Continuous condensation in nanogrooves
Physical review. E
We consider condensation in a capillary groove of width L and depth D, formed by walls that are completely wet (contact angle θ=0), which is in a contact with a gas reservoir of the chemical potential μ. On a mesoscopic level, the condensation process can be described in terms of the midpoint height ℓ of a meniscus formed at the liquid-gas interface. For macroscopically deep grooves (D→∞), and in the presence of long-range (dispersion) forces, the condensation corresponds to a second order
... transition, such that ℓ∼ (μ_cc-μ)^-1/4 as μ→μ_cc^- where μ_cc is the chemical potential pertinent to capillary condensation in a slit pore of width L. For finite values of D, the transition becomes rounded and the groove becomes filled with liquid at a chemical potential higher than μ_cc with a difference of the order of D^-3. For sufficiently deep grooves, the meniscus growth initially follows the power-law ℓ∼ (μ_cc-μ)^-1/4 but this behaviour eventually crosses over to ℓ∼ D-(μ-μ_cc)^-1/3 above μ_cc, with a gap between the two regimes shown to be δ̅μ∼ D^-3. Right at μ=μ_cc, when the groove is only partially filled with liquid, the height of the meniscus scales as ℓ^*∼ (D^3L)^1/4. Moreover, the chemical potential (or pressure) at which the groove is half-filled with liquid exhibits a non-monotonic dependence on D with a maximum at D≈ 3L/2 and coincides with μ_cc when L≈ D. Finally, we show that condensation in finite grooves can be mapped on the condensation in capillary slits formed by two asymmetric (competing) walls a distance D apart with potential strengths depending on L.