Analytical Prediction of Gas Permeation through Graphene Nanopores of Varying Sizes: Understanding Transitions across Multiple Transport Regimes

How Membrane Flexibility Impacts Permeation and Separation of Gas through Nanoporous Graphenes

In recent years, extensive research has used molecular dynamics simulations to investigate gas separation through nanoporous graphene (NPG) membranes. However, most studies have considered graphene membranes as rigid, overlooking the impact of their inherent flexibility. This study systematically quantifies the effect of graphene flexibility on gas permeation by comparing the diffusion of various gases through flexible and rigid single-layer NPG models. The results demonstrate that flexibility notably increases permeance, particularly for gases with larger molecular diameters/pore size ratios, by allowing gas molecules greater mobility within the pore. Interestingly, the effect of flexibility boils down to the expansion of the average pore size, and the detail of the membrane's vibrational dynamics is of little importance in quantifying permeance. Our work shows that accounting for flexibility in molecular models improves the alignment of simulation results with experimental data, emphasizing the importance of considering membrane flexibility in predictive models of NPG membrane performance.

Constructing a Microdiffusion-Seepage-Stress Multifield Coupling Model for Nanopore Gas

Existing research is difficult to fully capture the correlation between gas molecules and pore wall interactions, multiphase flow, and stress distribution in nanopores. Taking gas as an example, a microscopic model was constructed. At the same time, diffusion, seepage, and stress were considered to accurately predict and manage gas transport in nanopores. First, molecular dynamics (MD) simulation methods were adopted to simulate the motion trajectories and interactions of gas molecules in nanopores. Second, a multiscale model was established based on continuum mechanics to consider the interaction between pore walls and gas molecules, and a diffusion equation was established to describe the diffusion process of gas molecules in pores. Then, finite element analysis and porous media models were used to simulate the seepage behavior of gas in the nanopores. Finally, the stress distribution in the pores was analyzed, and the influence of the interaction between the pore wall and gas molecules on stress was considered. The multifield coupling model was experimentally evaluated from three aspects: diffusion coefficient, seepage behavior, and stress distribution. The root-mean-square error (RMSE) and mean absolute error (MAE) of the model in different testing directions were calculated using different simulation tools, such as COMSOL, ANSYS, OpenFOAM, and CFX. The mean values of RMSE and MAE were lower than 0.20 and 0.17, respectively. The constructed model can comprehensively describe gas transmission within nanopores, improving the management accuracy and efficiency.

Anti-Arrhenius passage of gaseous molecules through nanoporous two-dimensional membranes

The passage of molecules through membranes is known to follow an Arrhenius-like kinetics, i.e. the flux is accelerated upon heating and vice versa. There exist though stepwise processes whose rates can decrease with temperature if, for example, adsorbed intermediates are involved. In this study, we perform temperature-variable permeation experiments in the range from -50 to +50 °C and observe anti-Arrhenius behaviour of water and ammonia permeating in two-dimensional freestanding carbon nanomembranes (CNMs). The permeation rate of water vapour is found to decrease many-fold with warming, while the passage of ammonia molecules strongly increases when the membrane is cooled down to the dew point. Liquefaction of isobutylene shows no enhancement for its transmembrane flux which is consistent with the material's pore architecture. The effects are described by the Clausius-Clapeyron relationship and highlight the key role of gas-surface interactions in two-dimensional membranes.

Selective Photonic Gasification of Strained Oxygen Clusters on Graphene for Tuning Pore Size in the Å Regime

Controlling the size of single-digit pores, such as those in graphene, with an Å resolution has been challenging due to the limited understanding of pore evolution at the atomic scale. The controlled oxidation of graphene has led to Å-scale pores; however, obtaining a fine control over pore evolution from the pore precursor (i.e., the oxygen cluster) is very attractive. Herein, we introduce a novel "control knob" for gasifying clusters to form pores. We show that the cluster evolves into a core/shell structure composed of an epoxy group surrounding an ether core in a bid to reduce the lattice strain at the cluster core. We then selectively gasified the strained core by exposing it to 3.2 eV of light at room temperature. This allowed for pore formation with improved control compared to thermal gasification. This is because, for the latter, cluster-cluster coalescence via thermally promoted epoxy diffusion cannot be ruled out. Using the oxidation temperature as a control knob, we were able to systematically increase the pore density while maintaining a narrow size distribution. This allowed us to increase H2 permeance as well as H2 selectivity. We further show that these pores could differentiate CH4 from N2, which is considered to be a challenging separation. Dedicated molecular dynamics simulations and potential of mean force calculations revealed that the free energy barrier for CH4 translocation through the pores was lower than that for N2. Overall, this study will inspire research on the controlled manipulation of clusters for improved precision in incorporating Å-scale pores in graphene.

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.

Enumerating Stable Nanopores in Graphene and Their Geometrical Properties Using the Combinatorics of Hexagonal Lattices

Nanopores in two-dimensional (2D) materials, including graphene, can be used for a variety of applications, such as gas separations, water desalination, and DNA sequencing. So far, however, all plausible isomeric shapes of graphene nanopores have not been enumerated. Instead, a probabilistic approach has been followed to predict nanopore shapes in 2D materials, due to the exponential increase in the number of nanopores as the size of the vacancy increases. For example, there are 12 possible isomers when N = 6 atoms are removed, a number that theoretically increases to 11.7 million when N = 20 atoms are removed from the graphene lattice. In this regard, the development of a smaller, exhaustive data set of stable nanopore shapes can help future experimental and theoretical studies focused on using nanoporous 2D materials in various applications. In this work, we use the theory of 2D triangular "lattice animals" to create a library of all stable graphene nanopore shapes based on a modification of a well-known algorithm in the mathematical combinatorics of polyforms known as Redelmeier's algorithm. We show that there exists a correspondence between graphene nanopores and triangular polyforms (called polyiamonds) as well as hexagonal polyforms (called polyhexes). We develop the concept of a polyiamond ID to identify unique nanopore isomers. We also use concepts from polyiamond and polyhex geometries to eliminate unstable nanopores containing dangling atoms, bonds, and moieties. We verify using density functional theory calculations that such pores are indeed unstable. The exclusion of these unstable nanopores leads to a remarkable reduction in the possible nanopores from 11.7 million for N = 20 to only 0.184 million nanopores, thereby indicating that the number of stable nanopores is almost 2 orders of magnitude lower and is much more tractable. Not only that, by extracting the polyhex outline, our algorithm allows searching for nanopores with dimensions and shape factors in a specified range, thus aiding the design of the geometrical properties of nanopores for specific applications. We also provide the coordinate files of the stable nanopores as a library to facilitate future theoretical studies of these nanopores.

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.

Gas permeation through nanoporous single-walled carbon nanotubes: the confinement effect

The gas permeation through nanoscale membranes like graphene has been extensively studied by experiments and empirical models. In contrast to planar membranes, the single-walled carbon nanotube has a natural confined hollow structure, which shall affect the gas permeation process. We perform molecular dynamics simulations to investigate the effect of the nanotube diameter on the gas permeation process. It is found that the permeance constant increases with the increase of the nanotube diameter, which can not be explained by existing empirical models. We generalize the three-state model to describe the diameter dependence for the permeance constant, which discloses a distinctive confinement-induced adsorption phenomenon for the gas molecule on the nanotube's inner surface. This adsorption phenomenon effectively reduces the pressure of the bulk gas, leading to the decrease of the permeance constant. These results illustrate the importance of the adsorption within the confined space on the gas permeation process.

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.

The effect of layer number on the gas permeation through nanopores within few-layer graphene

Few-layer graphene has been widely regarded as an efficient filter for gas separation, but the effect of the layer number on the gas permeation process is still unclear. To explore the layer number effect, we perform molecular dynamics simulations to investigate the gas permeation through a nanopore within the few-layer graphene. Our numerical simulations show that the permeation constant decreases with increasing layer number, which is analyzed based on the macroscopic Kennard empirical model. The macroscopic model is in good agreement with the numerical result in the limit of large layer number, but there are obvious deviations for the medium layer number. We generalize the macroscopic model by considering the nanoscale effect from the surface morphology of the nanoscale pore, which can well describe the layer number dependence for the gas permeation constant in the full range. These results provide valuable information for the application of few-layer graphene in the gas permeation field.

Tuning the Transport Properties of Gases in Porous Graphene Membranes with Controlled Pore Size and Thickness

Porous graphene membranes have emerged as promising alternatives for gas‐separation applications due to their atomic thickness enabling ultrahigh permeance, but they suffer from low gas selectivity. Whereas decreasing the pore size below 3 nm is expected to increase the gas selectivity due to molecular sieving, it is rather challenging to generate a large number of uniform small pores on the graphene surface. Here, a pore‐narrowing approach via gold deposition onto porous graphene surface is introduced to tune the pore size and thickness of the membrane to achieve a large number of small pores. Through the systematic approach, the ideal combination is determined as pore size below 3 nm, obtained at the thickness of 100 nm, to attain high selectivity and high permeance. The resulting membrane shows a H2/CO2 separation factor of 31.3 at H2 permeance of 2.23 × 105 GPU (1 GPU = 3.35 × 10−10 mol s−1 m−2 Pa−1), which is the highest value reported to date in the 105 GPU permeance range. This result is explained by comparing the predicted binding energies of gas molecules with the Au surface, −5.3 versus −21 kJ mol−1 for H2 and CO2, respectively, increased surface–gas interactions and molecular‐sieving effect with decreasing pore size.

Tuning the Transport Properties of Gases in Porous Graphene Membranes with Controlled Pore Size and Thickness

Porous graphene membranes have emerged as promising alternatives for gas-separation applications due to their atomic thickness enabling ultrahigh permeance, but they suffer from low gas selectivity. Whereas decreasing the pore size below 3 nm is expected to increase the gas selectivity due to molecular sieving, it is rather challenging to generate a large number of uniform small pores on the graphene surface. Here, a pore-narrowing approach via gold deposition onto porous graphene surface is introduced to tune the pore size and thickness of the membrane to achieve a large number of small pores. Through the systematic approach, the ideal combination is determined as pore size below 3 nm, obtained at the thickness of 100 nm, to attain high selectivity and high permeance. The resulting membrane shows a H₂ /CO₂ separation factor of 31.3 at H₂ permeance of 2.23 × 10⁵ GPU (1 GPU = 3.35 × 10^-10  mol s^-1 m^-2 Pa^-1 ), which is the highest value reported to date in the 10⁵ GPU permeance range. This result is explained by comparing the predicted binding energies of gas molecules with the Au surface, -5.3 versus -21 kJ mol^-1 for H₂ and CO₂ , respectively, increased surface-gas interactions and molecular-sieving effect with decreasing pore size.

One-Atom-Thick Crystals as Emerging Proton Sieves

Two-dimensional (2D) crystals, despite their atomic thickness, have long been considered as impermeable membranes to all molecules and atoms under ambient conditions: even the smallest of atoms, hydrogen, is expected to take billions of years to penetrate the 2D lattice covered with dense electron clouds. Recently it has been found that monolayer graphene, hexagonal boron nitride, and some other one-atom-thick crystals are highly permeable to protons, raising fundamental questions about the details of the transport process. In this Perspective, we review the mechanism of proton transport through 2D crystals and the related room-temperature quantum effects; the potential applications of 2D membranes in proton-related separation and sieving techniques, including proton exchange membranes and hydrogen isotope separation; and factors that enhance proton permeation and in turn influence 2D membrane design.

Pore Size Dependence of Permeability in Bicontinuous Nanoporous Media

In this work, we employ many-body dissipative particle dynamics (mDPD) simulations to investigate the fluid flow process through bicontinuous nanoporous media, which are representative models for a broad class of nanoporous materials. The mDPD formulation includes attractive and repulsive interactions describing accurately fluid-fluid and fluid-solid interactions. As a mesoscale simulation method, mDPD can bridge the length and time scale gap between continuum and atomistic simulations. The bicontinuous nanoporous models are constructed considering a defined morphology, the porosity level, and varying pore sizes in the range from 3.41 to 13.63 nm. All models have a 0.65 porosity level and the same topology. The models provide a stochastic description of the morphology and pore size distribution and allow for a direct investigation of the dependence of permeability on the average pore size. The stationary nanoporous models are filled with fluid particles, and flow is induced by the action of confining pistons. Simulation results, obtained by imposing different pressure differences on the surfaces of the nanoporous media, indicate a linear pressure drop within the nanoporous model. Regardless of the complexities and different scales of the porous media considered, the steady-state fluid flow through the nanoporous models is proportional to the pressure gradient applied, in agreement with Darcy's law. The calculated pore size dependence of permeability is well described by the Hagen-Poiseuille law, considering a single shape correction factor that accounts for the flow resistance due to the complex nanoporous morphology. This work highlights the effect of the average pore size of a complex stochastic bicontinuous nanoporous medium on fluid properties. The results indicate rather a relatively simple dependence of permeability on the average pore size. The novel method we employ to generate the stochastic bicontinuous nanoporous structure allows the control of different geometric features that can be explored in future studies.

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.

Direct Chemical Vapor Deposition Synthesis of Porous Single-Layer Graphene Membranes with High Gas Permeances and Selectivities

Single-layer graphene containing molecular-sized in-plane pores is regarded as a promising membrane material for high-performance gas separations due to its atomic thickness and low gas transport resistance. However, typical etching-based pore generation methods cannot decouple pore nucleation and pore growth, resulting in a trade-off between high areal pore density and high selectivity. In contrast, intrinsic pores in graphene formed during chemical vapor deposition are not created by etching. Therefore, intrinsically porous graphene can exhibit high pore density while maintaining its gas selectivity. In this work, the density of intrinsic graphene pores is systematically controlled for the first time, while appropriate pore sizes for gas sieving are precisely maintained. As a result, single-layer graphene membranes with the highest H₂ /CH₄ separation performances recorded to date (H₂ permeance > 4000 GPU and H₂ /CH₄ selectivity > 2000) are fabricated by manipulating growth temperature, precursor concentration, and non-covalent decoration of the graphene surface. Moreover, it is identified that nanoscale molecular fouling of the graphene surface during gas separation where graphene pores are partially blocked by hydrocarbon contaminants under experimental conditions, controls both selectivity and temperature dependent permeance. Overall, the direct synthesis of porous single-layer graphene exploits its tremendous potential as high-performance gas-sieving 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.

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.

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.

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.

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.

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.

Predicting Gas Separation through Graphene Nanopore Ensembles with Realistic Pore Size Distributions

The development of nanoporous single-layer graphene membranes for gas separation has prompted increasing theoretical investigations of gas transport through graphene nanopores. However, computer simulations and theories that predict gas permeances through individual graphene nanopores are not suitable to describe experimental results, because a realistic graphene membrane contains a large number of nanopores of diverse sizes and shapes. With this need in mind, here, we generate nanopore ensembles in silico by etching carbon atoms away from pristine graphene with different etching times, using a kinetic Monte Carlo algorithm developed by our group for the isomer cataloging problem of graphene nanopores. The permeances of H₂, CO₂, and CH₄ through each nanopore in the ensembles are predicted using transition state theory based on classical all-atomistic force fields. Our findings show that the total gas permeance through a nanopore ensemble is dominated by a small fraction of large nanopores with low energy barriers of pore crossing. We also quantitatively predict the increase of the gas permeances and the decrease of the selectivities between the gases as functions of the etching time of graphene. Furthermore, by fitting the theoretically predicted selectivities to the experimental ones reported in the literature, we show that nanopores in graphene effectively expand as the temperature of permeation measurement increases. We propose that this nanopore "expansion" is due to the desorption of contaminants that partially clog the graphene nanopores. In general, our study highlights the effects of the pore size and shape distributions of a graphene nanopore ensemble on its gas separation properties and calls into attention the potential effect of pore-clogging contamination in experiments.

Gas separation using graphene nanosheet: insights from theory and simulation

The investigation of porous graphene, especially experimental research, is a challenging issue in related academic and technology and has become a hot topic in recent years. It is well known that the preparation of porous graphene is a difficult problem in experimental techniques. To prepare nanoporous graphene, much attention must focus on the quality of nanoporous structures and throughput array pores. Therefore, a comprehensive summary as much as possible has been made to provide a better understanding of the progress. A summary of synthesis techniques, the properties of nanoporous graphene membranes from the synthesis point of view, and potential applications of porous graphene and graphene oxide for gas separation on the basis of theoretical studies were given attention in this paper. Gas separation, including carbon dioxide capture, gas storage, natural gas sweetening, and flue gas purification through porous graphene, is of great interest. Porous graphene with narrow pore distribution provides exciting opportunities in gas separation processes.

Selective Etching of Graphene Membrane Nanopores: From Molecular Sieving to Extreme Permeance

Two-dimensional materials are the essential building blocks of breakthrough membrane technologies due to minimal permeation barriers across atomically thin pores. Tunable pore size fabrication combined with independently controlled pore number density is necessary for outstanding performance but remains a challenge. There is a great need for parallel, upscalable methods that can control pore size from sub-nm to >5 nm, a pore size range required for membranes with effective molecular separation. Here we report a dry, facile, and scalable process introducing atomic defects by design, followed by selective etching of graphene edge atoms able to controllably expand the nanopore dimensions from sub-nm to 5 nm. The attainable average pore sizes at 10¹⁵ m^-2 pore density promise applicability to various separation applications. We investigate the gas permeation and separation mechanisms, finding that these membranes display molecular sieving (H₂/CH₄ separation factor = 9.3; H₂ permeance = 3370 gas permeation units (GPU)) and reveal the presence of interweaved transport phenomena of pore chemistry, surface flow, and gas molecule momentum transfer. We observe the smooth transition from molecular sieving to effusion at unprecedented permeance (H₂/CH₄ separation factor = 3.7; H₂ permeance = 10⁷ GPU). Our scalable graphene membrane fabrication approach in combination with sub-5 nm pores opens a new route employing 2D membranes to study gas transport and effectively paving the way to industrial applications.

Nanoconfined Fluids: What Can We Expect from Them?

Nanoconfined fluids (NCFs), which are confined in nanospaces, exhibit distinctive nanoscale effects, including surface effects, small-size effects, quantum effects, and others. The continuous medium hypothesis in fluid mechanics is not valid in this context because of the comparable characteristic length of spaces and molecular mean free path, and accordingly, the classical continuum theories developed for the bulk fluids usually cannot describe the mass and energy transport of NCFs. In this Perspective, we summarize the nanoscale effects on the thermodynamics, mass transport, flow dynamics, heat transfer, phase change, and energy transport of NCFs and highlight the related representative works. The applications of NCFs in the fields of membrane separation, oil and gas production, energy harvesting and storage, and biological engineering are especially indicated. Currently, the theoretical description framework of NCFs is still missing, and it is expected that this framework can be established by adopting the classical continuum theories with the consideration of nanoscale effects.