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...

Millimolar bulk concentrations of the surfactant cetyltrimethylammonium bromide (CTAB) induce spreading of alkanes, H(CH(2))(n)H (denoted C(n)) 12< or =n< or =21, on the water surface, which is not otherwise wet by these alkanes. The novel Langmuir-Gibbs film (LGF) formed is a liquidlike monolayer comprising both alkanes and CTAB tails. Upon cooling, an ordering transition occurs, yielding a hexagonally packed, quasi-2D crystal. For 11< or =n< or =17 this surface-frozen LGF is a crystalline monolayer. For 18< or =n< or =21 the LGF is a bilayer with a crystalline, pure-alkane, upper monolayer, and a liquidlike lower monolayer. The phase diagram and film structure were determined by x-ray, ellipsometry, and surface tension measurements. A thermodynamic theory accounts quantitatively for the observations.

Hydrophobicity, the spontaneous segregation of oil and water, can be modified by surfactants. The way this modification occurs is studied at the oil-water interface for a range of alkanes and two ionic surfactants. A liquid interfacial monolayer, consisting of a mixture of alkane molecules and surfactant tails, is found. Upon cooling, it freezes at T s , well above the alkane's bulk freezing temperature, T b . The monolayer's phase diagram, derived by surface tensiometry, is accounted for by a mixtures-based theory. The monolayer's structure is measured by high-energy X-ray reflectivity above and below T s . A solid-solid transition in the frozen monolayer, occurring approximately 3°C below T s , is discovered and tentatively suggested to be a rotator-to-crystal transition.H ydrophobicity (1) is abundant in nature and in technology (2). It plays a dominant role in fields ranging from the structure of living matter, like cell membrane stabilization and protein folding, to microemulsion-mediated nanoparticle and quantum dot formation (1,(3)(4)(5)(6)(7). Although the macroscopic phenomenology of hydrophobicity is well studied, its theoretical understanding, particularly on a molecular level, is still incomplete (1,8). Recent progress in X-ray scattering from buried interfaces allowed determination of the structure of hydrophobic interfaces (including the oil-water one) with near-atomic resolution, leading to an animated debate on the molecular-scale origin and manifestations of the hydrophobic interaction (9-13). Surfactants are often used to modify the hydrophobic interactions in a manner that reduces the interfacial free energy. However, the microscopic structure of surfactant-modified bulk oil-water interfaces, the subject of the present study, has been studied by X-ray methods only for nonionic alkanol surfactants (14, 15). X-ray measurements for oil-water interfaces modified by ionic surfactants are not available in the literature. Macroscopic optical measurements have uncovered intriguing interface structure modifications (16), indicating that these more widely used and more complex electrically charged surfactants, which also have bulkier headgroups, may modify the interface differently from the nonionic ones. Thus, a key ingredient in the fundamental understanding of the relation between ionic surfactants and the hydrophobic interaction is still missing.Using X-ray reflectivity (XR) and surface tensiometry, we measured the atomic-resolution structure and thermodynamics of oil-water interfaces decorated by ionic surfactants (see Fig. 1A). Two different interfacial phases are observed. At high temperatures, a liquid interfacial monolayer is found; upon cooling, a frozen monolayer forms at the interface, separating the bulk liquid oil and aqueous phases. We measured the interfacial phase diagram and offer a simple thermodynamic model which fully accounts for the interfacial freezing (IF). At a lower temperature, the frozen monolayer is found to undergo an additional transition to full crystallinity where the m...

Recent extensive studies reveal that surfactant-stabilized spherical alkane emulsion droplets spontaneously adopt polyhedral shapes upon cooling below a temperature T while remaining liquid. Further cooling induces the growth of tails and spontaneous droplet splitting. Two mechanisms were offered to account for these intriguing effects. One assigns the effects to the formation of an intradroplet frame of tubules consisting of crystalline rotator phases with cylindrically curved lattice planes. The second assigns the sphere-to-polyhedron transition to the buckling of defects in a crystalline interfacial monolayer, known to form in these systems at some T > T. The buckling reduces the extensional energy of the crystalline monolayer's defects, unavoidably formed when wrapping a spherical droplet by a hexagonally packed interfacial monolayer. The tail growth, shape changes, and droplet splitting were assigned to the decrease and vanishing of surface tension, γ. Here we present temperature-dependent γ(T), optical microscopy measurements, and interfacial entropy determinations for several alkane/surfactant combinations. We demonstrate the advantages and accuracy of the in situ γ(T) measurements made simultaneously with the microscopy measurements on the same droplet. The in situ and coinciding ex situ Wilhelmy plate γ(T) measurements confirm the low interfacial tension, ≲0.1 mN/m, observed at T. Our results provide strong quantitative support validating the crystalline monolayer buckling mechanism.

No abstract