Thermodynamics and Characteristics of Heterogeneous Nucleation on Fractal Surfaces

Clarifying heterogeneous nucleation process on fractal surfaces is an important issue to understand its thermodynamic principles and forward the engineering aspects. We developed a thermodynamic model to capture the process of forming a crystal or drop embryo on fractal surfaces and the corresponding characteristic parameters. We showed that the differences between the critical size of the embryos on the fractal surfaces and those on the flat surfaces are negligible for the hydrophobic nuclei, but become significant for the hydrophilic nuclei. We reported the available domains of forming the critical embryos and obtained the shape function for the first time. The results also recover the data reported in the literature. Finally, we present the possible mechanisms of vanishing of the energy barriers against forming the critical embryos on the fractal surfaces as the apparent contact angle is relatively small. The obtained results may help to engineer the nucleation process by designing substrate surfaces in a fractal structure.