Equilibrium Statistical Physics

Density functional study of condensation in capped capillaries

“…This allows us to obtain isotherms of wetting and phase coexistence curves of various transitions. In order to verify the numerical implementation, we have performed convergence tests of the computer code developed to solve (14) in 2D with LDA and WDA for the hard sphere part of the functional, see Appendix B. We also verified that the exact Gibbs adsorption rule -see below -and the appropriate planar contact sum rules [25,43] are satisfied by the density profiles we obtain.…”

“…For fixed T we can obtain a set of solutions, {ρ (r)} µ , to the above equation parametrized by µ. The grand potential Ω (µ) is a concave function of µ [44], so the density profiles which satisfy (14) and correspond to stable (and metastable) fluid configurations, also correspond to concave branches of Ω [{ρ (r)} µ ] as a function of µ. The stable configurations (unlike the metastable ones) also form the lower envelope of Ω [{ρ (r)} µ ] as a function of µ.…”

“…Usually the bulk parts are equal in both coexisting phases, but the excess parts are different [45]. We solve (14) and (15) numerically. Wetting of a planar wall and a slit pore are treated as one-dimensional (1D) numerical problems, whereas a capped capillary and a right-angled wedge as two-dimensional (2D) problems.…”

“…In this case, α = π/4 and we can obtain T f by computing Θ (T ) and solving Θ (T f ) = π/4 graphically (see Appendix C and figure C1 therein). The fluid density distribution inside the wedge, ρ wdg (x, y), is found from (14) by using (7) to set V (r) ≡ V wdg (x, y) in (14). The curve µ wpf (T ) is obtained using (15).…”

“…The density functional theory (DFT) for fluids meets these requirements by offering a classical framework which introduces the spatial dependence of the fluid density in the equation of state by approximating the free energy of the fluid as a functional of the one-body fluid number density. Reasonably far from critical points, the results of DFT are rather robust in describing the interfacial properties and structure of soft systems [11][12][13][14]. One can obtain interfaces, menisci shapes, and even complete surface phase diagrams with the single systematic approach offered by DFT, which is also significantly less expensive computationally compared to molecular dynamics simulations [15,16].…”