Condensation of droplets on nanopillared hydrophobic substrates.

Using the constrained lattice density functional theory, we investigated the mechanism of droplet condensation, including droplet nucleation and growth, on nanopillared substrates. We find that similar to a macroscopic droplet on such a substrate, the critical nucleus also exhibits either the Wenzel or Cassie wetting state, depending on both the pillar height and the interpillar spacing. Our calculations show that there exists a critical value of the interpillar spacing, above which the critical nucleus is always in the Wenzel state and the pillared substrate always promotes the nucleation as compared to the smooth substrate, regardless of the pillar height. Below the critical interpillar spacing, however, the pillars always inhibit the nucleation, and the wetting state of the critical nucleus depends on the pillar height. Furthermore, our results demonstrate that the wetting state of the critical nuclei is not necessarily the wetting state of the formed microdroplets: droplets originated from the critical nuclei in the Wenzel state may change into the Cassie state spontaneously during the droplet growth process if the pillar height is greater than a critical value.