Nanodrop on a nanorough hydrophilic solid surface: contact angle dependence on the size, arrangement, and composition of the pillars

A two-dimensional nanodrop on a hydrophilic solid surface decorated with nanopillars is examined using a nonlocal density functional theory. It is shown that, in contrast to the commonly used Wenzel formula, even an extremely small roughness can considerably increase the contact angle. The contact angle depends on the distance between pillars, their height and width, as well as their composition. It was found that for all selected pillar heights and compositions, the largest contact angle is obtained when the distance between pillars acquires a size at which the liquid molecules can no longer penetrate between them. The further decrease in the interpillar distance decreases the contact angle, in qualitative agreement with the Cassie-Baxter formula. Considering pillars of various compositions, the role of the gradient of the fluid-solid interaction potential is examined. The presence of such a gradient does not allow the formation of a stable nanodrop on the surface. However, asymmetrical metastable nanodrops can be formed.