How faceted liquid droplets grow tails

Abstract

Liquid droplets, widely encountered in everyday life, have no flat facets. Here we show that water-dispersed oil droplets can be reversibly temperature-tuned to icosahedral and other faceted shapes, hitherto unreported for liquid droplets. These shape changes are shown to originate in the interplay between interfacial tension and the elasticity of the droplet's 2-nm-thick interfacial monolayer, which crystallizes at some T = T s above the oil's melting point, with the droplet's bulk remaining liquid. Strikingly, at still-lower temperatures, this interfacial freezing (IF) effect also causes droplets to deform, split, and grow tails. Our findings provide deep insights into molecular-scale elasticity and allow formation of emulsions of tunable stability for directed self-assembly of complex-shaped particles and other future technologies.emulsions | membranes' buckling | topological defects | two-dimensional crystals | spontaneous emulsification O f all same-volume shapes, a sphere has the smallest surface area A. Microscopic liquid droplets are, therefore, spherical, because this shape minimizes their interfacial energy γA for a surface tension γ > 0. Spontaneous transitions to a flat-faceted shape, which increases the surface area, have never been reported for droplets of simple liquids. Here we demonstrate that surfactantstabilized droplets of oil in water, of sizes ranging from 1 to 100 μm, known as "emulsions" or "macroemulsions" (1), can be tuned to sharp-edged, faceted, polyhedral shapes, dictated by the molecular-level topology of the closed surface. Furthermore, the physical mechanism which drives the faceting transition allows the sign of γ to be switched in a controllable manner, leading to a spontaneous increase in surface area of the droplets, akin to the spontaneous emulsification (SE) (1, 2), yet driven by a completely different, and reversible, process.At room temperature, the spherical shape of our emulsions' surfactant-stabilized oil droplets indicates shape domination by γ > 0 (oil: 16-carbon alkane, C 16 ; surfactant: trimethyloctadecylammonium bromide, C 18 TAB, see SI Appendix, Fig. S1). However, the observed shape change to an icosahedron at some T = T d , below the interfacial freezing temperature T s (Fig. 1A), demonstrates that γ has become anomalously low and no longer dominates the shape. This γ-decrease upon cooling starkly contrasts with the behavior of most other liquids, where γ increases upon cooling (1). Direct in situ γ-measurements in our emulsions (SI Appendix), as well as pendant drop tensiometry of millimetersized droplets, confirm the positive dγðTÞ=dT here (Fig. 2). Wilhelmy plate method γðTÞ measurements (3, 4) on planar interfaces between bulk alkanes and aqueous C 18 TAB solutions (blue circles in Fig. 2A) also demonstrate the same dγðTÞ=dT > 0 at T < T s . Thus, the anomalous positive dγ=dT below T s is confirmed for the C 16 /C 18 TAB system by three independent methodologies.To elucidate the implications of the positive dγ=dT, we note that thermodynamics equates an inte...

Control of drop shape transformations in cooled emulsions

“…However, the major points in the mechanistic explanation of the observed phenomenon, proposed in ref. [55], differ qualitatively from our explanations. In particular:…”

“…Thus we estimate a minimum value for K B ≥ 10 -14 J, which is several orders of magnitude higher than the known bending constants of frozen lipid bilayers or surfactant adsorption monolayers, K B ≈ 10 -18 to 10 -17 J [55,[65][66]. Therefore, the drop deformation may be caused only by the presence of a multilayer of ordered self-assembled molecules which are able to create a sufficiently high bending moment to curve the drop surface against the drop surface energy and capillary pressure which both act as to preserve the spherical drop shape.…”

“…At the end of the discussion section, let us mention a recent study [55], published soon after our previous paper [43], and reporting similar observations with the system C16/C 18 TAB, which we did not specifically study. This system is very similar to ours and, not surprisingly, many of the experimental observations resemble those reported in ref.…”

“…(1) Ultralow interfacial tension (γ ≪ 1 mN/m) was reported by Guttman et al [55] at temperatures below the freezing temperature of the surfactant adsorption layer. Even temporary negative tension was proposed to explain the formation of rod-like asperities.…”

Neutral versus charged defect patterns in curved crystals

“…most isotropic) non-flat geometry [1]. Motivating the goal to understand optimal ordering on spheres, known broadly as the generalized-Thomson problem, is structure formation in material systems as diverse as viral capsids [2,3], fullerenes [4], particle-coated droplets [5,6], curved bubble rafts [7], emulsion droplets [8] and spherical superconductors [9]. Ground states in these systems are characterized by topological defects, 5-and 7-fold disclinations in otherwise sixfold hexagonal packing, which carry, respectively, positive and negative topological charges s i = ±π/3 associated with the rotation of lattice directions around the defect [10].…”