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 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 Transport in Intelligent Nanochannels: A Comparative Analysis of the Role of Electric Field

This research delves into investigating ion transport behavior within nanochannels, enhanced through modification with a negatively charged polyelectrolyte layer (PEL), aimed at achieving superior control. The study examines two types of electric fields─direct current and alternating current with square, sinusoidal, triangular, and sawtooth waveforms─to understand their impact on ion transport. Furthermore, the study compares symmetric (cylindrical) and asymmetric (conical) nanochannel geometries to assess the influence of overlapping electrical double layers (EDLs) in generating specific electrokinetic behaviors such as ionic current rectification (ICR) and ion selectivity. The research employs the finite element method to solve the coupled Poisson-Nernst-Planck and Navier-Stokes equations under unsteady-state conditions. By considering factors such as electrolyte concentration, soft layer charge density, and electric field type, the study evaluates ion transport performance in charged nanochannels, investigating effects on concentration polarization, electroosmotic flow (EOF), ion current, rectification, and ion selectivity. Notably, the study accounts for ion partitioning between the PEL and electrolyte to simulate real conditions. Findings reveal that conical nanochannels, due to improved EDL overlap, significantly enhance ion transport and related characteristics compared to cylindrical ones. For instance, under ηε = ηD = 0.8, ημ = 2, C0 = 20 mM, and NPEL/NA = 80 mol m-3 conditions, the average EOF for conical and cylindrical geometries is 0.1 and 0.008 m/s, respectively. Additionally, the study explores ion selectivity and rectification based on the electric field type, unveiling the potential of nanochannels as ion gates or diodes. In cylindrical nanochannels, the ICR remains at unity, with lower ion selectivity across waveforms compared to conical channels. Furthermore, rectification and ion selectivity trends are identified as Rf,square > Rf,DC > Rf,triangular > Rf,sinusoidal > Rf,sawtooth and Ssawtooth > Ssinusoidal > Striangular > SDC > Ssquare for conical nanochannels. Our study of ion transport control in nanochannels, guided by tailored electric fields and unique geometries, offers versatile applications in the field of Analytical Chemistry. This includes enhanced sample separation, controlled drug delivery, optimized pharmaceutical analysis, and the development of advanced biosensing technologies for precise chemical analysis and detection. These applications highlight the diverse analytical contributions of our methodology, providing innovative solutions to challenges in chemical analysis and biosensing.

Smart nanochannels: tailoring ion transport properties through variation in nanochannel geometry

This research explores ion transport behavior and functionality in a hybrid nanochannel that consists of two conical and cylindrical parts. The numerical investigation focuses on analyzing the length of each part in the nanochannel. The nanochannels are hybrid cavities embedded in a membrane, where the size of the conical part varies as equal to, larger than, or smaller than the cylindrical part. The nanochannel is coated with a polyelectrolyte layer that exhibits a dense charge density distribution. The charge density of the soft layer is described using the soft step distribution function. We study the electroosmotic flow, ionic current, rectification, and selectivity of the nanochannel versus bulk electrolyte concentration, the charge density of the polyelectrolyte layer, and decay length, while considering the effect of ionic partitioning. The steady-state Poisson-Nernst-Planck and Navier-Stokes equations are solved using the finite element method. The findings reveal that the nanochannel with a more extensive conical section demonstrates increased rectification, with the rectification factor rising from 1.4 to 2 at a bulk concentration of 100 mM. Additionally, the nanochannel with a longer cylindrical part exhibits improved selectivity under negative voltage conditions, while positive voltage introduces a different situation. The nanochannel with equal cylindrical and conical parts significantly affects conductivity by modifying the charge density in the soft layer, resulting in a 3.125-fold increase in conductivity under positive voltage when the charge density in the polyelectrolyte layer is raised from 25 to 100 mol m-3. This research focuses on creating intelligent nanochannels by controlling mass concentration, charge density, and collapse length, improving system performance, and optimizing properties. It also offers valuable insights into ion transport mechanisms in nanochannel systems, advancing our understanding in this field.

Layer-by-Layer Nanofluidic Membranes for Promoting Blue Energy Conversion

Access to and use of energy resources are now crucial components of modern human existence thanks to the exponential growth of technology. Traditional energy sources provide significant challenges, such as pollution, scarcity, and excessive prices. As a result, there is more need than ever before to replace depleting resources with brand-new, reliable, and environmentally friendly ones. With the aid of reverse electrodialysis, the salinity gradient between rivers and seawater as a clean supply with easy and infinite availability is a viable choice for energy generation. The development of nanofluidic-based reverse electrodialysis (NRED) as a novel high-efficiency technology is attributable to the progress of nanoscience. However, understanding the predominant mechanisms of this process at the nanoscale is necessary to develop and disseminate this technology. One viable option to gain insight into these systems while saving expenses is to employ simulation tools. In this study, we looked at how a layer-by-layer (LBL) soft layer influences ion transport and energy production in charged nanochannels. We solved the steady-state Poisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations for three different types of nanochannels with a trumpet geometry, where the narrow part is covered with a built-up LbL soft layer and the rest is a hard wall with a surface charge density of σ = -10, 0, or +10 mC/m2. The findings show that in type (I) nanochannels, at NPEL/NA = 100 mol/m3 and pH = 7, the maximum power output rises 675-fold as the concentration ratio rises from 10 to 1000. The results of this study can aid in a better understanding of energy harvesting processes using nanofluidic-based reverse electrodialysis in order to identify optimal conditions for the design of an intelligent route with great controllability and minimal pollution.

Quantitative model for predicting the electroosmotic flow in dual-pole nanochannels

Developing and assessing nanofluidic systems is time-consuming and costly owing to the method's novelty; hence, modeling is essential to determine the optimal areas for implementation and to grasp its workings. In this work, we examined the influence of dual-pole surface and nanopore configuration on ion transfer simultaneously. To achieve this, the two trumpet and cigarette configuration were coated with a dual-pole soft surface so that the negative charge could be positioned in the nanopore's small aperture. Subsequently, the Poisson-Nernst-Planck and Navier-Stokes equations were simultaneously solved under steady-state circumstances using varied values physicochemical properties for the soft surface and electrolyte. The pore's selectivity was S Trumpet > S Cigarette ${S}_{{\rm{Trumpet}}} &gt; {S}_{{\rm{Cigarette}}}$ , and the rectification factor, on the other hand, was R f Cigarette < R f Trumpet ${R}_{{f}_{{\rm{Cigarette}}}} &lt; {R}_{{f}_{{\rm{Trumpet}}}}$ , when the overall concentration was very low. When the ion partitioning effect is taken into account, we clearly show that the rectifying variables for the cigarette configuration and the trumpet configuration can reach values of 45 and 49.2, when the charge density and mass concentration were 100 mol/m³ and 1 mM, respectively. By using dual-pole surfaces, the controllability of nanopores' rectifying behavior may be modified to produce superior separation performance.

Inner Wall and Outer Surface Distinguished Solid-State Nanopores for Sensing

Solid-state nanopores, inspired by biological nanopores, have the advantages of good mechanical properties, stability, and easy modification. They have attracted wide attention in the fields of sequencing, sensing, molecular sieving, nanofluidic devices, nanoelectrochemistry, and energy conversion. Because of the ion/molecule transport characteristic of the pore, the research on solid-state nanopores mainly focuses on the functional modification of its inner wall. In recent years, the outer surface of nanopores has also attracted the attention of researchers, and the functional elements on the outer surface have the functions of anti-interference and ionic signal enhancement. In this perspective, we review research progress of inner wall and outer surface distinguished solid-state nanopores, highlight their processing and advantages, summarize their functions and applications in sensing, and give insight into further research.

Nanopore-Based Detection of Trace Concentrations of Multivalent Ions When Impurity Ions Are Present

The feasibility of detecting a trace concentration of multivalent ions based on the ionic current rectification (ICR) of a nanopore when impurity ions might present is assessed. Adopting a bullet-shaped nanopore surface modified with tannic acid as an example, the detection of trace concentrations of Cu²⁺ (target ion) when Fe³⁺ (impurity) is present with K⁺ as background ions under various conditions is simulated. In particular, the influence of the reaction order of the association of target ions and tannic acid on the nanopore performance is examined. We show that the lower the background concentration the better the detection performance. For the examined background concentrations of 1, 10, 100, and 1000 mM, the optimal detection ranges are [0.5, 1000 μM] and [1, 1000 nM] for Cu²⁺ and Fe³⁺, respectively. The detection limits, 0.5 μM for Cu²⁺ and 1 nM for Fe³⁺, are lower than those that can be obtained from conventional instruments, suggesting the potential of applying the present nanopore-based approach. In addition, we also consider the presence of multiple ions, which can occur, for example, in detecting Cu²⁺ (target ion) when Fe³⁺ (impurity) might present or vice versa with K⁺ as background ions. The competitive adsorption of these three kinds of ions can yield complicated ICR behaviors.

Nanofluidic Membranes to Address the Challenges of Salinity Gradient Energy Harvesting: Roles of Nanochannel Geometry and Bipolar Soft Layer

Researchers are looking for new, clean, and accessible sources of energy due to rising global warming caused by the usage of fossil fuels and the irreversible harm that this does to the environment. Water salinity is one of the newest and most accessible renewable energy sources, which has sparked a lot of interest. Reverse electrodialysis (RED) has been utilized in the past to turn saline water into electricity. NRED, a reverse electrodialysis method utilizing nanofluidics, has gained popularity as nanoscale research advances. Developing and evaluating NRED systems is time-consuming and expensive due to the method's novelty; thus, modeling is required to identify the best locations for implementation and to comprehend its workings. In this work, we examined the influence of bipolar soft layer and nanochannel geometry on ion transfer and power production simultaneously. To achieve this, the two trumpet and cigarette geometries were coated with a bipolar soft layer so that both negative (type (I)) and positive (type (II)) charges could be positioned in the nanochannel's small aperture. After that, at steady state conditions, the Poisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations were solved concurrently. The findings revealed that altering the nanochannel coating from type (I) to type (II) alters the channel's selectivity from cations to anions. An approximately 22-fold improvement in energy conversion efficiency was achieved by raising the concentration ratio from 10 to 100 for the type (I) trumpet nanochannel. Type (I) cigarette geometry is advised for maximum power output at low and medium concentration ratios, whereas type (I) trumpet geometry is recommended for the maximum power production at high concentration ratios.

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.

Non-monotonic variation of flow strength in nanochannels grafted with end-charged polyelectrolyte layers

The electrokinetic transport of fluids, also called the electroosmotic flow (EOF), in micro/nanoscale devices occurs in promising applications such as electrokinetic energy conversion (EKEC) systems. Recently, EKEC systems grafted with end-charged polyelectrolyte (PE) layers (PELs) have been reported to exhibit higher efficiencies than those of intrinsic systems. Understanding the interplay between the end-charged PELs and electrical double layers (EDLs) on the EOF is crucial for designing highly efficient EKEC systems. The interplay between the end-charged PELs and EDLs on the strength of the EOF (V₀) is studied by explicitly modeling the EOF through nanochannels grafted with end-charged PELs using atomic simulations. The variation of V₀ is examined for nanochannels grafted with PELs at various separations (d = 3.5–0.4 nm) to cover various conformations of PEs, inlcuding mushroom, semi-dilute brushes, and concentrated brushes. We find that V₀ follows a non-monotonic variation as d decreases and this is correlated with the conformation of the PEs. Specifically, as d decreases, V₀ decreases first in the mushroom regime (d = 3.5–2.0 nm), and then V₀ increases in the concentrated brush regime (d = 0.75–0.4 nm). Navigated by the continuum Navier–Stokes–Brinkman model, the above observations are rationalized by the competition between the driving effect from the spatial shift of ions in EDLs and the drag effect from PELs. The insights obtained in this work are important to guide the design of highly efficient EKEC systems by grafting end-charged PELs onto channel surfaces.

A non-monotonic variation of the strength of electroosmotic flow (V₀) is reported for the electroosmotic flow through nanochannels grafted with end-charged polyelectrolytes at various separation using atomic simulations.

Design of Multifunctional Nanopore Using Polyampholyte Brush with Composition Gradient

Molecular organizations and charge patterns inside biological nanopores are optimized by evolution to enhance ionic and molecular transport. Inspired by the nuclear pore complex that employs asymmetrically arranged disordered proteins for its gating, we here design an artificial nanopore coated by an asymmetric polyampholyte brush as a model system to study the asymmetric mass transport under nanoconfinement. A nonequilibrium steady-state molecular theory is developed to account for the intricate charge regulation effect of the weak polyampholyte and to address the coupling between the polymer conformation and the external electric field. On the basis of this state-of-the-art theoretical method, we present a comprehensive theoretical description of the stimuli-responsive structural behaviors and transport properties inside the nanopore with all molecular details considered. Our model demonstrates that by incorporating a gradient of pH sensitivity into the polymer coatings of the nanopore, a variety of asymmetric charge patterns and functional structures can be achieved, in a pH-responsive manner that allows for multiple functions to be implemented into the designed system. The asymmetric charge pattern inside the nanopore leads to an electrostatic trap for major current carriers, which turns the nanopore into an ionic rectifier with a rectification factor above 1000 at optimized pH and salt concentration. Our theory further predicts that the nanopore design behaves like a double-gated nanofluidic device with pH-triggered opening of the gates, which can serve as an ion pump and pH-responsive molecular filter. These results deepen our understanding of asymmetric transport in nanoconfined systems and provide guidelines for designing polymer-coated smart nanopores.

Tripling the reverse electrodialysis power generation in conical nanochannels utilizing soft surfaces

We theoretically investigate the feasibility of enhancing the reverse electrodialysis power generation in nanochannels by covering the surface with a polyelectrolyte layer (PEL). Along these lines, two conical nanochannels are considered that differ in the extent of the covering. Each nanochannel connects two large reservoirs filled with KCl electrolytes of different ionic concentrations. Considering the Poisson-Nernst-Planck and Navier-Brinkman equations, finite-element-based numerical simulations are performed under a steady-state. The influences of the PEL properties and the salinity gradient on the reverse electrodialysis characteristics are examined in detail via a thorough parametric study. It is shown that the maximum power generated is an increasing function of the charge density and the thickness of the PEL. This means that the maximum power generated may be theoretically increased to any desired degree by covering the nanochannel surface with a sufficiently dense and thick PEL. Considering a typical PEL with a charge density of 100 mol m-3 and a thickness of 8 nm along with a high-to-low concentration ratio of 1000, we demonstrate that it is possible to extract a power density of 51.5 W m-2, which is nearly three times the maximum achievable value employing bare conical nanochannels at the same salinity gradient.

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.

Improved Rectification and Osmotic Power in Polyelectrolyte-Filled Mesopores

Ample studies have shown the use of nanofluidics in the ionic diode and osmotic power generation, but similar ionic devices performed with large-sized mesopores are still poorly understood. In this study, we model and realize the mesoscale ionic diode and osmotic power generator, composed of an asymmetric cone-shaped mesopore with its narrow opening filled with a polyelectrolyte (PE) layer with high space charges. We show that, only when the space charge density of a PE layer is sufficiently large (>1×106 C/m3), the considered mesopore system is able to create an asymmetric ionic distributions in the pore and then rectify ionic current. As a result, the output osmotic power performance can be improved when the filled PE carries sufficiently high space charges. For example, the considered PE-filled mesopore system can show an amplification of the osmotic power of up to 35.1-fold, compared to the bare solid-state mesopore. The findings provide necessary information for the development of large-sized ionic diode and osmotic power harvesting device.

Covering the conical nanochannels with dense polyelectrolyte layers significantly improves the ionic current rectification

Because of their asymmetry, conical nanochannels/nanopores exhibit various attractive electrokinetic features, including ion selectivity, ionic concentration polarization, and ionic current rectification. The polyelectrolyte layer (PEL)-covered (soft) conical nanochannels have recently attracted significant attention because of their unique rectification characteristics. In the modeling of soft nanochannels, it is usually assumed that the properties of the PEL and the electrolyte are the same, an assumption that is not true, especially for dense PELs. In the present work, the influence of the PEL-electrolyte property difference on the ionic current rectification in conical soft nanochannels is studied. To this end, adopting a finite-element approach, the Poisson-Nernst-Planck and Navier-Stokes equations are numerically solved for a steady-state by considering different values of permittivity, diffusivity, and dynamic viscosity for the PEL and the electrolyte. The model is validated by comparing the results with the available theoretical and experimental data. The results show that the PEL-electrolyte property difference leads to a significant improvement of the rectification behavior, especially at low and moderate salt concentrations. This not only highlights the importance of considering different properties for the PEL and the electrolyte but also implies that the rectification behavior of soft nanochannels/nanopores may be improved considerably by utilizing denser PELs.

Electrokinetic power generation in conical nanochannels: regulation effects due to conicity

Electrokinetic power generation is a promising clean energy production technology, which utilizes the electric double layer in a nanochannel to convert the hydrodynamic energy to electrical power. Previous research largely focused on electrokinetic power generation in nanochannels with a uniform cross-section. In this work, we perform a systematic investigation of electrokinetic power generation in a conical nanochannel. For this purpose, a multiphysical model consisting of the Planck-Nernst-Poisson equations and the Navier-Stokes equation is formulated and solved numerically. In particular, we discover various regulation effects in electrokinetic power generation in conical nanochannels, which manifest as the difference in the power generation characteristics (streaming potential, streaming current and current-voltage relationship) between two opposite pressure differences of the same magnitude. These regulation effects are found to originate from the conicity of the nanochannel. Furthermore, the regulation parameters are defined to quantify the observed regulation effects. Various regulation parameters can be up to severals tens of percent under extreme conditions (e.g., large pressure difference, high surface charge density or large conicity), indicating the substantial significance of the regulation effects in electrokinetic power generation. The conclusions from this work can serve as an important reference for the design and operation of nanofluidic electrokinetic power generation 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.

DNA translocation through polyelectrolyte-modified nanopores: An analytical approximation

An analytical model for the electrophoretic speed of DNA translocating through nanopore functionalized with polyelectrolyte (PE) brush is developed for the first time. The electrophoretic speed depends on DNA surface potential, applied electric field, viscosity, and permittivity of solution along with velocity and electrostatic potential at liquid-polyelectrolyte layer (PEL) interface where the interface seemed to behave similar to that of a solid-state nanopore wall. Under the limit of Debye-Hückel linearization, the electrostatic potential at liquid-PEL interface and at DNA surface have been calculated. Velocity at liquid-PEL interface has been estimated by assuming a linear variation of hydrodynamic frictional force within the PEL. It is observed that velocity and electrostatic potential at liquid-PEL interface strongly depend on PE charge density and softness parameter. Present analytical results show excellent agreement with exact numerical results (i.e., without any approximation) at a higher salt concentration where Debye-Hückel linearization is applicable.