Full correspondence between asymmetric filling of slits and first-order phase transition lines

Abstract

Adsorption on single planar walls and filling of slits with identical planar walls are investigated in the frame of the density functional theory. In this sort of slits the external potential is symmetric with respect to its central plane. Calculations were carried out by applying both the canonical and grand canonical ensembles (CE and GCE, respectively). The behavior is analyzed by varying the strength of the adsorbate-substrate attraction, the temperature T, and the coverage Γℓ. Results obtained for physisorption of Xe on alkaline surfaces are reported in the present work. Prewetting (PW) lines and wetting temperatures, Tw, are determined from the analysis of adsorption on single walls. The filling of slits is analyzed for temperatures T > Tw. It is found that whenever for a given Xe-substrate combination the adsorption on a single wall exhibits a first-order wetting transition then asymmetric profiles that break the left-right symmetry of the external potential appear in the filling of an equivalent slit. These spontaneously symmetry breaking (SSB) solutions occur in a restricted range of Γℓ with a T-dependent width. In the case of closed slits analyzed in the CE scheme, the obtained asymmetric profiles exhibit lower Helmholtz free energies than the symmetric species and, therefore, could be stabilized in this geometry. For open slits, the GCE scheme yields all the symmetric and SSB states in the corresponding convex regimes of the free energy. It is shown that both the CE and the GCE frames yield three coexistent states, two symmetric and one asymmetric twofold degenerate. Both a PW line and the related SSB effect terminate at the same temperature. For rather strongly attractive surfaces reentrant SSB states are found at a fixed value of T.

Statistical mechanics of fluids confined by polytopes: The hidden geometry of the cluster integrals

“…,n for only one edge (the n-th). Hence, the shape of U(r, ς) ∩ A is determined by both, the dihedral angle and the two-dimensional vector r (2) that lies in a plane orthogonal to ∂A 2,n and goes from ∂A 2,n to r, and thus, 2) ). A 3 is the vertex-type region…”

“…The set B 2,n \ A 2,n contains two disconnected regions one around each endpoint of ∂A 2,n (related to a given vertex). Each of these regions is 2) )dr (2) ,…”

“…where r (2) is the two-dimensional coordinate of a point in A ⊥ 2,n and the last integral is a function of the dihedral angle at the n-th edge. Hence, for the central term in the righthand side of Eq.…”

“…vertex (the n-th). Hence, the shape of U(r, ς) ∩ A is determined by both, the vertex angle and the vector r (2) that goes from ∂A 2,n to r, and thus, g(r) = g 2 (r) = g 2 (r (2) ).…”

“…They constitute a prototypical inhomogeneous system which occupies a small region of the space and may involve a small number of particles. It is well known that the spatial distribution of a fluid confined in a small pore may follow or not the symmetry of the cavity [1,2], and that its properties may be strongly influenced by the geometry of the container. To study the thermodynamic properties of these systems it is customary to introduce several strong assumptions or approximations that simplify the analysis.…”