Ion current rectification in funnel-shaped nanochannels: Hysteresis and inversion effects

Electroosmotic flow modulation and dispersion of uncharged solutes in soft nanochannel

We perform a systematic study on the modulation of electroosmotic flow (EOF), tuning the selectivity using electrolyte ions and hydrodynamic dispersion of the solute band across the soft nanochannel. The supporting walls of the channel are considered to be hydrophobic and bear non-zero surface charge. For such a channel, the inner side of the supporting rigid walls of the channel are coated with a soft polyelectrolyte layer (PEL). The inhomogeneous distribution of monomers and accompanying volume charge within the PEL is modelled via soft-step function. The dielectric permittivity of the PEL and electrolyte solution are in general different, which in turn leads to the ion partitioning effect. The impact of ion steric effects due to finite sized ions is further accounted through the modified ion activity coefficient. To model the EOF modulation considering the combined impact of the ion steric and ion partitioning effects as well as inhomogeneous distribution of monomers across the PEL, we adopt the modified Poisson-Boltzmann equation as the governing equation for electrostatic potential. The Debye-Bueche model is adopted to study the flow field across the PEL and the Stokes equation governs the EOF outside the PEL. In order to study the impact of the modulated EOF field on the dispersion of uncharged solution, we adopt three different models, i.e., a general 2D convective-diffusion model as well as cross-sectional averaged dispersion models due to Gill and late-time Taylor and Aris. Going beyond the widely employed Debye-Hückel approximation and uniform distribution of the monomer as well as accompanying volume charge, we find the results for the electric double layer (EDL) potential, EOF field and averaged throughput, by tuning the ion selectivity, etc., which is sufficient to analyze the transport of ionized liquid across the channel. The numerical results are supplemented with analytical results for the EDL potential as well as the EOF field under various limiting situations. Besides, we have further shown the impact of the modulated EOF field on the solute dispersion process. We have presented results that highlight the impact of parameters related to EOF field modulation, on solute dispersion governed by a convective-diffusive process, as well as obtaining the results for an effective dispersion coefficient. The dispersion models under the modulated EOF field adopted in the present study can thus be applied to study the dispersion process in engineered microdevices.

Improved ionic current rectification utilizing cylindrical nanochannels coated with polyelectrolyte layers of non-uniform thickness

Conical nanochannels employed to create ionic current rectification (ICR) in nanofluidic devices are prone to clogging due to the contraction at one end. As an alternative approach for creating ICR, a cylindrical nanochannel covered with a polyelectrolyte layer (PEL) of variable thickness is proposed in the present study. The efficacy of the proposed design is studied by numerically solving the governing equations including the Poisson, Nernst-Planck, and Stokes-Brinkman equations. Furthermore, the fundamental mechanism behind ICR is explained using a simplified one-dimensional model. The effects of the nanochannel radius, concentration of PEL fixed charges, and bulk ionic concentration on the rectification factor are then investigated in detail. It is shown that the proposed nanochannel provides larger rectification factors as compared to conical nanochannels over wide ranges of the fixed charge concentration and bulk ionic concentration. Such a performance can be achieved even at channel radii much larger than the tip radius of conical nanochannels, indicating not only the better performance of the proposed nanochannel but also its likely longer service life, because of reducing the probability of total ionic current blockage. This means that the proposed nanochannel could find widespread use in fluidic devices, as a replacement for conical nanofluidic diodes.

Designing with Iontronic Logic Gates─From a Single Polyelectrolyte Diode to an Integrated Ionic Circuit

This article presents the implementation of on-chip iontronic circuits via small-scale integration of multiple ionic logic gates made of bipolar polyelectrolyte diodes. These ionic circuits are analogous to solid-state electronic circuits, with ions as the charge carriers instead of electrons/holes. We experimentally characterize the responses of a single fluidic diode made of a junction of oppositely charged polyelectrolytes (i.e., anion and cation exchange membranes), with a similar underlying mechanism as a solid-state p- and n-type junction. This served to carry out predesigned logical computations in various architectures by integrating multiple diode-based logic gates, where the electrical signal between the integrated gates was transmitted entirely through ions. The findings shed light on the limitations affecting the number of logic gates that can be integrated, the degradation of the electrical signal, their transient response, and the design rules that can improve the performance of iontronic circuits.

Effect of Electrolyte Concentration and Pore Size on Ion Current Rectification Inversion

A thorough understanding of nanoscale transport properties is vital for the development and optimization of nanopore sensors. The thickness of the electrical double layers (EDLs) at the internal walls of a nanopore, as well as the dimensions of the nanopore itself, plays a crucial role in determining transport properties. Herein, we demonstrate the effect of the electrolyte concentration, which is inversely proportional to the EDL thickness, and the effect of pore size, which controls the extent of the electrical double layer overlap, on the ion current rectification phenomenon observed for conical nanopores. Experimental and numerical results showed that as the electrolyte concentration is decreased, the rectification ratio reaches a maximum, then decreases, and eventually inverts below unity. We also show that as the pore size is decreased, the rectification maximum and the inversion take place at higher electrolyte concentrations. Numerical investigations revealed that both phenomena occur due to the shifting of ion enrichment distributions within the nanopore as the electrolyte concentration or the pore size is varied.

Numerical Investigation of Diffusioosmotic Flow in a Tapered Nanochannel

Diffusioosmosis concerns ionic flow driven by a concentration difference in a charged nano-confinement and has significant applications in micro/nano-fluidics because of its nonlinear current-voltage response, thereby acting as an active electric gating. We carry out a comprehensive computation fluid dynamics simulation to investigate diffusioosmotic flow in a charged nanochannel of linearly varying height under an electrolyte concentration gradient. We analyze the effects of cone angle (α), nanochannel length (l) and tip diameter (dt), concentration difference (Δc = 0–1 mM), and external flow on the diffusioosmotic velocity in a tapered nanochannel with a constant surface charge density (σ). External flow velocity (varied over five orders of magnitude) shows a negligible influence on the diffusioosmotic flow inside the tapered nanochannel. We observed that a cone angle causes diffusioosmotic flow to move towards the direction of increasing gap thickness because of stronger local electric field caused by the overlapping of electric double layers near the smaller orifice. Moreover, the magnitude of average nanoflow velocity increases with increasing |α|. Flow velocity at the nanochannel tip increases when dt is smaller or when l is greater. In addition, the magnitude of diffusioosmotic velocity increases with increasing Δc. Our numerical results demonstrate the nonlinear dependence of tapered, diffusioosmotic flow on various crucial control parameters, e.g., concentration difference, cone angle, tip diameter, and nanochannel length, whereas an insignificant relationship on flow rate in the low Peclet number regime is observed.

Impedance-Based Nanoporous Anodized Alumina/ITO Platforms for Label-Free Biosensors

We report an experimental and computational approach for the fabrication and characterization of a highly sensitive and responsive label-free biosensor that does not require the presence of redox couples in electrolytes for sensitive electrochemical detection. The sensor is based on an aptamer-functionalized transparent electrode composed of nanoporous anodized alumina (NAA) grown on indium tin oxide (ITO)-covered glass. Electrochemical impedance changes in a thrombin binding aptamer (TBA)-functionalized NAA/ITO/glass electrode due to specific binding of α-thrombin are monitored for protein detection. The aptamer-functionalized electrode enables sensitive and specific thrombin protein detection with a detection limit of ∼10 pM and a high signal-to-noise ratio. The transient impedance of the alumina film-covered surface is computed using a computational electrochemical impedance spectroscopy (EIS) approach and compared to experimental observations to identify the dominant mechanisms underlying the sensor response. The computational and experimental results indicate that the sensing response is due to the modified ionic transport under the combined influence of steric hindrance and surface charge modification due to ligand/receptor binding between α-thrombin and the aptamer-covered alumina film. These results suggest that alumina film-covered electrodes utilize both steric and charge modulation for sensing, leading to tremendous improvement in the sensitivity and signal-to-noise ratio. The film configuration is amenable for miniaturization and can be readily incorporated into existing portable sensing systems.

Upstream events dictate interfacial slip in geometrically converging nanopores

Continuum computations of fluid flow in conduits approaching molecular scales are often executed with a certain level of abstractions via the imposition of a pre-defined slip condition at the wall. However, in reality, the interfacial slip may not be affixed a priori as a direct one-to-one mapping with the surface wettability and charge but is implicitly interconnected with the concomitant dynamical events that may be effectively captured only under flow conditions. The flow in nanofluidic channels with axially varying cross sections hallmarks such situations in which the effective slip at the wall gets dynamically modulated by upstream flow conditions and cannot be trivially stamped as guided by localized intermolecular interactions over interfacial scales alone. In an effort to capture such flows without resorting to full-domain molecular dynamics simulations, here we bring out advancements on hybrid molecular-continuum simulations and report predictions that closely capture molecular dynamics based predictions of water transport through converging nanopores. Our results turn out to be of significant implications toward designing of emerging nanoscale devices of multifarious applications ranging from miniaturized reactors to highly targeted drug delivery systems.

Ion Current Rectification in Extra-Long Nanofunnels

Nanofluidic systems offer new functionalities for the development of high sensitivity biosensors, but many of the interesting electrokinetic phenomena taking place inside or in the proximity of nanostructures are still not fully characterized. Here, to better understand the accumulation phenomena observed in fluidic systems with asymmetric nanostructures, we study the distribution of the ion concentration inside a long (more than 90 µm) micrometric funnel terminating with a nanochannel. We show numerical simulations, based on the finite element method, and analyze how the ion distribution changes depending on the average concentration of the working solutions. We also report on the effect of surface charge on the ion distribution inside a long funnel and analyze how the phenomena of ion current rectification depend on the applied voltage and on the working solution concentration. Our results can be used in the design and implementation of high-performance concentrators, which, if combined with high sensitivity detectors, could drive the development of a new class of miniaturized biosensors characterized by an improved sensitivity.

Thermal Dependence of the Mesoscale Ionic Diode: Modeling and Experimental Verification

Mesoscale ionic diodes, which can rectify ionic current at conditions at which their pore size is larger than 100 nm and thus over 100 times larger than the Debye length, have been recently discovered with potential applications in ionic circuits as well as osmotic power generation. Compared with the conventional nanoscale ionic diodes, the mesoscale ionic diodes can offer much higher conductance, ionic current resolution, and power generated. However, the thermal response, which has been proven playing a crucial role in nanofluidic devices, of the mesoscale ionic diode remains significantly unexplored. Here, we report the thermal dependence of the mesoscale ionic diode comprising a conical pore with a tip opening diameter of ∼400 nm. To capture its underlying physics more accurately, our model takes into account the practical equilibrium chemistry reaction of functional carboxyl groups on the pore surface. Modeling results predict that in the mesoscale ionic diode prepared currents increase but the performance decreases with the increase of temperature, which is consistent with our experimental data and indicates that the ion transport properties apparently depend on the presence of highly mobile hydroxide ions. The results gathered can provide important guidance for the design of new mesoscale ionic diodes, enriching their applications in thermoelectric power and thermoresponsive chemical sensors.

Tunable Electrorheological Fluid Microfluidic Rectifier: Irreversibility of Viscous Flow Due to Spatial Asymmetry Induced Memory Effects

Because of the reversibility of viscous flow it is not expected to obtain a fluidic rectifier simply from geometrical asymmetry without any moving mechanical parts. Here, we found a counterexample by using spatial asymmetry combined with an electric field to inject memory effects that render the flow irreversible. This stems from the strong dependency of the electrorheological fluid particle chaining on the flow direction. A funnel-shaped microfluidic rectifier with electrorheological fluid has been shown to be easily and rapidly tuned via the applied electric field to achieve an almost order of magnitude rectification along with pressure oscillations. These findings are of importance for the realization of fluidic diodes, rectifiers, and ratchets.

A numerical study of the selectivity of an isolated cylindrical or conical nanopore to a charged macro-ion

The selectivity of a single nanopore in a uniformly charged solid membrane to a charged analyte ion is studied using numerical simulation. A continuum model is used where the ions are regarded as point particles and characterized by a continuously varying number density. The problem is described by the coupled equations for the electrostatic potential, ion-transport, and hydrodynamic flow, which are solved under appropriate boundary conditions using a finite volume method. The nanopore geometry is considered conical, the cylindrical pore being a special case where the cone angle is zero. The selectivity is characterized by a dimensionless parameter: the pore selectivity index. Results are presented showing how the pore selectivity index varies with the membrane surface charge and other parameters of the problem. The role of hydrodynamic flow on transport properties is examined and found to be consistent with theoretical results on electroosmotic flow through nanopores.

Solid-state nanopore hydrodynamics and transport

The resistive pulse method based on measuring the ion current trace as a biomolecule passing through a nanopore has become an important tool in biotechnology for characterizing molecules. A detailed physical understanding of the translocation process is essential if one is to extract the relevant molecular properties from the current signal. In this Perspective, we review some recent progress in our understanding of hydrodynamic flow and transport through nanometer sized pores. We assume that the problems of interest can be addressed through the use of the continuum version of the equations of hydrodynamic and ion transport. Thus, our discussion is restricted to pores of diameter greater than about ten nanometers: such pores are usually synthetic. We address the fundamental nanopore hydrodynamics and ion transport mechanisms and review the wealth of observed phenomena due to these mechanisms. We also suggest future ionic circuits that can be synthesized from different ionic modules based on these phenomena and their applications.

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.

Conical Nanopores for Efficient Ion Pumping and Desalination

Previous experimental and theoretical studies have demonstrated that nanofabricated synthetic channels are able to pump ions using oscillating electric fields. We have recently proposed that conical pores with oscillating surface charges are particularly effective for pumping ions due to rectification that arises from their asymmetric structure. In this work, the energy and thermodynamic efficiency associated with salt pumping using the conical pore pump is studied, with emphasis on pumps needed to desalinate seawater. The energy efficiency is found to be as high as 0.60 to 0.83 mol/kJ when the radius of the tip side of the conical pore is two Debye lengths and the pump works with a concentration gradient smaller than 1.5. As a result, the energy consumption needed for seawater desalination with 20% salt rejection is 0.32 kJ/L. In addition, the energy consumption can be further reduced to 0.21 kJ/L (20% salt rejection) if the bias voltage is adaptively altered four times during the pump cycle while salt concentration is reduced. If the bias voltage is adaptively increased to higher values, then salt rejection can be improved to values that are needed to produce fresh water that satisfies standard requirements. Numerical analysis indicates that the energy consumption is 4.9 kJ/L for 98.6% salt rejection, which is smaller than the practical minimum energy requirement for RO-based methods. In addition, the pumping efficiency can be further improved by tuning the pump structure, increasing the surface charge, and employing more adaptive bias voltages. The conical pores are also found to more efficiently counteract the concentration gradient compared to cylindrical counterparts.

Multifunctional scanning ion conductance microscopy

Scanning ion conductance microscopy (SICM) is a nanopipette-based technique that has traditionally been used to image topography or to deliver species to an interface, particularly in a biological setting. This article highlights the recent blossoming of SICM into a technique with a much greater diversity of applications and capability that can be used either standalone, with advanced control (potential-time) functions, or in tandem with other methods. SICM can be used to elucidate functional information about interfaces, such as surface charge density or electrochemical activity (ion fluxes). Using a multi-barrel probe format, SICM-related techniques can be employed to deposit nanoscale three-dimensional structures and further functionality is realized when SICM is combined with scanning electrochemical microscopy (SECM), with simultaneous measurements from a single probe opening up considerable prospects for multifunctional imaging. SICM studies are greatly enhanced by finite-element method modelling for quantitative treatment of issues such as resolution, surface charge and (tip) geometry effects. SICM is particularly applicable to the study of living systems, notably single cells, although applications extend to materials characterization and to new methods of printing and nanofabrication. A more thorough understanding of the electrochemical principles and properties of SICM provides a foundation for significant applications of SICM in electrochemistry and interfacial science.