Contact angles on surfaces using mean field theory: nanodroplets vs. nanoroughness

With emerging systems and applications accessing features within the nanoregime, whether due to droplet size or feature size, understanding the wetting behaviours of these materials is an area of ongoing interest. Theoretical studies, providing a fundamental understanding of how contact angle behaviour changes at these length scales, are important to further such work. This study provides a comprehensive examination of the application of lattice density functional theory (LDFT) to a pillared surface to confirm the suitability of LDFT for studying more complex surfaces. Incorporation of the correct level of details for the fluid-wall interaction was found to produce all of the qualitative changes that have been observed in off-lattice theories. Though previous reports have provided apparently conflicting results, the more comprehensive examination of feature sizes provided here demonstrates that those behaviours are consistent with one another. The well-studied failure of macroscopic models that results from non-negligible line tension contributions and small droplets to feature size ratios was demonstrated using LDFT. Furthermore, the failure of macroscopic models resulting upon reduction in feature size, which has been considered less often, is clearly demonstrated. A key assumption of the macroscopic models is the consistent interaction between surface and fluid regardless of the flatness or roughness of the surface. The density functional results presented here show that, for the smallest features, this is not the case and demonstrate that macroscopic models do not predict the correct contact angle for droplets of any size on nanorough surfaces.