Geometry Dominated Fluid Adsorption on Sculptured Substrates

Experimental methods allow the shape 1, 2 and chemical composition 3 of solid surfaces to be controlled at a mesoscopic level. Exposing such structured substrates to a gas close to coexistence with its liquid can produce quite distinct adsorption characteristics compared to that occuring for planar systems 4 , which may well play an important role in developing technologies such as super-repellent surfaces 5, 6 or micro-fluidics 7, 8. Recent studies have concentrated on adsorption of liquids at rough 9–11 and heterogeneous 12 substrates and the charac-terisation of nanoscopic liquid films 13. However, the fundamental effect of geometry has hardly been addressed. Here we show that varying the shape of the substrate can exert a profound influence on the adsorption isotherms allowing us to smoothly connect wetting and capillary condensation through a number of novel and distinct examples of fluid interfacial phenomena. This opens the possibility of tailoring the adsorption properties of solid substrates by sculpturing their surface shape. The interaction of a gas with a solid surface is usually mediated by an ad-sorbed (microscopically thin) layer of liquid which is ultimately responsible for the rich behaviour of the solid-gas interface 14. When the gas coexists with its liquid, an increase in the temperature is accompanied by an increase in the thickness of this adsorbed layer which attains macroscopic character at the wetting temperature T w. At this temperature, the contact angle of a macroscopic drop placed on the surface vanishes and the liquid, which is said to wet that solid surface, spreads. Alternatively, this situation can be reached for a fixed temperature T above T w (but below the critical temperature T c) by increasing the pressure towards the coexistence value p co (T) or, equivalently, by increasing the chemical potential towards µ co (T) (see Fig. 1). This phase transition, known as complete wetting, has been intensely studied for fundamental as well as for important technological reasons 14. Theoretical predictions confirmed by experiments have shown that the thickness ℓ π of the adsorbed layer diverges when it approaches coexistence with a non-universal exponent β co which is dependent on the range of the (solid-fluid and fluid-fluid) particle interactions involved in the system: ℓ π ∼ |∆µ| −βco , where ∆µ ≡ µ−µ co is the chemical potential (relative to the chemical potential at coexistence) 14 which, for dilute gases, is related to the partial pressure by ∆µ = …