Topological wetting states of microdroplets on closed-loop structured surfaces: Breakdown of the Gibbs equation at the microscale

Microdroplets are a class of soft matter that has been extensively employed for chemical, biochemical, and industrial applications. However, fabricating microdroplets with largely controllable contact-area shape and apparent contact angle, a key prerequisite for their applications, is still a challenge. Here, by engineering a type of surface with homocentric closed-loop microwalls/microchannels, we can achieve facile size, shape, and contact-angle tunability of microdroplets on the textured surfaces by design. More importantly, this class of surface topologies (with universal genus value = 1) allows us to reveal that the conventional Gibbs equation (widely used for assessing the edge effect on the apparent contact angle of macrodroplets) seems no longer applicable for water microdroplets or nanodroplets (evidenced by independent molecular dynamics simulations). Notably, for the flat surface with the intrinsic contact angle ~0°, we find that the critical contact angle on the microtextured counterparts (at edge angle 90°) can be as large as >130°, rather than 90° according to the Gibbs equation. Experiments show that the breakdown of the Gibbs equation occurs for microdroplets of different types of liquids including alcohol and hydrocarbon oils. Overall, the microtextured surface design and topological wetting states not only offer opportunities for diverse applications of microdroplets such as controllable chemical reactions and low-cost circuit fabrications but also provide testbeds for advancing the fundamental surface science of wetting beyond the Gibbs equation.