From faceted vesicles to liquid icoshedra: Where topology and crystallography meet

The Spontaneous Vesicle-Micelle Transition in a Catanionic Surfactant System: A Chemical Trapping Study

Typically, the formation of vesicles requires the addition of salts or other additives to surfactant micelles. However, in the case of catanionic surfactants, unilamellar vesicles can spontaneously form upon dilution of the micellar solutions. Our study explores the intriguing spontaneous vesicle-to-micelle transition in catanionic surfactant systems, specifically cetyltrimethyl ammonium bromide (CTAB) and sodium octylsulfonate (SOS). To gain insights into the changes occurring at the interface, we employ a chemical trapping method to characterize variations in the molarities of sulfonate headgroups, water, and bromide ions during the transition. Our findings reveal the formation of ion pairs between the cationic component of CTAB and the anionic component of SOS, leading to tight interfacial packing in CTAB/SOS solutions. This interfacial packing promotes vesicle formation at low surfactant concentrations. Due to the significant difference in critical micelle concentration (cmc) between CTAB and SOS, an increase in the stoichiometric surfactant concentration results in a substantial rise in the SOS-to-CTAB ratio within the interfacial region. This enrichment of SOS in the aggregates triggers the transition from vesicles to micelles. Overall, our study may shed new light on the design of morphologies in catanionic and other surfactant systems.

Influence of the Triglyceride Composition, Surfactant Concentration and Time–Temperature Conditions on the Particle Morphology in Dispersions

Many applications for crystalline triglyceride-in-water dispersions exist in the life sciences and pharmaceutical industries. The main dispersion structures influencing product properties are the particle morphology and size distribution. These can be set by the formulation and process parameters, but temperature fluctuations may alter them afterwards. As the dispersed phase often consists of complex fats, there are many formulation variables influencing these product properties. In this study, we aimed to gain a better understanding of the influence of the dispersed-phase composition on the crystallization and melting behavior of these systems. We found that different particle morphologies can be obtained by varying the dispersed-phase composition. Droplets smaller than 1 µm were obtained after melting due to self-emulsification (SE), but these changes and coalescence events were only partly influenced by the melting range of the fat. With increasing surfactant concentration, the SE tendency increased. The smallest x50,3 of 3 µm was obtained with a surfactant concentration of 0.5 wt%. We attributed this to different mechanisms leading to the droplets’ breakup during melting, which we observed via thermo-optical microscopy. In addition, SE and coalescence are a function of the cooling and heating profiles. With slow heating (0.5 K/min), both phenomena are more pronounced, as the particles have more time to undergo the required mechanisms.

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.

Rotator phases in hexadecane emulsion drops revealed by X-ray synchrotron techniques

HYPOTHESIS

Micrometer sized alkane-in-water emulsion drops, stabilized by appropriate long-chain surfactants, spontaneously break symmetry upon cooling and transform consecutively into series of regular shapes (Denkov et al., Nature 2015, 528, 392). Two mechanisms were proposed to explain this phenomenon of drop "self-shaping". One of these mechanisms assumes that thin layers of plastic rotator phase form at the drop surface around the freezing temperature of the oil. This mechanism has been supported by several indirect experimental findings but direct structural characterization has not been reported so far.

EXPERIMENTS

We combine small- and wide-angle X-ray scattering (SAXS/WAXS) with optical microscopy and DSC measurements of self-shaping drops in emulsions.

FINDINGS

In the emulsions exhibiting drop self-shaping, the scattering spectra reveal the formation of intermediate, metastable rotator phases in the alkane drops before their crystallization. In addition, shells of rotator phase were observed to form in hexadecane drops, stabilized by C₁₆EO₁₀ surfactant. This rotator phase melts at ca. 16.6 °C which is significantly lower than the melting temperature of crystalline hexadecane, 18 °C. The scattering results are in a very good agreement with the complementary optical observations and DSC measurements.

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.

Buckling transitions and soft-phase invasion of two-component icosahedral shells

What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids.

Dislocation screening in crystals with spherical topology

Whereas disclination defects are energetically prohibitive in two-dimensional flat crystals, their existence is necessary in crystals with spherical topology, such as viral capsids, colloidosomes, or fullerenes. Such a geometrical frustration gives rise to large elastic stresses, which render the crystal unstable when its size is significantly larger than the typical lattice spacing. Depending on the compliance of the crystal with respect to stretching and bending deformations, these stresses are alleviated either by a local increase of the intrinsic curvature in proximity of the disclinations or by the proliferation of excess dislocations, often organized in the form of one-dimensional chains known as "scars." The associated strain field of the scars is such as to counterbalance the one resulting from the isolated disclinations. Here we develop a continuum theory of dislocation screening in two-dimensional closed crystals with genus one. Upon modeling the flux of scars emanating from a given disclination as an independent scalar field, we demonstrate that the elastic energy of closed two-dimensional crystals with various degrees of asphericity can be expressed as a simple quadratic function of the screened topological charge of the disclinations, at both zero and finite temperature. This allows us to predict the optimal density of the excess dislocations as well as the minimal stretching energy attained by the crystal.

Spontaneous particle desorption and "Gorgon" drop formation from particle-armored oil drops upon cooling

We study how the phenomenon of drop "self-shaping" (Denkov et al., Nature, 528, 2015, 392), in which oily emulsion drops undergo a spontaneous series of shape transformations upon emulsion cooling, is affected by the presence of adsorbed solid particles, like those used in Pickering emulsion stabilization. Experiments with several types of latex particles, and with added surfactant of low concentration to enable drop self-shaping, revealed several new unexpected phenomena: (1) adsorbed latex particles rearranged into regular hexagonal lattices upon freezing of the surfactant adsorption layer. (2) Spontaneous particle desorption from the drop surface was observed at a certain temperature - a remarkable phenomenon, as the solid particles are known to irreversibly adsorb on fluid interfaces. (3) Very strongly adhered particles to drop surfaces acted as a template to enable the formation of tens to hundreds of semi-liquid fibres, growing outwards from the drop surface, thus creating a shape resembling the Gorgon head from Greek mythology. Mechanistic explanations of all observed phenomena are provided using our understanding of the rotator phase formation on the surface of the cooled drops. The surface rotator phase creates positive line tension at the contact line formed between the particle surface and the fluid interface, which causes the particle ejection from the drop surface.

Rotator phases in alkane systems: In bulk, surface layers and micro/nano-confinements

Medium- and long-chain alkanes and their mixtures possess a remarkable physical property - they form intermediate structured phases between their isotropic liquid phase and their fully ordered crystal phase. These intermediate phases are called "rotator phases" or "plastic phases" (soft solids) because the incorporated alkane molecules possess a long-range positional order while preserving certain mobility to rotate, which results in complex visco-plastic rheological behaviour. The current article presents a brief overview of our current understanding of the main phenomena involved in the formation of rotator phases from single alkanes and their mixtures. In bulk, five rotator phases with different structures were identified and studied in detail. Along with the thermodynamically stable rotator phases, metastable and transient (short living) rotator phases were observed. Bulk rotator phases provided important information about several interfacial phenomena of high scientific interest, such as the energy of crystal nucleation, entropy and enthalpy of alkane freezing, interfacial energy between a crystal and its melt, etc. In alkane mixtures, the region of existence of rotator phases increases significantly, reflecting the disturbed packing of different molecules. All these phenomena are very important in the context of alkane applications as lubricants, in cosmetics, as phase-change materials for energy storage, etc. Significant expansion of the domain of rotator phases was observed also in confinements - in the pores of solid materials impregnated with alkanes, in polymeric microcapsules containing alkanes, and in micrometer sized emulsion droplets. The rotator phases were invoked to explain the mechanisms of two recently discovered phenomena in cooled alkane-in-water emulsions - the spontaneous "self-shaping" and the spontaneous "self-bursting" (fragmentation) of emulsion drops. The so-called "α-phases" formed by fatty acids and alcohols, and the "gel phase" formed in phospholipid and soap systems exhibit structural characteristics similar to those in the alkane rotator phases. The subtle connections between all these diverse systems are outlined, providing a unified outlook of the main phenomena related to the formation of such soft solid materials. The occurrence of alkane rotator phases in natural materials and in several technological applications is also reviewed to illustrate the general importance of these unique materials and the related phenomena.

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.

Formation and surface-stabilizing contributions to bare nanoemulsions created with negligible surface charge

The stabilization of nanoemulsions, nanosized oil droplets dispersed in water, is commonly achieved through the addition of surfactants and polymers. However, nanoemulsions in the absence of emulsifiers have been observed to acquire a significant negative charge at their surface, which ultimately contributes to their stability. While the source of this negative charge is disputed to this day, its presence is taken as an inherent property of the aqueous-hydrophobic interface. This report provides a look at the molecular structure and bonding characteristics of bare aqueous-hydrophobic nanoemulsion interfaces. We report the creation of bare nanoemulsions with near zero surface charge, which are marginally stable for several days. The process of creating these low-charge nanoemulsions (LCNEs) required rigorous cleaning procedures and proper solvent storage conditions. Using vibrational sum-frequency scattering spectroscopy, we measure the structure and bonding of the interfacial aqueous and hydrophobic phases. The surfaces of these LCNE samples possess a measurable free OH vibration, not found in previous studies and indicative of a clean interface. Tuning the nanoemulsion charge through addition of anionic surfactants, modeling potential surface-active contaminants, we observe the free OH to disappear and a reorientation of the interfacial hydrophobic molecules at micromolar surfactant concentrations. Notably, the free OH vibration provides evidence for stronger dispersion interactions between water molecules and the hydrophobic phase at the LCNE surface compared with similar planar water-alkane interfaces. We propose the stronger bonding interactions, in addition to an ordered interfacial aqueous layer, contribute to the delayed droplet coalescence and subsequent phase separation.

Multilayer Formation in Self-Shaping Emulsion Droplets

In several recent studies, we showed that micrometer-sized oil-in-water emulsion droplets from alkanes, alkenes, alcohols, triglycerides, or mixtures of these components can spontaneously "self-shape" upon cooling into various regular shapes, such as regular polyhedrons, platelets, rods, and fibers ( Denkov , N. , Nature 2015 , 528 , 392 ; Cholakova , D. , Adv. Colloid Interface Sci. 2016 , 235 , 90 ). These drop-shape transformations were explained by assuming that intermediate plastic rotator phase, composed of ordered multilayers of oily molecules, is formed beneath the drop surface around the oil-freezing temperature. An alternative explanation was proposed ( Guttman , S. , Proc. Natl. Acad. Sci. USA 2016 113 , 493 ; Guttman , S. , Langmuir 2017 , 33 , 1305 ), which is based on the assumption that the oil-water interfacial tension decreases to very low values upon emulsion cooling. Here, we present new results, obtained by differential scanning calorimetry (DSC), which quantify the enthalpy effects accompanying the drop-shape transformations. Using optical microscopy, we related the peaks in the DSC thermograms to the specific changes in the drop shape. Furthermore, from the enthalpies measured by DSC, we determined the fraction of the intermediate phase involved in the processes of drop deformation. The obtained results support the explanation that the drop-shape transformations are intimately related to the formation of ordered multilayers of alkane molecules with thickness varying between several and dozens of layers of alkane molecules, depending on the specific system. The new results provide the basis for a rational approach to the mechanistic explanation and to the fine control of this fascinating and industrially relevant phenomenon.

Efficient self-emulsification via cooling-heating cycles

In self-emulsification higher-energy micrometre and sub-micrometre oil droplets are spontaneously produced from larger ones and only a few such methods are known. They usually involve a one-time reduction in oil solubility in the continuous medium via changing temperature or solvents or a phase inversion in which the preferred curvature of the interfacial surfactant layer changes its sign. Here we harness narrow-range temperature cycling to cause repeated breakup of droplets to higher-energy states. We describe three drop breakup mechanisms that lead the drops to burst spontaneously into thousands of smaller droplets. One of these mechanisms includes the remarkable phenomenon of lipid crystal dewetting from its own melt. The method works with various oil-surfactant combinations and has several important advantages. It enables low surfactant emulsion formulations with temperature-sensitive compounds, is scalable to industrial emulsification and applicable to fabricating particulate drug carriers with desired size and shape.

Theory of Shape-Shifting Droplets

Recent studies of cooled oil emulsion droplets uncovered transformations into a host of flattened shapes with straight edges and sharp corners, driven by a partial phase transition of the bulk liquid phase. Here, we explore theoretically the simplest geometric competition between this phase transition and surface tension in planar polygons and recover the observed sequence of shapes and their statistics in qualitative agreement with experiments. Extending the model to capture some of the three-dimensional structure of the droplets, we analyze the evolution of protrusions sprouting from the vertices of the platelets and the topological transition of a puncturing planar polygon.

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 T_d 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_s > T_d. 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_d. Our results provide strong quantitative support validating the crystalline monolayer buckling mechanism.

On the Mechanism of Drop Self-Shaping in Cooled Emulsions

Two recent studies (Denkov et al., Nature 2015, 528, 392 and Guttman et al. Proc. Natl. Acad. Sci. U.S.A.2016, 113, 493) demonstrated that micrometer-sized n-alkane drops, dispersed in aqueous surfactant solutions, can break their spherical symmetry upon cooling and self-shape into a variety of regular shapes, such as fluid polyhedra, platelet-shaped hexagons, triangles, rhomboids, toroids, and submicrometer-diameter fibers. In the first study, the observed phenomenon was explained by a mechanism involving the formation of interfacial multilayer of self-assembled alkane molecules in the so-called rotator phases, templated by the frozen surfactant adsorption layer. Such phases are known to form in alkane droplets under similar conditions and are sufficiently strong to deform the droplets against the capillary pressure of a finite interfacial tension of several mN/m. The authors of the second study proposed a different explanation, namely, that the oil-water interfacial tension becomes ultralow upon cooling, which allows for surface extension and drop deformation at negligible energy penalty. To reveal which of these mechanisms is operative, we measure in the current study the temperature dependence of the interfacial tensions of several systems undergoing such drop-shape transitions. Our results unambiguously show that drop self-shaping is not related to ultralow oil-water interfacial tension, as proposed by Guttmann et al. These results support the mechanism proposed by Denkov et al., which implies that the large bending moment, required to deform an oil-water interface with an interfacial tension of 5 to 10 mN/m, is generated by an interfacial multilayer of self-assembled alkane molecules.