Capillary-bridge–derived particles with negative Gaussian curvature

Abstract

We report the preparation of millimeter-scale particles by thermal polymerization of liquid monomer capillary bridges to form catenoid-shaped particles that exhibit negative Gaussian curvature. The shape of the capillary bridges and resulting particles can be finely tuned using several addressable parameters: (i) the shape, size, and orientation of lithographic pinning features on the spanned surfaces; (ii) the distance between opposing support surfaces; and (iii) the lateral displacement (shear) of opposing features. The catenoid-shaped particles exhibit controllable optical properties as a result of their concave menisci, the shape of which can be easily manipulated. The particles self assemble in the presence of a condensing liquid (water) to form reversible neck-toneck pairs and less reversible end-to-end aggregates. We argue that this approach could be scaled down to micrometer dimensions by fabricating an array of micrometer-scale particles. We also argue, with a discussion of dynamic wetting, that these particles will exhibit interesting anisotropic adhesive properties.particle | capillary bridge | catenoid | negative Gaussian curvature | wetting P articles of designed shape and size are central to broad ranges of applications and fundamental studies (1-3). Significant effort has been expended to prepare particles with shapes such as spheres, cages, rods, tubes, and disks, as well as irregular shapes (4-9). It is noteworthy that all of these particles contain surfaces with positive or zero Gaussian curvature. This is understandable due to surface energy minimization during preparation. Although surfaces with negative Gaussian curvature (e.g., saddle-shaped surfaces) have been studied, including analyses of protein folding, soap films, and directed particle assembly (10-12), anisotropic particles with negative Gaussian curvature remain to be explored. Capillary bridges offer a convenient route to particles with this structure.When a droplet of liquid condenses or is placed between two solid surfaces with millimeter-scale or smaller separation, a capillary bridge forms that contains a liquid/air interface (meniscus) with constant mean curvature. The shape of the capillary bridge depends on the solid surface properties, liquid surface tension, liquid volume, contacting area, and the separation distance between the two surfaces (13-17). The capillary bridge will exhibit a convex meniscus with positive Gaussian curvature (G = 1 R 1 · 1 R2 , where R 1 and R 2 are the principal radii of curvature) if the liquid/ solid/vapor contact angle, θ, > 90°or a concave meniscus with negative Gaussian curvature if θ < 90°(18, 19). The latter is the usual situation because most liquids exhibit contact angles of less than 90°on most solids.We recently reported that observing shear distortion and failure of capillary bridges can lend insight into the wetting behavior of patterned and defect-containing surfaces (20). Although it was not our objective, we observed that the shape of capillary bridges between pinning features cou...

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