Thermodynamic analysis on wetting states and wetting state transitions of rough surfaces

Determining the equilibrium wetting states and exploring the conditions and mechanisms of the wetting state transition from the Cassie-Baxter (CB) state to the Wenzel (W) state (CB-W transition) have been a central topic in the study of superhydrophobic behavior on rough or textured surfaces. Although considerable progress has been made, some issues regarding this topic are still not completely understood. In this study, a systematic thermodynamic analysis has been performed to address several key issues related to this topic. Generalized theoretical expressions for determining the equilibrium wetting states (the threshold Young contact angle of the CB region) and evaluating the stability of the CB state (the energy barrier separating the CB and W states and the critical pressure for the CB-W transition) have been derived. Applying these expressions to four types of surfaces built with protrusions in paraboloid, truncated cone, inverted truncated cone and flat-top pillar shapes, the wetting equilibrium and resultant wetting states have been studied. The physical meanings of the threshold Young contact angle, the roles and mechanisms of the energy barrier and critical pressure in stabilizing the CB state have been discussed. Finally, a general guidance for achieving robust superhydrophobicity on the studied surfaces has been given.