Fundamental transport mechanisms, fabrication and potential applications of nanoporous atomically thin membranes

The interaction between atomic-scale pores and particles

Using first-principles calculations for angstrom-sized pores (3-10 Å), we investigate pore-particle interaction. The translocation energy barrier (TEB) plays important role for the angstrom-scale pores created in 2D-materials such as graphene which is calculated for the translocation of rare gases (He, Ne, Ar, Xe), diatomic molecules (H₂and N₂), CO₂, and CH₄. The critical incident angle (the premeance beyond that is zero) was found to be 40°, which is different from classical model's prediction of 19-37°. The calculated TEB (Δ) and the surface diffusion energy barrier (Δ') for the particles with small kinetic diameter (He, Ne and H₂), show that the direct flow is the dominant permeation mechanism (Δ ≈ 0 and Δ' > 30 meV). For the other particles with larger kinetic diameters (Ar, Kr, N₂, CH₄and CO₂), we found that both surface diffusion and direct flow mechanisms are possible, i.e. Δ and Δ' ≠ 0. This work provides important insights into the gas permeation theory and into the design and development of gas separation and filtration devices.

Nanoporous Graphene via a Pressing Organization Calcination Strategy for Highly Efficient Electrocatalytic Hydrogen Peroxide Generation

Nanoporous graphenes (NPGs) have recently attracted huge attention owing to their designable structures and diverse properties. Many important properties of NPGs are determined by their structural regularity and homogeneity. The mass production of NPGs with periodic well-defined pore structures under a solvent-free green synthesis poses a great challenge and is largely unexplored. A facile synthetic strategy of NPGs via pressing organization calcination (POC) of readily available halogenated polycyclic aromatic hydrocarbons is developed. The gram-scale synthesized NPGs have ordered structures and possess well-defined nanopores, which can be easily exfoliated to few layers and oxidized in controllable approaches. After being decorated with oxygen species, the oxidized NPGs with tunable catalytic centers exhibit high activity, selectivity, and stability toward electrochemical hydrogen peroxide generation.

Two-dimensional materials as solid-state nanopores for chemical sensing

Solid-state nanopores as a versatile alternative to biological nanopores have grown tremendously over the last two decades. They exhibit unique characteristics including mechanical robustness, thermal and chemical stability, easy modifications and so on. Moreover, the pore size of a solid-state nanopore could be accurately controlled from sub-nanometers to hundreds of nanometers based on the experimental requirements, presenting better adaptability than biological nanopores. Two-dimensional (2D) materials with single layer thicknesses and highly ordered structures have great potential as solid-state nanopores. In this perspective, we introduced three kinds of substrate-supported 2D material solid-state nanopores, including graphene, MoS2 and MOF nanosheets, which exhibited big advantages compared to traditional solid-state nanopores and other biological counterparts. Besides, we suggested the fabrication and modulation of 2D material solid-state nanopores. We also discussed the applications of 2D materials as solid-state nanopores for ion transportation, DNA sequencing and biomolecule detection.

Osmotic Transport at the Aqueous Graphene and hBN Interfaces: Scaling Laws from a Unified, First-Principles Description

Osmotic transport in nanoconfined aqueous electrolytes provides alternative venues for water desalination and "blue energy" harvesting. The osmotic response of nanofluidic systems is controlled by the interfacial structure of water and electrolyte solutions in the so-called electrical double layer (EDL), but a molecular-level picture of the EDL is to a large extent still lacking. Particularly, the role of the electronic structure has not been considered in the description of electrolyte/surface interactions. Here, we report enhanced sampling simulations based on ab initio molecular dynamics, aiming at unravelling the free energy of prototypical ions adsorbed at the aqueous graphene and hBN interfaces, and its consequences on nanofluidic osmotic transport. Specifically, we predicted the zeta potential, the diffusio-osmotic mobility, and the diffusio-osmotic conductivity for a wide range of salt concentrations from the ab initio water and ion spatial distributions through an analytical framework based on Stokes equation and a modified Poisson-Boltzmann equation. We observed concentration-dependent scaling laws, together with dramatic differences in osmotic transport between the two interfaces, including diffusio-osmotic flow and current reversal on hBN but not on graphene. We could rationalize the results for the three osmotic responses with a simple model based on characteristic length scales for ion and water adsorption at the surface, which are quite different on graphene and on hBN. Our work provides fundamental insights into the structure and osmotic transport of aqueous electrolytes on 2D materials and explores alternative pathways for efficient water desalination and osmotic energy conversion.

Bottom-up synthesis of graphene films hosting atom-thick molecular-sieving apertures

Incorporation of a high density of molecular-sieving nanopores in the graphene lattice by the bottom-up synthesis is highly attractive for high-performance membranes. Herein, we achieve this by a controlled synthesis of nanocrystalline graphene where incomplete growth of a few nanometer-sized, misoriented grains generates molecular-sized pores in the lattice. The density of pores is comparable to that obtained by the state-of-the-art postsynthetic etching (10¹² cm^-2) and is up to two orders of magnitude higher than that of molecular-sieving intrinsic vacancy defects in single-layer graphene (SLG) prepared by chemical vapor deposition. The porous nanocrystalline graphene (PNG) films are synthesized by precipitation of C dissolved in the Ni matrix where the C concentration is regulated by controlled pyrolysis of precursors (polymers and/or sugar). The PNG film is made of few-layered graphene except near the grain edge where the grains taper down to a single layer and eventually terminate into vacancy defects at a node where three or more grains meet. This unique nanostructure is highly attractive for the membranes because the layered domains improve the mechanical robustness of the film while the atom-thick molecular-sized apertures allow the realization of large gas transport. The combination of gas permeance and gas pair selectivity is comparable to that from the nanoporous SLG membranes prepared by state-of-the-art postsynthetic lattice etching. Overall, the method reported here improves the scale-up potential of graphene membranes by cutting down the processing steps.

Highly porous nanofiber-supported monolayer graphene membranes for ultrafast organic solvent nanofiltration

Scalable fabrication of monolayer graphene membrane on porous supports is key to realizing practical applications of atomically thin membranes, but it is technologically challenging. Here, we demonstrate a facile and versatile electrospinning approach to realize nanoporous graphene membranes on different polymeric supports with high porosity for efficient diffusion- and pressure-driven separations. The conductive graphene works as an excellent receptor for deposition of highly porous nanofibers during electrospinning, thereby enabling direct attachment of graphene to the support. A universal “binder” additive is shown to enhance adhesion between the graphene layer and polymeric supports, resulting in high graphene coverage on nanofibers made from different polymers. After defect sealing and oxygen plasma treatment, the resulting nanoporous membranes demonstrate record-high performances in dialysis and organic solvent nanofiltration, with a pure ethanol permeance of 156.8 liters m⁻² hour⁻¹ bar⁻¹ and 94.5% rejection to Rose Bengal (1011 g mol⁻¹) that surpasses the permeability-selectivity trade-off.

Molecular size-dependent subcontinuum solvent permeation and ultrafast nanofiltration across nanoporous graphene membranes

Selective solvent and solute transport across nanopores is fundamental to membrane separations, yet it remains poorly understood, especially for non-aqueous systems. Here, we design a chemically robust nanoporous graphene membrane and study molecular transport in various organic liquids under subnanometre confinement. We show that the nature of the solvent can modulate solute diffusion across graphene nanopores, and that breakdown of continuum flow occurs when pore size approaches the solvent's smallest molecular cross-section. By holistically engineering membrane support, modelling pore creation and defect management, high rejection and ultrafast organic solvent nanofiltration of dye molecules and separation of hexane isomers are achieved. The membranes exhibit stable fluxes across a range of solvents, consistent with flow across rigid pores whose size is independent of the solvent. These results demonstrate that nanoporous graphene is a rich materials system for controlling subcontinuum flow that could enable new membranes for a range of challenging separation needs.

Membrane Materials for Selective Ion Separations at the Water-Energy Nexus

Synthetic polymer membranes are enabling components in key technologies at the water-energy nexus, including desalination and energy conversion, because of their high water/salt selectivity or ionic conductivity. However, many applications at the water-energy nexus require ion selectivity, or separation of specific ionic species from other similar species. Here, the ion selectivity of conventional polymeric membrane materials is assessed and recent progress in enhancing selective transport via tailored free volume elements and ion-membrane interactions is described. In view of the limitations of polymeric membranes, three material classes-porous crystalline materials, 2D materials, and discrete biomimetic channels-are highlighted as possible candidates for ion-selective membranes owing to their molecular-level control over physical and chemical properties. Lastly, research directions and critical challenges for developing bioinspired membranes with molecular recognition are provided.

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.

Ab Initio Energetic Barriers of Gas Permeation across Nanoporous Graphene

Realizing membranes of atomic thickness functioning reliably constitutes a giant leap forward for a plethora of applications where the efficient separation of fluid constituents at the molecular level is critical. Here, by employing density functional theory, we explore the energy landscape of typical gas molecules attempting permeation through graphene nanopores and determine the minimum energy permeation pathways, based on the precise knowledge of the related molecular level interactions. With this approach we investigate two basic permeation routes: direct permeation and surface-based transport. We find that for subnanometer pores, the diffusion barrier of direct and surface transport depends on the pore chemical functionalization, while the molecule pore permeation barrier is independent of the gas-pore approach due to the overlap of surface and direct diffusion paths over the pore center. The overall minimum energy permeation pathway of He, H₂, CO₂, and CH₄ molecules, across nanopores of different dimensions and chemical functionalization, defines the pore diameter (∼1.2 nm) below which effusion theory is inaccurate, as well as the critical pore diameter (∼0.8 nm) required to achieve positive permeation barriers driving molecular sieving. We determine that achieving positive permeation barriers required for high selectivity gas separation is inseparably combined with postpermeation desorption barriers due to attractive van der Waals interactions. The discovered permeation energetics are pore-molecule-specific and are incorporated into an analytical model extending existing theory. Our results provide a scientific background for rational pore design in graphene membranes, which can lead to gas separation at a commercially relevant performance level.

Multipulsed Millisecond Ozone Gasification for Predictable Tuning of Nucleation and Nucleation-Decoupled Nanopore Expansion in Graphene for Carbon Capture

Predictable and tunable etching of angstrom-scale nanopores in single-layer graphene (SLG) can allow one to realize high-performance gas separation even from similar-sized molecules. We advance toward this goal by developing two etching regimes for SLG where the incorporation of angstrom-scale vacancy defects can be controlled. We screen several exposure profiles for the etchant, controlled by a multipulse millisecond treatment, using a mathematical model predicting the nucleation and pore expansion rates. The screened profiles yield a narrow pore-size-distribution (PSD) with a majority of defects smaller than missing 16 carbon atoms, suitable for CO₂/N₂ separation, attributing to the reduced pore expansion rate at a high pore density. Resulting nanoporous SLG (N-SLG) membranes yield attractive CO₂ permeance of 4400 ± 2070 GPU and CO₂/N₂ selectivity of 33.4 ± 7.9. In the second etching regime, by limiting the supply of the etchant, the nanopores are allowed to expand while suppressing the nucleation events. Extremely attractive carbon capture performance marked with CO₂ permeance of 8730 GPU, and CO₂/N₂ selectivity of 33.4 is obtained when CO₂-selective polymeric chains are functionalized on the expanded nanopores. We show that the etching strategy is uniform and scalable by successfully fabricating high-performance centimeter-scale membrane.

Recent Progress in Superhydrophilic Carbon-Based Composite Membranes for Oil/Water Emulsion Separation

The purification of stabilized oil/water emulsions is essential to meet the ever increasing demand for monitoring water in the environment, which has been addressed with superwetting carbon-based separation membranes. These include superhydrophilic carbon-based membranes whose progress in recent years and perspectives are reviewed in this paper. The membrane construction strategy is organized into four parts, vacuum-assisted self-assembly, sol-gel process, electrospinning, and vacuum-assisted filtration. In each section, the design strategies and their responding disadvantages have been comprehensively discussed. The challenges and prospects concerning the superhydrophilic carbon-based separation membranes for oily wastewater purification are also summarized to arouse researchers to carry out more studies.

Tunable Pore Size from Sub-Nanometer to a Few Nanometers in Large-Area Graphene Nanoporous Atomically Thin Membranes

Membranes are key components in chemical purification, biological separation, and water desalination. Traditional polymeric membranes are subjected to a ubiquitous trade-off between permeance and selectivity, which significantly hinders the separation performance. Nanoporous atomically thin membranes (NATMs), such as graphene NATMs, have the potential to break this trade-off. Owing to their uniqueness of two-dimensional structure and potential nanopore structure controllability, NATMs are expected to have outstanding selectivity through molecular sieving while achieving ultimate permeance at the same time. However, a drastic selectivity discrepancy exists between the proof-of-concept demonstrations and scalable separation applications in graphene membranes. In this paper, we offer a possible solution to narrow this discrepancy by tuning the pore density and pore size separately with two successive plasma treatments. We demonstrate that by narrowing the pore size distribution, the selectivity of graphene membranes can be greatly increased. Low-energy argon plasma is first applied to nucleate high density of defects in graphene. Controlled oxygen plasma is then utilized to selectively enlarge the defects into nanopores with desired sizes. This method is scalable, and the fabricated 1 cm2 graphene NATMs with sub-nanometer pores can separate KCl and Allura Red with a selectivity of 104 and a permeance of 1.1 × 10-6 m s-1. The pores in NATMs can be further tuned from gas-selective sub-nanometer pores to a few nanometer size. The fabricated NATMs show a selectivity of 35 between CO2 and N2. With longer enlargement time, a selectivity of 21.2 between a lysozyme and bovine serum albumin can also be achieved with roughly four times higher permeance than that of a commercial dialysis membrane. This research offers a solution to realize NATMs of tunable pore size with a narrow pore size distribution for different separation processes from sub-nanometer in gas separation or desalination to a few nanometers in dialysis.

Confinement-Controlled Aqueous Chemistry within Nanometric Slit Pores

In this Focus Review, we put the spotlight on very recent insights into the fascinating world of wet chemistry in the realm offered by nanoconfinement of water in mechanically rather rigid and chemically inert planar slit pores wherein only monolayer and bilayer water lamellae can be hosted. We review the effect of confinement on different aspects such as hydrogen bonding, ion diffusion, and charge defect migration of H⁺(aq) and OH^-(aq) in nanoconfined water depending on slit pore width. A particular focus is put on the strongly modulated local dielectric properties as quantified in terms of anisotropic polarization fluctuations across such extremely confined water films and their putative effects on chemical reactions therein. The stunning findings disclosed only recently extend wet chemistry in particular and solvation science in general toward extreme molecular confinement conditions.

Hydrocarbon contamination in angström-scale channels

Nonspecific molecular adsorption such as airborne contamination occurs on most surfaces including those of 2D materials and alters their properties. While surface contamination is studied using a plethora of techniques, the effect of contamination on confined systems such as nanochannels/pores leading to their clogging is still lacking. We report a systematic investigation of hydrocarbon adsorption in angstrom (Å) slit channels of varying heights. Hexane is chosen to mimic the hydrocarbon contamination and the clogging of the Å-channels is evaluated via a helium gas flow measurement. The level of hexane adsorption, in other words, the degree of clogging depends on the size difference between the channels and hexane. A dynamic transition of the clogging and revival process is shown in sub-2 nm thin channels. Long-term storage and stability of our Å-channels are demonstrated here for up to three years, alleviating the contamination and unclogging the channels using thermal treatment. This study highlights the importance of the nanochannels' stability and demonstrates the self-cleansing nature of sub-2 nm thin channels enabling a robust platform for molecular transport and separation studies. We provide a method to assess the cleanliness of nanoporous membranes, which is vital for the practical applications of nanofluidics in various fields such as molecular sensing, separation and power generation.

Physics of Selective Conduction and Point Mutation in Biological Ion Channels

We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutation. We derive an effective grand-canonical ensemble and generalized Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K^{+} channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical.

Channel-length dependence of particle diffusivity in confinement

Understanding the diffusive behavior of particles and large molecules in channels is of fundamental importance in biological and synthetic systems, such as channel proteins, nanopores, and nanofluidics. Although theoretical and numerical modelings have suggested some solutions, these models have not been fully supported with direct experimental measurements. Here, we demonstrate that experimental diffusion coefficients of particles in finite open-ended channels are always higher than the prediction based on the conventional theoretical model of infinitely long channels. By combining microfluidic experiments, numerical simulations, and analytical modeling, we show that diffusion coefficients are dependent not only on the radius ratio but also on the channel length, the boundary conditions of the neighboring reservoirs, and the compressibility of the medium.

Biomimetic N-Doped Graphene Membrane for Proton Exchange Membranes

Proton exchange membranes (PEMs) with both high selectivity and high permeance are of great demand in hydrogen-based applications, especially in fuel cells. Although graphene membranes have shown high selectivity of protons over other ions and molecules, the relatively low permeance of protons through perfect pristine graphene restricts its practical applications. Inspired by the nitrogen-assisted proton transport in biological systems, we introduced N-doping to increase the proton permeance and proposed a type of N-doped graphene membranes (NGMs) for proton exchange, which have both high proton permeance and high selectivity. Compared to the state-of-the-art commercial PEMs, the NGMs show significant increases in both areal proton conductivity (2-3 orders of magnitude) and selectivity of proton to methanol (1-2 orders of magnitude). The work realized the controllable tuning of proton permeance of the graphene membrane with N-doping and developed a new type of graphene-based PEMs with high performance for practical applications.

Water friction in nanofluidic channels made from two-dimensional crystals

Membrane-based applications such as osmotic power generation, desalination and molecular separation would benefit from decreasing water friction in nanoscale channels. However, mechanisms that allow fast water flows are not fully understood yet. Here we report angstrom-scale capillaries made from atomically flat crystals and study the effect of confining walls' material on water friction. A massive difference is observed between channels made from isostructural graphite and hexagonal boron nitride, which is attributed to different electrostatic and chemical interactions at the solid-liquid interface. Using precision microgravimetry and ion streaming measurements, we evaluate the slip length, a measure of water friction, and investigate its possible links with electrical conductivity, wettability, surface charge and polarity of the confining walls. We also show that water friction can be controlled using hybrid capillaries with different slip lengths at opposing walls. The reported advances extend nanofluidics' toolkit for designing smart membranes and mimicking manifold machinery of biological channels.

TEMPO-Oxidized Bacterial Cellulose Nanofibers/Graphene Oxide Fibers for Osmotic Energy Conversion

The large osmotic energy between river water and seawater is an inexhaustible blue energy source; however, the complicated manufacturing methods used for ion-exchange devices hinder the development of reverse electrodialysis (RED). Here, we use a wet-spinning method to continuously spin meter-scale 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO)-oxidized bacterial cellulose (TOBC) nanofiber filaments, which are then used to construct nanochannels for osmotic energy conversion. These are then used to build a nacre-like structure by adding graphene oxide (GO), which provides narrow nanochannels in one-dimensional and two-dimensional nanofluid systems for rapid ion transport. With a 50-fold concentration gradient, the nanochannels in the fibers generate electricity of 0.35 W m^-2, with an ionic mobility of 0.94 and an energy conversion efficiency of 38%. The assembly of GO and TOBC results in a high power density of 0.53 W m^-2 using artificial seawater and river water. The RED device fabricated from TOBC/GO fibers maintains a stable power density for 15 days. This research proposes a simple method to reduce the size of nanochannels to improve the ionic conductivity, ionic selectivity, and power density of cellulose-based nanofibers to increase the possibility of their application for the conversion of osmotic energy to electrical energy.

Rapid screening of nanopore candidates in nanoporous single-layer graphene for selective separations using molecular visualization and interatomic potentials

Nanoporous single-layer graphene is promising as an ideal membrane because of its extreme thinness, chemical resistance, and mechanical strength, provided that selective nanopores are successfully incorporated. However, screening and understanding the transport characteristics of the large number of possible pores in graphene are limited by the high computational requirements of molecular dynamics (MD) simulations and the difficulty in experimentally characterizing pores of known structures. MD simulations cannot readily simulate the large number of pores that are encountered in actual membranes to predict transport, and given the huge variety of possible pores, it is hard to narrow down which pores to simulate. Here, we report alternative routes to rapidly screen molecules and nanopores with negligible computational requirement to shortlist selective nanopore candidates. Through the 3D representation and visualization of the pores' and molecules' atoms with their van der Waals radii using open-source software, we could identify suitable C-passivated nanopores for both gas- and liquid-phase separation while accounting for the pore and molecule shapes. The method was validated by simulations reported in the literature and was applied to study the mass transport behavior across a given distribution of nanopores. We also designed a second method that accounts for Lennard-Jones and electrostatic interactions between atoms to screen selective non-C-passivated nanopores for gas separations. Overall, these visualization methods can reduce the computational requirements for pore screening and speed up selective pore identification for subsequent detailed MD simulations and guide the experimental design and interpretation of transport measurements in nanoporous atomically thin membranes.

Organic molecular sieve membranes for chemical separations

Molecular separations that enable selective transport of target molecules from gas and liquid molecular mixtures, such as CO2 capture, olefin/paraffin separations, and organic solvent nanofiltration, represent the most energy sensitive and significant demands. Membranes are favored for molecular separations owing to the advantages of energy efficiency, simplicity, scalability, and small environmental footprint. A number of emerging microporous organic materials have displayed great potential as building blocks of molecular separation membranes, which not only integrate the rigid, engineered pore structures and desirable stability of inorganic molecular sieve membranes, but also exhibit a high degree of freedom to create chemically rich combinations/sequences. To gain a deep insight into the intrinsic connections and characteristics of these microporous organic material-based membranes, in this review, for the first time, we propose the concept of organic molecular sieve membranes (OMSMs) with a focus on the precise construction of membrane structures and efficient intensification of membrane processes. The platform chemistries, designing principles, and assembly methods for the precise construction of OMSMs are elaborated. Conventional mass transport mechanisms are analyzed based on the interactions between OMSMs and penetrate(s). Particularly, the 'STEM' guidelines of OMSMs are highlighted to guide the precise construction of OMSM structures and efficient intensification of OMSM processes. Emerging mass transport mechanisms are elucidated inspired by the phenomena and principles of the mass transport processes in the biological realm. The representative applications of OMSMs in gas and liquid molecular mixture separations are highlighted. The major challenges and brief perspectives for the fundamental science and practical applications of OMSMs are tentatively identified.

Nanopores in two-dimensional materials: accurate fabrication

Two-dimensional (2D) materials such as graphene and molybdenum disulfide have been demonstrated with a wide range of applications in electronic devices, chemical catalysis, single-molecule detection, and energy conversion. In the 2D materials, nanopores can be created, and the 2D nanoporous membranes possess many unique properties such as ultrathin thickness, high surface area, and excellent particle sieving capability, showing extraordinary promise in plenty of applications, such as sea water desalination, gas separation, and DNA sequencing. The performances of these membranes are mainly determined by the nanopore size, structure, and density, which, in turn, rely on the fabrication techniques of the nanopores. This review covers the important progress of nanopore fabrication in 2D materials and comprehensively compares these methods for the features of the introduced nanopores and their formation processes. Future perspectives are discussed on the opportunities and challenges in fabricating high-grade 2D nanopores.

2D Heterostructured Nanofluidic Channels for Enhanced Desalination Performance of Graphene Oxide Membranes

The two-dimensional (2D) lamellar membrane assembly technique shows substantial potential for sustainable desalination applications. However, the relatively wide and size-variable channels of 2D membranes in aqueous solution result in inferior salt rejections. Here we show the establishment of nanofluidic heterostructured channels in graphene oxide (GO) membranes by adding g-C₃N₄ sheets into GO interlamination. Benefiting from the presence of stable and sub-nanometer wide (0.42 nm) GO/g-C₃N₄ channels, the GO/g-C₃N₄ membrane exhibits salt rejections of ∼90% with water permeances of above 30 L h^-1 m^-2 bar^-1, while the pure GO membrane only has salt rejections of below 30% accompanied by water permeances of below 4 L h^-1 m^-2 bar^-1. Combining experimental and theoretical investigations, size exclusion has proved to be the dominating mechanism for high rejections, and the ultralow friction water flow along g-C₃N₄ sheets is responsible for permeation enhancements. Importantly, the GO/g-C₃N₄ membrane shows promising long-term, antioxidation, and antipressure stability.

Viscoelasticity Enhances Nanometer-Scale Slip in Gigahertz-Frequency Liquid Flows

The interaction between flowing liquids and solid surfaces underpins many physical phenomena and technologies, such as the ability of an airfoil to generate lift and the mixing of liquids for industrial applications. These phenomena are often described using the Navier-Stokes equations and the no-slip boundary condition: the assumption that the liquid immediately adjacent to a solid surface does not move relative to the surface. Herein, we observe violation of the no-slip condition with strong enhancement of slip due to intrinsic viscoelasticity of the bulk liquid. This is achieved by measuring the 20 GHz acoustic vibrations of gold nanoparticles in glycerol/water mixtures, for which the underlying physics is explored using rigorous, theoretical models. The reported enhancement of slip revises current understanding of ultrafast liquid flows, with implications for technologies ranging from membrane filtration to nanofluidic devices and biomolecular sensing.

Theoretical description of molecular permeation via surface diffusion through graphene nanopores

We establish a theoretical model to describe the surface molecular permeation through two-dimensional graphene nanopores based on the surface diffusion equation and Fick's law. The model is established by considering molecular adsorption and desorption from the surface adsorption layer and the molecular diffusion and concentration gradient on the graphene surface. By comparing with the surface flux obtained from molecular dynamics simulations, it is shown that the model can predict well the overall permeation flux especially for strongly adsorbed molecules (i.e. CO₂ and H₂S) on graphene surfaces. Although good agreement between the theoretical and simulated density distribution is hard to achieve owing to the large uncertainty in the calculation of surface diffusion coefficients based on the Einstein equation, the model itself is very competent to describe the surface molecular permeation both from the aspects of the overall permeation flux and detailed density distribution. This model is believed to supplement the theoretical description of molecular permeation through graphene nanopores and provide a good reference for the description of mass transport through two-dimensional porous materials.

Nanopore-Based Power Generation from Salinity Gradient: Why It Is Not Viable

In recent years, the development of nanopore-based membranes has revitalized the prospect of harvesting salinity gradient (blue) energy. In this study, we systematically analyze the energetic performance of nanopore-based power generation (NPG) at various process scales, beginning with a single nanopore, followed by a multipore membrane coupon, and ending with a full-scale system. We confirm the high power densities attainable by a single nanopore and demonstrate that, at the coupon scale and above, concentration polarization severely hinders the power density of NPG, revealing the common, yet significant, error in linearly extrapolating single-pore performance to multipore membranes. Through our consideration of concentration polarization, we also importantly show that the development of materials with exceptional nanopore properties provides limited enhancement of practical process performance. For a full-scale NPG membrane module, we find an inherent tradeoff between power density and thermodynamic energy efficiency, whereby achieving a high power density sacrifices the energy efficiency. Furthermore, we derive a simple expression for the theoretical maximum energy efficiency of NPG, showing it is solely related to the membrane selectivity (i.e., S²/2). Through this relation, it is apparent that the energy efficiency of NPG is limited to only 50% (for a completely selective membrane, i.e., S = 1), reinforcing our optimistic full-scale simulations which result in a (practical) maximum energy efficiency of 42%. Finally, we assess the net extractable energy of a full-scale NPG system which mixes river water and seawater by including the energy losses from pretreatment and pumping, revealing that the NPG process-both in its current state of development and in the case of highly optimistic performance with minimized external energy losses-is not viable for power generation.

Facile Fabrication of Subnanopores in Graphene under Ion Irradiation: Molecular Dynamics Simulations

Two-dimensional (2D) nanoporous membranes have attracted great interest in water desalination, energy conversion, electrode, and gas separation. The performances of these membranes are mainly determined by the nanopores, and only with satisfactory subnanometer pores can applications such as high-precision ion separation be realized. Therefore, to efficiently create subnanopores in 2D materials is of great importance. Here, using molecular dynamics simulations, we demonstrate that the direct irradiation of energetic ion is capable of introducing subnanopores in monolayer graphene. By changing the energy of the incident Au ion, the averaged pore diameter can be adjusted from 4.2 to 5.6 Å, and pore diameter distributions are narrow. In the formation processes of the subnanopores, the cascade collisions caused by the primary knock-on atom (PKA) predominates, and pores can only be created in ion impact positions close to the PKA, especially for the incident ion with high energy. Our results show the promise of ion irradiation as a facile method to fabricate subnanopores in 2D materials. As hydrated ions, gases, and small organic molecules have diameters of several angstroms, close to the pore sizes, the created nanoporous membranes can be used to separate those matter, which is conducive to accelerating related applications.

Selective Gas Permeation in Defect-Engineered Bilayer Graphene

Defective graphene holds great potential to enable the permeation of gas molecules at high rates with high selectivity due to its one-atom thickness and resultant atomically small pores at the defect sites. However, precise control and tuning of the size and density of the defects remain challenging. In this work, we introduce atomic-scale defects into bilayer graphene via a decoupled strategy of defect nucleation using helium ion irradiation followed by defect expansion using hydrogen plasma treatment. The cotreated membranes exhibit high permeability and simultaneously high selectivity compared to those singly treated by ion irradiation or hydrogen plasma only. High permeation selectivity values for H₂/N₂ and H₂/CH₄ of 495 and 877, respectively, are achieved for optimally cotreated membranes. The method presented can also be scaled up to prepare large-area membranes for gas separation, e.g., for hydrogen purification and recovery from H₂/CH₄ and H₂/N₂ mixtures.

Decimeter-Scale Atomically Thin Graphene Membranes for Gas-Liquid Separation

Graphene holds great potential for fabricating ultrathin selective membranes possessing high permeability without compromising selectivity and has attracted intensive interest in developing high-performance separation membranes for desalination, natural gas purification, hemodialysis, distillation, and other gas-liquid separation. However, the scalable and cost-effective synthesis of nanoporous graphene membranes, especially designing a method to produce an appropriate porous polymer substrate, remains very challenging. Here, we report a facile route to fabricate decimeter-scale (∼15 × 10 cm²) nanoporous atomically thin membranes (NATMs) via the direct casting of the porous polymer substrate onto graphene, which was produced by chemical vapor deposition (CVD). After the vapor-induced phase-inversion process under proper experimental conditions (60 °C and 60% humidity), the flexible nanoporous polymer substrate was formed. The resultant skin-free polymer substrate, which had the proper pore size and a uniform spongelike structure, provided enough mechanical support without reducing the permeance of the NATMs. It was demonstrated that after creating nanopores by the O₂ plasma treatment, the NATMs were salt-resistant and simultaneously showed 3-5 times higher gas (CO₂) permeance than the state-of-the-art commercial polymeric membranes. Therefore, our work provides guidance for the technological developments of graphene-based membranes and bridges the gap between the laboratory-scale "proof-of-concept" and the practical applications of NATMs in the industry.

Scalable synthesis of nanoporous atomically thin graphene membranes for dialysis and molecular separations via facile isopropanol-assisted hot lamination

Scalable graphene synthesis and facile large-area membrane fabrication are imperative to advance nanoporous atomically thin membranes (NATMs) for molecular separations. Although chemical vapor deposition (CVD) allows for roll-to-roll high-quality monolayer graphene synthesis, facile transfer with atomically clean interfaces to porous supports for large-area NATM fabrication remains extremely challenging. Sacrificial polymer scaffolds commonly used for graphene transfer typically leave polymer residues detrimental to membrane performance and transfers without polymer scaffolds suffer from low yield resulting in high non-selective leakage through NATMs. Here, we systematically study the factors influencing graphene NATM fabrication and report on a novel roll-to-roll manufacturing compatible isopropanol-assisted hot lamination (IHL) process that enables scalable, facile and clean transfer of CVD graphene on to polycarbonate track etched (PCTE) supports with coverage ≥99.2%, while preserving support integrity/porosity. We demonstrate fully functional centimeter-scale graphene NATMs that show record high permeances (∼2-3 orders of magnitude higher) and better selectivity than commercially available state-of-the-art polymeric dialysis membranes, specifically in the 0-1000 Da range. Our work highlights a scalable approach to fabricate graphene NATMs for practical applications and is fully compatible with roll-to-roll manufacturing processes.

Size-Sensitive Thermoelectric Properties of Electrolyte-Based Nanofluidic Systems

In this work, we investigate the thermoelectric properties of aqueous KCl solutions confined in graphene nanochannels through molecular dynamics simulations. The channel height H ranges from 0.7 to 7.8 nm. It is found that the Seebeck coefficient, S_e, and the figure of merit, ZT, of the KCl solution are highly sensitive to H when H is small. For the nanochannel of H = 1.0 nm, S_e = 30.6 mV/K and ZT = 4.6 at room temperature, which are superior to most of the solid-state thermoelectric materials. The remarkable thermoelectric properties in small channels are attributed to the flow slip at the channel walls and the mean excess enthalpy density of the solution, which is mainly from the potential energy contribution. The molecular insight promotes the applications of nanofluidic devices for thermal energy harvesting.

Millisecond lattice gasification for high-density CO2- and O2-sieving nanopores in single-layer graphene

Etching single-layer graphene to incorporate a high pore density with sub-angstrom precision in molecular differentiation is critical to realize the promising high-flux separation of similar-sized gas molecules, e.g., CO₂ from N₂ However, rapid etching kinetics needed to achieve the high pore density is challenging to control for such precision. Here, we report a millisecond carbon gasification chemistry incorporating high density (>10¹² cm^-2) of functional oxygen clusters that then evolve in CO₂-sieving vacancy defects under controlled and predictable gasification conditions. A statistical distribution of nanopore lattice isomers is observed, in good agreement with the theoretical solution to the isomer cataloging problem. The gasification technique is scalable, and a centimeter-scale membrane is demonstrated. Last, molecular cutoff could be adjusted by 0.1 Å by in situ expansion of the vacancy defects in an O₂ atmosphere. Large CO₂ and O₂ permeances (>10,000 and 1000 GPU, respectively) are demonstrated accompanying attractive CO₂/N₂ and O₂/N₂ selectivities.

Fast Permeation of Small Ions in Carbon Nanotubes

Simulations and experiments have revealed enormous transport rates through carbon nanotube (CNT) channels when a pressure gradient drives fluid flow, but comparatively little attention has been given to concentration-driven transport despite its importance in many fields. Here, membranes are fabricated with a known number of single-walled CNTs as fluid transport pathways to precisely quantify the diffusive flow through CNTs. Contrary to early experimental studies that assumed bulk or hindered diffusion, measurements in this work indicate that the permeability of small ions through single-walled CNT channels is more than an order of magnitude higher than through the bulk. This flow enhancement scales with the ion free energy of transfer from bulk solutions to a nanoconfined, lower-dielectric environment. Reported results suggest that CNT membranes can unlock dialysis processes with unprecedented efficiency.