Artificial channels for confined mass transport at the sub-nanometre scale

Mass transport at the sub-nanometre scale, including selective transport of gases, liquids and ions, plays a key role in systems such as catalysis, energy generation and storage, chemical sensing and molecular separation. Highly efficient biological channels in living organisms have inspired the design of artificial channels with similar, or even higher, mass-transport efficiency, which can be used at a much larger scale. In this Review, we highlight synthetic-nanomaterials-enabled channels in the platforms of well-defined nanopores, 1D nanotubes and 2D nanochannels, and discuss their design principles, channel architectures and membrane or device fabrication. We focus on fundamental mechanisms of sub-nanometre confined mass transport and their relationships with the structure–property–performance. We then present the practicalities of these channels and discuss their potential impact on the development of next-generation sustainable technologies for use in applications related to energy, the environment and healthcare. Artificial channels that selectively transport small molecules at the sub-nanometre scale are used in many applications, but, in particular, in molecular separation. This Review discusses the design of channels, nanostructure, fabrication and mass-transport mechanisms, as well as outlining promising applications and the challenges ahead.

Solid-state channels with a confined space that selectively transport small molecules (for instance, gases, liquids and ions) at the sub-nanometre (sub-nm) scale have attracted growing interest over the past decades. In particular, these channels have shown tremendous potential for applications in the fields of energy storage and conversion, chemical sensing and molecular separation. However, their practical applications have continuously faced challenges with respect to efficiency, stability and scalability. To develop sub-nm channels, an understanding of the confined mass-transport properties is required, which, in turn, may enable the rational design of the channels.
Synthetic channels can be inspired from natural channels that abound in biological systems. With different structures and functions, the biological channels in living organisms play essential roles in many of life's processes. The channels are formed from specific proteins that can transport molecules and ions through membranes 1 , in order to pump nutrients into cells, generate electrical signals, regulate cell volume and secrete electrolytes across epithelial layers 2 . In fact, high transport efficiency has long been observed within these channels. For example, potassium ion channels exhibit a transport rate of 10 8 potassium ions per second (near to the diffusion limit), but reject other types of ions (including sodium ions) 3 . Biological water channels, such as aquaporin 1 (AQP1), have been shown to possess a superb water permeability (~3 × 10 9 water molecules per subunit per second) and an excellent rejection of all ions, including protons 4 . AQP1 is also a physiologically important channel for CO 2 molecules transport, for which the permeability reaches ~1.2 × 10 5 molecules per AQP1 subunit per second 5 . The high mass-transport efficiency stems from the unique channel structure, the uniform sub-nm confinement and the favourable interfacial properties 6,7 . However, these biological channels suffer from poor scale-up and low efficiency and stability when used in large-scale industrial applications that create physical and chemical environments completely different from those existing in living organisms.
Researchers have sought to develop artificial channels with mass-transport properties similar to their bio logical counterparts. To date, there are three main types of channel architectures: nanopores, 1D nanotubes and 2D nanochannels (Fig. 1). These channels have persistent cavities that can discriminate between similarly sized analytes, on a molecular scale. Transient gaps in flexible polymers that are created by segmental packing and motion are not the focus of this discussion. Nanoporous materials are one of the key components of the channels, which can be classified as: inorganics (such as zeolites) 8 , organics (for instance, microporous organic polymers 9,10 , porous organic cages (POCs) 11 and organic tubes 12 ), hybrids (for example, metalorganic frameworks (MOFs) 13,14 and metal-organic cages 15 ) and carbons (such as carbon nanotubes (CNTs) 16 and carbon molecular sieves 17 ). Since the rise of graphene and related materials 18 , 2D materials have been developed for the fabrication of porous mass-transport channels 19,20 . These synthetic channels are made in various sizes and adapted to different Artificial channels for confined mass transport at the sub-nanometre scale mass-transport mechanisms, at the (sub-)nanoscale. They show unprecedented mass-transport rates and precise separation properties, which can even outperform their biological counterparts.
In this Review, we discuss artificial channels of the sub-nm scale (that is, the channels for the selective transport of molecules or ions with sub-nm physical sizes or with size differences at the sub-nm scale) and review the progress that has been made in the design, fabrication and structural tuning of nanopores, 1D nanotubes and 2D nanochannels. We focus on confined mass-transport mechanisms, including details on how the architecture and the chemistry of the channels tune the transport behaviours of gases, liquids and ions. We also overview the development of processing these channels into membranes or devices for various applications, describe challenges and identify fruitful areas of future research.
Sub-nanometre-scale channels Sub-nanopores Channels in the form of nanopores can be fabricated by using 'bottom-up'-synthesized porous materials or by 'top-down'-creation of nanopores in non-porous materials 13,[21][22][23] . Here, we focus on materials with sub-nanopores shown in Table 1, which summarizes their structural tunability, channels size, rigidity and density for membranes or devices. Synthesized nanoporous materials can be classified based on their crystallinity. Crystalline nanoporous materials include zeolites 8 , MOFs 13 and related structures (such as Fig. 1 | Schematics and selected materials for mass transport through nanopores, 1D nanotubes and 2D nanochannels. a | A schematic of nanopores (left) and the structures of NaA zeolite, ZIF-8 metal-organic framework and all-hydrogen passivated graphene nanopore (carbon, black; hydrogen, light grey) (middle and right). b | A schematic of 1D nanotubes (left) and the structures of a single-walled carbon nanotube (SWCNT), a peptide-appended hybrid [4]arene (PAH [4]) and a single-walled aluminosilicate nanotube (SWANT). c | A schematic of 2D nanochannels (left) and the structures of selected 2D materials. hBN, hexagonal boron nitride; LDH, layered double hydroxide; MoS 2 , molybdenum disulfide. Panel a ZIF-8 structure adapted from reF. 179 , Springer Nature Limited; graphene structure adapted with permission from reF. 180 , ACS. Panel b SWCNT structure adapted from reF. 48 , Springer Nature Limited; PAH [4] structures adapted from reF. 12 , Springer Nature Limited; SWANT structure adapted with permission from reF. 181 , ACS. Panel c structures of graphene, MoS 2 and hBN adapted from reF. 182 , Springer Nature Limited; LDH structure adapted with permission from reF. 183 , Royal Society of Chemistry.
metal-organic cages 15 and metal-coordinating microporous polymers 24 ), covalent organic frameworks (COFs) 25 and POCs 26 , while non-crystalline nanoporous materials are comprised of carbon molecular sieves (CMSs) 27 , hyper-crosslinked polymers 28 , polymers of intrinsic microporosity (PIMs) 29 , conjugated microporous polymers 30 and porous aromatic frameworks 31 . Compared with non-crystalline materials, crystalline materials, especially MOFs and COFs, have more ordered arrangements of pores, more uniform pore sizes, higher pore density and, generally, their pore structures are more tunable. As a result, the architecture and chemistry of pores influence the selectivity towards the desired molecules. It remains challenging to synthesize non-crystalline materials with well-defined sub-nm pores and narrow pore distributions 32 . However, hydrophilic PIMs with tight chain packing have been shown to form sub-nm pores (<7 Å) with narrow pore-size distribution 33 , which is beneficial for sieving ions. In addition, non-crystalline CMSs with rigid, slit-like sub-nm (<7 Å) pores show high efficiency for molecular transport, even in a high-pressure regime 27,32 . Porous 2D materials with atomically precise structures are promising nanoscale structures with selective mass-transport channels 22 . The atomic thickness of 2D materials enables the minimum resistance for mass transport and maximum permeation flux. The intrinsic or created nanopores in the 2D lattices lead to precise sieving properties. The nanopores can be obtained by 'bottom-up' synthesis of porous nanosheets or by 'top-down' approaches using physiochemical perforation of inherently non-porous nanosheets 34 . 'Top-down'-fabricated 2D pores including graphene, MoS 2 and hexagonal boron nitride (hBN) with pore sizes ranging from 3 to 76 Å made by either ion irradiation, chemical or plasma etching or post-functionalization show high efficiency for gas, water and ion transport 22,[34][35][36] . 'Bottom-up'-synthesized 2D pores such as 2D carbon nitride 37 , MOFs 38,39 , COFs 40,41 and zeolites 42 have been reported for selective mass transport. Exploration of other 'bottom-up'-synthesized materials by using molecular precursors include nanoporous graphene 43 , graphyne 44 , stanene 45 and 2D polymers 46 is emerging.

1D nanotubes
Carbon nanotubes. CNTs are the most studied 1D nanomaterial for selective mass transport (Fig. 1b). Typically, the inner pore size of single-walled carbon nanotubes (SWCNTs) is ~8-20 Å. The openings and the exterior of CNTs can be chemically modified; however, there are currently no strategies to functionalize their interior space 47 . Instead, the inner surfaces of CNTs are molecularly smooth and enable ultra-fast molecular transport. Theoretical and experimental studies show that SWCNTs with diameters of 8.1 Å exhibit ultra-fast water transport in the channel 48,49 .
Organic and inorganic nanotubes. The insides of the channel walls of organic and inorganic tubes are not atomically smooth because they can be composed of a single molecule or an assembly of many molecules. However, these structures are more tailorable than CNTs in terms of pore chemistry, pore size (ranging from sub-nm to nanometre), alignment, processing and performance. The length of the organic tubes is tunable through different assembly strategies. Sub-nm-sized organic nanotubes for water channels have attracted increasing attention. For example, a 1D peptide-appended hybrid [4]arene (PAH [4]), created by eight phenylalanine tripeptides chains on hybrid [4]arene macrocycle molecules 12 (Fig. 1b), has sub-nm-sized channels for fast water permeation (~10 9 water molecules per second), but efficiently rejects ions. Organic nanotubes can be constructed from molecular subunits via non-covalent interactions, such as hydrogen bonding, electrostatic, hydrophobic, π-π and ion-π interactions. Examples include nanotubes of octylureido-ethylimidazole 50 , m-phenylene ethynylene 51 and helical macromolecules 52 . However, it is challenging to realize scalable processing to create robust membranes. Block copolymer films fabricated by self-assembly have vertically aligned 1D channels with pore size ranging from several nanometres to tens of nanometres for selective separation 53,54 . However, it is difficult to make sub-nm-pore-sized block copolymer channels (down to ~1.2 nm so far) 55 .
The inorganic tubes discussed here are mainly in the form of metal oxide, which are synthetic analogues of the nanotube mineral imogolite, including aluminosilicate-based or aluminogermanate-based nanotubes 56,57 . These nanotubes are synthesized by hydrothermal methods at low temperatures (~100 °C) and at mildly acidic pH. For example, a single-walled aluminosilicate nanotube structure built with hexagonal aluminium hydroxide as the outer wall and pendant silanol groups aligned linearly as the inner wall has channels with inner diameters of ~6.5 Å and high rigidity 58 (Fig. 1b). However, these inorganic tubes are rarely used in applications.

2D nanochannels
Graphene and graphene oxide. 2D graphene channels are formed by layer-by-layer stacking of graphene sheets. Graphene channels with hydrophobic, smooth and frictionless surfaces enable the fast flow of fluids, and may be used for water desalination 59,60 and gas separation 61 . Graphene oxide (GO) channels and membranes are other prototypes, which, until now, are more practical for application at large scales of molecular separation. The excellent solution dispersibility of GO enables its assembly into laminar macroscopic structures. Typically, the interlayer spacing in the GO laminate in a dry state is 9 ± 1 Å (reF. 62 ). Considering that the thickness of graphene is 3.4 Å, the interlayer empty space (a, that is, the space available for mass transport) between GO nanosheets is 5.6 ± 1 Å, allowing one or two layers of moving water within the channels. The sub-nanosized GO channels have been widely demonstrated for molecular separation 63 . However, this distance is still not small enough for the separation of gas molecules, which requires aperture sizes down to ~4-5 Å (reF. 32 ). Additionally, GO channels are flexible; for instance, the channels swell to 13 ± 1 Å when immersed in water 62 , sharply decreasing the selectivity for molecular or ionic separation. Different methods have been used to stabilize the interlayer channels, including chemically or thermally reducing GO 64 , or by intercalation with other molecules or nanomaterials 65 , or by graphene 66,67 .
MXenes. Transition-metal carbides or nitrides, termed as MXenes, are relatively new 2D materials 68 . Similar to GO, MXene nanosheets are hydrophilic and terminated with functional moieties, and show good solution processability. Ti 3 C 2 T x (where T x refers to functional moieties including −H, −O and −F) is the most studied MXene, with interlayer spacing in the dry state of ~13.5-15 Å (reFs 69,70 ). Considering that the single-layer thickness of Ti 3 C 2 T x is ~10 Å, the a value is ~3.5-5 Å, which is a suitable channel size for gas-molecules separation 69,70 . In water, a is ~6 Å for Ti 3 C 2 T x and the channels reject hydrated cations of a larger size 71 . The instability of the structure resulting from oxidation is a major limitation for applications.
Other 2D materials. Other 2D materials assembled to form 2D channels include transition-metal dichalcogenides (TMDs) (for example, MoS 2 , WS 2 and WSe 2 ), hBN and layered double hydroxides (LDHs). Similar to graphene, TMDs and hBN crystals are impermeable to molecules, but allow permeation between adjacent layers. Liquid-based exfoliation enables the assembly of laminar membranes using TMDs and hBN nanosheets 72,73 . These membranes, to some extent, outperform the GO membranes in terms of water stability because of the prevalence of van der Waals interactions between layers. Also, their smooth surface leads to low hydraulic resistance and, thus, high water flux 74 . Particularly, MoS 2 with three atomic layers exhibits higher rigidity in the out-of-plane direction than GO 75 . However, using TMDs and hBN membranes for molecular separation requires the fabrication of high-quality and defect-free membranes. However, it is intriguing that van-der-Waals-assembled 2D channels (such as MoS 2 and hBN) with sub-nm size exhibit unexpected transport phenomena of hydrogen isotopes 76 , gases 61 and ions 77,78 , which challenges the classic mass-transport theory and may boost applications. LDHs are composed of positively charged brucite-like 2D sheets, charge-compensated anions and solvation molecules located in interlayer spacings 79 . Further research is required to control grainboundary defects, the orientation of layers and the interlayer spacings of LDHs.
Large-area membranes or devices are required for the application of nanomaterials-enabled channels, particularly for molecular separation. Some fabrication techniques that are reliable and scalable are introduced in Fig. 2.
Channel structure and transport Channels at different length scales are dominated by a variety of mechanisms (Fig. 3a). An introduction of the mass transport from the nanometre to the micrometre scale is provided in Supplementary Box 1. As the channel sizes decrease to the sub-nm range, which is in the size range of gases, liquids and ions, the mass-transport behaviours vary based on distinct mechanisms (Fig. 3b). One of the most widely accepted mechanisms is solution-diffusion theory (Supplementary Box 1 and Fig. 1), which explains transport phenomena such as gas separation, reverse osmosis (RO), forward osmosis (driven by osmotic pressure difference), pervaporation (separating mixtures of liquids by partial vaporization through a selective membrane) and organic-solvent reverse osmosis (OSRO, separating organic molecules with subtle molecular-size differences in liquid organic mixtures). Aqueous nanofiltration and organic-solvent nanofiltration are combinations of solution-diffusion and pore-flow mechanisms 32,80 . Readers are referred to review articles 14,32,80,81 for discussions of these separation processes.
Current synthetic membranes, especially polymeric membranes, suffer from a trade-off between permeability and selectivity in almost all separation settings. Intrinsically, materials that have larger free volume (or pore size) are more permeable; however, they also have a wider distribution of free volume (or pore size), leading to a more open structure, and, thus, lower selectivity. This trade-off was studied by upper-bound models 82,83 . Channels with both high permeability and high selectivity to exceed the upper bound have emerged. The design of these channels is based on different mass-transport mechanisms, including molecular sieving, surface effect, electrical effect, channel-guest interaction and quantum effect (Fig. 3).

Sieving effect
Molecular sieving occurs when the channel sizes are exactly (or smaller than) the sizes of single molecules. For channels to separate molecules based on size, it is important to have channels of uniform size and high rigidity. Typically, high selectivity dominates when pore diameters are on the molecular scale (3-7 Å). Such an effect can be explained by coupling the solution-diffusion model and transition-state theory 32 (Supplementary Box 1), taking advantage of enthalpic and entropic factors.
Zeolites can act as molecular sieves with a clear 'cut-off ' , owing to their relatively fixed pore sizes. For example, membranes of NaA zeolite show high separation factors in alcohol-dehydration separations 84 . In another study, single-layer MFI nanosheets are able to sieve para-xylene over ortho-xylene (kinetic diameters of 5.8 and 6.8 Å, respectively), with separation factors as high as 8,000-10,000 (reF. 42 ). However, the structures of zeolites can change at high temperatures or by the adsorption of guest molecules, leading to the loss of molecular-sieving capabilities. Fortunately, NaA zeolite membranes synthesized by a modified seeding strategy show negligible defects even at 300 °C with water vapour 85 . CMSs show excellent separation by molecular sieving because of high channel rigidity (Fig. 4a). The rigid pores originate from their manufacture by carbonization of polymeric precursors, leading to reduced swelling and plasticization compared with polymer membranes. As a result, the entropic factor (equation 1 in Supplementary Box 1) contributes to the molecular separation, endowing the CMSs with capabilities for the sieving of similar-sized gas molecules and OSRO process 27,32 .
2D materials with sub-nm pores can also act as molecular sieves. Nanopores with size ~3.4 Å created in few-layer graphene films by UV light or ozone etching show preferential permeation of H 2 over N 2 with selectivity larger than 10,000 (reF. 86 ), albeit the tiny testing film area of 1.96 × 10 −5 mm 2 . A graphene film of larger area (~1 mm 2 ) may have non-selective defects 87 , and, thus, shows a sharp reduction in selectivity (H 2 over CH 4 with selectivity of ~25). However, the graphene film still shows a molecular-sieving effect with selectivity larger than the Knudsen selectivity of ~2.8. Single-layer graphene etched by oxygen plasma 88 has pores of ~5-10 Å (effective pore size of ~3-7 Å after considering the van der Waals diameter of a carbon atom) (Fig. 4b). The porous graphene membranes act as molecular sieves with nearly www.nature.com/natrevmats 100% rejection of ions but allowing water transport. However, single-layer or few-layer graphene membranes are yet to maintain molecular selectivity at high pressure. A recent work realizes the enhancement of the mechanical robustness of graphene membrane through depositing CNT networks on the surface 89 . Such a hybrid membrane shows salt rejection of about 90% at a pressure of 0.5 MPa under RO testing.
MOFs are another class of molecular sieves that have been widely used for applications from gas purification to liquid separation 14 . The well-defined pore structure of MOFs can be directly observed by high-resolution transmission electron microscopy at an atomic resolution [90][91][92] . For instance, the motion-corrected image taken along the [111] axis of a ZIF-8 crystal (Fig. 4c) shows the six-ring channels of ZIF-8 pores with the individual Zn atomic columns in triplet that are ~3.4 Å apart 91 . Such an array of sub-nm pores within membranes is favourable for selective mass transport. However, MOFs do not always maintain the pore sizes as observed. Pore flexibility is often found in MOFs, causing the 'gate-opening effect' , followed by loss of sieving capability. Taking ZIF-8 as an example, although with a crystallographic aperture size of ~3.4 Å (Figs 1a,4c), ZIF-8 pores have natural fluctuations in crystal structure (for instance, motion of ligands), which will reversibly expand to some extent. Actually, ZIF-8 is able to uptake guest molecules as large as ~7.6 Å (1,2,4-trimethylbenzene) 93 . Gas permeation through ZIF-8 membranes show that the effective pore size is 4.0-4.2 Å, sharply rejecting propane (4.2 Å) from  a | Solvothermal growth involves immersing the substrate in a solution containing linkers or precursors, followed by heating. Large-area zeolite membranes are possible 184 . b | Layer-by-layer assembly exposes the substrate to different solutions of linkers or materials in a circular manner. Layer-by-layer assembly in spray mode can achieve improved deposition compared with immersive mode because of the better materials distribution and alignment on the substrate 185,186 . c | Solution casting, followed by drying, can fabricate membranes made from polymers of intrinsic microporosity, porous organic cages, metal-coordinating microporous polymers and graphene oxide 24,33,187 . The thickness of the films (down to sub-micrometre) is controlled by a doctor blade. Mixed-matrix membranes (embedding the nanochannels into a polymeric matrix) can be fabricated on a large scale. d | In liquid-liquid interfacial growth, a porous substrate at an interface functions as the microchannels for the diffusion and reaction of linkers, and the support for the membrane layer. Covalent organic frameworks, metal-organic frameworks and polymers of intrinsic microporosity membranes can be made using this method. e | In gas-liquid interfacial assembly, a thin film is synthesized and compressed by barriers to ensure high-density packing. The film is then transferred to a substrate. f | Pressure filtration makes membranes of 2D nanochannels and 1D nanotubes. g | Graphene films with lengths <100 m can be fabricated using chemical vapour deposition (CVD) 123 . A technique combining CVD, roll-to-roll transfer and pore-drilling treatments (such as oxygen plasma) 88 is promising for the mass production of graphene membranes. Metal-organic framework membranes can also be fabricated by CVD 188 . h | Self-assembly of biological 1D channels into nanosheets with hexagonal 2D packing requires organic solvents and amphiphilic block copolymers 189 .
The section on self-assembly in the lower-right corner of panel h adapted from reF. 189 , Springer Nature Limited.
Efforts have been made to improve the rigidity of MOF nanopores by incorporating rigid linkers. A rare-earth MOF with a face-centred cubic (fcu) topology (Y-fum-fcu-MOF) featuring rigid pores with size of ~4.7 Å (Fig. 4d) has sieving behaviour with a sharp 'cut-off ' between n-C 4 H 10 and i-C 4 H 10 (reF. 96 ). In addition, Y-fum-fcu-MOF has a higher diffusivity for n-C 4 H 10 than for ZIF-8 (by 3 orders of magnitude), which is commercially attractive 96 98 , which both show excellent sieving for alkenes over alkanes. However, the materials require further study to demonstrate membrane-based diffusion. In addition to pore flexibility, the absence of linkers or clusters 92,99 , as well as coherent interface defects 91 , weaken molecular sieving in MOF pores. Thin films of ZIF-8 made by atomic layer deposition followed by ligand-vapour treatment may circumvent these problems 100 . The fabricated ZIF-8 membranes are shown to be defect-free, reproducible, capable of molecular sieving and may also be scalable.
The pore flexibility in MOFs can be tuned and, hence, the mass transport reversibly switched. For example, an external electric field (500 V mm −1 perpendicular to the MOF layer) causes the lattice polarization of ZIF-8 (Fig. 4e), followed by switching the ZIF-8 crystal structure from cubic to monoclinic and triclinic polymorphs 101 . The monoclinic polymorph shows a pore diameter of 3.6 Å, which is larger than that of the cubic polymorph (3.4 Å) of ZIF-8. However, the linker (2-methylimidazole) mobility in the monoclinic polymorph is more restricted than in the cubic polymorph, leading to stiffening of the ZIF-8 lattice and enhancing the molecular sieving of propene from propane (the selectivity of propene over propane increases from 6 to 8). MOF pores can also be switched by assembling linkers containing photoresponsive groups (Fig. 4f) under light irradiation, showing reversible changes of gas separation 102 . Tuning the pore flexibility of MOFs may have implications beyond separation, such as tunable catalysis, drug delivery and photoactuated or electrically actuated artificial tissues.
Other nanopores are also controlled by the molecularsieving effect, for example, microporous polymers 103 . However, the pores of microporous polymers are considered to be semi-rigid, because nm-scale or sub-nm-scale motion occurring at the backbones of polymer networks may cause the loss of enthalpic and entropic contributions to molecular sieving. Sieving effects in COF pores 104 , POC pores 105 and 1D organic or inorganic tubes 12,106 are observed but more study is needed, including the synthesis of materials and films, as well as mass-transport experiments.
2D nanochannels act as molecular sieves because of their assembled interlayer spacings. To study the mass-transport behaviours, nanofabrication was used to create van der Waals assemblies of 2D crystals with slit-like channels (with sizes down to several Ångstroms) (Fig. 5a). More specifically, two relatively thick (~100-nm) crystals (including graphite, hBN and MoS 2 ) are placed on top of each other, separated by stripes of another 2D crystal serving as spacers 60,78 . The trilayer assembly is kept together by van der Waals interactions, and the interlayer empty space (a) of the channels is the thickness of the 2D spacer layer. All the 2D crystals in the channel are obtained by mechanical exfoliation to provide flat 2D surfaces, which is vital for several reasons: first, the surface roughness at the atomic scale endows the 2D channels with precisely controlled dimensions and channel height. Second, flat surfaces result in   chemically inert channels with low (≤10 −4 C cm −2 ) surface charge 78 . Finally, the channel height can be tuned by the spacer layer at atomic precision. For example, the use of bilayer graphene or monolayer of MoS 2 as the spacer layers makes channels with a of ~6.6 Å (reF. 78 ). Water-transport and ion-transport experiments indicate that these 2D channels allow water permeation but reject ions with diameters larger than ~10 Å. Small,    www.nature.com/natrevmats hydrated ions with diameter ~7 Å, such as hydrated K + , Na + and Li + , can permeate through the slit-like channels, although they are larger than a. The permeation of the hydrated monovalent ions indicates that ions under nanoconfinement are not mechanically hard, namely, the hydration shells may be partially distorted, flattened or shredded before entering the channels 78,107 .
To enhance their sieving capability, 2D graphene channels with a ~3.4 Å are fabricated using a monolayer of graphene as a spacer layer with water molecules inside the slits, which prevent channel collapse 59 . These slits show excellent sieving behaviour by almost completely rejecting ions while allowing water and proton permeation. Water molecules are predicted to be aligned as a 2D monolayer within the slits, enabling the transport of protons by jumping between water molecules (Grotthuss mechanism) 59 . To be used in applications, these materials need to function at high pressure and at high concentrations of ions. These applications also require rigid channels because flexibility results in the loss of selectivity, as a consequence of the high chemical potential gradient that can force all molecules or ions to pass through the channels 32 .
Compared with van der Waals channels of uniform channel sizes, self-assembled 2D channels (such as the channels in GO membranes fabricated by filtration methods) have a wider distribution of sizes. However, these self-assembled channels still exhibit molecularsieving effects. For example, the GO membranes are reported to block solutes with sizes larger than 9 Å when immersed in water 62 . The swelling of GO channels in water impedes the use of GO to sieve small ions (hydrated diameter <9 Å), and various strategies have been used to overcome this issue. One strategy is physical confinement; more specifically, using epoxy to encapsulate the GO membrane to restrict the swelling of laminates exposed in water (Fig. 5b). 2D GO channels with a ranging from 6.4 to 9.8 Å can be tuned by humidity before epoxy encapsulation. Such GO channels show rejection of ions when immersed in water 108 . Intriguingly, cations can determine the interlayer spacing of GO membranes, leading to the cationic control of 2D GO channels 107 (Fig. 5c). Because of the cation-π and hydrogen-bonding interactions between GO layers and hydrated cations, membrane spacings controlled by one type of cation can selectively exclude other cations that have larger hydrated volumes. For instance, a GO membrane controlled by KCl can stably maintain the channel spacing at ~10 Å, and, thus, reject other ions, while still showing water flux of ~0.36 l m −2 h −1 under forward-osmosis processes (Fig. 5c).
Another method is to chemically crosslink the GO nanosheets 65,109 . The crosslinkers, diamine monomers 65 , react with oxygen functionalities on the GO via condensation and nucleophilic substitution reactions (Fig. 5d). This crosslinking hinders the water-induced swelling of GO channels, and the interlayer spacing is tuned to distinct values by changing the diamine monomers. Such GO membranes show sieving effects, with the pervaporative separation factor of water over ethanol as high as ~4,700 (which is ~70 times higher than that of pure GO membrane). Similar to the flexible MOF pores, the height of GO channels can be tuned by stimuli from the environment, showing a smart gating effect. Poly(N-isopropylacrylamide) (polyNIPAM), a temperature-responsive polymer, has been covalently bonded to GO by free-radical polymerization 110 (Fig. 5e). The intercalation of polymeric chains into GO channels switches the a value from ~18.6 to ~14.7 Å when the temperature changes from 25 to 50 °C (or by illuminating infrared light). Water flux can be tuned between 12.4 and 1.8 l m −2 h −1 bar −1 .

Surface effects
The inner surfaces of 1D and 2D channels are atomically smooth walls, allowing fast molecular transport. For example, ultra-fast water transport is found in CNT channels, showing slip flow behaviour with flow rates that exceed the predictions of the Hagen-Poiseuille equation 111 . Early experimental studies on water transport through membranes of vertically aligned multiwalled CNTs (~7 nm in diameter) have shown water slip lengths of 39-68 μm, indicating that the water flux is 4-5 orders of magnitude higher than the value predicted by the Hagen-Poiseuille equation with a no-slip boundary condition 112 . Recently, an enhancement of radius-dependent water flow has been demonstrated using single-CNT-channel measurements 113 . The slip length of water increases monotonically with a decrease in the CNT diameter from 100 to 30 nm. Interestingly, a further decrease in diameter, to a size approaching the van der Waals diameter of water molecules, can lead to a non-monotonic variation of slip length with CNT diameter 114 . CNTs with diameter of ~8 Å exhibit a one order of magnitude higher water flux than 15-Å CNTs, exceeding the water flux of AQP1 by a factor of 6 (reF. 49 ). This extraordinary water transport can be attributed to the confined space and smooth graphitic walls. Water molecules are forced into a 1D wire configuration in 8-Å CNTs (Fig. 6a), while they maintain a bulk-like arrangement in 15-Å CNTs.
This enhancement of water transport results from the fewer hydrogen bonds per water molecule in the narrower CNT pores 49 . In AQP1 channels, the amino acids slow down the water transport by kinetics of hydrogen-bond formation and breakage with water molecules. This mechanism is further demonstrated by showing fivefold enhancement of water permeability through 8-Å CNTs at acidic pH, where protonated carboxyl moieties at the nanotube rim hinder the hydrogen bonding with water. This 1D arrangement of water molecules occurs only on the sub-nm scale, and can facilitate proton transport via the Grotthuss mechanism 115 .
2D van der Waals channels open another avenue to study the surface effects under confinement. Unlike 1D CNTs, 2D graphene channels show similar water slip lengths regardless of the interlayer channel spacing, with simulated values of ~60 nm (reF. 60 ) and experimental values of ~16 nm (reF. 116 ). Fast water flow (up to 1 ms −1 ) is observed in graphene channels, as a consequence of the low friction of water against the graphene wall 60 . Unexpectedly, the water flux increased significantly when the channel size approached ~10 Å. This increase may be because of the rapidly rising driving force (capillary pressure above 1,000 bar), which is dominated by water-water interaction and watercarbon interaction under nanoconfinement. Interestingly, the viscosity of water is found to increase by a factor of 2 when the channel size decreases to the sub-nm scale. This increase can be ascribed to the formation of a more aligned water layer between the sub-nm confined 2D graphene 60,117 compared with bulk water. This 2D layered water is different from bulk water and has some intriguing phenomena. For instance, 2D square ice, an unusual phase of water, is observed in graphene nanocapillaries 117  --  www.nature.com/natrevmats pressure caused by van der Waals interactions between graphene sheets. The same phenomenon seems to appear in the water confined between MoS 2 sheet and mica 118 . In addition, the dielectric constant (ε) of water confined in nanoscale channels (composed of a bottom layer of graphene and a top layer of hBN) can be as low as ~2, far below that of bulk water (~80) 119 . The behaviour of interfacial water could be important for investigating the water transport and ion transport in sub-nm-scale channels. Ion transport through 2D van der Waals channels is also controlled by surface effects. Driven by pressure, K + mobility through graphene channels (a of ~6.8 Å) reached up to 3 × 10 −7 m 2 V −1 s −1 , which is even higher than the bulk potassium electrophoretic mobility (7.6 × 10 −8 m 2 V −1 s −1 ) 77 . This high mobility for ions may arise from the anomalously fast transport of water 59,60,116 (Fig. 6a). But for anions, for instance, Cl − is three times less mobile than K + in graphene channels (a of ~6.8 Å) 78 , even though the ions have the same hydrated diameter and similar mobilities in bulk solutions. This observation may be a consequence of the polarization of water on the surface of graphene channels, leading to the preferential orientation of −OH groups towards the channel walls. The hydration shell of Cl − has −OH groups pointing preferentially outside, while the exterior of K + is more covered by hydrogen atoms. Thus, the hydrated Cl − has a stronger interaction with the graphene surface than hydrated K + , leading to lower mobility of Cl − (reF. 78 ). Besides, van-der-Waals-assembled graphene and hBN channels (both with a of ~6.8 Å) exhibited distinct K + diffusion behaviours, which can be attributed to the differences in molecular friction of water and ions on these two materials, as well as the distinct electrical structures 77 .
The results of intercalation of solid-state ions into van der Waals channels also show an ultra-fast diffusion rate. For instance, the diffusion coefficients for Li + between the bilayer graphene can reach ~1.4 × 10 −7 m 2 V −1 s −1 at room temperature 120 . In situ low-voltage transmission electron microscopy has proved that the intercalated Li + form a super-dense and ordered packing of Li atoms between the bilayer graphene, with evidence of the appearance of crystalline 2D Li layers 121 . Instead of forming LiC 6 , the close packing of Li atoms leads to an increase of Li storage capacity. Interestingly, Li + diffusion varies in the channels, which are composed of different 2D materials, namely, the van der Waals heterointerface effect 122 . Compared with the channels interfaced by graphene/hBN or MoX 2 /MoX 2 (where X = S or Se), the graphene/MoX 2 heterostructure channels (Fig. 6a) exhibited much higher Li + accumulation via the marriage of a low-resistance electronic pathway by graphene and strong Li-binding affinity by MoX 2 .

Electrical effects
Mass transport, particularly ion transport, can also be tuned by electrical effects, including electrostatic interaction and applied electric potential. Electrostatic interaction is generated between the charged surfaces of channels and the flow of ions. In classical mean-field-electrostatics theories, when the channels are narrower than the Debye length (λ D ) of the electrolyte, the surface charges repel the co-ions and attract counter-ions. An electrochemical equilibrium, namely, the Donnan equilibrium, is established when an ionic solution is in contact with charged channels, forming the Donnan potential difference at the interphase of solution and channels. When a pressure gradient is applied for filtration, the Donnan potential excludes co-ions from the channels and must also exclude counter-ions, owing to the electroneutrality requirement. It is important that λ D is larger than the channel size, and the channels are in the dilute solution, then the Donnan exclusion behaviour dominates. In a concentrated ionic solution, however, λ D is comparable to the channel size and the rejection rate decreases rapidly.
Electrostatic interactions are dominant factors for ion transport through nanopores 123,124 and 1D 49,125 and 2D 20,66,126 nanochannels. The classic mean-field theories are less relevant for ion transport in channels under extreme confinement and in solution with a high concentration of ions 114 . For instance, ion transport through sub-nm graphene pores is observed to exhibit heterogeneous contributions by different individual pores 123 . The sub-continuum ion dehydration coupled with electrostatic effects in sub-nm pores is found to dominate the observed rectified and non-linear current-voltage characteristics. Cation to cation, or even cation to anion, sieving is observed in graphene 123 and MoS 2 (reF. 124 ) pores, 1D CNTs 49 and 2D GO channels 127 . The 8 Å CNTs (Fig. 6b) with carboxy groups at the rims of nanopores 49 can reject almost all co-ions (Cl − ) when the KCl concentration is 0.1 M at pH = 7.5, and show a K + :Cl − ion selectivity greater than 184:1 at a typical seawater salinity level of 0.6 M. In analogy with the biological channels based on the electrostatic-interaction effects, the sub-nm CNT channels, intriguingly, function as voltage gates that open or close in response to the changes of transmembrane potential, and, like diodes, to transport ions only in one direction 49,128 .
Ion separation enabled by electrostatic interaction can be regulated by manipulating the surface charges of channels. GO membranes with tunable surface charges can be obtained by coating the GO with positively or negatively charged polyelectrolytes 126 (Fig. 6b). The charge of the membrane surface, based on the protonation of amine groups or deprotonation of sulfonic, carboxy or hydroxy groups in water, is finely tuned by the intensity and the amount of these ionizable functional groups. The selectivities of H 2 O to MgCl 2 and H 2 O to Na 2 SO 4 can be enhanced, reaching as high as 2.2 × 10 5 and 5.4 × 10 5 , respectively 126 . The divalent cation A 2+ and anion B 2− with high interaction-energy barriers are excluded by positively and negatively charged GO membranes, respectively, and the electrostatically attracted low-valent counter-ions are rejected on the basis of electroneutrality requirements.
Graphene-based channels are intrinsically conductive, enabling their use as electrodes. Inspired by this trait, electric potential is applied across the channels to regulate the water and ion transport 129,130 . Water permeation can be affected by the ionization effect in water caused by an electric field 129 . With the application of an electric potential, the GO membranes containing moisture enable the creation of conductive filaments (conducting paths) within the channels (Fig. 6b). The electric field along the radical direction is as high as ~10 7 V m −1 , which can dissociate water molecules to produce hydronium (H 3 O + ) and hydroxyl (OH − ) ions. Hydrogen bonding between H 3 O + or OH − ions and surrounding water molecules leads to the formation of large hydrated clusters, which can reduce water permeability from ~150 to ~10 mg m −2 h −1 (reF. 129 ). Interestingly, interlayer spacing of the GO channels can be reversely switched from 9.2 to 8.5 Å, enabling their function as voltage gates for selective molecular transport.
Electric potential can also influence the transport of ions within charged channels by continuously changing the population and distribution of ions 131 . Simulations based on the Poisson-Nernst-Planck model 132 have shown that the flux of ions diffusing through the interfacial electrical double layers confined in nanochannels (size smaller than 2 nm) should decrease as the gate potential increases 130 . Surprisingly, experiments indicate that the flux of ions increases by up to seven times when the voltage shifts from 0 to −0.5 V (reF. 130 ). This observation may be because of the short-ranged, non-Coulombic correlation between the co-ions and counter-ions under nanoconfinement, which disturbs the electrical double layers structure and attracts more co-ions to facilitate ion transport 133,134 . Such a strong ion-ion correlation is dependent on the ion type, indicating the possibility to realize the sieving of ions. Controlled water and ion permeation enabled by electric fields is also promising for smart molecular gates for applications including tissue engineering and field-effect transistors.

Channel-guest interactions
Selective mass transport also occurs when the guest molecules show different channel-guest interactions. Typically, enhancing these interactions aids molecular transport of certain molecules, as well as the selectivity over other molecules. For example, a NaA zeolite membrane exhibits fast transport of water vapour by favourable charge-dipole interaction between Na + and water, but rejects light gas molecules (H 2 and CO 2 ) 85 . Selectivity of H 2 O over CO 2 reaches as high as ~11,000 even under high temperature and pressure (250 °C and 21 bar), boosting the conversion efficiency of CO 2 to methanol during the CO 2 hydrogenation reaction. Transport of CO 2 molecules in 1D CNTs is enhanced by modifying the channel walls with divalent metal cations 135 (Fig. 6c). These cations function as CO 2 carriers to facilitate CO 2 transport by providing suitable electronegativity to form π-complexation with CO 2 molecules.
MOFs are one of the most popular materials with tunable channel-guest interactions. Various chemical strategies can tune these interactions, such as open metal sites, secondary-building-units-based interactions, hydrophobicity and the presence of certain functional groups. For example, Fe 2 (O 2 )(dobdc) MOFs (dobdc 4− (2,5-dioxido-1,4-benzenedicarboxylate)) show preferential binding of C 2 H 6 over C 2 H 4 by iron-peroxo sites through hydrogen bonding (Fig. 6c), realizing highly selective separation of C 2 H 6 and C 2 H 4 (C 2 H 4 purity of 99.99% produced by a column-packed fixed bed) 136 .
If channel-guest interactions are too strong, the transport of molecules through membranes may be hindered. For example, the −NH 2 -modified MIL-53 membrane shows high CO 2 adsorption capability but low CO 2 permeance, and, thus, high selectivity of H 2 over CO 2 (reF. 137 ). The presence of certain functional groups can also influence the transport behaviour of aqueous ions. For example, modification of UiO-66 nanopores with −N + (CH 3 ) 3 groups leads to anion-to-anion separation in solution under an electric field. F − over Cl − selectivity reaches ~240, which arises from the specific interactions between F − ions and the binding sites in nanopores 138 . In addition, grafting amino-acid groups (such as L-histidine and L-glutamic acid) into MOF pores enhances the discrimination between chiral molecules 139,140 , enabling chiral separation by MOF-based membranes. Modification of nanopores with various functional groups has also been reported for COFs 25 , POCs 23 and porous 2D materials 34 .
Hydrophilicity facilitates water transport in 2D channels, including GO, MXene, MoS 2 and aminefunctionalized hBN. Water molecules are preferentially adsorbed onto the channel surface, and then diffuse 19 . This process leads to water-permeation rates in membranes comprising 2D channels ranging from dozens to thousands of l m −2 h −1 bar −1 . These rates are significantly higher than commercial membranes with similar retention values. As well as electrostatic interactions, ions and 2D channels interact with each other through cation-π interaction 107 and metal coordination 141 . For example, 2D Na-Cl crystals can be formed within the confined reduced GO channels. This phenomenon originates from cation-π interactions between the ions and the aromatic rings in the graphitic surface 142 . Interestingly, unconventional stoichiometries of these 2D Na-Cl crystals are found under ambient conditions, including Na 2 Cl and Na 3 Cl. These stoichiometries can be explained by strong Na + -π interaction and an excess of Na + caused by the charge transfer between the unoccupied valence orbitals of Na + and the delocalized π states of the aromatic ring structure in the graphene sheet 142 . This observation is useful for unravelling ion-transport mechanisms, as well as the magnetic, optical and mechanical properties of 2D ionic crystals.
Interactions between gas molecules and 2D channels are the leading effect for transporting gas molecules, especially for CO 2 molecules. Pure GO, MoS 2 and MXene channels show CO 2 -philic properties, which inhibit the CO 2 transport within the channels 69,143,144 . However, forming 2D channels with interlocked stacking structures leads to preferential permeation of CO 2 over other gases, including N 2 , CH 4 and H 2 . To switch the gas-permeation behaviours of MXene channels, borate and polyethylenimine molecules are introduced to functionalize MXene layers (Fig. 6c). After this functionalization, MXene membranes have a densely interlocked structure and enhanced CO 2 sorption capability, making the transformation from 'diffusion-controlled' to 'solution-controlled' channels. These modified MXene channels are CO 2 -selective rather than H 2 -selective 70 .

Quantum effects
The above mechanisms and theories do not explain mass transport through Ångstrom-sized channels. In these cases, such as the selective permeation of light molecules (H 2 , D 2 and He), quantum effects dominate. For isotope separation, typically, a heavier isotope with a shorter de Broglie wavelength λ i (a smaller effective particle size) has a lower energy barrier for entry into the channels, leading to a difference in isotope-transport rates. Various studies are conducted on the hydrogen-isotope separation using different materials, such as CMSs 145 , zeolites 146 , MOFs 147 , COFs 148 , POCs 149 and CNTs 150 . However, in most cases, relatively low temperatures (20-140 K) are needed for separation, requiring huge energy consumption. Alternatively, the isotope separation can be realized by 2D materials (such as graphene, hBN and MoS 2 ) at room temperature 151,152 .
Perfect monolayers of graphene and hBN with narrow hexagonal rings are impermeable for atoms and molecules. However, they are permeable for hydrogen ions (or protons) 153 . Proton transport occurs when the electron clouds are pierced by incident protons in the 2D materials. The difference in electron-density distribution of hBN, graphene and MoS 2 results in distinct rates of proton transport (Fig. 7a). In monolayers, the electron clouds of hBN (energy barrier E ≈ 0.3 eV) are more 'porous' than those of graphene (E ≈ 0.8 eV), while MoS 2 does not have any 'pores' in its electron cloud, and, so, does not conduct protons 154 . In principle, isotopes are identical in molecular size, but for isotopes of hydrogen ions, the size is exactly the size of nuclei, which is determined by the number of neutrons. As a result, heavy D + has a larger size than H + , resulting in a higher barrier while passing through graphene or hBN membrane. H + and D + are electrically pumped to pass through the perfect graphene or hBN monolayer 152 , and the separation factor of H over D is found, surprisingly, to be ~10. This efficient hydrogen-isotope separation is a consequence of the difference in zero-point energy of ~60 meV between H and D (Fig. 7b). Such proton transport can be enhanced by decorating the 2D layer with catalytic metal nanoparticles (for example, Pt) and by illuminating the layer with visible light 155 . With the response time in microseconds, the Pt-decorated graphene film generates ~10 4 protons per photon based on the unique photon-proton effect, holding potential for applications of fuel cells, light-induced water splitting, photocatalysis and photodetectors 155 .
Quantum confinement also occurs in the interlayer spacing of 2D van der Waals channels 61,76 . This spacing is ~3.34 Å for graphite and hBN, and ~6.15 Å for MoS 2 . These spacings are larger than the λ i of proton (1.45 Å) or deuteron (1.02 Å) atoms at 300 K, which suggests that protons and deuterons may transport through the interlayer of graphite, hBN and MoS 2 . However, these interlayer spacings are filled with electron clouds and, until recently, it was unclear whether this small space could be used for mass transport. Now, it has been demonstrated that these interlayer spacings are impermeable to molecules but allow the transport of protons and deuterons 76 . The channels are created by reactive-ion etching of the 2D crystals (~500-nm thick), followed by coating with a ~50-nm-thick palladium film, which enables proton transport. This transport is a thermally activated process, following an Arrhenius-type behaviour. The rates of proton transport through the channels decrease in the order, hBN > MoS 2 > graphite, and are dominated by the entry barriers (at the edge of channels) of the 2D interlayer, which increase in the order of graphite > MoS 2 > hBN. In fact, on the basis of the square-well confinement potential, the calculated effective widths for transporting H and D are ~0.52 Å for hBN and ~0.55 Å for MoS 2 , which is significantly smaller than the λ i for H and D (reF. 76 ). As shown in Fig. 7c, the entry resistance of D (ρ e D ) is smaller than H (ρ e H ) for hBN and MoS 2 interlayer channels (0.5 μm in length), which contrasts with transport in the direction perpendicular to the 2D crystals, showing larger entry resistance of D than H (reF. 152 ). The difference in the entry barriers for H compared with D, ∆E e , calculated as ~18 meV, is contributed by the differences in energy barriers in the Pd layer ( ε Δ Pd ) and in the van der Waals channels ( ε Δ c ) (Fig. 7c). This result demonstrates a faster diffusion of D than H when entering the quantum-confined van der Waals channels.
Interestingly, the quantum effect dominates gas permeation through van der Waals channels and shows a reversed isotope effect. More specifically, the mass flow of H 2 is notably higher than that of D 2 , which contrasts the relation expected for classical flows 61 . 2D channels exhibit a specular reflection of helium molecules off atomically flat walls (of graphene or hBN channels) 61 , allowing helium gas to flow almost 2 orders of magnitude faster than expected from Knudsen theory (based on random-angle molecular scattering) 61 . The helium permeability in graphene channels is 300-1,000 times higher than in MoS 2 channels, and is independent of channel length, indicating a ballistic transport of the helium atoms (Fig. 7d). Such a surface effect occurs because of the strong corrugations (~1 Å in height) of the MoS 2 atomic structure, which is comparable for the λ i of helium (0.5 Å) at room temperature. The van der Waals channels exhibit 30% ± 10% higher mass flow rate of H 2 than D 2 , which differs from the prediction by Knudsen theory (the mass flow rate should be a factor of √2 larger for D 2 than for H 2 ). This phenomenon may be caused by matter-wave effects that contribute to the specular reflection, suppressing heavier atoms (deuterium) with shorter λ i that are more likely to be hindered by channel-surface roughness than the lighter atoms (hydrogen).
The flow of water through CNTs is enhanced by exciting the phonon modes of the nanotube 156 . Molecular-dynamic simulations reveal that the friction force between water and double-walled CNTs oscillates regularly with time, as a consequence of the coupling of phonon modes of CNTs and water confined in the nanotube. The lowest odd-index longitudinal phonon modes can transfer momentum to the fluid, leading to an oscillating friction force and an increase of the transport rate of water via viscous diffusion (Fig. 7e). In particular, the increase of the water-diffusion coefficient is highest (up to 300%) for the slowest modes (0.3 THz), indicating that very small excitations of the modes lead to a large increase in the diffusion of the confined water molecules 157 . The vibrations of CNTs may also be directly observed, in real time, using a microcavity-based technique 158 . Discovering this coupling between CNT phonon modes and confined water opens a door for enhancing or tuning the mass-transport dynamics by physical excitation of the confined channels, which are important for applications of nanoelectromechanics.
The photoelectric effect dominates ion transport in 2D GO channels 159 . Upon asymmetric light illumination (that is, illuminating close to both ends of the GO membrane), cations are driven by light to flow through the negatively charged GO channels with a of sub-nm (Fig. 7f). The GO membrane exhibits anti-gradient transport behaviour, depending on the light intensity, illumination position and surface charge density of GO channels. This phenomenon is because electrons and holes are excited by a photoelectric effect, and they will diffuse from the illuminated regions to non-illuminated regions driven by the concentration gradients. However, the diffusivity and mobility of holes are higher than that of the electrons in GO-based materials, leading to an electric-potential difference along the axial direction. This difference can drive the cations from the non-illuminated regions to the illuminated regions.

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Outlook Artificial channels with unique mass-transport properties at the sub-nm scale need to be processed into membranes or devices for practical applications. Membranes comprising nanochannels with separation performances better than current commercialized membranes (mainly polymeric membranes) are promising for large-scale, energy-efficient separation technologies, including water desalination, gas separation and organic separation (Supplementary Table 1). However, most membranes are only at the stage of concept or on the laboratory scale, and efforts are needed to realize the success of artificial channels in real applications.
Fundamental research including the molecular-level design of channels is critical to ensure breakthroughs to boost the selectivity and permeability of separation membranes. This design should involve the control of channel size, rigidity and channel-guest interactions, as well as combining the electrical effects and quantum effects. In addition, improvement of mechanical, chemical and thermal stabilities of the channel materials in practical, complex environments will help streamline the transition from the laboratory to large-scale application.
Theoretical studies on transport mechanisms are still in their preliminary stage. Current studies are based on coupled thermodynamic and diffusion properties, with focus being placed on bulk-scale fluid mechanics. Moving forward, theories and principles at length scales ranging from atomistic to continuum will guide the rational design from single-channel to assembled membranes. Experimental studies at the single-channel level are important to deepen our understanding on mass-transport mechanisms. Research to explain some unusual phenomena that happen within nanoconfinement, including the phase transition 117 , phase separation 114 , molecular deformation and alignment 59,60,117,142 , and ionic Coulomb blockade effects 160,161 , may help to reveal the nanostructure-property-performance relationships of channels.
For industry applications, membranes of area >1,000 m 2 and with a low concentration of defects are required (for gas separation, below about 1 cm 2 of defects for every 10 5 cm 2 of membrane surface area) 54 . These requirements for membrane-based separation, to some extent, are more stringent compared with other applications, such as electronics. Better understanding of the origin of defects, not only during channels synthesis but in the membrane-fabrication process, will contribute to the realization of membranes on a large scale. Mixed-matrix membranes (formed by dispersing nanomaterials in continuous polymer matrix) is another way to achieve large-area fabrication. However, for mixed-matrix membranes, issues such as homogenous dispersion at high loading level and control of interface components need to be addressed. Optimizing the design of modules of membranes (in hollow-fibre or spiral-wound formats) and long-term testing of membranes under industrial-like conditions are necessary for artificial channels to realize practical membrane separation.
For water-desalination technologies, including nanofiltration, RO and forward osmosis, improving the water-to-solute (ions) selectivity (minimizing the solute passage) is more important than increasing the membrane permeance 80 . When designing nanochannels, the problems of membrane fouling, concentration polarization, oxidative stability (chlorine tolerant) and boric-acid removal from seawater must be considered. For gas separation, the resistance to plasticization (that is, penetrant-induced swelling followed by the loss of separation properties) needs to be considered. Separations of organics at the sub-nm scale include pervaporation and vapour permeation, and OSRO. Pervaporation and vapour permeation are likely to remain small-scale applications, because of the phase-change-induced energy cost. Swelling (similar to what happens in gas-separation membranes) problems of nanochannels should be addressed for the dehydration of organics (for example, removal of water from either ethanol or butanol) and organics pervaporative separation (for example, separation of xylene isomers or separation of thiophene and n-octane). OSRO, more like 'solvent-to-solvent' separation, is energy saving and has potential for industrial applications, including para-xylene recovery from xylene isomers, linear hydrocarbons from branched hydrocarbons, and alcohol and furan separations 32 . The high pressure required by OSRO needs to be considered before the membranes can be applied in this field.
In fuel cells, flow batteries and Li-S batteries, nanochannels that assemble into membrane separators are being used to selectively transport ions and improve ionic conductivity. A study shows that hydrophilic PIM membranes enable fast ion transport (for example, K + ) while blocking large redox-active molecules (molecular weights in the range of 140-800 Da), showing the potential to function as membrane separators in aqueous organic flow batteries 33 . However, the issues of chemical degradation and poor electrolyte compatibility of membranes need to be solved.
Asymmetric transport of ions through nanochannels can be used for osmotic energy harvesting 22 . Overlapping of Debye layers in nanoconfined channels leads to unipolar ion transport (selective transport of cations over anions), generating current flow. Concentration gradients of ions are one of the driving forces; for example, a single layer of MoS 2 nanopores acts as a nanopower generator based on salt gradients 124 . Additionally, confined channels that can efficiently transport liquid and gas molecules are useful for heterogeneous catalysis 85,162 by enabling size-selective or shape-selective catalysis, and favourable channel-reactants interactions. Fast transport of molecules or ions in confined nanochannels can also find applications in sensing devices (for instance, ion, gas and humidity sensors) 163,164 and electrochemical actuators 165 . Interestingly, nanochannels have been demonstrated to discriminate biomolecules (DNA, RNA and peptides) with Ångstrom precision 166,167 , which paves the way for nanochannel-based, single-molecule sensing and next-generation DNA-sequencing technologies. The vibrant field of artificial channels at the sub-nm scale will foster the development of advanced technologies and benefit the fields of energy, environmental protection, electronics and healthcare.

Published online 21 January 2021
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