Role of charge regulation and flow slip in the ionic conductance of nanopores: An analytical approach

Ultra-low noise measurements of ionic transport within individual single-walled carbon nanotubes

Despite 15 years of extensive investigation, the fabrication and study of nanofluidic devices that incorporate a single carbon nanotube (CNT) still represents a remarkable experimental challenge. In this study, we present the fabrication of nanofluidic devices that integrate an individual single-walled CNT (SWCNT), showcasing a notable reduction in noise by 1-3 orders of magnitude compared to conventional devices. This achievement was made possible by employing high dielectric constant materials for both the substrate and the CNT-covering layer. Furthermore, we provide a detailed account of the crucial factors contributing to the successful fabrication of SWCNT-based nanofluidic devices that are reliably leak-free, plug-free, and long-lived. Key considerations include the quality of the substrate-layer interface, the nanotube opening, and the effective removal of photoresist residues and trapped microbubbles. We demonstrate that these devices, characterized by a high signal-to-noise ratio, enable spectral noise analysis of ionic transport through an individual SWCNT, thus showing that SWCNTs obey Hooge's law in 1/f at low frequencies. Beyond advancing our fundamental understanding of ion transport in SWCNTs, these ultralow-noise measurements open avenues for leveraging SWCNTs in nanopore sensing applications for single-molecule detection, offering high sensitivity and identification capabilities.

Ion transport and ultra-efficient osmotic power generation in boron nitride nanotube porins

Nanotube porins form transmembrane nanomaterial-derived scaffolds that mimic the geometry and functionality of biological membrane channels. We report synthesis, transport properties, and osmotic energy harvesting performance of another member of the nanotube porin family: boron nitride nanotube porins (BNNTPs). Cryo-transmission electron microscopy imaging, liposome transport assays, and DNA translocation experiments show that BNNTPs reconstitute into lipid membranes to form functional channels of ~2-nm diameter. Ion transport studies reveal ion conductance characteristics of individual BNNTPs, which show an unusual C1/4 scaling with ion concentration and pronounced pH sensitivity. Reversal potential measurements indicate that BNNTPs have strong cation selectivity at neutral pH, attributable to the high negative charge on the channel. BNNTPs also deliver very large power density up to 12 kW/m2 in the osmotic gradient transport experiments at neutral pH, surpassing that of other BNNT-based devices by two orders of magnitude under similar conditions. Our results suggest that BNNTPs are a promising platform for mass transport and osmotic power generation.

Influence of the Quantum Capacitance on Electrolyte Conductivity through Carbon Nanotubes

In recent experiments, unprecedentedly large values for the conductivity of electrolytes through carbon nanotubes (CNTs) have been measured, possibly owing to flow slip and a high pore surface charge density whose origin remains debated. Here, we model the coupling between the CNT quantum capacitance and the classical electrolyte-filled pore one and study how electrolyte transport is modulated when a gate voltage is applied to the CNT. Our work shows that under certain conditions the quantum capacitance is lower than the pore one due to the finite quasi-1D CNT electronic density of states and therefore controls the CNT surface charge density that dictates the confined electrolyte conductivity. The dependence of the computed surface charge and conductivity on reservoir salt concentration and gate voltage is thus intimately related to the electronic properties of the CNT. This approach provides key insight into why metallic CNTs have larger experimentally measured conductivities than semiconducting ones.

Ion and Hydrodynamic Translucency in 1D van der Waals Heterostructured Boron-Nitride Single-Walled Carbon Nanotubes

An unresolved challenge in nanofluidics is tuning ion selectivity and hydrodynamic transport in pores, particularly for those with diameters larger than a nanometer. In contrast to conventional strategies that focus on changing surface functionalization or confinement degree by varying the radial dimension of the pores, we explore a unique approach for manipulating ion selectivity and hydrodynamic flow enhancement by externally coating single-walled carbon nanotubes (SWCNTs) with a few layers of hexagonal boron nitride (h-BN). For van der Waals heterostructured BN-SWCNTs, we observed a 9-fold increase in cation selectivity for K+ versus Cl- compared to pristine SWCNTs of the same 2.2 nm diameter, while hydrodynamic slip lengths decreased by more than an order of magnitude. These results suggest that the single-layer graphene inner surface may be translucent to charge-regulation and hydrodynamic-slip effects arising from h-BN on the outside of the SWCNT. Such 1D heterostructures could serve as synthetic platforms with tunable properties for exploring distinct nanofluidic phenomena and their potential applications.

Impact of Single-Walled Carbon Nanotube Functionalization on Ion and Water Molecule Transport at the Nanoscale

Nanofluidics has a very promising future owing to its numerous applications in many domains. It remains, however, very difficult to understand the basic physico-chemical principles that control the behavior of solvents confined in nanometric channels. Here, water and ion transport in carbon nanotubes is investigated using classical force field molecular dynamics simulations. By combining one single walled carbon nanotube (uniformly charged or not) with two perforated graphene sheets, we mimic single nanopore devices similar to experimental ones. The graphitic edges delimit two reservoirs of water and ions in the simulation cell from which a voltage is imposed through the application of an external electric field. By analyzing the evolution of the electrolyte conductivity, the role of the carbon nanotube geometric parameters (radius and chirality) and of the functionalization of the carbon nanotube entrances with OH or COO- groups is investigated for different concentrations of group functions.

Scaling of ionic conductance in a fluctuating single-layer nanoporous membrane

Single-layer membranes have emerged as promising candidates for applications requiring high transport rates due to their low resistance to molecular transport. Owing to their atomically thin structure, these membranes experience significant microscopic fluctuations, emphasizing the need to explore their impact on ion transport processes. In this study, we investigate the effects of membrane fluctuations on the elementary scaling behavior of ion conductance [Formula: see text] as a function of ion concentration [Formula: see text], represented as [Formula: see text], using molecular dynamics simulations. Our findings reveal that membrane fluctuations not only alter the conductance coefficient [Formula: see text] but also the power-law exponent [Formula: see text]. We identify two distinct frequency regimes of membrane fluctuations, GHz-scale and THz-scale fluctuations, and examine their roles in conductance scaling. Furthermore, we demonstrate that the alteration of conductance scaling arises from the non-linearity between ion conductance and membrane shape. This work provides a fundamental understanding of ion transport in fluctuating membranes.

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.

Electrical Conductance of Charged Nanopores

A nanopore's response to an electrical potential drop is characterized by its electrical conductance, . For the last two decades, it has been thought that at low electrolyte concentrations, , the conductance is concentration-independent such that . It has been recently demonstrated that surface charge regulation changes the dependency to , whereby the slope typically takes the values α = 1/3 or 1/2. However, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. Here, we elucidate the interplay between three mechanisms: surface charge regulation, convection, and slip lengths. We show that the inclusion of convection does not change the slope, and when the effects of hydrodynamic slip are included, the slope is doubled. We show that when all effects are accounted for, α can take any value between 0 and 1 where the exact value of the slope depends on the material properties. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Putting together the puzzle of ion transfer in single-digit carbon nanotubes: mean-field meets ab initio

Nature employs channel proteins to selectively pass water across cell membranes, which inspires the search for bio-mimetic analogues. Carbon nanotube porins (CNTPs) are intriguing mimics of water channels, yet ion transport in CNTPs still poses questions. As an alternative to continuum models, here we present a molecular mean-field model that transparently describes ion coupling, yet unlike continuum models, computes ab initio all required thermodynamic quantities for the KCl salt and H⁺ and OH^- ions present in water. Starting from water transfer, the model considers the transfer of free ions, along with ion-pair formation as a proxy of non-mean-field ion-ion interactions. High affinity to hydroxide, suggested by experiments, making it a dominant charge carrier in CNTPs, is revealed as an exceptionally favorable transfer of KOH pairs. Nevertheless, free ions, coexisting with less mobile ion-pairs, apparently control ion transport. The model well explains the observed effects of salt concentration and pH on conductivity, transport numbers, anion permeation and its activation energies, and current rectification. The proposed approach is extendable to other sub-nanochannels and helps design novel osmotic materials and devices.

Enhanced nanofluidic transport in activated carbon nanoconduits

Carbon has emerged as a unique material in nanofluidics, with reports of fast water transport, molecular ion separation and efficient osmotic energy conversion. Many of these phenomena still await proper rationalization due to the lack of fundamental understanding of nanoscale ionic transport, which can only be achieved in controlled environments. Here we develop the fabrication of 'activated' two-dimensional carbon nanochannels. Compared with nanoconduits with 'pristine' graphite walls, this enables the investigation of nanoscale ionic transport in great detail. We show that activated carbon nanochannels outperform pristine channels by orders of magnitude in terms of surface electrification, ionic conductance, streaming current and (epi-)osmotic currents. A detailed theoretical framework enables us to attribute the enhanced ionic transport across activated carbon nanochannels to an optimal combination of high surface charge and low friction. Furthermore, this demonstrates the unique potential of activated carbon for energy harvesting from salinity gradients with single-pore power density across activated carbon nanochannels, reaching hundreds of kilowatts per square metre, surpassing alternative nanomaterials.

Comparison Study on Single Nucleotide Transport Phenomena in Carbon Nanotubes

To be considered as a promising candidate for mimicking biological nanochannels, carbon nanotubes (CNTs) have been used to explore the mass transport phenomena in recent years. In this study, the single nucleotide transport phenomena are comparatively studied using individual CNTs with a length of ∼15 μm and diameters ranging from 1.5 to 2.5 nm. In the case of CNTs with a diameter of 1.57-1.98 nm, the current traces of nucleotide transport are independent with the metallicity of CNTs and consist of single peak current pulses, whereas extraordinary stepwise current signals are observed in CNT with a diameter of 2.33 nm. It suggests that there is only one molecule in the nanochannel at a time until the diameter of CNT increases to 2.33 nm. Furthermore, it also demonstrates that the single nucleotides can be identified statistically according to their current pulses, indicating the potential application of CNT-based sensors for nucleotides identification.

Competition between Born solvation, dielectric exclusion, and Coulomb attraction in spherical nanopores

The recent measurement of a very low dielectric constant, ε, of water confined in nanometric slit pores leads us to reconsider the physical basis of ion partitioning into nanopores. For confined ions in chemical equilibrium with a bulk of dielectric constant ε_{b}>ε, three physical mechanisms, at the origin of ion exclusion in nanopores, are expected to be modified due to this dielectric mismatch: dielectric exclusion at the water-pore interface (with membrane dielectric constant, ε_{m}<ε), the solvation energy related to the difference in Debye-Hückel screening parameters in the pore, κ, and in the bulk κ_{b}, and the classical Born solvation self-energy proportional to ε^{-1}-ε_{b}^{-1}. Our goal is to clarify the interplay between these three mechanisms and investigate the role played by the Born contribution in ionic liquid-vapor (LV) phase separation in confined geometries. We first compute analytically the potential of mean force (PMF) of an ion of radius R_{i} located at the center of a nanometric spherical pore of radius R. Computing the variational grand potential for a solution of confined ions, we then deduce the partition coefficients of ions in the pore versus R and the bulk electrolyte concentration ρ_{b}. We show how the ionic LV transition, directly induced by the abrupt change of the dielectric contribution of the PMF with κ, is favored by the Born self-energy and explore the decrease of the concentration in the pore with ε both in the vapor and liquid states. Phase diagrams are established for various parameter values and we show that a signature of this phase transition can be detected by monitoring the total osmotic pressure as a function of R. For charged nanopores, these exclusion effects compete with the electrostatic attraction that imposes the entry of counterions into the pore to enforce electroneutrality. This study will therefore help in deciphering the respective roles of the Born self-energy and dielectric mismatch in experiments and simulations of ionic transport through nanopores.

Effect of pH on Effective Slip Length and Surface Charge at Solid-Oil Interfaces of Roughness-Induced Surfaces

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Abstract

In the development of micro/nano fluid control systems, fluid resistance has always been one of the key factors restricting its development. According to previous studies, it is found that the boundary slip effect of the solid-liquid interface can effectively reduce the resistance of the microfluid and improve the transport efficiency of the microfluid. The boundary slip length is mainly affected by surface wettability, roughness, and surface charge density. Among them, the influence mechanism of surface charge density on the boundary slip is the most complicated, and there is a lack of relevant research, and further investigation is needed. In this paper, we present research on quantification of effective slip length and surface charge density, where the roughness effect is considered. The electrostatic and hydrodynamic force data obtained from atomic force microscopy (AFM) measurements were fitted and processed for comparative analysis. We obtained the variation of surface charge density and effective slip length when different oleophobic surface samples were immersed in ethylene glycol with different pH values. The effect of pH on the surface charge density and effective slip length was investigated by their variations. The mechanism of the effect of pH on the surface charge density was discussed. The experimental results show that in the ethylene glycol solution, no matter whether the pH value of the solution increases or decreases, the charge density of the surface with the same properties decreases, and the effective boundary slip length also shows a downward trend. In deionized water, the surface charge density and effective boundary slip length decreases with the decrease of PH value.

Coupling effects in electromechanical ion transport in graphene nanochannels

In this work, we use molecular dynamics simulations to study the transport of ions in electromechanical flows in slit-like graphene nanochannels. The variation of ionic currents indicates a nonlinear coupling between pressure-driven and electroosmotic flows, which enhances the ionic currents for electromechanical flows compared with the linear superposition of pressure-driven and electroosmotic flows. The nonlinear coupling is attributed to the reduction of the total potential energy barrier due to the density variations of ions and water molecules in the channel. The numerical results may offer molecular insights into the design of nanofluidic devices for energy conversion.

Ion Transport in Electrically Imperfect Nanopores

Ionic transport through a charged nanopore at low ion concentration is governed by the surface conductance. Several experiments have reported various power-law relations between the surface conductance and ion concentration, i.e., G_surf ∝ c₀^α. However, the physical origin of the varying exponent, α, is not yet clearly understood. By performing extensive coarse-grained Molecular Dynamics simulations for various pore diameters, lengths, and surface charge densities, we observe varying power-law exponents even with a constant surface charge and show that α depends on how electrically "perfect" the nanopore is. Specifically, when the net charge of the solution in the pore is insufficient to ensure electroneutrality, the pore is electrically "imperfect" and such nanopores can exhibit varying α depending on the degree of "imperfectness". We present an ionic conductance theory for electrically "imperfect" nanopores that not only explains the various power-law relationships but also describes most of the experimental data available in the literature.

Ions and Water Dancing through Atom-Scale Holes: A Perspective toward "Size Zero"

We provide an overview of atom-scale apertures in solid-state membranes, from "pores" and "tubes" to "channels", with characteristic sizes comparable to the sizes of ions and water molecules. In this regime of ∼1 nm diameter pores, water molecules and ions are strongly geometrically confined: the size of water molecules (∼0.3 nm) and the size of "hydrated" ions in water (∼0.7-1 nm) are similar to the pore diameters, physically limiting the ion flow through the hole. The pore sizes are comparable to the classical Debye screening length governing the spatial range of electrostatic interaction, ∼0.3 to 1 nm for 1 to 0.1 M KCl. In such small structures, charges can be unscreened, leading to new effects. We discuss experiments on ∼1 nm diameter nanopores, with a focus on carbon nanotube pores and ion transport studies. Finally, we present an outlook for artificial "size zero" pores in the regime of small diameters and small thicknesses. Beyond mimicking protein channels in nature, solid-state pores may offer additional possibilities where sensing and control are performed at the pore, such as in electrically and optically addressable solid-state materials.

Strong Electroosmotic Coupling Dominates Ion Conductance of 1.5 nm Diameter Carbon Nanotube Porins

Extreme confinement in nanometer-sized channels can alter fluid and ion transport in significant ways, leading to significant water flow enhancement and unusual ion correlation effects. These effects are especially pronounced in carbon nanotube porins (CNTPs) that combine strong confinement in the inner lumen of carbon nanotubes with the high slip flow enhancement due to smooth hydrophobic pore walls. We have studied ion transport and ion selectivity in 1.5 nm diameter CNTPs embedded in lipid membranes using a single nanopore measurement setup. Our data show that CNTPs are weakly cation selective at pH 7.5 and become nonselective at pH 3.0. Ion conductance of CNTPs exhibits an unusual 2/3 power law scaling with the ion concentration at both neutral and acidic pH values. Coupled Navier-Stokes and Poisson-Nernst-Planck simulations and atomistic molecular dynamics simulations reveal that this scaling originates from strong coupling between water and ion transport in these channels. These effects could result in development of a next generation of biomimetic membranes and carbon nanotube-based electroosmotic pumps.

Interfacial transport with mobile surface charges and consequences for ionic transport in carbon nanotubes

In this paper, we explore the effect of a finite surface charge mobility on the interfacial transport: conductance, streaming currents, electro- and diffusio-osmotic flows. We first show that the surface charge mobility modifies the hydrodynamic boundary condition for the fluid, which introduces a supplementary term depending on the applied electric field. In particular, the resulting slip length is found to decrease inversely with the surface charge. We then derive expressions for the various transport mobilities, highlighting that the surface charge mobility merely moderates the amplification effect of interfacial slippage, to the noticeable exception of diffusio-osmosis and surface conductance. Our calculations, obtained within Poisson-Boltzmann framework, highlight the importance of non-linear electrostatic contributions to predict the small concentration/large charge limiting regimes for the transport mobilities. We discuss these predictions in the context of recent electrokinetic experiments with carbon nanotubes.