Multiple electrokinetic actuators for feedback control of colloidal crystal size

Onset of Nonlinear Electroosmotic Flow under an AC Electric Field

Nonlinearity of electroosmotic flows (EOFs) is ubiquitous and plays a crucial role in ion transport, specimen mixing, electrochemistry reaction, and electric energy storage and utilization. When and how the transition from a linear regime to a nonlinear one occurs is essential for understanding, prohibiting, or utilizing nonlinear EOF. However, due to the lack of reliable experimental instruments with high spatial and temporal resolutions, the investigation of the onset of nonlinear EOF still remains in theory. Herein, we experimentally studied the velocity fluctuations of EOFs driven by an alternating current (AC) electric field via ultrasensitive fluorescent blinking tricks. The linear and nonlinear AC EOFs are successfully identified from both the time trace and energy spectra of velocity fluctuations. The transitional electric field (E_A,C) is determined by both the convection velocity (U) and AC frequency (f_f) as E_A,C ∼ f_f^0.48-0.027U. We hope the current investigation could be essential in the development of both theory and applications of nonlinear EOFs.

Controlling the Shape of Small Clusters with and without Macroscopic Fields

Despite major advances in the understanding of the formation and dynamics of nanoclusters in the past decades, theoretical bases for the control of their shape are still lacking. We investigate strategies for driving fluctuating few-particle clusters to an arbitrary target shape in minimum time with or without an external field. This question is recast into a first passage problem, solved numerically, and discussed within a high temperature expansion. Without field, large-enough low-energy target shapes exhibit an optimal temperature at which they are reached in minimum time. We then compute the optimal way to set an external field to minimize the time to reach the target, leading to a gain of time that grows when increasing cluster size or decreasing temperature. This gain can shift the optimal temperature or even create one. Our results could apply to clusters of atoms at equilibrium, and colloidal or nanoparticle clusters under thermo- or electrophoresis.

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

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

Cargo capture and transport by colloidal swarms

Controlling active colloidal particle swarms could enable useful microscopic functions in emerging applications at the interface of nanotechnology and robotics. Here, we present a computational study of controlling self-propelled colloidal particle propulsion speeds to cooperatively capture and transport cargo particles, which otherwise produce random dispersions. By sensing swarm and cargo coordinates, each particle's speed is actuated according to a control policy based on multiagent assignment and path planning strategies that navigate stochastic particle trajectories to targets around cargo. Colloidal swarms are shown to dynamically cage cargo at their center via inward radial forces while simultaneously translating via directional forces. Speed, power, and efficiency of swarm tasks display emergent coupled dependences on swarm size and pair interactions and approach asymptotic limits indicating near-optimal performance. This scheme exploits unique interactions and stochastic dynamics in colloidal swarms to capture and transport microscopic cargo in a robust, stable, error-tolerant, and dynamic manner.

Long-range, selective, on-demand suspension interactions: Combining and triggering soluto-inertial beacons

Structures and particles that slowly release solute into solution can attract or repel other particles in suspension via diffusiophoresis, a process we termed "soluto-inertial (SI) interactions." These SI interactions involve "beacons" that establish and sustain nonequilibrium solute fluxes over long durations. Here, we demonstrate the versatility of the SI concept and introduce distinct strategies to manipulate solute gradients and, hence, suspension behavior using beacons with different physicochemical properties. First, we demonstrate on-demand particle migration using beacons that can be actuated with a trigger. We then show the synergy between multiple, distinct beacons that modify solute fluxes in a way that allows directed, yet selective, colloidal migration to specific target sites. Moreover, this multibeacon harmony enhances migration velocities, and delays the equilibration of the SI effect. The different SI techniques highlighted here suggest previously unidentified possibilities for sorting and separating colloidal mixtures, targeting particle delivery, and enhancing rates of suspension flocculation.

Feedback control for shaping density distributions of colloidal particles in microfluidic devices

Directed self-assembly has great potential for the precise manufacture of structured materials at the micro/nano-scale. A local particle density often has to be controlled to make the assembly of complicated structures with no defects attainable. However, the control of spatial particle density distributions is challenged by the need for multiple actuators, kinetic trapping and the stochastic nature of self-assembly systems. In this paper, a novel feedback control approach for shaping spatial density distributions of colloidal particles is presented. The control objective is to maintain the ratio of the particle densities of two adjacent regions close to a desired value. A microfluidic device with a triple-parallel microelectrode is fabricated to provide multiple actuators for particle manipulation. The multiple-electrode actuators can be operated flexibly to either direct particles between two adjacent regions or to maintain particles within regions by preventing undesired particle movements. A feedback control scheme is implemented to control the density ratio over a broad range of tested set points. The method is generic and can be extended to include additional parallel electrodes for the control of density distributions at higher resolutions due to a modular design.

Non-equilibrium steady-state colloidal assembly dynamics

Simulations and experiments are reported for nonequilibrium steady-state assembly of small colloidal crystal clusters in rotating magnetic fields vs frequency and amplitude. High-dimensional trajectories of particle coordinates from image analysis of experiments and from Stokesian Dynamic computer simulations are fit to low-dimensional reaction coordinate based Fokker-Planck and Langevin equations. The coefficients of these equations are effective energy and diffusivity landscapes that capture configuration-dependent energy and friction for nonequilibrium steady-state dynamics. Two reaction coordinates that capture condensation and anisotropy of dipolar chains folding into crystals are sufficient to capture high-dimensional experimental and simulated dynamics in terms of first passage time distributions. Our findings illustrate how field-mediated nonequilibrium steady-state colloidal assembly dynamics can be modeled to interpret and design pathways toward target microstructures and morphologies.

Optimal Navigation of Self-Propelled Colloids

Controlling the navigation of self-propelled, Brownian colloids in complex microstructured environments ( e.g., porous media and tumor vasculature) is important to emerging applications ( e.g., enhanced oil recovery and drug delivery). Here, we report a feedback control strategy by which to navigate self-propelled colloids through free space and increasingly complex mazes. Colloid rod position and orientation within mazes is sensed in real time, and instantaneous propulsion along the rod long axis can be actuated via light intensity. However, because uncontrolled rod rotational diffusion determines the propulsion direction, feedback control based on a policy is required to decide how to actuate propulsion magnitude versus colloid position and orientation within mazes. By considering stochastic rod dynamics including self-propulsion, translational-rotational diffusion, and rod-maze interactions, a Markov decision process framework is used to determine optimal control policies to navigate between start and end points in minimal time. The free-space navigation optimal policy effectively reduces to a simple heuristic in which propulsion is actuated only when particles point toward the target. The emergent structure of optimal control policies in mazes is based on the practice of globally following the shortest geometric paths; however, locally, propulsion is actuated to either follow paths toward the target or to produce collisions with maze features as part of generating more-favorable positions and orientations. Findings show how the coupled effects of maze size, propulsion speed, control update time, and relative particle translational and rotational diffusivities influence navigation performance.

High-Throughput Acoustofluidic Self-Assembly of Colloidal Crystals

Colloidal crystals are encountered in a variety of energy-harvesting applications, where they serve as waveguides or filters for electromagnetic and electro-optic energy. Techniques such as electric or magnetic assembly are used to assemble colloidal crystals, but are limited by crystal size, yield, and throughput. This article demonstrates the continuous, high-throughput assembly of two-dimensional (2D)-colloidal crystals in an acoustofluidic flow cell. The device is fabricated using off-the-shelf components and does not require a clean-room access. An experimental state diagram shows how the fluid flow rate and voltage applied to the piezoelectric element in our device can tune the crystal microstructure. Highly ordered colloidal crystals are continuously assembled in less than a minute with a throughput yield of several hundred particles per minute using this device. The acoustically assembled ordered 2D crystals are immobilized using a UV-curable resin and extracted as ordered polymer-particle fibers, demonstrating the ability of using acoustic fields to assemble ordered structures embedded in bulk materials. Particle tracking is used to construct the cross-channel particle distribution to understand the effect of acoustic compression on colloidal crystal assembly. Microparticle image velocimetry data is compared to a theoretical transport model to quantify the effect fluid flow and acoustic trapping has on the colloidal crystal ensemble.

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

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

Role of Entropy in the Expulsion of Dopants from Optically Trapped Colloidal Assemblies

Controlling an assembly of colloidal particles under external forces can be helpful in developing soft nanomaterials with novel functionalities. How external impurities organize within such confined systems is of fundamental and technological interest, especially when the system sizes are so small that even a single dopant can interact with an appreciable fraction of the system. To address this question, we use a defocused laser beam to form two-dimensional colloidal crystallites containing foreign dopants. Our studies reveal a surprising position dependence in the fate of dopants getting either spontaneously expelled or permanently internalized within the crystallite. This phenomenon arises due to the subtle interplay between the effects of external confinement and the role of entropy in the thermodynamics of small assemblies of interacting particles.

Contact-Free Templating of 3-D Colloidal Structures Using Spatially Nonuniform AC Electric Fields

The formation of ordered and regularly shaped structures of colloidal particles with the aid of spatially nonuniform electric fields is a modern research area of great interest. This work illustrates how alternating current (AC) electrokinetic effects (dielectrophoresis, electroosmosis) can serve as contact-free templates, inside which colloidal microspheres can assemble into a variety of shapes and sizes. We show how three-dimensional colloidal structures of square, circular, and diamond shape of many tens of micrometers in size can be reproducibly formed with a single set of quadrupolar microelectrodes. Numerical simulations performed help to explain the role of AC electroosmosis and AC dielectrophoresis on the shaping of these structures as a function of applied voltage and frequency. We also demonstrate how the templating repertoire is further enhanced with the simultaneous application of a second, individually controlled AC electric field, which enables a variety of asymmetric colloidal structures to be produced using the same set of quadrupolar microelectrodes. As the preservation of shape and size of such electric-field templated structures after medium evaporation still remains a big challenge, here we also report on a novel method that permits the stabilization and isolation of these particle assemblies through medium gelation and subsequent hydrogel removal with a UV/ozone treatment.

Reconfigurable multi-scale colloidal assembly on excluded volume patterns

The ability to create multi-scale, periodic colloidal assemblies with unique properties is important to emerging applications. Dynamically manipulating colloidal structures via tunable kT-scale attraction can provide the opportunity to create particle-based nano- and microstructured materials that are reconfigurable. Here, we report a novel tactic to obtain reconfigurable, multi-scale, periodic colloidal assemblies by combining thermoresponsive depletant particles and patterned topographical features that, together, reversibly mediate local kT-scale depletion interactions. This method is demonstrated in optical microscopy experiments to produce colloidal microstructures that reconfigure between well-defined ordered structures and disordered fluid states as a function of temperature and pattern feature depth. These results are well described by Monte Carlo simulations using theoretical depletion potentials that include patterned excluded volume. Ultimately, the approach reported here can be extended to control the size, shape, orientation, and microstructure of colloidal assemblies on multiple lengths scales and on arbitrary pre-defined pattern templates.

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.

Colloidal crystal grain boundary formation and motion

The ability to assemble nano- and micro- sized colloidal components into highly ordered configurations is often cited as the basis for developing advanced materials. However, the dynamics of stochastic grain boundary formation and motion have not been quantified, which limits the ability to control and anneal polycrystallinity in colloidal based materials. Here we use optical microscopy, Brownian Dynamic simulations, and a new dynamic analysis to study grain boundary motion in quasi-2D colloidal bicrystals formed within inhomogeneous AC electric fields. We introduce "low-dimensional" models using reaction coordinates for condensation and global order that capture first passage times between critical configurations at each applied voltage. The resulting models reveal that equal sized domains at a maximum misorientation angle show relaxation dominated by friction limited grain boundary diffusion; and in contrast, asymmetrically sized domains with less misorientation display much faster grain boundary migration due to significant thermodynamic driving forces. By quantifying such dynamics vs. compression (voltage), kinetic bottlenecks associated with slow grain boundary relaxation are understood, which can be used to guide the temporal assembly of defect-free single domain colloidal crystals.

Real-time feedback control of pH within microfluidics using integrated sensing and actuation

We demonstrate a microfluidic system which applies engineering feedback principles to control the pH of a solution with a high degree of precision. The system utilizes an extended-gate ion-sensitive field-effect transistor (ISFET) along with an integrated pseudo-reference electrode to monitor pH values within a microfluidic reaction chamber. The monitored reaction chamber has an approximate volume of 90 nL. The pH value is controlled by adjusting the flow through two input channels using a pulse-width modulated signal applied to on-chip integrated valves. We demonstrate real-time control of pH through the feedback-controlled stepping of 0.14 pH increments in both the increasing and decreasing direction. The system converges to the pH setpoint within approximately 20 seconds of a step change. The integration of feedback theory into a microfluidic environment is a necessary step for achieving complete control over the microenvironment.

The effect of boundary adaptivity on hexagonal ordering and bistability in circularly confined quasi hard discs

The behaviour of materials under spatial confinement is sensitively dependent on the nature of the confining boundaries. In two dimensions, confinement within a hard circular boundary inhibits the hexagonal ordering observed in bulk systems at high density. Using colloidal experiments and Monte Carlo simulations, we investigate two model systems of quasi hard discs under circularly symmetric confinement. The first system employs an adaptive circular boundary, defined experimentally using holographic optical tweezers. We show that deformation of this boundary allows, and indeed is required for, hexagonal ordering in the confined system. The second system employs a circularly symmetric optical potential to confine particles without a physical boundary. We show that, in the absence of a curved wall, near perfect hexagonal ordering is possible. We propose that the degree to which hexagonal ordering is suppressed by a curved boundary is determined by the "strictness" of that wall.

Experimental modelling of single-particle dynamic processes in crystallization by controlled colloidal assembly

A comprehensive review of the experimental modeling of single particle dynamics in crystallization is presented.

Catalytically powered dynamic assembly of rod-shaped nanomotors and passive tracer particles

Nano- and microscale motors powered by catalytic reactions exhibit collective behavior such as swarming, predator-prey interactions, and chemotaxis that resemble those of biological microorganisms. A quantitative understanding of the catalytically generated forces between particles that lead to these behaviors has so far been lacking. Observations and numerical simulations of pairwise interactions between gold-platinum nanorods in hydrogen peroxide solutions show that attractive and repulsive interactions arise from the catalytically generated electric field. Electrokinetic effects drive the assembly of staggered doublets and triplets of nanorods that are moving in the same direction. None of these behaviors are observed with nanorods composed of a single metal. The motors also collect tracer microparticles at their head or tail, depending on the charge of the particles, actively assembling them into close-packed rafts and aggregates of rafts. These motor-tracer particle interactions can also be understood in terms of the catalytically generated electric field around the ends of the nanorod motors.