Intrinsic Ion Selectivity of Narrow Hydrophobic Pores

Ion-Ion Selectivity of Synthetic Membranes with Confined Nanostructures

Synthetic membranes featuring confined nanostructures have emerged as a prominent category of leading materials that can selectively separate target ions from complex water matrices. Further advancements in these membranes will pressingly rely on the ability to elucidate the inherent connection between transmembrane ion permeation behaviors and the ion-selective nanostructures. In this review, we first abstract state-of-the-art nanostructures with a diversity of spatial confinements in current synthetic membranes. Next, the underlying mechanisms that govern ion permeation under the spatial nanoconfinement are analyzed. We then proceed to assess ion-selective membrane materials with a focus on their structural merits that allow ultrahigh selectivity for a wide range of monovalent and divalent ions. We also highlight recent advancements in experimental methodologies for measuring ionic permeability, hydration numbers, and energy barriers to transport. We conclude by putting forth the future research prospects and challenges in the realm of high-performance ion-selective membranes.

Impact of Confinement and Zwitterionic Ligand Chemistry on Ion-Ion Selectivity of Functionalized Nanopores

Membranes incorporating zwitterionic chemistries have recently emerged as promising candidates for facilitating challenging ion-ion separations. Transport of ions in such membranes predominantly occurs in hydrated nanopores lined with zwitterionic monomers. To shed light on the physics of ion-ion selectivity underlying such materials, we conducted molecular dynamics simulations of sodium halide transport in model nanopores grafted with sulfobetaine methacrylate molecules. Our results reveal that in both functionalized and unfunctionalized nanopores smaller ions prefer to reside near the pore center, while the larger ions tend to reside near the pore walls. An enhancement in the selective transport of larger anions is observed within the unfunctionalized nanopores relative to that in salt-in-water solutions. Upon functionalization of the nanopores with zwitterions (ZIs), the disparities in the anionic distribution profiles within the pores coupled with differences in the anion-ZI interactions result in a slowdown of larger anions relative to smaller anions. Increasing the ZI grafting density exacerbates these effects, further promoting the selective transport of smaller anions. Our results suggest that selectivity toward large anions can be realized by using nanoporous membranes with ZI content that is high enough to facilitate ion/water partitioning into the pores while preserving the characteristic tendency of the unfunctionalized pores to facilitate faster transport of the larger anions. On the other hand, selectivity toward smaller anions can be achieved by targeting ZI content within the pores that is high enough to significantly slow down the transport of large anions but not high enough to hinder the partitioning of ions/water molecules into the pore due to steric effects.

Fabrication of Oriented MOF-Based Mixed Matrix Membrane via Ion-Induced Synchronous Synthesis

Developing a facile strategy for constructing oriented mixed matrix membranes (MMMs) with uniformly dispersed and high-loading metal-organic frameworks (MOFs) is a crucial scientific challenge in probing the enhanced capability and potential applications of MOF-polymer MMMs. Herein, a novel synchronous synthetic method for constructing oriented CuBDC/poly(m-phenylenediamine) (CuBDC/PmPD) MMM with uniform MOF dispersion at high loading at the air-solution interface via the dual function of metal ions is reported. The resulting MMM exhibits excellent separation performance in ion sieving and seawater desalination due to the structural integrity of the proposed membrane and the highly interconnected channels created through the oriented distribution of MOF in a polymer matrix. Such a cutting-edge approach may provide promising insights into the development of advanced MMMs with optimized structure and superior performances.

Tuning Pore Size in Graphene in the Angstrom Regime for Highly Selective Ion-Ion Separation

Zero-dimensional pores spanning only a few angstroms in size in two-dimensional materials such as graphene are some of the most promising systems for designing ion-ion selective membranes. However, the key challenge in the field is that so far a crack-free macroscopic graphene membrane for ion-ion separation has not been realized. Further, methods to tune the pores in the Å-regime to achieve a large ion-ion selectivity from the graphene pore have not been realized. Herein, we report an Å-scale pore size tuning tool for single layer graphene, which incorporates a high density of ion-ion selective pores between 3.5 and 8.5 Å while minimizing the nonselective pores above 10 Å. These pores impose a strong confinement for ions, which results in extremely high selectivity from centimeter-scale porous graphene between monovalent and bivalent ions and near complete blockage of ions with the hydration diameter, DH, greater than 9.0 Å. The ion diffusion study reveals the presence of an energy barrier corresponding to partial dehydration of ions with the barrier increasing with DH. We observe a reversal of K+/Li+ selectivity at elevated temperature and attribute this to the relative size of the dehydrated ions. These results underscore the promise of porous two-dimensional materials for solute-solute separation when Å-scale pores can be incorporated in a precise manner.

Cation Exchange Membranes and Process Optimizations in Electrodialysis for Selective Metal Separation: A Review

The selective separation of metal species from various sources is highly desirable in applications such as hydrometallurgy, water treatment, and energy production but also challenging. Monovalent cation exchange membranes (CEMs) show a great potential to selectively separate one metal ion over others of the same or different valences from various effluents in electrodialysis. Selectivity among metal cations is influenced by both the inherent properties of membranes and the design and operating conditions of the electrodialysis process. The research progress and recent advances in membrane development and the implication of the electrodialysis systems on counter-ion selectivity are extensively reviewed in this work, focusing on both structure-property relationships of CEM materials and influences of process conditions and mass transport characteristics of target ions. Key membrane properties, such as charge density, water uptake, and polymer morphology, and strategies for enhancing ion selectivity are discussed. The implications of the boundary layer at the membrane surface are elucidated, where differences in the mass transport of ions at interfaces can be exploited to manipulate the transport ratio of competing counter-ions. Based on the progress, possible future R&D directions are also proposed.

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.

Field-Induced Hydration Shell Reorganization Enables Electro-osmotic Flow in Nanochannels

Electro-osmotic flow is the motion of fluid driven by an applied electric field, for which an electric double layer near a charged surface is deemed essential. Here, we find that electro-osmotic flow can occur in electrically neutral nanochannels in the absence of definable electric double layers through extensive molecular dynamics simulations. An applied electric field is shown to cause an intrinsic channel selectivity between cations and anions, by reorienting the hydration shells of these confined ions. The ion selectivity then results in a net charge density in the channel that induces the unconventional electro-osmotic flow. The flow direction is amenable to manipulation by the field strength and the channel size, which will inform ongoing efforts to develop highly integrated nanofluidic systems capable of complex flow control.

Coupling solute interactions with functionalized graphene membranes: towards facile membrane-level engineering

Optimizing ion transport through nanoporous graphene membranes with intricate engineering at nanoscale levels finds applications ranging from ion segregation to desalination. Such membrane-level engineering often requires futuristic and state-of-the-art micro- and nanofabrication infrastructure making it less accessible to widespread applications. In this study, the effective membrane pore size is modulated using macroscopic membrane functionalization, which, when combined with the solute concentration, can prove to be facile nanoscale engineering towards achieving selectivity. By performing robust molecular dynamics (MD) simulations of aqueous NaCl solution through a nanoporous graphene membrane, we demonstrate that varying membrane wettability influences the structural organization of ions and water molecules both in the vicinity and inside the nanopore, which is manifested in the form of altered permeation characteristics. Moreover, the disparate solvation characteristics of the ionic species in conjunction with the variable van der Waals interactive forces affect the ion-selective nature (Cl^- over Na⁺) of the membrane. The relative hydrophilization, resulting from the effective functionalization of the nanoporous graphene membrane, not only allows greater control over the permeation characteristics of ions and water molecules mediated by an altered depletion ratio but also gives rise to the ion-selective nature of the membrane, thus providing a sound understanding of the transport properties of ion-water solutions through nanoporous materials.

Synergistic Effect of Bio-Inspired Nanochannels: Hydrophilic DNA Probes at Inner Wall and Hydrophobic Coating at Outer Surface for Highly Sensitive Detection

During the past few decades, bio-inspired nanochannels have been well developed and applied in biosensing, energy transfer, separation, and so on. Here, inspired by the synergistic effect of biological nanopores, biomimetic solid-state nanochannels with hydrophilic DNA probes at the inner wall (DNA@IW_Hydrophilic ) and hydrophobic coating at the outer surface (None@OS_Hydrophobic ) are designed. To demonstrate their prompted sensing properties, Hg²⁺ and its specific probe are selected as target and hydrophilic DNA probes, respectively. Compared with the traditional solid-state nanochannels with hydrophilic probes distributed on both the inner wall and outer surface, the nanochannels with DNA@IW_Hydrophilic +None@OS_Hydrophobic significantly decrease the limit of detection (LOD) by 10⁵ -fold. The obvious improvement of sensitivity (with LOD of 1 nM) is attributed to the synergistic effect: None@OS_Hydrophobic results in the nanochannel's effective diameter decrease and DNA@IW_Hydrophilic induces a specific sensing target. Meanwhile, nanomolar detection of Hg²⁺ in human serum and in vivo fish muscle are achieved. Through molecular dynamics simulation, the synergistic effect can be confirmed by ion fluxes increasement; the relative carbon nanotube increases from 135.64% to 135.84%. This work improves the understanding of nanochannels' synergistic effect and provides a significant insight for nanochannels with improved sensitivity.

Long-Chain Modification of the Tips and Inner Walls of MWCNTs and Their Nanocomposite Reverse Osmosis Membranes

Multi-walled carbon nanotubes (MWCNTs) were modified on the tips and inner walls by 12-chloro-12-oxododecanedioic acid-methyl ester groups and then added to the polyamide composite membranes to prepare MWCNT-CH₂OCOC₁₂H₂₃O₂ membranes for desalination. The characterization results of transmission electron microscopy, Fourier transform, infrared transform, and thermogravimetric analysis showed that the 12-chloro-12-oxododecanedioic acid-methyl ester group was successfully grafted to the entrances and inner walls of the MWCNTs. The performance of the MWCNTs' composite membranes was evaluated by scanning electron microscopy, contact angle, and filtration test. The modified membrane morphology is more uniform, and there is no structural damage. The grafting of carbon nanotubes with methyl 12-chloro-12-oxydodecyldicarboxylate could improve the hydrophilicity of the membrane. Under identical conditions, the water flux of MWCNT-CH₂OCOC₁₂H₂₃O₂ membranes was higher than that of the pristine carbon nanotube's membrane, and the desalination rate was also slightly improved.

Enhanced Ion Rejection in Carbon Nanotubes by a Lateral Electric Field

Reverse osmosis membranes hold great promise for dealing with global water scarcity. However, the trade-off between ion selectivity and water permeability is a serious obstacle to desalination. Herein, we introduce an effective strategy to enhance the desalination performance of the membrane. A series of molecular dynamics simulations manifest that an additional lateral electric field significantly promotes ion rejection in carbon nanotubes (CNTs) under the drive of longitudinal pressure. Specifically, with the increase in the electric field, the ion flux shows a deep linear decay, while the water flux decreases only slightly, resulting in a linear increase in ion rejection. The energy barriers of ions around the CNT inlet are obtained by calculating the potentials of mean force to explain enhanced ion rejection. The lateral electric field uniformly raises the energy barriers of ions by pushing them away from the CNT inlet, corresponding to the enhanced ion velocity in the field direction. Furthermore, with the increase in CNT diameter, there is a significant increase in the flux of both ions and water; however, the lateral electric field can also obviously enhance the ion rejection in wider CNTs. Consequently, the enhancement of ion rejection by lateral electric fields should be universal for different CNT diameters, which opens a new avenue for selective permeation and may have broad implications for desalination devices with large pore sizes.

A New Strategy for Highly Efficient Separation between Monovalent Cations by Applying Opposite-Oriented Pressure and Electric Fields

Biological ion channels exhibit excellent ion selectivity, but it has been challenging to design their artificial counterparts, especially for highly efficient separation of similar ions. Here, a new strategy to achieve high selectivity between alkali metal ions with artificial nanostructures is reported. Molecular dynamics (MD) simulations and experiments are combined to study the transportation of monovalent cations through graphene oxide (GO) nanoslits by applying pressure or/and electric fields. It is found that the ionic transport selectivity under the pressure driving reverses compared with that under the electric field driving. Moreover, MD simulations show that different monovalent cations can be separated with unprecedentedly high selectivity by applying opposite-oriented pressure and electric fields. This highly efficient separation originates from two distinctive ionic transporting modes, that is, hydration shells drive ions under pressure, but drag ions under the electric field. Hence, ions with different hydration strengths can be efficiently separated by tuning the net mobility induced by the two types of driving forces when the selected ions are kept moving while the other ones are immobilized. And nanoconfinement is confirmed to enhance the separation efficacy. This discovery paves a new avenue for separating similar ions without elaborately designing biomimetic nanostructures.

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.

Applying Transition-State Theory to Explore Transport and Selectivity in Salt-Rejecting Membranes: A Critical Review

Membrane technologies using reverse osmosis (RO) and nanofiltration (NF) have been widely implemented in water purification and desalination processes. Separation between species at the molecular level is achievable in RO and NF membranes due to a complex and poorly understood combination of transport mechanisms that have attracted the attention of researchers within and beyond the membrane community for many years. Minimizing existing knowledge gaps in transport through these membranes can improve the sustainability of current water-treatment processes and expand the use of RO and NF membranes to other applications that require high selectivity between species. Since its establishment in 1949, and with growing popularity in recent years, Eyring's transition-state theory (TST) for transmembrane permeation has been applied in numerous studies to mechanistically explore molecular transport in membranes including RO and NF. In this review, we critically assess TST applied to transmembrane permeation in salt-rejecting membranes, focusing on mechanistic insights into transport under confinement that can be gained from this framework and the key limitations associated with the method. We first demonstrate and discuss the limited ability of the commonly used solution-diffusion model to mechanistically explain transport and selectivity trends observed in RO and NF membranes. Next, we review important milestones in the development of TST, introduce its underlying principles and equations, and establish the connection to transmembrane permeation with a focus on molecular-level enthalpic and entropic barriers that govern water and solute transport under confinement. We then critically review the application of TST to explore transport in RO and NF membranes, analyzing trends in measured enthalpic and entropic barriers and synthesizing new data to highlight important phenomena associated with the temperature-dependent measurement of the activation parameters. We also discuss major limitations of the experimental application of TST and propose specific solutions to minimize the uncertainties surrounding the current approach. We conclude with identifying future research needs to enhance the implementation and maximize the benefit of TST application to transmembrane permeation.

Ion Hydration under Nanoscale Confinement: Dimensionality and Scale Effects

How ions are hydrated in nanoconfined spaces is crucial for understanding many natural phenomena and practical applications, such as biological functionalities and energy conversion devices. In real systems, nanoconfinement shows structural diversity, but the influence of dimensionality and scale on ion hydration remains considerably unrevealed. Here, we study ion hydration under various confinements by systematic molecular dynamics simulations. In a given dimension, the structure and dynamics of water molecules in the first hydration shell are altered to a degree inversely correlated with the confinement scale, as long as there is no central bulk-like region. Further comparison of ion hydration among different dimensional systems shows that this scale effect becomes more pronounced in systems with lower dimensionality, due to a more significant water layering effect and lower probability for ions to stay away from confining surfaces. These findings provide a qualitatively new understanding of ion transport in biological channels and are instrumental for the design of functional nanofluidic devices.

Control one-dimensional length of rectangular pore on graphene membrane for better desalination performance

At present, there is a general contradiction between permeability and selectivity of reverse osmosis (RO) membranes for desalination; a membrane with higher water permeability will give a lower salt rejection or selectivity, and vice versa. In this work, single-layer nanoporous graphene is used as RO membrane to investigate the effects of pore shape to reduce this contradiction by molecular dynamics simulations. Two kinds of pores (round and rectangular pores) with different sizes are simulated. For round pore, although the water permeability increases with the increase of the pore size, the salt rejection rate drops rapidly. For rectangular pore, reasonable designed pore structure can achieve improved water permeability and high salt rejection of graphene membrane by keeping one-dimensional length (i.e. the width) of the pore less than the size of the hydrated ions and increasing the other dimensional length. The restriction of one dimension can prevent the passage of hydrated ions through the pore effectively. This 'one-dimensional restriction' provides a simple strategy for designing RO membrane with variable pore structures to obtain a better desalination performance.

Revisit the Hydrated Cation-π Interaction at the Interface: A New View of Dynamics and Statistics

Carbon-based matter, such as biomolecules and graphitic structures, often form a liquid-solid/soft matter interface in salt solution and continuously affect the surrounding cations through hydrated cation-π interactions. In this Perspective, we revisit the effect of the hydrated cation-π interactions at the interface using statistical physics, which reveals how hydrated cation-π interactions affect every component dynamically and cause a time-dependent statistical effect at the liquid-solid/soft interface. We also highlight several pieces of experimental evidence from a statistical perspective and discuss the remarkable applications related to environmental protection, industrial manufacturing, and biological sciences.

The energetic barrier to single-file water flow through narrow channels

Various nanoscopic channels of roughly equal diameter and length facilitate single-file diffusion at vastly different rates. The underlying variance of the energetic barriers to transport is poorly understood. First, water partitioning into channels so narrow that individual molecules cannot overtake each other incurs an energetic penalty. Corresponding estimates vary widely depending on how the sacrifice of two out of four hydrogen bonds is accounted for. Second, entropy differences between luminal and bulk water may arise: additional degrees of freedom caused by dangling OH-bonds increase entropy. At the same time, long-range dipolar water interactions decrease entropy. Here, we dissect different contributions to Gibbs free energy of activation, ΔG ^‡, for single-file water transport through narrow channels by analyzing experimental results from water permeability measurements on both bare lipid bilayers and biological water channels that (i) consider unstirred layer effects and (ii) adequately count the channels in reconstitution experiments. First, the functional relationship between water permeabilities and Arrhenius activation energies indicates negligible differences between the entropies of intraluminal water and bulk water. Second, we calculate ΔG ^‡ from unitary water channel permeabilities using transition state theory. Plotting ΔG ^‡ as a function of the number of H-bond donating or accepting pore-lining residues results in a 0.1 kcal/mol contribution per residue. The resulting upper limit for partial water dehydration amounts to 2 kcal/mol. In the framework of biomimicry, our analysis provides valuable insights for the design of synthetic water channels. It thus may aid in the urgent endeavor towards combating global water scarcity.

In Situ Characterization of Dehydration during Ion Transport in Polymeric Nanochannels

The transport of hydrated ions across nanochannels is central to biological systems and membrane-based applications, yet little is known about their hydrated structure during transport due to the absence of in situ characterization techniques. Herein, we report experimentally resolved ion dehydration during transmembrane transport using modified in situ liquid ToF-SIMS in combination with MD simulations for a mechanistic reasoning. Notably, complete dehydration was not necessary for transport to occur across membranes with sub-nanometer pores. Partial shedding of water molecules from ion solvation shells, observed as a decrease in the average hydration number, allowed the alkali-metal ions studied here (lithium, sodium, and potassium) to permeate membranes with pores smaller than their solvated size. We find that ions generally cannot hold more than two water molecules during this sterically limited transport. In nanopores larger than the size of the solvation shell, we show that ionic mobility governs the ion hydration number distribution. Viscous effects, such as interactions with carboxyl groups inside the membrane, preferentially hinder the transport of the mono- and dihydrates. Our novel technique for studying ion solvation in situ represents a significant technological leap for the nanofluidics field and may enable important advances in ion separation, biosensing, and battery applications.

High-throughput molecular simulations reveal the origin of ion free energy barriers in graphene oxide membranes

Graphene oxide (GO) membranes are highly touted as materials for contemporary separation challenges including desalination, yet understanding of the interplay between their structure and salt rejection is limited. K⁺ ion permeation through hydrated GO membranes was investigated by combining structurally realistic molecular models and high-throughput molecular dynamics simulations. We show that it is essential to consider the complex GO microstructure to quantitatively reproduce experimentally-derived free energy barriers to K⁺ permeation for membranes with various interlayer distances less than 1.3 nm. This finding confirms the non-uniformity of GO nanopores and the necessity of the high-throughput approach for this class of material. The large barriers arise due to significant dehydration of K⁺ inside the membrane, which can have as few as 3 coordinated water molecules, compared to 7 in bulk solution. Thus, even if the membranes have an average pore size larger than the ion's hydrated diameter, the significant presence of pores whose size is smaller than the hydrated diameter creates bottlenecks for the permeation process.

NMR studies of adsorption and diffusion in porous carbonaceous materials

Porous carbonaceous materials have many important industrial applications including energy storage, water purification, and adsorption of volatile organic compounds. Most of their applications rely upon the adsorption of molecules or ions within the interior pore volume of the carbon particles. Understanding the behaviour and properties of adsorbate species on the molecular level is therefore key for optimising porous carbon materials, but this is very challenging owing to the complexity of the disordered carbon structure and the presence of multiple phases in the system. In recent years, NMR spectroscopy has emerged as one of the few experimental techniques that can resolve adsorbed species from those outside the pore network. Adsorbed, or "in-pore" species are shielded with respect to their free (or "ex-pore") counterparts. This shielding effect arises primarily due to ring currents in the carbon structure in the presence of a magnetic field, such that the observed chemical shift differences upon adsorption are independent of the observed nucleus to a first approximation. Theoretical modelling has played an important role in rationalising and explaining these experimental observations. Together, experiments and simulations have enabled a large amount of information to be gained on the adsorption and diffusion of adsorbed species, as well as on the structural and magnetic properties of the porous carbon adsorbent. Here, we review the methodological developments and applications of NMR spectroscopy and related modelling in this field, and provide perspectives on possible future applications and research directions.

Effect of Water Models on Transmembrane Self-Assembled Cyclic Peptide Nanotubes

Self-assembling cyclic peptide nanotubes can form nanopores when they are inserted in lipid bilayers, acting as ion and/or water permeable channels. In order to improve the versatility of these systems, it is possible to specifically design cyclic peptides with a combination of natural and non-natural amino acids, enabling the control of the nature of the inner cavity of the channels. Here, the behavior of two types of self-assembling peptide motifs, alternating α-amino acids with γ- or δ-aminocycloalkanecarboxylic acids, is studied via molecular dynamics (MD) simulations. The behavior of water molecules in nanopores is expected to affect the properties of these channels and therefore merits detailed examination. A number of water models commonly used in MD simulations have been validated by how well they reproduce bulk water properties. However, it is less clear how these water models behave in the nanoconfined condition inside a channel. The behavior of four different water models-TIP3P, TIP4P, TIP4P/2005, and OPC-are evaluated in MD simulations of self-assembled cyclic peptide nanotubes of distinct composition and diameter. The dynamic behavior of the water molecules and ions in these designed artificial channels depends subtly on the water model used. TIP3P water molecules move faster than those of TIP4P, TIP4P/2005, and OPC. This demeanor is clearly observed in the filling of the nanotube, in water diffusion within the pore, and in the number and stability of hydrogen bonds of the peptides with water. It was also shown that the water model influences the simulated ion flux through the nanotubes, with TIP3P producing the greatest ion flux. Additionally, the two more recent models, TIP4P/2005 and OPC, which are known to reproduce the experimental self-diffusion coefficient of bulk water quite well, exhibit very similar results under the nanoconfined conditions studied here. Because none of these models have been parametrized specifically for waters confined in peptide nanotubes, this study provides a point of reference for further validation.

Selectivity of ion transport in narrow carbon nanotubes depends on the driving force due to drag or drive nature of their active hydration shells

Molecular dynamics simulations have revealed the important roles of hydration shells of ions transported through ultrathin carbon nanotubes (CNTs). In particular, ions driven by electric fields tend to drag their hydration shells behind them, while for ions transported by pressure, their hydration shells can actively drive them. Given the different binding strengths of hydration shells to ions of different sizes, these active roles of hydration shells affect the relative entry rates and driving speeds of ions in CNTs.

Water and Ion Transfer to Narrow Carbon Nanotubes: Roles of Exterior and Interior

Narrow carbon nanotubes (CNTs) desalinate water, mimicking water channels of biological membranes, yet the physics behind selectivity, especially the effect of the membrane embedding CNTs on water and ion transfer, is still unclear. Here, we report ab initio analysis of the energies involved in transfer of water and K⁺ and Cl^- ions from solution to empty and water-filled 0.68 nm CNTs for different dielectric constants (ϵ) of the surrounding matrix. The transfer energies computed for 1 ≤ ϵ < ∞ permit a transparent breakdown of the transfer energy to three main contributions: binding to CNT, intra-CNT hydration, and dielectric polarization of the matrix. The latter scales inversely with ϵ and is of the order 10²/ϵ kJ/mol for both ions, which may change ion transfer from favorable to unfavorable, depending on ion, ϵ, and CNT diameter. This may have broad implications for designing and tuning selectivity of nanochannel-based devices.

Water mobility in MoS2 nanopores: effects of the dipole-dipole interaction on the physics of fluid transport

Use of nanoscale materials is a promising desalination technology. While fast water flow in nanotubes is well understood, this is not the case for water permeability in single-layer membranes. The advances in nanofluidics have opened up the possibility to shift the permeability-selectivity tradeoff. The physical-chemical balance between nanopore size, shape, and charge might be the answer. In this work, we investigate the role of the MoS2 nanopore charge distribution in water mobility by tuning its strength. We shed light on the competition between charge and nanopore size. The strong dipole interaction between water and the MoS2 nanopore is responsible for adding a constraint to the water angular orientation possibilities to travel through the nanopore, but this effect also depends on the nanopore size.

Diffusion Limitations and Translocation Barriers in Atomically Thin Biomimetic Pores

Ionic transport in nano- to sub-nano-scale pores is highly dependent on translocation barriers and potential wells. These features in the free-energy landscape are primarily the result of ion dehydration and electrostatic interactions. For pores in atomically thin membranes, such as graphene, other factors come into play. Ion dynamics both inside and outside the geometric volume of the pore can be critical in determining the transport properties of the channel due to several commensurate length scales, such as the effective membrane thickness, radii of the first and the second hydration layers, pore radius, and Debye length. In particular, for biomimetic pores, such as the graphene crown ether we examine here, there are regimes where transport is highly sensitive to the pore size due to the interplay of dehydration and interaction with pore charge. Picometer changes in the size, e.g., due to a minute strain, can lead to a large change in conductance. Outside of these regimes, the small pore size itself gives a large resistance, even when electrostatic factors and dehydration compensate each other to give a relatively flat-e.g., near barrierless-free energy landscape. The permeability, though, can still be large and ions will translocate rapidly after they arrive within the capture radius of the pore. This, in turn, leads to diffusion and drift effects dominating the conductance. The current thus plateaus and becomes effectively independent of pore-free energy characteristics. Measurement of this effect will give an estimate of the magnitude of kinetically limiting features, and experimentally constrain the local electromechanical conditions.

Selectivity of nitrate and chloride ions in microporous carbons: the role of anisotropic hydration and applied potentials

Understanding ion transport in porous carbons is critical for a wide range of technologies, including supercapacitors and capacitive deionization for water desalination, yet many details remain poorly understood. For instance, an atomistic understanding of how ion selectivity is influenced by the molecular shape of ions, morphology of the micropores and applied voltages is largely lacking. In this work, we combined molecular dynamics simulations with enhanced sampling methods to elucidate the mechanism of nitrate and chloride selectivity in subnanometer graphene slit-pores. We show that nitrate is preferentially adsorbed over chloride in the slit-like micropores. This preferential adsorption was found to stem from the weaker hydration energy and unique anisotropy of the ion solvation of nitrate. Beside the effects of ion dehydration, we found that applied potential plays an important role in determining the ion selectivity, leading to a lower selectivity of nitrate over chloride at a high applied potential. We conclude that the measured ion selectivity results from a complex interplay between voltage, confinement, and specific ion effects-including ion shape and local hydration structure.

Vertically Aligned Carbon Nanotube Membranes: Water Purification and Beyond

Vertically aligned carbon nanotube (VACNT) membranes have attracted significant attention for water purification owing to their ultra-high water permeability and antibacterial properties. In this paper, we critically review the recent progresses in the synthesis of VACNT arrays and fabrication of VACNT membrane methods, with particular emphasis on improving water permeability and anti-biofouling properties. Furthermore, potential applications of VACNT membranes other than water purification (e.g., conductive membranes, electrodes in proton exchange membrane fuel cells, and solar electricity–water generators) have been introduced. Finally, future outlooks are provided to overcome the limitations of commercialization and desalination currently faced by VACNT membranes. This review will be useful to researchers in the broader scientific community as it discusses current and new trends regarding the development of VACNT membranes as well as their potential applications.

Towards single-species selectivity of membranes with subnanometre pores

Synthetic membranes with pores at the subnanometre scale are at the core of processes for separating solutes from water, such as water purification and desalination. While these membrane processes have achieved substantial industrial success, the capability of state-of-the-art membranes to selectively separate a single solute from a mixture of solutes is limited. Such high-precision separation would enable fit-for-purpose treatment, improving the sustainability of current water-treatment processes and opening doors for new applications of membrane technologies. Herein, we introduce the challenges of state-of-the-art membranes with subnanometre pores to achieve high selectivity between solutes. We then analyse experimental and theoretical literature to discuss the molecular-level mechanisms that contribute to energy barriers for solute transport through subnanometre pores. We conclude by providing principles and guidelines for designing next-generation single-species selective membranes that are inspired by ion-selective biological channels.

Progress in supercapacitors: roles of two dimensional nanotubular materials

Overcoming the global energy crisis due to vast economic expansion with the advent of human reliance on energy-consuming labor-saving devices necessitates the demand for next-generation technologies in the form of cleaner energy storage devices. The technology accelerates with the pace of developing energy storage devices to meet the requirements wherever an unanticipated burst of power is indeed needed in a very short time. Supercapacitors are predicted to be future power vehicles because they promise faster charging times and do not rely on rare elements such as lithium. At the same time, they are key nanoscale device elements for high-frequency noise filtering with the capability of storing and releasing energy by electrostatic interactions between the ions in the electrolyte and the charge accumulated at the active electrode during the charge/discharge process. There have been several developments to increase the functionality of electrodes or finding a new electrolyte for higher energy density, but this field is still open to witness the developments in reliable materials-based energy technologies. Nanoscale materials have emerged as promising candidates for the electrode choice, especially in 2D sheet and folded tubular network forms. Due to their unique hierarchical architecture, excellent electrical and mechanical properties, and high specific surface area, nanotubular networks have been widely investigated as efficient electrode materials in supercapacitors, while maintaining their inherent characteristics of high power and long cycling life. In this review, we briefly present the evolution, classification, functionality, and application of supercapacitors from the viewpoint of nanostructured materials to apprehend the mechanism and construction of advanced supercapacitors for next-generation storage devices.

Reverse Translocation of Nucleotides through a Carbon Nanotube

We report molecular dynamics (MD) simulations of the reverse translocation of single nucleotides through a narrow carbon nanotube (CNT), with a diameter of 1.36 nm, immersed in a 1 M KCl electrolyte solution under an applied electric field along the tube axis. We observe ion selectivity by the narrow CNT, which leads to a high flow of K⁺ ions, in contrast to a negligible and opposing current of Cl^- ions. The K⁺ ions, driven by the electric field, force a negatively charged single nucleotide into the narrow CNT where it is trapped by the incoming K⁺ ions and water molecules, and the nucleotide is driven in the same direction as the K⁺ ions. This illustrates a novel mechanism of nucleotide reverse translocation that is controlled by ion selectivity. An increase in the CNT diameter to 2.71 nm or an increase in nucleotide chain length both lead to translocation in the normal direction of the applied field. The reverse translocation rate of single nucleotides is correlated to the ionic current of K⁺ ions in the narrow tube, unlike translocation in the normal direction in the wider tube.

Similarities and differences between potassium and ammonium ions in liquid water: a first-principles study

Understanding ion solvation in liquid water is critical in optimizing materials for a wide variety of emerging technologies, including water desalination and purification.

Resonance-driven ion transport and selectivity in prokaryotic ion channels

Ion channels exhibit a remarkably high accuracy in selecting uniquely its associated type of ion. The mechanisms behind ion selectivity are not well understood. Current explanations build mainly on molecular biology and bioinformatics. Here we propose a simple physical model for ion selectivity based on the driven damped harmonic oscillator (DDHO). The driving force for this oscillator is provided by self-organizing harmonic turbulent structures in the dehydrating ionic flow through the ion channel, namely, oscillating pressure waves in one dimension, and toroidal vortices in two and three dimensions. Density fluctuations caused by these turbulences efficiently transmit their energy to aqua ions that resonate with the driving frequency. Consequently, these release their hydration shell and exit the ion channel as free ions. Existing modeling frameworks do not express the required complex spatiotemporal dynamics, hence we introduce a macroscopic continuum model for ionic dehydration and transport, based on the hydrodynamics of a dissipative ionic flow through an ion channel, subject to electrostatic and amphiphilic interactions. This model combines three classical physical fields: Navier-Stokes equations from hydrodynamics, Gauss's law from Maxwell theory, and the convection-diffusion equation from continuum physics. Numerical experiments with mixtures of chemical species of ions in various degrees of hydration indeed reveal the emergence of strong oscillations in the ionic flow that are instrumental in the efficient dehydration and cause a strong ionic jet into the cell. As such, they provide a powerful engine for the DDHO mechanism. Theoretical predictions of the modeling framework match significantly with empirical patch-clamp data. The DDHO standard response curve defines a unique resonance frequency that depends on the mass and charge of the ion. In this way, the driving oscillations act as a selection mechanism that filters out one specific ion. Application of the DDHO model to real ion data shows that this mechanism indeed clearly distinguishes between chemical species and between aqua and bare ions with a large Mahalanobis distance and high oscillator quality. The DDHO framework helps to understand how SNP mutations can cause severe genetic pathologies as they destroy the geometry of the channel and so alter the resonance peaks of the required ion type.

Changing perspectives on how the permeation pathway through potassium channels is regulated

The primary means by which ion permeation through potassium channels is controlled, and the key to selective intervention in a range of pathophysiological conditions, is the process by which channels switch between non-conducting and conducting states. Conventionally, this has been explained by a steric mechanism in which the pore alternates between two conformations: a 'closed' state in which the conduction pathway is occluded and an 'open' state in which the pathway is sufficiently wide to accommodate fully hydrated ions. Recently, however, 'non-canonical' mechanisms have been proposed for some classes of K⁺ channels. The purpose of this review is to illuminate structural and dynamic relationships underpinning permeation control in K⁺ channels, indicating where additional data might resolve some of the remaining issues.

How ions block the single-file water transport through a carbon nanotube

Understanding the blockage of ions for water transport through nanochannels is crucial for the design of desalination nanofluidic devices. In this work, we systematically clarify how ions block the single-file water transport through a (6,6) carbon nanotube (CNT) by using molecular dynamics simulations. We consider various pressure differences and salt concentrations. With the increase of pressure difference, the water flux shows a linear growth that coincides with the Hagen-Poiseuille equation. Interestingly, the dependence of the CNT-ion interaction on the salt concentration results in a distinct ion blockage effect that ultimately leads to water flux bifurcation. The water translocation time shows a power law decay with pressure, depending on the salt concentration. Furthermore, with the increase of salt concentration, the water flux shows a linear decay with a larger slope for higher pressure, while the water translocation time shows an opposite behavior. Therefore, the ions can not only block the water entering but also slow down the water motion inside the CNT. Notably, the probability of cations and anions appearing at the CNT entrance is quite similar, suggesting a similar blockage effect; however, anions show deeper interactions with the CNT because of their larger size. We finally find a unique linear relation between the water flux and occupancy divided by the translocation time. Our results provide insightful information on the ion blockage effect for the single-file water transport, and are thus helpful for the design of novel filtration membranes.

Calculating Single-Channel Permeability and Conductance from Transition Paths

Permeability and conductance are the major transport properties of membrane channels, quantifying the rate of channel crossing by the solute. It is highly desirable to calculate these quantities in all-atom molecular dynamics simulations. When the solute crossing rate is low, however, direct methods would require prohibitively long simulations, and one thus typically adopts alternative strategies based on the free energy of single solute along the channel. Here we present a new method to calculate the crossing rate by initiating unbiased trajectories in which the solute is released at the free energy barrier. In this method, the total time the solute spends in the barrier region during a channel crossing (transition path) is used to determine the kinetic rate. Our method achieves a significantly higher statistical accuracy than the classical reactive flux method, especially for diffusive barrier crossing. Our test on ion permeation through a carbon nanotube verifies that the method correctly predicts the crossing rate and reproduces the spontaneous crossing events as in long equilibrium simulations. The rigorous and efficient method here will be valuable for quantitatively connecting simulations to experimental measurement of membrane channels.

Colloquium: Ionic phenomena in nanoscale pores through 2D materials

Ion transport through nanopores permeates through many areas of science and technology, from cell behavior to sensing and separation to catalysis and batteries. Two-dimensional materials, such as graphene, molybdenum disulfide (MoS2), and hexagonal boron nitride (hBN), are recent additions to these fields. Low-dimensional materials present new opportunities to develop filtration, sensing, and power technologies, encompassing ion exclusion membranes, DNA sequencing, single molecule detection, osmotic power generation, and beyond. Moreover, the physics of ionic transport through pores and constrictions within these materials is a distinct realm of competing many-particle interactions (e.g., solvation/dehydration, electrostatic blockade, hydrogen bond dynamics) and confinement. This opens up alternative routes to creating biomimetic pores and may even give analogues of quantum phenomena, such as quantized conductance, in the classical domain. These prospects make membranes of 2D materials - i.e., 2D membranes - fascinating. We will discuss the physics and applications of ionic transport through nanopores in 2D membranes.

Emerging tools for studying single entity electrochemistry

Electrochemistry studies charge transfer and related processes at various microscopic structures (atomic steps, islands, pits and kinks on electrodes), and mesoscopic materials (nanoparticles, nanowires, viruses, vesicles and cells) made by nature and humans, involving ions and molecules. The traditional approach measures averaged electrochemical quantities of a large ensemble of these individual entities, including the microstructures, mesoscopic materials, ions and molecules. There is a need to develop tools to study single entities because a real system is usually heterogeneous, e.g., containing nanoparticles with different sizes and shapes. Even in the case of "homogeneous" molecules, they bind to different microscopic structures of an electrode, assume different conformations and fluctuate over time, leading to heterogeneous reactions. Here we highlight some emerging tools for studying single entity electrochemistry, discuss their strengths and weaknesses, and provide personal views on the need for tools with new capabilities for further advancing single entity electrochemistry.