Hierarchical structured surfaces enhance the contact angle of the hydrophobic (meta-stable) state

Abstract

The relation between wetting properties and geometric parameters of fractal surfaces are widely discussed on the literature and, however, there are still divergences on this topic. Here we propose a simple theoretical model to describe the wetting properties of a droplet of water placed on a hierarchical structured surface and test the predictions of the model and the dependence of the droplet wetting state on the initial conditions using simulation of the 3-spin Potts model. We show that increasing the auto-similarity level of the hierarchy – called n – does not affect considerably the stable wetting state of the droplet but increases its contact angle. Simulations also explicit the existence of metastable states on this type of surfaces and shows that, when n increases, the metastability becomes more pronounced. Finally we show that the fractal dimension of the surface is not a good predictor of the contact angle of the droplet.

Chemical physics of controlled wettability and super surfaces

“…In reference [13], the impact of substrate fractality on the wetting behavior of droplets is investigated through a combination of a simple theoretical model and simulations employing the 3-spin Potts model for surfaces featuring hierarchical structures. This study provides insights into some open questions, including the relationship between the fractal dimension of the substrate and the contact angle of the droplet.…”

The fractal geometry of polymeric materials surfaces: surface area and fractal length scales

“…Models have been developed to describe macroscopic properties based on the nano- and micro-behaviour of fractal-like surfaces. 68–72 In ref. 72, a relation between wetting properties and geometric parameters of a deterministic fractal model has been suggested.…”

“…68–72 In ref. 72, a relation between wetting properties and geometric parameters of a deterministic fractal model has been suggested. It was found that the surface fractal dimension alone is a poor predictor of the contact angle of a droplet, suggesting that possibly the random nature of real surfaces is actually playing a major role.…”