Polarization and interactions of colloidal particles 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.

Dynamic light scattering for particle characterization subjected to ultrasound: a study on compact particles and acousto-responsive microgels

In this report, we investigate dynamic light scattering (DLS) from both randomly diffusing silica particles and acousto-responsive microgels in aqueous dispersions under ultrasonic vibration. Employing high-frequency ultrasound (US) with low amplitude ensures that the polymers remain intact without damage. We derive theoretical expressions for the homodyne autocorrelation function, incorporating the US term alongside the diffusion term. Subsequently, we successfully combined US with a conventional DLS system to experimentally characterize compact silica particles and microgels under the influence of US. Our model allows us to extract essential parameters, including particle size, frequency, and amplitude of particle vibration, based on the correlation function of the scattered light intensity. The studies involving non-responsive silica particles demonstrate that the US does not disrupt size determination, establishing them as suitable reference systems. In addition, we could be able to experimentally resolve the µs-order motion of particles for the first time. Microgels subjected to the US show the same swelling/shrinking behavior as that induced by temperature but with significantly faster kinetics. The findings of this study have potential applications in various industrial and biomedical fields such as smart coatings and drug delivery that benefit from the characterization of macromolecules subjected to the US. Furthermore, the current work may lead to characterizing the mechanical properties of soft particles based on their vibration amplitude extracted using this method.

Spontaneous shock waves in pulse-stimulated flocks of Quincke rollers

Active matter demonstrates complex spatiotemporal self-organization not accessible at equilibrium and the emergence of collective behavior. Fluids comprised of microscopic Quincke rollers represent a popular realization of synthetic active matter. Temporal activity modulations, realized by modulated external electric fields, represent an effective tool to expand the variety of accessible dynamic states in active ensembles. Here, we report on the emergence of shockwave patterns composed of coherently moving particles energized by a pulsed electric field. The shockwaves emerge spontaneously and move faster than the average particle speed. Combining experiments, theory, and simulations, we demonstrate that the shockwaves originate from intermittent spontaneous vortex cores due to a vortex meandering instability. They occur when the rollers' translational and rotational decoherence times, regulated by the electric pulse durations, become comparable. The phenomenon does not rely on the presence of confinement, and multiple shock waves continuously arise and vanish in the system.

Liquid Crystals as Multifunctional Interfaces for Trapping and Characterizing Colloidal Microplastics

Identifying and removing microplastics (MPs) from the environment is a global challenge. This study explores how the colloidal fraction of MPs assemble into distinct 2D patterns at aqueous interfaces of liquid crystal (LC) films with the goal of developing surface-sensitive methods for identifying MPs. Polyethylene (PE) and polystyrene (PS) microparticles are measured to exhibit distinct aggregation patterns, with addition of anionic surfactant amplifying differences in PS/PE aggregation patterns: PS changes from a linear chain-like morphology to a singly dispersed state with increasing surfactant concentration whereas PE forms dense clusters at all surfactant concentrations. Statistical analysis of assembly patterns using deep learning image recognition models yields accurate classification, with feature importance analysis confirming that dense, multibranched assemblies are unique features of PE relative to PS. Microscopic characterization of LC ordering at the microparticle surfaces leads to predict LC-mediated interactions (due to elastic strain) with a dipolar symmetry, a prediction consistent with the interfacial organization of PS but not PE. Further analysis leads to conclude that PE microparticles, due to their polycrystalline nature, possess rough surfaces that lead to weak LC elastic interactions and enhanced capillary forces. Overall, the results highlight the potential utility of LC interfaces for rapid identification of colloidal MPs based on their surface properties.

Directed Assembly of Nanomaterials for Making Nanoscale Devices and Structures: Mechanisms and Applications

Nanofabrication has been utilized to manufacture one-, two-, and three-dimensional functional nanostructures for applications such as electronics, sensors, and photonic devices. Although conventional silicon-based nanofabrication (top-down approach) has developed into a technique with extremely high precision and integration density, nanofabrication based on directed assembly (bottom-up approach) is attracting more interest recently owing to its low cost and the advantages of additive manufacturing. Directed assembly is a process that utilizes external fields to directly interact with nanoelements (nanoparticles, 2D nanomaterials, nanotubes, nanowires, etc.) and drive the nanoelements to site-selectively assemble in patterned areas on substrates to form functional structures. Directed assembly processes can be divided into four different categories depending on the external fields: electric field-directed assembly, fluidic flow-directed assembly, magnetic field-directed assembly, and optical field-directed assembly. In this review, we summarize recent progress utilizing these four processes and address how these directed assembly processes harness the external fields, the underlying mechanism of how the external fields interact with the nanoelements, and the advantages and drawbacks of utilizing each method. Finally, we discuss applications made using directed assembly and provide a perspective on the future developments and challenges.

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.

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

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

Emergence of Colloidal Patterns in ac Electric Fields

Suspended microparticles subjected to ac electrical fields collectively organize into band patterns perpendicular to the field direction. The bands further develop into zigzag shaped patterns, in which the particles are observed to circulate. We demonstrate that this phenomenon can be observed quite generically by generating such patterns with a wide range of particles: silica spheres, fatty acid, oil, and coacervate droplets, bacteria, and ground coffee. We show that the phenomenon can be well understood in terms of second order electrokinetic flow, which correctly predicts the hydrodynamic interactions required for the pattern formation process. Brownian particle simulations based on these interactions accurately recapitulate all of the observed pattern formation and symmetry-breaking events, starting from a homogeneous particle suspension. The emergence of the formed patterns can be predicted quantitatively within a parameter-free theory.

Activity waves and freestanding vortices in populations of subcritical Quincke rollers

Virtually all of the many active matter systems studied so far are made of units (biofilaments, cells, colloidal particles, robots, animals, etc.) that move even when they are alone or isolated. Their collective properties continue to fascinate, and we now understand better how they are unique to the bulk transduction of energy into work. Here we demonstrate that systems in which isolated but potentially active particles do not move can exhibit specific and remarkable collective properties. Combining experiments, theory, and numerical simulations, we show that such subcritical active matter can be realized with Quincke rollers, that is, dielectric colloidal particles immersed in a conducting fluid subjected to a vertical DC electric field. Working below the threshold field value marking the onset of motion for a single colloid, we find fast activity waves, reminiscent of excitable systems, and stable, arbitrarily large self-standing vortices made of thousands of particles moving at the same speed. Our theoretical model accounts for these phenomena and shows how they can arise in the absence of confining boundaries and individual chirality. We argue that our findings imply that a faithful description of the collective properties of Quincke rollers need to consider the fluid surrounding particles.

2D colloids in rotating electric fields: A laboratory of strong tunable three-body interactions

Many-body forces play a prominent role in structure and dynamics of matter, but their role is not well understood in many cases due to experimental challenges. Here, we demonstrate that a novel experimental system based on rotating electric fields can be utilised to deliver unprecedented degree of control over many-body interactions between colloidal silica particles in water. We further show that we can decompose interparticle interactions explicitly into the leading terms and study their specific effects on phase behaviour. We found that three-body interactions exert critical influence over the phase diagram domain boundaries, including liquid-gas binodal, critical and triple points. Phase transitions are shown to be reversible and fully controlled by the magnitude of external rotating electric field governing the tunable interactions. Our results demonstrate that colloidal systems in rotating electric fields are a unique laboratory to study the role of many-body interactions in physics of phase transitions and in applications, such as self-assembly, offering exciting opportunities for studying generic phenomena inherent to liquids and solids, from atomic to protein and colloidal systems.

Accelerated annealing of colloidal crystal monolayers by means of cyclically applied electric fields

External fields are commonly applied to accelerate colloidal crystallization; however, accelerated self-assembly kinetics can negatively impact the quality of crystal structures. We show that cyclically applied electric fields can produce high quality colloidal crystals by annealing local disorder. We find that the optimal off-duration for maximum annealing is approximately one-half of the characteristic melting half lifetime of the crystalline phase. Local six-fold bond orientational order grows more rapidly than global scattering peaks, indicating that local restructuring leads global annealing. Molecular dynamics simulations of cyclically activated systems show that the ratio of optimal off-duration for maximum annealing and crystal melting time is insensitive to particle interaction details. This research provides a quantitative relationship describing how the cyclic application of fields produces high quality colloidal crystals by cycling at the fundamental time scale for local defect rearrangements; such understanding of dynamics and kinetics can be applied for reconfigurable colloidal assembly.

Electric-Field-Driven Assembly of Dipolar Spheres Asymmetrically Confined between Two Electrodes

Externally applied electric fields have previously been utilized to direct the assembly of colloidal particles confined at a surface into a large variety of colloidal oligomers and nonclose-packed honeycomb lattices (J. Am. Chem. Soc. 2013, 135, 7839-7842). The colloids under such confinement and fields are observed to spontaneously organize into bilayers near the electrode. To extend and better understand how particles can come together to form quasi-two-dimensional materials, we have performed Monte Carlo simulations and complementary experiments of colloids that are strongly confined between two electrodes under an applied alternating current electric field, controlling field strength and particle area fraction. Of particular importance, we control the fraction of particles in the upper vs lower plane, which we describe as asymmetric confinement, and which effectively modulates the coordination number of particles in each plane. We model the particle-particle interactions using a Stockmayer potential to capture the dipolar interactions induced by the electric field. Phase diagrams are then delineated as a function of the control parameters, and a theoretical model is developed in which the energies of several idealized lattices are calculated and compared. We find that the resulting theoretical phase diagrams agree well with simulation. We have not only reproduced the structures observed in experiments using parameters that are close to experimental conditions but also found several previously unobserved phases in the simulations, including a network of rectangular bands, zig zags, and a sigma lattice, which we were then able to confirm in experiment. We further propose a simple way to precisely control the number ratio of particles between different planes, that is, superimposing a direct current electric field with the alternating current electric field, which can be implemented conveniently in experiments. Our work demonstrates that a diverse collection of materials can be assembled from relatively simple ingredients, which can be analyzed effectively through comparison of simulation, theory, and experiment. Our model further explains possible pathways between different phases and provides a platform for examining phases that have yet to be observed in experiments.

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.

Melting, freezing, and dynamics of two-dimensional dipole systems in screening bulk media

This paper reports on the molecular dynamics simulations of classical two-dimensional (2D) electric dipole systems. The properties of 2D systems with bare (nonscreened) and screened dipole-dipole interactions have been investigated. Based on the polygon construction method, we present simulation results on the phase transition, and we locate the melting and freezing points of 2D dipole systems in terms of a polygon disorder parameter, with the polygon disorder parameter being the sum of nontriangular polygon order parameters. It was found that the phase transition of the system occurs when the polygon disorder parameter has a value 0.165. This result was cross-checked by using both local and overall orientational order parameters. We also identified that the value of the average local orientational order parameter at the phase transition point is 0.67. These results are valid for the ordinary (bare) dipole-dipole interaction as well as the screened dipole-dipole interaction, and they are expected to be general for other 2D systems with repulsive pair interaction. We observed that both melting and freezing points shift to lower values of temperature due to screening. In the liquid state, the radial distribution function and polygon construction method show the loss of order in a structure as screening becomes more severe. Furthermore, the impact of screening on the system's collective excitation spectra and diffusive characteristics at liquid and solid states has been studied. Results show the decrease in the values of both longitudinal and transverse sound speeds and the emergence of anomalous superdiffusive motion in the liquid state due to screening.

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.

Confined 1D Propulsion of Metallodielectric Janus Micromotors on Microelectrodes under Alternating Current Electric Fields

There is mounting interest in synthetic microswimmers ("micromotors") as microrobots as well as a model system for the study of active matters, and spatial navigation is critical for their success. Current navigational technologies mostly rely on magnetic steering or guiding with physical boundaries, yet limitations with these strategies are plenty. Inspired by an earlier work with magnetic domains on a garnet film as predefined tracks, we present an interdigitated microelectrodes (IDE) system where, upon the application of AC electric fields, metallodielectric (e.g., SiO₂-Ti) Janus particles are hydrodynamically confined and electrokinetically propelled in one dimension along the electrode center lines with tunable speeds. In addition, comoving micromotors moved in single files, while those moving in opposite directions primarily reoriented and moved past each other. At high particle densities, turbulence-like aggregates formed as many-body interactions became complicated. Furthermore, a micromotor made U-turns when approaching an electrode closure, while it gradually slowed down at the electrode opening and was collected in large piles. Labyrinth patterns made of serpentine chains of Janus particles emerged by modifying the electrode configuration. Most of these observations can be qualitatively understood by a combination of electroosmotic flows pointing inward to the electrodes, and asymmetric electrical polarization of the Janus particles under an AC electric field. Emerging from these observations is a strategy that not only powers and confines micromotors on prefabricated tracks in a contactless, on-demand manner, but is also capable of concentrating active particles at predefined locations. These features could prove useful for designing tunable tracks that steer synthetic microrobots, as well as to enable the study of single file diffusion, active turbulence, and other collective behaviors of active matters.

Enhanced diffusion and magnetophoresis of paramagnetic colloidal particles in rotating magnetic fields

Dispersions of paramagnetic colloids can be manipulated with external magnetic fields to assemble structures via dipolar assembly and control transport via magnetophoresis. For fields held steady in time, the dispersion structure and dynamic properties are coupled. This coupling can be problematic when designing processes involving field-induced forces, as particle aggregation competes against and hinders particle transport. Time-varying fields drive dispersions out-of-equilibrium, allowing the structure and dynamics to be tuned independently. Rotating the magnetic field direction using two biaxial fields is a particularly effective mode of time-variation and has been used experimentally to enhance particle transport. Fundamental transport properties, like the diffusivity and magnetophoretic mobility, dictate dispersions' out-of-equilibrium responses to such time-varying fields, and are therefore crucial to understand to effectively design processes utilizing rotating fields. However, a systematic study of these dynamic quantities in rotating fields has not been performed. Here, we investigate the transport properties of dispersions of paramagnetic colloids in rotating magnetic fields using dynamic simulations. We find that self-diffusion of particles is enhanced in rotating fields compared to steady fields, and that the self-diffusivity in the plane of rotation reaches a maximum value at intermediate rotation frequencies that is larger than the Stokes-Einstein diffusivity of an isolated particle. We also show that, while the magnetophoretic velocity of particles through the bulk in a field gradient decreases with increasing rotation frequency, the enhanced in-plane diffusion allows for faster magnetophoretic transport through porous materials in rotating fields. We examine the effect of porous confinement on the transport properties in rotating fields and find enhanced diffusion at all pore sizes. The confined and bulk values of the transport properties are leveraged in simple models of magnetophoresis through tortuous porous media.

Size-Tunable Assembly of Gold Nanoparticles Using Competitive AC Electrokinetics

Alternating current (AC) electrokinetics is a facile way of patterning colloidal particles into advanced structures. We demonstrate the combined use of AC dielectrophoresis (AC-DEP) and AC electrohydrodynamics (AC-EHD) in a microwell electrode geometry for size-tunable assembly of gold nanoparticles (AuNPs) into one-dimensional microwires and two-dimensional films. The AC-DEP force scales with both particle size and field frequency, whereas the AC-EHD force depends only on the field frequency. So, a critical particle diameter ( d_c) exists, below which the EHD phenomenon becomes more important and beyond which the DEP force is dominating. We performed theoretical and experimental studies to determine " d_c" and how it gets affected by operating parameters like field frequency, voltage, particle number, electrolyte concentration, electrode size, and geometry. Our results show that the morphologies of the colloidal structures transition from films to microwires as the NP diameters vary from nanometers (< d_c) to microns (> d_c), and no assembly takes place at intermediate sizes (∼ d_c). While the film formation is governed purely by surface EHD flows, microwire synthesis is a result of EHD-assisted DEP phenomenon. Also, a minimum particle number, a low salt concentration, and an optimum frequency range is required to initiate assembly.

Tunable interactions between particles in conically rotating electric fields

Tunable interactions between colloidal particles in external conically rotating electric fields are calculated, while the (vertical) axis of the field rotation is normal to the (horizontal) particle motion plane. The comparison of different approaches, including the methods of noninteracting, self-consistent dipoles, and the boundary element method, indicates that the last method is the most suitable for tunable interaction analysis. Thorough analysis, performed for interactions in pairs and clusters of colloidal particles, indicate that two- and three-body interactions make the main contributions in the interaction energy, while the effect of high-order terms is negligible. The tunable interactions are determined by the dielectric properties of the particles and solvent and can be changed in a wide range, providing a rich variety for the experimental "design" of different interactions, including repulsion, attraction, combination of short-range repulsion with long-range attraction, barrier-type interactions with short-range attraction and long-range repulsion, and double-scale repulsive (core-shoulder) interactions. These conclusions can be generalized for magnetically induced tunable interactions. The results indicate that tunable interactions can be widely applied in self-assembly and particle-resolved studies of generic phenomena in fluids and crystals, and, therefore, are of broad interest in the fields of chemical physics, physical chemistry, materials science, and soft matter.

Energy transfer mechanisms in a dipole chain: From energy equipartition to the formation of breathers

We study the energy transfer in a classical dipole chain of N interacting rigid rotating dipoles. The underlying high-dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their stability in the common plane of rotation. Starting from the minimal energy configuration, the response of the chain to excitation of a single dipole is investigated. Using both the linearized and the exact Hamiltonian of the dipole chain, we detect an approximate excitation energy threshold between a weakly and a strongly nonlinear dynamics. In the weakly nonlinear regime, the chain approaches in the course of time the expected energy equipartition among the dipoles. For excitations of higher energy, strongly localized excitations appear whose trajectories in time are either periodic or irregular, relating to the well-known discrete or chaotic breathers, respectively. The phenomenon of spontaneous formation of domains of opposite polarization and phase locking is found to commonly accompany the time evolution of the chaotic breathers. Finally, the sensitivity of the dipole chain dynamics to the initial conditions is studied as a function of the initial excitation energy by computing a fast chaos indicator. The results of this study confirm the aforementioned approximate threshold value for the initial excitation energy, below which the dynamics of the dipole chain is regular and above which it is chaotic.

High-Resolution Large-Ensemble Nanoparticle Trapping with Multifunctional Thermoplasmonic Nanohole Metasurface

The intrinsic loss in a plasmonic metasurface is usually considered to be detrimental for device applications. Using plasmonic loss to our advantage, we introduce a thermoplasmonic metasurface that enables high-throughput large-ensemble nanoparticle assembly in a lab-on-a-chip platform. In our work, an array of subwavelength nanoholes in a metal film is used as a plasmonic metasurface that supports the excitation of localized surface plasmon and Bloch surface plasmon polariton waves upon optical illumination and provides a platform for molding both optical and thermal landscapes to achieve a tunable many-particle assembling process. The demonstrated many-particle trapping occurs against gravity in an inverted configuration where the light beam first passes through the nanoparticle suspension before illuminating the thermoplasmonic metasurface, a feat previously thought to be impossible. We also report an extraordinarily enhanced electrothermoplasmonic flow in the region of the thermoplasmonic nanohole metasurface, with comparatively larger transport velocities in comparison to the unpatterned region. This thermoplasmonic metasurface could enable possibilities for myriad applications in molecular analysis, quantum photonics, and self-assembly and creates a versatile platform for exploring nonequilibrium physics.

Field-Directed Self-Assembly of Mutually Polarizable Nanoparticles

Directed assembly of dielectric and paramagnetic nanoparticles can be used to synthesize diverse functional materials that polarize in response to an externally applied electric or magnetic field. However, theories capable of predicting the self-assembled states are lacking. In the proposed work, we develop a complete thermodynamic description of such assemblies for spherical nanoparticles. We show how an important physical feature of these types of particles, mutual polarization, sculpts the free energy landscape and has a remarkably strong influence on the nature of the self-assembled states. Modeling the mutual polarization among nanoparticles requires solving a many-bodied problem for the particle dipole moments. Typically, this computationally expensive task is avoided by neglecting mutual polarization and assuming that each particle in a concentrated dispersion acquires the same dipole moment as a single, isolated particle. Although valid in the limit of small dielectric or permeability contrasts between particles and solvent, this constant dipole assumption leads to qualitatively incorrect predictions for coexisting phases in equilibrium at large dielectric or permeability contrasts. Correctly accounting for mutual polarization enables a thermodynamic theory that describes the equilibrium phase diagram of polarizable dispersions in terms of experimentally controllable variables. Our theoretical predictions agree with the phase behavior we observe in dynamic simulations of these dispersions as well as that in experiments of field-directed structural transitions. In contrast to predictions of a constant dipole model, we find that dispersions of particles with different dielectric constants or magnetic permeabilities exhibit qualitatively different phase behavior. This new model also predicts the existence of a eutectic point at which two crystalline phases and a disordered phase of nanoparticles all simultaneously coexist.

Tuning thin-film bijels with applied external electric fields

The tunability of thin-film bijels using applied external electric fields is explored using a Cahn-Hilliard Langevin dynamics computational model. Dielectric contrast between liquid domains governs liquid domain alignment and was varied in the simulations. Dielectric contrast between colloidal particles and liquid matrix induces dipolar particle interactions and was also varied in the simulations. The study reveals unique internal morphologies including those with through-thickness liquid domains. Significant results include identification of electric field effects on phase evolution and final morphology as well as relevant mechanisms. It was also found that particle chains act as nucleation sites for phase separation. The resultant morphologies were analyzed in terms of particle attachment to phase interface regions as well as the average channel diameter. Electric field effects and mechanisms on morphology are identified and compared with other morphology-tuning parameters such as particle loading and liquid-liquid composition.

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.

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.

Electric-Field Assisted Assembly of Colloidal Particles into Ordered Nonclose-Packed Arrays

Nonclose-packed colloidal arrays have many potential applications ranging from plasmonic sensors, light trapping for photovoltaics, to transparent electrodes. However, scalable fabrication of those structures remains a challenge. In this Article, we investigate the robustness of an electric-field assisted approach systematically. A monolayer of nonclose-packed crystalline array is first created under a low-frequency alternating-current electric field in solution. We then apply a sequence of direct-current pulses to fix the particle array onto the substrate so that it remains intact even after both field removal and solvent evaporation. Key process parameters such as the alternating-current field strength, direct-current magnitude, particle concentration, and solvent-evaporation rate that affect both ordering and fixing of colloidal particles have been studied systematically. We find that direct currents with an intermediate magnitude induce electrophoretic motion of particles toward the substrate and facilitate their permanent adhesion on the substrate due to strong van der Waals attraction. A higher current, however, causes lateral aggregation of particles arising from electroosmotic flow of solvent and destroys the periodic ordering between particles. This approach, in principle, can be conveniently adapted into the continuous convective assembly process, thus making the fabrication of nonclose-packed colloidal arrays scalable.

Electric-Field-Induced Reversible Phase Transitions in Two-Dimensional Colloidal Crystals

Two-dimensional colloidal crystals confined within electric field traps on the surface of a dielectrophoretic cell undergo reversible phase transitions that depend on the strength of the applied AC electric field. At low field strengths, the particles adopt a two-dimensional hexagonal close-packed lattice with p6m plane group symmetry and the maximum achievable packing fraction of φ = 0.91. Higher electric field strengths induce dipoles in the particles that provoke a phase transition to structures that depend on the number of particles confined in the trap. Whereas traps containing N = 24 particles transform to a square-packed lattice with p4m symmetry and φ = 0.79 is observed, traps of the same size containing N = 23 particles can also pack in a lattice with p2 symmetry and φ = 0.66. Traps with N = 21, 22, and 25 particles exhibit a mixture of packing structures, revealing the influence of lateral compressive forces, in addition to induced dipole interactions, in stabilizing loosely packed arrangements. These observations permit construction of a phase diagram based on adjustable parameters of electric field strength (0-750 V/cm) and particle number (N = 21-25).

Moderately nonlinear diffuse-charge dynamics under an ac voltage

The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

Characterization of 2D colloids assembled by optically-induced electrohydrodynamics

We report the results of a study characterizing the behavior of colloid aggregations under manipulation of a technique known as Rapid Electrokinetic Patterning (REP) - this technique is capable of dynamically manipulating the crystallinity of 2D colloid aggregations, potentially enabling dynamically tunable photonic crystals. Herein, aggregations of spherical polystyrene particles 1.0 μm in diameter suspended in a low conductivity aqueous solution were collected at the surface of an indium-tin oxide coated glass slide. The uniform AC field coupled with laser-induced heating produced electrothermal hydrodynamics which is responsible for the self-assembly characteristics of the planar colloidal aggregation. REP was characterized experimentally by analyzing the mutual particle spacing within the aggregation as a function of the AC signal and laser power. Numerical simulations justified the assumption that the primary forces responsible for colloidal patterning herein are Stokes drag forces and dipole-dipole repulsive forces.

Effect of surface modification of SiO2@TiO2core–shell particles on the structural colour under an electric field

Surface modified colloidal SiO₂@TiO₂core–shell particles were chosen to study their responsive photonic properties and the effect of surface on structural colour under low electric field.

Direct measurement of field-induced polarization forces between particles in air

We have measured the effect of DC and AC electric fields (up to 15 kV/m) on the force between two 15 μm radius BaTiO3 glass spheres in air in the separation range 0-6 μm. These fields cause attractive forces that are much greater than van der Waals forces and therefore can be used to control and separate particles in many applications. The attractive force has a static and dynamic component. The static forces are about 9000 times greater than the prediction by multiple-moment methods but otherwise follow the expected trends for polarization forces. For example, the force scales with the square of the field, is constant over a range of field frequencies, and has the same force-separation profile predicted by multipole-moment methods. In contrast to the point dipole approximation, which depends inversely on the fourth power of the distance between the centers of the spheres, the measured static force approximately follows a power law, F ∝ -s(-0.75), that depends on the separation, s, between the nearest points of the spheres. This power law is very similar to the prediction by multipole-moment method for separations less than 1/10th of the radius. The dynamic response force occurs at twice the frequency of the drive and has a similar amplitude to the static force. The electrical field also causes a large increase in adhesion.

Crystallization of micrometer-sized particles with molecular contours

The crystallization of micrometer-sized particles with shapes mimicking those of tetrabenzoheptacene (TBH) and 1,2:5,6-dibenzanthracene (DBT), both flat polyacenes, in an electric field results in the formation of ordered 2D packings that mimic the plane group symmetries in their respective molecular crystal equivalents. Whereas the particles packed in low-density disordered arrangements under a gravitational gradient, dielectrophoresis (under an ac electric field) produced ordered high-density packings with readily identifiable plane group symmetry. The ordered colloidal assemblies were stable for hours, with the packing density decreasing slowly but with recognizable symmetry for up to 12 h for the TBH-shaped particles and up to 4 h for the DBT-shaped particles. This unexpected stability is attributed to jamming behavior associated with interlocking of the dogbone-shaped (TBH) and Z-block (DBT) particles, contrasting with the more rapid reduction of packing density and loss of hexagonal symmetry for disk-shaped particles upon removal of the electric field. The TBH-shaped and DBT-shaped particles assemble into the p2 plane group, which corresponds to the densest particle packing among the possible close-packed plane groups for these particle symmetries. The p2 symmetry observed for the TBH-shaped and DBT-shaped colloid crystal emulates the p2 symmetry of the (010) layers in their respective molecular crystals, which crystallize in monoclinic lattices. Notably, DBT-shaped particles also form ordered domains with pgg symmetry, replicating the plane group symmetry of the (100) layer in the orthorhombic polymorph of DBT. These observations illustrate that the 2D ordering of colloid particles can mimic the packing of molecules with similar shapes, demonstrating that packing can transcend length scales from the molecular to the colloidal.

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.

Frequency sweep rate dependence on the dielectrophoretic response of polystyrene beads and red blood cells

Alternating current (AC) dielectrophoresis (DEP) experiments for biological particles in microdevices are typically done at a fixed frequency. Reconstructing the DEP response curve from static frequency experiments is laborious, but essential to ascertain differences in dielectric properties of biological particles. Our lab explored the concept of sweeping the frequency as a function of time to rapidly determine the DEP response curve from fewer experiments. For the purpose of determining an ideal sweep rate, homogeneous 6.08 μm polystyrene (PS) beads were used as a model system. Translatability of the sweep rate approach to ∼7 μm red blood cells (RBC) was then verified. An Au/Ti quadrapole electrode microfluidic device was used to separately subject particles and cells to 10Vpp AC electric fields at frequencies ranging from 0.010 to 2.0 MHz over sweep rates from 0.00080 to 0.17 MHz/s. PS beads exhibited negative DEP assembly over the frequencies explored due to Maxwell-Wagner interfacial polarizations. Results demonstrate that frequency sweep rates must be slower than particle polarization timescales to achieve reliable incremental polarizations; sweep rates near 0.00080 MHz/s yielded DEP behaviors very consistent with static frequency DEP responses for both PS beads and RBCs.

Transition from dilute to concentrated electrokinetic behavior in the dielectric spectra of a colloidal suspension

Dielectric spectroscopy is used to measure the complex permittivity of 200 and 100 nm diameter polystyrene latex suspended in potassium chloride (KCl) solutions over the frequency range 10(4)-10(7) Hz as a function of particle volume fraction (ϕ) and ionic strength. Dilute suspension dielectric spectra are in excellent agreement with electrokinetic theory. A volume fraction dependence of the dielectric increment is observed for low electrolyte concentrations (0.01, 0.05, and 0.1 mM) above ϕ ≈ 0.02. This deviation from the dilute theory occurs at a critical frequency ω* that is a function of volume fraction, particle size, and ionic strength. The dielectric increment of suspensions at the highest salt concentration (1 mM) shows no volume fraction dependence up to ϕ = 0.09. Values of ω* are collapsed onto a master curve that accounts for the length and time scales of ion migration between neighboring particles. The measured conductivity increment is independent of volume fraction and agrees with theory after accounting for added counterions and nonspecific adsorption.

Directed self-assembly of colloidal crystals by dielectrophoretic ordering

In this Article, we report the dielectrophoretic assembly of colloidal particles and show how the kinetics of assembly and degree of ordering depend on the particle size, charge, solution ionic strength, and field strength and frequency. A special dielectrophoresis (DEP) sample cell is constructed and validated to quantitatively measure directed self-assembly via sequential light scattering and optical microscopy measurements. Our results confirm the recently established scaling for the order-disorder transition and extend it to higher scaled frequencies. The limiting scaling of the order-disorder transition and particle electrophoretic mobility are correctly predicted by the standard electrokinetic model (SEKM). In particular, the order-disorder transition line is predicted from the particle properties using a recently proposed empirical scaling law and the SEKM over an order of magnitude in particle size.