Does adsorption in a single nanogroove exhibit hysteresis?

A simple fluid, in a microscopic capillary capped at one end, is studied by means of fundamental measure density functional. The model represents a single, infinitely long nanogroove with long-range wall-fluid attractive (dispersion) forces. It is shown that the presence or absence of hysteresis in adsorption isotherms is determined by wetting properties of the wall as follows: Above wetting temperature, $T_w$, appropriate to a single wall of the groove, the adsorption is a continuous process corresponding to a rise of a meniscus from the capped to the open end of the groove. For a sufficiently deep capillary the meniscus rise is shown to be a steep, yet continuous process taking place near the capillary condensation of a corresponding slit. However, for temperatures lower than $T_w$ the condensation exhibits a first-order transition accompanied by hysteresis of the adsorption isotherm. Finally, it is shown that hysteresis may occur even for $T>T_w$ as a consequence of prewetting on the side and bottom walls of the groove.