Non-Classical Euler Buckling and Brazier Instability in Cylindrical Liquid Droplets.

Crystalline monolayers prevalent in nature and technology possess elusive elastic properties with important implications in fundamental physics, biology, and nanotechnology. Leveraging the recently discovered shape transitions of oil-in-water emulsion droplets, upon which these droplets adopt cylindrical shapes and elongate, we investigate the elastic characteristics of the crystalline monolayers covering their interfaces. To unravel the conditions governing Euler buckling and Brazier kink formation in these cylindrical tubular interfacial crystals, we strain the elongating cylindrical droplets within confining microfluidic wells. Our experiments unveil a nonclassical relation between the Young's modulus and the bending modulus of these crystals. Intriguingly, this relation varies with the radius of the cylindrical crystal, presenting a nonclassical mechanism for tuning of elasticity in nanotechnology applications.

"Magic Numbers" in Self-Faceting of Alcohol-Doped Emulsion Droplets.

Oil-in-water emulsion droplets spontaneously adopt, below some temperature Td , counterintuitive faceted and complex non-spherical shapes while remaining liquid. This transition is driven by a crystalline monolayer formed at the droplets' surface. Here, we show that ppm-level doping of the droplet's bulk by long-chain alcohols allows tuning Td by >50 °C, implying formation of drastically different interfacial structures. Furthermore, "magic" alcohol chain lengths maximize Td . This we show to arise from self-assembly of mixed alcohol:alkane interfacial structures of stacked alkane layers, co-crystallized with hydrogen-bonded alcohol dimers. These structures are accounted for theoretically and resolved by direct cryogenic transmission electron microscopy (cryoTEM), confirming the proposed structures. The discovered tunability of key properties of commonly-used emulsions by minute concentrations of specific bulk additives should benefit these emulsions' technological applicability.

Counterions under a Surface-Adsorbed Cationic Surfactant Monolayer: Structure and Thermodynamics.

The surface adsorption of ionic surfactants is fundamental for many widespread phenomena in life sciences and for a wide range of technological applications. However, direct atomic-resolution structural experimental studies of noncrystalline surface-adsorbed films are scarce. Thus, even the most central physical aspects of these films, such as their charge density, remain uncertain. Consequently, theoretical models based on contradicting assumptions as for the surface films' ionization are widely used for the description and prediction of surface thermodynamics. We employ X-ray reflectivity to obtain the Ångström-scale surface-normal structure of surface-adsorbed films of the cationic surfactant cetyltrimethylammonium bromide (CTAB) in aqueous solutions at several different temperatures and concentrations. In conjunction with published neutron reflectivity data, we determine the surface-normal charge distribution due to the dissociated surfactants' headgroups. The distribution appears to be inconsistent with the Gouy-Chapman model yet consistent with a compact Stern layer model of condensed counterions. The experimental surfactant adsorption thermodynamics conforms well to classical, Langmuir and Kralchevsky, adsorption models. Furthermore, the Kralchevsky model correctly reproduces the observed condensation of counterions, allowing the values of the adsorption parameters to be resolved, based on the combination of the present data and the published surface tension measurements.

Salt-induced stability and modified interfacial energetics in self-faceting emulsion droplets.

HYPOTHESIS: The counterintuitive temperature-controlled self-faceting of water-suspended, surfactant-stabilized, liquid oil droplets provides new opportunities in engineering of smart liquids, the properties of which are controllable by external stimuli. However, many emulsions exhibiting self-faceting phenomena have limited stability due to surfactant precipitation. The emulsions' stability may be enhanced, and their inter-droplet electrostatic repulsion tuned, through controlled charge screening driven by varying-concentration added salts. Moreover, in many technologically-relevant situations, salts may already exist in the emulsion's aqueous phase. Yet, salts' impact on self-faceting effects has never been explored. We hypothesize that the self-faceting transitions' temperatures, and stability against surfactant precipitation, of ionic-surfactants-stabilized emulsions are significantly modified by salt introduction. EXPERIMENTS: We explore the temperature-dependent impact of NaCl and CsCl salt concentration on the emulsions' phase diagrams, employing optical microscopy of emulsion droplet shapes and interfacial tension measurements, both sensitive to interfacial phase transitions. FINDINGS: A salt concentration dependent increase in the self-faceting transition temperatures is found, and its mechanism elucidated. Our findings allow for a significant enhancement of the emulsions' stability, and provide the physical understanding necessary for future progress in research and applications of self-faceting phenomena in salt-containing emulsions.

Anomalous Temperature-Controlled Concave-Convex Switching of Curved Oil-Water Menisci.

While the curvature of the classical liquid surfaces exhibits only a weak temperature dependence, we demonstrate here a reversible temperature-tunable concave-convex shape switching in capillary-contained, surfactant-decorated, oil-water interfaces. The observed switching gives rise to a concave-convex shape transition, which takes place as a function of the width of the containing capillary. This apparent violation of Young's equation results from a hitherto-unreported sharp reversible hydrophobic-hydrophilic transition of the glass capillary walls. The transition is driven by the interfacial freezing effect, which controls the balance between the competing surfactants' adsorption on, and consequent hydrophobization of, the capillary walls and their incorporation into the interfacially frozen monolayer. Since capillary wetting by surfactant solutions is fundamental for a wide range of technologies and natural phenomena, the present observations have important implications in many fields, from fluid engineering to biology, and beyond.

Faceting and Flattening of Emulsion Droplets: A Mechanical Model.

When cooled down, emulsion droplets stabilized by a frozen interface of alkane molecules and surfactants have been observed to undergo a spectacular sequence of morphological transformations: from spheres to faceted liquid icosahedra, down to flattened liquid platelets. While generally ascribed to the interplay between the elasticity of the frozen interface and surface tension, the physical mechanisms underpinning these transitions have remained elusive, despite different theoretical pictures having been proposed in recent years. In this Letter, we introduce a comprehensive mechanical model of morphing emulsion droplets, which quantitatively accounts for various experimental observations, including the size scaling behavior of the faceting transition. Our analysis highlights the role of gravity and the spontaneous curvature of the frozen interface in determining the specific transition pathway.

Polyhedral Water Droplets: Shape Transitions and Mechanism.

While classical liquid droplets are rounded, transitions have recently been discovered which render polyhedral water-suspended droplets of several oils. Yet, the mechanism of these transitions and the role of the droplets' interfacial curvature in inducing these transitions remain controversial. In particular, one of the two mechanisms suggested mandates a convex interface, in a view from the oil side. Here we show that oil-suspended water droplets can spontaneously assume polyhedral shapes, in spite of their concave interface. These results strongly support the alternative mechanism, where the faceting in both oil and water droplets is driven by the elasticity of a crystalline monolayer, known to self-assemble at the oil-water interface, independent of its curvature. The faceting transitions in the water droplets allow the fundamental elastic properties of two-dimensional matter to be probed, enable new strategies in faceted nanoparticle and nanoshell synthesis, and provide insight into the molecular mechanisms of morphogenesis.

Precise Self-Positioning of Colloidal Particles on Liquid Emulsion Droplets.

Decorating emulsion droplets by particles stabilizes foodstuff and pharmaceuticals. Interfacial particles also influence aerosol formation, thus impacting atmospheric CO2 exchange. While studies of particles at disordered droplet interfaces abound in the literature, such studies for ubiquitous ordered interfaces are not available. Here, we report such an experimental study, showing that particles residing at crystalline interfaces of liquid droplets spontaneously self-position to specific surface locations, identified as structural topological defects in the crystalline surface monolayer. This monolayer forms at temperature T = Ts, leaving the droplet liquid and driving at Td < Ts a spontaneous shape-change transition of the droplet from spherical to icosahedral. The particle's surface position remains unchanged in the transition, demonstrating these positions to coincide with the vertices of the sphere-inscribed icosahedron. Upon further cooling, droplet shape-changes to other polyhedra occur, with the particles remaining invariably at the polyhedra's vertices. At still lower temperatures, the particles are spontaneously expelled from the droplets. Our results probe the molecular-scale elasticity of quasi-two-dimensional curved crystals, impacting also other fields, such as protein positioning on cell membranes, controlling essential biological functions. Using ligand-decorated particles, and the precise temperature-tunable surface position control found here, may also allow using these droplets for directed supra-droplet self-assembly into larger structures, with a possible post-assembly structure fixation by UV polymerization of the droplet's liquid.

Periodic buckling and grain boundary slips in a colloidal model of solid friction.

The intermittent 'stick-slip' dynamics in frictional sliding of solid bodies is common in everyday life and technology. This dynamics has been widely studied on a macroscopic scale, where the thermal motion can usually be neglected. However, the microscopic mechanisms behind the periodic stick-slip events are yet unclear. We employ confocal microscopy of colloidal spheres, to study the frictional dynamics at the boundary between two quasi-two-dimensional (2D) crystalline grains, with a single particle resolution. Such unprecedentedly-detailed observations of the microscopic-scale frictional solid-on-solid sliding have never been previously carried out. At this scale, the particles undergo an intense thermal motion, which masks the avalanche-like nature of the underlying frictional dynamics. We demonstrate that the underlying sliding dynamics involving out-of-plane buckling events, is intermittent and periodic, like in macroscopic friction. However, unlike in the common models of friction, the observed periodic frictional dynamics is promoted, rather than just suppressed, by the thermal noise, which maximizes the entropy of the system.

Nanostructures, Faceting, and Splitting in Nanoliter to Yoctoliter Liquid Droplets.

Contrary to everyday experience, where all liquid droplets assume rounded, near-spherical shapes, the temperature-tuning of liquid droplets to faceted polyhedral shapes and to spontaneous splitting has been recently demonstrated in oil-in-water emulsions. However, the elucidation of the mechanism driving these surprising effects, as well as their many potential applications, ranging from faceted nanoparticle synthesis through new industrial emulsification routes to controlled-release drug delivery within the human body, have been severely hampered by the micron-scale resolution of the light microscopy employed to date in all in situ studies. Thus, the thickness of the interfacially frozen crystalline monolayer, suggested to drive these effects, could not be directly measured, and the low limit on the droplet size still showing these effects remained unknown. In this study, we employ a combination of super-resolution stimulated emission depletion microscopy, cryogenic transmission and freeze-fracture electron microscopy, to study these effects well into the nanometer length scale. We demonstrate the occurrence of the faceting transition in droplets spanning an incredible 12 decades in volume from nanoliters to yoctoliters and directly visualize the interfacially frozen, few nanometer thick, crystalline monolayer suggested to drive these effects. Furthermore, our measurements allow placing an upper-limit estimate on the two-dimensional Young modulus of the interfacial nanometer-thick surface crystal in the smallest droplets, providing insights into the virtually unexplored domain of nanoelasticity.

Imaging of nanoparticle dynamics in live and apoptotic cells using temporally-modulated polarization.

Gold nanoparticles are widely exploited in phototherapy. Owing to their biocompatibility and their strong visible-light surface plasmonic resonance, these particles also serve as contrast agents for cell image enhancement and super-resolved imaging. Yet, their optical signal is still insufficiently strong for many important real-life applications. Also, the differentiation between adjacent nanoparticles is usually limited by the optical resolution and the orientations of non-spherical particles are unknown. These limitations hamper the progress in cell research by direct optical microscopy and narrow the range of phototherapy applications. Here we demonstrate exploiting the optical anisotropy of non-spherical nanoparticles to achieve super-resolution in live cell imaging and to resolve the intracellular nanoparticle orientations. In particular, by modulating the light polarization and taking advantage of the polarization-dependence of gold nanorod optical properties, we realize the 'lock-in amplification', widely-used in electronic engineering, to achieve image enhancement in live cells and in cells that undergo apoptotic changes.

Self-faceting of emulsion droplets as a route to solid icosahedra and other polyhedra.

HYPOTHESIS: Temperature-controlled self-faceting of liquid droplets has been recently discovered in surfactant-stabilized alkane-in-water emulsions. We hypothesize that similar self-faceting may occur in emulsion droplets of UV-polymerizable linear hydrocarbons. We further hypothesize that the faceted droplet shapes can be fixed by UV-initiated polymerization, thus providing a new route towards the production of solid polyhedra. EXPERIMENTS: Temperature-induced shape variations were studied by optical microscopy in micron-size emulsion droplets of UV-polymerizable alkyl acrylate. When polymerized, the resultant solid particles' 3D shape and internal structure were determined by combined scanning electron microscopy (SEM) and focused ion beam (FIB) slicing. The SEM and FIB nanoscale resolution provided a far greater detail imaging than that achievable for the liquid droplets, which could only be studied by optical microscopy, severely limiting their 3D shape determination. FINDINGS: We demonstrate the formation of solid icosahedra, polyhedral platelets, and rods of hitherto-unreported sizes, well below the 3D-printing resolution (∼20µm). The presence of icosahedral shapes and the absence of any resolvable internal structure at sub-µm length scales, are in line with the surface-freezing-driven mechanism proposed for the faceting phenomenon. Further development of the method presented here may allow large-quantity production of shaped micron- to nano- sized colloidal building blocks for 3D metamaterials and other applications.

Axial Confocal Tomography of Capillary-Contained Colloidal Structures.

Confocal microscopy is widely used for three-dimensional (3D) sample reconstructions. Arguably, the most significant challenge in such reconstructions is posed by the resolution along the optical axis being significantly lower than in the lateral directions. In addition, the imaging rate is lower along the optical axis in most confocal architectures, prohibiting reliable 3D reconstruction of dynamic samples. Here, we demonstrate a very simple, cheap, and generic method of multiangle microscopy, allowing high-resolution high-rate confocal slice collection to be carried out with capillary-contained colloidal samples in a wide range of slice orientations. This method, realizable with any common confocal architecture and recently implemented with macroscopic specimens enclosed in rotatable cylindrical capillaries, allows 3D reconstructions of colloidal structures to be verified by direct experiments and provides a solid testing ground for complex reconstruction algorithms. In this paper, we focus on the implementation of this method for dense nonrotatable colloidal samples, contained in complex-shaped capillaries. Additionally, we discuss strategies to minimize potential pitfalls of this method, such as the artificial appearance of chain-like particle structures.

Temperature-Tuned Faceting and Shape Changes in Liquid Alkane Droplets.

Recent extensive studies reveal that surfactant-stabilized spherical alkane emulsion droplets spontaneously adopt polyhedral shapes upon cooling below a temperature Td 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 Ts > Td. 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 Td. Our results provide strong quantitative support validating the crystalline monolayer buckling mechanism.

Dipolar colloids in apolar media: direct microscopy of two-dimensional suspensions.

Spherical colloids, in an absence of external fields, are commonly assumed to interact solely through rotationally-invariant potentials, u(r). While the presence of permanent dipoles in aqueous suspensions has been previously suggested by some experiments, the rotational degrees of freedom of spherical colloids are typically neglected. We prove, by direct experiments, the presence of permanent dipoles in commonly used spherical poly(methyl methacrylate) (PMMA) colloids, suspended in an apolar organic medium. We study, by a combination of direct confocal microscopy, computer simulations, and theory, the structure and other thermodynamical properties of organic suspensions of colloidal spheres, confined to a two-dimensional (2D) monolayer. Our studies reveal the effects of the dipolar interactions on the structure and the osmotic pressure of these fluids. These observations have far-reaching consequences for the fundamental colloidal science, opening new directions in self-assembly of complex colloidal clusters.

Optical-tweezing-based linear-optics nanoscopy.

Previous works reported that linear optics could be used to observe sub-wavelength features with a conventional optical microscope. Yet, the ability to reach a sub-200 nm resolution with a visible light remains limited. We present a novel widely-applicable method, where particle trapping is employed to overcome this limit. The combination of the light scattered by the sample and by the trapped particles encodes super-resolution information, which we decode by post image processing, with the trapped particle locations predetermined. As the first proof of concept our method successfully resolved sample characteristic features down to 100 nm. Improved performance is achieved with the fluorescence of the trapped particles employed. Further improvement may be attained with trapped particles of a smaller size.

How faceted liquid droplets grow tails.

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 = Ts 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.

Photo-Crosslinkable Colloids: From Fluid Structure and Dynamics of Spheres to Suspensions of Ellipsoids.

Recently-developed photo-crosslinkable PMMA (polymethylmethacrylate) colloidal spheres are a highly promising system for fundamental studies in colloidal physics and may have a wide range of future technological applications. We synthesize these colloids and characterize their size distribution. Their swelling in a density- and index- matching organic solvent system is demonstrated and we employ dynamic light scattering (DLS), as also the recently-developed confocal differential dynamic microscopy (ConDDM), to characterize the structure and the dynamics of a fluid bulk suspension of such colloids at different particle densities, detecting significant particle charging effects. We stretch these photo-crosslinkable spheres into ellipsoids. The fact that the ellipsoids are cross-linked allows them to be fluorescently stained, permitting a dense suspension of ellipsoids, a simple model of fluid matter, to be imaged by direct confocal microscopy.

Crystallization and reentrant melting of charged colloids in nonpolar solvents.

We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We simultaneously charge the particles and add counterions to the solution with aerosol-OT (AOT) reverse micelles. At low AOT concentrations, the charged particles crystallize into body-centered-cubic (bcc) or face-centered-cubic (fcc) Wigner crystals; at high AOT concentrations, the increased screening drives a thus far unobserved reentrant melting transition. We observe an unexpected scaling of the data with particle size, and account for all behavior with a model that quantitatively predicts both the reentrant melting and the data collapse.