Dynamics of extended space charge in concentration polarization

Investigation of Operational Parameters for Nanoelectrokinetic Purification and Preconcentration

This work reports on experimental investigations into the operational parameters of nanoelectrokinetic purification and preconcentration, especially utilizing on ion concentration polarization (ICP). ICP as a nanoscale electrokinetic phenomenon has demonstrated promising advances in various fields utilizing an ion depletion zone (IDZ) with a steep electric field gradient inside the ICP layer. However, the inevitable electrokinetic instability occurring within the IDZ has posed a challenge in operating the ICP system stably. To address the need for a stable and efficient ICP operation in various devices and applications, we propose an operational strategy along with conducted research to determine optimal operating ranges. In order to investigate the operational parameters, a unit voltage (VTH) is introduced as the threshold for initiating ICP. We examined the applicability of VTH across various operating ranges to ensure its effectiveness and versatility. In ICP purification, we categorize three modes (steady, burst, and unsteady) based on IDZ expansion and stability under varying VTH and flow rate conditions, presenting optimal operational conditions that minimize the voltage margin. In ICP preconcentration, a systematic investigation is conducted to observe the influence of background electrolyte concentration and voltage conditions on preconcentration efficiency, offering insights into the correlation between preconcentration factor, electrical conditions, and preconcentration time. Therefore, this research would contribute to the practical understanding of nanoelectrokinetics, providing insight into experimental designs. These findings are expected to offer valuable guidance to researchers aiming to utilize ICP's potential across a spectrum of applications, from purification to preconcentration, in the realm of micro/nanofluidic systems.

Nanofluidic Ionic Memristors

Living organisms use ions and small molecules as information carriers to communicate with the external environment at ultralow power consumption. Inspired by biological systems, artificial ion-based devices have emerged in recent years to try to realize efficient information-processing paradigms. Nanofluidic ionic memristors, memory resistors based on confined fluidic systems whose internal ionic conductance states depend on the historical voltage, have attracted broad attention and are used as neuromorphic devices for computing. Despite their high exposure, nanofluidic ionic memristors are still in the initial stage. Therefore, systematic guidance for developing and reasonably designing ionic memristors is necessary. This review systematically summarizes the history, mechanisms, and potential applications of nanofluidic ionic memristors. The essential challenges in the field and the outlook for the future potential applications of nanofluidic ionic memristors are also discussed.

Charging Dynamics of Overlapping Double Layers in a Cylindrical Nanopore

The charging of electrical double layers inside a cylindrical pore has applications to supercapacitors, batteries, desalination and biosensors. The charging dynamics in the limit of thin double layers, i.e., when the double layer thickness is much smaller than the pore radius, is commonly described using an effective RC transmission line circuit. Here, we perform direct numerical simulations (DNS) of the Poisson-Nernst-Planck equations to study the double layer charging for the scenario of overlapping double layers, i.e., when the double layer thickness is comparable to the pore radius. We develop an analytical model that accurately predicts the results of DNS. Also, we construct a modified effective circuit for the overlapping double layer limit, and find that the modified circuit is identical to the RC transmission line but with different values and physical interpretation of the capacitive and resistive elements. In particular, the effective surface potential is reduced, the capacitor represents a volumetric current source, and the charging timescale is weakly dependent on the ratio of the pore radius and the double layer thickness.

Dynamic analysis of the extended space charge layer using chronopotentiometric measurements

In this paper, we experimentally verified the length (LESC) and the concentration (cESC) of the extended space charge (ESC) layer in front of the electrical double layer (EDL) using the chronopotentiometric measurement and the equivalent circuit model analysis. From the experimentation, the coupled-response of the EDL and the ESC layer was discriminated from the contribution of electro-osmotic flow (EOF). In addition, we derived the potential differences across the ESC (VESC) layer using the circuit model of the ICP layer under rigorous consideration of ESC and EDL. As a result, we obtained that VESC was linearly proportional to the square of the applied current (iapplied). Hence, LESC and cESC were quantitatively provided, where LESC is linear to the iapplied and cESC is constant regardless of iapplied. Thus, this experimentation could not only clarify an essential ICP theory but also guide in ESC-based applications.

Direct Visualization of Perm-Selective Ion Transportation

Perm-selective ion transportation in a nanoscale structure such as nanochannel, nanoporous membrane or nanojunction has been extensively studied with aids of nanofabrication technology for a decade. While theoretical and experimental advances pushed the phenomenon to seminal innovative applications, its basic observation has relied only on an indirect analysis such as current-voltage relation or fluorescent imaging adjacent to the nanostructures. Here we experimentally, for the first time, demonstrated a direct visualization of perm-selective ion transportation through the nanoscale space using an ionic plasma generation. A micro/nanofluidic device was employed for a micro bubble formation, plasma negation and penetration of the plasma along the nanojunction. The direct observation provided a keen evidence of perm-selectivity, i.e. allowing cationic species and rejecting anionic species. Furthermore, we can capture the plasma of lithium, which has lower mobility than sodium in aqueous state, passed the nanojunction faster than sodium due to the absence of hydrated shells around lithium. This simple, but essential visualization technique would be effective means not only for advancing the fundamental nanoscale electrokinetic study as well as interfacial ion transportation between liquid and plasma but also for providing the insight of new innovative engineering applications.

Transient response of nonideal ion-selective microchannel-nanochannel devices

We report evidence of variation in ion selectivity of a fabricated microchannel-nanochannel device resulting in the appearance of a distinct local maximum in the overlimiting chronopotentiometric response. In this system consisting of shallow microchannels joined by a nanochannel, viscous shear at the microchannel walls suppresses the electro-osmotic instability and prevents any associated contribution to the nonmonotonic response. Thus, this response is primarily electrodiffusive. Numerical simulations indicate that concentration polarization develops not only within the microchannel but also within the nanochannel itself, with a local voltage maximum in the chronopotentiometric response correlated with interfacial depletion and having the classic i^{-2} Sands time dependence. Furthermore, the occurrence of the local maxima is correlated with the change in selectivity due to internal concentration polarization. Understanding the transient nonideal permselective response is essential for obtaining fundamental insight and for optimizing efficient operation of practical fabricated nanofluidic and membrane devices.

Confined Electroconvective Vortices at Structured Ion Exchange Membranes

In this paper, we investigate electroconvective ion transport at cation exchange membranes with different geometry square-wave structures (line undulations) experimentally and numerically. Electroconvective microvortices are induced by strong concentration polarization once a threshold potential difference is applied. The applied potential required to start and sustain electroconvection is strongly affected by the geometry of the membrane. A reduction in the resistance of approximately 50% can be obtained when the structure size is similar to the mixing layer (ML) thickness, resulting in confined vortices with less lateral motion compared to the case of flat membranes. From electrical, flow, and concentration measurements, ion migration, advection, and diffusion are quantified, respectively. Advection and migration are dominant in the vortex ML, whereas diffusion and migration are dominant in the stagnant diffusion layer. Numerical simulations, based on Poisson-Nernst-Planck and Navier-Stokes equations, show similar ion transport and flow characteristics, highlighting the importance of membrane topology on the resulting electrokinetic and electrohydrodynamic behavior.

Transport-Induced Inversion of Screening Ionic Charges in Nanochannels

This work reveals a counterintuitive but basic process of ionic screening in nanofluidic channels. Steady-state numerical simulations and mathematical analysis show that, under significant longitudinal ionic transport, the screening ionic charges can be locally inverted in the channels: their charge sign becomes the same as that of the channel surface charges. The process is identified to originate from the coupling of ionic electro-diffusion transport and junction two-dimensional electrostatics. This finding may expand our understanding of ionic screening and electrical double layers in nanochannels. Furthermore, the charge inversion process results in a body-force torque on channel fluids, which is a possible mechanism for vortex generation in the channels and their nonlinear current-voltage characteristics.

Non-Negligible Diffusio-Osmosis Inside an Ion Concentration Polarization Layer

The first experimental and theoretical evidence was provided for the non-negligible role of a diffusio-osmosis in the ion concentration polarization (ICP) layer, which had been reported to be in a high Peclet number regime. Under the assumption that the hydrated shells of cations were stripped out with the amplified electric field inside the ICP layer, its concentration profile possessed a steep concentration gradient at the stripped location. Since the concentration gradient drove a strong diffusio-osmosis, the combination of electro-osmotic and diffusio-osmotic slip velocity had a form of an anomalous nonmonotonic function with both a single- and multiple-cationic solution. A direct measurement of electrolytic concentrations around the layer quantitatively validated our new investigations. This non-negligible diffusio-osmotic contribution in a micro- and nanofluidic platform or porous medium would be essential for clarifying the fundamental insight of nanoscale electrokinetics as well as guiding the engineering of ICP-based electrochemical systems.

Teorell instability in concentration polarization

We investigate the development of electro-osmotic (Teorell) oscillations at a weakly charged microporous membrane without a preimposed transmembrane electrolyte concentration drop. This drop, necessary for the occurrence of oscillations, develops spontaneously as a result of concentration polarization in the solution layers adjacent to the membrane. A three-layer model comprising a membrane flanked by two diffusion layers is proposed and analyzed for galvano- and potentiostatic regimes of operation.

Extended space charge near nonideally selective membranes and nanochannels

We demonstrate the role of selectivity variation in the structure of the nonequilibrium extended space charge using one-dimensional analytic and two-dimensional numerical Poisson-Nernst-Planck models for the electro-diffusive transport of a symmetric electrolyte. This provides a deeper understanding of the underlying mechanism behind a previously observed maximum in the resistance-voltage curve for a shallow micro-nanochannel interface device [Schiffbauer, Liel, Leibowitz, Park, and Yossifon, arXiv:1409.4548, Phys. Rev. E (to be published)]. The current study helps to establish a connection between parameters such as the geometry and nanochannel surface charge and the control of selectivity and resistance in the overlimiting current regime.

Time-dependent ion transport in heterogeneous permselective systems

The current study extends previous analytical and numerical solutions of chronopotentiometric response of one-dimensional systems consisting of three layers to the more realistic two-dimensional (2D) heterogeneous ion-permselective medium. An analytical solution for the transient concentration-polarization problem, under the local electroneutrality approximation and assumption of ideal permselectivity, was obtained using the Laplace transform and separation of variables technique. Then the 2D electric potential was obtained numerically and was compared to the full Poisson-Nernst-Planck solution. It was then shown that the resultant voltage drop across the system varies between the initial Ohmic response and that of the steady state accounting for concentration polarization. Also, the field-focusing effect in a 2D system is shown to result in a faster depletion of ions at the permselective interface.

Equilibrium electroconvective instability

Since its prediction 15 years ago, hydrodynamic instability in concentration polarization at a charge-selective interface has been attributed to nonequilibrium electro-osmosis related to the extended space charge which develops at the limiting current. This attribution had a double basis. On the one hand, it has been recognized that neither equilibrium electro-osmosis nor bulk electroconvection can yield instability for a perfectly charge-selective solid. On the other hand, it has been shown that nonequilibrium electro-osmosis can. The first theoretical studies in which electro-osmotic instability was predicted and analyzed employed the assumption of perfect charge selectivity for the sake of simplicity and so did the subsequent studies of various time-dependent and nonlinear features of electro-osmotic instability. In this Letter, we show that relaxing the assumption of perfect charge selectivity (tantamount to fixing the electrochemical potential of counterions in the solid) allows for the equilibrium electroconvective instability. In addition, we suggest a simple experimental test for determining the true, either equilibrium or nonequilibrium, origin of instability in concentration polarization.

Direct numerical simulation of electroconvective instability and hysteretic current-voltage response of a permselective membrane

We present a systematic, multiscale, fully detailed numerical modeling for dynamics of fluid flow and ion transport covering Ohmic, limiting, and overlimiting current regimes in conductance of ion-selective membrane. By numerically solving the Poisson-Nernst-Planck-Navier-Stokes equations, it is demonstrated that the electroconvective instability, arising from the electric field acting upon the extended space charge layer, and the induced strong vortical fluid flow are the dominant factors of the overlimiting current in the planar membrane system. More importantly, at the transition between the limiting and the overlimiting current regimes, hysteresis of electric current is identified. The hysteresis demonstrates the important role of the electroconvective flow in enhancing of current in electrolyte systems with ion-selective membrane.

Extended space charge in concentration polarization

This paper is concerned with ionic currents from an electrolyte solution into a charge-selective solid, such as, an electrode, an ion-exchange membrane or an array of nano-channels in a micro-fluidic system, and the related viscous fluid flows on the length scales varying from nanometers to millimeters. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization--formation of solute concentration gradients under the passage of a DC current. A number of seemingly different phenomena occurring in that range, such as anomalous rectification in cathodic copper deposition from a copper sulfate solution, super-fast vortexes near an ion-exchange granule, overlimiting conductance in electrodialysis and the recently observed non-equilibrium electroosmotic instability, result from the formation of an additional extended space charge layer next to that of a classical electrical double layer at the solid/liquid interface. In this paper we review the peculiar features of the non-equilibrium electric double layer and extended space charge and the possibility of their direct probing by harmonic voltage/current perturbations through a linear and non-linear system's response, by the methods of electrical impedance spectroscopy and via the anomalous rectification effect. On the relevant microscopic scales the ionic transport in the direction normal to the interface is dominated by drift-diffusion; hence, the extended space charge related viscous flows remain beyond the scope of this paper.