Gas flow through atomic-scale apertures

Recent Research Progress of Porous Graphene and Applications in Molecular Sieve, Sensor, and Supercapacitor

Porous graphene, including 2D and 3D porous graphene, is widely researched recently. One of the most attractive features is the proper utilization of graphene defects, which combine the advantages of both graphene and porous materials, greatly enriching the applications of porous graphene in biology, chemistry, electronics, and other fields. In this review, the defects of graphene are first discussed to provide a comprehensive understanding of porous graphene. Then, the latest advancements in the preparation of 2D and 3D porous graphene are presented. The pros and cons of these preparation methods are discussed in detail, providing a direction for the fabrication of porous graphene. Moreover, various superior properties of porous graphene are described, laying the foundation for their promising applications. Owing to its abundant morphology, wide distribution of pore size, and remarkable properties benefited from porous structure, porous graphene can not only promote molecular diffusion and electron transfer but also expose more active sites. Consequently, a serious of applications containing gas sieving, liquid separation, sensors, and supercapacitors, are presented. Finally, the challenges confronted during preparation and characterization of porous graphene are discussed, offering guidance for the future development of porous graphene in fabrication, characterization, properties, and applications.

Blue shifts in helium-surface bound-state resonances and quantum effects in cosine-law scattering

The scattering of gas from surfaces underpins technologies in fields such as gas permeation, heterogeneous catalysis and chemical vapour deposition. The effect of surface defects on the scattering is key in such technologies, but is still poorly understood. It is known empirically that unordered surfaces result-in random-angle scattering, with the effect thought to be classical. We here demonstrate the transition from quantum mechanical diffraction to cosine-scattering, and show that quantum bound-state resonances can greatly affect this transition. Further, we find that randomly distributed defects induce a blue-shift in the bound-state energies. We explore this phenomena, which can lay the basis for helium based quantum metrology of defects in 2D materials and material surfaces.

Size and Shape Exclusion in 2D Silicon Dioxide Membranes

2D membranes such as artificially perforated graphene are deemed to bring great advantages for molecular separation. However, there is a lack of structure-property correlations in graphene membranes as neither the atomic configurations nor the number of introduced sub-nanometer defects are known precisely. Recently, bilayer silica has emerged as an inherent 2D membrane with an unprecedentedly high areal density of well-defined pores. Mass transfer experiments with free-standing SiO₂ bilayers demonstrated a strong preference for condensable fluids over inert species, and the measured membrane selectivity revealed a key role of intermolecular forces in ångstrom-scale openings. In this study, vapor permeation measurements are combined with quantitative adsorption experiments and density functional theory (DFT) calculations to get insights into the mechanism of surface-mediated transport in vitreous 2D silicon dioxide. The membranes are shown to exhibit molecular sieving performance when exposed to vaporous methanol, ethanol, isopropanol, and tert-butanol. The results are normalized to the coverage of physisorbed molecules and agree well with the calculated energy barriers.

High durability and stability of 2D nanofluidic devices for long-term single-molecule sensing

Nanopores in two-dimensional (2D) membranes hold immense potential in single-molecule sensing, osmotic power generation, and information storage. Recent advances in 2D nanopores, especially on single-layer MoS2, focus on the scalable growth and manufacturing of nanopore devices. However, there still remains a bottleneck in controlling the nanopore stability in atomically thin membranes. Here, we evaluate the major factors responsible for the instability of the monolayer MoS2 nanopores. We identify chemical oxidation and delamination of monolayers from their underlying substrates as the major reasons for the instability of MoS2 nanopores. Surface modification of the substrate and reducing the oxygen from the measurement solution improves nanopore stability and dramatically increases their shelf-life. Understanding nanopore growth and stability can provide insights into controlling the pore size, shape and can enable long-term measurements with a high signal-to-noise ratio and engineering durable nanopore devices.

High-Throughput Nanopore Fabrication and Classification Using Xe-Ion Irradiation and Automated Pore-Edge Analysis

Large-area nanopore drilling is a major bottleneck in state-of-the-art nanoporous 2D membrane fabrication protocols. In addition, high-quality structural and statistical descriptions of as-fabricated porous membranes are key to predicting the corresponding membrane-wide permeation properties. In this work, we investigate Xe-ion focused ion beam as a tool for scalable, large-area nanopore fabrication on atomically thin, free-standing molybdenum disulfide. The presented irradiation protocol enables designing ultrathin membranes with tunable porosity and pore dimensions, along with spatial uniformity across large-area substrates. Fabricated nanoporous membranes are then characterized using scanning transmission electron microscopy imaging, and the observed nanopore geometries are analyzed through a pore-edge detection and analysis script. We further demonstrate that the obtained structural and statistical data can be readily passed on to computational and analytical tools to predict the permeation properties at both individual pore and membrane-wide scales. As an example, membranes featuring angstrom-scale pores are investigated in terms of their emerging water and ion flow properties through extensive all-atom molecular dynamics simulations. We believe that the combination of experimental and analytical approaches presented here will yield accurate physics-based property estimates and thus potentially enable a true function-by-design approach to fabrication for applications such as osmotic power generation and desalination/filtration.

Gas Separations using Nanoporous Atomically Thin Membranes: Recent Theoretical, Simulation, and Experimental Advances

Porous graphene and other atomically thin 2D materials are regarded as highly promising membrane materials for high-performance gas separations due to their atomic thickness, large-scale synthesizability, excellent mechanical strength, and chemical stability. When these atomically thin materials contain a high areal density of gas-sieving nanoscale pores, they can exhibit both high gas permeances and high selectivities, which is beneficial for reducing the cost of gas-separation processes. Here, recent modeling and experimental advances in nanoporous atomically thin membranes for gas separations is discussed. The major challenges involved, including controlling pore size distributions, scaling up the membrane area, and matching theory with experimental results, are also highlighted. Finally, important future directions are proposed for real gas-separation applications of nanoporous atomically thin membranes.

Gas permeation through graphdiyne-based nanoporous membranes

Nanoporous membranes based on two dimensional materials are predicted to provide highly selective gas transport in combination with extreme permeance. Here we investigate membranes made from multilayer graphdiyne, a graphene-like crystal with a larger unit cell. Despite being nearly a hundred of nanometers thick, the membranes allow fast, Knudsen-type permeation of light gases such as helium and hydrogen whereas heavy noble gases like xenon exhibit strongly suppressed flows. Using isotope and cryogenic temperature measurements, the seemingly conflicting characteristics are explained by a high density of straight-through holes (direct porosity of ∼0.1%), in which heavy atoms are adsorbed on the walls, partially blocking Knudsen flows. Our work offers important insights into intricate transport mechanisms playing a role at nanoscale.

2D nanoporous membranes are predicted to provide highly selective gas transport in combination with extreme permeance. Here authors demonstrate gas separation performance and transport mechanisms through membranes of graphdiyne, a quasi 2D material with a graphene-like structure.

Stress induced delamination of suspended MoS2 in aqueous environments

Applying hydrostatic pressure with suspended 2D material thin membranes allows probing the effects of lateral strain on the ion and fluid transport through nanopores. We demonstrate how both permanent and temporary delamination of 2D materials can be induced by pressure and potential differences between the membrane, causing a strong mechanosensitive modulation of ion transport. Our methodology is based on in situ measurements of ionic current and streaming modulation as the supporting membrane is indented or bulged with pressure. We demonstrate how indirect measurements of fluid transport through delaminated MoS₂ membranes is achieved through monitoring streaming current and potential. This is combined with TEM images of 2D material membranes before and after aqueous measurements, showing temporary delamination during mechanical or electrical stress. The obtained results allow a better understanding of measurements with supported 2D materials, i.e. avoiding misinterpreting measured data, and could be used to probe how the electrical field and fluid flow at the nanoscale influence the adhesion of supported 2D materials.

Mechanical and electrical stress can lead to the temporary and permanent 2D membrane delamination and consequent strong mechanosensitive modulation of ion transport measured in situ.

Exponentially selective molecular sieving through angstrom pores

Two-dimensional crystals with angstrom-scale pores are widely considered as candidates for a next generation of molecular separation technologies aiming to provide extreme, exponentially large selectivity combined with high flow rates. No such pores have been demonstrated experimentally. Here we study gas transport through individual graphene pores created by low intensity exposure to low kV electrons. Helium and hydrogen permeate easily through these pores whereas larger species such as xenon and methane are practically blocked. Permeating gases experience activation barriers that increase quadratically with molecules' kinetic diameter, and the effective diameter of the created pores is estimated as ∼2 angstroms, about one missing carbon ring. Our work reveals stringent conditions for achieving the long sought-after exponential selectivity using porous two-dimensional membranes and suggests limits on their possible performance.

Mass Transfer in Boronate Ester 2D COF Single Crystals

Unlike graphene and similar structures, 2D covalent organic frameworks (2D COFs) exhibit intrinsic porosity with a high areal density of well-defined and uniform openings. Given the pore size adjustability, 2D COFs are likely to outperform artificially perforated inorganic layers with respect to their prospects in membrane separation. Yet, exploring the mass transport in 2D COFs is hidden by the lack of laterally extended free-standing membranes. This work reports on direct molecular permeation measurements with single crystals of an interfacially synthesized boronate ester 2D COF. In accordance with the material topography, the atmospheric and noble gases readily pass the suspended nanosheets while their areal porosity is quantified to be almost 40% exceeding that in any 2D membranes known. However, bulkier aromatic hydrocarbons are found to deviate substantially from Graham's law of diffusion. Counterintuitively, the permeation rate is demonstrated to rise from benzene to toluene and further to xylene despite the increase in the molecular mass and dimensions. The results are interpreted in terms of adsorption-mediated flow that appears to be an important transport mechanism for microporous planar nanomaterials.

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.

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.