A new model for thermodynamic analysis on wetting behavior of superhydrophobic surfaces

Superhydrophobic surfaces have shown inspiring applications in microfluidics, and self-cleaning coatings owing to water-repellent and low-friction properties. However, thermodynamic mechanism responsible for contact angle hysteresis (CAH) and free energy barrier (FEB) have not been understood completely yet. In this work, we propose an intuitional 3-dimension (3D) droplet model along with a reasonable thermodynamic approach to gain a thorough insight into the physical nature of CAH. Based on this model, the relationships between radius of three-phase contact line, change in surface free energy (CFE), average or local FEB and contact angle (CA) are established. Moreover, a thorough theoretical consideration is given to explain the experimental phenomena related to the superhydrophobic behavior. The present study can therefore provide some guidances for the practical fabrications of the superhydrophobic surfaces.

Changes of droplet states while water being added into droplet (the microsyringe not being marked). (a) Initial state (being from less droplet after advancing), apparent CA of θw, radius of droplet and three-phase contact-line of R1 (as known value) and r1=R1sinθw, respectively; (b) pre-advancing state (three-phase contact line not being moved) as the instantaneous state (unsteady), advancing angle of θa, radius of droplet and three-phase contact-line of R2 and r2 = r1, respectively; (c) advancing state (three-phase contact line having been moved away), CA back to θw, radius of droplet and three-phase contact-line of R3 and r3 (r3 = r2), respectively, the volume of droplet (V2, V3 represents volume of the droplet in pre-advancing or advancing state, respectively) keeps constant from (b) to (c) (namely V3 = V2); (d) overall diagram of Longitudinal section of changes of states passing through the center while droplet advancing; (e) and (f) longitudinal section diagram passing through the center, before and after advancing, respectively.Highlights► A dynamic equation is intuitively established between static apparent CA and θa or θr. ► The relationships are established between CA, CAH, CFE, FEB and micro/nanoscale. ► Change of surfaces free energy (CFE), as measurement of ability of droplet. ► New concept of free energy barrier (FEB) is presented to illustrate CAH from macroscopic. ► Making strict explanations in math on CAH along with relevant phenomena.