Fluids and Electrolytes under Confinement in Single-Digit Nanopores.

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Ion concentration polarization causes a nearly pore-length-independent conductance of nanopores.

There has been a great amount of interest in nanopores as the basis for sensors and templates for preparation of biomimetic channels as well as model systems to understand transport properties at the nanoscale. The presence of surface charges on the pore walls has been shown to induce ion selectivity as well as enhance ionic conductance compared to uncharged pores. Here, using three-dimensional continuum modeling, we examine the role of the length of charged nanopores as well as applied voltage for controlling ion selectivity and ionic conductance of single nanopores and small nanopore arrays. First, we present conditions where the ion current and ion selectivity of nanopores with homogeneous surface charges remain unchanged, even if the pore length decreases by a factor of 6. This length-independent conductance is explained through the effect of ion concentration polarization (ICP), which modifies local ionic concentrations, not only at the pore entrances but also in the pore in a voltage-dependent manner. We describe how voltage controls the ion selectivity of nanopores with different lengths and present the conditions when charged nanopores conduct less current than uncharged pores of the same geometrical characteristics. The manuscript provides different measures of the extent of the depletion zone induced by ICP in single pores and nanopore arrays, including systems with ionic diodes. The modeling shown here will help design selective nanopores for a variety of applications where single nanopores and nanopore arrays are used.

Beyond the electrical double layer model: ion-dependent effects in nanoscale solvent organization.

The nanoscale organization of electrolyte solutions at interfaces is often described well by the electrical double-layer model. However, a recent study has shown that this model breaks down in solutions of LiClO4 in acetonitrile at a silica interface, because the interface imposes a strong structuring in the solvent that in turn determines the preferred locations of cations and anions. As a surprising consequence of this organisation, the effective surface potential changes from negative at low electrolyte concentration to positive at high electrolyte concentration. Here we combine previous ion-current measurements with vibrational sum-frequency-generation spectroscopy experiments and molecular dynamics simulations to explore how the localization of ions at the acetonitrile-silica interface depends on the sizes of the anions and cations. We observe a strong, synergistic effect of the cation and anion identities that can prompt a large difference in the ability of ions to partition to the silica surface, and thereby influence the effective surface potential. Our results have implications for a wide range of applications that involve electrolyte solutions in polar aprotic solvents at nanoscale interfaces.

Nanopores: synergy from DNA sequencing to industrial filtration - small holes with big impact.

Nanopores in thin membranes play important roles in science and industry. Single nanopores have provided a step-change in portable DNA sequencing and understanding nanoscale transport while multipore membranes facilitate food processing and purification of water and medicine. Despite the unifying use of nanopores, the fields of single nanopores and multipore membranes differ - to varying degrees - in terms of materials, fabrication, analysis, and applications. Such a partial disconnect hinders scientific progress as important challenges are best resolved together. This Viewpoint suggests how synergistic crosstalk between the two fields can provide considerable mutual benefits in fundamental understanding and the development of advanced membranes. We first describe the main differences including the atomistic definition of single pores compared to the less defined conduits in multipore membranes. We then outline steps to improve communication between the two fields such as harmonizing measurements and modelling of transport and selectivity. The resulting insight is expected to improve the rational design of porous membranes. The Viewpoint concludes with an outlook of other developments that can be best achieved by collaboration across the two fields to advance the understanding of transport in nanopores and create next-generation porous membranes tailored for sensing, filtration, and other applications.

Numerical Modeling of Anisotropic Particle Diffusion through a Cylindrical Channel.

The transport of molecules and particles through single pores is the basis of biological processes, including DNA and protein sequencing. As individual objects pass through a pore, they cause a transient change in the current that can be correlated with the object size, surface charge, and even chemical properties. The majority of experiments and modeling have been performed with spherical objects, while much less is known about the transport characteristics of aspherical particles, which would act as a model system, for example, for proteins and bacteria. The transport kinetics of aspherical objects is an especially important, yet understudied, problem in nanopore analytics. Here, using the Wiener process, we present a simplified model of the diffusion of rod-shaped particles through a cylindrical pore, and apply it to understand the translation and rotation of the particles as they pass through the pore. Specifically, we analyze the influence of the particles' geometrical characteristics on the effective diffusion type, the first passage time distribution, and the particles' orientation in the pore. Our model shows that thicker particles pass through the channel slower than thinner ones, while their lengths do not affect the passage time. We also demonstrate that both spherical and rod-shaped particles undergo normal diffusion, and the first passage time distribution follows an exponential asymptotics. The model provides guidance on how the shape of the particle can be modified to achieve an optimal passage time.

Gating ion and fluid transport with chiral solvent.

The development of modern membranes for ionic separations and energy-storage devices such as supercapacitors depends on the description of ions at solid interfaces, as is often provided by the electrical double layer (EDL) model. The classical EDL model ignores, however, important factors such as possible spatial organization of solvent at the interface and the influence of the solvent on the spatial dependence of the electrochemical potential; these effects in turn govern electrokinetic phenomena. Here we provide a molecular-level understanding of how solvent structure can dictate ionic distributions at interfaces using a model system of a polar, aprotic solvent, propylene carbonate, in its enantiomerically pure and racemic forms, at a silica interface. We link the interfacial structure to the tuning of ionic and fluid transport by the chirality of the solvent and the salt concentration. The results of nonlinear spectroscopic experiments and electrochemical measurements suggest that the solvent exhibits lipid-bilayer-like interfacial organization, with a structure that is dependent on the solvent chirality. The racemic form creates highly ordered layered structure that dictates local ionic concentrations, such that the effective surface potential becomes positive in a wide range of electrolyte concentrations. The enantiomerically pure form exhibits weaker ordering at the silica surface, which leads to a lower effective surface charge induced by ions partitioning into the layered structure. The surface charge in silicon nitride and polymer pores is probed through the direction of electroosmosis that the surface charges induce. Our findings add a new dimension to the nascent field of chiral electrochemistry, and emphasize the importance of including solvent molecules in descriptions of solid-liquid interfaces.

Scanning Ion Conductance Microscopy of Nafion-Modified Nanopores.

Single nanopores in silicon nitride membranes are asymmetrically modified with Nafion and investigated with scanning ion conductance microscopy, where Nafion alters local ion concentrations at the nanopore. Effects of applied transmembrane potentials on local ion concentrations are examined, with the Nafion film providing a reservoir of cations in close proximity to the nanopore. Fluidic diodes based on ion concentration polarization are observed in the current-voltage response of the nanopore and in approach curves of SICM nanopipette in the vicinity of the nanopore. Experimental results are supported with finite element method simulations that detail ion depletion and enrichment of the nanopore/Nafion/nanopipette environment.

Rectified and Salt Concentration Dependent Wetting of Hydrophobic Nanopores.

Nanopores lined with hydrophobic groups function as switches for water and all dissolved species, such that transport is allowed only when applying a sufficiently high transmembrane pressure difference or voltage. Here we show a hydrophobic nanopore system whose wetting and ability to transport water and ions is rectified and can be controlled with salt concentration. The nanopore we study contains a junction between a hydrophobic zone and a positively charged hydrophilic zone. The nanopore is closed for transport at low salt concentrations and exhibits finite current only when the concentration reaches a threshold value that is dependent on the pore opening diameter, voltage polarity and magnitude, and type of electrolyte. The smallest nanopore studied here had a 4 nm diameter and did not open for transport in any concentration of KCl or KI examined. A 12 nm nanopore was closed for all KCl solutions but conducted current in KI at concentrations above 100 mM for negative voltages and opened for both voltage polarities at 500 mM KI. Nanopores with a hydrophobic/hydrophilic junction can thus function as diodes, such that one can identify a range of salt concentrations where the pores transport water and ions for only one voltage polarity. Molecular dynamics simulations together with continuum models provided a multiscale explanation of the observed phenomena and linked the salt concentration dependence of wetting with an electrowetting model. Results presented are crucial for designing next-generation chemical and ionic separation devices as well as understanding fundamental properties of hydrophobic interfaces under nanoconfinement.

Enhanced electro-osmosis in propylene carbonate salt solutions.

Properties of solid-liquid interfaces and surface charge characteristics mediate ionic and molecular transport through porous systems, affecting many processes such as separations. Herein, we report experiments designed to probe the electrochemical properties of solid-liquid interfaces using a model system of a single polyethylene terephthalate (PET) pore in contact with aqueous and propylene carbonate solutions of LiClO4. First, the existence and polarity of surface charges were inferred from current-voltage curves recorded when a pore was placed in contact with a LiClO4 concentration gradient. Second, the electro-osmotic transport of uncharged polystyrene particles through the PET pore provided information on the polarity and the magnitude of the pore walls' zeta potential. Our experiments show that the PET pores become effectively positively charged when in contact with LiClO4 solutions in propylene carbonate, even though in aqueous LiClO4, the same pores are negatively charged. Additionally, the electro-osmotic velocity of the particles revealed a significantly higher magnitude of the positive zeta potential of the pores in propylene carbonate compared to the magnitude of the negative zeta potential in water. The presented methods of probing the properties of solid-liquid interfaces are expected to be applicable to a wide variety of solid and liquid systems.

Charge Inversion and Calcium Gating in Mixtures of Ions in Nanopores.

Calcium ions play important roles in many physiological processes, yet their concentration is much lower than the concentrations of potassium and sodium ions. The selectivity of calcium channels is often probed in mixtures of calcium and a monovalent salt, e.g., KCl or NaCl, prepared such that the concentration of cations is kept constant with the mole fraction of calcium varying from 0 and 1. In biological channels, even sub-mM concentration of calcium can modulate the channels' transport characteristics; this effect is often explained via the existence of high affinity Ca2+ binding sites on the channel walls. Inspired by properties of biological calcium-selective channels, we prepared a set of nanopores with tunable opening diameters that exhibited a similar response to the presence of calcium ions as biochannels. Nanopores in 15 nm thick silicon nitride films were drilled using focused ion beam and e-beam in a transmission electron microscope and subsequently rendered negatively charged through silanization. We found that nanopores with diameters smaller than 20 nm were blocked by calcium ions such that the ion currents in mixtures of KCl and CaCl2 and in CaCl2 were even ten times smaller than the ion currents in KCl solution. The ion current blockage was explained by the effect of local charge inversion where accumulated calcium ions switch the effective surface charge from negative to positive. The modulation of surface charge with calcium leads to concentration and voltage dependent local charge density and ion current. The combined experimental and modeling results provide a link between calcium ion-induced changes in surface charge properties and resulting ionic transport.

Modulation of Ionic Current Rectification in Ultrashort Conical Nanopores.

Nanopores that exhibit ionic current rectification (ICR) behave like diodes such that they transport ions more efficiently in one direction than in the other. Conical nanopores have been shown to rectify ionic current, but only those with at least 500 nm in length exhibit significant ICR. Here, through the finite element method, we show how ICR of conical nanopores with lengths below 200 nm can be tuned by controlling individual charged surfaces, that is, the inner pore surface (surfaceinner) and exterior pore surfaces on the tip and base side (surfacetip and surfacebase). The charged surfaceinner and surfacetip can induce obvious ICR individually, while the effects of the charged surfacebase on ICR can be ignored. The fully charged surfaceinner alone could render the nanopore counterion-selective and induces significant ion concentration polarization in the tip region, which causes reverse ICR compared to nanopores with all surfaces charged. In addition, the direction and degree of rectification can be further tuned by the depth of the charged surfaceinner. When considering the exterior membrane surface only, the charged surfacetip causes intrapore ionic enrichment and depletion under opposite biases, which results in significant ICR. Its effective region is within ∼40 nm beyond the tip orifice. We also found that individual charged parts of the pore system contributed to ICR in an additive way because of the additive effect on the ion concentration regulation along the pore axis. With various combinations of fully/partially charged surfaceinner and surfacetip, diverse ICR ratios from ∼2 to ∼170 can be achieved. Our findings shed light on the mechanism of ICR in ultrashort conical nanopores and provide a useful guide to the design and modification of ultrashort conical nanopores in ionic circuits and nanofluidic sensors.

Rectification of Concentration Polarization in Mesopores Leads To High Conductance Ionic Diodes and High Performance Osmotic Power.

Nanopores exhibit a set of interesting transport properties that stem from interactions of the passing ions and molecules with the pore walls. Nanopores are used, for example, as ionic diodes and transistors, biosensors, and osmotic power generators. Using nanopores is however disadvantaged by their high resistance, small switching currents in nA range, low power generated, and signals that can be difficult to distinguish from the background. Here, we present a mesopore with ionic conductance reaching µS that rectifies ion current in salt concentrations as high as 1 M. The mesopore is conically shaped, and its region close to the narrow opening is filled with high molecular weight poly-l-lysine. To elucidate the underlying mechanism of ion current rectification (ICR), a continuum model based on a set of Poisson-Nernst-Planck and Stokes-Brinkman equations was adopted. The results revealed that embedding the polyelectrolyte in a conical pore leads to rectification of the effect of concentration polarization (CP) that is induced by the polyelectrolyte, and observed as voltage polarity-dependent modulations of ionic concentrations in the pore, and consequently ICR. Our work reveals the link between ICR and CP, significantly extending the knowledge of how charged polyelectrolytes modulate ion transport on nano- and mesoscales. The osmotic power application is also demonstrated with the developed polyelectrolyte-filled mesopores, which enable a power of up to ∼120 pW from one pore, which is much higher than the reported values using single nanoscale pores.

Abnormal Ionic-Current Rectification Caused by Reversed Electroosmotic Flow under Viscosity Gradients across Thin Nanopores.

Single nanopores have attracted much scientific interest because of their versatile applications. The majority of experiments have been performed with nanopores being in contact with the same electrolyte on both sides of the membrane, although solution gradients across semipermeable membranes are omnipresent in natural systems. In this manuscript, we studied ionic and fluidic movement through thin nanopores under viscosity gradients both experimentally and using simulations. Ionic-current rectification was observed under these conditions because solutions with different conductivities filled across the pore under different biases caused by electroosmotic flow. We found that a pore filled with high-viscosity solutions exhibited a current increase with applied voltage in a steeper slope beyond a threshold voltage, which abnormally reduced the current-rectification ratio. Through simulations, we found that reversed electroosmotic flow, which filled the pore with aqueous solutions of lower viscosities, was responsible for this behavior. The reversed electroosmotic flow could be explained by slower depletion of co-ions than of counterions along the pore. By increasing the surface charge density of pore surfaces, current-rectification ratio could reach the value of the viscosity gradient across thin nanopores. Our findings shed light on fundamental aspects to be considered when performing experiments with viscosity gradients across nanopores and nanofluidic channels.

Probing ion current in solid-electrolytes at the meso- and nanoscale.

We present experimental approaches to probe the ionic conductivity of solid electrolytes at the meso- and nanoscales. Silica ionogel based electrolytes have emerged as an important class of solid electrolytes because they maintain both fluidic and high-conductivity states at the nanoscale, but at the macroscale they are basically solid. Single mesopores in polymer films are shown to serve as templates for cast ionogels. The ionic conductivity of the ionogels was probed by two experimental approaches. In the first approach, the single-pore/ionogel membranes were placed between two chambers of a conductivity cell, in a set-up similar to that used for investigating liquid electrolytes. The second approach involved depositing contacts directly onto the membrane and measuring conductivity without the bulk solution present. Ionic conductivity determined by the two methods was in excellent agreement with macroscopic measurements, which suggested that the electrochemical properties of ionogel based electrolytes are preserved at the mesoscale, and ionogels can be useful in designing meso-scaled energy-storage devices.

Information Dynamics of a Nonlinear Stochastic Nanopore System.

Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER) and specific entropy rate (SER) computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.

Direction Dependence of Resistive-Pulse Amplitude in Conically Shaped Mesopores.

Conically shaped pores such as glass pipets as well as asymmetric pores in polymers became an important analytics tool used for the detection of molecules, viruses, and particles. Electrokinetic or pressure driven passage of single particles through a single pore causes a transient change of the transmembrane current, called a resistive-pulse, whose amplitude is the measure of the particle volume. The shape of the pulse reflects the pore topography, and in a conical pore, resistive pulses have a shape of a tick point. Passage of particles in both directions was reported to produce pulses of the same amplitude and shapes that are mirror images of each other. In this manuscript we identify conditions at which the amplitude of resistive-pulses in a conical mesopore is direction dependent. Neutral particles entering the pore from the larger entrance of a conical pore, called the base, block the current to a larger extent than the particles traveling in the opposite direction. Negatively charged particles on the other hand size larger when being transported in the direction from tip to base. The findings are explained via voltage-regulated ionic concentrations in the pore such that for one voltage polarity a weak depletion zone is formed, which increases the current blockage caused by a particle. For the opposite polarity, an enhancement of ionic concentrations was predicted. The findings reported here are of crucial importance for the resistive-pulse technique, which relates the current blockage with the size of the passing object.