Influence of electroosmotic flow on the ionic current rectification in a pH-regulated, conical nanopore

Scan-Rate-Dependent Ion Current Rectification in Bipolar Interfacial Nanopores

This study presents a theoretical investigation into the voltammetric behavior of bipolar interfacial nanopores due to the effect of potential scan rate (1-1000 V/s). Finite element method (FEM) is utilized to explore the current-voltage (I-V) properties of bipolar interfacial nanopores at different bulk salt concentrations. The results demonstrate a strong impact of the scan rate on the I-V response of bipolar interfacial nanopores, particularly at relatively low concentrations. Hysteresis loops are observed in bipolar interfacial nanopores under specific scan rates and potential ranges and divided by a cross-point potential that remains unaffected by the scan rate employed. This indicates that the current in bipolar interfacial nanopores is not just reliant on the bias potential that is imposed but also on the previous conditions within the nanopore, exhibiting history-dependent or memory effects. This scan-rate-dependent current-voltage response is found to be significantly influenced by the length of the nanopore (membrane thickness). Thicker membranes exhibit a more pronounced scan-rate-dependent phenomenon, as the mass transfer of ionic species is slower relative to the potential scan rate. Additionally, unlike conventional bipolar nanopores, the ion current passing through bipolar interfacial nanopores is minimally affected by the membrane thickness, making it easier to detect.

Impact of surface charge density modulation on ion transport in heterogeneous nanochannels

The PNP nanotransistor, consisting of emitter, base, and collector regions, exhibits distinct behavior based on surface charge densities and various electrolyte concentrations. In this study, we investigated the impact of surface charge density on ion transport behavior within PNP nanotransistors at different electrolyte concentrations and applied voltages. We employed a finite-element method to obtain steady-state solutions for the Poisson-Nernst-Planck and Navier-Stokes equations. The ions form a depletion region, influencing the ionic current, and we analyze the influence of surface charge density on the depth of this depletion region. Our findings demonstrate that an increase in surface charge density results in a deeper depletion zone, leading to a reduction in ionic current. However, at very low electrolyte concentrations, an optimal surface charge density causes the ion current to reach its lowest value, subsequently increasing with further increments in surface charge density. As such, atV app = + 1 V andC 0 = 1 mM , the ionic current increases by 25% when the surface charge density rises from 5 to 20  mC . m - 2 , whereas atC 0 = 10 mM , the ionic current decreases by 65% with the same increase in surface charge density. This study provides valuable insights into the behavior of PNP nanotransistors and their potential applications in nanoelectronic devices.

Effect of Membrane Thickness on Ion Transport in pH-Regulated Zero-Depth Interfacial Nanopores

Zero-depth interfacial nanopores, which are formed by two crossed nanoscale channels at their intersection interface, have been proposed to increase the spatial resolution of solid-state nanopores. However, research on zero-depth interfacial nanopores is still in its early stages. Although it has been shown that the current passing through an interfacial nanopore is largely independent of the membrane thickness, existing studies have not fully considered the impact of membrane thickness on other ion transport characteristics within these nanopores. In this paper, we investigate the electrokinetic ion transport phenomenon in the zero-depth interfacial nanopores, especially focusing on the influence of membrane thickness on the ion transport phenomenon. Our model incorporates the Poisson-Nernst-Planck equations and the Navier-Stokes equations, featuring a pH-regulated surface charge density. We find that when the thickness of the nanochannels is close to the interface size of the formed interfacial nanopore, the phenomenon of ion transport in the interfacial nanopore is similar to that in a conventional cylindrical nanopore. However, when the thickness of the nanochannels is much greater than the interface size of the formed interfacial nanopore, several distinct phenomena occur. The surface charge density on the inner walls of the interfacial nanopores has a small peak at the interface of the two crossing nanochannels, and the anion concentration changes greatly between the two nanochannels; that is, a much greater anion concentration forms in the nanochannel near the anode side than in the nanochannel near the cathode side. When the surface charge is nonzero, the electric field within the interfacial nanopore creates three extreme points, and the directions of the local electric fields are opposite at the ends of the membrane.

Dynamic Response of Ionic Current in Conical Nanopores

Ionic current rectification (ICR) of charged conical nanopores has various applications in fields including nanofluidics, biosensing, and energy conversion, whose function is closely related to the dynamic response of nanopores. The occurrence of ICR originates from the ion enrichment and depletion in conical pores, whose formation is found to be affected by the scanning rate of voltages. Here, through time-dependent simulations, we investigate the variation of ion current under electric fields and the dynamic formation of ion enrichment and depletion, which can reflect the response time of conical nanopores. The response time of nanopores when ion enrichment forms, i.e., at the "on" state is significantly longer than that with the formation of ion depletion, i.e., at the "off" state. Our simulation results reveal the regulation of response time by different nanopore parameters including the surface charge density, pore length, tip, and base radius, as well as the applied conditions such as the voltage and bulk concentration. The response time of nanopores is closely related to the surface charge density, pore length, voltage, and bulk concentration. Our uncovered dynamic response mechanism of the ionic current can guide the design of nanofluidic devices with conical nanopores, including memristors, ionic switches, and rectifiers.

Negative Differential Resistance in Conical Nanopore Iontronic Memristors

Emerging ion transport dynamics with memory effects at nanoscale solution-substrate interfaces offers a unique opportunity to overcome the bottlenecks in traditional computational architectures, trade-offs in selectivity and throughput in separation, and electrochemical energy conversions. Negative differential resistance (NDR), a decrease in conductance with increasing potential, constitutes a new function from the perspective of time-dependent instead of steady-state nanoscale electrokinetic ion transport but remains unexplored in ionotronics to develop higher-order complexity and advanced capabilities. Herein, NDR is introduced in hysteretic and rectified ion transport through single conical nanopipettes (NPs) as ionic memristors. Deterministic and chaotic behaviors are controlled via an electric field as the sole stimulus. The NDR arises fundamentally from the availability and redistribution of the ionic charges during the hysteretic and rectified transport at asymmetric nanointerfaces. The elucidated mechanism is generalizable, and the drastically simplified operations enable tunable state-switching dynamics with higher-order complexity besides the first-order synaptic functions in multiple excitatory and inhibitory states.

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.

Ion current rectification properties of non-Newtonian fluids in conical nanochannels

Ionic current rectification generated by the geometric asymmetry of conical nanochannels has gradually attracted attention, but most studies have been limited to Newtonian fluids. In this study, the ionic current rectification characteristics in conical nanochannels filled with non-Newtonian fluids are investigated by numerical simulations. Electroosmotic flow and ion transport in Sisko fluids are solved using the Poisson-Nernst-Planck equations and the Navier-Stokes equations. The effects of the Debye parameter, power-law indexes and applied voltage on the ionic current, axial potential, ion concentration, radial velocity and rectification ratio in the nanopores are investigated. When κRt = 1, the current rectification ratio increases with the increase of the power-law index. However, when κRt = 6, the current rectification ratio first increases and then decreases with the increase of the power law index, reaching the maximum value at n = 1.0. These findings have positive implications for the construction of some nanodevices such as nanofluidic diodes.

Characterization of the surface charge property and porosity of track-etched polymer membranes

As an important property of porous membranes, the surface charge property determines many ionic behaviors of nanopores, such as ionic conductance and selectivity. Based on the dependence of electric double layers on bulk concentrations, ionic conductance through nanopores at high and low concentrations is governed by the bulk conductance and surface charge density, respectively. Here, through the investigation of ionic conductance inside track-etched single polyethylene terephthalate (PET) nanopores under various concentrations, the surface charge density of PET membranes is extracted as ∼-0.021 C/m² at pH 10 over measurements with 40 PET nanopores. Simulations show that surface roughness can cause underestimation in surface charge density due to the inhibited electroosmotic flow. Then, the averaged pore size and porosity of track-etched multipore PET membranes are characterized by the developed ionic conductance method. Through coupled theoretical predictions in ionic conductance under high and low concentrations, the averaged pore size and porosity of porous membranes can be obtained simultaneously. Our method provides a simple and precise way to characterize the pore size and porosity of multipore membranes, especially for those with sub-100 nm pores and low porosities.

Ion Transport in pH-Regulated Double-Barreled Nanopores

Single-molecule detection and characterization with nanopores is a powerful technique that does not require labeling. Multinanopore systems, especially double nanopores, have attracted wide attention and have been applied in many fields. However, theoretical studies of electrokinetic ion transport in nanopores mainly focus on single nanopores. In this paper, for the first time, a theoretical study of pH-regulated double-barreled nanopores is conducted using three-dimensional Poisson-Nernst-Planck equations and Navier-Stokes equations. Four ionic species and the surface chemistry on the walls of the nanopores are included. The results demonstrate that the properties of the bulk salt solution significantly affect nanopore conductivity and ion transport phenomena in nanopores. There are two ion-enriched zones and two ion-depleted zones in double-barreled nanopores. Due to the symmetry of the double-barreled nanopore structure and surface charge density, there is no ionic rectification effect in double-barreled nanopores. The ion selectivity is similar to that of conventional single pH-regulated nanopores.

Ion transport and current rectification in a charged conical nanopore filled with viscoelastic fluids

The ionic current rectification (ICR) is a non-linear current-voltage response upon switching the polarity of the potential across nanopore which is similar to the I–V response in the semiconductor diode. The ICR phenomenon finds several potential applications in micro/nano-fluidics (e.g., Bio-sensors and Lab-on-Chip applications). From a biological application viewpoint, most biological fluids (e.g., blood, saliva, mucus, etc.) exhibit non-Newtonian visco-elastic behavior; their rheological properties differ from Newtonian fluids. Therefore, the resultant flow-field should show an additional dependence on the rheological material properties of viscoelastic fluids such as fluid relaxation time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\lambda )$$\end{document}(λ) and fluid extensibility \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varepsilon )$$\end{document}(ε). Despite numerous potential applications, the comprehensive investigation of the viscoelastic behavior of the fluid on ionic concentration profile and ICR phenomena has not been attempted. ICR phenomena occur when the length scale and Debye layer thickness approaches to the same order. Therefore, this work extensively investigates the effect of visco-elasticity on the flow and ionic mass transfer along with the ICR phenomena in a single conical nanopore. The Poisson–Nernst–Planck (P–N–P) model coupled with momentum equations have been solved for a wide range of conditions such as, Deborah number, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\le De \le 100$$\end{document}1≤De≤100, Debye length parameter, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\le \kappa R_t \le 50$$\end{document}1≤κRt≤50, fluid extensibility parameter, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.05\le \varepsilon \le 0.25$$\end{document}0.05≤ε≤0.25, applied electric potential, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-40\le V \le 40$$\end{document}-40≤V≤40, and surface charge density \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma = -10$$\end{document}σ=-10 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-50$$\end{document}-50. Limited results for Newtonian fluid (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$De = 0$$\end{document}De=0, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon = 0$$\end{document}ε=0) have also been shown in order to demonstrate the effectiveness of non-Newtonian fluid behaviour over the Newtonian fluid behaviour. Four distinct novel characteristics of electro-osmotic flow (EOF) in a conical nanopore have been investigated here, namely (1) detailed structure of flow field and velocity distribution in viscoelastic fluids (2) influence of Deborah number and fluid extensibility parameter on ionic current rectification (ICR) (3) volumetric flow rate calculation as a function of Deborah number and fluid extensibility parameter (4) effect of viscoelastic parameters on concentration distribution of ions in the nanopore. At high applied voltage, both the extensibility parameter and Deborah number facilitate the ICR phenomena. In addition, the ICR phenomena are observed to be more pronounced at low values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa R_t$$\end{document}κRt than the high values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa R_t$$\end{document}κRt. This effect is due to the overlapping of the electric double layer at low values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa R_t$$\end{document}κRt.

Synchronized resistive-pulse analysis with flow visualization for single micro- and nanoscale objects driven by optical vortex in double orifice

Resistive-pulse analysis is a powerful tool for identifying micro- and nanoscale objects. For low-concentration specimens, the pulse responses are rare, and it is difficult to obtain a sufficient number of electrical waveforms to clearly characterize the targets and reduce noise. In this study, we conducted a periodic resistive-pulse analysis using an optical vortex and a double orifice, which repetitively senses a single micro- or nanoscale target particle with a diameter ranging from 700 nm to 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μm. The periodic motion results in the accumulation of a sufficient number of waveforms within a short period. Acquired pulses show periodic ionic-current drops associated with the translocation events through each orifice. Furthermore, a transparent fluidic device allows us to synchronously average the waveforms by the microscopic observation of the translocation events and improve the signal-to-noise ratio. By this method, we succeed in distinguishing single particle diameters. Additionally, the results of measured signals and the simultaneous high-speed observations are used to quantitatively and systematically discuss the effect of the complex fluid flow in the orifices on the amplitude of the resistive pulse. The synchronized resistive-pulse analysis by the optical vortex with the flow visualization improves the pulse-acquisition rate for a single specific particle and accuracy of the analysis, refining the micro- and nanoscale object identification.

Aptamer Conformational Change Enables Serotonin Biosensing with Nanopipettes

We report artificial nanopores in the form of quartz nanopipettes with ca. 10 nm orifices functionalized with molecular recognition elements termed aptamers that reversibly recognize serotonin with high specificity and selectivity. Nanoscale confinement of ion fluxes, analyte-specific aptamer conformational changes, and related surface charge variations enable serotonin sensing. We demonstrate detection of physiologically relevant serotonin amounts in complex environments such as neurobasal media, in which neurons are cultured in vitro. In addition to sensing in physiologically relevant matrices with high sensitivity (picomolar detection limits), we interrogate the detection mechanism via complementary techniques such as quartz crystal microbalance with dissipation monitoring and electrochemical impedance spectroscopy. Moreover, we provide a novel theoretical model for structure-switching aptamer-modified nanopipette systems that supports experimental findings. Validation of specific and selective small-molecule detection, in parallel with mechanistic investigations, demonstrates the potential of conformationally changing aptamer-modified nanopipettes as rapid, label-free, and translatable nanotools for diverse biological systems.

Electrokinetic behavior of bullet-shaped nanopores modified by functional groups: Influence of finite thickness of modified layer

We examined theoretically the electrokinetic behavior of a bullet-shaped nanopore modified by a functional layer, focusing on the influence of its thickness. The nanopore contains both fixed surface charge coming from the original bare surface, and space fixed charge from the modified layer. The results of numerical simulation reveal that the presence of this layer is crucial to the electrokinetic behavior of the nanopore. In particular, its softness is capable of influencing ionic profiles through electroosmotic flow (EOF). Unlike a conical nanopore where its surface normal vector is constant, that of the present bullet-shaped nanopore varies along the pore axis, thereby affecting the degree of EOF, which in turn, can make the ionic profile inside the modified layer more uniform. This is crucial to the applications of the nanopore, for example, in mimicking biological membranes and sensing metal ions.

Deconvolution of electroosmotic flow in hysteresis ion transport through single asymmetric nanopipettes

Unveiling the contributions of electroosmotic flow (EOF) in the electrokinetic transport through structurally-defined nanoscale pores and channels is challenging but fundamentally significant because of the broad relevance of charge transport in energy conversion, desalination and analyte mixing, micro and nano-fluidics, single entity analysis, capillary electrophoresis etc. This report establishes a universal method to diagnose and deconvolute EOF in the nanoscale transport processes through current-potential measurements and analysis without simulation. By solving Poisson, Nernst-Planck (PNP) with and without Navier-Stokes (NS) equations, the impacts of EOF on the time-dependent ion transport through asymmetric nanopores are unequivocally revealed. A sigmoidal shape in the I-V curves indicate the EOF impacts which further deviate from the well-known non-linear rectified transport features. Two conductance signatures, an absolute change in conductance and a 'normalized' one relative to ion migration, are proposed as EOF impact (factor). The EOF impacts can be directly elucidated from current-potential experimental results from the two analytical parameters without simulation. The EOF impact is found more significant in intermediate ionic strength, and potential and pore size dependent. The less-intuitive ionic strength and size dependence is explained by the combined effects of electrostatic screening and non-homogeneous charge distribution/transport at nanoscale interface. The time-dependent conductivity and optical imaging experiments using single nanopipettes validate the proposed method which is applicable to other channel type nanodevices and membranes. The generalizable approach eliminates the need of simulation/fitting of specific experiments and offers previously inaccessible insights into the nanoscale EOF impacts under various experimental conditions for the improvement of separation, energy conversions, high spatial and temporal control in single entity sensing/manipulation, and other related applications.

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.

Pressure-driven energy conversion of conical nanochannels: Anomalous dependence of power generated and efficiency on pH

Pressure-driven power generation is one of a simple, green, and promising energy sources. Owing to the overlapping of the electric double layer inside, nanochannel is capable of providing a platform for this power generation approach. Unfortunately, relevant studies, either experimental or theoretical, are very limited in the literature. Here, we present for the first time a comprehensively theoretical study on the pressure-driven energy conversion in a conical nanochannel having carboxyl functional groups, focusing on the influence of its tip size and the solution pH. An anomalous dependence of both the power generated and the efficiency on the latter are observed. Although the charge density on the nanochannel surface increases monotonically with increasing pH, both the power generated and the efficiency exhibit a local maximum as pH varies. This is because the streaming potential has a local maximum as pH varies. Power density (power generated/tip end cross sectional area) also shows a local maximum as the tip radius varies, and the radius at which the local maximum occurs decreases with increasing bulk salt concentration. In addition to explain successfully the behavior reported in the literature, our study also provides desirable and necessary information for designing relevant devices.

Regulating the ionic current rectification behavior of branched nanochannels by filling polyelectrolytes

The overlapping of the electric double layer (EDL) in a nanochannel yields many interesting and significant electrokinetic phenomena such as ionic current rectification (ICR), which occurs only at a relatively low bulk salt concentration (∼1 mM) where the EDL thickness is comparable to the nanochannel size. In an attempt to raise this concentration to higher levels and the ICR performance improved appreciably, a branched nanochannel filled with polyelectrolytes (PEs) is proposed in this study. We show that these objectives can be achieved by choosing appropriate PE. For example, if the stem side of an anodic aluminun oxide nanochannel is filled with polystyrene sulfonate (PSS) an ICR ratio up to 850 can be obtained at 1 mM, which was not reported in previous studies. Taking account of the effect of electroosmotic flow, the underlying mechanisms of the ICR phenomena observed are discussed and the influences of the solution pH, the bulk salt concentration, and how the region(s) of a nanochannel is filled with PE examined. We show that the ICR behavior of a branched nanochannel can be modulated satisfactorily by filling highly charged PE and the solution pH.

Quantitative Analysis of Factors Affecting the Event Rate in Glass Nanopore Sensors

While the solid-state nanopore sensors have shown exceptional promise with their single-molecule sensitivity and label-free operations, one of the most significant challenges in the nanopore sensor is the limited analyte translocation event rate that leads to prolonged sensor response time. This issue is more pronounced when the analyte concentration is below the nanomolar (nM) range, owing to the diffusion-limited mass transport. In this work, we systematically studied the experimental factors beyond the intrinsic analyte concentration and electrophoretic mobility that affect the event rate in glass nanopore sensors. We developed a quantitative model to capture the impact of nanopore surface charge density, ionic strength, nanopore geometry, and translocation direction on the event rate. The synergistic effects of these factors on the event rates were investigated with the aim to find the optimized experimental conditions for operating the glass nanopore sensor from the response time standpoint. The findings in the study would provide useful and practical insight to enhance the device response time and achieve a lower detection limit for various glass nanopore-sensing experiments.

On Rectification of Ionic Current in Nanopores

Rectification of ionic current, a frequently observed phenomenon with asymmetric nanopores varying in geometry and/or surface charge, has been utilized for studies of microfluidic circuits, nanopore sensors, and energy conversion devices. However, the physics behind the rectification phenomenon deserves further analysis, and the involved processes need renewed organization; however, the origin is known, and numerous simulations based on the Poisson-Nernst-Planck formalism provide details of the observation. Here, we present an analytical model by identifying the causal chain connecting the key physical factors and processes leading to rectification: the charge present on the pore sidewalls causing the selectivity of ion fluxes through the pore, the selectivity inducing enrichment-depletion of ions around the pore, and the established ion concentration gradient rendering the electric field redistribution in the pore. Our analytical model that considers nanopore geometry, surface charge density, and electrolyte concentration calculates the ionic current and corresponding rectification factor at given bias voltages. The model is validated by numerical simulations, and the model results agree well with experimental data. It is, therefore, a useful tool not only for gaining physical insights into ionic current rectification but also for providing practical guidelines in designing nanopore- and nanopipette-based ion sensors for a range of applications.

Nanoscale Fluid Vortices and Nonlinear Electroosmotic Flow Drive Ion Current Rectification in the Presence of Concentration Gradients

Ion current rectification (ICR) is a transport phenomenon in which an electrolyte conducts unequal currents at equal and opposite voltages. Here, we show that nanoscale fluid vortices and nonlinear electroosmotic flow (EOF) drive ICR in the presence of concentration gradients. The same EOF can yield negative differential resistance (NDR), in which current decreases with increasing voltage. A finite element model quantitatively reproduces experimental ICR and NDR recorded across glass nanopipettes under concentration gradients. The model demonstrates that spatial variations of electrical double layer properties induce the nanoscale vortices and nonlinear EOF. Experiments are performed in conditions directly related to scanning probe imaging and show that quantitative understanding of nanoscale transport under concentration gradients requires accounting for EOF. This characterization of nanopipette transport physics will benefit diverse experimentation, pushing the resolution limits of chemical and biophysical recordings.

Modulation of Charge Density and Charge Polarity of Nanopore Wall by Salt Gradient and Voltage

Surface charge plays a very important role in biological processes including ionic and molecular transport across a cell membrane. Placement of charges and charge patterns on walls of polymer and solid-state nanopores allowed preparation of ion-selective systems as well as ionic diodes and transistors to be applied in building biological sensors and ionic circuits. In this article, we show that the surface charge of a 10 nm diameter silicon nitride nanopore placed in contact with a salt gradient is not a constant value, but rather it depends on applied voltage and magnitude of the salt gradient. We found that even when a nanopore was in contact with solutions of pH equivalent to the isoelectric point of the pore surface, the pore walls became charged with voltage-dependent charge density. Implications of the charge gating for detection of proteins passing through a nanopore were considered, as well. Experiments performed with single 30 nm long silicon nitride nanopores were described by continuum modeling, which took into account the surface reactions on the nanopore walls and local modulation of the solution pH in the pore and at the pore entrances. The results revealed that manipulation of surface charge can occur without changing pH of the background electrolyte, which is especially important for applications where maintaining pH at a constant and physiological level is necessary. The system presented also offers a possibility to modulate polarity and magnitude of surface charges in a two-electrode setup, which previously was accomplished in more complex multielectrode systems.

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.

Electrokinetic ion transport in an asymmetric double-gated nanochannel with a pH-tunable zwitterionic surface

Bioinspired, artificial functional nanochannels for intelligent molecular and ionic transport control have versatile potential applications in nanofluidics, energy conversion, and controlled drug release. To simulate the gating and rectification functions of biological ion channels, we model the electrokinetic ion transport phenomenon in an asymmetric double-gated nanochannel having a pH-regulated, zwitterionic surface. Taking account of the effect of electroosmotic flow (EOF), the conductance of the nanochannel and its ion current rectification (ICR) behavior are investigated and the associated mechanisms interpreted. In particular, the influences of the solution pH, the bulk salt concentration, and the base opening radius and the surface curvature of the nanochannel on these behaviors are examined. We show that through adjusting the base opening radius and the surface curvature of a nanochannel, its ICR behavior can be tuned effectively. In addition to proposing underlying mechanisms for the phenomena observed, the results gathered in this study also provide necessary information for designing relevant devices.

Voltage-controlled ion transport and selectivity in a conical nanopore functionalized with pH-tunable polyelectrolyte brushes

Chemically functionalized bioinspired nanopores are widely adopted to control the ionic transport for various purposes. A detailed understanding of the underlying mechanisms is not only desirable but also necessary for device design and experimental data interpretation. Here, the conductance and the ion selectivity of a conical nanopore surface modified by a polyelectrolyte (PE) layer are studied through adjusting the pH, the bulk salt concentration, and the level of the applied potential bias. Possible mechanisms are proposed and discussed in detail. We show that the conductance is sensitive to the variation in the solution pH. The ion selectivity of the nanopore is influenced significantly by both the solution pH and the level of the applied potential bias. In particular, a cation-selective nanopore might become anion-selective through raising the applied potential bias. The ion transport behavior can be tuned easily by adjusting the level of pH, salt concentration, and applied potential bias, thereby providing useful information for the design of nanopore-based sensing devices.

Alternating electric field-induced ion current rectification and electroosmotic pump in ultranarrow charged carbon nanocones

Pumping fluid in ultranarrow (sub-2 nm) synthetic channels, analogous to protein channels, has widespread applications in nanofluidic devices, molecular separation, and related fields. In this work, molecular dynamics simulations were performed to study a symmetrical sinusoidal electric field-induced electroosmotic pump in ultranarrow charged carbon nanocone (CNC) channels. The results show that the CNC channels could rectify the ion current because of the different ion flow rates in the positive and negative half circles of the sinusoidal electric field. Electroosmotic flow (EOF) rectification yielded by the ion current rectification is also revealed, and net water flow from the base to the tip of the CNC channels is observed. The simulations also show that the preferential ion current conduction direction in the ultranarrow CNC channels (from base to tip) is opposite to that in conical nanochannels with tip diameters larger than 5 nm (from tip to base). However, the preferential EOF direction is the same as that of large conical nanochannels (from base to tip). We also investigated the influences of ion concentration and the amplitudes and periods of the sinusoidal electric field on the EOF pump. The results show that high ion concentration, large amplitudes, and long periods are desired for high EOF pumping efficiency. Finally, through comparison with a constant electric field and a pressure-induced water pump, we prove that the EOF pump under an alternating electric field has a higher pump efficiency. The approach outlined in this work provides a general scheme for pumping fluid in ultranarrow charged conical nanochannels.

Ionic Current Behaviors of Dual Nano- and Micropipettes

Ionic current rectification (ICR) phenomena within dual glass pipettes are investigated for the first time. We demonstrate that the ionic flow presents different behaviors in dual nano- and micropipettes when the two channels are filled with the same electrolyte KCl and hung in air. Bare dual nanopipettes cannot rectify the ionic current because of their geometric symmetry, but the ICR can be directly observed based on bare dual micropipettes. The phenomena based on dual micropipettes could be explained by the simulation of the Poisson-Nernst-Plank equation. After modification with different approaches, the dual nanopipettes have asymmetric charge patterns and show various ICR behaviors. They have been successfully employed to fabricate various nanodevices, such as ionic diodes and bipolar junction transistors. Due to the simple and fast fabrication with high reproducibility, these dual pipettes can provide a novel platform for controlling ionic flow in nano- and microfluidics, fabrication of novel nanodevices, and detection of biomolecules.

Influence of salt valence on the rectification behavior of nanochannels

Taking account of the influence of electroosmotic flow, the behavior of the ion current rectification of a charged conical nanochannel is studied theoretically focusing on the effect of ionic valence. A continuum-based model comprising coupled Poisson-Nernst-Planck (PNP) equations for the ionic mass transport and Navier-Stokes equations for the hydrodynamic field is adopted. We show that if the bulk salt concentration is fixed, the behavior of the current-voltage curve depends highly on the ionic valence, which arises from the difference in ionic strength and ion diffusivity. As the bulk salt concentration varies, the rectification factor shows a local maximum, and the bulk salt concentration at which it occurs depends upon the salt valence: the higher the valence the lower that concentration. However, regardless of the salt valence, the ionic strength at which that local maximum occurs is essentially the same, implying that the thickness of electric double layer is the key factor. Due to the difference in ionic diffusivity, the magnitude of the rectification factor depends upon the type of salt. For example, the rectification factor of KCl is larger than that of KNO₃. The qualitative behavior of the ion current rectification of a positively charged conical nanochannel is similar to that of a negatively charged nanochannel.

Nanopore-Based Strategy for Sequential Separation of Heavy-Metal Ions in Water

Developing novel methods for the removal of heavy-metal ions from wastewater with low costs, special selectivity and high efficiency is quite important in water restoration and comprehensive ecological improvement. In this work, a nanopore-based strategy was suggested and related segregation apparatus was built to separate multiple heavy-metal ions in water by selective complexation. The results indicated that the prioritization of the selecting order for the complexing agent (thiacalix[4]arene- p-tetrasulfonate (TCAS)) to heavy-metal ions was Cu(II) > Cd(II) > Pb(II) > Ba(II). Meanwhile, higher driven voltage corresponded to a faster separation speed, while it could cause the decomposition of complexed heavy-metal ions when excessed the threshold. On the other hand, pH value would affect the hydrolysis of heavy-metal ions, the complexation of the calixarene to the heavy-metal ions and the speed of the electroosmotic flow. In our experiments, the maximum separation efficiency was achieved when the driven voltage was 1.5 V and the pH value was 5.0, corresponding to the best separation rate of 94.8%, 95.2%, 92.8%, 93.6%, for Cu(II), Cd(II), Pb(II) and Ba(II), respectively.

Importance of polyelectrolyte modification for rectifying the ionic current in conically shaped nanochannels

Regulating the ICR behavior of a conical nanochannel can be achieved by modifying its surface appropriately.

Gate modulation of proton transport in a nanopore

Proton transport in confined spaces plays a crucial role in many biological processes as well as in modern technological applications, such as fuel cells. To achieve active control of proton conductance, we investigate for the first time the gate modulation of proton transport in a pH-regulated nanopore by a multi-ion model. The model takes into account surface protonation/deprotonation reactions, surface curvature, electroosmotic flow, Stern layer, and electric double layer overlap. The proposed model is validated by good agreement with the existing experimental data on nanopore conductance with and without a gate voltage. The results show that the modulation of proton transport in a nanopore depends on the concentration of the background salt and solution pH. Without background salt, the gated nanopore exhibits an interesting ambipolar conductance behavior when pH is close to the isoelectric point of the dielectric pore material, and the net ionic and proton conductance can be actively regulated with a gate voltage as low as 1 V. The higher the background salt concentration, the lower is the performance of the gate control on the proton transport.

Salt gradient driven ion transport in solid-state nanopores: the crucial role of reservoir geometry and size

The crucial influence of the reservoir geometry and size on the salt gradient driven ion transport in solid-state nanopores is unraveled.

Ion transport and selectivity in biomimetic nanopores with pH-tunable zwitterionic polyelectrolyte brushes

Inspired by nature, functionalized nanopores with biomimetic structures have attracted growing interests in using them as novel platforms for applications of regulating ion and nanoparticle transport. To improve these emerging applications, we study theoretically for the first time the ion transport and selectivity in short nanopores functionalized with pH tunable, zwitterionic polyelectrolyte (PE) brushes. In addition to background salt ions, the study takes into account the presence of H(+) and OH(-) ions along with the chemistry reactions between functional groups on PE chains and protons. Due to ion concentration polarization, the charge density of PE layers is not homogeneously distributed and depends significantly on the background salt concentration, pH, grafting density of PE chains, and applied voltage bias, thereby resulting in many interesting and unexpected ion transport phenomena in the nanopore. For example, the ion selectivity of the biomimetic nanopore can be regulated from anion-selective (cation-selective) to cation-selective (anion-selective) by diminishing (raising) the solution pH when a sufficiently small grafting density of PE chains, large voltage bias, and low background salt concentration are applied.