Spontaneous Formation of Eutectic Crystal Structures in Binary and Ternary Charged Colloids due to Depletion Attraction

Formation of various structures caused by particle size difference in colloidal heteroepitaxy

By performing isothermal-isochoric Monte Carlo simulations with depletion force, the author investigated the dependence of the epitxial layer structure on the differences in the particle size between the substrate in colloidal heteroepitaxy. By changing the size of epitaxial particles and performing simulations comprehensively, various structures including the structures observed in a experiment, such as a honeycomb, one created by hexagonal heptamers, and one consisting of both pentagonal tiles and triangular tiles, were created. When the ratio of particle sizes between the epitxial layer and substrate takes a specific value, two types of hexagonal structures were created. One is the hexagonal layer parallel to the substrate layer and the other layer is rotated by 60[Formula: see text] from the substrate layer. The former structure was created over a wide range of particle-size ratios, whereas the latter structure was created when the particle-size ratio was only around the specific ratio, and it seemed a metastable structure.

Regioselective Growth of Colloidal Crystals Induced by Depletion Attraction

Colloidal crystals display photonic stopbands that generate reflective structural colors. While micropatterning offers significant value for various applications, the resolution is somewhat limited for conventional top-down approaches. In this work, a simple, single-step bottom-up approach is introduced to produce photonic micropatterns through depletion-mediated regioselective growth of colloidal crystals. Lithographically-featured micropatterns with planar surfaces and nano-needle arrays as substrates are employed. Heterogeneous nucleation is drastically suppressed on nano-needle arrays due to minimal particle-to-needles overlap of excluded volumes, while it is promoted on planar surfaces with large particle-to-plane volume overlap, enabling regioselective growth of colloidal crystals. This strategy allows high-resolution micropatterning of colloidal photonic crystals, with a minimum feature size as small as 10 µm. Stopband positions, or structural colors, are controllable through concentration and depletant and salt, as well as particle size. Notably, secondary colors can be created through structural color mixing by simultaneously crystallizing two different particle sizes into their own crystal grains, resulting in two distinct reflectance peaks at controlled wavelengths. The simple and highly reproducible method for regioselective colloidal crystallization provides a general route for designing elaborate photonic micropatterns suitable for various applications.

Nonadditivities of the Particle Sizes Hidden in Model Pair Potentials and Their Effects on Physical Adsorptions

It is important to understand the mechanism of colloidal particle assembly near a substrate for development of drug delivery systems, micro-/nanorobots, batteries, heterogeneous catalysts, paints, and cosmetics. Understanding the mechanism is also important for crystallization of the colloidal particles and proteins. In this study, we calculated the physical adsorption of colloidal particles on a flat wall mainly using the integral equation theory, wherein small and large colloidal particles were employed. In the calculation system, like-charged electric double-layer potentials were used as pair potentials. In some cases, it was found that the small particles are more easily adsorbed. This result is unusual from the viewpoint of the Asakura-Oosawa theory, and we call it a "reversal phenomenon". Theoretical analysis revealed that the reversal phenomenon originates from the nonadditivities of the particle sizes. Using the knowledge obtained from this study, we invented a method to analyze the size nonadditivity hidden in model pair potentials. The method will be useful for confirmation of various simulation results regarding the adsorption and development of force fields for colloidal particles, proteins, and solutes.

Structural Color Mixing in Microcapsules through Exclusive Crystallization of Binary and Ternary Colloids

Colloidal crystals are designed as photonic microparticles for various applications. However, conventional microparticles generally have only one stopband from a single lattice constant, which restricts the range of colors and optical codes available. Here, photonic microcapsules are created that contain two or three distinct crystalline grains, resulting in dual or triple stopbands that offer a wider range of colors through structural color mixing. To produce distinct colloidal crystallites from binary or ternary colloidal mixtures, the interparticle interaction is manipulated using depletion forces in double-emulsion droplets. Aqueous dispersions of binary or ternary colloidal mixtures in the innermost droplet are gently concentrated in the presence of a depletant and salt by imposing hypertonic conditions. Different-sized particles crystallize into their own crystals rather than forming random glassy alloys to minimize free energy. The average size of the crystalline grains can be adjusted with osmotic pressure, and the relative ratio of distinct grains can be controlled with the mixing ratio of particles. The resulting microcapsules with small grains and high surface coverage are almost optically isotropic and exhibit highly-saturated mixed structural colors and multiple reflectance peaks. The mixed color and reflectance spectrum are controllable with the selection of particle sizes and mixing ratios.

Two-Dimensional Melting of Two- and Three-Component Mixtures

We elucidate the interplay between diverse two-dimensional melting pathways and establish solid-hexatic and hexatic-liquid transition criteria via the numerical simulations of the melting transition of two- and three-component mixtures of hard polygons and disks. We show that a mixture's melting pathway may differ from its components and demonstrate eutectic mixtures that crystallize at a higher density than their pure components. Comparing the melting scenario of many two- and three-component mixtures, we establish universal melting criteria: the solid and hexatic phases become unstable as the density of topological defects, respectively, overcomes ρ_{d,s}≃0.046 and ρ_{d,h}≃0.123.

Centrifugation-Assisted Growth of Single-Crystalline Grains in Microcapsules

Colloidal crystals have been tailored in a format of microspheres to use them as a building block to construct macroscopic photonic surfaces. However, the polycrystalline grains grown from the spherical surface usually exhibit low reflectivity. Although single-crystalline microspheres have been produced, it is difficult to control the crystal orientation. Here, we design spherical microcapsules with density anisotropy that contain single-crystalline grains along the heavy side. The microcapsules spontaneously align to have a heavy side down under the action of gravity and display a bright and uniform reflection color from the entire surface of the grains. Key to the success is the use of gentle centrifugal force to initiate nucleation and grow single-crystalline grains from the heavy side through depletion attraction. The microcapsules have density anisotropy due to the heterogeneity of the shell thickness, which causes them to self-align under centrifugation. At the same time, particles are accumulated on the heavy side, which produces many tiny grains on the heavy side immediately after the centrifugation. With controlled depletion attraction among particles, only a few grains survive during postincubation through Ostwald ripening, and one or a few giant single-crystalline grains are finally produced along the heavy side of each microcapsule.

Direct Determination of the Phase Diagram of a Depletion-Mediated Colloidal System

Depletion is one widely used potential to modulate colloidal interaction because it enables the production of a wide variety of crystalline and glassy phases of spherical and shape-tailored colloids. The attractive depletion potential gives rise to qualitatively new behavior. However, depletion-mediated phase behaviors have never been systematically investigated experimentally regarding pair potentials for aqueous suspensions. In this work, we implement three distinct phases of fluid, crystal, and glass by adjusting the concentrations of depletant and salt in the aqueous suspension of polystyrene particles. To define the phase boundary between the fluid and crystal, we calculate pair potential with a superposition of van der Waals, electrostatic, and depletion interactions. Two unknown parameters in the pair potential─the concentration of ionic impurities and the ratio of the molar concentration of depletant to osmolarity─are experimentally determined from sets of reflectance spectra. The interparticle spacing in the crystalline phase is extracted from the peak wavelength originating from Bragg diffraction, which corresponds to the interparticle separation at energy minimum in the pair potential. The boundary between the fluid and crystal is well defined with the depth of the energy well of 3k_BT. By contrast, the onset of glass formation is better characterized by not the well depth but the assembly rate, which is estimated from the slope of the pair potential from force balance. Glasses are produced as the speed exceeds 300 μm/s. That is, crystals are produced by enthalpy gain overwhelming entropy loss, whereas glasses are kinetically produced due to fast jamming.

Lattice Induced Short-Range Attraction between Like-Charged Colloidal Particles

We perform experiments and computer simulations to study the effective interactions between like-charged colloidal tracers moving in a two-dimensional fluctuating background of colloidal crystal. By a counting method that properly accounts for the configurational degeneracy of tracer pairs, we extract the relative probability of finding a tracer pair in neighboring triangular cells formed by background particles. We find that this probability at the nearest neighbor cell is remarkably greater than those at cells with larger separations, implying an effective attraction between the tracers. This effective attraction weakens sharply as the background lattice constant increases. Furthermore, we clarify that the lattice-mediated effective attraction originates from the minimization of free energy increase from deformation of the crystalline background due to the presence of diffusing tracers.

Heteroepitaxial fabrication of binary colloidal crystals by a balance of interparticle interaction and lattice spacing

HYPOTHESIS

The colloidal epitaxy utilizing a patterned substrate is used to fabricate colloidal crystals of the same structure and lattice spacing with the substrate, which is an effective technique for creating desired nanoscale architectures. However, this technique has been mainly limited to a single-component system. The colloidal epitaxy is versatile if multicomponent colloidal crystals can be produced, which is inspired by our previous study regarding binary colloidal crystals (b-CCs) fabricated at the edge of single-component crystals.

EXPERIMENTS

We have examined various particle size combinations of binary colloidal mixture and substrates for heteroepitaxial growth of b-CCs. Colloidal crystallization was achieved through depletion attraction induced by added polymers.

FINDINGS

We demonstrated heteroepitaxial growth of b-CCs on the foreign colloidal crystals as the substrate. Under depletion attraction, deviation from equilibrium interparticle distance because of lattice mismatch between the substrate and epitaxial layers induces strain energy among the particles, yielding the b-CCs to attain minimum strain energy. Various types of b-CCs are created by adjusting the particle size ratio and polymer concentration. The heteroepitaxial growth technique enables the fabrication of complex multicomponent colloidal crystals that greatly facilitate versatile applications of the colloidal crystals.

Reversible and spatiotemporal control of colloidal structure formation

Tuning colloidal structure formation is a powerful approach to building functional materials, as a wide range of optical and viscoelastic properties can be accessed by the choice of individual building blocks and their interactions. Precise control is achieved by DNA specificity, depletion forces, or geometric constraints and results in a variety of complex structures. Due to the lack of control and reversibility of the interactions, an autonomous oscillating system on a mesoscale without external driving was not feasible until now. Here, we show that tunable DNA reaction circuits controlling linker strand concentrations can drive the dynamic and fully reversible assembly of DNA-functionalized micron-sized particles. The versatility of this approach is demonstrated by programming colloidal interactions in sequential and spatial order to obtain an oscillatory structure formation process on a mesoscopic scale. The experimental results represent an approach for the development of active materials by using DNA reaction networks to scale up the dynamic control of colloidal self-organization.

Elastic Photonic Microcapsules Containing Colloidal Crystallites as Building Blocks for Macroscopic Photonic Surfaces

Colloidal crystals develop structural colors through wavelength-selective diffraction. Recently, a granular format of colloidal crystals has emerged as building blocks to construct macroscopic photonic surfaces or architectures with high reconfigurability through the secondary assembly. Here, we design elastic photonic microcapsules containing colloidal crystallites along the inner wall as a building block. Water-in-oil-in-water double-emulsion templates are microfluidically prepared to have an aqueous dispersion of polystyrene particles in the inner droplet and polydimethylsiloxane prepolymers in the shell. Colloidal particles are enriched in the presence of depletant and salt by osmotic compression, with the crystallization at the inner interface by depletion attraction. The number of nucleation sites depends on the rate of the enrichment, which enables control over the size and surface coverage of the crystallites with osmotic conditions. The enrichment is ceased by transferring the droplets into an isotonic solution, and the oil shell is cured to form an elastic membrane. As the elastic microcapsules have a large void in the core, they are deformable without structural damage in the crystallites. Therefore, the microcapsules can be closely packed to form macroscopic surfaces while achieving a high quality of structural colors with a collection of crystallites aligned along the flattened membrane.

Crystallization of charged gold particles mediated by nonadsorbing like-charged polyelectrolyte

We report that the aqueous dispersions of negatively charged submicron-sized colloidal Au particles formed non-close-packed colloidal crystals by the addition of a like-charged linear polyelectrolyte, sodium polyacrylate (NaPAA). Au particles often form irregular aggregates in dispersions because of a strong van der Waals force acting between them. To prevent aggregation, we introduced negative electric charges on particle surfaces. By the addition of NaPAA, colloidal crystals were formed on the bottom of a sample cell because of the supply of Au particles by sedimentation and 2D diffusion even under very dilute conditions. Interparticle potential calculations demonstrated that the addition of NaPAA caused depletion attraction between the particles as well as a significant reduction in the interparticle repulsion because of the electrostatic screening effect. However, the electrostatic repulsion was strong enough to prevent the direct contact of particles in the excluded region between Au particles. Large-area crystals could be obtained by tilting the sample cell. By drying the sample, the Au particles came into contact and the non-space-filling crystals changed into closest packed crystals. These closest packed crystals exhibited a significant enhancement of Raman scattering intensity because of high hot-spot density.

Repulsive and attractive depletion forces mediated by nonadsorbing polyelectrolytes in the Donnan limit

In mixtures of colloids and nonadsorbing polyelectrolytes, a Donnan potential arises across the region between surfaces that are depleted of the polyelectrolyte and the rest of the system. This Donnan potential tends to shift the polyelectrolyte density profile toward the colloidal surface and leads to the local accumulation of polyelectrolytes. We derive a zero-field theory for the disjoining pressure between two parallel flat plates. The polyelectrolyte is allowed to enter the confined interplate region at the cost of a conformational free energy penalty. The resulting disjoining pressure shows a crossover to a repulsive regime when the interplate separation gets smaller than the size of the polyelectrolyte chain, followed by an attractive part. We find a quantitative match between the model and self-consistent field computations that take into account the full Poisson-Boltzmann electrostatics.

Synchronized fractionation and phase separation in binary colloids

Fractionation is necessary for self-assembly in multicomponent mixtures. Here, reversible fractionation and crystallization are realized and studied in two-dimensional binary colloids which are supersaturated by enhancing the attraction between colloidal particles. As a deep and fast supersaturation results in gels with a uniform distribution of binary particles, a gradual quasistatic supersaturation process leads to a two-step crystallization in which small particles and large particles are fractionated as coexisting crystal and liquid phases respectively. Fractionation occurs as well in the quasistatic melting of gels. We show that the synchronized fractionation and phase separation arises from the competition between the size-dependent repulsion and the tunable attraction. The results in this study demonstrate a robust mechanism of fractionation via phase separation, and have important implication in understanding the reversible formation of membraneless organelles in living cells.

Effects of Solution Flow on the Growth of Colloidal Crystals

For the versatile potential applications of colloidal crystals, precisely controlling their growth is required to achieve properties such as high crystallinity and large-area crystals. Because colloidal crystallization is a self-assembly process of dispersed particles in a solution, solution flow directly and markedly changes the behavior of particles. Thus, the effects of solution flow on the growth of colloidal crystals were investigated in the present study. We found three different effects of solution flow on the growth of colloidal crystals: enlarging the first layer, facilitating the growth of superlattice structures, and forming a new circular packing structure. Specifically, in the single-component system, because the flow speed is lower closer to the bottom of the cell, the second and further layers dissolve owing to the large flow speed, whereas the first layer remains undissolved at the appropriate flow speed. The dissolved particles (particles that are detached from the crystals and returned back into the aqueous medium) are transported near the first layer, where they facilitate the growth of the first layer. In a binary system, when colloidal crystals with different particles are neighboring each other, the flow dissolves the surface of each crystal, which forms a dense, melt-like phase between crystals, from which a superlattice structure such as AB₂ grows. The flow often moves the second layer more than the first layer because the flow speed varies with the distance from the bottom. This causes the second layer to slide above the first layer of the neighboring crystals composed of different particle sizes, which transform from the initial face-centered cubic structure of the first layer into a circular pattern with strain. These findings contribute to establishing a sophisticated control method for growing colloidal crystals.

Tailored Colloidal Stability and Rheological Properties of Graphene Oxide Liquid Crystals with Polymer-Induced Depletion Attractions

Graphene oxide liquid crystallinity (GO LC) has been widely exploited for high-performance graphene-based applications. In this regard, colloidal stability of GO LC suspension is a crucial requirement, particularly while polymers are often added to the GO LC. Unfortunately, current level of knowledge on how polymers influence the structure and properties of GO LC is not sufficient to systematically guide the development of applications. Here, we investigate the microstructure and rheological properties of GO LC suspensions in the presence of polymer additives with varying molecular weights and concentrations. Similar to conventional colloidal systems, non-negligible polymer-induced interactions are found in GO LC suspensions, which can effectively modulate the interaction among GO platelets and the relevant physical properties. On the basis of extensive small-angle X-ray scattering and rheological measurements, we demonstrate that, contrary to the general perception, polymer-induced depletion attraction can increase the colloidal stability of GO, while also preventing the vitrification of GO LC. In addition, a proper level of polymer additive can reduce the viscosity of GO LC suspensions by orders of magnitude, providing an effective route to GO LC-based solution processing. After all, the colloidal stability and rheological properties of GO can significantly impact the quality of GO. Therefore, we believe that our finding will be of great interest in the field of graphene-based applications, as it presents effective strategies for improving properties.

Binary colloidal crystals (BCCs): Interactions, fabrication, and applications

The organization of matter into hierarchical structures is a fundamental characteristic of functional materials and living organisms. Binary colloidal crystal (BCC) systems present a diversified range of nanotopographic structures where large and small colloidal particles simultaneously self-assemble into either 2D monolayer or 3D hierarchical crystal lattices. More importantly, understanding how BCCs form opens up the possibility to fabricate more complex systems such as ternary or quaternary colloidal crystals. Monolayer BCCs can also offer the possibility to achieve surface micro- and nano-topographies with heterogeneous chemistries, which can be challenging to achieve with other traditional fabrication tools. A number of fabrication methods have been reported that enable generation of BCC structures offering high accuracy in growth with controllable stoichiometries; however, it is still a challenge to make uniform BCC structures over large surface areas. Therefore, fully understand the mechanism of binary colloidal self-assembly is crucial and new/combinational methods are needed. In this review, we summarize the recent advances in BCC fabrication using particles made of different materials, shapes, and dispersion medium. Depending on the potential application, the degree of order and efficiency of crystal formation has to be determined in order to induce variability in the intended lattice structures. The mechanisms involved in the formation of highly ordered lattice structures from binary colloidal suspensions and applications are discussed. The generation of BCCs can be controlled by manipulation of their extensive phase behavior, which facilitates a wide range potential applications in the fields of both material and biointerfacial sciences including photonics, biosensors, chromatography, antifouling surfaces, biomedical devices, and cell culture tools.

Heterogeneous Nucleation of Colloidal Crystals on a Glass Substrate with Depletion Attraction

The heterogeneous nucleation of colloidal crystals with attractive interactions has been investigated via in situ observations. We have found two types of nucleation processes: a cluster that overcomes the critical size for nucleation with a monolayer, and a method that occurs with two layers. The Gibbs free energy changes (ΔG) for these two types of nucleation processes are evaluated by taking into account the effect of various interfacial energies. In contrast to homogeneous nucleation, the change in interfacial free energy, Δσ, is generated for colloidal nucleation on a foreign substrate such as a cover glass in the present study. The Δσ and step free energy of the first layer, γ₁, are obtained experimentally based on the equation deduced from classical nucleation theory (CNT). It is concluded that the ΔG of q-2D nuclei is smaller than of monolayer nuclei, provided that the same number of particles are used, which explains the experimental result that the critical size in q-2D nuclei is smaller than that in monolayer nuclei.

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.

Two-Dimensional Nucleation on the Terrace of Colloidal Crystals with Added Polymers

Understanding nucleation dynamics is important both fundamentally and technologically in materials science and other scientific fields. Two-dimensional (2D) nucleation is the predominant growth mechanism in colloidal crystallization, in which the particle interaction is attractive, and has recently been regarded as a promising method to fabricate varieties of complex nanostructures possessing innovative functionality. Here, polymers are added to a colloidal suspension to generate a depletion attractive force, and the detailed 2D nucleation process on the terrace of the colloidal crystals is investigated. In the system, we first measured the nucleation rate at various area fractions of particles on the terrace, ϕ_area. In situ observations at single-particle resolution revealed that nucleation behavior follows the framework of classical nucleation theory (CNT), such as single-step nucleation pathway and existence of critical size. Characteristic nucleation behavior is observed in that the nucleation and growth stage are clearly differentiated. When many nuclei form in a small area of the terrace, a high density of kink sites of once formed islands makes growth more likely to occur than further nucleation because nucleation has a higher energy barrier than growth. The steady-state homogeneous 2D nucleation rate, J, and the critical size of nuclei, r*, are measured by in situ observations based on the CNT, which enable us to obtain the step free energy, γ, which is an important parameter for characterizing the nucleation process. The γ value is found to change according to the strength of attraction, which is tuned by the concentration of the polymer as a depletant.