Contact angles of microellipsoids at fluid interfaces

Nanoscale Porosity in Microellipsoids Cloaks Interparticle Capillary Attraction at Fluid Interfaces

Anisotropic particles pinned at fluid interfaces tend toward disordered multiparticle configurations due to large, orientationally dependent, capillary forces, which is a significant barrier to exploiting these particles to create functional self-assembled materials. Therefore, current interfacial assembly methods typically focus on isotropic spheres, which have minimal capillary attraction and no dependence on orientation in the plane of the interface. In order to create long-range ordered structures with complex configurations via interfacially trapped anisotropic particles, control over the interparticle interaction energy via external fields and/or particle engineering is necessary. Here, we synthesize colloidal ellipsoids with nanoscale porosity and show that their interparticle capillary attraction at a water-air interface is reduced by an order of magnitude compared to their smooth counterparts. This is accomplished by comparing the behavior of smooth, rough, and porous ellipsoids at a water-air interface. By monitoring the dynamics of two particles approaching one another, we show that the porous particles exhibit a much shorter-range capillary interaction potential, with scaling intriguingly different than theory describing the behavior of smooth ellipsoids. Further, interferometry measurements of the fluid deformation surrounding a single particle shows that the interface around porous ellipsoids does not possess the characteristic quadrupolar symmetry of smooth ellipsoids, and quantitatively confirms the decrease in capillary interaction energy. By engineering nanostructured surface features in this fashion, the interfacial capillary interactions between particles may be controlled, informing an approach for the self-assembly of complex two-dimensional microstructures composed of anisotropic particles.

Investigation of the Orientation and Assembly of Functionalized Microcubes at the Oil-Water Interface

The dependence of the preferred orientation of polystyrene microcubes on surface hydrophobicity at the water/hexadecane interface is reported. Similar to the water/air interfaces, the microcubes were shown to reside at the water/hexadecane interface with three distinct orientations: face-up, edge-up, and vertex-up. Concomitantly, ordered aggregates with flat plate, tilted linear, and close-packed hexagonal structures were formed, driven by capillary force. With increasing the hydrophobicity of five sides of the cubes, the preferential microcube orientation at the water/hexadecane interface changed sequentially from face-up to edge-up, to vertex-up, then back to edge-up, and to face-up. This dependence of the preferential microcube orientation on surface hydrophobicity at the water/hexadecane interface differs from that observed at the water/air interface, where the preferential orientation changed only from face-up to edge-up, then to vertex-up, as surface hydrophobicity increased. In addition, preformed microcube assemblies at the water/air interface could be dynamically reconfigured by replacing the air phase with hexadecane under stirring.

Capillary Assembly of Anisotropic Particles at Cylindrical Fluid-Fluid Interfaces

The unique behavior of colloids at liquid interfaces provides exciting opportunities for engineering the assembly of colloidal particles into functional materials. The deformable nature of fluid-fluid interfaces means that we can use the interfacial curvature, in addition to particle properties, to direct self-assembly. To this end, we use a finite element method (Surface Evolver) to study the self-assembly of rod-shaped particles adsorbed at a simple curved fluid-fluid interface formed by a sessile liquid drop with cylindrical geometry. Specifically, we study the self-assembly of single and multiple rods as a function of drop curvature and particle properties such as shape (ellipsoid, cylinder, and spherocylinder), contact angle, aspect ratio, and chemical heterogeneity (homogeneous and triblock patchy). We find that the curved interface allows us to effectively control the orientation of the rods, allowing us to achieve parallel, perpendicular, or novel obliquely orientations with respect to the cylindrical drop. In addition, by tuning particle properties to achieve parallel alignment of the rods, we show that the cylindrical drop geometry favors tip-to-tip assembly of the rods, not just for cylinders, but also for ellipsoids and triblock patchy rods. Finally, for triblock patchy rods with larger contact line undulations, we can achieve strong spatial confinement of the rods transverse to the cylindrical drop due to the capillary repulsion between the contact line undulations of the particle and the pinned contact lines of the sessile drop. Our capillary assembly method allows us to manipulate the configuration of single and multiple rod-like particles and therefore offers a facile strategy for organizing such particles into useful functional materials.

Hybrid Nanoparticles at Fluid-Fluid Interfaces: Insight from Theory and Simulation

Hybrid nanoparticles that combine special properties of their different parts have numerous applications in electronics, optics, catalysis, medicine, and many others. Of the currently produced particles, Janus particles and ligand-tethered (hairy) particles are of particular interest both from a practical and purely cognitive point of view. Understanding their behavior at fluid interfaces is important to many fields because particle-laden interfaces are ubiquitous in nature and industry. We provide a review of the literature, focusing on theoretical studies of hybrid particles at fluid-fluid interfaces. Our goal is to give a link between simple phenomenological models and advanced molecular simulations. We analyze the adsorption of individual Janus particles and hairy particles at the interfaces. Then, their interfacial assembly is also discussed. The simple equations for the attachment energy of various Janus particles are presented. We discuss how such parameters as the particle size, the particle shape, the relative sizes of different patches, and the amphiphilicity affect particle adsorption. This is essential for taking advantage of the particle capacity to stabilize interfaces. Representative examples of molecular simulations were presented. We show that the simple models surprisingly well reproduce experimental and simulation data. In the case of hairy particles, we concentrate on the effects of reconfiguration of the polymer brushes at the interface. This review is expected to provide a general perspective on the subject and may be helpful to many researchers and technologists working with particle-laden layers.

Exploiting Heteroaggregation to Quantify the Contact Angle of Charged Colloids at Interfaces

We exploit the aggregation between oppositely charged particles to visualize and quantify the equilibrium position of charged colloidal particles at the fluid-water interface. A dispersion of commercially available charge-stabilized nanoparticles was used as the aqueous phase to create oil-water and air-water interfaces. The colloidal particles whose charge was opposite that of the nanoparticles in the aqueous phase were deposited at the chosen fluid-water interface. Heteroaggregation, i.e., aggregation between oppositely charged particles, leads to the deposition of nanoparticles onto the larger particle located at the interface; however, this only occurs on the surface of the particle in contact with the aqueous phase. This selective deposition of nanoparticles on the surfaces of the particles exposed to water enables the distinct visualization of the circular three-phase contact line around the particles positioned at the fluid-water interface. Since the electrostatic association between the nanoparticles and the colloids at interfaces is strong, the nanoparticle assembly on the larger particles is preserved even after being transferred to solid substrates via dip-coating. This facilitates the easy visualization of the contact line by electron microscopy and the determination of the equilibrium contact angle of colloidal particles (θ) at the fluid-water interface. The suitability of the method is demonstrated by the measurement of the three-phase contact angle of positively and negatively charged polystyrene particles located at fluid-water interfaces by considering particles with sizes varying from 220 nm to 8.71 μm. The study highlights the effect of the size ratio between the nanoparticles in the aqueous phase and the colloidal particles on the accuracy of the measurement of θ.

Versatile strategy for homogeneous drying patterns of dispersed particles

After spilling coffee, a tell-tale stain is left by the drying droplet. This universal phenomenon, known as the coffee ring effect, is observed independent of the dispersed material. However, for many technological processes such as coating techniques and ink-jet printing a uniform particle deposition is required and the coffee ring effect is a major drawback. Here, we present a simple and versatile strategy to achieve homogeneous drying patterns using surface-modified particle dispersions. High-molecular weight surface-active polymers that physisorb onto the particle surfaces provide enhanced steric stabilization and prevent accumulation and pinning at the droplet edge. In addition, in the absence of free polymer in the dispersion, the surface modification strongly enhances the particle adsorption to the air/liquid interface, where they experience a thermal Marangoni backflow towards the apex of the drop, leading to uniform particle deposition after drying. The method is independent of particle shape and applicable to a variety of commercial pigment particles and different dispersion media, demonstrating the practicality of this work for everyday processes.

Using adsorption kinetics to assemble vertically aligned nanorods at liquid interfaces for metamaterial applications

Vertically aligned monolayers of metallic nanorods have a wide range of applications as metamaterials or in surface enhanced Raman spectroscopy. However the fabrication of such structures using current top-down methods or through assembly on solid substrates is either difficult to scale up or have limited possibilities for further modification after assembly. The aim of this paper is to use the adsorption kinetics of cylindrical nanorods at a liquid interface as a novel route for assembling vertically aligned nanorod arrays that overcomes these problems. Specifically, we model the adsorption kinetics of the particle using Langevin dynamics coupled to a finite element model, accurately capturing the deformation of the liquid meniscus and particle friction coefficients during adsorption. We find that the final orientation of the cylindrical nanorod is determined by their initial attack angle when they contact the liquid interface, and that the range of attack angles leading to the end-on state is maximised when nanorods approach the liquid interface from the bulk phase that is more energetically favorable. In the absence of an external field, only a fraction of adsorbing nanorods end up in the end-on state (≲40% even for nanorods approaching from the energetically favourable phase). However, by pre-aligning the metallic nanorods with experimentally achievable electric fields, this fraction can be effectively increased to 100%. Using nanophotonic calculations, we also demonstrate that the resultant vertically aligned structures can be used as epsilon-near-zero and hyperbolic metamaterials. Our kinetic assembly method is applicable to nanorods with a range of diameters, aspect ratios and materials and therefore represents a versatile, low-cost and powerful platform for fabricating vertically aligned nanorods for metamaterial applications.

Investigation of the Contact Angle and Packing Density of Silica Nanoparticles at a Pickering Emulsion Interface Fixed by UV Polymerization

The contact angle of colloidal particles at an oil-water interface plays a crucial role in determining Pickering emulsion stability and emulsion type, but the contact angle cannot be directly determined using conventional methods. In this work, a Pickering emulsion was prepared with photocurable resin as the internal phase containing silica nanoparticle stabilizers. Particles adsorbed at the oil-water interface were then fixed through UV curing, allowing for the investigation of various parameters that influence the contact angle of colloidal particles at the interface. After curing, the contact angle can then be observed using scanning electron microscopy and subsequently measured. The contact angle of interfacial adsorbed silica nanoparticles gradually decreases as the size increases due to the line tension at the three-phase contact line, but, more importantly, we found that the surface chemistry of the silica nanoparticles plays the most important role in determining the contact angle. The fast fixation of solid nanoparticles at emulsion interfaces facilitates accurate measurements of the partition of particles between oil and water, providing a new method for studying the factors that affect Pickering emulsion stability.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

Adsorption trajectories of nonspherical particles at liquid interfaces

The adsorption of colloidal particles at liquid interfaces is of great importance scientifically and industrially, but the dynamics of the adsorption process is still poorly understood. In this paper we use a Langevin model to study the adsorption dynamics of ellipsoidal colloids at a liquid interface. Interfacial deformations are included by coupling our Langevin dynamics to a finite element model while transient contact line pinning due to nanoscale defects on the particle surface is encoded into our model by renormalizing particle friction coefficients and using dynamic contact angles relevant to the adsorption timescale. Our simple model reproduces the monotonic variation of particle orientation with time that is observed experimentally and is also able to quantitatively model the adsorption dynamics for some experimental ellipsoidal systems but not others. However, even for the latter case, our model accurately captures the adsorption trajectory (i.e., particle orientation versus height) of the particles. Our study clarifies the subtle interplay between capillary, viscous, and contact line forces in determining the wetting dynamics of micron-scale objects, allowing us to design more efficient assembly processes for complex particles at liquid interfaces.

Gradient stretching to produce variable aspect ratio colloidal ellipsoids

Developing reliable synthetic methods for producing shape-anisotropic polymer colloids is essential for their use in novel functional materials. In designing such materials from ellipsoidal particles, it is often necessary to screen a wide range of particle sizes and aspect ratios to appropriately understand how microscopic particle characteristics dictate macroscopic material response. Here, we describe a technique to simultaneously produce a broad range of aspect ratio polymer ellipsoid samples from a single synthetic step. The technique extends the traditional film-stretching approach to create ellipsoids by introducing a gradient in strain and film cooling, which results in varying degrees of particle stretching. We empirically calibrate the device such that the final particle elongation may be predicted from the film characteristics, enabling the selective harvesting of ellipsoids with desired dimensions and which can be isolated by aspect ratio. The method is applied successfully to a wide range of seed particle diameters (500 nm - 10 μm) and enables the rapid synthesis of variable aspect ratio particles for systematic studies of anisotropic particles.

Detachment work of prolate spheroidal particles from fluid droplets: role of viscous dissipation

The force-displacement curve for removal of an elongated solid particle from the surface of liquid droplets or gas bubbles is calculated and compared to our previous reported results for spherical particles. The surface adsorption energy for prolate particles is known to be larger than that for spheres. We show that in fact the minimum possible work done upon removal of an elongated particle from surface can be less than that for a sphere. This result is obtained when the dissipation of interfacial energy, stored in the fluid film, attaching the particles to the surface during their displacement, is properly accounted for. This dissipation is unavoidable, even if the particles are removed infinitely slowly. Once the particle actually leaves the surface, the formed liquid bridge relaxes thus dissipating any stored interfacial energy as the surface returns to its original undistorted state. The difference between the work of removal of a particle from surface and its adsorption energy is seen to become increasingly larger with smaller particle to droplet size ratios. For example, for a size ratio of 1 : 100, the work of removal is 1.93 times greater than the adsorption energy. However, we also find that for any given size ratio, there is a value of particle aspect ratio for which the work of removal of particles (combined dissipated and adsorbed energy) attains its minimum value.

Adsorption and interfacial structure of nanocelluloses at fluid interfaces

Nanocelluloses (NCs), more specifically cellulose nanocrystals and nanofibrils, are a green alternative for the stabilization of fluid interfaces. The adsorption of NCs at oil-water interfaces facilitates the formation of stable and biocompatible Pickering emulsions. In contrast, unmodified NCs are not able to stabilize foams. As a consequence, NCs are often hydrophobized by covalent modifications or adsorption of surfactants, allowing also the stabilization of foams or functional inverse, double, and stimuli-responsive emulsions. Although the interfacial stabilization by NCs is readily exploited, the driving force of adsorption and stabilization mechanisms remained long unclear. Here, we summarize the recent advances in the understanding of NC adsorption regarding kinetics, isotherms, and energetic aspects, as well as their interfacial structure, surface coverage, and contact angle. We thereby distinguish unmodified NCs, covalently modified NCs, and surfactant enhanced adsorption.

Direct observation of the attachment behavior of hydrophobic colloidal particles onto a bubble surface

The attachment of solid particles to the surface of immersed gas bubbles plays a fundamental role in surface science, and hence plays key roles in various engineering fields ranging from industrial separation processes to the fabrication of functional materials. However, detailed investigation from a microscopic view on how a single particle attaches to a bubble surface and how the particle properties affect the attachment behavior has been so far scarcely addressed. Here, we observed the attachment of a single particle to a bubble surface using a high-speed camera and systematically investigated the effects of the wettability and shape of particles. We found that hydrophobic particles abruptly "jumped into" the bubble while sliding down the bubble surface to eventually satisfy their static contact angles, the behavior of which induced a much stronger attachment to the bubble surface. Interestingly, the determinant factor for the attachment efficiency of spherical particles was not the wettability of the spherical particles but the location of the initial collision with the bubble surface. In contrast, the attachment efficiency of anisotropically-shaped particles was found to increase with the hydrophobicity caused by a larger contact area to the bubble surface. Last but not least, a simple formulation is suggested to recover the contact angle based on the jump-in behavior.

Adsorption of charged anisotropic nanoparticles at oil-water interfaces

The adsorption of nanoparticles at fluid interfaces is of profound importance in the field of nanotechnology. Recent developments aim at pushing the boundaries beyond spherical model particles towards more complex shapes and surface chemistries, with particular interest in particles of biological origin. Here, we report on the adsorption of charged, shape-anisotropic cellulose nanocrystals (CNCs) for a wide range of oils with varying chemical structure and polarity. CNC adsorption was found to be independent of the chain length of aliphatic n-alkanes, but strongly dependent on oil polarity. Surface pressures decreased for more polar oils due to lower particle adsorption energies. Nanoparticles were increasingly wetted by polar oils, and interparticle Coulomb interactions across the oil phase thus increase in importance. No surface pressure was measurable and the O/W emulsification capacity ceased for the most polar octanol, suggesting limited CNC adsorption. Further, salt-induced charge screening enhanced CNC adsorption and surface coverage due to lower interparticle and particle-interface electrostatic repulsion. An empiric power law is presented which predicts the induced surface pressure of charged nanoparticles based on the specific oil-water interface tension.

Super-resolution microscopy on single particles at fluid interfaces reveals their wetting properties and interfacial deformations

Solid particles adsorbed at fluid interfaces are crucial for the mechanical stability of Pickering emulsions. The key parameter which determines the kinetic and thermodynamic properties of these colloids is the particle contact angle, θ. Several methods have recently been developed to measure the contact angle of individual particles adsorbed at liquid-liquid interfaces, as morphological and chemical heterogeneities at the particle surface can significantly affect θ. However, none of these techniques enables the simultaneous visualization of the nanoparticles and the reconstruction of the fluid interface to which they are adsorbed, in situ. To tackle this challenge, we utilize a newly developed super-resolution microscopy method, called iPAINT, which exploits non-covalent and continuous labelling of interfaces with photo-activatable fluorescent probes. Herewith, we resolve with nanometer accuracy both the position of individual nanoparticles at a water-octanol interface and the location of the interface itself. First, we determine single particle contact angles for both hydrophobic and hydrophilic spherical colloids. These experiments reveal a non-negligible dependence of θ on particle size, from which we infer an effective line tension, τ. Next, we image elliptical particles at a water-decane interface, showing that the corresponding interfacial deformations can be clearly captured by iPAINT microscopy.

Equilibrium configurations and capillary interactions of Janus dumbbells and spherocylinders at fluid-fluid interfaces

We numerically investigate the adsorption of a variety of Janus particles (dumbbells, elongated dumbbells and spherocylinders) at a fluid-fluid interface by using a numerical method that takes into account the interfacial deformations. We first determine the equilibrium configuration of a single adsorbed particle, and we find that the overall shape of the induced deformation field has a strong hexapolar mode while non-Janus particles of the same shape do not induce any interfacial deformation. We then calculate the capillary interactions between two Janus spherocylinders adsorbed at an interface. The hexapolar deformation field induces capillary attractions for laterally aligned Janus spherocylinders and repulsions for laterally anti-aligned ones. We also experimentally synthesize micrometer-sized charged Janus dumbbells and let them adsorb at a water-decane interface. After several hours we observe the formation of aggregates of dumbbells predominantly induced by interactions that appear to be capillary in nature. Our Janus dumbbells attach laterally and are all aligned, as predicted by our numerical calculations.

Colloidal particles at fluid interfaces: behaviour of isolated particles

The adsorption of colloidal particles to fluid interfaces is a phenomenon that is of interest to multiple disciplines across the physical and biological sciences. In this review we provide an entry level discussion of our current understanding on the physical principles involved and experimental observations of the adsorption of a single isolated particle to a liquid-liquid interface. We explore the effects that a variation of the morphology and surface chemistry of a particle can have on its ability to adhere to a liquid interface, from a thermodynamic as well as a kinetic perspective, and the impact of adsorption behaviour on potential applications. Finally, we discuss recent developments in the measurement of the interfacial behaviour of nanoparticles and highlight open questions for future research.

Shape-Anisotropic Colloids at Interfaces

Research in the 1980s demonstrated the formation of monolayers of particles achieved by interfacial particle trapping as a model system for investigating colloids in two dimensions. Since then, microscopy visualization of two-dimensional particle monolayers and quantification of the microstructure have led to significant fundamental understanding of a number of phenomena such as crystallization, freezing and melting transitions, dislocation dynamics, aggregation kinetics, and others. On the application front, particles at curved interfaces, as often the case in particle-stabilized emulsions and foams, have received considerable attention in the last few decades. The growing interest in the search for novel particles and new strategies to effect emulsion stabilization stems from their application in several disciplines. Moreover, particle-stabilized Pickering emulsions and foams can also be used to derive a number of advanced functional materials. Compared to several accounts of research on spherical colloids at fluid-fluid interfaces, investigations of the behavior of shape-anisotropic particles at interfaces, albeit receiving considerable attention in recent years, are still in a nascent stage. The objective of this feature article is to highlight our recent work in this area. In particular, the adsorption of shape-anisotropic particles to interfaces, wetting behavior, interfacial self-assembly, the response of nonspherical-particle-coated interfaces to compression and shear, and their ability to stabilize emulsions are discussed.

A Dirty Story: Improving Colloidal Monolayer Formation by Understanding the Effect of Impurities at the Air/Water Interface

Colloidal monolayers are important tools to fabricate surface structures at the nanoscale. A typical monolayer fabrication strategy involves the self-assembly of colloidal building blocks at liquid interfaces, which are subsequently deposited on a solid substrate. Even though this process is well established, the resulting order of the particles within the colloidal monolayer differs between batches of colloidal particles and can even change with the age of the dispersion. In this study, we investigate the origins of this variation of monolayer quality for polystyrene particles synthesized by surfactant-free emulsion polymerization. We correlate the interfacial behavior of the colloidal particles at the air/water interface on a Langmuir trough with the resulting quality of the monolayer after transfer to a solid substrate. We identify surface-active impurities as a major cause for a disturbed self-assembly of the colloidal particles. These impurities form during the particle synthesis and consist of copolymers of styrene, the comonomer acrylic acid, and sulfonate species from the initiator. We show that they can be removed by cleaning protocols to increase the monolayer quality. However, our experiments demonstrate that the impurities reappear over time even for cleaned dispersions, indicating desorption from the surface of the colloidal particles. We identify strategies to avoid the presence of the impurities at the air/water interface or to inhibit their effect on the self-assembly process. These simple guidelines improve the quality of the resulting colloidal monolayer, which is a prerequisite for the reliable fabrication of high-quality surface nanostructures from colloidal templates.

Interfacial rheology of model particles at liquid interfaces and its relation to (bicontinuous) Pickering emulsions

Interface-dominated materials are commonly encountered in both science and technology, and typical examples include foams and emulsions. Conventionally stabilised by surfactants, emulsions can also be stabilised by micron-sized particles. These so-called Pickering-Ramsden (PR) emulsions have received substantial interest, as they are model arrested systems, rather ubiquitous in industry and promising templates for advanced materials. The mechanical properties of the particle-laden liquid-liquid interface, probed via interfacial rheology, have been shown to play an important role in the formation and stability of PR emulsions. However, the morphological processes which control the formation of emulsions and foams in mixing devices, such as deformation, break-up, and coalescence, are complex and diverse, making it difficult to identify the precise role of the interfacial rheological properties. Interestingly, the role of interfacial rheology in the stability of bicontinuous PR emulsions (bijels) has been virtually unexplored, even though the phase separation process which leads to the formation of these systems is relatively simple and the interfacial deformation processes can be better conceptualised. Hence, the aims of this topical review are twofold. First, we review the existing literature on the interfacial rheology of particle-laden liquid interfaces in rheometrical flows, focussing mainly on model latex suspensions consisting of polystyrene particles carrying sulfate groups, which have been most extensively studied to date. The goal of this part of the review is to identify the generic features of the rheology of such systems. Secondly, we will discuss the relevance of these results to the formation and stability of PR emulsions and bijels.

Self-assembly of cubic colloidal particles at fluid-fluid interfaces by hexapolar capillary interactions

Colloidal particles adsorbed at fluid-fluid interfaces can self-assemble, thanks to capillary interactions, into 2D ordered structures. Recently, it has been predicted by theoretical and numerical calculations [G. Soligno et al., Phys. Rev. Lett., 2016, 116, 258001] that cubes with smooth edges adsorbed at a flat fluid-fluid interface generate hexapolar capillary deformations that cause the particles to self-assemble into honeycomb and hexagonal lattices, at equilibrium and for Young's contact angle π/2. Here we extend these results. Firstly, we show that capillary interactions induced by hexapolar deformations can drive the particles at the interface to form also thermodynamically-stable square lattices, in addition to honeycomb and hexagonal lattices. Then, we study the effects of tuning the particle shape on the particle self-assembly at the interface, considering, respectively, smooth-edge cubes, sharp-edge cubes, slightly truncated-edge cubes, and highly truncated-edge cubes. In our calculations, both capillary and hard-particle interactions are taken into account. We show that such variations in the particle shape significantly affect both qualitatively and quantitatively the self-assembly of the particles at the interface, and we sum up our results in the form of temperature-density phase diagrams. For example, using typical experimental parameters, our results show that only 4-to-5 nm sized sharp-edge and smooth-edge cubes can self-assemble into a honeycomb lattice, while slightly and highly truncated-edge cubes can form a honeycomb lattice only if they have a 8-to-12 and 10-to-16 nm size, respectively, for the same experimental parameters. Also, our results show that the capillarity-induced square lattice phase is stable only for the smooth-edge and truncated-edge cubes, but not for the sharp-edge cubes.

Deformation of the contact line around spherical particles bound at anisotropic fluid interfaces

When a particle adsorbs at a liquid interface, the 3-phase contact line geometry depends on the shape of the particle and of the liquid interface. The shape of the contact line is the key to controlling capillary forces among particles, and is therefore a useful means to direct assembly of interfacial particles. We measured the shape of the contact line around millimeter-sized PDMS-coated glass spheres at water/air interfaces with anisotropic shapes. We studied the advancing and receding conditions separately. We focused on interfaces with a cylindrical shape, where the predominant deformation of the meniscus and the contact line both have quadrupolar cos(2ϕ) symmetry. We related the measured magnitude of the quadrupolar deformation to the applied vertical force on the sphere and the interface's deviatoric curvature, D₀. For modest curvature (D₀ < 0.1 × sphere radius), our results agree with the theoretical prediction for free particles. At higher curvature, the measurements exceed the theory. The theory appears to apply even when there is contact-angle hysteresis, as long as the measured contact angle is used rather than the equilibrium (Young-Dupré) angle. The magnitude of the quadrupolar deformation depends on the applied force. Together, these results show the range of validity of the theory.

Structure and Interfacial Tension of a Hard-Rod Fluid in Planar Confinement

The structural properties and interfacial tension of a fluid of rodlike hard-spherocylinder particles in contact with hard structureless flat walls are studied by means of Monte Carlo simulation. The calculated surface tension between the rod fluid and the substrate is characterized by a nonmonotonic trend as a function of the bulk concentration (density) over the range of isotropic bulk concentrations. As suggested by earlier theoretical studies, a surface-ordering scenario is confirmed by our simulations: the local orientational order close to the wall changes from uniaxial to biaxial nematic when the bulk concentration reaches about 85% of the value at the onset of the isotropic-nematic phase transition. The surface ordering coincides with a wetting transition whereby the hard wall is wetted by a nematic film. Accurate values of the fluid-solid surface tension, the adsorption, and the average particle-wall contact distance are reported (over a broad range of densities into the dense nematic region for the first time), which can serve as a useful benchmark for future theoretical and experimental studies on confined rod fluids. The simulation data are supplemented with predictions from second-virial density functional theory, which are in good qualitative agreement with the simulation results.

Nano- and microparticles at fluid and biological interfaces

Systems with interfaces are abundant in both technological applications and biology. While a fluid interface separates two fluids, membranes separate the inside of vesicles from the outside, the interior of biological cells from the environment, and compartmentalize cells into organelles. The physical properties of interfaces are characterized by interface tension, those of membranes are characterized by bending and stretching elasticity. Amphiphilic molecules like surfactants that are added to a system with two immiscible fluids decrease the interface tension and induce a bending rigidity. Lipid bilayer membranes of vesicles can be stretched or compressed by osmotic pressure; in biological cells, also the presence of a cytoskeleton can induce membrane tension. If the thickness of the interface or the membrane is small compared with its lateral extension, both can be described using two-dimensional mathematical surfaces embedded in three-dimensional space. We review recent work on the interaction of particles with interfaces and membranes. This can be micrometer-sized particles at interfaces that stabilise emulsions or form colloidosomes, as well as typically nanometer-sized particles at membranes, such as viruses, parasites, and engineered drug delivery systems. In both cases, we first discuss the interaction of single particles with interfaces and membranes, e.g. particles in external fields, non-spherical particles, and particles at curved interfaces, followed by interface-mediated interaction between two particles, many-particle interactions, interface and membrane curvature-induced phenomena, and applications.

Effects of Contact-Line Pinning on the Adsorption of Nonspherical Colloids at Liquid Interfaces

The effects of contact-line pinning are well known in macroscopic systems but are only just beginning to be explored at the microscale in colloidal suspensions. We use digital holography to capture the fast three-dimensional dynamics of micrometer-sized ellipsoids breaching an oil-water interface. We find that the particle angle varies approximately linearly with the height, in contrast to results from simulations based on the minimization of the interfacial energy. Using a simple model of the motion of the contact line, we show that the observed coupling between translational and rotational degrees of freedom is likely due to contact-line pinning. We conclude that the dynamics of colloidal particles adsorbing to a liquid interface are not determined by the minimization of interfacial energy and viscous dissipation alone; contact-line pinning dictates both the time scale and pathway to equilibrium.

Adsorption of Ellipsoidal Particles at Liquid-Liquid Interfaces

The adsorption of particles at liquid-liquid interfaces is of great scientific and technological importance. In particular, for nonspherical particles, the capillary forces that drive adsorption vary with position and orientation, and complex adsorption pathways have been predicted by simulations. On the basis of the latter, it has been suggested that the timescales of adsorption are determined by a balance between capillary and viscous forces. However, several recent experimental results point out the role of contact line pinning in the adsorption of particles to interfaces and even suggest that the adsorption dynamics and pathways are completely determined by the latter, with the timescales of adsorption being determined solely by particle characteristics. In the present work, the adsorption trajectories of model ellipsoidal particles are investigated experimentally using cryo-SEM and by monitoring the altitudinal orientation angle using high-speed confocal microscopy. By varying the viscosity and the viscosity jump across the interfaces, we specifically interrogate the role of viscous forces.

Ellipsoidal Colloids with a Controlled Surface Roughness via Bioinspired Surface Engineering: Building Blocks for Liquid Marbles and Superhydrophobic Surfaces

Understanding the important role of the surface roughness of nano/colloidal particles and harnessing them for practical applications need novel strategies to control the particles' surface topology. Although there are many examples of spherical particles with a specific surface roughness, nonspherical ones with similar surface features are rare. The current work reports a one-step, straightforward, and bioinspired surface engineering strategy to prepare ellipsoidal particles with a controlled surface roughness. By manipulating the unique chemistry inherent to the oxidation-induced self-polymerization of dopamine into polydopamine (PDA), PDA coating of polymeric ellipsoids leads to a library of hybrid ellipsoidal particles (PS@PDA) with a surface that decorates with nanoscale PDA protrusions of various densities and sizes. Together with the advantages originated from the anisotropy of ellipsoids and rich chemistry of PDA, such a surface feature endows these particles with some unique properties. Evaporative drying of fluorinated PS@PDA particles produces a homogeneous coating with superhydrophobicity that arises from the two-scale hierarchal structure of microscale interparticle packing and nanoscale roughness of the constituent ellipsoids. Instead of water repelling that occurs for most of the lotus leaf-like superhydrophobic surfaces, such coating exhibits strong water adhesion that is observed with certain species of rose pedals. In addition, the as-prepared hybrid ellipsoids are very efficient in preparing liquid marble-isolated droplets covered with solid particles. Such liquid marbles can be placed onto many surfaces and might be useful for the controllable transport and manipulation of small volumes of liquids.

Shape-Induced Deformation, Capillary Bridging, and Self-Assembly of Cuboids at the Fluid-Fluid Interface

The controlled assembly of anisotropic particles through shape-induced interface deformations is shown to be a potential route for the fabrication of novel functional materials. In this article, the shape-induced interface deformation, capillary bridging, and directed self-assembly of cuboidal-shaped hematite particles at fluid-fluid interfaces are reported. The multipolar nature of the interface distortions is directly visualized using high-resolution scanning electron microscopy and 3D optical surface profiling. The nature of the interface deformations around cuboidal particles vary from monopolar to octupolar types depending on their orientation and position with respect to the interface. The deformations are of either hexapolar or octupolar type in the face-up orientation, quadrupolar or monopolar type in the edge-up orientation, and monopolar type in the vertex-up orientation. The particles adsorbed at the interface interact through the interface deformations, forming capillary bridges that lead to isolated assemblies of two or more particles. The arrangement of particles in any assembly is such that the condition for capillary attraction is satisfied, that is, in accordance with predictions based on the nature of interface deformations. At sufficient particle concentrations, these isolated structures interact to form a percolating network of cuboids. Furthermore, the difference in the nature of the assembly structures formed at the air-water interface and in the bulk water phase indicates that the interfacial assembly of these particles is controlled by the capillary interactions.

Self-assembly of repulsive interfacial particles via collective sinking

Charged colloidal particles trapped at an air-water interface are well known to form an ordered crystal, stabilized by a long ranged repulsion; the details of this repulsion remain something of a mystery, but all experiments performed to date have confirmed a dipolar-repulsion, at least at dilute concentrations. More complex arrangements are often observed, especially at higher concentration, and these seem to be incompatible with a purely repulsive potential. In addition to electrostatic repulsion, interfacial particles may also interact via deformation of the surface: so-called capillary effects. Pair-wise capillary interactions are well understood, and are known to be too small (for these colloidal particles) to overcome thermal effects. Here we show that collective effects may significantly modify the simple pair-wise interactions and become important at higher density, though we remain well below close packing throughout. In particular, we show that the interaction of many interfacial particles can cause much larger interfacial deformations than do isolated particles, and show that the energy of interaction per particle due to this "collective sinking" grows as the number of interacting particles grows. Though some of the parameters in our simple model are unknown, the scaling behaviour is entirely consistent with experimental data, strongly indicating that estimating interaction energy based solely on pair-wise potentials may be too simplistic for surface particle layers.

Contact-line pinning controls how quickly colloidal particles equilibrate with liquid interfaces

Previous experiments have shown that spherical colloidal particles relax to equilibrium slowly after they adsorb to a liquid-liquid interface, despite the large interfacial energy gradient driving the adsorption. The slow relaxation has been explained in terms of transient pinning and depinning of the contact line on the surface of the particles. However, the nature of the pinning sites has not been investigated in detail. We use digital holographic microscopy to track a variety of colloidal spheres-inorganic and organic, charge-stabilized and sterically stabilized, aqueous and non-aqueous-as they breach liquid interfaces. We find that nearly all of these particles relax logarithmically in time over timescales much larger than those expected from viscous dissipation alone. By comparing our results to theoretical models of the pinning dynamics, we infer the area per defect to be on the order of a few square nanometers for each of the colloids we examine, whereas the energy per defect can vary from a few kT for non-aqueous and inorganic spheres to tens of kT for aqueous polymer particles. The results suggest that the likely pinning sites are topographical features inherent to colloidal particles-surface roughness in the case of silica particles and grafted polymer "hairs" in the case of polymer particles. We conclude that the slow relaxation must be taken into account in experiments and applications, such as Pickering emulsions, that involve colloids attaching to interfaces. The effect is particularly important for aqueous polymer particles, which pin the contact line strongly.

Particle contact angles at fluid interfaces: pushing the boundary beyond hard uniform spherical colloids

Micro and nanoparticles at fluid interfaces have been attracting increasing interest in the last few decades as building blocks for materials, as mechanical and structural probes for complex interfaces and as models for two-dimensional systems. The three-phase contact angle enters practically all aspects of the particle behavior at the interface: its thermodynamics (binding energy to the interface), dynamics (motion and drag at the interface) and interactions with the interface (adsorption and wetting). Moreover, many interactions among particles at the interface also strongly depend on the contact angle. These concepts have been extensively discussed for non-deformable, homogeneous and mostly spherical particles, but recent progress in particle synthesis and fabrication has instead moved in the direction of producing more complex micro and nanoscale objects, which can be responsive, deformable, heterogenous and/or anisotropic in shape, surface chemistry and material properties. These new particles have a much greater potential for applications and new science, and the study of their behavior at interfaces has only very recently started. In this paper, we critically review the current state of the art of the experimental methods available to measure the contact angle of micro and nanoparticles at fluid interfaces, indicating their strengths and limitations. We then comment on new particle systems that are currently attracting increasing interest in relation to their adsorption and assembly at fluid interfaces and discuss if and which ones of the current techniques are suited to investigate their properties at interfaces. Based on this discussion, we will finally try to indicate a direction in which new experimental methods should develop in the future to tackle the new challenges posed by the novel types of particles that more and more often are used at interfaces.

Immobilization of Colloidal Monolayers at Fluid⁻Fluid Interfaces

Monolayers of colloidal particles trapped at an interface between two immiscible fluids play a pivotal role in many applications and act as essential models in fundamental studies. One of the main advantages of these systems is that non-close packed monolayers with tunable inter-particle spacing can be formed, as required, for instance, in surface patterning and sensing applications. At the same time, the immobilization of particles locked into desired structures to be transferred to solid substrates remains challenging. Here, we describe three different strategies to immobilize monolayers of polystyrene microparticles at water⁻decane interfaces. The first route is based on the leaking of polystyrene oligomers from the particles themselves, which leads to the formation of a rigid interfacial film. The other two rely on in situ interfacial polymerization routes that embed the particles into a polymer membrane. By tracking the motion of the colloids at the interface, we can follow in real-time the formation of the polymer membranes and we interestingly find that the onset of the polymerization reaction is accompanied by an increase in particle mobility determined by Marangoni flows at the interface. These results pave the way for future developments in the realization of thin tailored composite polymer-particle membranes.

Self-Assembly of Cubes into 2D Hexagonal and Honeycomb Lattices by Hexapolar Capillary Interactions

Particles adsorbed at a fluid-fluid interface induce capillary deformations that determine their orientations and generate mutual capillary interactions which drive them to assemble into 2D ordered structures. We numerically calculate, by energy minimization, the capillary deformations induced by adsorbed cubes for various Young's contact angles. First, we show that capillarity is crucial not only for quantitative, but also for qualitative predictions of equilibrium configurations of a single cube. For a Young's contact angle close to 90°, we show that a single-adsorbed cube generates a hexapolar interface deformation with three rises and three depressions. Thanks to the threefold symmetry of this hexapole, strongly directional capillary interactions drive the cubes to self-assemble into hexagonal or graphenelike honeycomb lattices. By a simple free-energy model, we predict a density-temperature phase diagram in which both the honeycomb and hexagonal lattice phases are present as stable states.

Brownian diffusion of a partially wetted colloid

The dynamics of colloidal particles at interfaces between two fluids plays a central role in microrheology, encapsulation, emulsification, biofilm formation, water remediation and the interface-driven assembly of materials. Common intuition corroborated by hydrodynamic theories suggests that such dynamics is governed by a viscous force lower than that observed in the more viscous fluid. Here, we show experimentally that a particle straddling an air/water interface feels a large viscous drag that is unexpectedly larger than that measured in the bulk. We suggest that such a result arises from thermally activated fluctuations of the interface at the solid/air/liquid triple line and their coupling to the particle drag through the fluctuation-dissipation theorem. Our findings should inform approaches for improved control of the kinetically driven assembly of anisotropic particles with a large triple-line-length/particle-size ratio, and help to understand the formation and structure of such arrested materials.

Aqueous foams stabilized by chitin nanocrystals

The aim of the present study was to explore the potential use of chitin nanocrystals, as colloidal rod-like particles, to stabilize aqueous foams. Chitin nanocrystals (ChN) were prepared by acid hydrolysis of crude chitin and foams were generated mainly by sonicating the respective dispersions. The foamability of the chitin nanocrystals was evaluated and the resulting foams were assessed for their stability, in terms of foam volume reduction and serum release patterns, during storage. Additionally, the samples were studied with light scattering and optical microscopy in order to explore the bubble size distribution and morphology of the foam. Nanocrystal concentration and charge density was varied to alter the packing of the crystals at the interface. At low concentrations of ChNs, foams were stable against coalescence and disproportionation for a period of three hours, whereas at higher concentrations, the foams were stable for several days. The enhanced stability of foams prepared with ChNs, compared to surfactant-stabilized foams, can be mainly attributed to the irreversible adsorption of the ChNs at the air-water interface, thereby providing Pickering stabilization. Both foam volume and stability of the foam were increased with an increase in ChNs concentration, and at pH values around the chitin's pKa (pH 7.0). Under these conditions, the ChNs show minimal electrostatic repulsion and therefore a higher packing of the nanocrystals is promoted. Moreover, decreased electrostatic repulsion enhances network formation between the ChNs in the aqueous films, thereby providing additional stability by gel formation. Overall, ChNs were proven to be effective in stabilizing foams, and may be useful in the design of Pickering-stabilized food grade foams.

Contact angle distribution of particles at fluid interfaces

Recent measurements have implied a distribution of interfacially adsorbed particles' contact angles; however, it has been impossible to measure statistically significant numbers for these contact angles noninvasively in situ. Using a new microscopy method that allows nanometer-scale resolution of particle's 3D positions on an interface, we have measured the contact angles for thousands of latex particles at an oil/water interface. Furthermore, these measurements are dynamic, allowing the observation of the particle contact angle with high temporal resolution, resulting in hundreds of thousands of individual contact angle measurements. The contact angle has been found to fit a normal distribution with a standard deviation of 19.3°, which is much larger than previously recorded. Furthermore, the technique used allows the effect of measurement error, constrained interfacial diffusion, and particle property variation on the contact angle distribution to be individually evaluated. Because of the ability to measure the contact angle noninvasively, the results provide previously unobtainable, unique data on the dynamics and distribution of the adsorbed particles' contact angle.

Micro and macrorheology at fluid-fluid interfaces

Interfacial transport phenomena play an important role in the dynamics of liquid interfaces found in emulsions, foams, and membranes. Both macroscopic and microscopic measurements of interfacial transport and rheology can be made, the former typically relying on the use of at least millimeter-scale probes, and the latter exploiting the motion of micrometer-scale probes. Recent publications have shown multiple orders of magnitude differences between experimentally observed diffusivities in passive microrheology, and the diffusivities expected based on macroscopic measurements of the surface rheology. In the present work, interfacial rheological measurements were made with both microrheological and macrorheological methods and the results are compared for different monolayers at an air-water interface. We have identified multiple aspects of particle-tracking microrheology that can contribute to orders-of-magnitude disagreement with macrorheological methods. In particular, unintentional tracking of particles not residing at the interface, the presence of large-scale interfacial heterogeneities, and underestimating static noise can all decrease estimates of surface viscosity from particle-tracking microrheology by orders of magnitude. After taking care to address these artifacts, we show that viscosities obtained from both methods agree well for poly(tert-butyl methacrylate) (PtBMA), and for dipalmitoylphosphatidylcholine (DPPC), but disagree by orders of magnitude for hexadecanol. In poly(tert-butyl acrylate) (PtBA), large-scale heterogeneities prevented us from obtaining representative surface viscosities. By making surface viscosity measurements in an interfacial stress rheometer (ISR) with needles of different aspect ratio, we show that compressibility or Marangoni stress related effects may be contributing to the orders of magnitude disagreement in micro and macrorheological measurements observed in the hexadecanol system.

Adsorption of sub-micron amphiphilic dumbbells to fluid interfaces

We investigate the adsorption of submicrometer bulk-synthesized polymer dumbbells to oil-water interfaces using freeze-fracture, shadow-casting (FreSCa) cryo-scanning electron microscopy. We find that the dumbbells are amphiphilic and adsorb to the interface with a preferred orientation. Most particles adsorb in a tilted configuration, with the polar and apolar lobes intersecting the interface and pointing toward the water and oil, respectively. Some particles adsorb with only one lobe attached to the interface. Moreover, we find that each lobe has a preferred angle of contact with the interface, identical in all observed configurations. A simple geometrical calculation using these contact angles accurately predicts the dominant configuration of particles at the interface. This calculation provides insight into how the shape and composition of dumbbells can be tuned to stand upright and pack efficiently on curved interfaces.