In this work, we propose a method to stabilize a nucleus in the framework of lattice density-functional theory (LDFT) by imposing a suitable constraint. Using this method, the shape of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as input. As an application of this method, we study the nucleation behavior of vapor-liquid transition in nanosquare pores with infinite length and relate the observed hysteresis loop on an adsorption isotherm to the nucleation mechanism. According to the dependence of hysteresis and the nucleation mechanism on the fluid-wall interaction, w , in this work, we have classified w into three regions ( w>0.9 , 0.1< or =w< or =0.9 , and w<0.1 ), which are denoted as strongly, moderately, and weakly attractive fluid-wall interaction, respectively. The dependence of hysteresis on the fluid-wall interaction is interpreted by the different nucleation mechanisms. Our constrained LDFT calculations also show that the different transition paths may induce different nucleation behaviors. The transition path dependence should be considered if morphological transition of nuclei exists during a nucleation process.

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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.

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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.