One- and two-dimensional assembly of colloidal ellipsoids in ac electric fields

Morphologies of electric-field-driven cracks in dried dispersions of ellipsoids

We report an experimental and theoretical study of the morphology of desiccation cracks formed in deposits of hematite ellipsoids dried in an externally applied alternating current (ac) electric field. A series of transitions in the crack morphology is observed by modulating the frequency and the strength of the applied field. We also found a clear transition in the morphology of cracks as a function of the aspect ratio of the ellipsoid. We show that these transitions in the crack morphology can be explained by a linear stability analysis of the equation describing the effective dynamics of an ellipsoid placed in an externally applied ac electric field.

Multistate Dynamic Pathways for Anisotropic Colloidal Assembly and Reconfiguration

We report the controlled interfacial assembly and reconfiguration of rectangular prism colloidal particles between microstructures of varying positional and orientational order including stable, metastable, and transient states. Structurally diverse states are realized by programming time dependent electric fields that mediate dipolar interactions determining particle position, orientation, compression, and chaining. We identify an order parameter set that defines each state as a combination of the positional and orientational order. These metrics are employed as reaction coordinates to capture the microstructure evolution between initial and final states upon field changes. Assembly trajectory manifolds between states in the low-dimensional reaction coordinate space reveal a dynamic pathway map including information about pathway accessibility, reversibility, and kinetics. By navigating the dynamic pathway map, we demonstrate reconfiguration between states on minute time scales, which is practically useful for particle-based materials processing and device responses. Our findings demonstrate a conceptually general approach to discover dynamic pathways as a basis to control assembly and reconfiguration of self-organizing building blocks that respond to global external stimuli.

Anisotropic particle multiphase equilibria in nonuniform fields

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1-9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid-nematic, fluid-crystal, and fluid-nematic-crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal-nematic and crystal-fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications.

Assembly and manipulation of responsive and flexible colloidal structures by magnetic and capillary interactions

The long-ranged interactions induced by magnetic fields and capillary forces in multiphasic fluid-particle systems facilitate the assembly of a rich variety of colloidal structures and materials. We review here the diverse structures assembled from isotropic and anisotropic particles by independently or jointly using magnetic and capillary interactions. The use of magnetic fields is one of the most efficient means of assembling and manipulating paramagnetic particles. By tuning the field strength and configuration or by changing the particle characteristics, the magnetic interactions, dynamics, and responsiveness of the assemblies can be precisely controlled. Concurrently, the capillary forces originating at the fluid-fluid interfaces can serve as means of reconfigurable binding in soft matter systems, such as Pickering emulsions, novel responsive capillary gels, and composites for 3D printing. We further discuss how magnetic forces can be used as an auxiliary parameter along with the capillary forces to assemble particles at fluid interfaces or in the bulk. Finally, we present examples how these interactions can be used jointly in magnetically responsive foams, gels, and pastes for 3D printing. The multiphasic particle gels for 3D printing open new opportunities for making of magnetically reconfigurable and "active" structures.

Design rules for 2D field mediated assembly of different shaped colloids into diverse microstructures

Assembling different shaped particles into ordered microstructures is an open challenge in creating multifunctional particle-based materials and devices. Here, we report the two-dimensional (2D) AC electric field mediated assembly of different shaped colloidal particles into amorphous, liquid crystalline, and crystalline microstructures. Particle shapes investigated include disks, ellipses, squares, and rectangles, which show how systematic variations in anisotropy and corner curvature determine the number and type of resulting microstructures. AC electric fields induce dipolar interactions to control particle positional and orientational order. Microstructural states are determined via particle tracking to compute order parameters, which agree with computer simulations and show how particle packing and dipolar interactions together produce each structure. Results demonstrate how choice of particle shape and field conditions enable kinetically viable routes to assemble nematic, tetratic, and smectic liquid crystal structures as well as crystals with stretched 4- and 6-fold symmetry. Results show it is possible to assemble all corresponding hard particle phases, but also show how dipolar interactions influence and produce additional microstructures. Our findings provide design rules for the assembly of diverse microstructures of different shaped particles in AC electric fields, which could enable scalable and reconfigurable particle-based materials, displays, and printing technologies.

1D Colloidal chains: recent progress from formation to emergent properties and applications

Integrating nanoscale building blocks of low dimensionality (0D; i.e., spheres) into higher dimensional structures endows them and their corresponding materials with emergent properties non-existent or only weakly existent in the individual building blocks. Constructing 1D chains, 2D arrays and 3D superlattices using nanoparticles and colloids therefore continues to be one of the grand goals in colloid and nanomaterial science. Amongst these higher order structures, 1D colloidal chains are of particular interest, as they possess unique anisotropic properties. In recent years, the most relevant advances in 1D colloidal chain research have been made in novel synthetic methodologies and applications. In this review, we first address a comprehensive description of the research progress concerning various synthetic strategies developed to construct 1D colloidal chains. Following this, we highlight the amplified and emergent properties of the resulting materials, originating from the assembly of the individual building blocks and their collective behavior, and discuss relevant applications in advanced materials. In the discussion of synthetic strategies, properties, and applications, particular attention will be paid to overarching concepts, fresh trends, and potential areas of future research. We believe that this comprehensive review will be a driver to guide the interdisciplinary field of 1D colloidal chains, where nanomaterial synthesis, self-assembly, physical property studies, and material applications meet, to a higher level, and open up new research opportunities at the interface of classical disciplines.

Shape Matters in Magnetic-Field-Assisted Assembly of Prolate Colloids

An anisotropic colloidal shape in combination with an externally tunable interaction potential results in a plethora of self-assembled structures with potential applications toward the fabrication of smart materials. Here we present our investigation on the influence of an external magnetic field on the self-assembly of hematite-silica core-shell prolate colloids for two aspect ratios ρ = 2.9 and 3.69. Our study shows a rather counterintuitive but interesting phenomenon, where prolate colloids self-assemble into oblate liquid crystalline (LC) phases. With increasing concentration, particles with smaller ρ reveal a sequence of LC phases involving para-nematic, nematic, smectic, and oriented glass phases. The occurrence of a smectic phase for colloidal ellipsoids has been neither predicted nor reported before. Quantitative shape analysis of the particles together with extensive computer simulations indicate that in addition to ρ, a subtle deviation from the ideal ellipsoidal shape dictates the formation of this unusual sequence of field-induced structures. Particles with ρ = 2.9 exhibit a hybrid shape containing features from both spherocylinders and ellipsoids, which make their self-assembly behavior richer than that observed for either of the "pure" shapes. The shape of the particles with higher ρ matches closely with the ideal ellipsoids, as a result their phase behavior follows the one expected for a "pure" ellipsoidal shape. Using anisotropic building blocks and external fields, our study demonstrates the ramifications of the subtle changes in the particle shape on the field-directed self-assembled structures with externally tunable properties.

Anisotropic colloidal interactions & assembly in AC electric fields

We match experimental and simulated configurations of anisotropic epoxy colloidal particles in high frequency AC electric fields by identifying analytical potentials for dipole-field and dipole-dipole interactions. We report an inverse Monte Carlo simulation algorithm to determine optimal fits of analytical potentials by matching simulated and experimental distribution functions for non-uniform liquid, liquid crystal, and crystal microstructures in varying amplitude electric fields. Two potentials that include accurate particle volume and dimensions along with a concentration dependent prefactor quantitatively capture experimental observations. At low concentrations, an effective ellipsoidal point dipole potential works well, whereas a novel stretched point dipole potential is found to be suitable at all concentrations, field amplitudes, and degrees of ordering. The simplicity, accuracy, and adjustability of the stretched point dipole potential suggest it can be applied to model field mediated microstructures and assembly of systematically varying anisotropic particle shapes.

Directed Assembly of Particles for Additive Manufacturing of Particle-Polymer Composites

Particle-polymer dispersions are ubiquitous in additive manufacturing (AM), where they are used as inks to create composite materials with applications to wearable sensors, energy storage materials, and actuation elements. It has been observed that directional alignment of the particle phase in the polymer dispersion can imbue the resulting composite material with enhanced mechanical, electrical, thermal or optical properties. Thus, external field-driven particle alignment during the AM process is one approach to tailoring the properties of composites for end-use applications. This review article provides an overview of externally directed field mechanisms (e.g., electric, magnetic, and acoustic) that are used for particle alignment. Illustrative examples from the AM literature show how these mechanisms are used to create structured composites with unique properties that can only be achieved through alignment. This article closes with a discussion of how particle distribution (i.e., microstructure) affects mechanical properties. A fundamental description of particle phase transport in polymers could lead to the development of AM process control for particle-polymer composite fabrication. This would ultimately create opportunities to explore the fundamental impact that alignment has on particle-polymer composite properties, which opens up the possibility of tailoring these materials for specific applications.

Fabrication and Electric Field-Driven Active Propulsion of Patchy Microellipsoids

Active colloids are a synthetic analogue of biological microorganisms that consume external energy to swim through viscous fluids. Such motion requires breaking the symmetry of the fluid flow in the vicinity of a particle; however, it is challenging to understand how surface and shape anisotropies of the colloid lead to a particular trajectory. Here, we attempt to deconvolute the effects of particle shape and surface anisotropy on the propulsion of model ellipsoids in alternating current (AC) electric fields. We first introduce a simple process for depositing metal patches of various shapes on the surfaces of ellipsoidal particles. We show that the shape of the metal patch is governed by the assembled structure of the ellipsoids on the substrate used for physical vapor deposition. Under high-frequency AC electric field, ellipsoids dispersed in water show linear, circular, and helical trajectories which depend on the shapes of the surface patches. We demonstrate that features of the helical trajectories such as the pitch and diameter can be tuned by varying the degree of patch asymmetry along the two primary axes of the ellipsoids, namely longitudinal and transverse. Our study reveals the role of patch shape on the trajectory of ellipsoidal particles propelled by induced charge electrophoresis. We develop heuristics based on patch asymmetries that can be used to design patchy particles with specified nonlinear trajectories.

Directional and Reconfigurable Assembly of Metallodielectric Patchy Particles

Colloidal particles with surface patches can self-assemble with high directionality, but the resulting assemblies cannot reconfigure unless the patch arrangement (number, symmetry, etc.) is altered. While external fields with tunable inputs can guide the assembly of dynamic structures, they encourage particle alignment relative to its shape rather than the surface patterns. Here, we report on the synthesis of metallodielectric patchy particles and their assembly under the AC electric field, which gives rise to a series of structures including two-layer alternating chains, open-brick walls, staggering stacks, and vertical chains that are directed by the patches yet reconfigurable by the field. The configurations of the assemblies (e.g., the chains) can be further switched between a rigid and a flexible state emulating the conformations of polymers. Our work suggests that, for directed colloidal assembly, the particle complexities (patches and shapes) can be coupled with the external manipulations in a cooperative manner for creating materials with precise yet reconfigurable structures.

Gradient stretching to produce variable aspect ratio colloidal ellipsoids

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

Quantifying patterns in optical micrographs of one- and two-dimensional ellipsoidal particle assemblies

Current developments in colloidal science include the assembly of anisotropic colloids with broad geometric diversity. As the complexity of particle assemblies increases, the need for ubiquitous algorithms that quantitatively analyze images of the assemblies to deliver key information such as quantification of crystal structures becomes more urgent. This contribution describes algorithms capable of image analysis for classifying colloidal structures based on abstracted interparticle relationship information and quantitatively analyzing the abundance of each structure in mixed pattern assemblies. The algorithm parameters can be adjusted, allowing for the algorithms to be adapted for different image analyses. Three different ellipsoidal particle assembly images are presented to demonstrate the effectiveness of the algorithms: a one-dimensional (1D) particle chain assembly and two two-dimensional (2D) polymorphic crystals each consisting of assemblies of two distinct plane symmetry groups. Angle relationships between neighbouring particles are calculated and neighbour counts of each particle are determined. Combining these two parameters as rules for classification criteria allows for the labeling and quantification of each particle into a defined symmetry class within an assembly. The algorithms provide a labelled image comprising classification results and particle counts of each defined class. For multiple images or individual frames from a video, the script can be looped to achieve automatic processing. The yielded classification data allow for more in-depth image analysis of mixed pattern particle assemblies. We envision that these algorithms will have utility in quantitative analysis of images comprising ellipsoidal colloidal materials, nanoparticles, or biological matter.

Anisotropy effects on the kinetics of colloidal crystallization and melting: comparison of spheres and ellipsoids

We use alternating current (AC) electric field assisted self-assembly to produce two-dimensional, millimeter scale arrays of ellipsoidal colloids and study the kinetics of their phase reconfiguration by means of confocal microscopy, light scattering, and computer simulation. We find that the kinetics of orientational and positional ordering can be manipulated by changing the shape of the colloids: ellipsoids with aspect ratio 2.0 melt into disordered structures 5.7 times faster compared to spheres. On the other hand, ellipsoids self-assemble into ordered crystals at a similar rate to spheres. Confocal microscopy is used to directly visualize defects in the self-assembled structures. Small-angle light scattering (SALS) quantifies the light diffraction response, which is sensitive to the kinetics of positional and orientational ordering in the self-assembled anisotropic structures. We find three different light diffraction patterns: a phase with high orientational order (with chain-like structure in real space), a phase with high positional and orientational order (characteristic of a close-packed structure), and a phase that is disordered in position but with intermediate orientational order. The large influence of aspect ratio on the kinetics of the positionally and orientationally ordered phase is explored through simulation; it is found that the number of particle degrees of freedom controls the difference between the melting rates of the ellipsoids and spheres. This research contributes to the understanding of reconfiguration kinetics and optical properties of colloidal crystals produced from anisotropic colloids.

Interfacial Assembly of Tunable Anisotropic Nanoparticle Architectures

We propose a strategy for assembling spherical nanoparticles (NPs) into anisotropic architectures in a polymer matrix. The approach takes advantage of the interfacial tension between two mutually immiscible polymers forming a bilayer and differences in the compatibility of the two polymer layers with polymer grafts on particles to trap NPs within two-dimensional planes parallel to the interface. The ability to precisely tune the location of the entrapment planes via the NP grafting density, and to trap multiple interacting particles within distinct planes, can then be used to assemble NPs into unconventional arrangements near the interface. We carry out molecular dynamics simulations of polymer-grafted NPs in a polymer bilayer to demonstrate the viability of the proposed approach in both trapping NPs at tunable distances from the interface and assembling them into a variety of unusual nanostructures. We illustrate the assembly of NP clusters, such as dimers with tunable tilt relative to the interface and trimers with tunable bending angle, as well as anisotropic macroscopic phases, including serpentine and branched structures, ridged hexagonal monolayers, and square-ordered bilayers. We also develop a theoretical model to predict the preferred positions and free energies of NPs trapped at or near the interface that could help guide the design of polymer-grafted NPs for achieving target NP architectures. Overall, this work suggests that interfacial assembly of NPs could be a promising approach for fabricating next-generation polymer nanocomposites with potential applications in plasmonics, electronics, optics, and catalysis where precise arrangement of polymer-embedded NPs is required for function.

Sphere-Tubule Superstructures through Supramolecular and Supracolloidal Assembly Pathways

While colloids have been widely employed as models for atoms and molecules, the current study proposes to extend their use as building blocks for supracolloidal frameworks. Hereby, the self-assembly between highly anisotropic supramolecular microtubules and soft spherical fluorescent microgels is explored using confocal laser scanning microscopy. The influence of the particle size and charge with respect to the catanionic tubule composition, which consists of two oppositely charged bile salt derivatives, is investigated. Under certain conditions, microgel particles are found to specifically interact with the extremities of the tubular aggregates and hierarchically self-assemble into various superstructures varying from virus-like assemblies to supracolloidal networks. The reported approach is envisioned to open new self-assembly routes toward ordered hybrid superstructures where the spherical colloids act as responsive linkers of tubular structures.

Tools and Functions of Reconfigurable Colloidal Assembly

We review work in reconfigurable colloidal assembly, a field in which rapid, back-and-forth transitions between the equilibrium states of colloidal self-assembly are accomplished by dynamic manipulation of the size, shape, and interaction potential of colloids, as well as the magnitude and direction of the fields applied to them. It is distinguished from the study of colloidal phase transitions by the centrality of thermodynamic variables and colloidal properties that are time switchable; by the applicability of these changes to generate transitions in assembled colloids that may be spatially localized; and by its incorporation of the effects of generalized potentials due to, for example, applied electric and magnetic fields. By drawing upon current progress in the field, we propose a matrix classification of reconfigurable colloidal systems based on the tool used and function performed by reconfiguration. The classification distinguishes between the multiple means by which reconfigurable assembly can be accomplished (i.e., the tools of reconfiguration) and the different kinds of structural transitions that can be achieved by it (i.e., the functions of reconfiguration). In the first case, the tools of reconfiguration can be broadly classed as (i) those that control the colloidal contribution to the system entropy-as through volumetric and/or shape changes of the particles; (ii) those that control the internal energy of the colloids-as through manipulation of colloidal interaction potentials; and (iii) those that control the spatially resolved potential energy that is imposed on the colloids-as through the introduction of field-induced phoretic mechanisms that yield colloidal displacement and accumulation. In the second case, the functions of reconfiguration include reversible: (i) transformation between different phases-including fluid, cluster, gel, and crystal structures; (ii) manipulation of the spacing between colloids in crystals and clusters; and (iii) translation, rotation, or shape-change of finite-size objects self-assembled from colloids. With this classification in hand, we correlate the current limits on the spatiotemporal scales for reconfigurable colloidal assembly and identify a set of future research challenges.

Elucidating the mechanism governing cell rotation under DEP using the volumetric polarization and integration method

Cell rotation can be achieved by utilizing rotating electric fields through which torques are generated due to phase difference between the dipole moment of cells and the external electric field. While reports of cell rotation under non-rotating electrical fields, such as dielectrophoresis (DEP), are abound, the underlying mechanism is not fully understood. Because of this, contradicting arguments remain regarding if a single cell can rotate under conventional DEP. What's more, the current prevailing DEP theory is not adequate for identifying the cause for such disagreements. In this work we applied our recently developed Volumetric Polarization and Integration (VPI) method to investigate the possible causes for cell rotation under conventional DEP. Three-dimensional (3D) computer models dealing with a cell in a DEP environment were developed to quantify the force and torque imparted on the cell by the external DEP field using COMSOL Multiphysics software. Modeling results suggest that eccentric inclusions with low conductivity inside the cell will generate torques (either in clockwise or counter-clockwise directions) sufficient to cause cell rotation under DEP. For validation of modeling predictions, experiments with rat adipose stem cells containing large lipid droplets were conducted. Good agreement between our modeling and experimental results suggests that the VPI method is powerful in elucidating the underlying mechanisms governing the complicated DEP phenomena.

Elucidating the Mechanisms of Two Unique Phenomena Governed by Particle-Particle Interaction under DEP: Tumbling Motion of Pearl Chains and Alignment of Ellipsoidal Particles

Particle-particle interaction plays a crucial role in determining the movement and alignment of particles under dielectrophoresis (DEP). Previous research efforts focus on studying the mechanism governing the alignment of spherical particles with similar sizes in a static condition. Different approaches have been developed to simulate the alignment process of a given number of particles from several up to thousands depending on the applicability of the approaches. However, restricted by the simplification of electric field distribution and use of identical spherical particles, not much new understanding has been gained apart from the most common phenomenon of pearl chain formation. To enhance the understanding of particle-particle interaction, the movement of pearl chains under DEP in a flow condition was studied and a new type of tumbling motion with unknown mechanism was observed. For interactions among non-spherical particles, some preceding works have been done to simulate the alignment of ellipsoidal particles. Yet the modeling results do not match experimental observations. In this paper, the authors applied the newly developed volumetric polarization and integration (VPI) method to elucidate the underlying mechanism for the newly observed movement of pearl chains under DEP in a flow condition and explain the alignment patterns of ellipsoidal particles. The modeling results show satisfactory agreement with experimental observations, which proves the strength of the VPI method in explaining complicated DEP phenomena.

Measurement of Anisotropic Particle Interactions with Nonuniform ac Electric Fields

Optical microscopy measurements are reported for single anisotropic polymer particles interacting with nonuniform ac electric fields. The present study is limited to conditions where gravity confines particles with their long axis parallel to the substrate such that particles can be treated using quasi-2D analysis. Field parameters are investigated that result in particles residing at either electric field maxima or minima and with long axes oriented either parallel or perpendicular to the electric field direction. By nonintrusively observing thermally sampled positions and orientations at different field frequencies and amplitudes, a Boltzmann inversion of the time-averaged probability of states yields kT-scale energy landscapes (including dipole-field, particle-substrate, and gravitational potentials). The measured energy landscapes show agreement with theoretical potentials using particle conductivity as the sole adjustable material property. Understanding anisotropic particle-field energy landscapes vs field parameters enables quantitative control of local forces and torques on single anisotropic particles to manipulate their position and orientation within nonuniform fields.

Energy landscapes for ellipsoids in non-uniform AC electric fields

We report a closed-form analytical model for energy landscapes of ellipsoidal particles in non-uniform high-frequency AC electric fields to identify all possible particle positions and orientations. Three-dimensional equilibrium positions and orientations of prolate (r_x = r_y < r_z), oblate (r_x = r_z > r_y), and scalene (r_x≠r_y≠r_z) ellipsoids are reported vs. field frequency and amplitude, which are determined from energy landscape minima. For ellipsoids within non-uniform electric fields between co-planar parallel electrodes, the number of configurations of position and orientation is 6 for prolate, 5 for oblate, and 9 for scalene ellipsoids. In addition, for coplanar electrodes, conditions are identified when particles can be treated using a quasi-2D analysis in the plane of their most probable elevation near an underlying surface. The reported expressions are valid for time-averaged interactions of ellipsoid particles in arbitrary AC electric field configurations, such that our results are applicable to electromagnetic tweezers interacting with particles having an appropriate material property contrast with the medium in the frequency range of interest.

Directed Self-Assembly of Polarizable Ellipsoids in an External Electric Field

The interplay between shape anisotropy and directed long-range interactions enables the self-assembly of complex colloidal structures. As a recent highlight, ellipsoidal particles polarized in an external electric field were observed to associate into well-defined tubular structures. In this study, we systematically investigate such directed self-assembly using Monte Carlo simulations of a two-point-charge model of polarizable prolate ellipsoids. In spite of its simplicity and computational efficiency, we demonstrate that the model is capable of capturing the complex structures observed in experiments on ellipsoidal colloids at low volume fractions. We show that, at sufficiently high electric field strength, the anisotropy in shape and electrostatic interactions causes a transition from three-dimensional crystal structures observed at low aspect ratios to two-dimensional sheets and tubes at higher aspect ratios. Our work thus illustrates the rich self-assembly behavior accessible when exploiting the interplay between competing long- and short-range anisotropic interactions in colloidal systems.

Dielectrophoretic assembly of dimpled colloids into open packing structures

Reversible solid-state phase transitions between open- and close-packed structures in two-dimensional colloidal crystals comprising 1.8 μm dimpled spherical colloids were observed using negative dielectrophoresis. These asymmetrically-shaped colloids adopted lattices with cmm plane group symmetry and a packing fraction, ϕ, of 0.68 at low electric field strengths. At high electric field strengths, the close-packed p6m symmetry was observed, with ϕ = 0.90. The transition between open and close-packed structures was found to be reversible, depending on the applied electric field strength and frequency. Finite Fourier transform analysis and COMSOL simulations revealed the existence of repulsive interactions between colloids perpendicular to the electric field lines due to a concentration of the electric field at the edges of the dimpled regions of the colloids. The repulsive interactions resulted in a stretching of the hexagonal lattice perpendicular to the electric field lines, the magnitude of which depended on the electric field strength. By screening the colloids from the electric field in local potential wells, the entropically favored close-packed hexagonal lattice with ϕ = 0.91 was recovered.

General Potential for Anisotropic Colloid-Surface Interactions

A general closed-form, analytical potential is developed for the interaction of planar surfaces with superellipsoidal particles (which includes shapes such as spheres, ellipsoids, cylinders, polygons, superspheres, etc.). The Derjaguin approximation is used with DLVO half-space interactions (e.g., electrostatics and van der Waals) to yield potentials for arbitrary particle-wall separation and orientation. The resulting potential is a function of the minimum distance between surfaces and the particle's local Gaussian curvature at the minimum distance position. The validity of the solution is reported in terms of the local Gaussian curvature (Γ) and characteristic interaction range (e.g., Debye length, κ^-1, for electrostatics) based on the limits of the Derjaguin approximation. This solution is limited for superellipsoids with convex shapes and orientations where the condition κ/Γ^1/2 > 2 is satisfied. The potentials reported in this work should be useful for modeling a wide range of natural and synthetic nonspherical and anisotropic colloidal particles in environmental, biological, and advanced material applications.

Hierarchical Fullerene Assembly: Seeded Coprecipitation and Electric Field Directed Assembly

Hierarchical C₆₀ colloidal films are assembled from nanoscale to macroscale. Fullerene molecular crystals are grown via seeded cosolvent precipitation with mixed solvent [tetrahydronaphthalene (THN)/trimethylpyridine (TMP)] and antisolvent 2-propanol. The fullerene solutions are aged under illumination, which due to the presence of TMP reduces the free monomer concentration through fullerene aggregation into nanoparticles. The nanoparticles seed the growth of monodisperse fullerene colloids on injection into the antisolvent. Diverse colloidal morphologies are prepared as a function of injection volume and fullerene solution concentration. The high fullerene solubility of THN enables C₆₀ colloids to be prepared in quantities sufficient for assembly (5 × 10⁸ ). Electric fields are applied to colloidal C₆₀ platelets confined to two dimensions. The particles assemble under dipolar forces, dielectrophoretic forces, and electrohydrodynamic flows. Frequency-dependent phase transitions occur at the critical Maxwell-Wagner crossover frequency, where the effective polarizability of the particles in the medium is substantially reduced. Structures form as a function of field strength, frequency, and confinement including hexagonal, oblique, string fluid, coexistent hexagonal-rhombic, and tetratic.

Template-Free Assembly in Living Bacterial Suspension under an External Electric Field

Although template-assisted self-assembly methods are very popular in materials and biological systems, they have certain limitations such as lack of tunability and switchable functionality because of the irreversible association of cells and their matrix components. With an aim to achieve more tunability, we have made an attempt to investigate the self-assembly behavior of rod-shaped living bacteria subjected to an external alternating electric field using confocal microscopy. We demonstrate that rod-shaped living bacteria dispersed in a low salinity aqueous medium form different types of reversible freely suspended structures when subjected to an external alternating electric field. At low field strength, an oriented phase is observed where individual bacterium orients with its major axis aligned along the field direction. At intermediate field strength, bacteria align in the form of one-dimensional (1D) chains that lie along the field direction. Further, at high field strength, more bacteria associate with these 1D chains laterally to form a two-dimensional (2D) array. At higher bacterial concentration, these field-induced 2D arrays extend to form three-dimensional columnar structures. These results are discussed in the context of previously reported studies on bacterial self-assembly.

Multiscale directed self-assembly of composite microgels in complex electric fields

This study explored the application of localized electric fields for reversible directed self-assembly of colloidal particles in 3 dimensions. Electric field microgradients, arising from the use of micro-patterned electrodes, were utilized to direct the localization and self-assembly of polarizable (charged) particles resulting from a combination of dielectrophoretic and multipolar forces. Deionized dispersions of spherical and ellipsoidal core-shell microgels were employed for investigating their assembly under an external alternating electric field. We demonstrated that the frequency of the field allowed for an exquisite control over the localization of the particles and their self-assembled structures near the electrodes. We extended this approach to concentrated binary dispersions consisting of polarizable and less polarizable composite microgels. Furthermore, we utilized the thermosensitivity of the microgels to adjust the effective volume fraction and the dynamics of the system, which provided the possibility to dynamically "solidify" the assembly of the field-responsive particles by a temperature quench from their initial fluid state into an arrested crystalline state. Reversible solidification enables us to re-write/reconstruct various 3 dimensional assemblies by varying the applied field frequency.

Two-dimensional assemblies of nematic colloids in homeotropic cells and their response to electric fields

Micrometer-sized colloidal particles dispersed in nematic liquid crystals interact with each other through anisotropic interactions induced by orientational deformation of the nematic field. In the case of so-called dipole nematic colloids, their interaction is of the dipole-dipole type. Two-dimensional, non-close-packed colloidal assemblies having various characteristics were fabricated using optical tweezers by exploiting the attraction between anti-parallel dipole nematic colloids in homeotropically aligned nematic cells. Structures comprising polygons, squares, and tetrahedra were built using equal-sized particles, and hexagonal structures were built using particles of two sizes. As the nematic field is sensitive to electric fields, the response of the fabricated assemblies toward an alternating electric field was also studied. All assemblies exhibited homogeneous reversible shrinkage, and their shrinkage rates were dependent on the structure. The maximum shrinkage rate in the linear dimension of the assemblies was over 20% at 5 Vrms for a hexagon comprising tetrahedral units.

Anisotropic responsive microgels with tuneable shape and interactions

Highly monodisperse polystyrene/poly(N-isopropylmethacrylamide) (PS-PNIPMAM) core-shell composite microgels were synthesized and further nanoengineered in either ellipsoidal, faceted or bowl-shaped particles. Beside their anisotropy in shape, the microgel design enables an exquisite control of the particle conformation, size and interactions from swollen and hydrophilic to collapsed and hydrophobic using temperature as an external control variable. The post-processing procedures and the characterization of the different particles are first presented. Their potential as model systems for the investigation of the effects of anisotropic shape and interactions on the phase behavior is further demonstrated. Finally, the self-assembly of bowl-shaped composite microgel particles is discussed, where the temperature and an external AC electric field are employed to control the interactions from repulsive to attractive and from soft repulsive to dipolar, respectively.

Formation and frequency response of two-dimensional nanowire lattices in an applied electric field

Ordered two-dimensional (2D) lattices were formed by assembling silica-coated solid and segmented Au nanowires between coplanar electrodes using alternating current (ac) electric fields. Dielectrophoretic forces from the ac field concentrated wires between the electrodes, with their long axis aligned parallel to the field lines. After reaching a sufficient particle density, field-induced dipolar interactions resulted in the assembly of dense 2D lattices that spanned the electrodes, a distance of at least ten wire lengths. The ends of neighboring Au wires or segments overlapped a fraction of their length to form lattice structures with a "running bond" brickwork-like pattern. The observed lattice structures were tunable in three distinct ways: (1) particle segmentation pattern, which fixed the lattice periodicity for a given field condition; (2) ac frequency, which varied lattice periodicity in real time; and (3) switching the field on/off, which converted between lattice and smectic particle organizations. Electric field simulations were performed to understand how the observed lattice periodicity depends on the assembly conditions and particle segmentation. Directed self-assembly of well-ordered 2D metallic nanowire lattices that can be designed by Au striping pattern and reconfigured by changes in field conditions could enable new types of switchable optical or electronic devices.

Nematic ordering of polarizable colloidal rods in an external electric field: theory and experiment

The orientation of dielectric colloidal rods dispersed in a dielectric fluid medium exposed to an external electric field: theory and confocal microscopy measurements.

Field-induced assembly of colloidal ellipsoids into well-defined microtubules

Current theoretical attempts to understand the reversible formation of stable microtubules and virus shells are generally based on shape-specific building blocks or monomers, where the local curvature of the resulting structure is explicitly built-in via the monomer geometry. Here we demonstrate that even simple ellipsoidal colloids can reversibly self-assemble into regular tubular structures when subjected to an alternating electric field. Supported by model calculations, we discuss the combined effects of anisotropic shape and field-induced dipolar interactions on the reversible formation of self-assembled structures. Our observations show that the formation of tubular structures through self-assembly requires much less geometrical and interaction specificity than previously thought, and advance our current understanding of the minimal requirements for self-assembly into regular virus-like structures.

An electric-field induced dynamical state in dispersions of charged colloidal rods

The response of concentrated dispersions of charged colloids to low-frequency electric fields is governed by field-induced inter-colloidal interactions resulting from the polarization of electric double layers and the layer of condensed ions, association and dissociation of condensed ions, as well as hydrodynamic interactions through field-induced electro-osmotic flow. The phases and states that can be formed by such field-induced interactions are an essentially unexplored field of research. Experiments on concentrated suspensions of rod-like colloids (fd-virus particles), within the isotropic-nematic phase coexistence region, showed that a number of phases/states are induced, depending on the field amplitude and frequency [Soft Matter, 2010, 6, 273]. In particular, a dynamical state is found where nematic domains form and melt on a time scale of the order of seconds. We discuss the microscopic origin of this dynamical state, which is attributed to the cyclic, electric-field induced dissociation and association of condensed ions. A semi-quantitative theory is presented for the dynamics of melting and formation of nematic domains, including a model for the field-induced dissociation/association of condensed ions. The resulting equation of motion for the orientational order parameter is solved numerically for parameters complying with the fd-virus system. A limit-cycle is found, with a cycling-time that diverges at the transition line in the field-amplitude versus frequency plane where the dynamical state first appears, in accord with experimental findings.

Reconfigurable assemblies of Janus rods in AC electric fields

We investigate the electric field-induced assembly of Janus colloids composed of silica rods patterned with gold patches in both side- and tip-coated motifs. These shape and chemically anisotropic particles assemble into reconfigurable chains, whose structure depends on patch location, AC electric field strength, and frequency.

Dielectrophoretic coassembly of binary colloidal mixtures in AC electric fields

We report the novel use of dielectrophoresis (DEP) for fabricating a new class of composite structures composed of binary mixtures of micrometer-sized colloidal particles. Latex-latex and latex-yeast cells have been coassembled in a combinatorial manner into one- (1D) and two-dimensional (2D) architectures in spatially varying external alternating current (AC) electric fields using two different electrode geometries. The effects of voltage, frequency, particle size, particle concentration, and particle type are investigated in detail to determine how the relative polarizabilities of the particles can be tuned to influence the overall coassembly process. Our observations reveal key differences in the latex-latex and latex-yeast cell assembly behavior especially in the case of 2D structure formation arising mainly due to the intrinsically high polarizability and polydispersity of the cells. This study is useful for making a potpourri of new hybrid structures with advanced functionalities for photonic and biosensing applications.

Self-assembly of Janus ellipsoids II: Janus prolate spheroids

In self-assembly, the anisotropy of the building blocks and their formation of complex structures have been the subject of considerable recent research. Extending recent research on Janus particles and completing the study of Janus spheroids, we conduct a systematic investigation on the self-assembly of Janus prolate spheroids based on a primitive model that we proposed. Janus prolate spheroids are particles that have a prolate spheroidal body and two hemi-surfaces along the major axis coded with different chemical properties. Using Monte Carlo simulations, we investigate the effects of the aspect ratio on the self-assembly process. In contrast to the vesicle-like aggregates for Janus oblate spheroids, we obtain various ordered cluster structures for Janus prolate spheroids through self-assembly. With an increasing aspect ratio, we find a transition of cluster morphology, from vesicles to tubular micelles and micelles. In particular, a relatively small change in the aspect ratio leads to a rather significant change in morphology. We apply a cluster analysis to understand the mechanism associated with such a transition.

Two-dimensional directed assembly of dicolloids

The assembly of ordered dicolloid monolayers is directed by an electric field. The dicolloid particles are polystyrene latex with a maximum equatorial diameter 3.45 μm and length 4.63 μm. The monolayer structure is characterized using small-angle light scattering and bright-field microscopy. With increasing field strength from 26.7 to 200 V(RMS)/cm, a transition from a disordered monolayer, to first orientationally ordered, and then translationally ordered two-dimensional (2D) arrays occurs. A c2mm plane group symmetry dominates the ordered structure but is present alongside structures with p2 symmetry, leading to a spread in the angular distribution of the light scattering peaks. The order-disorder transition dependence on field strength and frequency is similar to that observed for colloidal spheres; at higher frequencies, stronger fields are required to assemble particles. Optimal ordered structures reflect a balance between inducing sufficiently strong interparticle interactions while limiting the rate of formation to ensure the growth of large crystalline domains.

Liquid crystal order in colloidal suspensions of spheroidal particles by direct current electric field assembly

DC electric fields are used to produce colloidal assemblies with orientational and layered positional order from a dilute suspension of spheroidal particles. These 3D assemblies, which can be visualized in situ by confocal microscopy, are achieved in short time spans (t < 1 h) by the application of a constant voltage across the capacitor-like device. This method yields denser and more ordered assemblies than had been previously reported with other assembly methods. Structures with a high degree of orientational order as well as layered positional order normal to the electrode surface are observed. These colloidal structures are explained as a consequence of electrophoretic deposition and field-assisted assembly. The interplay between the deposition rate and the rotational Brownian motion is found to be critical for the optimal ordering, which occurs when these rates, as quantified by the Peclet number, are of order one. The results suggest that the mechanism leading to ordering is equilibrium self-assembly but with kinetics dramatically accelerated by the application of the DC electric field. Finally, the crystalline symmetry of the densest structure formed is determined and compared with previously studied spheroidal assemblies.

Directed orientation of asymmetric composite dumbbells by electric field induced assembly

Assembly and directed orientation of anisotropic particles with an external ac electric field in a range from 1 kHz to 2 MHz were studied for asymmetric composite dumbbells incorporating a silica, titania, or titania/silica (titania:silica = 75:25 vol %) sphere. The asymmetric composite dumbbells, which were composed of a polymethylmethacrylate (PMMA)-coated sphere (core-shell part) and a polystyrene (PSt) lobe, were synthesized with a soap-free emulsion polymerization to prepare PMMA-coated inorganic spheres and another soap-free emulsion polymerization to form a polystyrene (PSt) lobe from the PMMA-coated inorganic spheres. The composite dumbbells dispersed in water were directly observed with optical microscopy. The dumbbells incorporating a silica sphere oriented parallel to an electric field in the whole frequency range and they formed a pearl chain structure at a high frequency of 2 MHz. The titania-incorporated dumbbells formed chain structures, in which they contacted their core-shell parts and oriented perpendicularly to a low-frequency (kHz) field, whereas they oriented parallel to a high-frequency (MHz) field. Since the alignment of dumbbells in the chains depends not only on the interparticle forces but also on the torque that the induced dipoles in the dumbbells experience in the electric field, the orientation of dumbbells perpendicular to the electric field was the case dominated by the interparticle force, whereas the other orientation was the case dominated by the torque. The present experiments show that the incorporation of inorganic dumbbells is an effective way to control the assembled structure and orientation with an electric field.

Role of anisotropy in electrodynamically induced colloidal aggregates

We investigate the assembly of spherical and anisotropic colloidal particles with the shape of peanuts when subjected to an external alternating electric field. By varying the strength and frequency of the applied field, we observe that both types of particles form clusters at low frequencies due to attractive electrohydrodynamic interactions or disperse into a liquidlike phase at high frequencies due to repulsive dipolar interactions. We characterize the observed structures via pair correlation functions and radius of gyration, and observe a clear difference in the ordering process between the isotropic and anisotropic colloids. Further on, we interpret the cluster formation kinetics in terms of dynamic scaling theory, and observe a faster aggregation of the anisotropic colloids with respect to the isotropic ones.