Magneto-capillary particle dynamics at curved interfaces: inference and criticism of dynamical models

Time-varying fields drive the motion of magnetic particles adsorbed on liquid drops due to interfacial constraints that couple magnetic torques to capillary forces. Such magneto-capillary particle dynamics and the associated fluid flows are potentially useful for propelling drop motion, mixing drop contents, and enhancing mass transfer between phases. The design of such functions benefits from the development and validation of predictive models. Here, we apply methods of Bayesian data analysis to identify and validate a dynamical model that accurately predicts the field-driven motion of a magnetic particle adsorbed at the interface of a spherical droplet. Building on previous work, we consider candidate models that describe particle tilting at the interface, field-dependent contributions to the magnetic moment, gravitational forces, and their combinations. The analysis of each candidate is informed by particle tracking data for a magnetic Janus sphere moving in a precessing field at different frequencies and angles. We infer the uncertain parameters of each model, criticize their ability to describe and predict experimental data, and select the most probable candidate, which accounts for gravitational forces and the tilting of the Janus sphere at the interface. We show how this favored model can predict complex particle trajectories with micron-level accuracy across the range of driving fields considered. We discuss how knowledge of this "best" model can be used to design experiments that inform accurate parameter estimates or achieve desired particle trajectories.

Active Colloids as Models, Materials, and Machines

Active colloids use energy input at the particle level to propel persistent motion and direct dynamic assemblies. We consider three types of colloids animated by chemical reactions, time-varying magnetic fields, and electric currents. For each type, we review the basic propulsion mechanisms at the particle level and discuss their consequences for collective behaviors in particle ensembles. These microscopic systems provide useful experimental models of nonequilibrium many-body physics in which dissipative currents break time-reversal symmetry. Freed from the constraints of thermodynamic equilibrium, active colloids assemble to form materials that move, reconfigure, heal, and adapt. Colloidal machines based on engineered particles and their assemblies provide a basis for mobile robots with increasing levels of autonomy. This review provides a conceptual framework for understanding and applying active colloids to create material systems that mimic the functions of living matter. We highlight opportunities for chemical engineers to contribute to this growing field.

Designing negative feedback loops in enzymatic coacervate droplets

Membraneless organelles within the living cell use phase separation of biomolecules coupled with enzymatic reactions to regulate cellular processes. The diverse functions of these biomolecular condensates motivate the pursuit of simpler in vitro models that exhibit primitive forms of self-regulation based on internal feedback mechanisms. Here, we investigate one such model based on complex coacervation of the enzyme catalase with an oppositely charge polyelectrolyte DEAE-dextran to form pH-responsive catalytic droplets. Upon addition of hydrogen peroxide "fuel", enzyme activity localized within the droplets causes a rapid increase in the pH. Under appropriate conditions, this reaction-induced pH change triggers coacervate dissolution owing to its pH-responsive phase behavior. Notably, this destabilizing effect of the enzymatic reaction on phase separation depends on droplet size owing to the diffusive delivery and removal of reaction components. Reaction-diffusion models informed by the experimental data show that larger drops support larger changes in the local pH thereby enhancing their dissolution relative to smaller droplets. Together, these results provide a basis for achieving droplet size control based on negative feedback between pH-dependent phase separation and pH-changing enzymatic reactions.

Synchronization and alignment of model oscillators based on Quincke rotation

Colloidal spheres in weakly conductive fluids roll back and forth across the surface of a plane electrode when subject to strong electric fields. The so-called Quincke oscillators provide a basis for active matter based on self-oscillating units that can move, align, and synchronize within dynamic particle assemblies. Here, we develop a dynamical model for oscillations of a spherical particle and investigate the coupled dynamics of two such oscillators in the plane normal to the field. Building on existing descriptions of Quincke rotation, the model describes the dynamics of the charge, dipole, and quadrupole moments due to charge accumulation at the particle-fluid interface and particle rotation in the external field. The dynamics of the charge moments are coupled by the addition of a conductivity gradient, which describes asymmetries in the rates of charging near the electrode. We study the behavior of this model as a function of the field strength and gradient magnitude to identify the conditions required for sustained oscillations. We investigate the dynamics of two neighboring oscillators coupled by far field electric and hydrodynamic interactions in an unbounded fluid. Particles prefer to align and synchronize their rotary oscillations along the line of centers. The numerical results are reproduced and explained by accurate low-order approximations of the system dynamics based on weakly coupled oscillator theory. The coarse-grained dynamics of the oscillator phase and angle can be used to investigate collective behaviors within ensembles of many self-oscillating colloids.

Accelerating the Design of Self-Guided Microrobots in Time-Varying Magnetic Fields

Mobile robots combine sensory information with mechanical actuation to move autonomously through structured environments and perform specific tasks. The miniaturization of such robots to the size of living cells is actively pursued for applications in biomedicine, materials science, and environmental sustainability. Existing microrobots based on field-driven particles rely on knowledge of the particle position and the target destination to control particle motion through fluid environments. Often, however, these external control strategies are challenged by limited information and global actuation where a common field directs multiple robots with unknown positions. In this Perspective, we discuss how time-varying magnetic fields can be used to encode the self-guided behaviors of magnetic particles conditioned on local environmental cues. Programming these behaviors is framed as a design problem: we seek to identify the design variables (e.g., particle shape, magnetization, elasticity, stimuli-response) that achieve the desired performance in a given environment. We discuss strategies for accelerating the design process using automated experiments, computational models, statistical inference, and machine learning approaches. Based on the current understanding of field-driven particle dynamics and existing capabilities for particle fabrication and actuation, we argue that self-guided microrobots with potentially transformative capabilities are close at hand.

Convection Confounds Measurements of Osmophoresis for Lipid Vesicles in Solute Gradients

Lipid vesicles immersed in solute gradients are predicted to migrate from regions of high to low solute concentration due to osmotic flows induced across their semipermeable membranes. This process─known as osmophoresis─is potentially relevant to biological processes such as vesicle trafficking and cell migration; however, there exist significant discrepancies (several orders of magnitude) between experimental observations and theoretical predictions for the vesicle speed. Here, we seek to reconcile predictions of osmophoresis with observations of vesicle motion in osmotic gradients. We prepare quasi-steady solute gradients in a microfluidic chamber using density-matched solutions of sucrose and glucose to eliminate buoyancy-driven flows. We quantify the motions of giant DLPC vesicles and Brownian tracer particles in such gradients using Bayesian analysis of particle tracking data. Despite efforts to mitigate convective flows, we observe directed motion of both lipid vesicles and tracer particles in a common direction at comparable speeds of order 10 nm/s. These observations are not inconsistent with models of osmophoresis, which predict slower motion at ca. 1 nm/s; however, experimental uncertainty and the confounding effects of fluid convection prohibit a quantitative comparison. In contrast to previous reports, we find no evidence for anomalously fast osmophoresis of lipid vesicles when fluid convection is mitigated and quantified. We discuss strategies for enhancing the speed of osmophoresis using high permeability membranes and geometric confinement.

Insights into Chemically Fueled Supramolecular Polymers

Supramolecular polymerization can be controlled in space and time by chemical fuels. A nonassembled monomer is activated by the fuel and subsequently self-assembles into a polymer. Deactivation of the molecule either in solution or inside the polymer leads to disassembly. Whereas biology has already mastered this approach, fully artificial examples have only appeared in the past decade. Here, we map the available literature examples into four distinct regimes depending on their activation/deactivation rates and the equivalents of deactivating fuel. We present increasingly complex mathematical models, first considering only the chemical activation/deactivation rates (i.e., transient activation) and later including the full details of the isodesmic or cooperative supramolecular processes (i.e., transient self-assembly). We finish by showing that sustained oscillations are possible in chemically fueled cooperative supramolecular polymerization and provide mechanistic insights. We hope our models encourage the quantification of activation, deactivation, assembly, and disassembly kinetics in future studies.

Automating Bayesian inference and design to quantify acoustic particle levitation

Self-propulsion of micro- and nanoparticles powered by ultrasound provides an attractive strategy for the remote manipulation of colloidal matter using biocompatible energy inputs. Quantitative understanding of particle motion and its dependence on size, shape, and composition requires accurate characterization of the acoustic field, which depends sensitively on the experimental setup. Here, we show how automated experiments based on Bayesian inference and design can accurately and efficiently characterize the acoustic field within resonant chambers used to propel acoustic nanomotors. Repeated cycles of observation, inference, and design (OID) are guided by a physical model that describes the rate at which levitating particles approach the nodal plane. Using video microscopy, we observe the relaxation of tracer particles to this plane following the application of the acoustic field. We use sequential Monte Carlo methods to infer model parameters such as the amplitude and frequency of the resonant chamber while accounting for particle-level measurement noise and population-level heterogeneity in the field. Guided by simulated outcomes, we select the optimal design for the next experiment as to maximize the information gain in the relevant parameters. We show how this iterative process serves to discriminate between competing hypotheses and efficiently converges to accurate parameter estimates using only few automated experiments. We discuss the need for model criticism to ensure the validity of the guiding model throughout automated cycles of observation, inference, and design. This work demonstrates how Bayesian methods can learn the parameters of nonlinear, hierarchical models used to describe video microscopy data of active colloids.

Quincke Oscillations of Colloids at Planar Electrodes

Dielectric particles in weakly conducting fluids rotate spontaneously when subject to strong electric fields. Such Quincke rotation near a plane electrode leads to particle translation that enables physical models of active matter. In this Letter, we show that Quincke rollers can also exhibit oscillatory dynamics, whereby particles move back and forth about a fixed location. We explain how oscillations arise for micron-scale particles commensurate with the thickness of a field-induced boundary layer in the nonpolar electrolyte. This work enables the design of colloidal oscillators.

Fabrication and Electric Field-Driven Active Propulsion of Patchy Microellipsoids

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

Programmable topotaxis of magnetic rollers in time-varying fields

We describe how spatially uniform, time-periodic magnetic fields can be designed to power and direct the migration of ferromagnetic spheres up (or down) local gradients in the topography of a solid substrate. Our results are based on a dynamical model that considers the time-varying magnetic torques on the particle and its motion through the fluid at low Reynolds number. We use both analytical theory and numerical simulation to design magnetic fields that maximize the migration velocity up (or down) an inclined plane. We show how "topotaxis" of spherical particles relies on differences in the hydrodynamic resistance to rotation about axes parallel and perpendicular to the plane. Importantly, the designed fields can drive multiple independent particles to move simultaneously in different directions as determined by gradients in their respective environments. Experiments on ferromagnetic spheres provide evidence for topotactic motions up inclined substrates. The ability to program the autonomous navigation of driven particles within anisotropic environments is relevant to the design of colloidal robots.

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.

Swelling Cholesteric Liquid Crystal Shells to Direct the Assembly of Particles at the Interface

Cholesteric liquid crystals can exhibit spatial patterns in molecular alignment at interfaces that can be exploited for particle assembly. These patterns emerge from the competition between bulk and surface energies, tunable with the system geometry. In this work, we use the osmotic swelling of cholesteric double emulsions to assemble colloidal particles through a pathway-dependent process. Particles can be repositioned from a surface-mediated to an elasticity-mediated state through dynamically thinning the cholesteric shell at a rate comparable to that of colloidal adsorption. By tuning the balance between surface and bulk energies with the system geometry, colloidal assemblies on the cholesteric interface can be molded by the underlying elastic field to form linear aggregates. The transition of adsorbed particles from surface regions with homeotropic anchoring to defect regions is accompanied by a reduction in particle mobility. The arrested assemblies subsequently map out and stabilize topological defects. These results demonstrate the kinetic arrest of interfacial particles within definable patterns by regulating the energetic frustration within cholesterics. This work highlights the importance of kinetic pathways for particle assembly in liquid crystals, of relevance to optical and energy applications.

Magneto-Capillary Particle Dynamics at Curved Interfaces: Time-Varying Fields and Drop Mixing

Spatially uniform magnetic fields induce nonzero forces on magnetic particles adsorbed at curved liquid interfaces thereby driving their motion. Such motions, prohibited in bulk fluids, arise due to interfacial constraints that couple magnetic torques to capillary forces at curved interfaces. Here, we show that time-varying (spatially uniform) magnetic fields can be used to drive a variety of steady particle motions on water drops in decane. Upon application of a precessing field, magnetic Janus particles with amphiphilic surface chemistry move either along circular orbits at the drop poles or along zigzag paths at the drop equator. The different magneto-capillary motions depend on the frequency and precession angle of the field as well as the initial position of the particle on the drop surface. Our experimental observations are reproduced and explained by a mathematical model that accounts for the relevant magnetic, capillary, and hydrodynamic forces and torques that contribute to particle motion. In addition to ferromagnetic Janus particles, we show that similar dynamics can be achieved using superparamagnetic carbonyl iron particles, which are manufactured on industrial scales and respond to even weaker magnetic fields. We demonstrate how the field-driven motion of such particles at the drop interface can induce fluid flows that effectively mix the drop interior. These results suggest that magneto-capillary particle motions could be used to enhance mass transfer within emulsions stabilized by magnetic particles.

Learning Retrosynthetic Planning through Simulated Experience

The problem of retrosynthetic planning can be framed as a one-player game, in which the chemist (or a computer program) works backward from a molecular target to simpler starting materials through a series of choices regarding which reactions to perform. This game is challenging as the combinatorial space of possible choices is astronomical, and the value of each choice remains uncertain until the synthesis plan is completed and its cost evaluated. Here, we address this search problem using deep reinforcement learning to identify policies that make (near) optimal reaction choices during each step of retrosynthetic planning according to a user-defined cost metric. Using a simulated experience, we train a neural network to estimate the expected synthesis cost or value of any given molecule based on a representation of its molecular structure. We show that learned policies based on this value network can outperform a heuristic approach that favors symmetric disconnections when synthesizing unfamiliar molecules from available starting materials using the fewest number of reactions. We discuss how the learned policies described here can be incorporated into existing synthesis planning tools and how they can be adapted to changes in the synthesis cost objective or material availability.

Directed propulsion of spherical particles along three dimensional helical trajectories

Active colloids are a class of microparticles that ‘swim’ through fluids by breaking the symmetry of the force distribution on their surfaces. Our ability to direct these particles along complex trajectories in three-dimensional (3D) space requires strategies to encode the desired forces and torques at the single particle level. Here, we show that spherical colloids with metal patches of low symmetry self-propel along non-linear 3D trajectories when powered remotely by an alternating current (AC) electric field. In particular, particles with triangular patches of approximate mirror symmetry trace helical paths along the axis of the field. We demonstrate that the speed and shape of the particle’s trajectory can be tuned by the applied field strength and the patch geometry. We show that helical motion can enhance particle transport through porous materials with implications for the design of microrobots that can navigate complex environments.

The development of functional microrobots calls for new strategies to design locomotion facilitating navigation through complex environments. Here, Lee et al. show how to realize and program helical motion in three dimensions using patchy microspheres under an alternating current electric field.

Measurement and mitigation of free convection in microfluidic gradient generators

Microfluidic gradient generators are used to study the movement of living cells, lipid vesicles, and colloidal particles in response to spatial variations in their local chemical environment. Such gradient driven motions are often slow (less than 1 μm s-1) and therefore influenced or disrupted by fluid flows accompanying the formation and maintenance of the applied gradient. Even when external flows are carefully eliminated, the solute gradient itself can drive fluid motions due to combinations of gravitational body forces and diffusioosmotic surface forces. Here, we develop a microfluid gradient generator based on the in situ formation of biopolymer membranes and quantify the fluid flows induced by steady solute gradients. The measured velocity profiles agree quantitatively with those predicted by analytical approximations of relevant hydrodynamic models. We discuss how the speed of gradient-driven flows depends on system parameters such as the gradient magnitude, the fluid viscosity, the channel dimensions, and the solute type. These results are useful in identifying and mitigating undesired flows within microfluidic gradient systems.

Magneto-capillary dynamics of amphiphilic Janus particles at curved liquid interfaces

A homogeneous magnetic field can exert no net force on a colloidal particle. However, by coupling the particle's orientation to its position on a curved interface, even static homogeneous fields can be used to drive rapid particle motions. Here, we demonstrate this effect using magnetic Janus particles with amphiphilic surface chemistry adsorbed at the spherical interface of a water drop in decane. Application of a static homogeneous field drives particle motion to the drop equator where the particle's magnetic moment can align parallel to the field. As explained quantitatively by a simple model, the effective magnetic force on the particle scales linearly with the curvature of the interface. For particles adsorbed on small droplets such as those found in emulsions, these magneto-capillary forces can far exceed those due to magnetic field gradients in both magnitude and range. This mechanism may be useful in creating highly responsive emulsions and foams stabilized by magnetic particles.

Contact Charge Electrophoresis: Fundamentals and Microfluidic Applications

Contact charge electrophoresis (CCEP) uses steady electric fields to drive the oscillatory motion of conductive particles and droplets between two or more electrodes. In contrast to traditional forms of electrophoresis and dielectrophoresis, CCEP allows for rapid and sustained particle motions driven by low-power dc voltages. These attributes make CCEP a promising mechanism for powering active components for mobile microfluidic technologies. This Feature Article describes our current understanding of CCEP as well as recent strategies to harness it for applications in microfluidics and beyond.

Shape-Directed Microspinners Powered by Ultrasound

The propulsion of micro- and nanoparticles using ultrasound is an attractive strategy for the remote manipulation of colloidal matter using biocompatible energy inputs. However, the physical mechanisms underlying acoustic propulsion are poorly understood, and our ability to transduce acoustic energy into different types of particle motions remains limited. Here, we show that the three-dimensional shape of a colloidal particle can be rationally engineered to direct desired particle motions powered by ultrasound. We investigate the dynamics of gold microplates with twisted star shape ( C _nh symmetry) moving within the nodal plane of a uniform acoustic field at megahertz frequencies. By systematically perturbing the parametric shape of these "spinners", we quantify the relationship between the particle shape and its rotational motion. The experimental observations are reproduced and explained by hydrodynamic simulations that describe the steady streaming flows and particle motions induced by ultrasonic actuation. Our results suggest how particle shape can be used to design colloids capable of increasingly complex motions powered by ultrasound.

Electric generation and ratcheted transport of contact-charged drops

We describe a simple microfluidic system that enables the steady generation and efficient transport of aqueous drops using only a constant voltage input. Drop generation is achieved through an electrohydrodynamic dripping mechanism by which conductive drops grow and detach from a grounded nozzle in response to an electric field. The now-charged drops are transported down a ratcheted channel by contact charge electrophoresis powered by the same voltage input used for drop generation. We investigate how the drop size, generation frequency, and transport velocity depend on system parameters such as the liquid viscosity, interfacial tension, applied voltage, and channel dimensions. The observed trends are well explained by a series of scaling analyses that provide insight into the dominant physical mechanisms underlying drop generation and ratcheted transport. We identify the conditions necessary for achieving reliable operation and discuss the various modes of failure that can arise when these conditions are violated. Our results demonstrate that simple electric inputs can power increasingly complex droplet operations with potential opportunities for inexpensive and portable microfluidic systems.

Directed Motion of Metallodielectric Particles by Contact Charge Electrophoresis

We investigate the dynamics of metallodielectric Janus particles moving via contact charge electrophoresis (CCEP) between two parallel electrodes. CCEP uses a constant voltage to repeatedly charge and actuate conductive particles within a dielectric fluid, resulting in rapid oscillatory motion between the electrodes. In addition to particle oscillations, we find that micrometer-scale Janus particles move perpendicular to the field at high speeds (up to 600 μm/s) and over large distances. We characterize particle motions and propose a mechanism based on the rotation-induced translation of the particle following charge transfer at the electrode surface. The propulsion mechanism is supported both by experiments with fluorescent particles that reveal their rotational motions and by simulations of CCEP dynamics that capture the relevant electrostatics and hydrodynamics. We also show that interactions among multiple particles can lead to repulsion, attraction, and/or cooperative motions depending on the position and phase of the respective particle oscillators. Our results demonstrate how particle asymmetries can be used to direct the motions of active colloids powered by CCEP.

Particle Zeta Potentials Remain Finite in Saturated Salt Solutions

The zeta potential of a particle characterizes its motion in an electric field and is often thought to be negligible at high ionic strength (several moles per liter) due to thinning of the electrical double layer (EDL). Here, we describe zeta potential measurements on polystyrene latex (PSL) particles at monovalent salt concentrations up to saturation (∼5 M NaCl) using electrophoresis in sinusoidal electric fields and high-speed video microscopy. Our measurements reveal that the zeta potential remains finite at even the highest concentrations. Moreover, we find that the zeta potentials of sulfated PSL particles continue to obey the classical Gouy-Chapman model up to saturation despite significant violations in the model's underlying assumptions. By contrast, amidine-functionalized PSL particles exhibit qualitatively different behaviors such as zero zeta potentials at high concentrations of NaCl and KCl and even charge inversion in KBr solutions. The experimental results are reproduced and explained by Monte Carlo simulations of a simple lattice model of the EDL that accounts for effects due to ion size and ion-ion correlations. At high salt conditions, the model suggests that quantitative changes in the magnitude of surface charge can result in qualitative changes in the zeta potential-most notably, charge inversion of highly charged surfaces. These findings have important implications for electrokinetic phenomena such as diffusiophoresis within salty environments such as oceans, geological reservoirs, and living organisms.

Coarsening dynamics of binary liquids with active rotation

Active matter comprised of many self-driven units can exhibit emergent collective behaviors such as pattern formation and phase separation in both biological (e.g., mussel beds) and synthetic (e.g., colloidal swimmers) systems. While these behaviors are increasingly well understood for ensembles of linearly self-propelled "particles", less is known about the collective behaviors of active rotating particles where energy input at the particle level gives rise to rotational particle motion. A recent simulation study revealed that active rotation can induce phase separation in mixtures of counter-rotating particles in 2D. In contrast to that of linearly self-propelled particles, the phase separation of counter-rotating fluids is accompanied by steady convective flows that originate at the fluid-fluid interface. Here, we investigate the influence of these flows on the coarsening dynamics of actively rotating binary liquids using a phenomenological, hydrodynamic model that combines a Cahn-Hilliard equation for the fluid composition with a Navier-Stokes equation for the fluid velocity. The effect of active rotation is introduced though an additional force within the Navier-Stokes equations that arises due to gradients in the concentrations of clockwise and counter-clockwise rotating particles. Depending on the strength of active rotation and that of frictional interactions with the stationary surroundings, we observe and explain new dynamical behaviors such as "active coarsening" via self-generated flows as well as the emergence of self-propelled "vortex doublets". We confirm that many of the qualitative behaviors identified by the continuum model can also be found in discrete, particle-based simulations of actively rotating liquids. Our results highlight further opportunities for achieving complex dissipative structures in active materials subject to distributed actuation.

Contact charge electrophoresis: experiment and theory

Contact charge electrophoresis (CCEP) uses steady electric fields to drive the continuous, oscillatory motion of conductive particles and droplets between two or more electrodes. These rapid oscillations can be rectified to direct the motion of objects within microfluidic environments using low-power, dc voltage. Here, we compare high precision experimental measurements of CCEP within a microfluidic system to equally detailed theoretical predictions on the motion of a conductive particle between parallel electrodes. We use a simple, capillary microfluidic platform that combines high-speed imaging with precision electrical measurements to enable the synchronized acquisition of both the particle location and the electric current due to particle motion. The experimental results are compared to those of a theoretical model, which relies on a Stokesian dynamics approach to accurately describe both the electrostatic and hydrodynamic problems governing particle motion. We find remarkable agreement between theory and experiment, suggesting that particle motion can be accurately captured by a combination of classical electrostatics and low-Reynolds number hydrodynamics. Building on this agreement, we offer new insight into the charge transfer process that occurs when the particle nears contact with an electrode surface. In particular, we find that the particle does not make mechanical contact with the electrode but rather that charge transfer occurs at finite surface separations of >0.1 μm by means of an electric discharge through a thin lubricating film. We discuss the implications of these findings on the charging of the particle and its subsequent dynamics.

Microfluidic mixing of nonpolar liquids by contact charge electrophoresis

We present a simple and effective ratcheted microfluidic mixer that uses contact charge electrophoresis (CCEP) of a micron-scale particle to rapidly mix nonpolar liquids. CCEP combines contact charging and electrostatic actuation to drive the continuous oscillatory motion of a conductive particle between two electrodes subject to a constant (DC) voltage. We show how this oscillatory motion can be harnessed to mix laminar flows by using dielectric "ramps" to direct the particle along non-reciprocal, orbital trajectories, which repeatedly stretch and fold the flowing streams. Complete mixing requires that the speed of the particle is much larger than the fluid velocity such that the particle completes many orbits as the fluid flows through the mixing region. The extent of mixing also depends strongly on the size of the particle and the shape of its trajectory; effective mixers relied on larger particles (comparable to the size of the channel) moving along non-reciprocal orbits. While the present study uses mineral oil as a convenient nonpolar liquid, we also screened fifteen common solvents to determine the applicability of CCEP for mixing other organic liquids. Owing to its simple design and low power requirements (~100 nW), the orbital mixer presented here demonstrates the utility and versatility of ratcheted electrostatic actuation in powering active microfluidic operations.

Self-assembly of nanoparticle amphiphiles with adaptive surface chemistry

We investigate the self-assembly of amphiphilic nanoparticles (NPs) functionalized with mixed monolayers of hydrophobic and hydrophilic ligands in water. Unlike typical amphiphilic particles with "fixed" surface chemistries, the ligands used here are not bound irreversibly but can rearrange dynamically on the particles' surface during their assembly from solution. Depending on the assembly conditions, these adaptive amphiphiles form compact micellar clusters or extended chain-like assemblies in aqueous solution. By controlling the amount of hydrophobic ligands on the particles' surface, the average number of nearest neighbors--that is, the preferred coordination number--can be varied systematically from ∼ 1 (dimers) to ∼ 2 (linear chains) to ∼ 3 (extended clusters). To explain these experimental findings, we present an assembly mechanism in which hydrophobic ligands organize dynamically to form discrete patches between proximal NPs to minimize contact with their aqueous surroundings. Monte Carlo simulations incorporating these adaptive hydrophobic interactions reproduce the three-dimensional assemblies observed in experiment. These results suggest a general strategy based on reconfigurable "sticky" patches that may allow for tunable control over particle coordination number within self-assembled structures.

Ratcheted electrophoresis for rapid particle transport

Ratcheted electrophoresis of contact-charged particles allows for high speed transport through microfluidic channels over large distances and even against fluid flows. Using a set of predictive design heuristics, we demonstrate an extension of this microfluidic ratchet to separate conductive particles from a particle suspension.

When and Why Like-Sized, Oppositely Charged Particles Assemble into Diamond-like Crystals

Like-sized, oppositely charged nanoparticles are known to assemble into large crystals with diamond-like (ZnS) ordering, in sharp contrast to analogous molecular ions and micrometer-scale colloids, which invariably favor more closely packed structures (NaCl or CsCl). Here, we show that these experimental observations can be understood as a consequence of ionic screening and the slight asymmetry in surface charge present on the assembling particles. With this asymmetry taken into account, free-energy calculations predict that the diamond-like ZnS lattice is more favorable than other 1:1 ionic structures, namely, NaCl or CsCl, when the Debye screening length is considerably larger than the particle size. A thermodynamic model describes how the presence of neutralizing counterions within the interstitial regions of the crystal acts to bias the formation of low-volume-fraction structures. The results provide general insights into the self-assembly of non-close-packed structures via electrostatic interactions.

ac electric fields drive steady flows in flames

We show that time-oscillating electric fields applied to plasmas present in flames create steady flows of gas. Ions generated within the flame move in the field and migrate a distance δ before recombining; the net flow of ions away from the flame creates a time-averaged force that drives the steady flows observed experimentally. A quantitative model describes the response of the flame and reveals how δ decreases as the frequency of the applied field increases. Interestingly, above a critical frequency, ac fields can be used to manipulate flames at a distance without the need for proximal electrodes.

Using shape for self-assembly

A 1980 poem by Alan Mackay outlines his aspiration 'to see what all have seen but think what none have thought': a daunting task, which he accomplished not once, but several times. A 'truly myriadminded, manysided man-a veritable triacontahedron' in the words of his colleagues and friends, Alan Mackay pursued a lifelong interest in the problems of morphogenesis and form, a comprehension of which necessitated him crisscrossing the borders of the inanimate and animate world of soft and hard materials, through the integration of concepts and methods of chemistry, physics, mathematics and biology. In other words, he realized in his time a genuinely interdisciplinary approach to complex problems that still to this day remains beyond much of the academic community. Being invited to contribute a paper on the theme 'beyond crystals', we naturally wondered how Alan Mackay would think about the world of nanoscale self-assembly where so much depends on shape and form.

Templated synthesis of amphiphilic nanoparticles at the liquid-liquid interface

A simple and reliable method is described to produce inorganic nanoparticles functionalized asymmetrically with domains of hydrophobic and hydrophilic ligands on their respective hemispheres. These amphiphilic, Janus-type particles form spontaneously by a thermodynamically controlled process, in which the particle cores and two competing ligands assemble at the interface between two immiscible liquids to reduce the interfacial energy. The asymmetric surface chemistry resulting from this process was confirmed using contact angle measurements of water droplets on nanoparticle monolayers deposited onto hydrophobic and hydrophilic substrates-particles presenting their hydrophobic face give contact angles of ∼96°, those presenting their hydrophilic face ∼19°. The spontaneous assembly process is rationalized by a thermodynamic model, which accounts both for the energetic contributions driving the assembly and for the entropic penalties that must be overcome. Consistent with the model, amphiphilic NPs form only when there is sufficient interfacial area to accommodate them; however, this potential limitation is easily overcome by mechanical agitation of the two-phase mixture. While it is straightforward to vary the ratio of hydrophobic and hydrophilic ligands, the accumulation of amphiphilic particles at the interface is maximal for ligand ratios near 1:1. In addition to gold nanoparticles and thiolate ligands, we demonstrate the generality of this approach by extending it to the preparation of amphiphilic iron oxide nanoparticles using two types of diol-terminated ligands. Depending on the material properties of the inorganic cores, the resulting amphiphilic particles should find applications as responsive particle surfactants that respond dynamically to optical (plasmonic particles) and/or magnetic (magnetic particles) fields.

Charged nanoparticles as supramolecular surfactants for controlling the growth and stability of microcrystals

Microcrystals of desired sizes are important in a range of processes and materials, including controlled drug release, production of pharmaceutics and food, bio- and photocatalysis, thin-film solar cells and antibacterial fabrics. The growth of microcrystals can be controlled by a variety of agents, such as multivalent ions, charged small molecules, mixed cationic-anionic surfactants, polyelectrolytes and other polymers, micropatterned self-assembled monolayers, proteins and also biological organisms during biomineralization. However, the chief limitation of current approaches is that the growth-modifying agents are typically specific to the crystalizing material. Here, we show that oppositely charged nanoparticles can function as universal surfactants that control the growth and stability of microcrystals of monovalent or multivalent inorganic salts, and of charged organic molecules. We also show that the solubility of the microcrystals can be further tuned by varying the thickness of the nanoparticle surfactant layers and by reinforcing these layers with dithiol crosslinks.

Bubbles navigating through networks of microchannels

This paper describes the behavior of bubbles suspended in a carrier liquid and moving within microfluidic networks of different connectivities. A single-phase continuum fluid, when flowing in a network of channels, partitions itself among all possible paths connecting the inlet and outlet. The flow rates along different paths are determined by the interaction between the fluid and the global structure of the network. That is, the distribution of flows depends on the fluidic resistances of all channels of the network. The movement of bubbles of gas, or droplets of liquid, suspended in a liquid can be quite different from the movement of a single-phase liquid, especially when they have sizes slightly larger than the channels, so that the bubbles (or droplets) contribute to the fluidic resistance of a channel when they are transiting it. This paper examines bubbles in this size range; in the size range examined, the bubbles are discrete and do not divide at junctions. As a consequence, a single bubble traverses only one of the possible paths through the network, and makes a sequence of binary choices ("left" or "right") at each branching intersection it encounters. We designed networks so that, at each junction, a bubble enters the channel into which the volumetric flow rate of the carrier liquid is highest. When there is only a single bubble inside a network at a time, the path taken by the bubble is, counter-intuitively, not necessarily the shortest or the fastest connecting the inlet and outlet. When a small number of bubbles move simultaneously through a network, they interact with one another by modifying fluidic resistances and flows in a time dependent manner; such groups of bubbles show very complex behaviors. When a large number of bubbles (sufficiently large that the volume of the bubbles occupies a significant fraction of the volume of the network) flow simultaneously through a network, however, the collective behavior of bubbles-the fluxes of bubbles through different paths of the network-can resemble the distribution of flows of a single-phase fluid.