Wetting of nanopatterned surfaces: the hexagonal disk surface

Metropolis Monte Carlo simulations are used to investigate the wetting of chemically nanopatterned surfaces, for the case of hexagonal disk patterns where liquid wishes to wet high-energy circular patches but not wet the background surface. We calculate the density profiles of saturated liquid adsorbed on a variety of such substrates, spanning the nanoscale to atomic scale patterns. In addition, statistical mechanical sum rules are used to obtain interfacial order parameters and interfacial free energies. We observe that Cassie's law is typically obeyed, together with an associated breakdown of the mechanical interpretation of Young's equation, for pattern wavelengths greater than 15 molecular diameters. Here, the adsorbed fluid exists as an array of hemi-drops. At about half this wavelength, the breakdown of Cassie's law lies within realistic energy scales and is associated with the unbending of the outer surface of adsorbed films. For atomic scale patterns, the usual interpretation of Young's equation is restored for films thicker than one monolayer. At high chemical contrast, when the monolayer in contact with high-energy regions would prefer to be crystalline, we observe a variety of exotic interfacial phenomena that may have technological significance.