Self-assembly of two-dimensional colloidal clusters by tuning the hydrophobicity, composition, and packing geometry

Buzza DM. Programmable 2D materials through shape-controlled capillary forces

In recent years, self-assembly has emerged as a powerful tool for fabricating functional materials. Since self-assembly is fundamentally determined by the particle interactions in the system, if we can gain full control over these interactions, it would open the door for creating functional materials by design. In this paper, we exploit capillary interactions between colloidal particles at liquid interfaces to create two-dimensional (2D) materials where particle interactions and self-assembly can be fully programmed using particle shape alone. Specifically, we consider colloidal particles which are polygonal plates with homogeneous surface chemistry and undulating edges as this particle geometry gives us precise and independent control over both short-range hard-core repulsions and longer-range capillary interactions. To illustrate the immense potential provided by our system for programming self-assembly, we use minimum energy calculations and Monte Carlo simulations to show that polygonal plates with different in-plane shapes (hexagons, truncated triangles, triangles, squares) and edge undulations of different multipolar order (hexapolar, octopolar, dodecapolar) can be used to create a rich variety of 2D structures, including hexagonal close-packed, honeycomb, Kagome, and quasicrystal lattices. Since the required particle shapes can be readily fabricated experimentally, we can use our colloidal system to control the entire process chain for materials design, from initial design and fabrication of the building blocks, to final assembly of the emergent 2D material.

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.

A computational toolbox for the assembly yield of complex and heterogeneous structures

The self-assembly of complex structures from a set of non-identical building blocks is a hallmark of soft matter and biological systems, including protein complexes, colloidal clusters, and DNA-based assemblies. Predicting the dependence of the equilibrium assembly yield on the concentrations and interaction energies of building blocks is highly challenging, owing to the difficulty of computing the entropic contributions to the free energy of the many structures that compete with the ground state configuration. While these calculations yield well known results for spherically symmetric building blocks, they do not hold when the building blocks have internal rotational degrees of freedom. Here we present an approach for solving this problem that works with arbitrary building blocks, including proteins with known structure and complex colloidal building blocks. Our algorithm combines classical statistical mechanics with recently developed computational tools for automatic differentiation. Automatic differentiation allows efficient evaluation of equilibrium averages over configurations that would otherwise be intractable. We demonstrate the validity of our framework by comparison to molecular dynamics simulations of simple examples, and apply it to calculate the yield curves for known protein complexes and for the assembly of colloidal shells.

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.

Jamming to unjamming: Phase transition in cyclodextrin-based emulsions mediated by sodium casein

HYPOTHESIS

Cyclodextrin (CD) can spontaneously build up the solid particle membrane with CD-oil inclusion complexes (ICs) by a self-assembly process. Sodium casein (SC) is expected to preferentially adsorb at the interface to transform the type of interfacial film. The high-pressure homogenization can increase interfacial contact opportunities of the components, which promote the phase transition of the interfacial film.

EXPERIMENTS

We added SC by sequential and simultaneous orders to mediate the assembly model of the CD-based films, examined the patterns in which the films adopt phase transitions to retard emulsion flocculation, and studied the physic-chemical properties of the emulsions and films from the structural arrest, interface tension, interfacial rheology, linear rheology, and nonlinear viscoelasticities through Fourier transform (FT)-rheology and Lissajous-Bowditch plots.

FINDINGS

The interfacial and large amplitude oscillatory shear (LAOS) rheological results showed that the films changed from jammed to unjammed. We divide the unjammed films into two types: one is SC dominated liquid-like film, which is fragile and related to droplet coalescence; the other is cohesive SC-CD film, which helps droplet rearrangement and retards droplet flocculation. Our results highlight the potential of mediating phase transformation of interfacial films to improve emulsion stability.

Pickering Emulsions Stabilized by Binary Mixtures of Colloidal Particles: Synergies between Contrasting Properties

Pickering emulsions that are stabilized by colloidal particles have attracted substantial research attention because of their potential applications in various industries. Previously, single colloidal particles have usually been used to fabricate Pickering emulsions and to investigate the stabilization mechanism. However, surface modification of the colloidal stabilizer is normally required to adjust the particle wettability, which often involves chemical modification, the adsorption of a surfactant or polymer, and the addition of an electrolyte. Such a modification is expensive, time-consuming, and thus only partially effective. In this Perspective, we describe an alternative approach that uses binary mixtures of particles as stabilizers and could be an effective solution to the above-described problems with Pickering emulsions. We introduce various types of Pickering emulsions stabilized by binary mixtures of particles with different functional groups, opposite charges, or opposite wettabilities (i.e., they are hydrophilic or hydrophobic). Examples of stabilizing mechanisms are discussed, showing that compared with emulsions stabilized by single colloidal particles, emulsions stabilized by binary mixtures of particles are generated via simpler particle-pretreatment processes and have higher stability and customizable properties and thus can enable the exploration of the next generation of Pickering emulsions.

Hydrodynamic interactions between charged and uncharged Brownian colloids at a fluid-fluid interface

HYPOTHESIS

The cluster formation and self-assembly of floating colloids at a fluid/fluid interface is a delicate force balance involving deterministic lateral interaction forces, viscous resistance to relative colloid motion along the surface and thermal (Brownian) fluctuations. As the colloid dimensions get smaller, thermal forces and associated drag forces become important and can affect the self assembly into ordered patterns and crystal structures that are the starting point for various materials applications.

NUMERICS

Langevin dynamic simulations for particle pairs straddling a liquid-liquid interface with a high viscosity contrast are presented to describe the lateral interfacial assembly of particles in Brownian and non-Brownian dominated regimes. These simulations incorporate capillary attraction, electrostatic repulsion, thermal fluctuations and hydrodynamic interactions (HI) between particles (including the effect of the particle immersion depth). Simulation results are presented for neutrally wetted particles which form a contact angle θ=90⁰ at the interface.

FINDINGS

The simulation results suggest that clustering, fractal growth and particle ordering become favorable outcomes at critically large values of the Pe numbers, while smaller Pe numbers exhibit higher probabilities of final configurations where particle motion remains uncorrelated in space and particle pairs are found to be more widely separated especially upon the introduction of HI.

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.

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.

Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is vital for the prediction and characterization of yield and the study of how memory is stored in disordered materials. Here, we investigate the evolution of local structural homogeneity on an individual particle level in amorphous jammed two-dimensional (athermal) systems under oscillatory shear and relate this evolution to rearrangement, memory, and macroscale rheological measurements. We define the structural metric crystalline shielding, and show that it is predictive of rearrangement propensity and structural volatility of individual particles under shear. We use this metric to identify localized regions of the system in which the material's memory of its preparation is preserved. Our results contribute to a growing understanding of how local structure relates to dynamic response and memory in disordered systems.

Evaporative self-assembly of the binary mixture of soft colloids

We have reported experimental studies on the self-assembly and degree of ordering of a binary mixture of soft colloids in monolayer deposits obtained by controlled evaporation. A sessile drop containing soft colloids is evaporated on a solid surface to achieve a loosely-packed two-dimensional deposit with a hexagonal arrangement. The soft microgel particles possess a hard core with a compliant corona, which plays a crucial role in retaining the crystallinity of the binary particle monolayer. The ordered arrangement of the binary mixture is observed even when the bulk diameter of one type of particle is 25% higher than the other, irrespective of their mixing ratio (1 : 3, 1 : 1, and 3 : 1). The microgel particles of both sizes are found to be homogeneously distributed throughout the deposit, completely suppressing the size-dependent particle segregation. Furthermore, in contrast to the self-assembly of bidisperse hard colloids, wherein the lattice distorts to accommodate particles of disparate sizes, in soft colloids, the particles deform at the interface to preserve the crystalline lattice. Moreover, unlike the gradual order-to-disorder transition observed in the deposits consisting of monodisperse microgel particles, the deposits of a binary mixture of microgels exhibit no noticeable trend. The areal disorder parameter, pair correlation function and the shape factor which quantifies the local ordering of particles in the deposit indicate the absence of a distinct order-to-disorder transition for the binary mixtures.

The macroscopic shape of assemblies formed from microparticles based on host-guest interaction dependent on the guest content

Biological macroscopic assemblies have inspired researchers to utilize molecular recognition to develop smart materials in these decades. Recently, macroscopic self-assemblies based on molecular recognition have been realized using millimeter-scale hydrogel pieces possessing molecular recognition moieties. During the study on macroscopic self-assembly based on molecular recognition, we noticed that the shape of assemblies might be dependent on the host-guest pair. In this study, we were thus motivated to study the macroscopic shape of assemblies formed through host-guest interaction. We modified crosslinked poly(sodium acrylate) microparticles, i.e., superabsorbent polymer (SAP) microparticles, with β-cyclodextrin (βCD) and adamantyl (Ad) residues (βCD(x)-SAP and Ad(y)-SAP microparticles, respectively, where x and y denote the mol% contents of βCD and Ad residues). Then, we studied the self-assembly behavior of βCD(x)-SAP and Ad(y)-SAP microparticles through the complexation of βCD with Ad residues. There was a threshold of the βCD content in βCD(x)-SAP microparticles for assembly formation between x = 22.3 and 26.7. On the other hand, the shape of assemblies was dependent on the Ad content, y; More elongated assemblies were formed at a higher y. This may be because, at a higher y, small clusters formed in an early stage can stick together even upon collisions at a single contact point to form elongated aggregates, whereas, at a smaller y, small clusters stick together only upon collisions at multiple contact points to give rather circular assemblies. On the basis of these observations, the shape of assembly formed from microparticles can be controlled by varying y.

Influence of salt concentration on the formation of Pickering emulsions

Here we study emulsification in a model experimental system comprised of water, an oil and colloidal particles. The particles are charge-stabilised colloidal silica; unsurprisingly, by varying the concentration of salt the degree of flocculation of the particles can be modified. The influence of salt on the formation of particle-stabilised oil droplets goes well beyond considerations of the colloidal stability of the particles. Our results demonstrate that the influence of salt on the particle-particle interaction is less important for emulsion formation than the influence of salt on both the particle wettability and the particle-interface interaction.

Self-assembly of spiral patterns in confined systems with competing interactions

Colloidal particles in polymer solutions and functionalized nanoparticles often exhibit short-range attraction coupled with long-range repulsion (SALR) leading to the spontaneous formation of symmetric patterns. Chiral nanostructures formed by thin films of SALR particles have not been reported yet. In this study, we observe striking topological transitions from a symmetric pattern of concentric rings to a chiral structure of a spiral shape, when the system is in hexagonal confinement. We find that the spiral formation can be induced either by breaking the system symmetry with a wedge, or by melting of the rings. In the former case, the chirality of the spiral is determined by the orientation of the wedge and thus can be controlled. In the latter, the spiral arises due to thermally induced defects and is absent in the average particle distribution, which forms highly regular hexagonal patterns in the central part of the system. These hexagonal patterns can be explained by interference of planar density waves. Thermodynamic considerations indicate that equilibrium spirals can appear spontaneously in any stripe-forming system confined in a hexagon with a small wedge, provided that certain conditions are satisfied by a set of phenomenological parameters.

Interfacial Viscoelasticity of Self-Assembled Hydrophobic/Hydrophilic Particles at an Air/Water Interface

Hydrophobic/hydrophilic mixtures of latex particles at an air/water interface self-assemble, creating space filling, interconnected aggregates as the relative surface fractions of the dissimilar particles approach 0.5, which is reflected both in qualitative observation and fractal dimension of the microstructure. It is hypothesized that this change in microstructure occurs due to an asymmetry in the electrostatic interaction between similar and dissimilar particles caused by polarization of hydrophilic particles by hydrophobic particles. The changes in both microstructure and interparticle interactions significantly impact the interfacial viscoelasticity. As greater shape complexity is observed, interfacial complex moduli can increase by as much as 3 orders of magnitude and interfaces become more elastic.

Building Reconfigurable Devices Using Complex Liquid-Fluid Interfaces

Liquid-fluid interfaces provide a platform both for structuring liquids into complex shapes and assembling dimensionally confined, functional nanomaterials. Historically, attention in this area has focused on simple emulsions and foams, in which surface-active materials such as surfactants or colloids stabilize structures against coalescence and alter the mechanical properties of the interface. In recent decades, however, a growing body of work has begun to demonstrate the full potential of the assembly of nanomaterials at liquid-fluid interfaces to generate functionally advanced, biomimetic systems. Here, a broad overview is given, from fundamentals to applications, of the use of liquid-fluid interfaces to generate complex, all-liquid devices with a myriad of potential applications.

Designing Structural-Color Patterns Composed of Colloidal Arrays

Structural coloration provides a great potential for various applications due to unique optical properties distinguished from conventional pigment colors. Structural colors are nonfading, iridescent, and tunable, which is difficult to achieve with pigments. In addition, structural color is potentially less toxic than pigments. However, it is challenging to develop structural colors because elaborate nanostructures are a prerequisite for the coloration. Furthermore, it is highly suggested the nanostructures be patterned at various length scales on a large area to provide practical formats. There have been intensive studies to develop pragmatic methods for producing structural-color patterns in a controlled manner using either colloidal crystals or glasses. This article reviews the current state of the art in the structural-color patterning based on the colloidal arrays. We first discuss common and different features between colloidal crystals and glasses. We then categorize colloidal arrays into six distinct structures of 3D opals, inverse opals, non-close-packed arrays, 2D colloidal crystals, 1D colloidal strings, and 3D amorphous arrays and study various methods to make them patterned from recent key contributions. Finally, we outline the current challenges and future perspectives of the structural-color patterns.

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.

Capillary Interaction and Self-Assembly of Tilted Magnetic Ellipsoidal Particles at Liquid Interfaces

Magnetic ellipsoidal particles adsorbed at a liquid interface provide exciting opportunities for creating switchable functional materials, where self-assembly can be switched on and off using an external field [Davies et al., Adv. Mater., 2014, 26, 6715]. In order to gain a deeper understanding of this novel system in the presence of an external field, we study the capillary interaction and self-assembly of tilted ellipsoids using analytical theory and finite element simulations. We derive an analytical expression for the dipolar capillary interaction between tilted ellipsoids in elliptical polar coordinates, which exhibits a 1/r ² power law dependence in the far field (i.e., large particle separations r) and correctly captures the orientational dependence of the capillary interactions in the near field. Using this dipole potential and finite element simulations, we further analyze the energy landscape of particle clusters consisting of up to eight tilted ellipsoids in contact. For clusters of two particles, we find that the side-to-side configuration is stable, whereas the tip-to-tip configuration is unstable. However, for clusters of more than three particles, we find that circular loops of side-to-side particles become globally stable, whereas linear chains of side-to-side particles become metastable. Furthermore, the energy barrier for the linear-to-loop transition decreases with increasing particle number. Our results explain both thermodynamically and kinetically why tilted ellipsoids assemble side-to-side locally but have a strong tendency to form loops on larger length scales.

Driving Forces for Accumulation of Cellulose Nanofibrils at the Oil/Water Interface

Understanding the adsorption and organization of nanocelluloses at oil/water interfaces is crucial to develop a promising route to fabricate functional materials from the bottom-up. Here, we prepare acetylated cellulose nanofibrils (CNFs) with 2 degrees of substitution and investigate their assembly behavior at the oil/water interface. We study the adsorption process by tracking the dynamic interfacial tension using pendant drop tensiometry and further characterize the viscoelasticity of the CNF interfacial films as a function of ionic strength. The results show that the adsorption of the CNFs at the interface is dominated by energy barriers associated with electrostatic repulsion. With the addition of NaCl, the fibrils are rapidly accumulated at the oil/water interface and jammed into a solidlike film. The overall accumulation of the fibrils is related to the competition between van der Waals attractive forces and electrostatic repulsive forces according to the Derjaguin-Landau-Verwey-Overbeek theory. By screening on the fibril-fibril and fibril-interface electrostatic repulsive forces, the salt addition facilitates the formation of packed fibril clusters and the development of the clusters into a solidlike film. Moreover, the salt addition is assumed to trigger an abrupt density fluctuation in the vicinity of the interface (the formation of locally dense clusters and voids), leading to an increase in brittleness of the film.

Hunting mermaids in real space: known knowns, known unknowns and unknown unknowns

We review efforts to realise so-called mermaid (or short-ranged attraction/long ranged repulsion) interactions in 3d real space. The repulsive and attractive contributions to these interactions in charged colloids and colloid-polymer mixtures, may be accurately realised, by comparing particle-resolved studies with colloids to computer simulation. However, when we review work where these interactions have been combined, despite early indications of behaviour consistent with predictions, closer analysis reveals that in the non-aqueous systems used for particle-resolved studies, the idea of summing the attractive and repulsive components leads to wild deviations with experiment. We suggest that the origin lies in the weak ion dissociation in these systems with low dielectric constant solvents. Ultimately this leads even to non-centro-symmetric interactions and a new level of complexity in these systems.

Phase Inversion of Colored Pickering Emulsions Stabilized by Organic Pigment Particle Mixtures

Pickering emulsions stabilized by a mixture of colored organic pigment particles of different hydrophobicity have been investigated at equal oil/water ratio and a fixed overall particle concentration by several complementary methods. Transitional phase inversion of emulsions from water-in-oil to oil-in-water can be effected by increasing the fraction of hydrophilic pigment orange in mixtures with either hydrophobic pigment yellow, red, indigo, or blue. In two mixtures, we find that a distinct change in the color of emulsions occurs at phase inversion. Although the fraction of pigment orange required depends on the particular hydrophobic pigment selected, phase inversion occurs at a similar surface energy of the particle mixture, which lies between that of the hydrophilic pigment and those of the hydrophobic pigments. We show that both pigment types are present at the oil-water interface simultaneously, giving rise to emulsions that are extremely stable to coalescence. The average drop size for both emulsion types increases toward phase inversion, in line with an increase in the extent of sedimentation/creaming at long times.

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.

Light and Magnetic Dual-Responsive Pickering Emulsion Micro-Reactors

Emulsion droplets can serve as ideal compartments for reactions. In fact, in many cases, the chemical reactions are supposed to be triggered at a desired position and time without change of the system environment. Here, we present a type of light and magnetic dual-responsive Pickering emulsion microreactor by coadsorption of light-sensitive titania (TiO₂) and super paramagnetic iron oxide (Fe₃O₄) nanoparticles at the oil-water interface of emulsion droplets. The droplets encapsulating different reactants in advance can be driven close to each other by an external magnetic field, and then the chemical reaction is triggered by UV illumination due to the contact of the isolated reactants as a result of droplet coalescence. An insight into the incorporation of hydrophobic TiO₂ and hydrophilic Fe₃O₄ nanoparticles simultaneously at the emulsion interface is achieved. On the basis of that, an account is given of the coalescence mechanism of the Pickering emulsion microreactors. Our work not only provides a novel Pickering emulsion microreactor platform for triggering chemical reactions in a nonintrusive and well-controlled way but also opens a promising avenue to construct multifunctional Pickering emulsions by assembly of versatile building block nanoparticles at the interface of emulsion droplets.

Ethyl Cellulose Nanoparticles at the Alkane-Water Interface and the Making of Pickering Emulsions

Pickering emulsions stabilized by nanoparticles have recently received great attention for their remarkable stability, in part a consequence of irreversible adsorption. In this study, we generate Pickering oil-in-water emulsions stabilized by ethyl cellulose (EC) nanoparticles without the addition of surfactants. Over a range of ionic strength and EC nanoparticle concentrations, a series of dynamic interfacial tension (IFT) measurements complemented by extended DLVO theoretical computations are conducted to quantitatively describe the behavior of EC nanoparticles at the interface of water with different alkanes. Regardless of ionic strength, there is no barrier against the adsorption of EC nanoparticles at the alkane-water interfaces studied and the particles tightly cover these interfaces with near maximal coverage (i.e., 91%). Remarkably, the rate of approach to maximum coverage of the alkane-water interface by EC nanoparticles during the later stages of adsorption is accelerated in the presence of salt at concentrations below the critical coagulation concentration (CCC), unlike the air-water interface. Above the CCC, alkane-water interfaces behave similar to air-water interfaces, showing decay in the adsorption flux which is attributed to an increase in surface blocking originating from the attachment of nanoparticles to nanoparticles already adsorbed at the interface. These findings shed light on particle-particle and particle-interface colloidal interactions at and near fluid-fluid interfaces, thereby improving our ability to use hydrophobic EC nanoparticles as emulsion stabilizers.

Approaches to self-assembly of colloidal monolayers: A guide for nanotechnologists

Self-assembly of quasi-spherical colloidal particles in two-dimensional (2D) arrangements is essential for a wide range of applications from optoelectronics to surface engineering, from chemical and biological sensing to light harvesting and environmental remediation. Several self-assembly approaches have flourished throughout the years, with specific features in terms of complexity of the implementation, sensitivity to process parameters, characteristics of the final colloidal assembly. Selecting the proper method for a given application amidst the vast literature in this field can be a challenging task. In this review, we present an extensive classification and comparison of the different techniques adopted for 2D self-assembly in order to provide useful guidelines for scientists approaching this field. After an overview of the main applications of 2D colloidal assemblies, we describe the main mechanisms underlying their formation and introduce the mathematical tools commonly used to analyse their final morphology. Subsequently, we examine in detail each class of self-assembly techniques, with an explanation of the physical processes intervening in crystallization and a thorough investigation of the technical peculiarities of the different practical implementations. We point out the specific characteristics of the set-ups and apparatuses developed for self-assembly in terms of complexity, requirements, reproducibility, robustness, sensitivity to process parameters and morphology of the final colloidal pattern. Such an analysis will help the reader to individuate more easily the approach more suitable for a given application and will draw the attention towards the importance of the details of each implementation for the final results.

Colloidal molecules assembled from binary spheres under an AC electric field

Colloidal particles are envisioned as analogues of atoms and molecules, however they often lack the complexities present in their counterparts. In this work, we report the assembly of colloidal molecules from a binary mixture of polystyrene spheres (1, 1.6, 2, and 4 μm) under an alternating current electric field. The rich family of assembled oligomers typically consists of a large sphere that is closely surrounded by a number of smaller petal particles, driven by the dipolar attraction between large and small particles. In deionized water, the number of satellite particles, i.e., the coordination number increases with the increasing size ratio of the constituent particles. For a given size ratio, the coordination number decreases with the increasing frequency of the applied field. These trends have also been correctly captured by computing the electric energy of different oligomers based on induced dipolar and double-layer interactions. By suspending the particles in polyvinylpyrrolidone aqueous solution, we can further tune the bond length of the oligomers independent of their coordination numbers. The addition of polyvinylpyrrolidone also allows us to lock the assembled colloidal molecules so that they remain intact after the electric field is turned off. Our method provides a robust way to produce a family of colloidal molecules with well-defined geometry and high yield.

Magnetic cylindrical colloids at liquid interfaces exhibit non-volatile switching of their orientation in an external field

We study the orientation of magnetic cylindrical particles adsorbed at a liquid interface in an external field using analytical theory and high resolution finite element simulations. Cylindrical particles are interesting since they possess multiple locally stable orientations at the liquid interface so that the orientational transitions induced by an external field will not disappear when the external field is removed, i.e., the switching effect is non-volatile. We show that, in the absence of an external field, as we reduce the aspect ratio α of the cylinders below a critical value (αc≈ 2) the particles undergo spontaneous symmetry breaking from a stable side-on state to one of two equivalent stable tilted states, similar to the spontaneous magnetisation of a ferromagnet going through the Curie point. By tuning both the aspect ratio and contact angle of the cylinders, we show that it is possible to engineer particles that have one, two, three or four locally stable orientations. We also find that the magnetic responses of cylinders with one or two stable states are similar to that of paramagnets and ferromagnets respectively, while the magnetic response of systems with three or four stable states are even more complex and have no analogs in simple magnetic systems. Magnetic cylinders at liquid interfaces therefore provide a facile method for creating switchable functional monolayers where we can use an external field to induce multiple non-volatile changes in particle orientation and self-assembled structure.

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.

Influence of an Additive-Free Particle Spreading Method on Interactions between Charged Colloidal Particles at an Oil/Water Interface

The assembly and manipulation of charged colloidal particles at oil/water interfaces represent active areas of fundamental and applied research. Previously, we have shown that colloidal particles can spontaneously generate unstable residual charges at the particle/oil interface when spreading solvent is used to disperse them at an oil/water interface. These residual charges in turn affect the long-ranged electrostatic repulsive forces and packing of particles at the interface. To further uncover the influence arising from the spreading solvents on interfacial particle interactions, in the present study we utilize pure buoyancy to drive the particles onto an oil/water interface and compare the differences between such a spontaneously adsorbed particle monolayer to the spread monolayer based on solvent spreading techniques. Our results show that the solvent-free method could also lead particles to spread well at the interface, but it does not result in violent sliding of particles along the interface. More importantly, this additive-free spreading method can avoid the formation of unstable residual charges at the particle/oil interface. These findings agree well with our previous hypothesis; namely, those unstable residual charges are triboelectric charges that arise from the violently rubbing of particles on oil at the interface. Therefore, if the spreading solvents could be avoided, then we would be able to get rid of the formation of residual charges at interfaces. This finding will provide insight for precisely controlling the interactions among colloidal particles trapped at fluid/fluid interfaces.

The apparent charge of nanoparticles trapped at a water interface

Charged spherical nanoparticles trapped at the interface between water and air or water and oil exhibit repulsive electrostatic forces that contain a long-ranged dipolar and a short-ranged exponentially decaying component. The former are induced by the unscreened electrostatic field through the non-polar low-permittivity medium, and the latter result from the overlap of the diffuse ion clouds that form in the aqueous phase close to the nanoparticles. The magnitude of the long-ranged dipolar interaction is largely determined by the residual charges that remain attached to the air- (or oil-) exposed region of the nanoparticle. In the present work we address the question to what extent the charges on the water-immersed part of the nanoparticle provide an additional contribution to the dipolar interaction. To this end, we model the electrostatic properties of a spherical particle - a nanoparticle or a colloid - that partitions equatorially to the air-water interface, thereby employing nonlinear Poisson-Boltzmann theory in the aqueous solution and accounting for the propagation of the electric field through the interior of the particle. We demonstrate that the apparent charge density on the air-exposed region of the particle, which determines the dipole potential, is influenced by the electrostatic properties in the aqueous solution. We also show that this electrostatic coupling through the particle can be reproduced qualitatively by a simple analytic planar capacitor model. Our results help to rationalize the experimentally observed weak but non-vanishing salt dependence of the forces that stabilize ordered two-dimensional arrays of interface-trapped nanoparticles or colloids.

Hydrodynamics of Particles at an Oil-Water Interface

This study is a theoretical and experimental investigation of the hydrodynamics of the mutual approach of two floating spherical particles moving along an oil-water interface. An analytical expression is obtained for the (inertialess) Stokes drag for an isolated particle translating on a flat interface as a function of the immersion depth into the water phase for the case in which the viscosity of the oil is much larger than that of the water. An approximation for the viscous drag due to the mutual approach of identical spheres is formulated as the product of the isolated drag multiplied by the resistance of approaching spheres in an infinite medium. Experiments are undertaken on the capillary attraction of large, millimeter-sized Teflon spheres floating at the interface between a very viscous oil and water. With the use of image visualization and particle tracking, the separation distance as a function of time [[Formula: see text](t)] is measured along with the immersion depth and predicted by setting the capillary attraction force equal to the viscous drag resistance. The excellent agreement validates the approximating formula.

Soft repulsive interactions, particle rearrangements and size selection in the self-assembly of nanoparticles at liquid interfaces

In the adsorption of nanoparticles at liquid interfaces, soft and short ranged repulsive effective interactions between the nanoparticles at the interface may eventually induce crowding, slow dynamics and jamming at high surface coverage. These phenomena can interfere during the adsorption process, significantly slowing down its kinetics. Here, by means of numerical simulations, we find that modifying the effective interactions, which can be achieved for example by grafting differently functionalized polymer shells on the bare nanoparticles, may qualitatively change such interplay. In particular our results suggest that, in the presence of ultrasoft particle interactions such as the ones described by a Gaussian Core Model potential, a small size polydispersity can be sufficient to decouple the adsorption kinetics from the slow dynamics that develops at the interface, due to a qualitative change from an irreversible adsorption controlled by particle rearrangements at the interface to one dominated by size selection mechanisms. These findings may be useful to achieve higher surface coverages and faster adsorption kinetics.

Molecular-scale hydrophilicity induced by solute: molecular-thick charged pancakes of aqueous salt solution on hydrophobic carbon-based surfaces

We directly observed molecular-thick aqueous salt-solution pancakes on a hydrophobic graphite surface under ambient conditions employing atomic force microscopy. This observation indicates the unexpected molecular-scale hydrophilicity of the salt solution on graphite surfaces, which is different from the macroscopic wetting property of a droplet standing on the graphite surface. Interestingly, the pancakes spontaneously displayed strong positively charged behavior. Theoretical studies showed that the formation of such positively charged pancakes is attributed to cation–π interactions between Na⁺ ions in the aqueous solution and aromatic rings on the graphite surface, promoting the adsorption of water molecules together with cations onto the graphite surface; i.e., Na⁺ ions as a medium adsorbed to the graphite surface through cation–π interactions on one side while at the same time bonding to water molecules through hydration interaction on the other side at a molecular scale. These findings suggest that actual interactions regarding carbon-based graphitic surfaces including those of graphene, carbon nanotubes, and biochar may be significantly different from existing theory and they provide new insight into the control of surface wettability, interactions and related physical, chemical and biological processes.

Surface charge regulation of carboxyl terminated polystyrene latex particles and their interactions at the oil/water interface

We study electrostatic interactions of polystyrene particles at an oil/water interface controlled by a chemical reaction of carboxylate surface functional groups. By replacing the carboxyl functional groups with hydrocarbon chains using the well-known EDC (1-ethyl-3-(3-(dimethylamino)propyl)carbodiimide) coupling reaction, the surface charge density decreases while the hydrophobicity of the colloid surface increases. Direct visualization of the particle-laden interface reveals that, depending on the extent of hydrocarbon coupling, the strength of the electrostatic repulsion can be regulated: the repulsive interaction increases with the reaction, removing aggregates, but rapidly decreases if the reaction proceeds too much, forming a large aggregation. This simple reaction, thus, dramatically changes the structures of the colloidal monolayers at the oil/water interface. We conclude that such structural change is the result of change of the repulsive interactions from the oil phase, although interactions in the water phase are also changed slightly.

The influence of particle size and residual charge on electrostatic interactions between charged colloidal particles at an oil-water interface

Electrostatic repulsive interaction forces between charged spherical colloidal particles at an oil-water interface are numerically studied by solving the standard three-dimensional Poisson-Nernst-Planck model. We directly compute the electrostatic force on a finite-size spherical particle and our results are applicable to all inter-particle distances without distinguishing short ranges and long ranges. The model successfully captures the scaling relationship of the force and the separation distance (d) between two charged particles at both short ranges (exponential dependence) and long ranges (∼d(-4)). The model also bridges these two ranges and provides quantitative information in the middle range. In addition, by assuming that there is a small residual electric charge at the particle-oil interface, the standard model is capable of quantitatively predicting the repulsive particle-particle interaction force over a large range of the separation distance between two particles. The favorable agreement between experiments and theoretical predictions also leads one to conclude that the standard model adequately describes the particle-particle interactions trapped at the oil-water interface.

Tunable assembly of heterogeneously charged colloids

The self-assembly of colloidal particles is a route to designed materials production that combines high flexibility, cost effectiveness, and the opportunity to create ordered structures at length scales ranging from nano- to micrometers. For many practical applications in electronics, photovoltaics, and biomimetic material synthesis, ordered mono- and bilayers are often needed. Here we present a novel and simple way to tune via external parameters the ordering of heterogeneously charged colloids into quasi two-dimensional structures. Depending on the charges of the underlying substrate and of the particles, a rich and versatile assembly scenario takes place, resulting from the complex interplay between directional attractive and repulsive particle-particle and particle-substrate interactions. Upon subtle variations of the relative charge of the system components, emerging via pH modification, reversible changes either from extended aggregates to a monomeric phase or from triangular to square domains are observed.

Pattern formation and coarse-graining in two-dimensional colloids driven by multiaxial magnetic fields

We study the pattern formation in a two-dimensional system of superparamagnetic colloids interacting via spatially coherent induced interactions driven by an external precessing magnetic field. On the pair level, upon changing the opening angle of the external field, the interactions smoothly vary from purely repulsive (opening angle equal to zero) to purely attractive (time-averaged pair interactions at an opening angle of 90°). In the experiments, we observed ordered hexagonal crystals at the repulsive end and coarsening frothlike structures for purely attractive interactions. In both of these limiting cases, the dense colloidal systems can be sufficiently accurately described by assuming pairwise additivity of the interaction potentials. However, for a range of intermediate angles, pronounced many-body depolarization effects compete with the direct induced interactions, resulting in inherently anisotropic effective interactions. Under such conditions, we observed the decay of hexagonal order with the concomitant formation of short chains and percolated networks of chains coexisting with free colloids. In order to describe and investigate these systems theoretically, we developed a coarse-grained model of a binary mixture of patchy and nonpatchy particles with the ratio of patchy and nonpatchy colloids as the order parameter. Combining genetic algorithms with Monte Carlo simulations, we optimized the model parameters and quantitatively reproduced the experimentally observed sequence of colloidal structures. The results offer new insight into the anisotropy induced by the many-body effects. At the same time, they allow for a very efficient description of the system by means of a pairwise-additive Hamiltonian, whereupon the original, one-component system features a two-component mixture of isotropic and patchy colloids.

Assembly of nanoparticles at liquid interfaces: crowding and ordering

Experiments with the self-assembly of nanoparticles at liquid interfaces suggest that cooperative and slow dynamical processes due to particle crowding at the interface govern the adsorption and properties of the final assembly. Here we report a numerical approach to studying nonequilibrium adsorption, which elucidates these experimental observations. The analysis of particle rearrangements shows that local ordering processes are directly related to adsorption events at high interface coverage. Interestingly, this feature and the mechanism coupling local ordering to adsorption do not seem to change qualitatively upon increasing particle size polydispersity, although the latter changes the interface microstructure and its final properties. Our results indicate how adsorption kinetics can be used for the fabrication of 2D nanocomposites with controlled microstructure.