Ion selectivity of graphene nanopores

Lithography-based fabrication of nanopore arrays in freestanding SiN and graphene membranes

We report a simple and scalable technique for the fabrication of nanopore arrays on freestanding SiN and graphene membranes based on electron-beam lithography and reactive ion etching. By controlling the dose of the single-shot electron-beam exposure, circular nanopores of any size down to 16 nm in diameter can be fabricated in both materials at high accuracy and precision. We demonstrate the sensing capabilities of these nanopores by translocating dsDNA through pores fabricated using this method, and find signal-to-noise characteristics on par with transmission-electron-microscope-drilled nanopores. This versatile lithography-based approach allows for the high-throughput manufacturing of nanopores and can in principle be used on any substrate, in particular membranes made out of transferable two-dimensional materials.

Angstrom-Size Defect Creation and Ionic Transport through Pores in Single-Layer MoS2

Atomic-defect engineering in thin membranes provides opportunities for ionic and molecular filtration and analysis. While molecular-dynamics (MD) calculations have been used to model conductance through atomic vacancies, corresponding experiments are lacking. We create sub-nanometer vacancies in suspended single-layer molybdenum disulfide (MoS₂) via Ga⁺ ion irradiation, producing membranes containing ∼300 to 1200 pores with average and maximum diameters of ∼0.5 and ∼1 nm, respectively. Vacancies exhibit missing Mo and S atoms, as shown by aberration-corrected scanning transmission electron microscopy (AC-STEM). The longitudinal acoustic band and defect-related photoluminescence were observed in Raman and photoluminescence spectroscopy, respectively. As the irradiation dose is increased, the median vacancy area remains roughly constant, while the number of vacancies (pores) increases. Ionic current versus voltage is nonlinear and conductance is comparable to that of ∼1 nm diameter single MoS₂ pores, proving that the smaller pores in the distribution display negligible conductance. Consistently, MD simulations show that pores with diameters <0.6 nm are almost impermeable to ionic flow. Atomic pore structure and geometry, studied by AC-STEM, are critical in the sub-nanometer regime in which the pores are not circular and the diameter is not well-defined. This study lays the foundation for future experiments to probe transport in large distributions of angstrom-size pores.

Maxwell-Hall access resistance in graphene nanopores

The resistance due to the convergence from bulk to a constriction, for example, a nanopore, is a mainstay of transport phenomena. In classical electrical conduction, Maxwell, and later Hall for ionic conduction, predicted this access or convergence resistance to be independent of the bulk dimensions and inversely dependent on the pore radius, a, for a perfectly circular pore. More generally, though, this resistance is contextual, it depends on the presence of functional groups/charges and fluctuations, as well as the (effective) constriction geometry/dimensions. Addressing the context generically requires all-atom simulations, but this demands enormous resources due to the algebraically decaying nature of convergence. We develop a finite-size scaling analysis, reminiscent of the treatment of critical phenomena, that makes the convergence resistance accessible in such simulations. This analysis suggests that there is a "golden aspect ratio" for the simulation cell that yields the infinite system result with a finite system. We employ this approach to resolve the experimental and theoretical discrepancies in the radius-dependence of graphene nanopore resistance.

Anti-fouling graphene-based membranes for effective water desalination

The inability of membranes to handle a wide spectrum of pollutants is an important unsolved problem for water treatment. Here we demonstrate water desalination via a membrane distillation process using a graphene membrane where water permeation is enabled by nanochannels of multilayer, mismatched, partially overlapping graphene grains. Graphene films derived from renewable oil exhibit significantly superior retention of water vapour flux and salt rejection rates, and a superior antifouling capability under a mixture of saline water containing contaminants such as oils and surfactants, compared to commercial distillation membranes. Moreover, real-world applicability of our membrane is demonstrated by processing sea water from Sydney Harbour over 72 h with macroscale membrane size of 4 cm², processing ~0.5 L per day. Numerical simulations show that the channels between the mismatched grains serve as an effective water permeation route. Our research will pave the way for large-scale graphene-based antifouling membranes for diverse water treatment applications.

Intrinsic limitations of nanoporous graphene limit its applications in water treatment. Here the authors produce post-treatment-free, low-cost graphene-based membranes from renewable biomass and demonstrate their high water permeance and antifouling properties using real seawater.

Selective ion-permeation through strained and charged graphene membranes

By means of molecular dynamics simulations and density functional theory calculations, we demonstrate that stretched and charged graphene can act as ion sieve membranes. It is observed that loading 30% strain on graphene can induce pores in the dense electron cloud to allow ions to pass through the aromatic rings. Meanwhile, a charged surface is helpful to peel the hydration layers from the ions and decrease the energy barrier for ion translocation through nanopores. Our results suggest that with a membrane charge density of 6.80 e nm^-2, Li⁺ can be highly purified from the mixed solution including Li⁺, K⁺, Na⁺ and Cl^- ions. Further increasing the charge density to 15.78 e nm^-2 can obtain excellent Na⁺/K⁺ selectivity. The potential of mean force profiles of ion permeation reveal that the potential for each ion is quite different. By fine tuning membrane charge density, pristine monolayer graphene can act as ion sieves with both high permeability and high selectivity.

Fabrication of multiple nanopores in a SiNx membrane via controlled breakdown

This paper reports a controlled breakdown (CBD) method to fabricate multiple nanopores in a silicon nitride (SiN_x) membrane with control over both nanopore count and nanopore diameter. Despite the stochastic process of the breakdown, we found that the nanopores created via CBD, tend to be of the same diameter. We propose a membrane resistance model to explain and control the multiple nanopores forming in the membrane. We prove that the membrane resistance can reflect the number of nanopores in the membrane and that the diameter of the nanopores is controlled by the exposure time and strength of the electric field. This controllable multiple nanopore formation via CBD avoids the utilization of complicated instruments and time-intensive manufacturing. We anticipate CBD has the potential to become a nanopore fabrication technique which, integrated into an optical setup, could be used as a high-throughput and multichannel characterization technique.

Simulation of osmotic energy conversion in nanoporous materials: a concise single-pore model

A concise single-pore model with a finite reservoir is sufficiently accurate to simulate osmotic energy conversion in nanoporous materials.

Ion transport through a nanoporous C2N membrane: the effect of electric field and layer number

Using all-atom molecular dynamic simulations, we show that a monolayer C₂N membrane possesses higher permeability and excellent ion selectivity, and that multilayer C₂N membranes have promising potential for water desalination.

Punctured Two-Dimensional Sheets for Harvesting Blue Energy

The challenges of global climate change and the world's growing demand for energy have brought the need for new renewable energy sources to the top of the international community's agenda. We have known for many centuries that energy is released upon mixing seawater and freshwater, yet it was just a few decades ago that it became clear how this energy can be converted into electricity instead of heat. As a result, the blue energy rush has raised and set new strategies in different science and technology sectors, leading to the construction of a new generation of plants and other technological investments. Among many approaches, pressure-retarded osmosis has emerged as a promising method to collect the largest amount of produced blue energy. In this Perspective, we highlight the advances in the development of ultrathin membranes based on two-dimensional materials. We discuss the most relevant synthetic methods devised to generate atomically thin membranes for pressure-retarded osmosis and retarded electrodialysis applications, and we provide some critical views on the greatest challenges in this thrilling research area.

Enantioselective Molecular Transport in Multilayer Graphene Nanopores

Multilayer superstructures based on stacked layered nanomaterials offer the possibility to design three-dimensional (3D) nanopores with highly specific properties analogous to protein channels. In a layer-by-layer design and stacking, analogous to molecular printing, superstructures with lock-and-key molecular nesting and transport characteristics could be prepared. To examine this possibility, we use molecular dynamics simulations to study electric field-driven transport of ions through stacked porous graphene flakes. First, highly selective, tunable, and correlated passage rates of monovalent atomic ions through these superstructures are observed in dependence on the ion type, nanopore type, and relative position and dynamics of neighboring porous flakes. Next, enantioselective molecular transport of ionized l- and d-leucine is observed in graphene stacks with helical nanopores. The outlined approach provides a general scheme for synthesis of functional 3D superstructures.

Physical Model for Rapid and Accurate Determination of Nanopore Size via Conductance Measurement

Nanopores have been explored for various biochemical and nanoparticle analyses, primarily via characterizing the ionic current through the pores. At present, however, size determination for solid-state nanopores is experimentally tedious and theoretically unaccountable. Here, we establish a physical model by introducing an effective transport length, L_eff, that measures, for a symmetric nanopore, twice the distance from the center of the nanopore where the electric field is the highest to the point along the nanopore axis where the electric field falls to e^-1 of this maximum. By [Formula: see text], a simple expression S₀ = f (G, σ, h, β) is derived to algebraically correlate minimum nanopore cross-section area S₀ to nanopore conductance G, electrolyte conductivity σ, and membrane thickness h with β to denote pore shape that is determined by the pore fabrication technique. The model agrees excellently with experimental results for nanopores in graphene, single-layer MoS₂, and ultrathin SiN_x films. The generality of the model is verified by applying it to micrometer-size pores.

Nanopore extended field-effect transistor for selective single-molecule biosensing

There has been a significant drive to deliver nanotechnological solutions to biosensing, yet there remains an unmet need in the development of biosensors that are affordable, integrated, fast, capable of multiplexed detection, and offer high selectivity for trace analyte detection in biological fluids. Herein, some of these challenges are addressed by designing a new class of nanoscale sensors dubbed nanopore extended field-effect transistor (nexFET) that combine the advantages of nanopore single-molecule sensing, field-effect transistors, and recognition chemistry. We report on a polypyrrole functionalized nexFET, with controllable gate voltage that can be used to switch on/off, and slow down single-molecule DNA transport through a nanopore. This strategy enables higher molecular throughput, enhanced signal-to-noise, and even heightened selectivity via functionalization with an embedded receptor. This is shown for selective sensing of an anti-insulin antibody in the presence of its IgG isotype.

Efficient detection of single molecules is vital to many biosensing technologies, which require analytical platforms with high selectivity and sensitivity. Ren et al. combine a nanopore sensor and a field-effect transistor, whereby gate voltage mediates DNA and protein transport through the nanopore.

Nanoporous Atomically Thin Graphene Membranes for Desalting and Dialysis Applications

Dialysis is a ubiquitous separation process in biochemical processing and biological research. State-of-the-art dialysis membranes comprise a relatively thick polymer layer with tortuous pores, and suffer from low rates of diffusion leading to extremely long process times (often several days) and poor selectivity, especially in the 0-1000 Da molecular weight cut-off range. Here, the fabrication of large-area (cm² ) nanoporous atomically thin membranes (NATMs) is reported, by transferring graphene synthesized using scalable chemical vapor deposition (CVD) to polycarbonate track-etched supports. After sealing defects introduced during transfer/handling by interfacial polymerization, a facile oxygen-plasma etch is used to create size-selective pores (≤1 nm) in the CVD graphene. Size-selective separation and desalting of small model molecules (≈200-1355 Da) and proteins (≈14 000 Da) are demonstrated, with ≈1-2 orders of magnitude increase in permeance compared to state-of-the-art commercial membranes. Rapid diffusion and size-selectivity in NATMs offers transformative opportunities in purification of drugs, removal of residual reactants, biochemical analytics, medical diagnostics, therapeutics, and nano-bio separations.

Polycationic Polymer-Regulated Assembling of 2D MOF Nanosheets for High-Performance Nanofiltration

Herein, a two-dimensional metal-organic framework (2D MOF) made of iron porphyrin complex (TCP(Fe)) interconnected with divalent metal ion (M = Zn, Co, and Cu) is used to construct a selective layer, which is explored as an ultrafast and energy-saving nanofiltration (NF) membrane for removing organic dyes from water. Among the layered 2D M-TCP(Fe) membranes, Zn-TCP(Fe) membranes display the highest water permeance, which is 3 times higher than graphene-based membranes with similar rejection. To further improve the separation performances, we utilize polycations to anchor the periphery carboxylic groups of nanosheets, regulating the assembly of 2D Zn-TCP(Fe) nanosheets to produce a new class of crack-free selective layer possessing ultrathin and highly ordered nanochannels for efficient NF. Benefiting from these structural features, our polycation-regulated 2D Zn-TCP(Fe) membranes could offer ultrahigh permeance of 4243 L m^-2 h^-1 bar^-1 (2-fold higher than its pristine) and excellent rejection rates (over 90%) for organic dye with size larger than 0.8 × 1.1 nm. This permeance value is about 2 orders of magnitude higher than the commercial polymeric NF membrane. Additionally, the membranes demonstrate 20-40% salt rejection.

Ionic selectivity and filtration from fragmented dehydration in multilayer graphene nanopores

Selective ion transport is a hallmark of biological ion channel behavior but is a major challenge to engineer into artificial membranes. Here, we demonstrate, with all-atom molecular dynamics simulations, that bare graphene nanopores yield measurable ion selectivity that varies over one to two orders of magnitude simply by changing the pore radius and number of graphene layers. Monolayer graphene does not display dehydration-induced selectivity until the pore radius is small enough to exclude the first hydration layer from inside the pore. Bi- and tri-layer graphene, though, display such selectivity already for a pore size that barely encroaches on the first hydration layer, which is due to the more significant water loss from the second hydration layer. Measurement of selectivity and activation barriers from both first and second hydration layer barriers will help elucidate the behavior of biological ion channels. Moreover, the energy barriers responsible for selectivity - while small on the scale of hydration energies - are already relatively large, i.e., many k_BT. For separation of ions from water, therefore, one can exchange longer, larger radius pores for shorter, smaller radius pores, giving a practical method for maintaining exclusion efficiency while enhancing other properties (e.g., water throughput).

Dehydration as a Universal Mechanism for Ion Selectivity in Graphene and Other Atomically Thin Pores

Ion channels play a key role in regulating cell behavior and in electrical signaling. In these settings, polar and charged functional groups, as well as protein response, compensate for dehydration in an ion-dependent way, giving rise to the ion selective transport critical to the operation of cells. Dehydration, though, yields ion-dependent free-energy barriers and thus is predicted to give rise to selectivity by itself. However, these barriers are typically so large that they will suppress the ion currents to undetectable levels. Here, we establish that graphene displays a measurable dehydration-only mechanism for selectivity of K⁺ over Cl^-. This fundamental mechanism, one that depends only on the geometry and hydration, is the starting point for selectivity for all channels and pores. Moreover, while we study selectivity of K⁺ over Cl^- we find that dehydration-based selectivity functions for all ions, that is, cation over cation selectivity (e.g., K⁺ over Na⁺). Its likely detection in graphene pores resolves conflicting experimental results, as well as presents a new paradigm for characterizing the operation of ion channels and engineering molecular/ionic selectivity in filtration and other applications.

Tunable sieving of ions using graphene oxide membranes

Graphene oxide membranes show exceptional molecular permeation properties, with promise for many applications. However, their use in ion sieving and desalination technologies is limited by a permeation cutoff of ∼9 Å (ref. 4), which is larger than the diameters of hydrated ions of common salts. The cutoff is determined by the interlayer spacing (d) of ∼13.5 Å, typical for graphene oxide laminates that swell in water. Achieving smaller d for the laminates immersed in water has proved to be a challenge. Here, we describe how to control d by physical confinement and achieve accurate and tunable ion sieving. Membranes with d from ∼9.8 Å to 6.4 Å are demonstrated, providing a sieve size smaller than the diameters of hydrated ions. In this regime, ion permeation is found to be thermally activated with energy barriers of ∼10-100 kJ mol^-1 depending on d. Importantly, permeation rates decrease exponentially with decreasing sieve size but water transport is weakly affected (by a factor of <2). The latter is attributed to a low barrier for the entry of water molecules and large slip lengths inside graphene capillaries. Building on these findings, we demonstrate a simple scalable method to obtain graphene-based membranes with limited swelling, which exhibit 97% rejection for NaCl.

Assessment and control of the impermeability of graphene for atomically thin membranes and barriers

Two-dimensional materials such as graphene offer fundamentally transformative opportunities in membrane separations and as impermeable barriers, but the lack of facile methods to assess and control its 'impermeability' critically limits progress. Here we show that a simple etch of the growth catalyst (Cu) through defects in monolayer graphene synthesized by chemical vapor deposition (CVD) can be used to effectively assess graphene quality for membrane/barrier applications. Using feedback from the method to tune synthesis, we realize graphene with nearly no nanometer-scale defects as assessed by diffusion measurements, in contrast to commercially available graphene that is largely optimized for electronic applications. Interestingly, we observe clear evidence of leakage through larger defects associated with wrinkles in graphene, which are selectively sealed to realize centimeter-scale atomically thin barriers exhibiting <2% mass transport compared to the graphene support. Our work provides a facile method to assess and control the 'impermeability' of graphene and shows that future work should be directed towards the control of leakage associated with wrinkles.

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

Graphene and other two-dimensional materials offer a new approach to controlling mass transport at the nanoscale. These materials can sustain nanoscale pores in their rigid lattices and due to their minimum possible material thickness, high mechanical strength and chemical robustness, they could be used to address persistent challenges in membrane separations. Here we discuss theoretical and experimental developments in the emerging field of nanoporous atomically thin membranes, focusing on the fundamental mechanisms of gas- and liquid-phase transport, membrane fabrication techniques and advances towards practical application. We highlight potential functional characteristics of the membranes and discuss applications where they are expected to offer advantages. Finally, we outline the major scientific questions and technological challenges that need to be addressed to bridge the gap from theoretical simulations and proof-of-concept experiments to real-world applications.

Selective Nanoscale Mass Transport across Atomically Thin Single Crystalline Graphene Membranes

Atomically thin single crystals, without grain boundaries and associated defect clusters, represent ideal systems to study and understand intrinsic defects in materials, but probing them collectively over large area remains nontrivial. In this study, the authors probe nanoscale mass transport across large-area (≈0.2 cm² ) single-crystalline graphene membranes. A novel, polymer-free picture frame assisted technique, coupled with a stress-inducing nickel layer is used to transfer single crystalline graphene grown on silicon carbide substrates to flexible polycarbonate track etched supports with well-defined cylindrical ≈200 nm pores. Diffusion-driven flow shows selective transport of ≈0.66 nm hydrated K⁺ and Cl^- ions over ≈1 nm sized small molecules, indicating the presence of selective sub-nanometer to nanometer sized defects. This work presents a framework to test the barrier properties and intrinsic quality of atomically thin materials at the sub-nanometer to nanometer scale over technologically relevant large areas, and suggests the potential use of intrinsic defects in atomically thin materials for molecular separations or desalting.

Large Rectification Effect of Single Graphene Nanopore Supported by PET Membrane

Graphene is an ideal candidate for the development of solid state nanopores due to its thickness at the atomic scale and its high chemical and mechanical stabilities. A facile method was adopted to prepare single graphene nanopore supported by PET membrane (G/PET nanopore) within the three steps assisted by the swift heavy ion irradiation and asymmetric etching technology. The inversion of the ion rectification effect was confirmed in G/PET nanopore while comparing with bare PET nanopore in KCl electrolyte solution. By modifying the wall charge state of PET conical nanopore with hydrochloric acid from negative to positive, the ion rectification effect of G/PET nanopore was found to be greatly enhanced and the large rectification ratio up to 190 was obtained during this work. Moreover, the high ionic flux and high ion separation efficiency was also observed in the G/PET nanopore system. By comparing the "on" and "off" state conductance of G/PET nanopore while immersed in the solution with pH value lower than the isoelectric point of the etched PET (IEP, pH = 3.8), the voltage dependence of the off conductance was established and it was confirmed that the large rectification effect was strongly dependent on the particularly low off conductance at higher applied voltage.

Ultrafast Nanofiltration through Large-Area Single-Layered Graphene Membranes

Perforated single-layered graphene has demonstrated selectivity and flux that is orders of magnitude greater than state-of-the-art polymer membranes. However, only individual graphene sheets with sizes up to tens of micrometers have been successfully fabricated for pressurized permeation studies. Scaling-up and reinforcement of these atomic membranes with minimum cracks and pinholes remains a major hurdle for practical applications. We develop a large-area in situ, phase-inversion casting technique to create 63 cm² high-quality single-layered perforated graphene membranes for ultrafast nanofiltration that can operate at pressures up to 50 bar. This result demonstrates the feasibility of our technique for creating robust large-area, high quality, single-layered graphene and its potential use as a pressurized nanofiltration membrane.

Extrinsic Cation Selectivity of 2D Membranes

From a systematic study of the concentration driven diffusion of positive and negative ions across porous 2D membranes of graphene and hexagonal boron nitride (h-BN), we prove their cation selectivity. Using the current-voltage characteristics of graphene and h-BN monolayers separating reservoirs of different salt concentrations, we calculate the reversal potential as a measure of selectivity. We tune the Debye screening length by exchanging the salt concentrations and demonstrate that negative surface charge gives rise to cation selectivity. Surprisingly, h-BN and graphene membranes show similar characteristics, strongly suggesting a common origin of selectivity in aqueous solvents. For the first time, we demonstrate that the cation flux can be increased by using ozone to create additional pores in graphene while maintaining excellent selectivity. We discuss opportunities to exploit our scalable method to use 2D membranes for applications including osmotic power conversion.

Modulation of Molecular Flux Using a Graphene Nanopore Capacitor

Modulation of ionic current flowing through nanoscale pores is one of the fundamental biological processes. Inspired by nature, nanopores in synthetic solid-state membranes are being developed to enable rapid analysis of biological macromolecules and to serve as elements of nanofludic circuits. Here, we theoretically investigate ion and water transport through a graphene-insulator-graphene membrane containing a single, electrolyte-filled nanopore. By means of all-atom molecular dynamics simulations, we show that the charge state of such a graphene nanopore capacitor can regulate both the selectivity and the magnitude of the nanopore ionic current. At a fixed transmembrane bias, the ionic current can be switched from being carried by an equal mixture of cations and anions to being carried almost exclusively by either cationic or anionic species, depending on the sign of the charge assigned to both plates of the capacitor. Assigning the plates of the capacitor opposite sign charges can either increase the nanopore current or reduce it substantially, depending on the polarity of the bias driving the transmembrane current. Facilitated by the changes of the nanopore surface charge, such ionic current modulations are found to occur despite the physical dimensions of the nanopore being an order of magnitude larger than the screening length of the electrolyte. The ionic current rectification is accompanied by a pronounced electro-osmotic effect that can transport neutral molecules such as proteins and drugs across the solid-state membrane and thereby serve as an interface between electronic and chemical signals.

Energetics and diffusion of liquid water and hydrated ions through nanopores in graphene: ab initio molecular dynamics simulation

The energetics and diffusion of water molecules and hydrated ions (Na⁺, Cl⁻) passing through nanopores in graphene are addressed by dispersion-corrected density functional theory calculations and ab initio molecular dynamics (MD) simulations.

Interaction between a water drop and holey graphene: retarded imbibition and generation of novel water–graphene wetting states

Water nanodrop imbibition in holey graphene is studied unraveling novel fiber-like wetting state that enhances water–accessible graphene surface area.