Addressing the isomer cataloguing problem for nanopores in two-dimensional materials

Experimental and Theoretical Insights into Interfacial Properties of 2D Materials for Selective Water Transport Membranes: A Critical Review

Interfacial properties, such as wettability and friction, play critical roles in nanofluidics and desalination. Understanding the interfacial properties of two-dimensional (2D) materials is crucial in these applications due to the close interaction between liquids and the solid surface. The most important interfacial properties of a solid surface include the water contact angle, which quantifies the extent of interactions between the surface and water, and the water slip length, which determines how much faster water can flow on the surface beyond the predictions of continuum fluid mechanics. This Review seeks to elucidate the mechanism that governs the interfacial properties of diverse 2D materials, including transition metal dichalcogenides (e.g., MoS2), graphene, and hexagonal boron nitride (hBN). Our work consolidates existing experimental and computational insights into 2D material synthesis and modeling and explores their interfacial properties for desalination. We investigated the capabilities of density functional theory and molecular dynamics simulations in analyzing the interfacial properties of 2D materials. Specifically, we highlight how MD simulations have revolutionized our understanding of these properties, paving the way for their effective application in desalination. This Review of the synthesis and interfacial properties of 2D materials unlocks opportunities for further advancement and optimization in desalination.

Machine Learning in Membrane Design: From Property Prediction to AI-Guided Optimization

Porous membranes, either polymeric or two-dimensional materials, have been extensively studied because of their outstanding performance in many applications such as water filtration. Recently, inspired by the significant success of machine learning (ML) in many areas of scientific discovery, researchers have started to tackle the problem in the field of membrane design using data-driven ML tools. In this Mini Review, we summarize research efforts on three types of applications of machine learning in membrane design, including (1) membrane property prediction using ML, (2) gaining physical insight and drawing quantitative relationships between membrane properties and performance using explainable artificial intelligence, and (3) ML-guided design, optimization, or virtual screening of membranes. On top of the review of previous research, we discuss the challenges associated with applying ML for membrane design and potential future directions.

Interfacial Assembly of 2D Graphene-Derived Ion Channels for Water-Based Green Energy Conversion

The utilization of sustained and green energy is believed to alleviate increasing menace of global environmental concerns and energy dilemma. Interfacial assembly of 2D graphene-derived ion channels (2D-GDICs) with tunable ion/fluid transport behavior enables efficient harvesting of renewable green energy from ubiquitous water, especially for osmotic energy harvesting. In this review, various interfacial assembly strategies for fabricating diverse 2D-GDICs are summarized and their ion transport properties are discussed. This review analyzes how particular structure and charge density/distribution of 2D-GDIC can be modulated to minimize internal resistance of ion/fluid transport and enhance energy conversion efficiency, and highlights stimuli-responsive functions and stability of 2D-GDIC and further examines the possibility of integrating 2D-GDIC with other energy conversion systems. Notably, the presented preparation and applications of 2D-GDIC also inspire and guide other 2D materials to fabricate sophisticated ion channels for targeted applications. Finally, potential challenges in this field is analyzed and a prospect to future developments toward high-performance or large-scale real-word applications is offered.

Thermodynamic Window for Size-Controlled Pore Formation in Graphene for Large-Scale Molecular Sieves

Nanopores in graphene monolayers are a promising option for molecular separation applications, such as desalination and carbon capture. Graphene's atomic thickness allows for an optimal balance between molecular selectivity and permeability, while its chemical stability and robust mechanical properties make it appealing for a wide range of commercial applications. However, scaling to large areas with controlled pore size distribution is an open challenge in ultrathin membranes. Here, using first-principles calculations, we identify a suitable thermodynamic window in a chemical vapor deposition system for directly growing graphene monolayers with a controlled pore size distribution. As an example, our calculations show that a postgrowth annealing step with a supersaturation range of 19.7-25 kJ/mol at 1000 K results in the creation of a controllable pore density at graphene grain boundaries, with pore sizes falling within the range of 5-8 Å. Such pores isolate hydrated Cl ions from water molecules, effectively desalinating seawater. Thus, it allows the design of targeted synthesis of large-scale 2D layers for membrane applications.

Design, synthesis, and application of some two-dimensional materials

Two-dimensional (2D) materials are widely used as key components in the fields of energy conversion and storage, optoelectronics, catalysis, biomedicine, etc. To meet the practical needs, molecular structure design and aggregation process optimization have been systematically carried out. The intrinsic correlation between preparation methods and the characteristic properties is investigated. This review summarizes the recent research achievements of 2D materials in the aspect of molecular structure modification, aggregation regulation, characteristic properties, and device applications. The design strategies to fabricate functional 2D materials starting from precursor molecules are introduced in detail referring to organic synthetic chemistry and self-assembly technology. It provides important research ideas for the design and synthesis of related materials.

Impacts of Random Atomic Defects on Critical Buckling Stress of Graphene under Different Boundary Conditions

Buckled graphene has potential applications in energy harvest, storage, conversion, and hydrogen storage. The investigation and quantification analysis of the random porosity in buckled graphene not only contributes to the performance reliability evaluation, but it also provides important references for artificial functionalization. This paper proposes a stochastic finite element model to quantify the randomly distributed porosities in pristine graphene. The Monte Carlo stochastic sampling process is combined with finite element computation to simulate the mechanical property of buckled graphene. Different boundary conditions are considered, and the corresponding results are compared. The impacts of random porosities on the buckling patterns are recorded and analyzed. Based on the large sampling space provided by the stochastic finite element model, the discrepancies caused by the number of random porosities are discussed. The possibility of strengthening effects in critical buckling stress is tracked in the large sampling space. The distinguishable interval ranges of probability density distribution for the relative variation of the critical buckling stress prove the promising potential of artificial control by the atomic vacancy amounts. In addition, the approximated Gaussian density distribution of critical buckling stress demonstrates the stochastic sampling efficiency by the Monte Carlo method and the artificial controllability of porous graphene. The results of this work provide new ideas for understanding the random porosities in buckled graphene and provide a basis for artificial functionalization through porosity controlling.

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.

In Situ Nucleation-Decoupled and Site-Specific Incorporation of Å-Scale Pores in Graphene Via Epoxidation

Generating pores in graphene by decoupled nucleation and expansion is desired to achieve a fine control over the porosity, and is desired to advance several applications. Herein, epoxidation is introduced, which is the formation of nanosized epoxy clusters on the graphitic lattice as nucleation sites without forming pores. In situ gasification of clusters inside a transmission electron microscope shows that pores are generated precisely at the site of the clusters by surpassing an energy barrier of 1.3 eV. Binding energy predictions using ab initio calculations combined with the cluster nucleation theory reveal the structure of the epoxy clusters and indicate that the critical cluster is an epoxy dimer. Finally, it is shown that the cluster gasification can be manipulated to form Å-scale pores which then effectively sieve gas molecules based on their size. This decoupled cluster nucleation and pore formation will likely pave the way for an independent control of pore size and density.

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.

Long-Term Evolution of Vacancies in Large-Area Graphene

Devices based on two-dimensional (2D) materials such as graphene and molybdenum disulfide have shown extraordinary potential in physics, nanotechnology, and electronics. The performances of these applications are heavily affected by defects in utilized materials. Although great efforts have been spent in studying the formation and property of various defects in 2D materials, the long-term evolution of vacancies is still unclear. Here, using a designed program based on the kinetic Monte Carlo method, we systematically investigate the vacancy evolution in monolayer graphene on a long-time and large spatial scale, focusing on the variation of the distribution of different vacancy types. In most cases, the vacancy distribution remains nearly unchanged during the whole evolution, and most of the evolution events are vacancy migrations with a few being coalescences, while it is extremely difficult for multiple vacancies to dissolve. The probabilities of different categories of vacancy evolutions are determined by their reaction rates, which, in turn, depend on corresponding energy barriers. We further study the influences of different factors such as the energy barrier for vacancy migration, coalescence, and dissociation on the evolution, and the coalescence energy barrier is found to be dominant. These findings indicate that vacancies (also subnanopores) in graphene are thermodynamically stable for a long period of time, conducive to subsequent characterizations or applications. Besides, this work provides hints to tune the ultimate vacancy distribution by changing related factors and suggests ways to study the evolution of other defects in various 2D materials.

Magnetism and interlayer bonding in pores of Bernal-stacked hexagonal boron nitride

When single-layer h-BN is subjected to a high-energy electron beam, triangular pores with nitrogen edges are formed. Because of the broken sp² bonds, these pores are known to possess magnetic states. We report on the magnetism and electronic structure of triangular pores as a function of their size. Moreover, in the Bernal-stacked h-BN (AB-h-BN), multilayer pores with parallel edges can be created, which is not possible in the commonly fabricated multilayer AA'-h-BN. Given that these pores can be manufactured in a well-controlled fashion using an electron beam, it is important to understand the interactions of pores in neighboring layers. We find that in certain configurations, the edges of the neighboring pores remain open and retain their magnetism, and in others, they form interlayer bonds. We present a comprehensive report on these configurations for small nanopores. We find that at low temperatures, these pores have near degenerate magnetic configurations, and may be utilized in magnetoresistance and spintronics applications. In the process of forming larger multilayer nanopores, interlayer bonds can form, reducing the magnetization. Yet, unbonded parallel multilayer edges remain available at all sizes. Understanding these pores is also helpful in a multitude of applications such as DNA sequencing and quantum emission.

Multifunctional graphene heterogeneous nanochannel with voltage-tunable ion selectivity

Ion-selective nanoporous two-dimensional (2D) materials have shown extraordinary potential in energy conversion, ion separation, and nanofluidic devices; however, different applications require diverse nanochannel devices with different ion selectivity, which is limited by sample preparation and experimental techniques. Herein, we develop a heterogeneous graphene-based polyethylene terephthalate nanochannel (GPETNC) with controllable ion sieving to overcome those difficulties. Simply by adjusting the applied voltage, ion selectivity among K⁺, Na⁺, Li⁺, Ca²⁺, and Mg²⁺ of the GPETNC can be immediately tuned. At negative voltages, the GPETNC serves as a mono/divalent ion selective device by impeding most divalent cations to transport through; at positive voltages, it mimics a biological K⁺ nanochannel, which conducts K⁺ much more rapidly than the other ions with K⁺/ions selectivity up to about 4.6. Besides, the GPETNC also exhibits the promise as a cation-responsive nanofluidic diode with the ability to rectify ion currents. Theoretical calculations indicate that the voltage-dependent ion enrichment/depletion inside the GPETNC affects the effective surface charge density of the utilized graphene subnanopores and thus leads to the electrically controllable ion sieving. This work provides ways to develop heterogeneous nanochannels with tunable ion selectivity toward broad applications.

Nanoporous 2D materials have shown promising potential for ion sieving applications due to their physical and chemical properties. Here authors develop a heterogeneous graphene-based polyethylene terephthalate nanochannel with ion sieving ability that is controlled by adjusting the applied voltage.

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.

Single nucleobase identification for transversally-confined ssDNA using longitudinal ionic currents

High-fidelity DNA sequencing using solid-state nanopores remains a big challenge, partly due to difficulties related to efficient molecular capture and subsequent control of the dwell time. To help address these issues, here we propose a sequencing platform consisting of stacked two-dimensional materials with tailored structures containing a funnel-shaped step defect and a nanopore drilled inside the nanochannel. Our all-atom molecular dynamics (MD) simulations showed that, assisted by the step defect, single-stranded DNA (ssDNA) can be transported to the nanopore in a deterministic way by pulsed transversal electric fields. Furthermore, different types of DNA bases can reside in the pore for a sufficiently long time which can be successfully differentiated by longitudinal ionic currents. By using the decoupled driving forces for ssDNA transport and ionic current measurements, this approach holds potential for high-fidelity DNA sequencing.

Tailoring Nanoporous Graphene via Machine Learning: Predicting Probabilities and Formation Times of Arbitrary Nanopore Shapes

Nanopores in graphene, a 2D material, are currently being explored for various applications, such as gas separation, water desalination, and DNA sequencing. The shapes and sizes of nanopores play a major role in determining the performance of devices made out of graphene. However, given an arbitrary nanopore shape, anticipating its creation probability and formation time are challenging inverse problems, solving which could help develop theoretical models for nanoporous graphene and guide experiments in tailoring pore sizes/shapes. In this work, we develop a machine learning (ML) framework to predict these target variables, based on data generated using kinetic Monte Carlo simulations and chemical graph theory. Thereby, we enable the rapid quantification of the ease of formation of a given nanopore shape in graphene via silicon-catalyzed electron-beam etching and provide an experimental handle to realize it in practice. We use structural features such as the number of carbon atoms removed, the number of edge atoms, the diameter of the nanopore, and its shape factor, which can be readily extracted from the nanopore shape. We show that the trained models can accurately predict nanopore probabilities and formation times with R2 values on the test set of 0.97 and 0.95, respectively. Not only that, we obtain physical insight into the working of the model and discuss the role played by the various structural features in modulating nanopore formation. Overall, our work provides a solid foundation for experimental studies to manipulate nanopore sizes/shapes and for theoretical studies to consider realistic structures of nanopores in graphene.

Chemical vapor deposition of 2D materials: A review of modeling, simulation, and machine learning studies

Chemical vapor deposition (CVD) is extensively used to produce large-area two-dimensional (2D) materials. Current research is aimed at understanding mechanisms underlying the nucleation and growth of various 2D materials, such as graphene, hexagonal boron nitride (hBN), and transition metal dichalcogenides (e.g., MoS₂/WSe₂). Herein, we survey the vast literature regarding modeling and simulation of the CVD growth of 2D materials and their heterostructures. We also focus on newer materials, such as silicene, phosphorene, and borophene. We discuss how density functional theory, kinetic Monte Carlo, and reactive molecular dynamics simulations can shed light on the thermodynamics and kinetics of vapor-phase synthesis. We explain how machine learning can be used to develop insights into growth mechanisms and outcomes, as well as outline the open knowledge gaps in the literature. Our work provides consolidated theoretical insights into the CVD growth of 2D materials and presents opportunities for further understanding and improving such processes

How Grain Boundaries and Interfacial Electrostatic Interactions Modulate Water Desalination via Nanoporous Hexagonal Boron Nitride

To fulfill the increasing demand for drinking water, researchers are currently exploring nanoporous two-dimensional materials, such as hexagonal boron nitride (hBN), as potential desalination membranes. A prominent, yet unsolved challenge is to understand how such membranes will perform in the presence of defects or surface charge in the membrane material. In this work, we study the effect of grain boundaries (GBs) and interfacial electrostatic interactions on the desalination performance of bicrystalline nanoporous hBN using classical molecular dynamics simulations supported by quantum-mechanical density functional theory (DFT) calculations. We investigate three different nanoporous bicrystalline hBN configurations, with symmetric tilt GBs having misorientation angles of 13.2, 21.8, and 32.2°. Using lattice dynamics calculations, we find that grain boundaries alter the areas and shapes of nanopores in bicrystalline hBN, as compared to the nanopores in monocrystalline hBN. We observe that, although bicrystalline nanoporous hBN with a misorientation angle of 13.2° shows an improved water flow rate by ∼30%, it demonstrates reduced Na⁺ ion rejection by ∼6%, as compared to monocrystalline hBN. We also uncover the role of the nanopore shape in water desalination, finding that more elongated pores with smaller sizes (in 21.8- and 32.2°-misoriented bicrystalline hBN) can match water permeation through less elongated pores of slightly larger sizes, with a concomitant ∼3-4% decrease in Na⁺ rejection. Simulations also predict that the water flow rate is significantly affected by interfacial electrostatic interactions. Indeed, the water flow rate is the highest when altered partial charges on B and N atoms were determined using DFT calculations, as compared to when no partial charges or bulk partial charges (i.e., charged hBN) were considered. Overall, our work on water/ion transport through nanopores in bicrystalline hBN indicates that the presence of GBs and surface charge can lead, respectively, to a decrease in the ion rejection and water permeation performance of hBN membranes.

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.

Modulating Water Slip Using Atomic-Scale Defects: Friction on Realistic Hexagonal Boron Nitride Surfaces

Atomic-scale defects are ubiquitous in nanomaterials, yet their role in modulating fluid flow is inadequately understood. Hexagonal boron nitride (hBN) is an important two-dimensional material with applications in desalination and osmotic power. Although pristine hBN offers higher friction to the flow of water than graphene, we show here that certain defects can enhance water slippage on hBN. Using classical molecular dynamics simulations assisted by quantum-mechanical density functional theory, we compute the friction coefficient of water on hBN containing various vacancies (B, N, BN, B₂N, and B₃N) and the Stone-Wales defect. By investigating two defect concentrations, we obtain friction coefficients ranging from 0.4 to 2.6 times that of pristine hBN, leading to a maximum water slip length of 18.1 nm on hBN with a N vacancy or a Stone-Wales defect. Our work informs the use of defects to tune water flow and reveals defective hBN as an alternative high-slip surface to graphene.

Nanopores in Atomically Thin 2D Nanosheets Limit Aqueous Single-Stranded DNA Transport

Nanopores in 2D materials are highly desirable for DNA sequencing, yet achieving single-stranded DNA (ssDNA) transport through them is challenging. Using density functional theory calculations and molecular dynamics simulations we show that ssDNA transport through a pore in monolayer hexagonal boron nitride (h-BN) is marked by a basic nanomechanical conflict. It arises from the notably inhomogeneous flexural rigidity of ssDNA and causes high friction via transient DNA desorption costs exacerbated by solvation effects. For a similarly sized pore in bilayer h-BN, its self-passivated atomically smooth edge enables continuous ssDNA transport. Our findings shed light on the fundamental physics of biopolymer transport through pores in 2D materials.

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.

Atomically Precise Control of Carbon Insertion into hBN Monolayer Point Vacancies using a Focused Electron Beam Guide

Precise controlled filling of point vacancies in hBN with carbon atoms is demonstrated using a focused electron beam method, which guides mobile C atoms into the desired defect site. Optimization of the technique enables the insertion of a single C atom into a selected monovacancy, and preferential defect filling with sub-2 nm accuracy. Increasing the C insertion process leads to thicker 3D C nanodots seeded at the hBN point vacancy site. Other light elements are also observed to bind to hBN vacancies, including O, opening up a wide range of complex defect structures that include B, C, N, and O atoms. The ability to selectively fill point vacancies in hBN with C atoms provides a pathway for creating non-hydrogenated covalently bonded C molecules embedded in the insulating hBN.

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.

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.

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.

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.

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.

Broadening the Gas Separation Utility of Monolayer Nanoporous Graphene Membranes by an Ionic Liquid Gating

Ultrathin two-dimensional (2D) monolayer atomic crystal materials offer great potential for extending the field of novel separation technology due to their infinitesimal thickness and mechanical strength. One difficult and ongoing challenge is to perforate the 2D monolayer material with subnanometer pores with atomic precision for sieving similarly sized molecules. Here, we demonstrate the exceptional separation performance of ionic liquid (IL)/graphene hybrid membranes for challenging separation of CO₂ and N₂. Notably, the ultrathin ILs afford dynamic tuning of the size and chemical affinity of nanopores while preserving the high permeance of the monolayer nanoporous graphene membranes. The hybrid membrane yields a high CO₂ permeance of 4000 GPU and an outstanding CO₂/N₂ selectivity up to 32. This rational hybrid design provides a universal direction for broadening gas separation capability of atomically thin nanoporous membranes.

Metal-Halide Perovskite Design for Next-Generation Memories: First-Principles Screening and Experimental Verification

Memory devices have been advanced so much, but still it is highly required to find stable and reliable materials with low-power consumption. Halide perovskites (HPs) have been recently adopted for memory application since they have advantages of fast switching based on ionic motion in crystal structure. However, HPs also suffer from poor stability, so it is necessary to improve the stability of HPs. In this regard, combined first-principles screening and experimental verification are performed to design HPs that have high environmental stability and low-operating voltage for memory devices. First-principles screening identifies 2D layered AB2X5 structure as the best candidate switching layer for memory devices, because it has lower formation energy and defect formation energy than 3D ABX3 or other layered structures (A3B2X7, A2BX4). To verify results, all-inorganic 2D layered CsPb2Br5 is synthesized and used in memory devices. The memory devices that use CsPb2Br5 show much better stability and lower operating voltages than devices that use CsPbBr3. These findings are expected to provide new opportunity to design materials for reliable device applications based on calculation, screening, and experimental verification.

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

Nanoporous graphene is a promising candidate material for gas separation membranes, due to its atomic thickness and low cross-membrane transport resistance. The mechanisms of gas permeation through graphene nanopores, in both the large and small pore size limits, have been reported in the literature. However, mechanistic insights into the crossover from the small pore size limit to the large pore size limit are still lacking. In this study, we develop a comprehensive theoretical framework to predict gas permeance through graphene nanopores having a wide range of diameters using analytical equations. We formulate the transport kinetics associated with the direct impingement from the bulk and with the surface diffusion from the adsorption layer on graphene and then combine them to predict the overall gas permeation rate using a reaction network model. We also utilize molecular dynamics simulations to validate and calibrate our theoretical model. We show that the rates of both the direct impingement and the surface diffusion pathways need to be corrected using different multiplicative factors, which are functions of temperature, gas kinetic diameter, and pore diameter. Further, we find a minor spillover pathway that originates from the surface adsorption layer, but is not included in our theoretical model. Finally, we utilize the corrected model to predict the permeances of CO₂, CH₄, and Ar through graphene nanopores. We show that as the pore diameter increases, gas transport through graphene nanopores can transition from being translocation dominated (pore diameter < 0.7 nm), to surface pathway dominated (pore diameter 1-2 nm), and finally to direct pathway dominated (pore diameter > 4 nm). The various gas permeation mechanisms outlined in this study will be particularly useful for the rational design of membranes made out of two-dimensional materials such as graphene for gas separation applications.

Building and exploring libraries of atomic defects in graphene: Scanning transmission electron and scanning tunneling microscopy study

The presence and configurations of defects are primary components determining materials functionality. Their population and distribution are often nonergodic and dependent on synthesis history, and therefore rarely amenable to direct theoretical prediction. Here, dynamic electron beam-induced transformations in Si deposited on a graphene monolayer are used to create libraries of possible Si and carbon vacancy defects. Deep learning networks are developed for automated image analysis and recognition of the defects, creating a library of (meta) stable defect configurations. Density functional theory is used to estimate atomically resolved scanning tunneling microscopy (STM) signatures of the classified defects from the created library, allowing identification of several defect types across imaging platforms. This approach allows automatic creation of defect libraries in solids, exploring the metastable configurations always present in real materials, and correlative studies with other atomically resolved techniques, providing comprehensive insight into defect functionalities.

From GROMACS to LAMMPS: GRO2LAM : A converter for molecular dynamics software

Atomistic simulations have progressively attracted attention in the study of physical-chemical properties of innovative nanomaterials. GROMACS and LAMMPS are currently the most widespread open-source software for molecular dynamics simulations thanks to their good flexibility, numerous functionalities and responsive community support. Nevertheless, the very different formats adopted for input and output files are limiting the possibility to transfer GROMACS simulations to LAMMPS. In this article, we present GRO2LAM, a modular and open-source Python 2.7 code for rapidly translating input files and parameters from GROMACS to LAMMPS format. The robustness of the tool has been assessed by comparing the simulation results obtained by GROMACS and LAMMPS, after the format conversion by GRO2LAM. Specifically, three nanoscale configurations of interest in both engineering and biomedical fields are studied, namely a carbon nanotube, an iron oxide nanoparticle, and a protein immersed in water. In perspective, GRO2LAM may be the first step to achieve a full interoperability between molecular dynamics software. This would allow to easily exploit their complementary potentialities and post-processing functionalities. Moreover, GRO2LAM could facilitate the cross-check of simulation results, guaranteeing the reproducibility of molecular dynamics models and testing their robustness. Graphical Abstract GRO2LAM, a modular and open-source Python code for rapidly translating input files and parameters from GROMACS to LAMMPS format.

On-Surface Synthesis of a Nonplanar Porous Nanographene

On-surface synthesis provides an effective approach toward the formation of graphene nanostructures that are difficult to achieve via traditional solution chemistry. Here, we report on the design and synthesis of a nonplanar porous nanographene with 78 sp² carbon atoms, namely C78. Through a highly selective oxidative cyclodehydrogenation of 2,3,6,7,10,11-hexa(naphthalen-1-yl)triphenylene (2), propeller nanographene precursor 1 was synthesized in solution. Interestingly, although 1 could not be cyclized further in solution, porous nanographene C78 was successfully achieved from 1 by on-surface assisted cyclodehydrogenation on Au(111). The structure and electronic properties of C78 have been investigated by means of scanning tunneling microscopy, noncontact atomic force microscopy, and scanning tunneling spectroscopy, complemented by computational investigations. Our results provide perspectives for the on-surface synthesis of porous graphene nanostructures, offering a promising strategy for the engineering of graphene materials with tailor-made properties.

Dependence of the fluorination intercalation of graphene toward high-quality fluorinated graphene formation

High-quality fluorinated graphene with an ultrahigh interlayer distance (9.7 Å) after exfoliating was achieved utilizing fluorination intercalation dependence.

A direct gas–solid reaction between fluorine gas (F₂) and graphene is expected to become an inexpensive, continuous and scalable production method to prepare fluorinated graphene. However, the dependence of the fluorination intercalation of graphene is still poorly understood, which prevents the formation of high-quality fluorinated graphene. Herein, we demonstrate that chemical defects (oxygen group defects) on graphene sheets play a leading role in promoting fluorination intercalation, whereas physical defects (point defects), widely considered to be an advantage due to more diffusion channels for F₂, were not influential. Tracing the origins, compared with the point defects, the unstable hydroxyl and epoxy groups produced active radicals and the relatively stable carbonyl and carboxyl groups activated the surrounding aromatic regions, thereby both facilitating fluorination intercalation, and the former was a preferential and easier route. Based on the above investigations, we successfully prepared fluorinated graphene with an ultrahigh interlayer distance (9.7 Å), the largest value reported for fluorinated graphene, by customizing graphene with more hydroxyl and epoxy groups. It presented excellent self-lubricating ability, with an ultralow interlayer interaction of 0.056 mJ m^–2, thus possessing a far lower friction coefficient compared with graphene, when acting as a lubricant. Moreover, it was also easy to exfoliate by shearing, due to the diminutive interlayer friction and eliminated commensurate stacking. The exfoliated number of layers of less than three exceeded 80% (monolayer rate ≈ 40%), and no surfactant was applied to prevent further stacking.