Optimal geometrical design for superhydrophobic surfaces: effects of a trapezoid microtexture

It is now becoming possible to control and tailor micro/nanoscale chemical structures with different geometrical patterns on various substrates to achieve so-called superhydrophobic surfaces, which show promising industrial applications. In spite of significant advances in preparation of such surfaces, to date the effects of surface patterns or geometries on superhydrophobicity have not been understood completely, in particular, in the theoretical aspect. It has therefore been a challenge to design optimal geometry for ideal superhydrophobic behavior. In this study, a trapezoid microtextured superhydrophobic surface has been thermodynamically analyzed using a 2-D model. Furthermore, based on the calculations of free energy (FE) and free energy barrier (FEB), the effects of all the geometrical parameters for the trapezoid microtexture on contact angle (CA) and contact angle hysteresis (CAH) have been investigated systematically. It is demonstrated that besides height, base angle plays a significant important role in equilibrium contact angle (ECA) and CAH; in particular, a critical base angle for the present geometrical system is necessary for the transition from noncomposite to composite states. Moreover, the trapezoid base width affects strongly various CAs; a small base width is necessary for the large ECA and the small CAH. However, the effects of trapezoid base spacing are considerably complex. For the above transition, a small base spacing is necessary, but decreasing base spacing can decrease the ECA only for the composite state and can increase CAH only for the noncomposite state. Based on the above findings, some fundamental principles for the design of optimal geometry of ideal superhydrophobic surfaces are therefore suggested, which are also consistent with the experimental observations and previous theoretical investigations.