2-D assembly of colloidal particles on a planar electrode

Gold on the horizon: unveiling the chemistry, applications and future prospects of 2D monolayers of gold nanoparticles (Au-NPs)

Noble 2D monolayers of gold nanoparticles (Au-NPs) have garnered significant attention due to their unique physicochemical properties, which are instrumental in various technological applications. This review delves into the intricate physical chemistry underlying the formation of Au-NP monolayers, highlighting key interactions such as electrostatic forces, van der Waals attractions, and ligand-mediated stabilization. The discussion extends to the size- and shape-dependent assembly processes of these NP monolayers, elucidating how nanoparticle dimensions and morphologies influence monolayer formation and stability. Moreover, the review explores the diverse interfaces-solid, liquid, and air-where Au-NP monolayers are employed, each presenting distinct advantages and challenges. In the realm of applications, Au-NP monolayers have shown remarkable promises. In memory devices, their ability to facilitate high-density data storage through enhanced electron transport mechanisms is examined. Biosensing applications benefit from the monolayers' exceptional sensitivity and specificity, which are crucial for detecting biomolecular interactions. Furthermore, the role of Au-NP monolayers in electrocatalysis is explored, with a focus on their catalytic efficiency and stability in various electrochemical reactions. Despite their potential, the deployment of Au-NP monolayers faces several challenges. The review addresses current limitations such as scalability, reproducibility, and long-term stability, proposing potential strategies to overcome these hurdles. Future prospects are also discussed, including the development of multifunctional monolayers and integration with other nanomaterials to enhance performance across different applications. In conclusion, while significant strides have been made in understanding and utilizing 2D Au-NP monolayers, ongoing research is imperative to fully exploit their capabilities. Addressing existing challenges through innovative approaches will pave the way for their widespread adoption in advanced technological applications.

Electrostatic force on a spherical particle confined between two planar surfaces

A charge-free particle in a uniform electric field experiences no net force in an unbounded domain. A boundary, however, breaks the symmetry and the particle can be attracted or repelled to it, depending on the applied field direction [Z. Wang et al., Phys. Rev. E, 2022, 106, 034607]. Here, we investigate the effect of a second boundary because of its common occurrence in practical applications. We consider a spherical particle suspended between two parallel walls and subjected to a uniform electric field, applied in a direction either normal or tangential to the surfaces. All media are modeled as leaky dielectrics, thus allowing for the accumulation of free charge at interfaces, while bulk media remain charge-free. The Laplace equation for the electric potential is solved using a multipole expansion and the boundaries are accounted for by a set of images. The results show that in the case of a normal electric field, which corresponds to a particle between two electrodes, the force is always attractive to the nearer boundary and, in general, weaker that the case of only one wall. Intriguingly, for a given particle-wall separation we find that the force may vary nonmonotonically with confinement and its magnitude may exceed the one-wall value. In the case of tangential electric field, which corresponds to a particle between insulating boundaries, the force follows the same trends but it is always repulsive.

Microrobots powered by concentration polarization electrophoresis (CPEP)

Second-order electrokinetic flow around colloidal particles caused by concentration polarization electro-osmosis (CPEO) can result in a phoretic motion of asymmetric particle dimers in a homogeneous AC electrical field, which we refer to as concentration polarization electro-phoresis (CPEP). To demonstrate this actuation mechanism, we created particle dimers from micron-sized silica spheres with sizes 1.0 μm and 2.1 μm by connecting them with DNA linker molecules. The dimers can be steered along arbitrarily chosen paths within a 2D plane by controlling the orientation of the AC electric field in a fluidic chamber with the joystick of a gamepad. Further utilizing induced dipole-dipole interactions, we demonstrate that particle dimers can be used to controllably pick up monomeric particles and release them at any desired position, and also to assemble several particles into groups. Systematic experiments exploring the dependence of the dimer migration speed on the electric field strength, frequency, and buffer composition align with the theoretical framework of CPEO and provide parameter ranges for the operation of our microrobots. Furthermore, experiments with a variety of asymmetric particles, such as fragmented ceramic, borosilicate glass, acrylic glass, agarose gel, and ground coffee particles, as well as yeast cells, demonstrate that CPEP is a generic phenomenon that can be expected for all charged dielectric particles.

Asymmetric rectified electric and concentration fields in multicomponent electrolytes with surface reactions

Recent experimental studies have utilized AC electric fields and electrochemical reactions in multicomponent electrolyte solutions to control colloidal assembly. However, theoretical investigations have thus far been limited to binary electrolytes and have overlooked the impact of electrochemical reactions. In this study, we address these limitations by analyzing a system with multicomponent electrolytes, while also relaxing the assumption of ideally blocking electrodes to capture the effect of surface electrochemical reactions. Through a regular perturbation analysis in the low-applied-potential regime, we solve the Poisson-Nernst-Planck equations and obtain effective equations for electrical potential and ion concentrations. By employing a combination of numerical and analytical calculations, our analysis reveals a significant finding: electrochemical reactions alone can generate asymmetric rectified electric fields (AREFs), i.e., time-averaged, long-range electric fields, even when the diffusivities of the ionic species are equal. This finding expands our understanding beyond the conventional notion that AREFs arise solely from diffusivity contrast. Furthermore, we demonstrate that AREFs induced by electrochemical reactions can be stronger than those resulting from asymmetric diffusivities. Additionally, we report the emergence of asymmetric rectified concentration fields (ARCFs), i.e., time-averaged, long-range concentration fields, which supports the electrodiffusiophoresis mechanism of colloidal assembly observed in experiments. We also derive analytical expressions for AREFs and ARCFs, emphasizing the role of imbalances in ionic strength and charge density, respectively, as the driving forces behind their formation. The results presented in this article advance the field of colloidal assembly and also have implications for improved understanding of electrolyte transport in electrochemical devices.

Controlling the direction of steady electric fields in liquid using nonantiperiodic potentials

When applying an oscillatory electric potential to an electrolyte solution, it is commonly assumed that the choice of which electrode is grounded or powered does not matter because the time average of the electric potential is zero. Recent theoretical, numerical, and experimental work, however, has established that certain types of multimodal oscillatory potentials that are "nonantiperiodic" can induce a net steady field toward either the grounded or powered electrode [A. Hashemi et al., Phys. Rev. E 105, 065001 (2022)2470-004510.1103/PhysRevE.105.065001]. Here, we elaborate on the nature of these steady fields through numerical and theoretical analyses of the asymmetric rectified electric field (AREF). We demonstrate that AREFs induced by a nonantiperiodic electric potential, e.g., by a two-mode waveform with modes at 2 and 3Hz, invariably yields a steady field that is spatially dissymmetric between two parallel electrodes, such that swapping which electrode is powered changes the direction of the field. Furthermore, we show that, while the single-mode AREF occurs in asymmetric electrolytes, nonantiperiodic electric potentials create a steady field in electrolytes even if the cations and anions have the same mobilities. Additionally, using a perturbation expansion, we demonstrate that the dissymmetric AREF occurs due to odd nonlinear orders of the applied potential. We further generalize the theory by demonstrating that the dissymmetric field occurs for all classes of zero-time-average (no dc bias) periodic potentials, including triangular and rectangular pulses, and we discuss how these steady fields can tremendously change the interpretation, design, and applications of electrochemical and electrokinetic systems.

Formation Techniques Used in Shape-Forming Microrobotic Systems with Multiple Microrobots: A Review

Multiple robots are used in robotic applications to achieve tasks that are impossible to perform as individual robotic modules. At the microscale/nanoscale, controlling multiple robots is difficult due to the limitations of fabrication technologies and the availability of on-board controllers. This highlights the requirement of different approaches compared to macro systems for a group of microrobotic systems. Current microrobotic systems have the capability to form different configurations, either as a collectively actuated swarm or a selectively actuated group of agents. Magnetic, acoustic, electric, optical, and hybrid methods are reviewed under collective formation methods, and surface anchoring, heterogeneous design, and non-uniform control input are significant in the selective formation of microrobotic systems. In addition, actuation principles play an important role in designing microrobotic systems with multiple microrobots, and the various control systems are also reviewed because they affect the development of such systems at the microscale. Reconfigurability, self-adaptable motion, and enhanced imaging due to the aggregation of modules have shown potential applications specifically in the biomedical sector. This review presents the current state of shape formation using microrobots with regard to forming techniques, actuation principles, and control systems. Finally, the future developments of these systems are presented.

Customized metallodielectric colloids and their behavior in dielectrophoretic fields

A synthetic strategy for fabricating colloidal particles with spatially segregated amine-functionalized lobes enables regioselective coating with gold to afford metallodielectric particles with a variety of shapes and lobe sizes. This approach can produce either dissymmetric dumbbell-shaped two-lobed Au-TPM particles (Au-T) or dissymmetric or symmetric three-lobed particles with gold coating on one (Au-T-T and T-Au-T) or two lobes (Au-T-Au). Dielectrophoretic (DEP) forces exerted by an AC field confined between two opposing electrodes generate aggregates ranging from 1D chains to 2D close-packed lattices, depending on the particle shape and lobe arrangement. The aggregate structures reflect the lowest energy configurations resulting from the induced dipole moments created in particle lobes within the confined electric field.

Particle-surface interactions in a uniform electric field

The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to be weakly conducting, so that that the leaky dielectric model applies. The Laplace equation for the electric potential is solved in bipolar coordinate system and the potential is obtained in terms of a series expansion of Legendre polynomials. The force on the particle is calculated using the Maxwell tensor. We find that in the case of normal electric field, which corresponds to a particle near an electrode, the force is always attractive but at a given separation it varies nontrivially with particle-suspending medium conductivity ratio; the force on a particle that is more conducting than the suspending medium is much larger compared to the force on a particle less conducing than the suspending medium. In the case of tangential electric field, which corresponds to a particle near an insulating boundary, the force is always repulsive.

Travelling-Wave Electrophoresis, Electro-Hydrodynamics, Electro-Rotation, and Symmetry- Breaking of a Polarizable Dimer in Non-Uniform Fields

A theoretical framework is presented for calculating the polarization, electro-rotation, travelling-wave dielectrophoresis, electro-hydrodynamics and induced-charge electroosmotic flow fields around a freely suspended conducting dimer (two touching spheres) exposed to non-uniform direct current (DC) or alternating current (AC) electric fields. The analysis is based on employing the classical (linearized) Poisson–Nernst–Planck (PNP) formulation under the standard linearized ‘weak-field’ assumption and using the tangent-sphere coordinate system. Explicit expressions are first derived for the axisymmetric AC electric potential governed by the Robin (mixed) boundary condition applied on the dimer surface depending on the resistance–capacitance circuit (RC) forcing frequency. Dimer electro-rotation due to two orthogonal (out-of-phase) uniform AC fields and the corresponding mobility problem of a polarizable dimer exposed to a travelling-wave electric excitation are also analyzed. We present an explicit solution for the non-linear induced-charge electroosmotic (ICEO) flow problem of a free polarized dimer in terms of the corresponding Stokes stream function determined by the Helmholtz–Smoluchowski velocity slip. Next, we demonstrate how the same framework can be used to obtain an exact solution for the electro-hydrodynamic (EHD) problem of a polarizable sphere lying next to a conducting planar electrode. Finally, we present a new solution for the induced-charge mobility of a Janus dimer composed of two fused spherical colloids, one perfectly conducting and one dielectrically coated. So far, most of the available electrokinetic theoretical studies involving polarizable nano/micro shapes dealt with convex configurations (e.g., spheres, spheroids, ellipsoids) and as such the newly obtained electrostatic AC solution for a dimer provides a useful extension for similar concave colloids and engineered particles.

pH-Mediated Aggregation-to-Separation Transition for Colloids Near Electrodes in Oscillatory Electric Fields

Colloids in low-frequency (<1 kHz) oscillatory electric fields near planar electrodes aggregate in neutral pH electrolytes due to electrohydrodynamic (EHD) flow but separate in alkaline pH electrolytes. Colloid ζ-potential and electrolyte ion mobilities are thought to play roles in the underlying mechanism for this phenomenon, but a unifying theory for why particles aggregate in some electrolytes and separate in others remains to be established. Here, we show that increasing local pH near the electrode with an electrochemical reaction causes a colloidal aggregation-to-separation transition in oscillatory electric fields that induce strong attractive EHD flows. An electroactive molecule, para-benzoquinone, was electrochemically reduced at the electrode to locally increase the solution pH near the colloids. Superimposing a sufficiently large steady electrochemical potential onto an oscillatory potential caused a reversible aggregation-to-separation transition. Counterintuitively, decreasing frequency, which increases attractive EHD drag forces, caused a similar aggregation-to-separation transition. Even more interesting, multiple transitions were observed while varying the oscillatory potential. Taken together, these results suggested that the oscillatory potential induced a repulsive hydrodynamic drag force. Scaling arguments for the recently discovered asymmetric rectified electric field (AREF) showed that a repulsive AREF-induced electroosmotic (EO) flow competed with attractive EHD flow. A pairwise colloidal force balance including these competing flows exhibited flow inversions qualitatively consistent with experimentally observed aggregation-to-separation transitions. Broadly, these results emphasize the importance of AREF-induced EO flows in colloid aggregation and separation in low-frequency oscillatory electric fields.

Derjaguin-Landau-Verwey-Overbeek energy landscape of a Janus particle with a nonuniform cap

A colloidal particle is often termed "Janus" when some portion of its surface is coated by a second material which has distinct properties from the native particle. The anisotropy of Janus particles enables unique behavior at interfaces. However, rigorous methodologies to predict Janus particle dynamics at interfaces are required to implement these particles in complex fluid applications. Previous work studying Janus particle dynamics does not consider van der Waals interactions and realistic, nonuniform coating morphology. Here we develop semianalytic equations to accurately calculate the potential landscape, including van der Waals interactions, of a Janus particle with nonuniform coating thickness above a solid boundary. The effects of both nonuniform coating thickness and van der Waals interactions significantly influence the potential landscape of the particle, particularly in high ionic strength solutions, where the particle samples positions very close to the solid boundary. The equations developed herein facilitate more simple, accurate, and less computationally expensive characterization of conservative interactions experienced by a confined Janus particle than previous methods.

A perturbation solution to the full Poisson-Nernst-Planck equations yields an asymmetric rectified electric field

We derive a perturbation solution to the one-dimensional Poisson-Nernst-Planck (PNP) equations between parallel electrodes under oscillatory polarization for arbitrary ionic mobilities and valences. Treating the applied potential as the perturbation parameter, we show that the second-order solution yields a nonzero time-average electric field at large distances from the electrodes, corroborating the recent discovery of Asymmetric Rectified Electric Fields (AREFs) via numerical solution to the full nonlinear PNP equations [Hashemi Amrei et al., Phys. Rev. Lett., 2018, 121, 185504]. Importantly, the first-order solution is analytic, while the second-order AREF is semi-analytic and obtained by numerically solving a single linear ordinary differential equation, obviating the need for full numerical solutions to the PNP equations. We demonstrate that at sufficiently high frequencies and electrode spacings the semi-analytical AREF accurately captures both the complicated shape and the magnitude of the AREF, even at large applied potentials.

Coupling between electrokinetics and electrode kinetics by bipolar faradaic depolarisation processes in microfluidic channels

This article is concerned with the nature and impact of bipolar faradaic electron transfer processes in the context of measuring electrokinetic parameters at the interface between an electronically conductive substrate such as a solid metal layer, and a liquid medium. More specifically, it analyses the steady state electric current through the electrodic substrate layer in terms of its short-circuiting effect on the system's electrokinetic quantities, such as the streaming potential. Ample attention is paid to the electrodic behaviour of the chosen metal and its electron transfer characteristics with respect to redox functions in the medium. The electrochemical reversibility of redox couple species is expressed in terms of their oxidation and reduction rate constants as compared to their diffusive transport rates under lateral flow conditions. High values for rate constants lead to high reversibilities and large bipolar leaking currents through the metal substrate. In turn, high electron transfer rate constants generate large reductions in measured values for electrokinetic quantities such as streaming potentials that further become a non-linear function of the pressure gradient applied through the fluidic chamber. The present article presents an overview of theoretical and experimental approaches of this intricate coupling between bipolar electrode kinetics and electrokinetics and the impact from Hans Lyklema's contributions. It highlights not only the implications of bipolar faradaic depolarisation processes in electrokinetics but also the importance of bipolar electrochemistry principles in various electroanalytical applications reported for e.g. the control of microfluidic flows, for surfaces functionalisation, particles manipulation or for the wireless detection of electroactive analytes.

Asymmetric rectified electric fields between parallel electrodes: Numerical and scaling analyses

Recent computational and experimental work has established the existence of asymmetric rectified electric fields (AREFs), a type of steady electric field that occurs in liquids in response to an applied oscillatory potential, provided the ions present have different mobilities [Hashemi Amrei et al., Phys. Rev. Lett. 121, 185504 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.185504]. Here we use scaling analyses and numerical calculations to elaborate the nature of one-dimensional AREFs between parallel electrodes. The AREF magnitude is shown to increase quadratically with applied potential at low potentials, increase nonlinearly at intermediate potentials, then increase with a constant rate slower than quadratically at sufficiently high potentials, with no impact at any potential on the spatial structure of the AREF. In contrast, the AREF peak location increases linearly with a frequency-dependent diffusive length scale for all conditions tested, with corresponding decreases in both the magnitude and number of sign changes in the directionality of AREF. Furthermore, both the magnitude and spatial structure of the AREF depend sensitively on the ionic mobilities, valencies, and concentrations, with a potential-dependent peak AREF magnitude occurring at an ionic mobility ratio of D_{-}/D_{+}⪅5. The results are summarized with approximate scaling expressions that will facilitate interpretation of the steady component for oscillatory fields in liquid systems.

Oscillating Electric Fields in Liquids Create a Long-Range Steady Field

We demonstrate that application of an oscillatory electric field to a liquid yields a long-range steady field, provided the ions present have unequal mobilities. The main physics is illustrated by a two-ion harmonic oscillator, yielding an asymmetric rectified field whose time average scales as the square of the applied field strength. Computations of the fully nonlinear electrokinetic model corroborate the two-ion model and further demonstrate that steady fields extend over large distances between two electrodes. Experimental measurements of the levitation height of micron-scale colloids versus applied frequency accord with the numerical predictions. The heretofore unsuspected existence of a long-range steady field helps explain several long-standing questions regarding the behavior of particles and electrically induced fluid flows in response to oscillatory potentials.

Direct Assembly of Large Area Nanoparticle Arrays

A major goal of nanotechnology is the assembly of nanoscale building blocks into functional optical, electrical, or chemical devices. Many of these applications depend on an ability to optically or electrically address single nanoparticles. However, positioning large numbers of single nanocrystals with nanometer precision on a substrate for integration into solid-state devices remains a fundamental roadblock. Here, we report fast, scalable assembly of thousands of single nanoparticles using electrophoretic deposition. We demonstrate that gold nanospheres down to 30 nm in size and gold nanorods <100 nm in length can be assembled into predefined patterns on transparent conductive substrates within a few seconds. We find that rod orientation can be preserved during deposition. As proof of high fidelity scale-up, we have created centimeter scale patterns comprising more than 1 million gold nanorods.

Direct Visualization of Planar Assembly of Plasmonic Nanoparticles Adjacent to Electrodes in Oscillatory Electric Fields

Electric field-directed assembly of colloidal nanoparticles (NPs) has been widely adopted for fabricating functional thin films and nanostructured surfaces. While first-order electrokinetic effects on NPs are well-understood in terms of classical models, effects of second-order electrokinetics that involve induced surface charge are still poorly understood. Induced charge electroosmotic phenomena, such as electrohydrodynamic (EHD) flow, have long been implicated in electric field-directed NP assembly with little experimental basis. Here, we use in situ dark-field optical microscopy and plasmonic NPs to directly observe the dynamics of planar assembly of colloidal NPs adjacent to a planar electrode in low-frequency (<1 kHz) oscillatory electric fields. We exploit the change in plasmonic NP color resulting from interparticle plasmonic coupling to visualize the assembly dynamics and assembly structure of silver NPs. Planar assembly of NPs is unexpected because of strong electrostatic repulsion between NPs and indicates that there are strong attractive interparticle forces oriented perpendicular to the electric field direction. A parametric investigation of the voltage- and frequency-dependent phase behavior reveals that planar NP assembly occurs over a narrow frequency range below which irreversible ballistic deposition occurs. Two key experimental observations are consistent with EHD flow-induced NP assembly: (1) NPs remain mobile during assembly and (2) electron microscopy observations reveal randomly close-packed planar assemblies, consistent with strong interparticle attraction. We interpret planar assembly in terms of EHD fluid flow and develop a scaling model that qualitatively agrees with the measured phase regions. Our results are the first direct in situ observations of EHD flow-induced NP assembly and shed light on long-standing unresolved questions concerning the formation of NP superlattices during electric field-induced NP deposition.

Electrohydrodynamic aggregation with vertically inverted systems

Flow patterns surrounding particles suspended near electrodes within an electrolyte solution can be induced with an electric field due to an electrohydrodynamic (EHD) force. Depending on electrolyte, particle, and field properties, a variety of particle packing and stability states have been observed in EHD flow. In this work, we report evidence of EHD flow-induced aggregation of 2-μm sulfonated latex beads in NaCl and NaOH electrolyte solutions, in inverted particle-electrode orientations. Experimental conditions were chosen to match previous work where aggregation was observed at a bottom electrode. Particles remain stable at the top electrode for times greater than 1 h, and aggregation behavior is quantified in terms of growth rate and particle packing density and order. Similar aggregation behavior is seen at both top and bottom electrodes, with aggregate growth occurring more quickly within NaCl solutions than NaOH solutions at both the bottom and top electrode. In addition, an observed secondary location of stability for the vertical position of particles in NaOH electrolyte at the bottom electrode is not seen at the top electrode. Comparing these metrics to predictions made by a scaling model for EHD flow, particle aggregation behavior is successfully predicted at both top and bottom electrodes, but some of the observed differences in aggregate packing are not. Thus we suggest that modifications to existing models or their interpretation may be needed to improve predictions of the behavior of such systems.

Change the Collective Behaviors of Colloidal Motors by Tuning Electrohydrodynamic Flow at the Subparticle Level

As demonstrated in biological systems, breaking the symmetry of surrounding hydrodynamic flow is the key to achieve autonomous locomotion of microscopic objects. In recent years, a variety of synthetic motors have been developed based on different propulsion mechanisms. Most work, however, focuses on the propulsion of individual motors. Here, we study the collective behaviors of colloidal dimers actuated by a perpendicularly applied AC electric field, which controls the electrohydrodynamic flow at subparticle levels. Although these motors experience strong dipolar repulsion from each other and are highly active, surprisingly, they assemble into a family of stable planar clusters with handedness. We show that this type of unusual structure arises from the contractile hydrodynamic flow around small lobes but extensile flow around the large lobes. We further reveal that the collective behavior, assembled structure, and assembly dynamics of these motors all depend on the specific directions of electrohydrodynamic flow surrounding each lobe of the dimers. By fine-tuning the surface charge asymmetry on particles and salt concentration in solution, we demonstrate the ability to control their collective behaviors on demand. This novel type of active assembly via hydrodynamic interactions has the potential to grow monodisperse clusters in a self-limiting fashion. The underlying concept revealed in this work should also apply to other types of active and asymmetric particles.

Driving Chemical Reactions in Plasmonic Nanogaps with Electrohydrodynamic Flow

Nanoparticles from colloidal solution-with controlled composition, size, and shape-serve as excellent building blocks for plasmonic devices and metasurfaces. However, understanding hierarchical driving forces affecting the geometry of oligomers and interparticle gap spacings is still needed to fabricate high-density architectures over large areas. Here, electrohydrodynamic (EHD) flow is used as a long-range driving force to enable carbodiimide cross-linking between nanospheres and produces oligomers exhibiting sub-nanometer gap spacing over mm² areas. Anhydride linkers between nanospheres are observed via surface-enhanced Raman scattering (SERS) spectroscopy. The anhydride linkers are cleavable via nucleophilic substitution and enable placement of nucleophilic molecules in electromagnetic hotspots. Atomistic simulations elucidate that the transient attractive force provided by EHD flow is needed to provide a sufficient residence time for anhydride cross-linking to overcome slow reaction kinetics. This synergistic analysis shows assembly involves an interplay between long-range driving forces increasing nanoparticle-nanoparticle interactions and probability that ligands are in proximity to overcome activation energy barriers associated with short-range chemical reactions. Absorption spectroscopy and electromagnetic full-wave simulations show that variations in nanogap spacing have a greater influence on optical response than variations in close-packed oligomer geometry. The EHD flow-anhydride cross-linking assembly method enables close-packed oligomers with uniform gap spacings that produce uniform SERS enhancement factors. These results demonstrate the efficacy of colloidal driving forces to selectively enable chemical reactions leading to future assembly platforms for large-area nanodevices.

Tunable two-dimensional assembly of colloidal particles in rotating electric fields

Tunable interparticle interactions in colloidal suspensions are of great interest because of their fundamental and practical significance. In this paper we present a new experimental setup for self-assembly of colloidal particles in two-dimensional systems, where the interactions are controlled by external rotating electric fields. The maximal magnitude of the field in a suspension is 25 V/mm, the field homogeneity is better than 1% over the horizontal distance of 250 μm, and the rotation frequency is in the range of 40 Hz to 30 kHz. Based on numerical electrostatic calculations for the developed setup with eight planar electrodes, we found optimal experimental conditions and performed demonstration experiments with a suspension of 2.12 μm silica particles in water. Thanks to its technological flexibility, the setup is well suited for particle-resolved studies of fundamental generic phenomena occurring in classical liquids and solids, and therefore it should be of interest for a broad community of soft matter, photonics, and material science.

Superhydrophobic, highly adhesive arrays of copper hollow spheres produced by electro-colloidal lithography

We report the patterning of copper surfaces which display both superhydrophobicity and high adhesion thanks to a new feature geometry, and without resorting to chemical modification. Polystyrene beads organized in 2D crystals under an AC electric field act as a template for the growth of copper deposited via cupric ion-loaded multi-lamellar vesicles. After the removal of the beads, hexagonal arrays of supported hollow spheres or copper bowls are generated, depending on the amount of deposited copper. While the bowl-covered surfaces display a predictable decreasing wettability (Cassie model) as their wall height increases, the hollow sphere-covered surfaces exhibit both high adhesion and superhydrophobicity (Cassie-Baxter state).

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

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

Colloidal molecules assembled from binary spheres under an AC electric field

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

Response of a doublet to a nearby dc electrode of uniform potential

The electric-field-assisted directed assembly of spherical colloidal particles near an electrode has been studied for nearly three decades. Recently, focus has shifted to the electric-field-assisted assembly and propulsion of nonspherical (i.e., anisotropic) particles. This paper describes calculations and results for a doublet of asymmetric ζ potential and size responding to a dc electric field. The doublet experienced a net vertical force that depended on both the asymmetry in ζ potential and lobe size. In addition, the doublet experienced a net lateral force perpendicular to the applied electric field. The lateral force depended on the difference in ζ potential of the two lobes, the lobe size asymmetry, and also the angle of inclination of the doublet. The net force was used to predict an apparent lateral velocity, which was found to be perpendicular to the applied electric field. In addition, the particle experienced rotation from a net torque that depended on the lobe size asymmetry and also the angle of inclination of the doublet. The magnitude of the predicted velocity was of the same order of magnitude as has been observed for particles responding to ac electric fields in experiments. These results demonstrate that lobe ζ potential, lobe size, and orientation of a colloidal doublet can be tuned to achieve propulsion.

Influence of Electrolyte Concentration on the Aggregation of Colloidal Particles near Electrodes in Oscillatory Fields

Micron-scale particles suspended in various aqueous electrolytes have been widely observed to aggregate near electrodes in response to oscillatory electric fields, a phenomenon believed to result from electrically induced flows around the particles. Previous work has focused on elucidating the effects of the applied field strength, frequency, and electrolyte type on the aggregation rate of particles, with less attention paid to the ionic strength. Here we demonstrate that an applied field causes micron-scale particles in aqueous NaCl to rapidly aggregate over a wide range of ionic strengths, but with significant differences in aggregation morphology. Optical microscopy observations reveal that at higher ionic strengths (∼1 mM) particles arrange as hexagonally closed-packed (HCP) crystals, but at lower ionic strengths (∼0.05 mM) the particles arrange in randomly closed-packed (RCP) structures. We interpret this behavior in terms of two complementary effects: an increased particle diffusivity at lower ionic strengths due to increased particle height over the electrode and the existence of a deep secondary minimum in the particle pair interaction potential at higher ionic strength that traps particles in close proximity to one another. The results suggest that electrically induced crystallization will readily occur only over a narrow range of ionic strengths.

Surface-enabled propulsion and control of colloidal microwheels

Propulsion at the microscale requires unique strategies such as the undulating or rotating filaments that microorganisms have evolved to swim. These features however can be difficult to artificially replicate and control, limiting the ability to actuate and direct engineered microdevices to targeted locations within practical timeframes. An alternative propulsion strategy to swimming is rolling. Here we report that low-strength magnetic fields can reversibly assemble wheel-shaped devices in situ from individual colloidal building blocks and also drive, rotate and direct them along surfaces at velocities faster than most other microscale propulsion schemes. By varying spin frequency and angle relative to the surface, we demonstrate that microwheels can be directed rapidly and precisely along user-defined paths. Such in situ assembly of readily modified colloidal devices capable of targeted movements provides a practical transport and delivery tool for microscale applications, especially those in complex or tortuous geometries.

Inducing Propulsion of Colloidal Dimers by Breaking the Symmetry in Electrohydrodynamic Flow

We show that dielectric colloidal dimers with broken symmetry in geometry, composition, or interfacial charges can all propel in directions that are perpendicular to the applied ac electric field. The asymmetry in particle properties ultimately results in an unbalanced electrohydrodynamic flow on two sides of the particles. Consistent with scaling laws, the propulsion direction, speed, and orientation of dimers can be conveniently tuned by frequency. The new propulsion mechanism revealed here is important for building colloidal motors and studying collective behavior of active matter.

Simultaneous Aggregation and Height Bifurcation of Colloidal Particles near Electrodes in Oscillatory Electric Fields

Micrometer-scale particles suspended in NaCl solutions aggregate laterally near the electrode upon application of a low-frequency (∼100 Hz) field, but the same particles suspended in NaOH solutions are instead observed to separate laterally. The underlying mechanism for the electrolyte dependence remains obscure. Recent work by Woehl et al. (PRX, 2015) revealed that, contrary to previous reports, particles suspended in NaOH solutions indeed aggregate under some conditions while simultaneously exhibiting a distinct bifurcation in average height above the electrode. Here we elaborate on this observation by demonstrating the existence of a critical frequency (∼25 Hz) below which particles in NaOH aggregate laterally and above which they separate. The results indicate that the current demarcation of electrolytes as either aggregating or separating is misleading and that the key role of the electrolyte instead is to set the magnitude of a critical frequency at which particles transition between the two behaviors.

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.

Observing Electrokinetic Janus Particle-Channel Wall Interaction Using Microparticle Image Velocimetry

Three-dimensional/two-component microparticle image velocimetry is used to examine the hydrodynamic flow patterns around metallodielectric Janus particles 15 μm in diameter adjacent to insulating and conducting walls. Far from the walls, the observed flow patterns are in good qualitative agreement with previous experimental and analytical models. However, close to the conducting wall, strong electrohydrodynamic flows are observed at low frequencies, which result in fluid being injected toward the particle. The proximity of the metallic hemisphere to the conducting wall is also shown to produce a localized field gradient, which results in dielectrophoretic trapping of 300 nm polystyrene particles across a broad range of frequencies.

A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations

Derjaguin's approximation provides the electrical-double-layer interaction force between two arbitrary convex surfaces as the product of the corresponding one-dimensional parallel-plate interaction potential and an effective radius R (function of the radii of curvature and relative orientation of the two surfaces at minimum separation). The approximation holds when both the Debye length 1/κ and minimum separation h are small compared to R. We show here that a simple transformation, R⇒[R]√[[K1][K2]/K1K2], yields an approximation uniformly valid for arbitrary separations h; here, Ki is the Gaussian curvature of particle i at minimum separation, and [  ⋅  ] is an operator which adds h/2 to all radii of curvature present in the expression on which it acts. We derive this result in two steps. First, we extend the two-dimensional ray-theory analysis of Schnitzer [Phys. Rev. E 91, 022307 (2015)], valid for κh, κR ≫ 1, to three dimensions. We thereby obtain a general closed form expression for the force by matching nonlinear diffuse-charge boundary layers with a WKBJ-type expansion describing the bulk potential, and subsequent integration via Laplace's method of the traction over the medial surface generated by all spheres maximally inscribed between the two surfaces. Second, we exploit the existence of an overlap domain, 1 ≪ κh ≪ κR, where both the ray-theory and the Derjaguin approximations hold, to systematically form the generalized mapping. The validity of the result is demonstrated by comparison with numerical computations.

Electric-field-induced assembly and propulsion of chiral colloidal clusters

Chiral molecules with opposite handedness exhibit distinct physical, chemical, or biological properties. They pose challenges as well as opportunities in understanding the phase behavior of soft matter, designing enantioselective catalysts, and manufacturing single-handed pharmaceuticals. Microscopic particles, arranged in a chiral configuration, could also exhibit unusual optical, electric, or magnetic responses. Here we report a simple method to assemble achiral building blocks, i.e., the asymmetric colloidal dimers, into a family of chiral clusters. Under alternating current electric fields, two to four lying dimers associate closely with a central standing dimer and form both right- and left-handed clusters on a conducting substrate. The cluster configuration is primarily determined by the induced dipolar interactions between constituent dimers. Our theoretical model reveals that in-plane dipolar repulsion between petals in the cluster favors the achiral configuration, whereas out-of-plane attraction between the central dimer and surrounding petals favors a chiral arrangement. It is the competition between these two interactions that dictates the final configuration. The theoretical chirality phase diagram is found to be in excellent agreement with experimental observations. We further demonstrate that the broken symmetry in chiral clusters induces an unbalanced electrohydrodynamic flow surrounding them. As a result, they rotate in opposite directions according to their handedness. Both the assembly and propulsion mechanisms revealed here can be potentially applied to other types of asymmetric particles. Such kinds of chiral colloids will be useful for fabricating metamaterials, making model systems for both chiral molecules and active matter, or building propellers for microscale transport.

Ray-theory approach to electrical-double-layer interactions

A novel approach is presented for analyzing the double-layer interaction force between charged particles in electrolyte solution, in the limit where the Debye length is small compared with both interparticle separation and particle size. The method, developed here for two planar convex particles of otherwise arbitrary geometry, yields a simple asymptotic approximation limited to neither small zeta potentials nor the "close-proximity" assumption underlying Derjaguin's approximation. Starting from the nonlinear Poisson-Boltzmann formulation, boundary-layer solutions describing the thin diffuse-charge layers are asymptotically matched to a WKBJ expansion valid in the bulk, where the potential is exponentially small. The latter expansion describes the bulk potential as superposed contributions conveyed by "rays" emanating normally from the boundary layers. On a special curve generated by the centers of all circles maximally inscribed between the two particles, the bulk stress-associated with the ray contributions interacting nonlinearly-decays exponentially with distance from the center of the smallest of these circles. The force is then obtained by integrating the traction along this curve using Laplace's method. We illustrate the usefulness of our theory by comparing it, alongside Derjaguin's approximation, with numerical simulations in the case of two parallel cylinders at low potentials. By combining our result and Derjaguin's approximation, the interaction force is provided at arbitrary interparticle separations. Our theory can be generalized to arbitrary three-dimensional geometries, nonideal electrolyte models, and other physical scenarios where exponentially decaying fields give rise to forces.

Colloidal structures of asymmetric dimers via orientation-dependent interactions

We apply an AC electric field to induce anisotropic interactions among asymmetric colloidal dimers. These anisotropic interactions, being shape-specific and orientation-dependent, can create complex and unique structures that are not possible for spherical particles or symmetric dimers. More specifically, we show a series of novel structures that closely resemble one- and two-dimensional antiferromagnetic lattices, including small clusters, linear chains, square lattices, and frustrated triangular arrays. All of them are uniquely formed by alternating association between dimers with opposite orientations. Our theoretical model attributes those patterns to an exquisite balance between electrostatic (primarily dipolar) and electrohydrodynamic interactions. Although similarly oriented dimers are strongly repulsive, the oppositely oriented dimers possess a concave shoulder in the pair interaction, which favors clustering to minimize the number of overlaps between neighboring particles. By combining the anisotropy in both particle geometry and field-induced interaction, our work suggests a new way to tailor colloidal interactions on anisotropic particles, which is important for both scientific understanding and practical applications.

Controlling colloidal particles with electric fields

In this instructional review, we discuss how to control individual colloids and ensembles of colloids using electric fields. We provide background on the electrokinetic transport mechanisms and kT-scale equilibrium colloidal interactions that enable such control. We also describe the experimental configurations, microscopy methods, image analyses, and material systems for which these mechanisms have been successfully employed. Methods are presented for creating various structures including colloidal chains, quasi-2D colloidal crystals, and 3D colloidal crystals. We also describe electric-field-mediated feedback control of the colloidal crystal size as well as colloidal crystal assembly and disassembly. Finally, we discuss future extensions of these methods that aim to incorporate accurate colloidal crystallization dynamic models into electric-field-mediated feedback control to allow rapid assembly, disassembly, and repair of defect-free colloidal structures.

Use of electrochemical impedance spectroscopy to determine double-layer capacitance in doped nonpolar liquids

Electrochemical impedance spectroscopy in a thin cell (10 μm) was used to infer conductivity, permittivity and the differential double-layer capacitance of solutions of dodecane doped with OLOA 11000 [poly(isobutylene) succinimide] for concentrations of dopant between 0.1% and 10% by weight. All spectra (frequencies between 1 Hz and 100 kHz) were well fit by an equivalent circuit having four elements including a constant-phase element representing the double-layer capacitance. Using Gouy-Chapman theory for small zeta potentials and assuming univalent charge carriers, the double-layer capacitances were converted into charge carrier concentration which was found to be directly proportional to the weight percent of dopant with a 1 wt% solution having 87 carriers/μm(3) (the concentration of either positive or negative charges). This is only 17 ppm of the total monomer concentration calculated from the average molecule weight of the dopant. Dividing the measured conductivities by the charge carrier concentration, we inferred the mobility and hydrodynamic diameters for the charged micelles. The hydrodynamic diameters of carriers were significantly larger than the average diameter of all micelles measured independently by dynamic light scattering. This suggests that only large micelles become charged.

Electric-field-induced phase separation and homogenization dynamics in colloidal suspensions of dichroic rod-shaped pigment particles

We report a reversible phase separation phenomenon in nonpolar colloidal suspensions of rod-shaped dichroic pigment particles in an electric field. The voltage-frequency phase diagram features a variety of phases with different morphologies. Single static particle-rich islands, chains of islands, and dynamic patterns were found in this system. We demonstrate that those patterns exhibit complex relaxation dynamics toward the homogeneous field-free state once the external field is removed.

Electrolyte-Dependent Aggregation of Colloidal Particles near Electrodes in Oscillatory Electric Fields

Colloidal particles adjacent to electrodes have been observed to exhibit drastically different aggregation behavior depending on the identity of the suspending electrolyte. For example, particles suspended in potassium chloride aggregate laterally near the electrode upon application of a low-frequency (∼100 Hz) oscillatory electric field, but the same particles suspended in potassium hydroxide are instead observed to separate. Previous work has interpreted the particle aggregation or separation in terms of various types of electrically induced fluid flow around the particle, but the details remain poorly understood. Here we present experimental evidence that the aggregation rate is highly correlated to both the particle zeta potential and the electric field amplitude, both of which depend on the electrolyte type. Measurement of the aggregation rate in 26 unique electrolyte-particle combinations demonstrates that the aggregation rate decreases with increasing zeta potential magnitude (i.e., particles with a large zeta potential tended to separate regardless of sign). Likewise, direct measurements of the oscillatory electric field in different electrolytes revealed that the aggregation rate was negatively correlated with solution conductivity and thus positively correlated with the field strength. We tested the experimentally measured aggregation rates against a previously developed point dipole model and found that the model fails to capture the observed electrolyte dependence. The results point to the need for more detailed modeling to capture the effect of electrolyte on the zeta potential and solution conductivity to predict fluid flow around colloids near electrodes.

Nonlinear oscillations in an electrolyte solution under ac voltage

The response of an electrolyte solution bounded between two blocking electrodes subjected to an ac voltage is considered. We focus on the pertinent thin-double-layer limit, where this response is governed by a reduced dynamic model [L. Højgaard Olesen, M. Z. Bazant, and H. Bruus, Phys. Rev. E 82, 011501 (2010)]. During a transient stage, the system is nonlinearly entrained towards periodic oscillations of the same frequency as that of the applied voltage. Employing a strained-coordinate perturbation scheme, valid for moderately large values of the applied voltage amplitude V, we obtain a closed-form asymptotic approximation for the periodic orbit which is in remarkable agreement with numerical computations. The analysis elucidates the nonlinear characteristics of the system, including a slow (logarithmic) growth of the zeta-potential amplitude with V and a phase straining scaling as V-1lnV. In addition, an asymptotic current-voltage relation is provided, capturing the numerically observed rapid temporal variations in the electric current.