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

Recent advancement in induced-charge electrokinetic phenomena and their micro- and nano-fluidic applications

Induced-charge electrokinetics (ICEK) remains a hot topic due to its promising applications in micro- and nano-fluidics. Over the past decade, researchers have made a great advancement in both fundamental studies and application developments. They captured (I) a flow reversal in induced-charge electroosmosis (ICEO) and attributed it to the phase delay effect of ions, (II) a chaotic ICEO and attributed it to the concentration polarization in the bulk solution, (III) a non-quadratic correlation for ICEO of non-Newtonian fluids and attributed it to the power-law viscosity, (IV) an induced-charge electrophoretic (ICEP) rotation of Janus doublets, etc. Furthermore, various ICEK-based micro- and nano-fluidic devices have been developed, namely, micropumps, particle focusers, trappers, sorters, and nanopore ion diodes. The present article provides a comprehensive review on the recent advancement of ICEK. Firstly, the fundamental studies of ICEK are introduced; then the micro- and nano-fluidic applications based on ICEK are presented; lastly, promising future directions for both fundamental and applications are discussed. This review presents the basic framework of ICEK, and can facilitate the development of ICEK-based applications.

Spontaneous Electrokinetic Magnus Effect

Colloids dispersed in electrolytes and exposed to an electric field produce a locally polarized cloud of ions around them. Above a critical electric field strength, an instability occurs causing these ion clouds to break symmetry leading to spontaneous rotation of particles about an axis orthogonal to the applied field, a phenomenon named Quincke rotation. In this Letter, we characterize a new mode of electrokinetic transport. If the colloids have a net charge, Quincke rotation couples with electrophoretic motion and propels particles in a direction orthogonal to both the applied field and the axis of rotation. This motion is a spontaneous, electrokinetic analogue to the well-known Magnus effect. Typically, motion orthogonal to a field requires anisotropy in particle shape, dielectric properties, or boundary geometry. Here, the electrokinetic Magnus (EKM) effect occurs for spheres with isotropic properties in an unbounded environment, with the Quincke rotation instability providing the broken symmetry needed to drive orthogonal motion. We study the EKM effect using explicit ion, Brownian dynamics simulations and develop a simple, continuum, analytic electrokinetic theory, which are in agreement. We also explain how nonlinearities in the theoretical description of the ions affect Quincke rotation and the EKM effect.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

Modeling hydration-mediated ion-ion interactions in electrolytes through oscillating Yukawa potentials

Classical Poisson-Boltzmann theory represents a mean-field description of the electric double layer in the presence of only Coulomb interactions. However, aqueous solvents hydrate ions, which gives rise to additional hydration-mediated ion-ion interactions. Experimental and computational studies suggest damped oscillations to be a characteristic feature of these hydration-mediated interactions. We have therefore incorporated oscillating Yukawa potentials into the mean-field description of the electric double layer. This is accomplished by allowing the decay length of the Yukawa potential to be complex valued. Ion specificity emerges from assigning individual strengths and phases to the Yukawa potential for anion-anion, anion-cation, and cation-cation pairs as well as for anions and cations interacting with an electrode or macroion. Excluded volume interactions between ions are approximated by replacing the ideal gas entropy by that of a lattice gas. We derive mean-field equations for the Coulomb and Yukawa potentials and use their solutions to compute the differential capacitance for an isolated planar electrode and the pressure that acts between two planar, like-charged macroion surfaces. Attractive interactions appear if the surface charge density of the macroions is sufficiently small.

Frequency Response of Induced-Charge Electrophoretic Metallic Janus Particles

The ability to manipulate and control active microparticles is essential for designing microrobots for applications. This paper describes the use of electric and magnetic fields to control the direction and speed of induced-charge electrophoresis (ICEP) driven metallic Janus microrobots. A direct current (DC) magnetic field applied in the direction perpendicular to the electric field maintains the linear movement of particles in a 2D plane. Phoretic force spectroscopy (PFS), a phase-sensitive detection method to detect the motions of phoretic particles, is used to characterize the frequency-dependent phoretic mobility and drag coefficient of the phoretic force. When the electric field is scanned over a frequency range of 1 kHz-1 MHz, the Janus particles exhibit an ICEP direction reversal at a crossover frequency at ~30 kH., Below this crossover frequency, the particle moves in a direction towards the dielectric side of the particle, and above this frequency, the particle moves towards the metallic side. The ICEP phoretic drag coefficient measured by PFS is found to be similar to that of the Stokes drag. Further investigation is required to study microscopic interpretations of the frequency at which ICEP mobility switched signs and the reason why the magnitudes of the forward and reversed modes of ICEP are so different.

Asymmetric double-layer charging in a cylindrical nanopore under closed confinement

This article presents a physical-mathematical treatment and numerical simulations of electric double layer charging in a closed, finite, and cylindrical nanopore of circular cross section, embedded in a polymeric host with charged walls and sealed at both ends by metal electrodes under an external voltage bias. Modified Poisson-Nernst-Planck equations were used to account for finite ion sizes, subject to an electroneutrality condition. The time evolution of the formation and relaxation of the double layers was explored. Moreover, equilibrium ion distributions and differential capacitance curves were investigated as functions of the pore surface charge density, electrolyte concentration, ion sizes, and pore size. Asymmetric properties of the differential capacitance curves reveal that the structure of the double layer near each electrode is controlled by the charge concentration along the pore surface and by charge asymmetry in the electrolyte. These results carry implications for accurately simulating cylindrical capacitors and electroactuators.

Dipolophoresis and Travelling-Wave Dipolophoresis of Metal Microparticles

We study theoretically and numerically the electrokinetic behavior of metal microparticles immersed in aqueous electrolytes. We consider small particles subjected to non-homogeneous ac electric fields and we describe their motion as arising from the combination of electrical forces (dielectrophoresis) and the electroosmotic flows on the particle surface (induced-charge electrophoresis). The net particle motion is known as dipolophoresis. We also study the particle motion induced by travelling electric fields. We find analytical expressions for the dielectrophoresis and induced-charge electrophoresis of metal spheres and we compare them with numerical solutions. This validates our numerical method, which we also use to study the dipolophoresis of metal cylinders.

Surfactant concentration modulates the motion and placement of microparticles in an inhomogeneous electric field

This study examined the effects of surfactants on the motion and positioning of microparticles in an inhomogeneous electric field. The microparticles were suspended in oil with a surfactant and the electric field was generated using sawtooth-patterned electrodes. The microparticles were trapped, oscillating, or attached to the electrodes. The proportion of microparticles in each state was defined by the concentration of surfactant and the voltage applied to the electrodes. Based on the trajectory of the microparticles in the electric field, we developed a new physical model in which the surfactant adsorbed on the microparticles allowed the microparticles to be charged by contact with the electrodes, with either positive or negative charges, while the non-adsorbed surfactant micellizing in the oil contributed to charge relaxation. A simulation based on this model showed that the charging and charge relaxation, as modulated by the surfactant concentration, can explain the trajectories and proportion of the trapped, oscillating, and attached microparticles. These results will be useful for the development of novel self-assembly and transport technologies and colloids sensitive to electricity.

Electrostatically Governed Debye Screening Length at the Solution-Solid Interface for Biosensing Applications

Biosensors based on field-effect devices (bioFETs) offer numerous advantages over current technologies and therefore have attracted immense research over the decades. However, short Debye screening length in highly ionic physiological solutions remains the main obstacle for bioFET realization. This challenge becomes considerably more acute at the electrolyte-oxide interface of the sensing area due to high ion concentration induced by the charged amphoteric sites, which prohibits any attempt to employ the field-effect mechanism to "sense" any charged biomolecules. In this work, we present an electrostatic approach by which the double layer (DL) excess ion concentration is removed, thus forcing the DL ion concentration to match the bulk concentration, which subsequently forces bulk screening length at the DL, thereby "exposing" target biomolecules to the underlying bioFET. To this end, we employ local tunable surface electric fields, introduced to the DL using surface passivated-metal electrodes. We examine numerically and analytically the effect of these electric fields on the DL ion distribution. We also numerically demonstrate the feasibility of the proposed approach for a fully depleted silicon-on-insulator based bioFET and show how the threshold voltage shift induced by the presence of target molecules increases by almost two orders of magnitude upon the removal of the surface excess ion population.

Development of high-speed ion conductance microscopy

Scanning ion conductance microscopy (SICM) can image the surface topography of specimens in ionic solutions without mechanical probe-sample contact. This unique capability is advantageous for imaging fragile biological samples but its highest possible imaging rate is far lower than the level desired in biological studies. Here, we present the development of high-speed SICM. The fast imaging capability is attained by a fast Z-scanner with active vibration control and pipette probes with enhanced ion conductance. By the former, the delay of probe Z-positioning is minimized to sub-10 µs, while its maximum stroke is secured at 6 μm. The enhanced ion conductance lowers a noise floor in ion current detection, increasing the detection bandwidth up to 100 kHz. Thus, temporal resolution 100-fold higher than that of conventional systems is achieved, together with spatial resolution around 20 nm.

Slow Discharge Theory and Calculation of the Potential Drop across the Compact Layer at High Electrode Voltages

A novel approach presented in this work allows one to calculate the potential drop across the compact layer in electrostatic atomization with high voltages applied at the electrode. Ionic conductor liquids employed in electrostatic atomization have a low dielectric constant, which causes almost all of the potential drop across the double layer to occur inside the compact layer. In the previous article of this group (Sankarn, A., et al. Langmuir 2017, 33, 1375-1384), it was shown that faradaic reactions in the kinetics-limited regime are responsible for liquid electrification in electrostatic atomization. Here, we apply the Frumkin slow discharge theory to calculate the electric potential at the interface of the compact and diffuse layers. The electric potential value at the interface of the compact and diffuse layers is required in computational models accounting for the discharge of counterions due to faradaic reactions when solving the ionic transport equations. The activation energy of the electron transfer reaction is calculated through the Marcus theory. Knowing the counterion flux value at the electrode surface from the concurrent experimental measurements, the ionic concentration and net charge distribution across the polarized diffuse layer are also found from the numerical simulations. Considering canola oil to be the ionic conductor liquid, two different examples are used to demonstrate the application of this approach to calculate the electric potential at the interface of compact and diffuse layers.

Frequency-dependent force between ac-voltage-biased plates in electrolyte solutions

We analyze the frequency dependence of the force between ac-voltage-biased plates in electrolyte solutions. To this end we solve analytically the Poisson-Nernst-Planck transport model in the dilute concentration and low voltage regime for a 1:1 symmetric electrolyte with blocking electrodes under a dc+ac applied voltage. The total force, which is the resultant of the electric and osmotic forces, shows a complex dependence on plate separation, frequency, ion concentration, and compact layer properties, different from that predicted from electrostatic current models or equivalent circuit models, due to the relevance of the osmotic force contribution in almost the whole range of frequencies. For the total dc force, we show that it decays at fixed ion concentration, linearly with plate separation for separations larger than a few times the Debye screening length. This linear dependence is due to the assumption about the conservation of the number of ions in the system. Moreover, the 1ω and 2ω ac harmonics of the total force show a broad peak at intermediate frequencies; it is centered at about the inverse of the charging time of the double layer capacitance, and covers the frequency range between the inverse of the diffusion time and the inverse of the electrolyte dielectric relaxation time. Finally, the 1ω ac harmonic component attains its high frequency asymptotic value at frequencies much higher than the inverse of the electrolyte dielectric relaxation time due to the very slow relaxation of the osmotic 1ω harmonic component at high frequencies. The derived analytical expressions for the total force remain valid up to voltages of the order of the thermal voltage, as has been assessed by means of numerical calculations. The numerical calculations are also used to explore the onset of higher force harmonics for larger applied voltages. Understanding the frequency dependence of the force acting on voltage-biased plates in electrolyte solutions can be of relevance for electrical actuation strategies in microelectromechanical systems and for the interpretation of some emerging electric scanning probe force microscopy techniques operating in electrolyte solutions.

Theory of Surface Forces in Multivalent Electrolytes

Aqueous electrolyte solutions containing multivalent ions exhibit various intriguing properties, including attraction between like-charged colloidal particles, which results from strong ion-ion correlations. In contrast, the classical Derjaguin-Landau-Verwey-Overbeek theory of colloidal stability, based on the Poisson-Boltzmann mean-field theory, always predicts a repulsive electrostatic contribution to the disjoining pressure. Here, we formulate a general theory of surface forces, which predicts that the contribution to the disjoining pressure resulting from ion-ion correlations is always attractive and can readily dominate over entropic-induced repulsions for solutions containing multivalent ions, leading to the phenomenon of like-charge attraction. Ion-specific short-range hydration interactions, as well as surface charge regulation, are shown to play an important role at smaller separation distances but do not fundamentally change these trends. The theory is able to predict the experimentally observed strong cohesive forces reported in cement pastes, which result from strong ion-ion correlations involving the divalent calcium ion.

Theoretical and Numerical Study of Formation of Near-Electrode Layers in Ionic Conductor Liquids at High Voltages

A novel approach is developed to predict the thickness of the equivalent one-dimensional Stern layer near conducting electrodes subjected to high voltage and carrying electric current. The nonspecific (nonelectric) ion adsorption responsible for the formation of the Stern compact layer at the electrode surface is attributed to the Langmuir-Brunauer-Emmett-Teller mechanism. The compact Stern layer is implied to be intrinsically two-dimensional and forming on the oxide or impurity islands on the electrode surface, which prevents electron transfer to or from the adsorbed ions. On the other hand, electrons are transferred through the open parts of the metallic electrode surface by electron transfer faradaic reactions characterized by the Frumkin-Butler-Volmer kinetics. Then, the one-dimensional Stern layer appears to be an approximation of the abovementioned two-dimensional model. In the framework of this model, the equivalent one-dimensional Stern layer thickness is predicted, rather than used as an adjustable parameter, as frequently done in the literature.

Structure, Thermodynamics, and Dynamics of Thin Brine Films in Oil-Brine-Rock Systems

Thin brine films are ubiquitous in oil-brine-rock systems such as oil reservoirs and play a crucial role in applications such as enhanced oil recovery. We report the results of molecular simulations of brine films that are confined between model oil (n-decane) and rock (neutral or negatively charged quartz slabs), with a focus on their structure, electrical double layers (EDLs), disjoining pressure, and dynamics. As brine films are squeezed to ∼0.7 nm (∼3 water molecule layers), the structures of the water-rock and water-oil interfaces change only marginally, except that the oil surface above the brine film becomes less diffuse. As the film is thinned from ∼1.0 to ∼0.7 nm, ions are enriched (depleted) near the rock (oil) surface, especially at a bath ion concentration of 0.1 M. These changes are caused primarily by the reduced dielectric screening of water and the weakened ion hydration near water-oil interfaces and, to a smaller extent, by the increased confinement. When the brine film is ∼1.0 nm thick, hydration and EDL forces contribute to the disjoining pressure between the charged rock and the oil. The EDL forces are reduced substantially as the ion concentration increases from 0.1 to 1.0 M, and the magnitude of the reduction is close to that predicted by the Poisson-Boltzmann equation. When the brine film is thinned from ∼1.0 to ∼0.7 nm, the disjoining pressure increases by ∼10 MPa, which is mostly due to an increase in the hydration forces. The first layer of water on the rock surface is nearly stagnant, even in 0.74 nm-thick brine films, whereas the viscosity of water beyond the first layer is bulk-like, and the slip coefficient of oil-water interfaces is close to that under unconfined conditions. The insights that are obtained here help lay a foundation for the rational application of technologies such as low-salinity waterflooding.

Large Variations in the Composition of Ionic Liquid-Solvent Mixtures in Nanoscale Confinement

Mixtures of an ionic liquid with an organic solvent are widely used as electrolytes in supercapacitors where they are often confined in porous electrodes with pore widths only slightly larger than the sizes of bare ions or solvent molecules. The composition of the electrolyte inside these pores, which may depend on the pore width and choice of electrolyte, can affect supercapacitor performance but remains poorly understood. Here, we perform all-atom molecular dynamics simulations of solutions of two different ionic liquids in acetonitrile under confinement between graphene sheets forming slit pores of various widths. We observe significant oscillations in the in-pore ionic liquid mole fraction with varying pore widths. Ions are excluded from very narrow pores, while for pore widths that tightly fit a single layer of ions, we observe an in-pore ionic liquid mole fraction over three times greater than that in the bulk. At slightly larger pore widths, we observe for different ionic liquids either a nearly complete exclusion of ions from the pore or a slight depletion of ions, while ion population again increases as pore width further increases. We develop an analytical model that can qualitatively predict the in-pore ionic liquid mole fraction based on the effective molar volumes and the pore wall interaction energies of each species. Our work suggests a new avenue for tuning the ionic liquid mole fraction in nanopores with potentially significant implications for designing systems involving nanoconfined liquid electrolytes such as supercapacitors where in-pore ion population can affect charging dynamics.

Enhancing the Ion-Size-Based Selectivity of Capacitive Deionization Electrodes

Capacitive deionization (CDI) is an emerging water treatment technology often applied to brackish water desalination and water softening. Typical CDI cells consist of two microporous carbon electrodes sandwiching a dielectric separator, and desalt feedwater flowing through the cell by storing ions in electric double layers (EDLs) within charged micropores. CDI cells have demonstrated size-based ion selectivity wherein smaller hydrated ions are preferentially electrosorbed over larger hydrated ions. We demonstrate that such size-based selectivity can be substantially enhanced through the addition of chemical charge to micropores via surface functionalization. We develop a micropore EDL theory that includes both finite ion size effects and micropore chemical charge, which predicts such enhancements and elucidates that they result from denser counterion packing in micropores. With our experimental CDI cell, we desalted an electrolyte consisting of equimolar potassium (K⁺) and lithium (Li⁺) ions. We show that use of a surface-functionalized (oxidized) cathode significantly increased the electrosorption ratio of smaller K⁺ to larger Li⁺ compared to a cell with a pristine cathode, for example, from ∼1 to 1.84 for a charging voltage of 0.4 V. Our model predicts yet-higher electrosorption ratios are attainable, but our experimental cell suffered from significant cathode chemical charge degradation at applied voltages of ∼1 V.

Multifrequency Induced-Charge Electroosmosis

We present herein a unique concept of multifrequency induced-charge electroosmosis (MICEO) actuated directly on driving electrode arrays, for highly-efficient simultaneous transport and convective mixing of fluidic samples in microscale ducts. MICEO delicately combines transversal AC electroosmotic vortex flow, and axial traveling-wave electroosmotic pump motion under external dual-Fourier-mode AC electric fields. The synthetic flow field associated with MICEO is mathematically analyzed under thin layer limit, and the particle tracing experiment with a special powering technique validates the effectiveness of this physical phenomenon. Meanwhile, the simulation results with a full-scale 3D computation model demonstrate its robust dual-functionality in inducing fully-automated analyte transport and chaotic stirring in a straight fluidic channel embedding double-sided quarter-phase discrete electrode arrays. Our physical demonstration with multifrequency signal control on nonlinear electroosmosis provides invaluable references for innovative designs of multifunctional on-chip analytical platforms in modern microfluidic systems.

Net fluid flow and non-Newtonian effect in induced-charge electro-osmosis of polyelectrolyte solutions

This paper reports an interesting net fluid flow in the induced-charge electro-osmosis (ICEO) of poly(sodium 4-styrenesulfonate) (NaPSS) solutions measured through microparticle image velocimetry (μPIV). The net fluid flow is attributed to the significantly unequal cations and poly-anions of NaPSS. Owing to the phase delay effect of ions, different flow patterns appear with the alternating electric field. The inflow velocity and outflow velocity are found to be unequal and their relative magnitude shows a dependence on the electric field strength. The ICEO velocity is positively correlated with the NaPSS concentration. As NaPSS introduces the non-Newtonian effect, the well-known quadratic relationship between ICEO velocity and electric field strength in Newtonian fluids breaks. The ICEO velocity varies differently with the electric field strength as the NaPSS concentration changes. These new findings can contribute to the understanding of ICEO of complex fluids, e.g., biofluids.

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

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

Energetics of counterion adsorption in the electrical double layer

The energetics of the electrical double layer (EDL) is studied in a systematic way to define how different components of the chemical potential help or hinder cation adsorption at a negatively charged wall. Specifically, the steric (i.e., excluded-volume interactions), mean electrostatic, and screening (i.e., electrostatic correlations beyond the mean field) components were computed using classical density functional theory of the primitive model of ions (i.e., ions as charged, hard spheres in a background dielectric). The reduced physics of the primitive model allows for an extensive analysis over a large parameter space: cation valences +1, +2, and +3, cation diameters 0.15, 0.30, 0.60, and 0.90 nm, bulk concentrations ranging from 1 µM to 1M, and surface charges ranging from 0 to -0.50 C/m². Our results show that all components are necessary to understand the physics of the EDL. The screening component is always significant; for small monovalent cations such as K⁺, it is generally much larger than the steric component, and for multivalent ions, charge inversion cannot occur without it. At moderate surface charges, the screening component makes the electrostatic potential less negative than in classical Poisson-Boltzmann theory, sometimes even positive (charge inversion). At high surface charges, this is overcome by the repulsive potential of the steric component as the first ion layer becomes extremely crowded. Large negative electrostatic potentials counteract this to draw even more cations into the first layer. Although we used an approximate model of the EDL, the physics inherent in these trends appears to be quite general.

Space-Charge Effects at the Li7La3Zr2O12/Poly(ethylene oxide) Interface

Composites consisting of garnet-type Li₇La₃Zr₂O₁₂ (LLZO) ceramic particles dispersed in a solid polymer electrolyte based on poly(ethylene oxide) (PEO) have recently been investigated as a possible electrolyte material in all solid state Li ion batteries. The interface between the two materials, that is, LLZO/PEO, is of special interest for the transport of lithium ions in the composite. For obtaining the desired high ionic conductivity, Li⁺ ions have to pass easily across this interface. However, previous research found that the interface is highly resistive. Here, we further investigate the interface between Al-substituted LLZO and PEO-LiClO₄ electrolytes in the frame of a theoretical description, which is based on space-charge layers. By theoretical calculations supported by experiments, we find that the interface is highly resistive. From the results, we have deduced that the highest contribution to this resistance comes from a high activation energy and not from electrostatic repulsion of lithium.

Label-free detection of conformational changes in switchable DNA nanostructures with microwave microfluidics

Detection of conformational changes in biomolecular assemblies provides critical information into biological and self-assembly processes. State-of-the-art in situ biomolecular conformation detection techniques rely on fluorescent labels or protein-specific binding agents to signal conformational changes. Here, we present an on-chip, label-free technique to detect conformational changes in a DNA nanomechanical tweezer structure with microwave microfluidics. We measure the electromagnetic properties of suspended DNA tweezer solutions from 50 kHz to 110 GHz and directly detect two distinct conformations of the structures. We develop a physical model to describe the electrical properties of the tweezers, and correlate model parameters to conformational changes. The strongest indicator for conformational changes in DNA tweezers are the ionic conductivity, while shifts in the magnitude of the cooperative water relaxation indicate the addition of fuel strands used to open the tweezer. Microwave microfluidic detection of conformational changes is a generalizable, non-destructive technique, making it attractive for high-throughput measurements.

Methods to study conformational changes in biomolecules are limited in resolution and require labelling or other modifications of target analytes. Here the authors present a label-free, microwave microfluidic approach to detect conformational changes of DNA nanostructures based on ionic conductivity.

Electrokinetics of metal cylinders

We study theoretically the rotation induced on an uncharged metal nanocylinder immersed in an electrolyte by AC electric fields. We consider the rotation of the cylinder when subjected to a rotating electric field (electrorotation) and the orientation of the cylinder in an AC field with constant direction (electro-orientation). The cylinder rotation is due to two mechanisms: the electric field interaction with the induced dipole on the particle and the hydrodynamic stress on the particle originated by the induced-charge electro-osmotic (ICEO) flow around the particle. The cylinder rotation induced by the ICEO mechanism can be calculated by using the Lorentz reciprocal theorem, while the rotation due to the induced dipole is calculated from the cylinder polarizability. We employ 3D numerical computations using finite elements for the general case as well as analytical methods for slender cylinders. Both calculations use the thin-double-layer approximation. We compare the results for slender cylinders of both methods showing good agreement. The electro-orientation (EOr) due to dipole torque aligns the axis of slender cylinders with the applied field, but aligns the axis of short cylinders perpendicularly to the field. The EOr due to ICEO torque always aligns the axis of cylinders with the field. The rotation induced by ICEO torque tends to disappear for frequencies of the applied field much greater than the characteristic frequency for charging the double-layer capacitance of the metal-electrolyte interface.

Continuum models of the electrochemical diffuse layer in electronic-structure calculations

Continuum electrolyte models represent a practical tool to account for the presence of the diffuse layer at electrochemical interfaces. However, despite the increasing popularity of these in the field of materials science, it remains unclear which features are necessary in order to accurately describe interface-related observables such as the differential capacitance (DC) of metal electrode surfaces. We present here a critical comparison of continuum diffuse-layer models that can be coupled to an atomistic first-principles description of the charged metal surface in order to account for the electrolyte screening at electrified interfaces. By comparing computed DC values for the prototypical Ag(100) surface in an aqueous solution to experimental data, we validate the accuracy of the models considered. Results suggest that a size-modified Poisson-Boltzmann description of the electrolyte solution is sufficient to qualitatively reproduce the main experimental trends. Our findings also highlight the large effect that the dielectric cavity parameterization has on the computed DC values.

Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials

Properties of solid-liquid interfaces are of immense importance for electrocatalytic and electrochemical systems, but modeling such interfaces at the atomic level presents a serious challenge and approaches beyond standard methodologies are needed. An atomistic computational scheme needs to treat at least part of the system quantum mechanically to describe adsorption and reactions, while the entire system is in thermal equilibrium. The experimentally relevant macroscopic control variables are temperature, electrode potential, and the choice of the solvent and ions, and these need to be explicitly included in the computational model as well; this calls for a thermodynamic ensemble with fixed ion and electrode potentials. In this work, a general framework within density functional theory (DFT) with fixed electron and ion chemical potentials in the grand canonical (GC) ensemble is established for modeling electrocatalytic and electrochemical interfaces. Starting from a fully quantum mechanical description of multi-component GC-DFT for nuclei and electrons, a systematic coarse-graining is employed to establish various computational schemes including (i) the combination of classical and electronic DFTs within the GC ensemble and (ii) on the simplest level a chemically and physically sound way to obtain various (modified) Poisson-Boltzmann (mPB) implicit solvent models. The detailed and rigorous derivation clearly establishes which approximations are needed for coarse-graining as well as highlights which details and interactions are omitted in vein of computational feasibility. The transparent approximations also allow removing some of the constraints and coarse-graining if needed. We implement various mPB models within a linear dielectric continuum in the GPAW code and test their capabilities to model capacitance of electrochemical interfaces as well as study different approaches for modeling partly periodic charged systems. Our rigorous and well-defined DFT coarse-graining scheme to continuum electrolytes highlights the inadequacy of current linear dielectric models for treating properties of the electrochemical interface.

Modeling the AC Electrokinetic Behavior of Semiconducting Spheres

We study theoretically the dielectrophoresis and electrorotation of a semiconducting microsphere immersed in an aqueous electrolyte. To this end, the particle polarizability is calculated from first principles for arbitrary thickness of the Debye layers in liquid and semiconductor. We show that the polarizability dispersion arises from the combination of two relaxation interfacial phenomena: charging of the electrical double layer and the Maxwell⁻Wagner relaxation. We also calculate the particle polarizability in the limit of thin electrical double layers, which greatly simplifies the analytical calculations. Finally, we show the model predictions for two relevant materials (ZnO and doped silicon) and discuss the limits of validity of the thin double layer approximation.

Electro-Orientation of Silver Nanowires in Alternating Fields

In this work, we analyze the orientation of silver nanowires immersed in aqueous solutions, under the effect of alternating electric fields in a broad frequency range covering from a few Hz to several MHz. The degree of orientation is experimentally determined by electro-optical techniques, which present the advantage of measuring multiple particles at the same time. In the electro-orientation spectrum, we observe frequency dispersion in the kHz range and provide a theoretical explanation for this behavior: at high frequencies, charge separation in the nanoparticles leads to a large induced dipole responsible for strong orientation. On the other hand, at low frequencies, redistribution of the ions in solution gives rise to an induced double layer that screens the dipolar fields, and as a consequence, the degree of orientation decreases. Moreover, we measure the transient response when the electric field is switched off, from which the size distribution of the polydisperse sample is obtained. The results match those given by electron microscopy determinations.

Liquid Crystals-Enabled AC Electrokinetics

Phenomena of electrically driven fluid flows, known as electro-osmosis, and particle transport in a liquid electrolyte, known as electrophoresis, collectively form a subject of electrokinetics. Electrokinetics shows a great potential in microscopic manipulation of matter for various scientific and technological applications. Electrokinetics is usually studied for isotropic electrolytes. Recently it has been demonstrated that replacement of an isotropic electrolyte with an anisotropic, or liquid crystal (LC), electrolyte, brings about entirely new mechanisms of spatial charge formation and electrokinetic effects. This review presents the main features of liquid crystal-enabled electrokinetics (LCEK) rooted in the field-assisted separation of electric charges at deformations of the director that describes local molecular orientation of the LC. Since the electric field separates the charges and then drives the charges, the resulting electro-osmotic and electrophoretic velocities grow as the square of the applied electric field. We describe a number of related phenomena, such as alternating current (AC) LC-enabled electrophoresis of colloidal solid particles and fluid droplets in uniform and spatially-patterned LCs, swarming of colloids guided by photoactivated surface patterns, control of LCEK polarity through the material properties of the LC electrolyte, LCEK-assisted mixing at microscale, separation and sorting of small particles. LC-enabled electrokinetics brings a new dimension to our ability to manipulate dynamics of matter at small scales and holds a major promise for future technologies of microfluidics, pumping, mixing, sensing, and diagnostics.

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

Artificial charged membranes, similar to the biological membranes, are self-assembled nanostructured materials constructed from macromolecules. The mutual interactions of parts of macromolecules leads to phase separation and appearance of microheterogeneities within the membrane bulk. On the other hand, these interactions also cause spontaneous microheterogeneity on the membrane surface, to which macroheterogeneous structures can be added at the stage of membrane fabrication. Membrane bulk and surface heterogeneity affect essentially the properties and membrane performance in the applications in the field of separation (water desalination, salt concentration, food processing and other), energy production (fuel cells, reverse electrodialysis), chlorine-alkaline electrolysis, medicine and other. We review the models describing ion transport in ion-exchange membranes and electromembrane systems with an emphasis on the role of micro- and macroheterogeneities in and on the membranes. Irreversible thermodynamics approach, “solution-diffusion” and “pore-flow” models, the multiphase models built within the effective-medium approach are examined as the tools for describing ion transport in the membranes. 2D and 3D models involving or not convective transport in electrodialysis cells are presented and analysed. Some examples are given when specially designed surface heterogeneity on the membrane surface results in enhancement of ion transport in intensive current electrodialysis.

Theory of Transport-Induced-Charge Electroosmotic Pumping toward Alternating Current Resistive Pulse Sensing

In this work, we study transport-induced-charge electroosmosis toward alternating current resistive pulse sensing for the next generation of biomedical applications. Transport-induced-charge electroosmosis, being a new class of electrokinetic phenomenon, occurs as a salt concentration gradient works in synergy with an electric field in ultrathin nanopores. Apart from the conventional electric double layer-governed electroosmotic flow in which the flow behavior is subject to the surface charge, it is found that the transport-induced-charge electroosmotic flow behaves independently of surface charge magnitude but can be linearly regulated by the bulk salt concentration bias. The reversal of the electric field simultaneously inverses the induced charge allowing the establishment of a unidirectional flow under the application of a periodic alternating current field. This unique phenomenon permits continuous water and nanoparticles pumping through a two-dimensional material nanopore in spite of the reversal of the electric field. Built upon this mechanism, we propose a theoretical prototype of alternating current resistive pulse sensing in a two-dimensional nanopore system.

Role of Stefan-Maxwell fluxes in the dynamics of concentrated electrolytes

This theoretical analysis quantifies the effect of coupled ionic fluxes on the charging dynamics of an electrochemical cell. We consider a model cell consisting of a concentrated, binary electrolyte between parallel, blocking electrodes, under a suddenly applied DC voltage. It is assumed that the magnitude of the applied voltage is small compared to the thermal voltage scale, RT/F, where R is the universal gas constant, T is the temperature and F is the Faraday's constant. We employ the Stefan-Maxwell equations to describe the hydrodynamic coupling of ionic fluxes that arise in concentrated electrolytes. These equations inherently account for asymmetry in the mobilities of the ions in the electrolyte. A modified set of Poisson-Nernst-Planck equations, obtained by incorporating Stefan-Maxwell fluxes into the species balances, are formulated and solved in the limit of weak applied voltages. A long-time asymptotic analysis reveals that the electrolyte dynamics occur on two distinct time scales. The first is a faster "RC" time, τ_RC = κ^-1L/D_E, where κ^-1 is the Debye length, L is the length of the half-cell, and D_E is an effective diffusivity, which characterizes the evolution of charge density at the electrode. The effective diffusivity, D_E, is a function of the ambi-polar diffusivity of the salt, D_a, as well as a cross-diffusivity, D_+-, of the ions. This time scale also dictates the initial exponential decay of current in the external circuit. At times longer than τ_RC, the external current again decays exponentially on a slower, diffusive time scale, τ_D∼L²/D_a, where D_a is the ambi-polar diffusivity of the salt. This diffusive time scale is due to the unequal ion mobilities that result in a non-uniform bulk concentration of the salt during the charging process. Finally, we propose an approach by which our theory may be used to measure the cross-diffusivity in concentrated electrolytes.

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

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