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

Deformation of confined liquid interfaces by inhomogeneous electric fields and localized particle forces

HYPOTHESIS

Oil-water interfaces that are created by confining a certain amount of oil in a square shaped pixel (∼200 x 200 μm2 with a height of ∼10 μm) topped by a layer of water, have a curvature that depends on the amount of oil that happens to be present in the confining area. Under the application of an electric field normal to the interface, the interface will deform due to inhomogeneities in the electric field. These inhomogeneities are expected to arise from the initial curvature of the meniscus, from fringe fields that emerge at the confining pixel walls and, if applicable, from interfacially adsorbed particles.

MODELING AND EXPERIMENTS

We model the shape of the confined oil-water interface invoking capillarity and electrostatics. Furthermore, we measure the initial curvature by tracking the position of interfacially adsorbed particles depending on sample tilt.

FINDINGS

We found that the pixels exhibited meniscus curvature radii ranging from 0.6-7 mm. The corresponding model based minimum oil film thicknesses range between 0.7 and 9 μm. Furthermore, the model shows that the initial meniscus curvature can increase up to 76 percent relative to the initial curvature by the electric field before the oil film becomes unstable. The pixel wall and particles are shown to have minimal impact on the interface deformation.

Capillary Forces Lead to Pendant Crystals at the Liquid-Air Interface of Evaporating Salt Solutions

We investigated the nucleation and growth processes of individual NaCl crystals from an evaporating salt solution that is supersaturated. We find that crystals nucleate at the liquid/vapor interface, resulting in distinct "pendant" crystals, which reach millimeter dimensions. The substantial size of the crystals induces deformation of the interface. This process and the evaporation rate, in turn, determine the final crystal shape, which features a deep central cavity. Our findings reveal that a delicate balance exists between gravity, buoyancy, and the surface tension of the liquid/vapor interface that allows the crystal to remain pendant. When the contact angle of the crystal with the meniscus reaches 90°, the crystal disconnects from the interface and falls into the solution. We quantitatively predict the critical mass at which this occurs.

Effect of Particle Size on the Orientation and Order of Assemblies of Functionalized Microscale Cubes Formed at the Water/Air Interface

The impact of the particle size and wettability on the orientation and order of assemblies obtained by self-organization of functionalized microscale polystyrene cubes at the water/air interface is reported. An increase in the hydrophobicity of 10- and 5-μm-sized self-assembled monolayer-functionalized polystyrene cubes, as assessed by independent water contact angle measurements, led to a change of the preferred orientation of the assembled cubes at the water/air interface from face-up to edge-up and further to vertex-up, irrespective of microcube size. This tendency is consistent with our previous studies with 30-μm-sized cubes. However, the transitions among these orientations and the capillary force-induced structures, which change from flat plate to tilted linear and further to close-packed hexagonal arrangements, were observed to shift to larger contact angles for smaller cube size. Likewise, the order of the formed aggregates decreased significantly with decreasing cube size, which is tentatively attributed to the small ratio of inertial force to capillary force for smaller cubes in disordered aggregates, which results in more difficulties to reorient in the stirring process. Experiments with small fractions of larger cubes added to the water/air interface increased the order of smaller homo-aggregates to values similar to neat 30 μm cube assemblies. Hence, collisions of larger cubes or aggregates are shown to play a decisive role in breaking metastable structures to approach a global energy minimum assembly.

Shape-induced crystallization of binary DNA-functionalized nanocubes

Leveraging the anisotropic shape of DNA-functionalized nanoparticles holds potential for shape-directed crystallization of a wide collection of superlattice structures. Using coarse-grained molecular dynamics simulations, we study the self-assembly of a binary mixture of cubic gold nanoparticles, which are functionalized by complementary DNA strands. We observe the spontaneous self-assembly of simple cubic (SC), plastic body-centered tetragonal (pBCT), and compositionally disordered plastic body-centered tetragonal (d-pBCT) phases due to hybridization of the DNA strands. We systematically investigate the effect of length, grafting density, as well as rigidity of the DNA strands on the self-assembly behavior of cubic nanoparticles. We measure the potential of mean force between DNA-functionalized nanocubes for varying rigidity of the DNA strands and DNA lengths. Using free-energy calculations, we find that longer and flexible DNA strands can lead to a phase transformation from SC to the pBCT phase due to a gain in entropy arising from the orientational degrees of freedom of the nanocubes in the pBCT phase. Our results may serve as a guide for self-assembly experiments on DNA-functionalized cubic nanoparticles.

A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes

A recurring motif in soft matter and biophysics is modeling the mechanics of interacting particles on fluid membranes. One of the main outstanding challenges in these applications is the need to model the strong coupling between the substrate deformation and the particles' positions as the latter freely move on the former. This work presents a thin-shell finite element formulation based on subdivision surfaces to compute equilibrium configurations of a thin fluid shell with embedded particles. We use a variational Lagrangian framework to couple the mechanics of the particles and the substrate without having to resort to ad hoc constraints to anchor the particles to the surface. Unlike established methods for such systems, the particles are allowed to move between elements of the finite element mesh. This is achieved by parametrizing the particle locations on the reference configuration. Using the Helfrich-Canham energy as a model for fluid shells, we present the finite element method's implementation and an efficient search algorithm required to locate particles on the reference mesh. Several analyses with varying numbers of particles are finally presented reproducing symmetries observed in the classic Thomson problem and showcasing the coupling between interacting particles and deformable membranes.

Shape and interaction decoupling for colloidal preassembly

Creating materials with structure that is independently controllable at a range of scales requires breaking naturally occurring hierarchies. Breaking these hierarchies can be achieved via the decoupling of building block attributes from structure during assembly. Here, we demonstrate, through computer simulations and experiments, that shape and interaction decoupling occur in colloidal cuboids suspended in evaporating emulsion droplets. The resulting colloidal clusters serve as "preassembled" mesoscale building blocks for larger-scale structures. We show that clusters of up to nine particles form mesoscale building blocks with geometries that are independent of the particles' degree of faceting and dipolar magnetic interactions. To highlight the potential of these superball clusters for hierarchical assembly, we demonstrate, using computer simulations, that clusters of six to nine particles can assemble into high-order structures that differ from bulk self-assembly of individual particles. Our results suggest that preassembled building blocks present a viable route to hierarchical materials design.

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.

Novel analytical expressions for determining van der Waals interaction between a particle and air-water interface: Unexpected stronger van der Waals force than capillary force

HYPOTHESIS

Analytical expressions for calculating Hamaker constant (HC) and van der Waals (VDW) energy/force for interaction of a particle with a solid water interface has been reported for over eighty years. This work further developed novel analytical expressions and numerical approaches for determining HC and VDW interaction energy/force for the particle approaching and penetrating air-water interface (AWI), respectively.

METHODS

The expressions of HC and VDW interaction energy/force before penetrating were developed through analysis of the variation in free energy of the interaction system with bringing the particle from infinity to the vicinity of the AWI. The surface element integration (SEI) technique was modified to calculate VDW energy/force after penetrating.

FINDINGS

We explain why repulsive VDW energy exists inhibiting the particle from approaching the AWI. We found very significant VDW repulsion for a particle at a concave AWI after penetration, which can even exceed the capillary force and cause strong retention in water films on a solid surface and at air-water-solid interface line. The methods and findings of this work are critical to quantification and understanding of a variety of engineered processes such as particle manipulation (e.g., bubble flotation, Pickering emulsion, and particle laden interfaces).

Effect of gravity on the orientation and detachment of cubic particles adsorbed at soap film or liquid interfaces

We investigate the interaction that occurs between a light solid cube falling under gravity and a horizontal soap film that is pinned to a circular ring. We observe in both experiments and quasi-static simulations that the final orientation of a cube that becomes entrapped by a soap film is strongly dependent on the Bond number. A cube is rotated by a soap film into one of three main orientations in a process that is driven by energy minimisation. The likelihood of observing each of these final orientations is shown to depend on the Bond number, and the most energetically favourable orientation depends on the terminal height reached by the cube. We also find a critical value for the Bond number, above which a cube is no longer supported by a soap film and detachment occurs, to be less than one.

Oriented Attachment: From Natural Crystal Growth to a Materials Engineering Tool

ConspectusIntuitively, chemists see crystals grow atom-by-atom or molecule-by-molecule, very much like a mason builds a wall, brick by brick. It is much more difficult to grasp that small crystals can meet each other in a liquid or at an interface, start to align their crystal lattices and then grow together to form one single crystal. In analogy, that looks more like prefab building. Yet, this is what happens in many occasions and can, with reason, be considered as an alternative mechanism of crystal growth. Oriented attachment is the process in which crystalline colloidal particles align their atomic lattices and grow together into a single crystal. Hence, two aligned crystals become one larger crystal by epitaxy of two specific facets, one of each crystal. If we simply consider the system of two crystals, the unifying attachment reduces the surface energy and results in an overall lower (free) energy of the system. Oriented attachment often occurs with massive numbers of crystals dispersed in a liquid phase, a sol or crystal suspension. In that case, oriented attachment lowers the total free energy of the crystal suspension, predominantly by removal of the nanocrystal/liquid interface area. Accordingly, we should start by considering colloidal suspensions with crystals as the dispersed phase, i.e., "sols", and discuss the reasons for their thermodynamic (meta)stability and how this stability can be lowered such that oriented attachment can occur as a spontaneous thermodynamic process. Oriented attachment is a process observed both for charge-stabilized crystals in polar solvents and for ligand capped nanocrystal suspensions in nonpolar solvents. In this last system different facets can develop a very different reactivity for oriented attachment. Due to this facet selectivity, crystalline structures with very specific geometries can be grown in one, two, or three dimensions; controlled oriented attachment suddenly becomes a tool for material scientists to grow architectures that cannot be reached by any other means. We will review the work performed with PbSe and CdSe nanocrystals. The entire process, i.e., the assembly of nanocrystals, atomic alignment, and unification by attachment, is a very complex and intriguing process. Researchers have succeeded in monitoring these different steps with in situ wave scattering methods and real-space (S)TEM studies. At the same time coarse-grained molecular dynamics simulations have been used to further study the forces involved in self-assembly and attachment at an interface. We will briefly come back to some of these results in the last sections of this review.

Chains of cubic colloids at fluid-fluid interfaces

Inspired by recent experimental observations of spontaneous chain formation of cubic particles adsorbed at a fluid-fluid interface, we theoretically investigate whether capillary interactions can be responsible for this self-assembly process. We calculate adsorption energies, equilibrium particle orientations, and interfacial deformations, not only for a variety of contact angles but also for single cubes as well as an infinite 2D lattice of cubes at the interface. This allows us to construct a ground-state phase diagram as a function of areal density for several contact angles, and upon combining the capillary energy of a 2D lattice with a simple expression for the entropy of a 2D fluid we also construct temperature-density or size-density phase diagrams that exhibit large two-phase regions and triple points. We identify several regimes with stable chainlike structures, in line with the experimental observations.

Interfacial viscoelasticity and jamming of colloidal particles at fluid-fluid interfaces: a review

Colloidal particles can be adsorbed at fluid-fluid interfaces, a phenomenon frequently observed in particle-stabilized foams, Pickering emulsions, and bijels. Particles adsorbed at interfaces exhibit unique physical and chemical behaviors, which affect the mechanical properties of the interface. Therefore, interfacial colloidal particles are of interest in terms of both fundamental and applied research. In this paper, we review studies on the adsorption of colloidal particles at fluid-fluid interfaces, from both thermodynamic and mechanical points of view, and discuss the differences as compared with surfactants and polymers. The unique particle interactions induced by the interfaces as well as the particle dynamics including lateral diffusion and contact line relaxation will be presented. We focus on the rearrangement of the particles and the resultant interfacial viscoelasticity. Particular emphasis will be given to the effects of particle shape, size, and surface hydrophobicity on the interfacial particle assembly and the mechanical properties of the obtained particle layer. We will also summarize recent advances in interfacial jamming behavior caused by adsorption of particles at interfaces. The buckling and cracking behavior of particle layers will be discussed from a mechanical perspective. Finally, we suggest several potential directions for future research in this area.

Unravelling three-dimensional adsorption geometries of PbSe nanocrystal monolayers at a liquid-air interface

The adsorption, self-organization and oriented attachment of PbSe nanocrystals (NCs) at liquid-air interfaces has led to remarkable nanocrystal superlattices with atomic order and a superimposed nanoscale geometry. Earlier studies examined the NC self-organization at the suspension/air interface with time-resolved in-situ X-ray scattering. Upon continuous evaporation of the solvent, the NC interfacial layer will finally contact the (ethylene glycol) liquid substrate on which the suspension was casted. In order to obtain structural information on the NC organization at this stage of the process, we examined the ethylene glycol/NC interface in detail for PbSe NCs of different sizes, combining in-situ grazing-incidence small-and-wide-angle X-ray scattering (GISAXS/GIWAXS), X-ray reflectivity (XRR) and analytical calculations of the adsorption geometry of these NCs. Here, we observe in-situ three characteristic adsorption geometries varying with the NC size. Based on the experimental evidence and simulations, we reveal fully three-dimensional arrangements of PbSe nanocrystals at the ethylene glycol-air interface with and without the presence of rest amounts of toluene.

Reconfigurable Microcube Assemblies at the Liquid/Air Interface: The Impact of Surface Tension on Orientation and Capillary-Force-Interaction-Driven Assembly

The systematic investigation of the dependence of the orientation and capillary interaction of hydrophobized polystyrene microcubes at the liquid/air interface on the surface tension of the aqueous subphase is reported. By decreasing the subphase surface tension, the preferential orientation of the cubes was observed to change independent of the surfactant type from the vertex up to the edge up and finally to the face up. Concomitantly, the structure of the aggregates obtained by cube assembly was observed to change from a close-packed hexagonal to tilted linear and finally to flat plate. In particular, the preferential orientation of the cubes was virtually independent of the surfactant charge at a constant surface tension. In addition, reconfigurable microcube assemblies at the liquid/air interface, which respond to the surface tension of the subphase, were observed for the first time. The dynamic reconfigurability of preformed microcube aggregates induced by adding surfactant to the subphase may open new pathways to dynamic assemblies at liquid/air interfaces, which may be interesting, e.g., for sensing applications.

Control of Orientation, Formation of Ordered Structures, and Self-Sorting of Surface-Functionalized Microcubes at the Air-Water Interface

The dependence of the orientation of microscale PS cubes, which are surface functionalized on only five faces, at the water/air interface and the ordered aggregates formed by capillary force assembly are reported. Depending on the wettability of the faces, the cubes were shown to adopt a preferred orientation that changes with decreasing wettability from face up to edge up and further to vertex up. Concomitantly, stable aggregates with different structures were formed by capillary force self-assembly. The unmodified bottom face of the cubes was localized by fluorescence labeling. Finally, self-sorting of differently surface functionalized microcubes was realized for the first time, due to the stronger capillary interactions of quadrupole-quadrupole and hexapole-hexapole interactions compared to quadrupole-hexapole interaction.

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.

Asymmetric multifunctional 3D cell microenvironments by capillary force assembly

The fabrication and characterization of advanced 3D cell culture microenvironments that enable systematic structure–property relationship studies are reported.

Capillary-driven binding of thin triangular prisms at fluid interfaces

We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 μm, and the thickness of the prism is varied between 2 and 20 μm. For thickness to length (T/L) ratios of 1/10 or less, pairs of triangles preferentially bind in either tip-to-tip or tip-to-midpoint edge configurations; for pairs of prisms of thickness T/L = 1/5, the tip of one triangle binds to any position along the other triangle's edge. The distinct binding configurations for small T/L ratios result from physical bowing of the prisms, a property that arises during their fabrication. When bowed prisms are placed at the air-water interface, two distinct polarity states arise: prisms either sit with their center of mass above or below the interface. The interface pins to the edge of the prism's concave face, resulting in an interface profile that is similar to that of a capillary hexapole, but with important deviations close to the prism that enable directed binding. We present corresponding theoretical and numerical analysis of the capillary interactions between these prisms and show how prism bowing and contact-line pinning yield a capillary hexapole-like interaction that results in the two sets of distinct, highly-directional binding events. Prisms of all T/L ratios self-assemble into space-spanning open networks; the results suggest design parameters for the fabrication of building blocks of ordered open structures such as the Kagome lattice.