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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.

Using the constrained lattice density functional theory, in this work we show that when the size of critical nucleus for vapor-liquid transition is comparable to the distance between seed particles (or active sites on solid surfaces), a cooperative effect in nucleation processes is found. More specifically, neighboring seed particles are found to nucleate jointly the phase transition with a lower nucleation barrier and a different morphology of critical nucleus compared to those from an isolated seed particle. In addition, the cooperative effect, including the decrease of nucleation barrier and the morphology change of critical nucleus, is found to depend on the distance between seed particles, the fluid-solid interaction, and the particle size.

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