Phase loops in density-functional-theory calculations of adsorption in nanoscale pores

Abstract

Phase loops with multiple solutions are observed in calculations of lattice density-functional theory. It is shown that the standard numerical methods for solving such problems distort the solution. A technique is proposed to obtain multiple solutions for phase equilibria in confined fluids. This method gives the entire phase equilibrium curve, including hidden points which determine wetting transitions and capillary condensation. A synergetic effect of walls on adsorption in nanoscale pores is analyzed.

Adsorption and Phase Transitions in Slit-like Pores with Differently Adsorbing Walls

“…No more than one molecule is permitted at a given lattice site, and each pair of molecules in adjacent sites contributes ε to the potential energy. It can be shown (11)(12)(13)(14) that in the mean-field approximation the grand potential of the system is = (ε/2) …”

“…According to our best knowledge no such studies have been carried out so far. Our investigations are carried out by using a lattice gas model and a 1 To whom correspondence should be addressed.Bragg-Williams (mean-field) (11, 12) type [called also (13,14) "density functional"] approach.Let us formulate the model first. We consider a gas on a cubic lattice, confined within a slit-like pore of the width L + 2.…”

Reliable density‐functional‐theory calculations of adsorption in nanoscale pores

“…As empha-Ž . sized by Aranovich and Donohue 1999 , failure to find all the stationary points may not only result in the loss of important information, but also in an incorrect or distorted view of the adsorption isotherm predicted by the model. Therefore, there is a clear need for a nonlinear equation solving method capable of reliably finding all the stationary points.…”

“…In many situations a more reliable approach is the method of Ara-Ž . novich and Donohue 1998Donohue , 1999 . This is a ''path tracking'' Ž .…”

“…mans, 1962;Altenberger and Stecki, 1970 . However, in other situations, especially in regions of phase transitions and hysteresis effects, which are often the regions of most interest, the equation system to be solved has multiple solutions ŽAranovich and Donohue, 1999;Ravikovitch, . 1998, 2000;Lastoskie et al, 1993 , and therefore, solving the system is not straightforward.…”