Eliminating the limiting-current phenomenon by geometric field focusing into nanopores and nanoslots

Ion transport through short nanopores modulated by charged exterior surfaces

Short nanopores find extensive applications, capitalizing on their high throughput and detection resolution. Ionic behaviors through long nanopores are mainly determined by charged inner-pore walls. When pore lengths decrease to sub-200 nm, charged exterior surfaces provide considerable modulation to ion current. We find that the charge status of inner-pore walls affects the modulation of ion current from charged exterior surfaces. For 50-nm-long nanopores with neutral inner-pore walls, the charged exterior surfaces on the voltage (surfaceV) and ground (surfaceG) sides enhance and inhibit the ion transport by forming ion enrichment and depletion zones inside nanopores, respectively. For nanopores with both charged inner-pore and exterior surfaces, continuous electric double layers enhance the ion transport through nanopores significantly. The charged surfaceV results in higher ion current by simultaneously weakening the ion depletion at pore entrances and enhancing the intra-pore ion enrichment. The charged surfaceG expedites the exit of ions from nanopores, resulting in a decrease in ion enrichment at pore exits. Through adjustment in the width of charged-ring regions near pore boundaries, the effective charged width of the charged exterior is explored at ∼20 nm. Our results may provide a theoretical guide for further optimizing the performance of nanopore-based applications, such as seawater desalination, biosensing, and osmotic energy conversion.

Ion Current Rectification and Long-Range Interference in Conical Silicon Micropores

Fluidic devices exhibiting ion current rectification (ICR), or ionic diodes, are of broad interest for applications including desalination, energy harvesting, and sensing, among others. For such applications a large conductance is desirable, which can be achieved by simultaneously using thin membranes and wide pores. In this paper we demonstrate ICR in micrometer sized conical channels in a thin silicon membrane with pore diameters comparable to the membrane thickness but both much larger than the electrolyte screening length. We show that for these pores the entrance resistance is key not only to Ohmic conductance around 0 V but also for understanding ICR, both of which we measure experimentally and capture within a single analytic theoretical framework. The only fit parameter in this theory is the membrane surface potential, for which we find that it is voltage dependent and its value is excessively large compared to the literature. From this we infer that surface charge outside the pore strongly contributes to the observed Ohmic conductance and rectification by a different extent. We experimentally verify this hypothesis in a small array of pores and find that ICR vanishes due to pore-pore interactions mediated through the membrane surface, while Ohmic conductance around 0 V remains unaffected. We find that the pore-pore interaction for ICR is set by a long-ranged decay of the concentration which explains the surprising finding that the ICR vanishes for even a sparsely populated array with a pore-pore spacing as large as 7 μm.

Overlimiting current near a nanochannel a new insight using molecular dynamics simulations

In this paper, we report for the first time overlimiting current near a nanochannel using all-atom molecular dynamics (MD) simulations. Here, the simulated system consists of a silicon nitride nanochannel integrated with two reservoirs. The reservoirs are filled with [Formula: see text] potassium chloride (KCl) solution. A total of [Formula: see text] million atoms are simulated with a total simulation time of [Formula: see text] over [Formula: see text] 30000 CPU hours using 128 core processors (Intel(R) E5-2670 2.6 GHz Processor). The origin of overlimiting current is found to be due to an increase in chloride ([Formula: see text]) ion concentration inside the nanochannel leading to an increase in ionic conductivity. Such effects are seen due to charge redistribution and focusing of the electric field near the interface of the nanochannel and source reservoir. Also, from the MD simulations, we observe that the earlier theoretical and experimental postulations of strong convective vortices resulting in overlimiting current are not the true origin for overlimiting current. Our study may open up new theories for the mechanism of overlimiting current near the nanochannel interconnect devices.

Tutorial review: Enrichment and separation of neutral and charged species by ion concentration polarization focusing

Ion concentration polarization focusing (ICPF) is an electrokinetic technique, in which analytes are enriched and separated along a localized electric field gradient in the presence of a counter flow. This field gradient is generated by depletion of ions of the background electrolyte at an ion permselective junction. In this tutorial review, we summarize the fundamental principles and experimental parameters that govern selective ion transport and the stability of the enriched analyte plug. We also examine faradaic ICP (fICP), in which local ion concentration is modulated via electrochemical reactions as an attractive alternative to ICP that achieves similar performance with a decrease in both power consumption and Joule heating. The tutorial covers important challenges to the broad application of ICPF including undesired pH gradients, low volumetric throughput, samples that induce biofouling or are highly conductive, and limited approaches to on- or off-chip analysis. Recent developments in the field that seek to address these challenges are reviewed along with new approaches to maximize enrichment, focus uncharged analytes, and achieve enrichment and separation in water-in-oil droplets. For new practitioners, we discuss practical aspects of ICPF, such as strategies for device design and fabrication and the relative advantages of several types of ion selective junctions and electrodes. Lastly, we summarize tips and tricks for tackling common experimental challenges in ICPF.

Elimination of pseudo-negative conductance by coercive steady state in perm-selective ion transportation

Ion concentration polarization (ICP) has drawn unprecedented attention due to its new underlying physics and engineering applications such as biomolecular preconcentrator and electrofluidic desalination. Typically, the current-voltage characteristic of ICP has three distinctive regimes with a positive slope in all regimes, but an unintentional negative slope ("overshoot current") was often observed in the Ohmic/limiting regime. This phenomenon impeded an exact estimation of electrokinetic properties of the ICP platform. Therefore, in this work, we eliminated overshoot current by limiting the length of the diffuse layer using a coercive injection of a fresh electrolyte solution. Both the visualization of ICP layer propagation and the measurement of current-voltage characteristics verifying the time for reaching the steady state within an effective length of a microchannel played a critical role. The most relevant parameter was shown to be the diffusion relaxation time which was directly correlated with the sweep rate of an external voltage. Using this new measurement platform, one can significantly reduce the time and labor for the electrokinetic studies and applications based on them.

Ion concentration polarization (ICP) of proteins at silicon micropillar nanogaps

Fast detection of low-abundance protein remains a challenge because detection speed is limited by analyte transport to the detection site of a biosensor. In this paper, we demonstrate a scalable fabrication process for producing vertical nanogaps between micropillars which enable ion concentration polarization (ICP) enrichment for fast analyte detection. Compared to horizontal nanochannels, massively paralleled vertical nanogaps not only provide comparable electrokinetics, but also significantly reduce fluid resistance, enabling microbead-based assays. The channels on the device are straightforward to fabricate and scalable using conventional lithography tools. The device is capable of enriching protein molecules by >1000 fold in 10 min. We demonstrate fast detection of IL6 down to 7.4 pg/ml with only a 10 min enrichment period followed by a 5 min incubation. This is a 162-fold enhancement in sensitivity compared to that without enrichment. Our results demonstrate the possibility of using silicon/silica based vertical nanogaps to mimic the function of polymer membranes for the purpose of protein enrichment.

Electrothermal based active control of ion transport in a microfluidic device with an ion-permselective membrane

The ability to induce regions of high and low ionic concentrations adjacent to a permselective membrane or a nanochannel subject to an externally applied electric field (a phenomenon termed concentration-polarization) has been used for a broad spectrum of applications ranging from on-chip desalination, bacteria filtration to biomolecule preconcentration. But these applications have been limited by the ability to control the length of the diffusion layer that is commonly indirectly prescribed by the fixed geometric and surface properties of a nanofluidic system. Here, we demonstrate that the depletion layer can be dynamically varied by inducing controlled electrothermal flow driven by the interaction of temperature gradients with the applied electric field. To this end, a series of microscale heaters, which can be individually activated on demand are embedded at the bottom of the microchannel and the relationship between their activation and ionic concentration is characterized. Such spatio-temporal control of the diffusion layer can be used to enhance on-chip electro-dialysis by producing shorter depletion layers, to dynamically reduce the microchannel resistance relative to that of the nanochannel for nanochannel based (bio)sensing, to generate current rectification reminiscent of a diode like behavior and control the location of the preconcentrated plug of analytes or the interface of brine and desalted streams.

A Cationic Diode Based on Asymmetric Nafion Film Deposits

A thin film of Nafion, of approximately 5 μm thickness, asymmetrically deposited onto a 6 μm thick film of poly(ethylene terephthalate) (PET) fabricated with a 5, 10, 20, or 40 μm microhole, is shown to exhibit prominent ionic diode behavior involving cation charge carrier ("cationic diode"). The phenomenon is characterized via voltammetric, chronoamperometric, and impedance methods. Phenomenologically, current rectification effects are comparable to those observed in nanocone devices where space-charge layer effects dominate. However, for microhole diodes a resistive, a limiting, and an overlimiting potential domain can be identified and concentration polarization in solution is shown to dominate in the closed state.

Influence of temperature gradients on charge transport in asymmetric nanochannels

Imposing a temperature gradient over a charge-selective asymmetric nanochannel enhances the selectivity, total current and rectification of the nanochannel.

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.

Observation and experimental investigation of confinement effects on ion transport and electrokinetic flows at the microscale

Electrokinetic effects adjacent to charge-selective interfaces (CSI) have been experimentally investigated in microfluidic platforms in order to gain understanding on underlying phenomena of ion transport at elevated applied voltages. We experimentally investigate the influence of geometry and multiple array densities of the CSI on concentration and flow profiles in a microfluidic set-up using nanochannels as the CSI. Particle tracking obtained under chronoamperometric measurements show the development of vortices in the microchannel adjacent to the nanochannels. We found that the direction of the electric field and the potential drop inside the microchannel has a large influence on the ion transport through the interface, for example by inducing immediate wall electroosmotic flow. In microfluidic devices, the electric field may not be directed normal to the interface, which can result in an inefficient use of the CSI. Multiple vortices are observed adjacent to the CSI, growing in size and velocity as a function of time and dependent on their location in the microfluidic device. Local velocities inside the vortices are measured to be more than 1.5 mm/s. Vortex speed, as well as flow speed in the channel, are dependent on the geometry of the CSI and the distance from the electrode.

Effect of field-focusing and ion selectivity on the extended space charge developed at the microchannel-nanochannel interface

We present results demonstrating the effect of varying microchannel depth and bulk conductivity on the space charge-mediated transition between classical, diffusion-limited current and over-limiting current in microchannel-nanochannel devices. The extended space charge layer develops at the depleted microchannel-nanochannel entrance when the limiting current is exceeded and is correlated with a distinctive maximum in the dc resistance. This maximum is shown to be affected by the microchannel depth, via field-focusing, and solution conductivity. In particular, we observe that upon their increase, the maximum becomes flatter and shifts to higher voltages.

Induced-charge electrokinetics, bipolar current, and concentration polarization in a microchannel-Nafion-membrane system

The presence of a floating electrode array located within the depletion layer formed due to concentration polarization across a microchannel-membrane interface device may produce not only induced-charge electro-osmosis (ICEO) but also bipolar current resulting from the induced Faradaic reaction. It has been shown that there exists an optimal thickness of a thin dielectric coating that is sufficient to suppress bipolar currents but still enables ICEO vortices that stir the depletion layer, thereby affecting the system's current-voltage response. In addition, the use of alternating-current electro-osmosis by activating electrodes results in further enhancement of the fluid stirring and opens new routes for on-demand spatiotemporal control of the depletion layer length.

Numerical simulation of electrochemical desalination

We present an effective numerical approach to simulate electrochemically mediated desalination of seawater. This new membraneless, energy efficient desalination method relies on the oxidation of chloride ions, which generates an ion depletion zone and local electric field gradient near the junction of a microchannel branch to redirect sea salt into the brine stream, consequently producing desalted water. The proposed numerical model is based on resolution of the 3D coupled Navier-Stokes, Nernst-Planck, and Poisson equations at non-uniform spatial grids. The model is implemented as a parallel code and can be employed to simulate mass-charge transport coupled with surface or volume reactions in 3D systems showing an arbitrarily complex geometrical configuration.

Future microfluidic and nanofluidic modular platforms for nucleic acid liquid biopsy in precision medicine

Nucleic acid biomarkers have enormous potential in non-invasive diagnostics and disease management. In medical research and in the near future in the clinics, there is a great demand for accurate miRNA, mRNA, and ctDNA identification and profiling. They may lead to screening of early stage cancer that is not detectable by tissue biopsy or imaging. Moreover, because their cost is low and they are non-invasive, they can become a regular screening test during annual checkups or allow a dynamic treatment program that adjusts its drug and dosage frequently. We briefly review a few existing viral and endogenous RNA assays that have been approved by the Federal Drug Administration. These tests are based on the main nucleic acid detection technologies, namely, quantitative reverse transcription polymerase chain reaction (PCR), microarrays, and next-generation sequencing. Several of the challenges that these three technologies still face regarding the quantitative measurement of a panel of nucleic acids are outlined. Finally, we review a cluster of microfluidic technologies from our group with potential for point-of-care nucleic acid quantification without nucleic acid amplification, designed to overcome specific limitations of current technologies. We suggest that integration of these technologies in a modular design can offer a low-cost, robust, and yet sensitive/selective platform for a variety of precision medicine applications.

Interplay between Nanochannel and Microchannel Resistances

Current nanochannel system paradigm commonly neglects the role of the interfacing microchannels and assumes that the ohmic electrical response of a microchannel-nanochannel system is solely determined by the geometric properties of the nanochannel. In this work, we demonstrate that the overall response is determined by the interplay between the nanochannel resistance and various microchannel attributed resistances. Our experiments confirm a recent theoretical prediction that in contrast to what was previously assumed at very low concentrations the role of the interfacing microchannels on the overall resistance becomes increasingly important. We argue that the current nanochannel-dominated conductance paradigm can be replaced with a more correct and intuitive microchannel-nanochannel-resistance-model-based paradigm.

Capillarity ion concentration polarization for spontaneous biomolecular preconcentration mechanism

Ionic hydrogel-based ion concentration polarization devices have been demonstrated as platforms to study nanoscale ion transport and to develop engineering applications, such as protein preconcentration and ionic diodes/transistors. Using a microfluidic system composed of a perm-selective hydrogel, we demonstrated a micro/nanofluidic device for the preconcentration of biological samples using a new class of ion concentration polarization mechanism called "capillarity ion concentration polarization" (CICP). Instead of an external electrical voltage source, the capillary force of the perm-selective hydrogel spontaneously generated an ion depletion zone in a microfluidic channel by selectively absorbing counter-ions in a sample solution. We demonstrated a reasonable preconcentration factor (∼100-fold/min) using the CICP device. Although the efficiency was lower than that of conventional electrokinetic ICP operation due to the absence of a drift ion migration, this mechanism was free from the undesirable instability caused by a local amplified electric field inside the ion depletion zone so that the mechanism should be suitable especially for an application where the contents were electrically sensitive. Therefore, this simple system would provide a point-of-care diagnostic device for which the sample volume is limited and a simplified sample handling is demanded.

Asymmetry-induced electric current rectification in permselective systems

For a symmetric ion permselective system, in terms of geometry and bulk concentrations, the system response is also symmetric under opposite electric field polarity. In this work we derive an analytical solution for the concentration distribution, electric potential, and current-voltage response for a four-layered system comprised of two microchambers connected by two permselective regions of varying properties. It is shown that any additional asymmetry in the system, in terms of the geometry, bulk concentration, or surface charge property of the permselective regions, results in current rectification. Our work is divided into two parts: when both permselective regions have the same surface charge sign and the case of opposite signs. For the same sign case we are able to show that the system behaves as a dialytic battery while accounting for field-focusing effects. For the case of opposite signs (i.e., bipolar membrane), our system exhibits the behavior of a bipolar diode where the magnitude of the rectification can be of order 10^{2}-10^{3}.

Probing space charge and resolving overlimiting current mechanisms at the microchannel-nanochannel interface

We present results demonstrating the space charge-mediated transition between classical, diffusion-limited current and surface-conduction dominant over-limiting current in a shallow microchannel-nanochannel device. The extended space charge layer develops at the depleted microchannel-nanochannel entrance at high current and is correlated with a distinctive maximum in the dc resistance. Experimental results for a shallow surface-conduction dominated system are compared with theoretical models, allowing estimates of the effective surface charge at high voltage to be obtained. In comparison to an equilibrium estimate of the surface charge obtained from electrochemical impedance spectroscopy, it is further observed that the effective surface charge appears to change under applied voltage.

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.

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

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

Leveraging electrokinetics for the active control of dendritic fullerene-1 release across a nanochannel membrane

General adoption of advanced treatment protocols such as chronotherapy will hinge on progress in drug delivery technologies that provide precise temporal control of therapeutic release. Such innovation is also crucial to future medicine approaches such as telemedicine. Here we present a nanofluidic membrane technology capable of achieving active and tunable control of molecular transport through nanofluidic channels. Control was achieved through application of an electric field between two platinum electrodes positioned on either surface of a 5.7 nm nanochannel membrane designed for zero-order drug delivery. Two electrode configurations were tested: laser-cut foils and electron beam deposited thin-films, configurations capable of operating at low voltage (≤1.5 V), and power (100 nW). Temporal, reproducible tuning and interruption of dendritic fullerene 1 (DF-1) transport was demonstrated over multi-day release experiments. Conductance tests showed limiting currents in the low applied potential range, implying ionic concentration polarization (ICP) at the interface between the membrane's micro- and nanochannels, even in concentrated solutions (≤1 M NaCl). The ability of this nanotechnology platform to facilitate controlled delivery of molecules and particles has broad applicability to next-generation therapeutics for numerous pathologies, including autoimmune diseases, circadian dysfunction, pain, and stress, among others.

An electrokinetic study on tunable 3D nanochannel networks constructed by spatially controlled nanoparticle assembly

This paper proposes a novel method to form ion-selective nanochannel networks between two microfluidic channels using geometrically controlled in situ self-assembled nanoparticles. We present a thorough experimental and theoretical analysis of nanoscale electrokinetics using the proposed microplatform. The nano-interstices between these assembled nanoparticles serve as the nanopores of ion-selective membranes with equivalent pore size. Its inherent characteristics (compared with the conventional one-dimensional nanochannels) are a high ionic flux and a low fluidic resistance because these nanopore clusters have a role as collective three-dimensional nanochannel networks, which result in a highly efficient performance beneficial for various applications. Another uniqueness of our system is that the electrical characteristics (such as ion transport through the nanochannel networks and the decrease in the limiting current region) can be tuned quantitatively or even optimized by changing the geometry of the microchannel and the pH condition of the working solution or by appropriately selecting the size and materials of the assembled nanoparticles. The correlation between these tuning parameters and nanoscale electrokinetics is deeply investigated with carefully designed experiments and their mechanism is thoroughly examined by a theoretical study. We expect that the presented system and methodology can contribute to opening new application fields, such as biomolecule separation/filtering/accumulation/analysis, bioelectronics, and energy generation.

Bridging the gap between an isolated nanochannel and a communicating multipore heterogeneous membrane

To bridge the gap between single and isolated pore systems to multipore systems, such as membranes and electrodes, we studied an array of nanochannels with varying interchannel spacing that controlled the degree of channel communication. Instead of treating them as individual channels connected in parallel or an assembly like a homogeneous membrane, this study resolves the pore-pore interaction. We found that increased channel isolation leads to current intensification, whereas at high voltages electroconvective effects control the degree of communication via suppression of the diffusion layer growth.

Mixed mosaic membranes prepared by layer-by-layer assembly for ionic separations

Charge mosaic membranes, which possess distinct cationic and anionic domains that traverse the membrane thickness, are capable of selectively separating dissolved salts from similarly sized neutral solutes. Here, the generation of charge mosaic membranes using facile layer-by-layer assembly methodologies is reported. Polymeric nanotubes with pore walls lined by positively charged polyethylenimine moieties or negatively charged poly(styrenesulfonate) moieties were prepared via layer-by-layer assembly using track-etched membranes as sacrificial templates. Subsequently, both types of nanotubes were deposited on a porous support in order to produce mixed mosaic membranes. Scanning electron microscopy demonstrates that the facile deposition techniques implemented result in nanotubes that are vertically aligned without overlap between adjacent elements. Furthermore, the nanotubes span the thickness of the mixed mosaic membranes. The effects of this unique nanostructure are reflected in the transport characteristics of the mixed mosaic membranes. The hydraulic permeability of the mixed mosaic membranes in piezodialysis operations was 8 L m(-2) h(-1) bar(-1). Importantly, solute rejection experiments demonstrate that the mixed mosaic membranes are more permeable to ionic solutes than similarly sized neutral molecules. In particular, negative rejection of sodium chloride is observed (i.e., the concentration of NaCl in the solution that permeates through a mixed mosaic membrane is higher than in the initial feed solution). These properties illustrate the ability of mixed mosaic membranes to permeate dissolved ions selectively without violating electroneutrality and suggest their utility in ionic separations.

Influence of electric-double-layer structure on the transient response of nanochannels

A fundamental Poisson-Nernst-Planck-Stokes model is presented for the impedance response of a long nanochannel under zero bias, capturing the effects of surface conduction and the coupling between transverse momentum and axial ion distribution in a manner reminiscent of Taylor dispersion. This is shown to result in a shift of the impedance frequency spectrum with bulk concentration similar to previous experimental observation [Schiffbauer, Liel, and Yossifon, Phys. Rev. E 89, 033017 (2014)]. It further predicts an additional downward shift in frequency with increasing viscosity. Finally, the introduction of a phenomenological model for the impedance response of a dynamic Stern layer in parallel with the diffuse layer transport model is shown to yield good agreement between theory and experiment. As a result, we are able to obtain an equivalent circuit model based on the fundamental model and proposed corrections.

Effect of geometry on concentration polarization in realistic heterogeneous permselective systems

This study extends previous analytical solutions of concentration polarization occurring solely in the depleted region, to the more realistic geometry consisting of a three-dimensional (3D) heterogeneous ion-permselective medium connecting two opposite microchambers (i.e., a three-layer system). Under the local electroneutrality approximation, the separation of variable methods is used to derive an analytical solution of the electrodiffusive problem for the two opposing asymmetric microchambers. The assumption of an ideal permselective medium allows for the analytic calculation of the 3D concentration and electric potential distributions as well as a current-voltage relation. It is shown that any asymmetry in the microchamber geometries will result in current rectification. Moreover, it is demonstrated that for non-negligible microchamber resistances, the conductance does not exhibit the expected saturation at low concentrations but instead shows a continuous decrease. The results are intended to facilitate a more direct comparison between theory and experiments, as now the voltage drop is across a realistic 3D and three-layer system.

Concentration dependence of nanochannel impedance and the determination of surface charge

In this paper, we demonstrate the variation of nanochannel impedance with bulk (reservoir) electrolyte concentration. The impedance of a nanochannel is shown to correspond to a characteristic deformed semicircular arc. The degree of deformation decreases with increasing concentration, and at a sufficiently low concentration the complex impedance saturates, becoming essentially independent of the reservoir concentration. This behavior is indicative of a surface-conduction dominant regime. Here we demonstrate that this effect extends beyond dc conductance and affects the ac response of the system as well, including both phase relationship and magnitude. The nanochannel resistance, obtained from low-voltage ac measurements, is then used to extract the nanochannel surface charge density. This is found to increase in magnitude with increasing electrolyte concentration.

Effects of three-dimensional geometric field focusing on concentration polarization in a heterogeneous permselective system

The current study extends previous two-dimensional (2D) analysis of concentration polarization to account for three-dimensional effects in realistic heterogeneous ion-permselective systems, e.g., microchamber-nanoslot devices. An analytical solution of the electrodiffusive problem, decoupled from electroconvection along with the local electroneutrality approximation, was obtained using the separation of variables technique. It is able to account for the previously neglected effects of microchamber and nanoslot heights on concentration polarization in terms of concentration profiles, limiting current, and current-voltage curves. The resultant heterogeneity in the third dimension adds to that already existing in the 2D in plane problem to further increase geometric field-focusing effects. As a result the currents no longer scale linearly with the nanoslot area, but rather depend on its shape and relative size compared to that of the nonconducting region (i.e., level of heterogeneity). This is turn leads to pronounced current density intensification with increased system heterogeneity found to be in qualitative agreement with previously reported experiments in which both microchamber and nanoslot geometries were varied.

Microfluidic systems with ion-selective membranes

When integrated into microfluidic chips, ion-selective nanoporous polymer and solid-state membranes can be used for on-chip pumping, pH actuation, analyte concentration, molecular separation, reactive mixing, and molecular sensing. They offer numerous functionalities and are hence superior to paper-based devices for point-of-care biochips, with only slightly more investment in fabrication and material costs required. In this review, we first discuss the fundamentals of several nonequilibrium ion current phenomena associated with ion-selective membranes, many of them revealed by studies with fabricated single nanochannels/nanopores. We then focus on how the plethora of phenomena has been applied for transport, separation, concentration, and detection of biomolecules on biochips.

Hydrodynamic flow in the vicinity of a nanopore induced by an applied voltage

Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. The results show the existence of concentration polarization layers on the surfaces of the membrane. The nonuniformity of the ionic distribution gives rise to an electric pressure that drives vortical motion in the fluid. There is also a net hydrodynamic flow through the nanopore due to an asymmetry induced by the membrane surface charge. The qualitative behavior is similar to that observed in a previous study using molecular dynamic simulations. The current-voltage characteristics show some nonlinear features but are not greatly affected by the hydrodynamic flow in the parameter regime studied. In the limit of thin Debye layers, the electric resistance of the system can be characterized using an equivalent circuit with lumped parameters. Generation of vorticity can be understood qualitatively from elementary considerations of the Maxwell stresses. However, the flow strength is a strongly nonlinear function of the applied field. Combination of electrophoretic and hydrodynamic effects can lead to ion selectivity in terms of valences and this could have some practical applications in separations.

Electrical impedance spectroscopy of microchannel-nanochannel interface devices

We report experimental verification of the depression of the slope in the Warburg branch of the electrochemical impedance spectrum using a fabricated microchannel-nanochannel device. This was previously theoretically predicted to occur with increasing dc bias voltage as a result of nanochannel electro-osmotic flow and provides an example of the influence of net fluid flow on electrokinetic transport. The dominant influence of nanochannel polarization in the kHz range of the impedance response is also demonstrated experimentally. This latter effect may be significant in both fundamental electrokinetics of micronanochannel devices as well as in practical molecular sensing applications.

Role of electro-osmosis in the impedance response of microchannel-nanochannel interfaces

The influence of net fluid flow on the low-frequency ac response of a microchannel-nanochannel interface under dc bias is studied theoretically using a simple 1D model based on the Poisson-Nernst-Planck-Stokes equations. The model describes cross-sectional averaged transport wherein the electro-osmotic flow is controlled by the magnitude of the dc bias and captures essential features of the problem related to the micro-nano interface, specifically geometric focusing effects and nanochannel control of the net fluid flow. This model predicts behavior which differs from that predicted by a purely electrodiffusive formulation. The high-frequency edge of the Warburg branch of the complex impedance plot has a slope which deviates from the π/4 Warburg value, decreasing with increasing bias, and there are corresponding changes in the overall phase as seen in the Bode plots. This can be attributed to a streaming contribution to the capacitive reactance of the device as well an increase in the conductance of the depleted region, both due to net fluid flow. The increase in conductance, corresponding to reduced interfacial depletion, also permits dc currents above the classical electrodiffusive limit.

Electrokinetic instability in microchannels

The effect of geometric confinement on electroconvective instability due to nonequilibrium electro-osmotic slip at the interface of an electrolytic fluid and charge-selective solid is studied. It is shown that the topology of the marginal stability curves and the behavior of the critical parameters depend strongly on both channel geometry and dimensionless Debye length at low voltages for sufficiently deep channels, corresponding to the Rubinstein-Zaltzman instability mechanism, but that stability is governed almost entirely by channel depth for narrow channels at higher voltages. For shallow channels, it is shown that above a transition threshold, determined by both channel depth and Debye length, the low-voltage instability is completely suppressed.

Evolution with time of hydrophobicity and microrelief of a cation-exchange membrane surface and its impact on overlimiting mass transfer

Surface properties were measured together with electrochemical characteristics of a CMX (Neosepta, Tokuyama Corp.) cation-exchange membrane. Relative hydrophobicity was controlled by the contact angle; XPS and SEM were used for characterizing chemical composition and microrelief of the surface, respectively. Voltammetry, chronopotentiometry, and mass transfer rate measurements were made as well. A "fresh" membrane and samples after 10, 25, 100, and 150 h of operation in an electrodialysis cell at an overlimiting current equal to 3 theoretical limiting currents, in a 0.02 M NaCl solution, were characterized. Some electrochemical properties were also measured for a Neosepta cation-exchange membrane, aged 2 years, in an industrial food process. It was found that the hydrophobicity of the CMX membrane has increased after the first 10 h of operation; more and more cavities of the dimension of the order of 1 μm have appeared with time testifying electrochemical erosion of the surface. The limiting current density (i(lim)) and the overlimiting transfer rate through the CMX membrane increased with time of its operation under overlimiting current. In the case of new CMX, i(lim) was very close to the theoretical value i(lim)(theor) calculated by the Lévêque equation. After 10 h of operation, i(lim) increased by 5%, and after 25, 100, and 150 h, the increase was by 30%, 70%, and 100%, respectively. Similarly, the mass transfer rate was found to increase up to 5 times (when desalting 0.005 M NaCl under 3 V) in comparison with the theoretical value. The ensemble of data was explained by the hypothesis that the passage of intensive current produces erosion of the ion-exchange polymer forming a continuous phase in CMX. This erosion results in exposure at the surface of the other constituent of CMX: small (about 100 nm) particles of relatively hydrophobic polyvinylchloride. Increasing surface hydrophobicity facilitates the slip of electroconvective vortexes along the surface. Besides, the geometry of the cavities gives rise to appearing tangential electric force applied to the extended space charge density at cavity's walls. As the local limiting current density within a cavity is lower than at the flat surface, electroconvective vortices arise at current densities lower than i(lim)(theor). With time, the number and the size of cavities increase (apparently, due to paired electroconvective vortices occurring inside them) that seems the main reason for overlimiting transfer increase.

Changing nanoslot ion flux with a dynamic nanocolloid ion-selective filter: secondary overlimiting currents due to nanocolloid-nanoslot interaction

Nanocolloids trapped at the depleted side (anodic) of a fluidic nanoslot entrance are shown to sensitively regulate dc ion transport through the nanoslot, such that a second limiting-overlimiting transition occurs in its nonlinear current-voltage characteristics. The nanocolloids, brought to the entrance by electro-osmosis, are not stationary but are confined to closed circular and toroidal streamlines, driven by a back-pressure corner vortex and an orthogonal electroconvection vortex instability. The transition from the corner vortex to a complex torus with both vortical motions coincides with the first overlimiting transition, while electrostatic interaction of nanocolloids in these vortices with the nanoslot entrance drives the second limiting transition.