A statistical model for the wettability of surfaces with heterogeneous pore geometries
- Author(s): Brockway, Lance
- Taylor, Hayden
- et al.
We describe a new approach to modeling the wetting behavior of micro- and nano-textured surfaces with varying degrees of geometrical heterogeneity. Surfaces are modeled as pore arrays with a Gaussian distribution of sidewall reentrant angles and a characteristic wall roughness. Unlike conventional wettability models, our model considers the fraction of a surface’s pores that are filled at any time, allowing us to capture more subtle dependences of a liquid’s apparent contact angle on its surface tension. The model has four fitting parameters and is calibrated for a particular surface by measuring the apparent contact angles between the surface and at least four probe liquids. We have calibrated the model for three heterogeneous nanoporous surfaces that we have fabricated: a hydrothermally grown zinc oxide, a film of polyvinylidene fluoride (PVDF) microspheres formed by spinodal decomposition, and a polytetrafluoroethylene (PTFE) film with pores defined by sacrificial polystyrene microspheres. These three surfaces show markedly different dependences of a liquid’s apparent contact angle on the liquid’s surface tension, and the results can be explained by considering geometric variability. The highly variable PTFE pores yield the most gradual variation of apparent contact angle with probe liquid surface tension. The PVDF microspheres are more regular in diameter and, although connected in an irregular manner, result in a much sharper transition from non-wetting to wetting behavior as surface tension reduces. We also demonstrate, by terminating porous zinc oxide with three alternative hydrophobic molecules, that a single geometrical model can capture a structure’s wetting behavior for multiple surface chemistries and liquids. Finally, we contrast our results with those from a highly regular, lithographically-produced structure which shows an extremely sharp dependence of wettability on surface tension. This new model could be valuable in designing and evaluating processes for manufacturing liquid-repellent surfaces on an industrial scale.