Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

Resolving Anomalies in Predicting Electrokinetic Energy Conversion Efficiencies of Nanofluidic Devices

We devise a new approach for capturing complex interfacial interactions over reduced length scales, towards predicting electrokinetic energy conversion efficiencies of nanofluidic devices. By embedding several aspects of intermolecular interactions in continuum based formalism, we show that our simple theory becomes capable of representing complex interconnections between electro-mechanics and hydrodynamics over reduced length scales. The predictions from our model are supported by reported experimental data, and are in excellent quantitative agreement with molecular dynamics simulations. The present model, thus, may be employed to rationalize the discrepancies between low energy conversion efficiencies of nanofluidic channels that have been realized from experiments, and the impractically high energy conversion efficiencies that have been routinely predicted by the existing theories.

Dynamics of Ion Transport in Ionic Liquids

A gap in understanding the link between continuum theories of ion transport in ionic liquids and the underlying microscopic dynamics has hindered the development of frameworks for transport phenomena in these concentrated electrolytes. Here, we construct a continuum theory for ion transport in ionic liquids by coarse graining a simple exclusion process of interacting particles on a lattice. The resulting dynamical equations can be written as a gradient flow with a mobility matrix that vanishes at high densities. This form of the mobility matrix gives rise to a charging behavior that is different to the one known for electrolytic solutions, but which agrees qualitatively with the phenomenology observed in experiments and simulations.

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.

Systematic interpretation of differential capacitance data

Differential capacitance (DC) data have been widely used to characterize the structure of electrolyte solutions near charged interfaces and as experimental validation of models for electrolyte structure. Fixing a large class of models of electrolyte free energy that incorporate finite-volume effects, a reduction is identified which permits the identification of all free energies within that class that return identical DC data. The result is an interpretation of DC data through the equivalence classes of nonideality terms, and associated boundary layer structures, that cannot be differentiated by DC data. Specifically, for binary salts, DC data, even if measured over a range of ionic concentrations, are unable to distinguish among models which exhibit charge asymmetry, charge reversal, and even ion crowding. The reduction applies to capacitors which are much wider than the associated Debye length and to finite-volume terms that are algebraic in charge density. However, within these restrictions the free energy is shown to be uniquely identified if the DC data are supplemented with measurements of the excess chemical potential of the system in the bulk state.

The suppression and promotion of DNA charge inversion by mixing counterions

In the preset study, we report the suppression and promotion of DNA charge inversion by mixing a quadrivalent counterion (spermine) with mono-, di- and trivalent counterions by dynamic light scattering (DLS) and single molecule electrophoresis (SME) methods. We find that the electrophoretic mobility of DNA in spermine solution decreases in the presence of monovalent sodium ions and divalent magnesium ions. It means that the charge neutralization of DNA by the quadrivalent counterion is suppressed when adding extra mono- or divalent counterions. More specifically, at a high concentration of spermine, the positive mobility can switch back to a negative value by adding mono- and divalent counterions. Thus, charge neutralization and inversion of DNA by quadrivalent counterions is suppressed in the mono- and divalent ion solution. However, the scenario changes dramatically when we add trivalent ions into the solution of DNA and spermine. In this case, the charge neutralization and inversion of DNA is promoted rather than suppressed by mixing with trivalent ions. The negative electrophoretic mobility can be promoted to a positive value, which corresponds to the charge inversion, by trivalent counterions. Thus trivalent and quadrivalent counterions work cooperatively in DNA charge neutralization and inversion. This promotion also occurs when highly positively charged chitosan is introduced into the solution. We explain the observation by the counterion complexation that is related to DNA condensation, which is supported by the images of atomic force microscopy (AFM).

Induced-charge electroosmotic trapping of particles

Position-controllable trapping of particles on the surface of a bipolar metal strip by induced-charge electroosmotic (ICEO) flow is presented herein. We demonstrate a nonlinear ICEO slip profile on the electrode surface accounting for stable particle trapping behaviors above the double-layer relaxation frequency, while no trapping occurs in the DC limit as a result of a strong upward fluidic drag induced by a linear ICEO slip profile. By extending an AC-flow field effect transistor from the DC limit to the AC field, we reveal that fixed-potential ICEO exceeding RC charging frequency can adjust the particle trapping position flexibly by generating controllable symmetry breaking in a vortex flow pattern. Our results open up new opportunities to manipulate microscopic objects in modern microfluidic systems by using ICEO.

Effects of finite ionic size and solvent polarization on the dynamics of electrolytes probed through harmonic disturbances

We address the implications of finite ionic size and solvent polarization on the response of the electric double layer (EDL) at two cation-selective electrodes in nonequilibrium conditions. The current between the electrodes is driven by a steady-state dc bias in conjunction with a probing high-frequency ac voltage. We report that the finite ionic size (steric) effect is prominent at high voltages near the electrodes where the ion densities are high, while the solvent polarization dramatically alters impedance characteristics for thick EDLs owing to the alteration of solvent permittivity in regions with a high electric field. Depending on the magnitude of the dc bias, our results show that the steric effects and solvent polarization lead to dramatic alterations in the net impedance for moderately thick electric double layers as compared to an extremely thin one. We also highlight that the solvent polarization suppresses the anomalous growth of dc current (anomalous rectification effect) for applied high-frequency ac voltages.

Electric double-layer structure in primitive model electrolytes: comparing molecular dynamics with local-density approximations

We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the Carnahan-Starling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as well as the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drive strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles.

Experimental verification of overlimiting current by surface conduction and electro-osmotic flow in microchannels

Direct evidence is provided for the transition from surface conduction (SC) to electro-osmotic flow (EOF) above a critical channel depth (d) of a nanofluidic device. The dependence of the overlimiting conductance (OLC) on d is consistent with theoretical predictions, scaling as d(-1) for SC and d(4/5) for EOF with a minimum around d=8  μm. The propagation of transient deionization shocks is also visualized, revealing complex patterns of EOF vortices and unstable convection with increasing d. This unified picture of surface-driven OLC can guide further advances in electrokinetic theory, as well as engineering applications of ion concentration polarization in microfluidics and porous media.

Kelvin probe force microscopy in liquid using electrochemical force microscopy

Conventional closed loop-Kelvin probe force microscopy (KPFM) has emerged as a powerful technique for probing electric and transport phenomena at the solid-gas interface. The extension of KPFM capabilities to probe electrostatic and electrochemical phenomena at the solid-liquid interface is of interest for a broad range of applications from energy storage to biological systems. However, the operation of KPFM implicitly relies on the presence of a linear lossless dielectric in the probe-sample gap, a condition which is violated for ionically-active liquids (e.g., when diffuse charge dynamics are present). Here, electrostatic and electrochemical measurements are demonstrated in ionically-active (polar isopropanol, milli-Q water and aqueous NaCl) and ionically-inactive (non-polar decane) liquids by electrochemical force microscopy (EcFM), a multidimensional (i.e., bias- and time-resolved) spectroscopy method. In the absence of mobile charges (ambient and non-polar liquids), KPFM and EcFM are both feasible, yielding comparable contact potential difference (CPD) values. In ionically-active liquids, KPFM is not possible and EcFM can be used to measure the dynamic CPD and a rich spectrum of information pertaining to charge screening, ion diffusion, and electrochemical processes (e.g., Faradaic reactions). EcFM measurements conducted in isopropanol and milli-Q water over Au and highly ordered pyrolytic graphite electrodes demonstrate both sample- and solvent-dependent features. Finally, the feasibility of using EcFM as a local force-based mapping technique of material-dependent electrostatic and electrochemical response is investigated. The resultant high dimensional dataset is visualized using a purely statistical approach that does not require a priori physical models, allowing for qualitative mapping of electrostatic and electrochemical material properties at the solid-liquid interface.

Effect of finite ion sizes in electric double layer mediated interaction force between two soft charged plates

A new theory quantifies the effect of finite ion size in osmotic pressure (Πosm) between two soft charged plates.

Induced-charge electro-osmosis around metal and Janus spheres in water: Patterns of flow and breaking symmetries

We establish experimentally the flow patterns of induced-charge electro-osmosis around immobilized metallic spheres in aqueous electrolyte. The ac field modifies local electrolyte concentration and causes quadrupolar flows with inward velocities being smaller than the outward ones. At high fields, the flow becomes irregular, with vortices smaller than the size of the sphere. Janus metallodielectric spheres create dipolar flows and pump the fluid from the dielectric toward the metallic part. The experimentally determined far-field flows decay with distance as r^{-3}.

Temperature effects on energy production by salinity exchange

In recent years, the capacitance of the interface between charged electrodes and ionic solutions (the electric double layer) has been investigated as a source of clean energy. Charge is placed on the electrodes either by means of ion-exchange membranes or of an external power source. In the latter method, net energy is produced by simple solution exchange in open circuit, due to the associated decrease in the capacitance of the electric double layer. In this work, we consider the change in capacitance associated with temperature variations: the former decreases when temperature is raised, and, hence, a cycle is possible in which some charge is put on the electrode at a certain potential and returned at a higher one. We demonstrate experimentally that it is thus viable to obtain energy from electric double layers if these are successively contacted with water at different temperatures. In addition, we show theoretically and experimentally that temperature and salinity variations can be conveniently combined to maximize the electrode potential increase. The resulting available energy is also estimated.

Filling of charged cylindrical capillaries

We provide an analytical model to describe the filling dynamics of horizontal cylindrical capillaries having charged walls. The presence of surface charge leads to two distinct effects: It leads to a retarding electrical force on the liquid column and also causes a reduced viscous drag force because of decreased velocity gradients at the wall. Both these effects essentially stem from the spontaneous formation of an electric double layer (EDL) and the resulting streaming potential caused by the net capillary-flow-driven advection of ionic species within the EDL. Our results demonstrate that filling of charged capillaries also exhibits the well-known linear and Washburn regimes witnessed for uncharged capillaries, although the filling rate is always lower than that of the uncharged capillary. We attribute this to a competitive success of the lowering of the driving forces (because of electroviscous effects), in comparison to the effect of weaker drag forces. We further reveal that the time at which the transition between the linear and the Washburn regime occurs may become significantly altered with the introduction of surface charges, thereby altering the resultant capillary dynamics in a rather intricate manner.

Concentration gradient focusing and separation in a silica nanofluidic channel with a non-uniform electroosmotic flow

The simultaneous concentration gradient focusing and separation of proteins in a silica nanofluidic channel of various geometries is investigated experimentally and theoretically. Previous modelling of a similar device [Inglis et al., Angew. Chem. Int. Ed., 2011, 50, 7546] assumed a uniform velocity profile along the length of the nanochannel. Using detailed numerical analysis incorporating charge regulation and viscoelectric effects, we show that in reality the varying axial electric field and varying electric double layer thickness caused by the concentration gradient, induce a highly non-uniform velocity profile, fundamentally altering the protein trapping mechanism: the direction of the local electroosmotic flow reverses and two local vortices are formed near the centreline of the nanochannel at the low salt concentration end, enhancing trapping efficiency. Simulation results for yellow/red fluorescent protein R-PE concentration enhancement, peak focusing position and peak focusing width are in good agreement with experimental measurements, validating the model. The predicted separation of yellow/red (R-PE) from green (Dyl-Strep) fluorescent proteins mimics that from a previous experiment [Inglis et al., Angew. Chem. Int. Ed., 2011, 50, 7546] conducted in a slightly different geometry. The results will inform the design of new class of matrix-free particle focusing and separation devices.

Induced charge electroosmosis micropumps using arrays of Janus micropillars

We report on a microfluidic AC-driven electrokinetic pump that uses Induced Charge Electro-Osmosis (ICEO) to generate on-chip pressures. ICEO flows occur when a bulk electric field polarizes a metal object to induce double layer formation, then drives electroosmotic flow. A microfabricated array of metal-dielectric Janus micropillars breaks the symmetry of ICEO flow, so that an AC electric field applied across the array drives ICEO flow along the length of the pump. When pumping against an external load, a pressure gradient forms along the pump length. The design was analyzed theoretically with the reciprocal theorem. The analysis reveals a maximum pressure and flow rate that depend on the ICEO slip velocity and micropillar geometry. We then fabricate and test the pump, validating our design concept by demonstrating non-local pressure driven flow using local ICEO slip flows. We varied the voltage, frequency, and electrolyte composition, measuring pump pressures of 15-150 Pa. We use the pump to drive flows through a high-resistance microfluidic channel. We conclude by discussing optimization routes suggested by our theoretical analysis to enhance the pump pressure.

Enhanced charging kinetics of porous electrodes: surface conduction as a short-circuit mechanism

We use direct numerical simulations of the Poisson-Nernst-Planck equations to study the charging kinetics of porous electrodes and to evaluate the predictive capabilities of effective circuit models, both linear and nonlinear. The classic transmission line theory of de Levie holds for general electrode morphologies, but only at low applied potentials. Charging dynamics are slowed appreciably at high potentials, yet not as significantly as predicted by the nonlinear transmission line model of Biesheuvel and Bazant. We identify surface conduction as a mechanism which can effectively "short circuit" the high-resistance electrolyte in the bulk of the pores, thus accelerating the charging dynamics and boosting power densities. Notably, the boost in power density holds only for electrode morphologies with continuous conducting surfaces in the charging direction.

Nonlinear thermokinetic phenomena due to the Seebeck effect

We propose a novel mechanism to produce nonlinear thermokinetic vortex flows around a circular cylinder with ideally high thermal conductivity in an electrolyte. That is, the nonlinear thermokinetic slip velocity, which is proportional to the square of the temperature gradient [∇(T)0(2)], is derived based on the electrolyte Seebeck effect, heat conduction equation, and Helmholtz–Smoluchowski formula. Different from conventional linear thermokinetic theory, our theory predicts that the inversion of the temperature gradient does not change the direction of the thermokinetic flows and thus a Janus particle using this phenomenon can move to the both hotter and colder regions in a temperature gradient field by changing the direction of its dielectric end. Our findings bridge the gap between the electro- and thermo-kinetic phenomena and provide an integrated physical viewpoint for the interface science.

Coarse-grained simulations of an ionic liquid-based capacitor: II. Asymmetry in ion shape and charge localization

In this work, which is a continuation of part I, we introduce a primitive model for an ionic liquid (IL) that can account for the planar shape of cations typical for ILs like imidazolium. The model consists of a spherical anion and a triangular cation consisting of three spheres, where one or all three vertices of the triangle can carry electric charge. We use molecular dynamics simulations to study the differential capacitance Cd of an ionic liquid confined between two planar electrodes. Our goal is to elucidate the complex dependence of Cd on the electrode potential U in terms of simple entities such as the shape and charge distribution of the ions. For this purpose, we compare the results from the current model to the results based on the models with spherical cations that possess asymmetry in ion valence and shape that were analyzed in detail in part I of this work. We show that the various possible stackings of the triangles near the cathode lead to noticeable new features in Cd(U) as compared to the spherical models. Different distributions of charges on the triangle lead to different preferred orientations of the cations near the cathode that are moreover potential dependent.

Dynamics of electrical double layer formation in room-temperature ionic liquids under constant-current charging conditions

We report detailed simulation results on the formation dynamics of an electrical double layer (EDL) inside an electrochemical cell featuring room-temperature ionic liquids (RTILs) enclosed between two planar electrodes. Under relatively small charging currents, the evolution of cell potential from molecular dynamics (MD) simulations during charging can be suitably predicted by the Landau-Ginzburg-type continuum model proposed recently (Bazant et al 2011 Phys. Rev. Lett. 106 046102). Under very large charging currents, the cell potential from MD simulations shows pronounced oscillation during the initial stage of charging, a feature not captured by the continuum model. Such oscillation originates from the sequential growth of the ionic space charge layers near the electrode surface. This allows the evolution of EDLs in RTILs with time, an atomistic process difficult to visualize experimentally, to be studied by analyzing the cell potential under constant-current charging conditions. While the continuum model cannot predict the potential oscillation under such far-from-equilibrium charging conditions, it can nevertheless qualitatively capture the growth of cell potential during the later stage of charging. Improving the continuum model by introducing frequency-dependent dielectric constant and density-dependent ion diffusion coefficients may help to further extend the applicability of the model. The evolution of ion density profiles is also compared between the MD and the continuum model, showing good agreement.

Time-dependent density functional theory for ion diffusion in electrochemical systems

We introduce a generic form of time-dependent density functional theory (TDDFT) to describe ion diffusion in electrochemical systems to account for steric effects and electrostatic correlations neglected in the Poisson-Nernst-Planck equations. An efficient numerical algorithm is proposed to analyze the charging kinetics of electric double layers in model electrochemical systems that consist of spherical ions in a dielectric continuum confined between two planar electrodes. By comparing the theoretical predictions from TDDFT and conventional electrokinetic methods for constant-voltage charging of the model electrochemical cells, we demonstrate that thermodynamic non-ideality plays a pivotal role in electrodiffusion even at relatively low electrolyte concentrations, and this effect cannot be captured by the lattice-gas model for the excluded volume effects. In particular, TDDFT predicts 'wave-like' variation of the ionic density profiles that has not been identified in previous investigations. At conditions where there are no significant correlations between electric double layers from opposite electrodes, the charging kinetics follows an exponential behavior with a linear dependence of the relaxation time on the cell thickness in excellent agreement with the equivalent circuit model. However, the conventional electrokinetic model breaks down when the electrodes are at small separation, in particular for systems with low ionic strength or high charging voltage. We also find that ionic screening retards the charging kinetics at low salt concentrations, but has the opposite effect at large salt concentrations.

The influence of particle size and residual charge on electrostatic interactions between charged colloidal particles at an oil-water interface

Electrostatic repulsive interaction forces between charged spherical colloidal particles at an oil-water interface are numerically studied by solving the standard three-dimensional Poisson-Nernst-Planck model. We directly compute the electrostatic force on a finite-size spherical particle and our results are applicable to all inter-particle distances without distinguishing short ranges and long ranges. The model successfully captures the scaling relationship of the force and the separation distance (d) between two charged particles at both short ranges (exponential dependence) and long ranges (∼d(-4)). The model also bridges these two ranges and provides quantitative information in the middle range. In addition, by assuming that there is a small residual electric charge at the particle-oil interface, the standard model is capable of quantitatively predicting the repulsive particle-particle interaction force over a large range of the separation distance between two particles. The favorable agreement between experiments and theoretical predictions also leads one to conclude that the standard model adequately describes the particle-particle interactions trapped at the oil-water interface.

Kinetic Charging Inversion in Ionic Liquid Electric Double Layers

The charging kinetics of electric double layers (EDLs) has a pivotal role in the performance of a wide variety of nanostructured devices. Despite the prevalent use of ionic liquids as the electrolyte, relatively little is known on the charging behavior from a microscopic perspective. Here, we study the charging kinetics of ionic liquid EDLs using a classical time-dependent density functional theory that captures the molecular excluded volume effects and electrostatic correlations. By examining variations of the ionic density profiles and the charging density in response to an electrode voltage, we find that at certain conditions, the electrode charge shows a rapid surge in its initial response, rises quickly to the maximum, and then slowly decays toward equilibrium. The electrode charge and voltage may have opposite signs when the cell width is commensurate with the layer-by-layer ionic distributions. This unusual charging behavior can be explained in terms of the oscillatory structure of ionic liquids near the electrodes.

dc Step response of induced-charge electro-osmosis between parallel electrodes at large voltages

Induced-charge electro-osmosis (ICEO) is important since it can be used for realizing high performance microfluidic devices. Here, we analyze the simplest problem of ion relaxation around a circular polarizable cylinder between parallel blocking electrodes in a closed cell by using a multiphysics coupled simulation technique. This technique is based on a combination of the finite-element method and finite-volume method for the Poisson-Nernst-Planck (PNP) equations having a flow term and the Stokes equation having an electric stress term. Through this analysis, we successfully demonstrate that on application of dc voltages, quadorapolar ICEO vortex flows grow during the charging time of the cylinder for both unbounded and bounded problems and decay during the charging time of the parallel electrodes only for the bounded problem using blocking electrodes. Further, by proposing a simple model that considers the two-dimensional (2D) PNP equations analytically, we successfully explain the step response time of the ICEO flow for the both unbounded and bounded problems. Furthermore, at low applied voltages, we find analytical formulations on steady diffused-ion problems and steady ICEO-flow problems and examine that our numerical results agree well with the analytical results. Moreover, by considering an ion-conserving condition with 2D Poisson-Boltzmann equations, we explain significant decrease of the maximum slip velocity at large applied voltages fairly well. We believe that our analysis will contribute greatly to the realistic designs of prospective high-performance microfluidic devices.

Electro-orientation of a metal nanowire counterbalanced by thermal torques

The rotational diffusion of electrically polarized metal nanowires suspended in an electrolyte is studied. The alignment of a Brownian nanowire in an ac field with a given direction is not complete due to thermal (fluctuating) torques. The orientation distribution allows us to examine the electrokinetic torques acting on the nanowire for smaller voltages than in previous deterministic experiments. In addition, the torques are obtained without recurring to the rotational friction coefficient as in dynamic deterministic experiments. The present results are in accordance with previous deterministic results of electro-orientation of metal nanowires. Nanowire rotation is originated by both the electrical torque on the induced dipole and by induced-charge electro-osmotic flow around the particle. At low frequencies of the applied ac field, induced-charge electro-osmotic orientation dominates while induced dipole torque orientation dominates at high frequencies. The angular standard deviation and the rotational rate are calculated from the measured fluctuating angle as a function of time, and good agreement with theoretical predictions is found. The experiments at high frequency indicate that the electrical torque on a nanowire near an insulating wall is reduced with respect to the bulk.

Probing charge screening dynamics and electrochemical processes at the solid-liquid interface with electrochemical force microscopy

The presence of mobile ions complicates the implementation of voltage-modulated scanning probe microscopy techniques such as Kelvin probe force microscopy (KPFM). Overcoming this technical hurdle, however, provides a unique opportunity to probe ion dynamics and electrochemical processes in liquid environments and the possibility to unravel the underlying mechanisms behind important processes at the solid-liquid interface, including adsorption, electron transfer and electrocatalysis. Here we describe the development and implementation of electrochemical force microscopy (EcFM) to probe local bias- and time-resolved ion dynamics and electrochemical processes at the solid-liquid interface. Using EcFM, we demonstrate contact potential difference measurements, consistent with the principles of open-loop KPFM operation. We also demonstrate that EcFM can be used to investigate charge screening mechanisms and electrochemical reactions in the probe-sample junction. We further establish EcFM as a force-based imaging mode, allowing visualization of the spatial variability of sample-dependent local electrochemical properties.

Strong electro-osmotic flows about dielectric surfaces of zero surface charge

We analyze electro-osmotic flow about a dielectric solid of zero surface charge, using the prototypic configurations of a spherical particle and an infinite circular cylinder. We assume that the ratio δ of Debye width to particle size is asymptotically small, and consider the flow engendered by the application of a uniform electric field; the control parameter is E-the voltage drop on the particle (normalized by the thermal scale) associated with this field. For moderate fields, E=O(1), the induced ζ potential scales as the product of the applied-field magnitude and the Debye width; being small compared with the thermal voltage, its resolution requires addressing one higher asymptotic order than that resolved in the comparable analysis of electrophoresis of charged particles. For strong fields, E=O(δ-1), the ζ potential becomes comparable to the thermal voltage, depending nonlinearly on δ and E. We obtain a uniform approximation for the ζ-potential distribution, valid for both moderate and strong fields; it holds even under intense fields, E≫δ-1, where it scales as log|E|. The induced-flow magnitude therefore undergoes a transition from an E2 dependence at moderate fields to an essentially linear variation with |E| at intense fields. Remarkably, surface conduction is negligible as long as E≪δ-2: the ζ potential, albeit induced, remains mild even under intense fields. Thus, unlike the related problem of induced-charge flow about a perfect conductor, the theoretical velocity predictions in the present problem may actually be experimentally realized.

Chaotic induced-charge electro-osmosis

We present direct numerical simulations of the coupled Poisson-Nernst-Planck and Navier-Stokes equations for an electrolyte around a polarizable cylinder subject to an external electric field. For high fields, a novel chaotic flow phenomenon is discovered. Our calculations indicate significant improvement in the prediction of the mean flow relative to standard asymptotic models. These results open possibilities for chaos-enhanced mixing in microdevices and provide insight into barriers to efficient electrokinetic micropumps with broad applications in electrochemical and lab-on-a-chip systems.

Transport of particles in liquid crystals

Colloidal particles in a liquid crystal (LC) behave very differently from their counterparts in isotropic fluids. Elastic nature of the orientational order and surface anchoring of the director cause long-range anisotropic interactions and lead to the phenomenon of levitation. The LC environment enables new mechanisms of particle transport that are reviewed in this work. Among them the motion of particles caused by gradients of the director, and effects in the electric field: backflow powered by director reorientations, dielectrophoresis in LC with varying dielectric permittivity and LC-enabled nonlinear electrophoresis with velocity that depends on the square of the applied electric field and can be directed differently from the field direction.

Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

Mapping alternating current electroosmotic flow at the dielectrophoresis crossover frequency of a colloidal probe

AC electroosmotic (ACEO) flow above the gap between coplanar electrodes is mapped by the measurement of Stokes forces on an optically trapped polystyrene colloidal particle. E²-dependent forces on the probe particle are selected by amplitude modulation (AM) of the ACEO electric field (E) and lock-in detection at twice the AM frequency. E²-dependent DEP of the probe is eliminated by driving the ACEO at the probe's DEP crossover frequency. The location-independent DEP crossover frequency is determined, in a separate experiment, as the limiting frequency of zero horizontal force as the probe is moved toward the midpoint between the electrodes. The ACEO velocity field, uncoupled from probe DEP effects, was mapped in the region 1-9 μm above a 28 μm gap between the electrodes. By use of variously sized probes, each at its DEP crossover frequency, the frequency dependence of the ACEO flow was determined at a point 3 μm above the electrode gap and 4 μm from an electrode tip. At this location the ACEO flow was maximal at ∼117 kHz for a low salt solution. This optical trapping method, by eliminating DEP forces on the probe, provides unambiguous mapping of the ACEO velocity field.