p. They correspond to the grand canonical (,u-V-7) ensemble and are below referred to as GCE DFT. In this paper, we apply two new versions of the DFT, which correspond to the canonical ensemble (CE DFT) and the Gibbs ensemble (GE DFT) respectively. We study capillary condensation of Ar in nanopores of MCM-41 mesoporous molecular sieves and Kr adsorption on carbon. The GCE DFT studies of these systems have been reported in the previous MRS meeting [5]. It was shown that GCE DFT qualitatively describes these phenomena and is in a satisfactory agreement with experimental adsorption/desorption. CE DFT allowed us to trace not only the stable and the metastable states along the hysteresis loop, which can be done with GCE DFT, but also the unstable states inside the hysteresis loop. The obtained isotherms are alike the van-de
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