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

Electric field induced associations in the double layer of salt-in-ionic-liquid electrolytes

Ionic liquids (ILs) are an extremely exciting class of electrolytes for energy storage applications. Upon dissolving alkali metal salts, such as Li or Na based salts, with the same anion as the IL, an intrinsically asymmetric electrolyte can be created for use in batteries, known as a salt-in-ionic liquid (SiIL). These SiILs have been well studied in the bulk, where negative transference numbers of the alkali metal cation have been observed from the formation of small, negatively charged clusters. The properties of these SiILs at electrified interfaces, however, have received little to no attention. Here, we develop a theory for the electrical double layer (EDL) of SiILs where we consistently account for the thermoreversible association of ions into Cayley tree aggregates. The theory predicts that the IL cations first populate the EDL at negative voltages, as they are not strongly bound to the anions. However, at large negative voltages, which are strong enough to break the alkali metal cation-anion associations, these IL cations are exchanged for the alkali metal cation because of their higher charge density. At positive voltages, we find that the SiIL actually becomes more aggregated while screening the electrode charge from the formation of large, negatively charged aggregates. Therefore, in contrast to conventional intuition of associations in the EDL, SiILs appear to become more associated in certain electric fields. We present these theoretical predictions to be verified by molecular dynamics simulations and experimental measurements.

Competition between ion-ion electrostatic correlations and hydrodynamic slip radically changes diffusioosmosis

Existing theories can predict separately the effects of hydrodynamic slip and ion-ion electrostatic correlations on diffusioosmosis. However, a predictive model for the coupled dynamics of hydrodynamic slip and electrostatic correlations in diffusioosmosis is lacking. In this work, we develop a mathematical model to compute the diffusioosmotic mobilities of valence-symmetric electrolytes in a charged parallel-plate channel. We employ the Navier slip condition to model the hydrodynamic slip at the channel walls and the modified Poisson equation to model ion-ion electrostatic correlations. We report two key findings arising from the competition between electrostatic correlations and hydrodynamic slip, which radically change diffusioosmosis. First, in a divalent electrolyte, a minute hydrodynamic slip defers the reversal in the direction of diffusioosmosis caused by electrostatic correlations to a higher concentration. Hydrodynamic slip can even eliminate the diffusioosmosis reversal in a monovalent electrolyte. Second, electrostatic correlations limit the change in the mobility due to hydrodynamic slip, by hindering the slip-enhanced ionic transport via surface charge overscreening. Electrostatic correlations can reduce the change in the mobility by ≈60% in a monovalent electrolyte, whereas the stronger electrostatic correlations in a divalent electrolyte can even reduce the change by an order of magnitude. The model developed from this work can be used to understand and predict diffusioosmosis in natural settings such as metamorphic transformation, in addition to that in applications such as colloidal species separation, nanoparticle drug delivery, and enhanced oil recovery.

Unveiling Gating Behavior in Piezoionic Effect: toward Neuromimetic Tactile Sensing

The human perception system's information processing is intricately linked to the nonlinear response and gating effect of neurons. While piezoionics holds potential in emulating the pressure sensing capability of biological skin, the incorporation of information processing functions seems neglected. Here, ionic gating behavior in piezoionic hydrogels is uncovered as a notable extension beyond the previously observed linear responses. The hydrogel can generate remarkably high voltages (700 mV) and currents (7 mA) when indentation forces surpass the threshold. Through a comprehensive analysis involving simulations and experimental investigations, it is proposed that the gating behavior emerges due to significant diffusion differences between cations and anions. To showcase the practical implications of this breakthrough, the piezoionic hydrogels are successfully integrated with prostheses and robot hands, demonstrating that the gating effect enables accurate discrimination between gentle and harsh touch. The advancement in neuromimetic tactile sensing has significant potential for emerging applications such as humanoid robotics and biomedical engineering, offering valuable opportunities for further development of embodied neuromorphic intelligence.

Effect of Mixed Morphology (Simple Cubic, Face-Centered Cubic, and Body-Centered Cubic)-Based Electrodes on the Electric Double Layer Capacitance of Supercapacitors

Supercapacitors store energy due to the formation of an electric double layer (EDL) at the interface of the electrodes and electrolyte. The present article deals with the finite element study of equilibrium electric double layer capacitance (EDLC) in the mixed morphology electrodes comprising all three fundamental crystal structures, simple cubic (SC), body-centered cubic (BCC), and face-centered cubic morphologies (FCC). Mesoporous-activated carbon forms the electrode in the supercapacitor with (C2H5)4NBF4/propylene carbonate organic electrolyte. Electrochemical interference is clearly demonstrated in the supercapacitors with the formation of the potential bands, as in the case of interference theory due to the increasing packing factor. The effects of electrode thickness varying from a wide range of 50 nm to 0.04 mm on specific EDLC have been discussed in detail. The interfacial geometry of the unit cell in contact with the electrolyte is the most important parameter determining the properties of the EDL. The critical thickness of the electrodes is 1.71 μm in all the morphologies. Polarization increases the interfacial potential and leads to EDL formation. The Stern layer specific capacitance is 167.6 μF cm-2 in all the morphologies. The maximum capacitance is in the decreasing order of interfacial geometry, as FCC > BCC > SC, dependent on the packing factor. The minimum transmittance in all the morphologies is 98.35%, with the constant figure of merit at higher electrode thickness having applications in the chip interconnects. The transient analysis shows that the interfacial current decreases with increasing polarization in the EDL. The capacitance also decreases with the increase of the scan rate.

Asymmetric Rectified Electric Fields for Symmetric Electrolytes

In this paper, building upon the numerical discovery of asymmetric rectified electric fields (AREFs), we explore the generation of AREF by applying a sawtooth-like voltage to 1:1 electrolytes with equal diffusion coefficients confined between two planar blocking electrodes. This differs from an earlier approach based on a sinusoidal AC voltage applied to 1:1 electrolytes with unequal diffusion coefficients. By numerically solving the full Poisson-Nernst-Planck equations, we demonstrate that AREF can be generated by a slow rise and a fast drop of the potential (or vice versa), even for electrolytes with equal diffusion coefficients of the cations and anions. We employ an analytically constructed equivalent electric circuit to explain the underlying physical mechanism. Importantly, we find that the strength of AREF can be effectively tuned from zero to its maximal value by only manipulating the time dependence of the driving voltage, eliminating the necessity to modify the electrolyte composition between experiments. This provides valuable insights to control the manipulation of AREF, which facilitates enhanced applications in diverse electrochemical systems.

Effects of finite counterion size and nonhomogeneous permittivity and viscosity of the solution on the electrokinetics of a concentrated salt-free colloid

In the present work, a general model of the electrokinetics and dielectric response of a concentrated salt-free colloid is developed which includes consideration of the finite size of the counterions released by the particles to the solution, a nonhomogeneous permittivity of the solution, the existence of Born and dielectrophoretic forces acting on the counterions, and especially the fact that the solution viscosity and diffusion counterion coefficient are allowed to be functions of the local counterion concentration. These effects have recently been discussed by J. J. López-García et al. [Phys. Rev. Fluids 4, 103702 (2019)10.1103/PhysRevFluids.4.103702] in the case of dilute colloids in general electrolyte solutions. The objective of this work is to explore the new effects and their influence on the electrokinetic response of concentrated salt-free systems. Present results confirm previous findings regarding the important increases of the dc electrophoretic mobility and dc electrical conductivity, as well as huge increments of the dynamic electrophoretic mobilities at high frequencies when finite-ion-size effects were taken into account. In addition, consideration of the viscosity of the solution and of the counterion diffusion coefficient as functions of the local counterion concentration leads to a decrease of the magnitude of the previous electrokinetic results. The theory incorporates a more convenient hard-sphere hydrodynamic model to account for the nonhomogeneous viscosity of the solution than others proposed in previous works in the literature. A comparison is elaborated on between electrokinetic and dielectric responses with different levels of complexity of the theoretical model, starting from the case of pointlike counterions and following with the inclusion in sequence of additional aspects such as finite counterion size, nonhomogeneous electrical permittivity with associated Born and dielectrophoretic effects, and, finally, position-dependent viscosity and diffusion counterion coefficient, and clearly shows the influence of individual effects on the general electrokinetic response and especially the relevant role the nonhomogeneous viscosity on the dc and ac electrokientic behavior of salt-free colloids.

Bacterial Electrophysiology

Bacterial ion fluxes are involved in the generation of energy, transport, and motility. As such, bacterial electrophysiology is fundamentally important for the bacterial life cycle, but it is often neglected and consequently, by and large, not understood. Arguably, the two main reasons for this are the complexity of measuring relevant variables in small cells with a cell envelope that contains the cell wall and the fact that, in a unicellular organism, relevant variables become intertwined in a nontrivial manner. To help give bacterial electrophysiology studies a firm footing, in this review, we go back to basics. We look first at the biophysics of bacterial membrane potential, and then at the approaches and models developed mostly for the study of neurons and eukaryotic mitochondria. We discuss their applicability to bacterial cells. Finally, we connect bacterial membrane potential with other relevant (electro)physiological variables and summarize methods that can be used to both measure and influence bacterial electrophysiology.

Diffusioosmotic flow reversals due to ion-ion electrostatic correlations

Existing theories of diffusioosmosis have neglected ion-ion electrostatic correlations, which are important in concentrated electrolytes. Here, we develop a mathematical model to numerically compute the diffusioosmotic mobilities of binary symmetric electrolytes across low to high concentrations in a charged parallel-plate channel. We use the modified Poisson equation to model the ion-ion electrostatic correlations and the Bikerman model to account for the finite size of ions. We report two key findings. First, ion-ion electrostatic correlations can cause a unique reversal in the direction of diffusioosmosis. Such a reversal is not captured by existing theories, occurs at ≈ 0.4 M for a monovalent electrolyte, and at a much lower concentration of ≈ 0.003 M for a divalent electrolyte in a channel with the same surface charge. This highlights that diffusioosmosis of a concentrated electrolyte can be qualitatively different from that of a dilute electrolyte, not just in its magnitude but also its direction. Second, we predict a separate diffusioosmotic flow reversal, which is not due to electrostatic correlations but the competition between the underlying chemiosmosis and electroosmosis. This reversal can be achieved by varying the magnitude of the channel surface charge without changing its sign. However, electrostatic correlations can radically change how this flow reversal depends on the channel surface charge and ion diffusivity between a concentrated and a dilute electrolyte. The mathematical model developed here can be used to design diffusioosmosis of dilute and concentrated electrolytes, which is central to applications such as species mixing and separation, enhanced oil recovery, and reverse electrodialysis.

Induced-charge electrophoresis of a tilted metal nanowire near an insulating wall

Electric fields are commonly used to control the orientation and motion of microscopic metal particles in aqueous suspensions. For example, metallodielectric Janus spheres are propelled by the induced-charge electro-osmotic flow occurring on their metallic side, the most common case in electrokinetics of exploiting symmetry breaking of surface properties for achieving net particle motion. In this work, we demonstrate that a homogeneous metal rod can translate parallel to a dielectric wall as a result of the hydrodynamic wall-particle interaction arising from the induced-charge electro-osmosis on the rod surface. The applied electric field could be either dc or low-frequency ac. The only requirement for a nonvanishing particle velocity is that the axis of the rod be inclined with respect to the wall, i.e., it cannot be neither parallel nor perpendicular. We show numerical results of the rod velocity as a function of rod orientation and distance to the wall. The maximum particle velocity is found for an orientation of between ∼30^{∘} and ∼50^{∘}, depending on the position and aspect ratio of the cylinder. Particle velocities of up to tens of µm/s are predicted for typical conditions in electrokinetic experiments.

Modulating selective ionic enrichment and depletion zones in straight nanochannels via the interplay of surface charge modulation and electric field mediated fluid-thickening

We report the possibilities of achieving highly controlled segregation of ion-enriched and ion-depleted regions in straight nanochannels. This is achieved via harnessing the interplay of an axial gradient of the induced transverse electric field on account of electrical double layer phenomenon and the localized thickening of the fluid because of intensified electric fields due to the large spatial gradients of the electrical potential in extreme confinements. By considering alternate surface patches of different charge densities over pre-designed axial spans, we illustrate how these effects can be exploited to realize selectively ion-enriched and ion-depleted zones. Physically, this is attributed to setting up of an axial concentration gradient that delves on the ionic advection due to the combined effect of an externally applied electric field and induced back-pressure gradient along the channel axis and electro-migration due to the combinatorial influences of the applied and the induced electrostatic fields. With an explicit handle on the pertinent parameters, our results offer insights on the possible means of imposing delicate controls on the solute-enrichment and depletion phenomena, a paradigm that remained unexplored thus far.

NaCl, MgCl2, and AlCl3 Surface Coverages on Fused Silica and Adsorption Free Energies at pH 4 from Nonlinear Optics

We employ amplitude- and phase-resolved second harmonic generation experiments to probe interactions of fused silica:aqueous interfaces with Al3+, Mg2+, and Na+ cations at pH 4 and as a function of metal cation concentration. We quantify the second-order nonlinear susceptibility and the total interfacial potential in the presence and absence of a 10 mM screening electrolyte to understand the influence of charge screening on cation adsorption. Strong cation:surface interactions are observed in the absence of the screening electrolyte. The total potential is then employed to estimate the total number of absorbed cations cm-2. The contributions to the total potential from the bound and mobile charges were separated using Gouy-Chapman-Stern model estimates. All three cations bind fully reversibly, indicating physisorption as the mode of interaction. Of the isotherm models tested, the Kd adsorption model fits the data with binding constants of 3-30 and ∼300 mol-1 for the low (<0.1 mM) and high (0.1-3 mM) concentration regimes, corresponding to adsorption free energies of -13 to -18 and -24 kJ mol-1 at room temperature, respectively. The maximum surface coverages are around 1013 cations cm-2, matching the number of deprotonated silanol groups on silica at pH 4. Clear signs of decoupled Stern and diffuse layer nonlinear optical responses are observed and found to be cation-specific.

Electro-optics of confined systems

Confinement in microenvironments occurs in many natural systems and technological applications. However, little is known about the behaviour of the immersed nanoparticles. In this work we show that their diffusion, electro-orientation and electric field induced polarization can be determined through electric birefringence experiments. We analyze aqueous dispersions of silver nanowires and clay particles confined inside microdroplets. We have observed that confinement reduces the amount of particles that can be oriented by the external electric field. However, the polarizability of the oriented particles is not affected by the presence of the oil/water boundary, and it is the same as in unbounded media, which agrees with the fact that the electric polarization and related phenomena are short-ranged.

A Universal Approximation for Conductance Blockade in Thin Nanopore Membranes

Nanopore-based sensing platforms have transformed single-molecule detection and analysis. The foundation of nanopore translocation experiments lies in conductance measurements, yet existing models, which are largely phenomenological, are inaccurate in critical experimental conditions such as thin and tightly fitting pores. Of the two components of the conductance blockade, channel and access resistance, the access resistance is poorly modeled. We present a comprehensive investigation of the access resistance and associated conductance blockade in thin nanopore membranes. By combining a first-principles approach, multiscale modeling, and experimental validation, we propose a unified theoretical modeling framework. The analytical model derived as a result surpasses current approaches across a broad parameter range. Beyond advancing our theoretical understanding, our framework's versatility enables analyte size inference and predictive insights into conductance blockade behavior. Our results will facilitate the design and optimization of nanopore devices for diverse applications, including nanopore base calling and data storage.

Optimization of upstream particle concentration from flow using AC electro-osmosis and dielectrophoresis

There are many applications where upstream sample processing is required to concentrate dispersed particles in flow; this may be to increase the concentration (e.g., to enhance biosensor accuracy) or to decrease it (e.g., by removing contaminants from flow). The AC electrokinetic phenomenon, dielectrophoresis (DEP), has been used widely for particle trapping for flow, but the magnitude of the force drops reduces rapidly with distance from electrode edges, so that nm-scale particles such as viruses and bacteria are only trapped when near the electrode surface. This limits the usable flow rate in the device and can render the final device unusable for practical applications. Conversely, another electrokinetic phenomenon, AC electro-osmosis (ACEO), can be used to move particles to electrode surfaces but is unable to trap them from flow, limiting their ability for sample cleanup or trap-and-purge concentration. In this paper, we describe the optimization of ACEO electrodes aligned parallel to pressure-driven flow as a precursor/preconditioner to capture particles from a flow stream and concentrate them adjacent to the channel wall to enhance DEP capture. This is shown to be effective at flow rates of up to 0.84 ml min-1. Furthermore, the analysis of the 3D flow structure in the ACEO device by both simulation and confocal microscopy suggests that while the system offers significant benefits, the flow structure in the volume near the channel lid is such that while substantial trapping can occur, particles in this part of the chamber cannot be trapped, independent of the chamber height.

Bidirectional and Stepwise Rotation of Cells and Particles Using Induced Charge Electroosmosis Vortexes

The rotation of cells is of significant importance in various applications including bioimaging, biophysical analysis and microsurgery. Current methods usually require complicated fabrication processes. Herein, we proposed an induced charged electroosmosis (ICEO) based on a chip manipulation method for rotating cells. Under an AC electric field, symmetric ICEO flow microvortexes formed above the electrode surface can be used to trap and rotate cells. We have discussed the impact of ICEO and dielectrophoresis (DEP) under the experimental conditions. The capabilities of our method have been tested by investigating the precise rotation of yeast cells and K562 cells in a controllable manner. By adjusting the position of cells, the rotation direction can be changed based on the asymmetric ICEO microvortexes via applying a gate voltage to the gate electrode. Additionally, by applying a pulsed signal instead of a continuous signal, we can also precisely and flexibly rotate cells in a stepwise way. Our ICEO-based rotational manipulation method is an easy to use, biocompatible and low-cost technique, allowing rotation regardless of optical, magnetic or acoustic properties of the sample.

Asymmetric rectified electric fields: nonlinearities and equivalent circuits

Recent experiments [S. H. Hashemi et al., Phys. Rev. Lett., 2018, 121, 185504] have shown that a long-ranged steady electric field emerges when applying an oscillating voltage over an electrolyte with unequal mobilities of cations and anions confined between two planar blocking electrodes. To explain this effect we analyse full numerical calculations based on the Poisson-Nernst-Planck equations by means of analytically constructed equivalent electric circuits. Surprisingly, the resulting equivalent circuit has two capacitive elements, rather than one, which introduces a new timescale for electrolyte dynamics. We find a good qualitative agreement between the numerical results and our simple analytic model, which shows that the long-range steady electric field emerges from the different charging rates of cations and anions in the electric double layers.

Nature of Overcharging and Charge Inversion in Electrical Double Layers

Understanding overcharging and charge inversion is one of the long-standing challenges in soft matter and biophysics. To study these phenomena, we employ the modified Gaussian renormalized fluctuation theory, which allows for the self-consistent accounting of spatially varying ionic strength as well as the spatial variations in dielectric permittivity and excluded volume effects. The underlying dependence of overcharging on the electrostatic coupling is elucidated by varying the surface charge, counterion valency, and dielectric contrast. Consistent with simulations, three characteristic regimes corresponding to weak, moderate, and strong coupling are identified. Important features like the inversion of zeta potential, crowding, and ionic layering at the surface are successfully captured. For weak coupling, there is no overcharging. In the moderate coupling regime, overcharging increases with the surface charge. Finally, in the strong coupling regime, ionic crowding and saturation in overcharging are observed. Our theory predicts a nonmonotonic dependence of charge inversion on multivalent salt concentration as well as the addition of monovalent salt, in quantitative agreement with experiments.

Multiscale Modeling of Aqueous Electric Double Layers

From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.

Theoretical Analysis of the Influence of Spacers on Salt Ion Transport in Electromembrane Systems Considering the Main Coupled Effects

This article considers a theoretical analysis of the influence of the main coupled effects and spacers on the transfer of salt ions in electromembrane systems (EMS) using a 2D mathematical model of the transfer process in a desalting channel with spacers based on boundary value problems for the coupled system of Nernst-Planck-Poisson and Navier-Stokes equations. The basic patterns of salt ion transport have been established, taking into account diffusion, electromigration, forced convection, electroconvection, dissociation/recombination reactions of water molecules, as well as spacers located inside the desalting channel. It has been shown that spacers and taking into account the dissociation/recombination reaction of water molecules significantly change both the formation and development of electroconvection. This article confirms the fact of the exaltation of the limiting current studied by Harkatz, where it is shown that the current (flux) of salt ions increases when the dissociation reaction begins by a certain value called the exaltation current, which is proportional to the flow of water dissociation products. A significant combined effect of electroconvection and dissociation/recombination reactions as well as the spacer system in the desalting channel on the transport of salt ions are shown. The complex, nonlinear, and non-stationary interaction of all the main effects of concentration polarization and spacers in the desalting channel are also considered in the work.

Dynamic Response of Ion Transport in Nanoconfined Electrolytes

Ion transport in nanoconfined electrolytes exhibits nonlinear effects caused by large driving forces and pronounced boundary effects. An improved understanding of these impacts is urgently needed to guide the design of key components of the electrochemical energy systems. Herein, we employ a nonlinear Poisson-Nernst-Planck theory to describe ion transport in nanoconfined electrolytes coupled with two sets of boundary conditions to mimic different cell configurations in experiments. A peculiar nonmonotonic charging behavior is discovered when the electrolyte is placed between a blocking electrode and an electrolyte reservoir, while normal monotonic behaviors are seen when the electrolyte is placed between two blocking electrodes. We reveal that impedance shapes depend on the definition of surface charge and the electrode potential. Particularly, an additional arc can emerge in the intermediate-frequency range at potentials away from the potential of zero charge. The obtained insights are instrumental to experimental characterization of ion transport in nanoconfined electrolytes.

Sedimentation of a Charged Spherical Particle in a Viscoelastic Electrolyte Solution

When a charged particle translates through an electrolyte solution, the electric double layer around it deforms in response to the fluid motion and creates an electric force opposite the direction of motion, decreasing the settling velocity. This is a multidisciplinary phenomenon that combines fluid mechanics and electrodynamics, differentiating it from the classical problem of an uncharged sedimenting particle. It has many applications varying from mechanical to biomedical, such as in drug delivery in blood through charged microparticles. Related studies so far have focused on Newtonian fluids, but recent studies have proven that many biofluids, such as human blood plasma, have elastic properties. To this end, we perform a computational study of the steady sedimentation of a spherical, charged particle in human blood plasma due to the centrifugal force. We used the Giesekus model to describe the rheological behavior of human blood plasma. Assuming axial symmetry, the governing equations include the momentum and mass balances, Poisson's equation for the electric field, and the species conservation. The finite size of the ions is considered through the local-density approximation approach of Carnahan-Starling. We perform a detailed parametric analysis, varying parameters such as the ζ potential, the size of the ions, and the centrifugal force exerted upon the particle. We observe that as the ζ potential increases, the settling velocity decreases due to a stronger electric force that slows the particle. We also conduct a parametric analysis of the relaxation time of the material to investigate what happens generally in viscoelastic electrolyte solutions and not only in human blood plasma. We conclude that elasticity plays a crucial role and should not be excluded from the study. Finally, we examine under which conditions the assumption of point-like ions gives different predictions from the Carnahan-Starling approach.

Unified quantum theory of electrochemical kinetics by coupled ion-electron transfer

A general theory of coupled ion-electron transfer (CIET) is presented, which unifies Marcus kinetics of electron transfer (ET) with Butler-Volmer kinetics of ion transfer (IT). In the limit of large reorganization energy, the theory predicts normal Marcus kinetics of "electron-coupled ion transfer" (ECIT). In the limit of large ion transfer energies, the theory predicts Butler-Volmer kinetics of "ion-coupled electron transfer" (ICET), where the charge transfer coefficient and exchange current are connected to microscopic properties of the electrode/electrolyte interface. In the ICET regime, the reductive and oxidative branches of Tafel's law are predicted to hold over a wide range of overpotentials, bounded by the ion-transfer energies for oxidation and reduction, respectively. The probability distribution of transferring electron energies in CIET smoothly interpolates between a shifted Gaussian distribution for ECIT (as in the Gerischer-Marcus theory of ET) to an asymmetric, fat-tailed Meixner distribution centered at the Fermi level for ICET. The latter may help interpret asymmetric line shapes in x-ray photo-electron spectroscopy (XPS) and Auger electron spectroscopy (AES) for metal surfaces in terms of shake-up relaxation of the ionized atom and its image polaron by ICET. In the limit of large overpotentials, the theory predicts a transition to inverted Marcus ECIT, leading to a universal reaction-limited current for metal electrodes, dominated by barrierless quantum transitions. Uniformly valid, closed-form asymptotic approximations are derived that smoothly transition between the limiting rate expressions for ICET and ECIT for metal electrodes, using simple but accurate mathematical functions. The theory is applied to lithium intercalation in lithium iron phosphate (LFP) and found to provide a consistent description of the observed current dependence on overpotential, temperature and concentration. CIET theory thus provides a critical bridge between quantum electrochemistry and electrochemical engineering, which may find many other applications and extensions.

Ion Steric Effect Induces Giant Enhancement of Thermoelectric Conversion in Electrolyte-Filled Nanochannels

Ionic thermoelectricity in nanochannels has received increasing attention because of its advantages, such as high Seebeck coefficient and low cost. However, most studies have focused on dilute simple electrolytes that neglect the effects of finite ion sizes and short-range electrostatic correlation. Here, we reveal a new thermoelectric mechanism arising from the coupling of the ion steric effect due to finite ion sizes and ion thermodiffusion in electric double layers, using both theoretical and numerical methods. We show that this mechanism can significantly enhance the thermoelectric response in nanoconfined electrolytes depending on the properties of electrolytes and nanochannels. Compared to the previously known mechanisms, the new mechanism can increase the Seebeck coefficient by 100% or even 1 order of magnitude enhancement under optimal conditions. Moreover, we demonstrate that the short-range electrostatic correlation can help preserve the Seebeck coefficient enhancement in a weaker confinement or in more concentrated electrolytes.

Critical considerations in determining the surface charge of small extracellular vesicles

Small extracellular vesicles (EVs) have emerged as a focal point of EV research due to their significant role in a wide range of physiological and pathological processes within living systems. However, uncertainties about the nature of these vesicles have added considerable complexity to the already difficult task of developing EV-based diagnostics and therapeutics. Whereas small EVs have been shown to be negatively charged, their surface charge has not yet been properly quantified. This gap in knowledge has made it challenging to fully understand the nature of these particles and the way they interact with one another, and with other biological structures like cells. Most published studies have evaluated EV charge by focusing on zeta potential calculated using classical theoretical approaches. However, these approaches tend to underestimate zeta potential at the nanoscale. Moreover, zeta potential alone cannot provide a complete picture of the electrical properties of small EVs since it ignores the effect of ions that bind tightly to the surface of these particles. The absence of validated methods to accurately estimate the actual surface charge (electrical valence) and determine the zeta potential of EVs is a significant knowledge gap, as it limits the development of effective label-free methods for EV isolation and detection. In this study, for the first time, we show how the electrical charge of small EVs can be more accurately determined by accounting for the impact of tightly bound ions. This was accomplished by measuring the electrophoretic mobility of EVs, and then analytically correlating the measured values to their charge in the form of zeta potential and electrical valence. In contrast to the currently used theoretical expressions, the employed analytical method in this study enabled a more accurate estimation of EV surface charge, which will facilitate the development of EV-based diagnostic and therapeutic applications.

Incorporating ion-specific van der Waals and soft repulsive interactions in the Poisson-Boltzmann theory of electrical double layers

Electrical double layers (EDLs) arise when an electrolyte is in contact with a charged surface, and are encountered in several application areas including batteries, supercapacitors, electrocatalytic reactors, and colloids. Over the last century, the development of Poisson-Boltzmann (PB) models and their modified versions have provided significant physical insight into the structure and dynamics of the EDL. Incorporation of physics such as finite-ion-size effects, dielectric decrement, and ion-ion correlations has made such models increasingly accurate when compared to more computationally expensive approaches such as molecular simulations and classical density functional theory. However, a prominent knowledge gap has been the exclusion of van der Waals (vdW) and soft repulsive interactions in modified PB models. Although short-ranged as compared to electrostatic interactions, we show here that vdW and soft repulsive interactions can play an important role in determining the structure of the EDL via the formation of a Stern layer and in modulating the differential capacitance of an electrode in an electrolyte. To this end, we incorporate ion-ion and wall-ion vdW attraction and soft repulsion via a 12-6 Lennard-Jones (LJ) potential, resulting in a modified PB-LJ approach. The wall-ion LJ interactions were found to have a significant effect on the electrical potential and concentration profiles, especially close to the wall. However, ion-ion LJ interactions do not affect the EDL structure at low bulk ion concentrations (<1 M). We also derive dimensionless numbers to quantify the impact of ion-ion and wall-ion LJ interactions on the EDL. Furthermore, in the pursuit of capturing ion-specific effects, we apply our model by considering various ions such as Na, K+, Mg2+, Cl-, and SO42-. We observe how varying parameters such as the electrolyte concentration and electrode potential affect the structure of the EDL due to the competition between ion-specific LJ and electrostatic interactions. Lastly, we show that the inclusion of vdW and soft repulsion interactions, as well as hydration effects, leads to a better qualitative agreement of the PB models with experimental double-layer differential capacitance data. Overall, the modified PB-LJ approach presented herein will lead to more accurate theoretical descriptions of EDLs in various application areas.

Nonlinear dielectric decrement of electrolyte solutions: An effective medium approach

HYPOTHESIS

The dielectric constant of an electrolyte solution, which determines electrostatic interactions between colloids and interfaces, depends nonlinearly on the salinity and also on the type of salt. The linear decrement at dilute solutions is due to the reduced polarizability in the hydration shell around an ion. However, the full hydration volume cannot explain the experimental solubility, which indicates the hydration volume should decrease at high salinity. Volume reduction of the hydration shell is supposed to weaken dielectric decrement and thus should be relevant to the nonlinear decrement.

SIMULATIONS

According to the effective medium theory for the permittivity of heterogeneous media, we derive an equation which relates the dielectric constant with the dielectric cavities created by the hydrated cations and anions, and the effect of partial dehydration at high salinity is taken into account.

FINDINGS

Analysis of experiments on monovalent electrolytes suggests that weakened dielectric decrement at high salinity originates primarily from the partial dehydration. Furthermore, the onset volume fraction of the partial dehydration is found to be salt-specific, and is correlated with the solvation free energy. Our results suggest that while the reduced polarizability of the hydration shell determines the linear dielectric decrement at low salinity, ion-specific tendency of dehydration is responsible for nonlinear dielectric decrement at high salinity.

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

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

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

A Magnetically and Electrically Powered Hybrid Micromotor in Conductive Solutions: Synergistic Propulsion Effects and Label-Free Cargo Transport and Sensing

Electrically powered micro- and nanomotors are promising tools for in vitro single-cell analysis. In particular, single cells can be trapped, transported, and electroporated by a Janus particle (JP) using an externally applied electric field. However, while dielectrophoretic (DEP)-based cargo manipulation can be achieved at high-solution conductivity, electrical propulsion of these micromotors becomes ineffective at solution conductivities exceeding ≈0.3 mS cm-1 . Here, JP cargo manipulation and transport capabilities to conductive near-physiological (<6 mS cm-1 ) solutions are extended successfully by combining magnetic field-based micromotor propulsion and navigation with DEP-based manipulation of various synthetic and biological cargos. Combination of a rotating magnetic field and electric field results in enhanced micromotor mobility and steering control through tuning of the electric field frequency. In addition, the micromotor's ability of identifying apoptotic cell among viable and necrotic cells based on their dielectrophoretic difference is demonstrated, thus, enabling to analyze the apoptotic status in the single-cell samples for drug discovery, cell therapeutics, and immunotherapy. The ability to trap and transport live cells towards regions containing doxorubicin-loaded liposomes is also demonstrated. This hybrid micromotor approach for label-free trapping, transporting, and sensing of selected cells within conductive solutions opens new opportunities in drug delivery and single-cell analysis, where close-to-physiological media conditions are necessary.

Unraveling the impact of nano-scaling on silicon field-effect transistors for the detection of single-molecules

Electrolyte-gated silicon field-effect transistors (FETs) capable of detecting single molecules could enable high-throughput molecular sensing chips to advance, for example, genomics or proteomics. For solid-gated silicon FETs it is well-known that nano-scaled devices become sensitive to single elementary charges near the silicon-oxide interface. However, in electrolyte-gated FETs, electrolyte screening strongly reduces sensitivity to charges near the gate oxide. The question arises whether nano-scaling electrolyte-gated FETs can entail a sufficiently large signal-to-noise ratio (SNR) for the detection of single molecules. We enhanced a technology computer-aided design tool with electrolyte screening models to calculate the impact of the FET geometry on the single-molecule signal and FET noise. Our continuum FET model shows that a sufficiently large single-molecule SNR is only obtained when nano-scaling all FET channel dimensions. Moreover, we show that the expected scaling trend of the single-molecule SNR breaks down and no longer results in improvements for geometries approaching the decananometer size. This is the characteristic size of the FET channel region modulated by a typical molecule. For gate lengths below 50 nm, the overlap of the modulated region with the highly conductive junctions leads to saturation of the SNR. For cross-sections below 10-30 nm, SNR degrades due to the overlap of the modulated region with the convex FET corners where a larger local gate capacitance reduces charge sensitivity. In our study, assuming a commercial solid-state FET noise amplitude, we find that a suspended nanowire FET architecture with 35 nm length and 5 × 10 nm² cross-section results in the highest SNR of about 10 for a 15-base DNA oligo in a 15 mM electrolyte. In contrast with typical silicon nanowire FET sensors which possess micron-scale gate lengths, we find it to be key that all channel dimensions are scaled down to the decananometer range.

Effects of 3D electrodes arrangement in a novel AC electroosmotic micropump: Numerical modeling and experimental validation

To date, a comprehensive systematic optimization framework, capable of accurately predicting an efficient electrode geometry, is not available. Here, different geometries, including 3D step electrodes, have been designed in order to fabricate AC electroosmosis micropumps. It is essential to optimize both geometrical parameters of electrode, such as width and height of steps on each base electrode and their location in one pair, the size of each base electrode (symmetric or asymmetric), the gap of electrode pairs, and nongeometrical parameters such as fluid flow in a channel and electrical characteristics (e.g., frequency and voltage). The governing equations comprising of electric domain and fluid domain have been coupled using finite element method. The developed model was employed to investigate the effect of electrode geometric parameters on electroosmotic slip velocity and its subsequent effect on pressure and flow rate. Numerical simulation indicates that the optimal performance can be achieved using a design with varying step height and displacement, at a given voltage (2.5 V) and frequency (1 kHz). Finally, in order to validate the numerical simulation, the optimal microchip was fabricated using a combination of photolithography, electroplating, and a polydimethylsiloxane microchannel. Our results indicate that our micropump is capable of generating a pressure, velocity, and flow rate of 74.2 Pa, 1.76 mm/s, and 14.8 µl/min, respectively. This result reveals that our proposed geometry outperforms the state-of-the-art micropumps previously reported in the literature by improving the fluid velocity by 32%, with 80% less electrodes per unit length, and whereas the channel length is ∼80% shorter.

Density-Potential Functional Theory of Electrochemical Double Layers: Calibration on the Ag(111)-KPF6 System and Parametric Analysis

The density-potential functional theory (DPFT) of electrochemical double layer (EDL) is upgraded by adopting (generalized) gradient approximations for kinetic, exchange, and correlation functionals of metal electrons. A new numerical scheme that is more stable and converges faster is proposed to solve the DPFT model. The DPFT model is calibrated with existing differential double-layer capacitance (C_dl) data of the EDL at Ag(111)-KPF₆ aqueous interface at five concentrations at room temperature. Metal electronic effects are essential to explain why the two peaks of the camel-shaped C_dl curves are almost symmetric in spite of the size difference of the hydrated cations and anions. A systematic parametric analysis is then conducted in terms of key EDL properties, including the potential of zero charge and the differential capacitance. The parametric analysis, on the one hand, elucidates how quantum mechanical behaviors of metal electrons as well as interactions between metal electrons and the electrolyte solution impact the EDL properties and, on the other hand, identifies key parameters of the DPFT model, which should be calibrated using first-principles calculations and/or advanced experiments in the future.

Electro-Orientation and Electro-Rotation of Metallodielectric Janus Particles

The electro-rotation (EROT) and electro-orientation (EOR) behavior of metallodielectric spherical Janus particles (JP) are studied analytically and verified experimentally. This stands in contrast to previous either heuristic or numerically computed models of JP dipoles. First, we obtain frequency-dependent analytic expressions for the corresponding dipole terms for a JP composed of dielectric and metallic hemispheres by applying the "standard" (weak-field) electrokinetic model and using a Fourier-Legendre collocation method for solving two sets of linear equations. EROT and EOR spectra, describing the variation of the JP's angular velocity on the forcing frequency of a rotating and nonrotating spatially uniform electric field, respectively, are explicitly determined and compared against experiments (different JP sizes and solution conductivities). While a favorably good agreement between theory and experimental measurements was found for the frequency response (∼8% difference), there is still a factor of ∼2 difference in the amplitude of the angular velocity, which necessitates further future improvements to the model.

Gating with Charge Inversion to Control Ionic Transport in Nanopores

Multivalent ions modify the properties of the solid/liquid interfaces, and in some cases, they can even invert the polarity of surface charge, having large consequences for separation processes based on charge. The so-called charge inversion is observed as a switch from negative surface charge in monovalent salts, e.g., KCl, to effective positive surface charge in multivalent salts that is possible through a strong accumulation and correlation of the multivalent ions at the surface. It is not known yet, however, whether the density of the positive charge induced by charge inversion depends on the pore opening diameter, especially in extreme nanoconfinement. Here, we probe how the effective surface charge induced by charge inversion is influenced by the pore opening diameter using a series of nanopores with an opening between 4 and 25 nm placed in contact with trivalent chromium ions in tris(ethylenediamine)chromium(III) sulfate at different concentrations. Our results suggest that the effective positive charge density can indeed be modified by nanoconfinement to the extent that is dependent on the pore diameter, salt concentration, and applied voltage. In addition, the correlated ions can increase the transmembrane current in nanopores with an opening diameter down to 10 nm and cause a significant blockage of the current for narrower pores. The results provide guidelines to control ionic transport at the nanoscale with multivalent ions and demonstrate that in the same experimental conditions, differently sized pores in the same porous material can feature different surface charge density and possibly ion selectivity.

Ion and Water Transport in Ion-Exchange Membranes for Power Generation Systems: Guidelines for Modeling

Artificial ion-exchange and other charged membranes, such as biomembranes, are self-organizing nanomaterials built from macromolecules. The interactions of fragments of macromolecules results in phase separation and the formation of ion-conducting channels. The properties conditioned by the structure of charged membranes determine their application in separation processes (water treatment, electrolyte concentration, food industry and others), energy (reverse electrodialysis, fuel cells and others), and chlore-alkali production and others. The purpose of this review is to provide guidelines for modeling the transport of ions and water in charged membranes, as well as to describe the latest advances in this field with a focus on power generation systems. We briefly describe the main structural elements of charged membranes which determine their ion and water transport characteristics. The main governing equations and the most commonly used theories and assumptions are presented and analyzed. The known models are classified and then described based on the information about the equations and the assumptions they are based on. Most attention is paid to the models which have the greatest impact and are most frequently used in the literature. Among them, we focus on recent models developed for proton-exchange membranes used in fuel cells and for membranes applied in reverse electrodialysis.

Simulation Study of Electric Double-Layer Capacitance of Ordered Carbon Electrodes

Supercapacitors are electrochemical energy storage devices having high capacitance, high power density, long cycle life, low cost, easy maintenance, and negligible environmental pollution. The formation of an electric double layer at the electrode-electrolyte interface is mostly responsible for supercapacitors' energy storage. The simulation study of equilibrium electric double-layer capacitance (EDLC) in 3D arranged mesoporous carbon electrodes with a simple cubic morphology and interdigitated electrodes has been done. Continuum theory has been utilized to study the underlying processes involved in EDLC. Interfacial polarization and ion crowding depend on the electrode's critical thickness. Porosity increases the capacitance due to the increase in the electrode surface area. The diffuse-layer specific capacitance of ordered mesoporous carbon electrodes in a (C₂H₅)₄NBF₄/propylene carbonate organic electrolyte is in the range of 3.2-13.3 μF cm^-2, varying according to the electrode thickness. The Stern-layer specific capacitance is 167.6 μF cm^-2, and total equilibrium EDLC is in the range of 3.1-12.3 μF cm^-2. The effect of the electric field at the electrode-electrolyte interface on reducing electrolyte permittivity has also been discussed. The EDLC of carbonized interdigitated electrodes is analyzed in a 6 M KOH electrolyte. The diffuse-layer specific capacitance ranges from 118.7 to 352.0 μF cm^-2 depending on the width of the interdigitated electrodes. The Stern-layer specific capacitance is 91.2 μF cm^-2, and the total EDLC value is 51.6-72.4 μF cm^-2. The modeling and simulation approach can be applied to different mesoporous electrodes by varying the supercapacitor component's parameters and geometry.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Gelation, Clustering and Crowding in the Electrical Double Layer of Ionic Liquids

Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew et al. developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible Cayley tree clusters and a percolating ionic network (gel). Here we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a crowding regime dominated by free ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition.

Polar liquids at charged interfaces: A dipolar shell theory

The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.

The role of particle-electrode wall interactions in mobility of active Janus particles driven by electric fields

HYPOTHESIS

The interaction of active particles with walls can explain discrepancies between experiments and theory derived for particles in the bulk. For an electric field driven metallodielectric Janus particle (JP) adjacent to an electrode, interaction between the asymmetric particle and the partially screened electrode yields a net electrostatic force - termed self-dielectrophoresis (sDEP) - that competes with induced-charge electrophoresis (ICEP) to reverse particle direction.

EXPERIMENTS

The potential contribution of hydrodynamic flow to the reversal is evaluated by visualizing flow around a translating particle via micro-particle image velocimetry and chemically suppressing ICEP with poly(l-lysine)-g-poly(ethylene glycol) (PLL-PEG). Mobility of Polystyrene-Gold JPs is measured in KCl electrolytes of varying concentration and with a capacitive SiO₂ coating at the metallic JP surface or electrode. Results are compared with theory and numerical simulations accounting for electrode screening.

FINDINGS

PLL-PEG predominantly suppresses low-frequency mobility where propulsive electro-hydrodynamic jetting is observed; supporting the hypothesis of an electrostatic driving force at high frequencies. Simulations and theory show the magnitude, direction and frequency dispersion of JP mobility are obtained by superposition of ICEP and sDEP using the JP height and capacitance as fitting parameters. Wall proximity enhances ICEP and sDEP and manifests a secondary ICEP charge relaxation time dominating in the contact limit.

Stability of Two-Dimensional Liquid Foams under Externally Applied Electric Fields

Liquid foams are highly complex systems consisting of gas bubbles trapped within a solution of surfactant. Electroosmotic effects may be employed to induce fluid flows within the foam structure and impact its stability. The impact of external electric fields on the stability of a horizontally oriented monolayer of foam (2D foam) composed of anionic, cationic, non-ionic, and zwitterionic surfactants was investigated, probing the effects of changing the gas-liquid and solid-liquid interfaces. Time-lapse recordings were analyzed to investigate the evolution of foam over time subject to varying electric field strengths. Numerical simulations of electroosmotic flow of the same system were performed using the finite element method. Foam stability was affected by the presence of an external electric field in all cases and depended on the surfactant type, strength of the electric field, and the solid material used to construct the foam cell. For the myristyltrimethylammonium bromide (MTAB) foam in a glass cell, the time to collapse 50% of the foam was increased from ∼25 min under no electric field to ∼85 min under an electric field strength of 2000 V/m. In comparison, all other surfactants trialed exhibited faster foam collapse under external electric fields. Numerical simulations provided insight as to how different zeta potentials at the gas-liquid and solid-liquid interfaces affect fluid flow in different elements of the foam structure under external electric fields, leading to a more stable or unstable foam.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.