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...

Metal-oxide-semiconductor field-effect transistors (MOSFETs) on CdTe/HgTe/CdTe heterostructures are fabricated with silicon dioxide gate insulators. In these devices, the density of the quasi two-dimensional electron gas in the HgTe quantum well can be tuned in a wide range. In low magnetic fields we observe beating patterns in the Shubnikov-de Haas oscillations that render possible the determination of the coefficient α of the Rashba term in the Hamiltonian as a function of electron density. This coefficient consistently describes the splittings observed in cyclotron resonance in low magnetic fields.

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We electron-dope single crystal samples of SrTiO3 by exposing them to Ar+ irradiation and observe carrier mobility similar in its magnitude and temperature dependence to the carrier mobility in other electron-doped SrTiO3 systems. We find that some transport properties are time dependent. In particular, the sheet resistance increases with time at a temperature-dependent rate, suggesting an activation barrier on the order of 1eV. We attribute the relaxation effects to diffusion of oxygen vacancies—a process with energy barrier similar to the observed activation energy.