Confined gas transport in low-dimensional materials

ABSTRACT Gas transport under confinement exhibits a plethora of physical and chemical phenomena that differ from those observed in bulk media, owing to the deviations of continuum description at the molecular level. In biological systems, gas channels play indispensable roles in various physiological functions by regulating gas transport across cell membranes. Therefore, investigating gas transport under such confinement is crucial for comprehending cellular physiological activities. Moreover, leveraging these underlying mechanisms can enable the construction of bioinspired artificial nanofluidic devices with tailored gas transport properties akin to those found in biological channels. This review provides a comprehensive summary of confined gas transport mechanisms, focusing on the unique effects arising from nanoconfinement. Additionally, we categorize nanoconfinement spaces based on dimensionality to elucidate their control over gas transport behavior. Finally, we highlight the potential of bioinspired smart gas membranes that mimic precise modulation of transportation observed in organisms. To conclude, we present a concise outlook on the challenges and opportunities in this rapidly expanding field. Graphical abstract


Introduction
Gas transport at the nano and angstrom scale is a topic of immense theoretical and applied interest, playing a significant role in various areas including energy recovery and storage, purification, chemical sensing, and medical physiology.In biological systems, gas is traditionally considered to cross cell membranes by diffusing through membrane lipids [1].However, several unexpected physiological phenomena have challenged this dogma.Firstly, the interaction between hydrophilic phospholipid head and certain hydrophobic gases impedes their penetration through the lipid bilayer [2].Secondly, some cell membranes have no demonstrable permeability to carbon dioxide (CO 2 ) and ammonia (NH 3 ) that play crucial roles in organism [3][4][5].Finally, slower gas diffusion through the bilayer fails to explain certain gas-related physiological functions, like paracrine actions by rapid nitric oxide (NO) transportation between two adjacent cells [2,6].Henceforth, there must exist other mechanisms facilitating gas transport across cell membranes.In 1998, Boron's group discovered the promotion effect of AQP1 aquaporin to CO 2 permeability, and postulated the existence of gas channels for the first time [7], which was subsequently confirmed by the same group [8].Since then, numerous studies have been conducted to unravel out these significant physiological processes [1,2,9].For example, it has been found that Aquaporins and Rhesus proteins can serve as pathways for NO, CO 2 and NH 3 transport, and the selectivities of gases vary with the types of proteins [1,2,9,10].Conformational changes occurring within these biological channels could lead to dysregulation of gas transport thereby impacting disease progression [1,9].These biological phenomena underscore the importance of nanoconfinement on gas transport, in which the fluid behaviors deviate significantly from those in microfluidics due to the dominance of surface effects resulting from an increased surface-to-volume ratio [11].However, the regulatory mechanisms governing the expression of gas channels still remain enigmatic, which arises from the difficulty to fabricate the gas channels at nano or even atomic level and to observe the gas transport through such confinement.
Recently, with the emergence of novel materials and advancements in nanofabrication techniques in recent years, plenty of artificial nanostructures have been fabricated to demonstrate intriguing gas transport phenomena [11][12][13][14].According to their topological features, these structures can be classified into nanopores, one-dimensional (1D) nanotubes, and two-dimensional (2D) nanochannels.However, the underlying mechanisms are highly diverse due to the wide range of artificial structures and intricate intermolecular interactions (such as van der Waals interactions and hydrogen bonds).Therefore, a comprehensive understanding of gas transport under nanoconfinement is required to elucidate physiological processes within cellular systems, which, in turn, could also potentially develop rational design strategies for artificial devices.
In this review, we firstly discuss the mechanisms underlying confined gas transport, with an emphasis on the unique effects that emerge under nanoconfinement.Secondly, we review artificial structures in terms of dimensionality to explore their control of gas transportation.Finally, we highlight the potential of bioinspired smart gas membranes that mimic precise modulation of gas transport in organisms, and provide the prospects in the development at this emerging frontier.

The mechanism of confined gas transport
The gas transport can be partitioned into four main regimes according to the Knudsen number Kn (Figure 1(a)), which is defined as where λ is the mean free path and l 0 is the characteristic dimension of the structure.In the regime where Kn � 0:01, transport is primarily governed by intermolecular collisions and described by continuum theory-based Navier-Stokes equations (N-S equations), with Poiseuille and Sampson equations describing gas flow through a channel and an aperture, respectively (Figure 1(a)) [13,15,16].In this regime, the flow rate Q ~1=μ, where μ is the fluid viscosity.When 0:01 � Kn � 0:1, the flow is in the slip flow regime.In this regime, the no-slip boundary condition of classical N-S equations departs from experiments and thus Maxwell's velocity slip boundary conditions are utilized [16,17].When 0:1 � Kn � 10, continuum and thermodynamic equilibrium assumptions start to fail due to rarefaction effects, and the slip models require complex higher-order corrections [16,17].This regime is called the transition flow regime, where some alternative methods have been proposed to describe transportation, such as direct simulation Monte Carlo [16,17].When Kn � 10, collisions between gas molecules and the wall dominate gas flow (Figure 1(a)), which is known as molecular flow.Confined gas flow at nanoscale is typically in this regime, which will be emphatically discussed below.It should be noted that distinct from Knudsen number; l 0 , characteristic dimension of the structure; λ, gas mean free path; D k , gas kinetic diameter; Q, flow rate; μ, fluid viscosity; m, the molecular mass; ∆H ads , heat of adsorption; E, interaction energy (potential energy) between a single gas molecule and an aperture; E a , energy barrier of translocation; ∆S, the entropy difference; ε, adsorption potential depth; E 0 , zero-point energy; σ, molecular hard core radius; r, pore radius.(b) A schematic of gas flow through a channel and generalized flow resistances.R E , resistance of effusion; R S,A , resistance of surface diffusion to the aperture; R a , resistance of activated transport; R K , resistance of Knudsen diffusion; R S,C , resistance of surface diffusion in the channel.
gaseous fluid, the intermolecular interactions among liquid molecules within nanoconfined spaces remain significant.The liquid flow can still be described by N-S equation without obvious deviation when the dimension is larger than 1 nm, taking into consideration surface effects, structuring effects, and other contributing factors [13].A comprehensively outline of the mechanisms governing liquid transport and the concurrent transport of solutes, such as ions, can be found in literatures [11,13].
Back to gas transport, for a channel with radius r and length l that match l � r, the flow rate can be predicted by Knudsen equation, defined as [18]: where m is the molecular mass of the gas, k B is the Boltzmann constant, T is temperature, ∆P is the pressure difference between two reservoirs connected by the channel.The theory stands on the assumption that diffuse reflection occurs during the gas-wall collision and the momentum of gas molecules along the flow direction is not preserved.Smoluchowski [19] then considered the existence of both diffuse and specular collisions (Figure 1(a)), and provided a generalized Knudsen equation: where α is the accommodation coefficient (0 � α � 1) and represents the fraction of diffuse reflection [16].α ¼ 1 indicates complete diffuse reflection, where all momentum along the flow direction is transferred from gas molecules to the wall [16].Conversely, α ¼ 0 represents complete specular reflection, where gas molecules momentum remains preserved and there is no resistance to the gas flow through the channel [16].The proportion of diffuse or specular reflection highly depends on surface roughness [16,[20][21][22].Recently, frictionless gas flow has been achieved by angstrom-scale slit-like channels with atomically flat surface [21].
When the channel length decreases and r � l, the channel transforms into an aperture, through which the gas transport is described by effusion, and the flow rate is [13] In addition, in the context of frictionless flow in a channel, the effusion would prevail as the dominant role of transport, commonly referred to as entrance effect.Typically, for a channel with comparable dimensions (r and l), the flow resistance R (R ¼ ΔP=Q [23]) associated with Knudsen flow and effusion should be considered in series.
As the dimension continues to decrease, additional surface diffusion flow should be considered in the nanoconfined transport (Figure 1(a)).Typically, the adsorption with enthalpy values in the region of −20 kJ mol −1 is referred to as physisorption, whereas the adsorption with enthalpy values in the region of −200 kJ mol −1 and formation of chemical bond is referred to as chemisorption [24].The adsorption/desorption behaviors in transport can be described by Henry's law, Langmuir type adsorption (monolayer adsorption), and Brunauer−Emmett−Teller type adsorption (multilayer adsorption) [16,24,25].For the surface diffusion through an aperture, surface pathway plays the role of a reservoir, like the bulk phase, and the flow rate is defined as [25] where C S is adsorbed gas concentration on surface, H 0 s is the adsorption prefactor, and ∆H ads is heat of adsorption.Sun et al. found that the flow rate of surface pathway through the graphene angstrom-scale aperture was orders of magnitude higher than that of effusion [26].However, excessive gas-wall interactions can instead impede the transport [27].For instance, in certain amino-functionalized metal-organic frameworks (MOFs), the highest adsorption heats of CO 2 are responsible for the lowest gas permeability [28].For the flow in a channel, molecules hopping along the channel surface could also contribute to the flow, defined as [16] where D S is the surface diffusion coefficient related to C S and . When the radius r decreases and becomes comparable to or smaller than gas kinetic diameter D k , an energy barrier for gas transport becomes prominent at the entrance due to repulsive interactions between gas molecules and atoms surrounding the entrance.D k describes the molecular size as a gas-gas collision target and is generally larger than the atomic diameter defined by the atom's electron shell.This transport regime is commonly referred to as the activated regime (Figure 1(a)).The energy barrier E a can be approximately determined by the Lennard-Jones potential, defines as [12]: where ε and σ are Lennard-Jones parameters associated with physical and chemical molecule properties, and a is the distance between adjacent atoms around the entrance.Considering the activated transport process as a barrier overcoming event, the flow rate through an aperture can be described by transition state theory [25,26,30] where ν is the impingement rate of molecules into the aperture mouth and ∆S is the entropy difference before and during the transition.By combining Equation 7and Equation 8, it can be inferred that the flow rate will be highly sensitive to interactions between gas molecules and atoms around the entrance, which are influenced by factors including the relative size of gas molecule and entrance, molecular configuration, and chemical composition.Via water-assisted low energy electron etching, Sun et al. fabricated angstrom scale aperture in graphene with apparent energy barriers for H 2 and CH 4 , and realized exponential selectivity (selectivity of hydrogen (H 2 )/methane (CH 4 ) up to 10 7 ) [26].The enhanced water vapor transport through NaA zeolite was demonstrated by Li et al., which exhibited permeability three orders of magnitude higher than common gases (Figure 6(a)) [31].This can be attributed to the interaction between Na + ions and water (H 2 O) molecules with pronounced polarity, resulting in a reduced energy barrier.
The practical scenario necessitates the consideration of all aforementioned pathways, leading to the proposal of a comprehensive transport resistance model (Figure 1(b)).The model comprises two main parts: aperture or entrance resistance and the channel resistance, associated with effusion/Knudsen diffusion, surface diffusion, and activated translocation.Due to variations in flow resistances based on structural size, surface properties, and other factors, different dominant resistances exist for various low-dimensional materials.For instance, Yuan et al. found a transition in flow regimes within a graphene aperture as a function of aperture diameter D a at 300 K, from 0.5 to 6 nm [25].For an aperture with D a smaller than 0.72 nm, activated translocation dominates CO 2 transport, while for D a between 1 nm and 2 nm, the surface diffusion pathway prevails [25].When D a exceeds 3.4 nm, gas flow entirely transitions into effusion [25].Notably, the model in Figure 1(b) neglects coupling effects of different pathways, which can be significant for transportation.For example, although additional surface diffusion normally enhances the overall flow rate, it may decrease the rate in a channel with atomic flatness and negligible Knudsen flow resistance.In such case, an adsorbed molecule leaving the surface is independent of the incidence direction and follows a cosine distribution similar to diffusive reflection [32], leading to a reduced fraction of specular deflection.However, the exploration of coupling effect poses a challenge as the existing detection technology can only measure the total flow and lacks the capability to differentiate individual transport pathways.
For dense polymeric membranes with undefined structures of gas transport pathways, 'solution-diffusion' mechanism dominates the transportation [33][34][35][36][37].The gas permeation processes include three steps: 1) dissolution of gas molecules into the membrane on the upstream side, 2) diffusion through the membrane, and 3) desorption from the membrane on the downstream side [33,36].Diffusion is the rate-limiting step, governed by thermally stimulated creation of transient gaps for transport among the polymer chains.The gas permeability coefficient P i and selectivity α i,j of two gases can be defined as [33] where S i and D i are solubility coefficient and diffusion coefficient of gas i, respectively.For a specific gas, S i normally remains consistent in a wide range of polymeric membranes, except for certain polymer materials that have specific interactions with gases [35].This consistency arises from the fact that gas solution in most polymers is similar to that in ideal liquids and all ideal liquids should display consistent solution characteristics for the same gas [35].In contrast, D i varies widely with polymer materials, which largely accounts for the difference in membrane selectivity among various polymer materials [35].Furthermore, the thermally activated diffusion of gas molecules obeys the Arrhenius equation, and the activation energy exhibits a linear relationship with the square of penetrant molecule diameter, serving as the foundation for gas selectivity [33].
However, a more selective polymeric membrane generally behaves less permeability, and this trade-off relationship between selectivity and permeability is known as the Robeson limit [38].Therefore, the ability to break this limit becomes a crucial criterion for evaluating novel membrane materials.Numerous strategies have been explored to fabricate membranes with both high permeability and high selectivity, including the modification of surface chemical environments, molecular sieving, and atomic membrane thickness, which will be elaborated in the next section.
In addition, entropic effect and quantum sieving also play significant roles in confined gas transport.The entropic effect arises from the loss of rotational and vibrational modes of molecules in confined spaces, thus being closely related to the molecular shape and size (Figure 1(a)) [30,39].The exponential relationship in Equation 8 suggests that entropy can significantly influence flow rate, and related selectivity is called entropic selectivity.Sigh et al. verified a substantial effect of entropy on diffusion coefficient of oxygen (O 2 ) and nitrogen (N 2 ), with entropic selectivity of O 2 /N 2 up to 14.7 for 4A zeolite with the pore diameter of 3.8 Å [40].Quantum sieving occurs when the difference between molecular hard core radius (σ) and pore radius (r) is comparable to the de Broglie wavelength of the molecule and the zero-point energy (E 0 ) overcompensates for the adsorption potential depth (ε) of the wall, shown as shadow region in Figure 1(a) [41].The resulting flow rate is directly proportional to the Boltzmann factor exp[(ε-E 0 )/k B T] [42].Due to exactly same kinetic diameter, configuration, and thermodynamic properties, it is impossible to realize the separation of hydrogen isotopes by molecule sieving [42].But deuterium (D 2 ) possesses a shorter de Broglie wavelength and slightly smaller effective particle size than H 2 because of its higher molecular mass.This disparity can be exploited by a narrow pore, resulting in higher mobility of D 2 and isotope separation.
The preceding discussions indicate that dimension-dependent gas flow rate (or gas permeability) and its related selectivity have various affecting factors.In the continuum flow regime, the flow rate is inversely proportional to the dynamic viscosity, and for Knudsen flow and effusion, it is inversely proportional to ffi ffi ffi ffi m p .These flow regimes, however, do not effectively separate different gases.As the dimension continues to decrease, intermolecular interactions between surface and gas molecules begin to prominently influence gas transport, and additional surface diffusion flow should be considered.The flow rate becomes influenced by adsorption concentration, and gas selectivity can be achieved by various gas adsorption energy.When the dimension is comparable to or smaller than the size of gas molecules, these molecules need to overcome energy barriers to permeate through membranes and the barriers are sensitive to molecular size, which facilitates high gas selectivity.For dense polymeric membrane without defined channels, gas permeability is dominated by solubility and diffusivity.Moreover, within molecularscale confinement, entropic effect, and quantum sieving also play significant roles.
During the past decades, the progress in material design and fabrication technology has enabled the exploration of gas transport at nanoscale confinement spaces with precise control, including nanopores, 1D nanotubes, and 2D nanochannels.Within these confined spaces, confinement effects discussed in this section come into play and gas transport will strongly depend on the characteristic dimensions and intermolecular interactions between gas molecules and nanoconfined structures.By achieving confinement approaching the kinetic diameters of gases and fine-tuning the chemical environments, it becomes possible to substantially regulate gas permeance through these artificial structures while significantly enhancing selectivity, which breaks through polymer membranes' trade-off between permeance and selectivity (also called Robeson's upper bound [38]).This demonstrates promising prospects for advanced gas separation techniques.Herein, in next three sections, we will provide insights into the structural characteristics of these artificial materials together with their implications on gas transport behaviors, according to their topological feature.

Nanoporous atomically thin membranes
Since the Geim group's groundbreaking experiments of graphene in 2004 [43], various atomically thin materials have emerged and demonstrated significant potential in the advancement of high-performance membranes [12], including transition metal dichalcogenide (TMD) and hexagonal boron nitride (h-BN).As the thinnest physical barrier, the pristine lattice of these atomically thin materials exhibits impermeability to small molecules (even helium (He)) [44], which was first proved by micro-sized graphene balloon measurement (Figure 2(a)) [45].Afterward, Sun et al. observed abnormal H 2 permeation through single-layer pristine graphene [46], stemming from H 2 dissociation at catalytically active graphene ripples and subsequent translocation of these atomic H through the lattice (Figure 2(b)) [44,46].For h-BN, its polar nature of B-N bonds causes larger opening in the electron cloud and less energy barrier in proton (H + ) translocation compared with graphene [47]; while for TMD, instead, the three layers lead to much denser electron clouds, which makes it impermeable to H atoms [46,47].
The impermeability of these 2D materials indicates that tunable gas transport can be achieved by the introduction of zero-dimensional (0D) pores with controllable size and chemistry.Simulation showed that graphene membranes with designed sub-nanometer pores could achieve high selectivity and permeance for gas separation [49].However, it is (AFM) image of multilayer graphene with higher gas pressure in the microcavity (bottom) [45].Inset is the optical image of a suspended single-layer graphene.(b) Deflection-time curves of 12 different single-layer graphene nanoballoon caused by permeation of H atoms in molecular hydrogen [46].Insets are representative changes of deflection with time taken by AFM (top) and illustration of the flipping process of hydrogen atoms permeation (bottom).(c) Measured gas leak rates of bi-layer graphene before and after etching.Inset is schematic of molecule sieving of a porous graphene [48].
still a debate whether stable (sub)nanopores with molecular sieving ability could be fabricated into atomically thin membranes for separation.In 2012, Koenig et al., for the first time, achieved the successful fabrication of angstrom-scale pores in graphene, and demonstrated that porous graphene membrane could be utilized as molecular sieves, with the observed H 2 /CH 4 selectivity of 10 4 for a few-pores micro-sized membrane (Figure 2(c)) [48].When considering detection noise from gas diffusion through silica substrate, the actual selectivity could be even higher.This work put an end to the above controversy, and established an experimental foundation for the utilization of atomically thin membranes in nanofluidic research and as next-generation membranes materials.Afterward, Sun et al. replaced the SiO 2 cavity to a less permeable graphite cavity, thus leading to an improvement in the detection limit of devices and a dramatic enhancement in the detectable gas selectivity by orders of magnitude (selectivity of H 2 /CH 4 up to 10 7 ) [26].The outstanding selectivity is attributed to the exponential relationship between gas flow rate and energy barrier in activated regime where the confined dimension is comparable to the gas molecular size, as depicted in Equation 8, which also indicates the ultra-sensitivity of gas flow to such refined structures.Wang et al. reported fluctuated gas transport through the angstrom-sized graphene pores, which was assumed to stem from the thermally activated rearrangement of pore structures [50].
Researchers then expanded the above single-or few-pores systems to multi-pores systems to meet the demands for practical molecule sieving applications [51,52,53,54,55].Yuan et al. utilized intrinsic pores in chemical vapor deposition (CVD) single-layer graphene for gas separation and achieved ultrahigh H 2 /CH 4 selectivity (>2000) with H 2 permeance > 4000 GPU (1 GPU = 3.348 × 10 −10 mol m −2 s −1 Pa −1 ) [54].Huang et al. precisely introduced angstrom-sized pores in CVD graphene by ozone etching, with selectivity of He/CH 4 exceeding 100 [55].It is noted that gas selectivities of multi-pores systems are significantly lower than those observed in single-or few-pores systems (Figure 3(a)) [51,52,53,54,55].This phenomenon can be potentially attributed to the log-normal distribution of pore sizes (Figure 3 (b) and (c)) [48,52,53].Specifically, the presence of largest pores in the right tail of angstrom-scaled pore distribution will significantly influence gas permeation and decrease selectivity from the value of mean pore size [56].When the mean pore size is much larger than D K , a clear transition from effusion to Sampson flow was observed by precisely perforating double-layer graphene, with a narrow distribution of diameters from <10 nm to 1 μm (Figure 3(d)) [57].Due to the atomic thickness, gas permeance was enhanced by orders of magnitude compared with existing membranes with similar selectivity [57].Besides graphene, tungsten disulfide (WS 2 ) was also proved as a candidate to study confined gas flow.For the atomic vacancy aperture in monolayer WS 2 with size less than twice D k of He, Knudsen flow was still dominant in He permeation (Figure 3(e)) [58].
Finally, altering the pore rim chemistry to regulate the interaction between the pore and gas molecules represents an effective approach for transport regulation, albeit current studies are limited to simulations [49,[59][60][61][62][63].Rodriguez et al. found that the energy barriers of gas transport depended on the pore chemical functionalization [59].In terms of CO 2 transport, hydrogen-functionalized pores exhibited superior permeance among the apertures with same diameter (Figure 3(f)), resulting from reduced edge stiffness.For oxygen-and carbon-functionalized pores, CO 2 demonstrated faster permeance through oxygen-functionalized pores, while CH 4 behaved oppositely.With the combination of atomic thickness and specific molecular interaction, functionalized nanoporous graphene shows significant potential in gas separation.However, challenges persist in efficient introduction of functional groups (e.g. the precise control of functionalization sites and the number of groups) under angstrom-sized confinement, warranting further investigation.

Metal-organic frameworks
Compared with graphene and other atomically thin membranes that require perforation for gas separation, metal-organic frameworks (MOFs), comprised of metal nodes or clusters linked by organic ligands, inherently possess highly ordered and uniform pore  [26,48,51,[53][54][55].The black line shows the upper bound of 1-μm-thick polymer membrane [38].Considering that permeance is not applicable for few-pores system, the horizontal dash line is used to represent selectivity with green dash line for ref.  [57].Inset is the scanning electron microscope (SEM) image of array of 50-nm-wide apertures in the suspended graphene (scale bar, 500 nm).(e) Comparison of normalized permeance of irradiated samples and controls, with the Knudsen predictions [58].Inset is aberration-corrected high-angle annular dark-field (AC-HAADF) image of ion-irradiated monolayer WS 2 flake and bright spots indicate W atoms. (f) CO 2 per-porepermeance of pores with different functionalization [59].Insets are schematics of graphene pores with oxygen edge atoms (up) and hydrogen edge atoms (down).The red, white, and dark gray balls are oxygen, hydrogen, and carbon separately.
structures.Since their first report in 1995 [64], MOFs have found significant applications in gas adsorption and separation due to their exceptionally high porosity and surface area, abundant open metal sites, and structural/functional tunability [39].As illustrated in Figure 4(a), MOFs are featured with hierarchical pore structures at multiscale.In terms of gas separation, a key design principle is to leverage distinct transport behaviors of various gases in these pore structures, which can be modulated by adjusting the pore size and chemical functionality of MOF pores.
Gas diffusion in MOF nanopores is a thermally activated process with the energy barrier dependent on the relative size of gas molecules and pore windows [39].Generally, larger pore size poses lower activation energy for gas diffusion.Therefore, gas transport can be substantially regulated by the effective pore aperture of MOFs and physical size sieving effect.Notably, when considering the effective pore aperture of MOFs, framework flexibility caused by the structural breathing, structural swelling, and rotation of organic linkers is a nonnegligible factor (Figure 4(b)).Zeolitic imidazolate framework-8 (ZIF-8) is a representative MOF with flexible crystal structure, consisting of zinc ions and 2-methylimidazolate linkers in a zeolite-like topology with large sod cages of 1.12 nm in diameter (Figure 4(a)).While the diameter of crystallographic pores in ZIF-8 is 0.34 nm [62], a study on the thermodynamically corrected diffusivities of probe molecules from He (0.26 nm) to iso-C 4 H 10 (0.5 nm) revealed that the effective pore size of ZIF-8 is approximately 0.40-0.42[65].Bottom: corresponding permeance of propylene and propane [65].(e) Isosteric heats of adsorption and permeances at 288 K of H 2 , CH 4 , N 2 and CO 2 for NH 2 -MIL-53(Al) [28].
nm (Figure 4(c)) [63], which is ascribed to the rotation of methyl groups of 2-methylimidazolate linker.As illustrated in Figure 4(c), the diffusivity through ZIF-8 nanopores decreases with increased molecular diameter due to the enhanced steric hindrance [63].Utilizing this size sieving effect, ZIF-8 can realize high kinetic selectivities for C 3 H 6 /C 3 H 8 (130), iso-C 4 H 8 /iso-C 4 H 10 (180) and n-C 4 H 10 /iso-C 4 H 10 (2.5 × 10 6 ) [63]. Lee et al. further exploited a postsynthetic linker exchange approach to substitute 2-methylimidazolate in ZIF-8 with 2-imidazolecarboxaldehyde [65], the linker of ZIF-90, which possesses a higher pore aperture of 5.0 Å [66].As shown in Figure 4(d), the MOF membrane with decreased effective ZIF-8 thickness showed an increase in propylene permeance by about four times while maintaining relatively high C 3 H 6 /C 3 H 8 separation factor, ascribed to the enlargement of effective pore diameter and the resulting decrease in diffusional activation energy [65].Zhu et al. also utilized polyphenol tannic acid modification to create hollow cavities inside ZIF-8 crystals to reduce the gas transport resistance through polymer matrix membranes [67].Besides, the framework flexibility of ZIF-8 leads to moderate CO 2 selectivity over N 2 or CH 4 .Targeting CO 2 capture applications, Ban et al. incorporated ionic liquid into the sod cages of ZIF-8 to further reduce the effective cutoff size, leading to high selectivities of 152 for CO 2 /N 2 and 66 for CO 2 /CH 4 [68].
Ligand functionalization with amino group, hydroxyl group, sulfonyl group, and so forth, is another commonly adopted strategy to modulate gas permeance in MOFs, which is usually based on enhanced adsorption toward certain gas through Lewis acid-base interaction [28,69,70] or polar interaction [71] between the functional groups and gas molecules.For example, amino-functionalized MOFs are of particular interest for CO 2 -related adsorption and separation due to the robust acid-base interaction between CO 2 and the amino group.The enhanced CO 2 adsorption capability can significantly reduce CO 2 mobility in MOF nanopores, hence decreasing CO 2 permeance [27].It has been observed that for NH 2 -MIL-53(Al) (pore diameter close to 0.75 nm) with amino functional groups a decrease in heats of adsorption in an order of CO 2 >N 2 >CH 4 ≈H 2 resulted in a reversed sequence of H 2 >CH 4 >N 2 >CO 2 for gas permeance (Figure 4(e)) [28].In solution-diffusion dominated transport, the adsorption affinity of MOFs toward certain gases can result in higher solubility selectivity.Inspired by symbiosis between rhizobium and plant roots, He et al. designed in situ bottom-up synthesis for defect-free mixed matrix membranes with high ZIF-8 loading [72].While the presence of ZIF-8 compromised the diffusivity selectivity due to its flexible pore size, the solubility selectivity was substantially increased due to the adsorption affinity of ZIF-8 toward CO 2 , leading to increased selectivity of 24.8 for CO 2 /N 2 and 18.8 for CO 2 /CH 4 [72].However, for MOFs with narrow windows of approximately 0.3-0.4nm, molecular size sieving effect should also be considered, and both the chemical environment and pore size determine gas permeance through MOF membranes.Yin et al. synthesized amino-functionalized CAU-1 membrane, which showed a higher CO 2 permeance than N 2 and CO 2 /N 2 selectivity of 17.4-22.8despite the adsorption affinity of amino groups for CO 2 , emphasizing the prominent effect of narrow window of CAU-1 (0.3-0.4 nm) in this case [73].Overall, when developing novel MOF-based gas separation membranes, whether the enhanced adsorption affinity toward certain gas can promote or suppress gas permeability, as well as the coupling between the affinity effect and size sieving effect, needs to be considered meticulously to guarantee desired gas separation performances.

Covalent organic frameworks
Covalent organic frameworks (COFs) are another class of porous crystalline materials that have shown significant potential for separation membranes [74].Different from MOFs, COFs are exclusively constructed from organic building blocks connected by robust covalent bonds.Most reported COFs are 2D structures assembled by stacking nanosheets.A critical concern in COF membranes-based gas separation is that pore diameter is typically ranging from 0.6 to 3 nm [75], which limits their ability to achieve molecular size sieving for most gases.A commonly adopted solution to this problem is pore narrowing by the staggered AB stacking of COF nanosheets.Molecular dynamics simulations by Tong et al. on a representative COF, CTF-1 (with a pore size of 1.2 nm), demonstrated that while both single-layered and perfectly overlapped two-layered CTF-1 membranes exhibit typical Knudsen transport for CO 2 and N 2 permeation, shifting the layers to narrow the pore size of interlayer passages can effectively convert the nonselective membrane into a highly selective one even at the molecular sieving level [76].This conversion brought about an impressive CO 2 /N 2 selectivity (up to 190), with CO 2 permeance remaining approximately 10 6 GPU [76].In experimental studies, such a strategy for pore narrowing is usually realized through alternate stacking of nanosheets from two different 2D COFs [77][78][79]80,81].For example, Fan et al. fabricated COF-LZU1-ACOF-1 bilayer composite membrane using temperature-swing solvothermal synthesis, which showed a significantly higher H 2 permeance (2.45 × 10 −7 mol•m −2 •s −1 ) than CO 2 , N 2 and CH 4 [77].Ying et al. proposed another controlled staggered stacking method utilizing the electrostatic attractive interaction between two oppositely charged ionic covalent organic nanosheets, i.e. cationic TpEBr and anionic TpPa-SO 3 Na nanosheets (Tp = 1,3,5-triformylphloroglucinol, EBr = ethidium bromide, Pa-SO 3 Na = sodium 2,5-diaminobenzene sulfate).This approach also led to improved H 2 /CO 2 separation performances (Figure 5(b)) [79].Besides stacking of two different COF nanosheets, single-phase COF nanosheet membranes in staggered stacking mode have been developed as well [80].Employing a hot-drop coating method, Wang et al. successfully prepared three kinds of β-ketoenamine-type 2D COF membranes [80].Notably, the as-prepared TpPa-2 (Pa-2 = 2,5-dimethylbenzene-1,4-diamine) staggered stacking nanosheet exhibited the highest CO 2 /H 2 selectivity of 22, which was ascribed to the narrowed pore diameter from 1.2 nm to 0.6 nm due to the staggered stacking mode and facilitated CO 2 permeation derived from CO 2 -philic adsorption [80].Pore narrowing and enhanced separation performances of COF membranes can also be realized through assembly of COF nanosheets with extrinsic polymers.It should be noted that the incorporation of polymers will change the chemical environment of COF channels and hence the effect of adsorption affinity should be taken into consideration in this case.Recently, Wang et al. studied a polyelectrolyte-mediated assembly strategy to promote fabrication of ultrathin COF membranes, bridging anionic TpPa-SO 3 H nanosheets with cationic polyethyleneimine (PEI) (Figure 5(c)) [82]. Wile PEI polymer chains reduced the effective pore size leading to decreased gas permeance, it also resulted in improved CO 2 /N 2 selectivity ascribed to the abundant amine groups in PEI, which could concentrate CO 2 on membrane surface due to high affinity toward CO 2 and acted as Brønsted base carriers to reversibly convert CO 2 to HCO 3 − in the presence of water (Figure 5(d)).

Other nanoporous materials
Besides nanoporous materials mentioned above, other materials such as zeolites, 2D bilayer silica, and graphdiyne have shown great potential for gas separation.
Zeolites with rigid frameworks constitute a distinct category of porous crystalline materials that have garnered significant attention to gas transport and separation [83].Featured with pore or window openings formed by 12, 10, or 8 oxygen anions, zeolites can regulate gas transport through molecular size sieving.In particular, zeolites with 8-membered ring hold great promise for gas separation since their pore diameter typically ranges from 0.3 to 0.4 nm, which is close to the kinetic diameters of most gases.For example, SSZ-13 zeolite with 8-membered rings of 0.37 nm × 0.42 nm in size exhibited a high CO 2 /CH 4 selectivity of up to 300 with CO 2 permeance of 2.0 × 10 −7 mol s −1 m −2 Pa −1 [84].Conversely, 10-and 12membered-ring zeolites are less suitable for gas separation as a result of larger pore diameter (~5-6 Å for 10-membered rings and ~ 7 Å for 12-membered rings) [85,86].Notably, zeolites would undergo structural change upon temperature elevation or gas adsorption, resulting in a reduction in their molecular-sieving abilities [14].Moreover, it is worth noting that gas transport through zeolite can also be modulated by changing the chemical environment around the pore.Li et al. developed a gas-impeding water-conduction membrane based on NaA zeolite, which exhibited a water vapor permeability two to three orders of magnitude higher than that of common gases (Figure 6(a)) [31].The pore structure of NaA zeolite is dominated by 8-oxygen rings with diameter of 0.42 nm (Figure 6(b)), where Na + ions are positioned inside zeolite nanocavities with three locations.The existence of Na + partially blocked nanochannels and subsequently hindered gas permeance, while water permeance was instead promoted by the interaction of Na + and polar H 2 O [31].Density functional theory (DFT) simulations revealed a significantly lower energy barrier for H 2 O entering the aperture compared to that of H 2 and CO 2 , consistent with the experimental permeation results (Figure 6(b)) [31].Integration of this water-conduction membrane into catalytic reactor demonstrated substantial improvements in CO 2 conversion and CH 4 yield during CO 2 hydrogenation, due to  [87].Bottom: H 2 /CO 2 separation performances of FAU membrane versus temperature [87].(d) Schematics of gas selectivity of bilayer silica (top) and atomic structure of bilayer silica (bottom) [88].(e) Permeances of tested gases through vitreous bilayer silica [88].(f) Schematic of monolayer graphdiyne's structure (top) and TEM image of quasi-2D graphdiyne layer [89].(g) Gas permeance through graphdiyne layer [89].Blue line shows the best fit by Knudsen dependence using data for light gases from 3 He to Ne.
efficient removal of by-product water.Another demonstration for gas permeance modulated by pore-gas interaction is manifested in faujasite-type zeolites (FAU) [87], which has a pore size of 0.74 nm and exhibits no molecular sieving function for small molecules.But accessible Na + sites in FAU can interact with quadrupole moment of CO 2 , which accounts for the lower CO 2 permeance compared with other larger gases such as N 2 and CH 4 (Figure 6(c)) [87].For H 2 /CO 2 separation, permeance versus temperature of the prepared FAU membrane is shown in Figure 6(c).At low temperature, the adsorbed CO 2 blocked H 2 diffusion and resulted in a low H 2 permeance.When temperature increased, the amount of adsorbed CO 2 decreased and consequently led to an enhanced H 2 permeance.
2D bilayer silica, discovered in 2010, is a promising membrane structure that possesses intrinsic subnanometer pinholes with four-to nine-membered rings (Figure 6(d)), thus no perforation [90] process is required for membrane separation compared to intrinsically impermeable graphene.Naberezhnyi et al. first conducted permeation measurements on freestanding vitreous 2D bilayer silica membranes [88].Unexpectedly, the results showed that gas permeation of inert gases through bilayer silica was hindered (except for He with a detectable permeance of 1.5 × 10 −8 mol s −1 m −2 Pa −1 ), whereas larger gas molecules, such as herein heavy water (HW), 1-propanol (PA) and methyl isobutyl ketone (MIBK), were found to permeate much faster with orders of magnitude higher permeances of 4.5 × 10 −5 , 1.7 × 10 −5 , and 1.9 × 10 −4 mol s −1 m −2 Pa −1 , respectively (Figure 6(e)) [88].Such anomalous permeation results can be attributed to an adsorption-based diffusion mechanism for gas transport through the as-synthesized bilayer silica membrane [88].On one hand, probability for impingement of gas molecules right into the center of nanopores in silica was extremely low and thus no molecular effusion could occur, leading to low permeances of inert gases [88].On the other hand, DFT combined with adsorption measurements verified the adsorption affinity of silica toward HW, PA and MIBK with surface coverage of the physisorption following the sequence of MIBK ≫ PA ≫ HW [88].Notably, although HW exhibited lower adsorption surface coverage compared to PA, a higher permeance was observed for HW, which revealed that molecular size also affected the gas transport behavior [88].It was proposed that HW with smaller size could pass six-membered and larger rings while larger PA and MIBK molecules could only permeate through seven-to nine-membered rings [88].
Graphdiyne, a carbon allotrope with intrinsic triangular angstrom-scale pores, has also triggered extensive research in gas separation technologies.Experimental investigation on gas transport through graphdiyne-based membrane (Figure 6(f)) has been reported by Zhou et al. recently [89], in which suspended multilayer graphdiyne membrane of several micrometers in diameter and ~90 nm in thickness was prepared.Gas permeation measurements revealed that light gases 3 He, 4 He, D 2 , HD and Ne purely obeyed Knudsen flow with pressure-normalized permeance propotional to m À 1=2 , whereas the permeances of heavy gases Ar, Kr, and Xe were obviously deviated from Knudsen description (Figure 6(g)) [89].Furthermore, binary mixture permeation measurements of 4 He and other heavy noble gases demonstrated that the presence of heavy gases could substantially suppress helium permeation [89].These phenomena were attributed to adsorption of heavy gases, leading to partial pore blockade and reduced effective pore size [89].

Gas transport through 1D nanotube structures
Figure 7(a) illustrates the molecular structures of various nanotubular materials, encompassing inorganic nanotubes and organic nanotubes.Inorganic nanotubes include carbon nanotubes (CNTs), boron nitride nanotubes (BNNTs), metal oxide nanotubes, and tubular alumina-based materials.Among these, CNTs are the most widely studied in nanofluidics [13,14].The intrinsic atomic smoothness of the inner surface of CNTs minimizes diffusive reflections, thereby facilitating rapid mass transportation [20,91,92].Holt et al. measured enhanced gas flow through less than 2-nmdiameter carbon nanotubes, exceeding Knudsen flow by more than an order of magnitude (Figure 7(b)) [91].Meanwhile, hydrocarbon gases showed faster transport than other gases with similar molecular weight, which may originate from surface diffusion along the nanotube [91].Although it is hard to functionalize inner wall of CNTs for its relatively unreactive electronic structure [93,94], controllable gas transport associated with reflection behavior and surface diffusion could be theoretically achieved by defect and doping engineering [,95,96,97].However, the minimum diameter of CNTs utilized for mass transport is approximately 0.8 nm [98,99], much larger than the D k of most gases, which restricts gas flow to Knudsen flow or surface diffusion, and results in insufficient selectivity.
BNNTs can be regarded as a structural analog to CNTs; however, their electronic properties differ significantly owing to the presence of B and N atoms [104].Consequently, they demonstrate immense potential in nanofluidic applications such as ultrafast water transport [105], osmotic energy generation [106], and hydrogen storage capabilities [104].Nevertheless, similar to CNTs, further investigation into gas transport is also impeded by the limitations of their structure.
For both organic and metal oxide nanotubes, their assembly from molecular subunits provides a higher degree of flexibility compared with CNTs and BNNTs, enabling customization of inner wall chemistry, channel size, and other properties [14].However, it should be noted that the interior surface smoothness of organic and metal oxide nanotubes falls short of atomic perfection [14].Moreover, gas transport properties of these structures have been rarely explored.Therefore, only the structural properties will be discussed further.The organic nanotubes are assembled through non-covalent interactions, and the representative nanotubes types include helical macromolecules [107], m-phenylene ethynylene [108], octylureido-ethylimidazole [101], and peptideappended hybrid [4]arenes [109].These structures exhibit a diameter range from 0.26 to 0.64 nm, and possess various functional groups, including alkyl, ethylimidazole, and carbanyl groups, which may play a crucial role in the gas separation.However, the lack of robustness in the non-covalent interaction-based structure hinders its further scalability for membrane fabrication [14].Metal oxide nanotubes include aluminosilicate or aluminogermanate-based nanotubes [94].The inner pore size can now be down to 0.65 nm [14] and controlled with angstrom precision by reactant composition and related precursor shapes [110].Besides, the hydroxylated surfaces both inside and outside can be modified through various grafting reactions to introduce diverse functional groups [94].
For anodic aluminum oxidation (AAO)-based membranes, highly uniform tubular channels can be achieved by precisely controlled structures and wall composition [111].The thickness of AAO membranes can range from 0.5 to 200 μm with pore diameters between 20 and 200 nm [111].By further utilization of atomic layer deposition (ALD), layers of oxides or other materials can be deposited onto the channel walls, effectively reducing their diameter while also altering their composition [111].Lee et al. fabricated liquid/vapor interfaces within hydrophilic AAO channels featuring short hydrophobic nanopores that effectively trap vapor (Figure 7(c)).The resulting bubble facilitated the permeation of water vapor through Knudsen flow, while simultaneously achieving a remarkable salt rejection rate of 99.9% [103].Although the anti-fouling property and stability of the nanobubbles remain open questions in actual desalination applications, this research introduces a novel concept to construct osmotic membranes.

Lamellar nanosheet-based membranes
Owing to convenient and scalable fabrication, 2D lamellar nanosheet-based membranes with precisely controlled nanochannel dimensions are perspective for achieving accurate molecular separation and facilitating nanofluidic applications [112].As illustrated in Figure 8(a), two transport pathways through assembled laminates are considered: one is the interlayer nanochannels formed by face-to-face nanosheet interactions, and another is in-plane nanosheet pores and/or slit-like pores formed by edge-to-edge nanosheet interactions [113].
Graphene-based materials, primarily graphene oxide (GO), draw considerable attention for gas transport and separation in recent years [115,[116][117][118][119][120].The laminar GO membrane can be fabricated by assembling GO nanosheets through filtration, spincoating, and other methods [113].GO nanosheet exhibits atomic thickness with lateral dimension reaching tens of micrometers, and contains rich oxygen functional groups on the edge and basal planes, such as carboxyl, epoxy, and hydroxyl groups (Figure 8(b)) [113,114,121].These groups play a crucial role in maintaining the relatively large interlayer spacing distance d: in the dry state, typical d between tightly assembled nanosheets is about 1 nm, and the decreased d of about 0.4 nm was observed for the reduced GO membrane [115].
In 2012, Nair et al. first reported unimpeded water transport through 0.1-10 μm-thick GO membranes, which were instead impermeable to many small-molecule gases, including He (Figure 8(c)) [115].One year later, Kim et al. and Li et al. observed excellent gas selectivity for few-layered GO (Figure 8(d) and (e)) [116,117], showing promising prospects in applications such as carbon capture and hydrogen purification.The noteworthy selectivity was attributed to nanopores within GO flakes rather than the interlayer spacing  [112].(b) Schematic of graphene oxide structure [114].(c) Permeability of water and other small molecules through GO membrane [115].(d and e) selective gas transport through few-layer GO membranes in comparison with other reported membranes [116,117].Black lines indicate the upper bound of polymeric membranes.(f) Schematic of gas permeation mechanism through graphene oxide nanoribbons (Gonr)/poly(ethylene oxide) (PEO) membrane [118].(g) Schematic of GO-brush membrane [119].The blue and red brushes represent the grafted agents on the top and bottom surface of GO, separately.(h) Schematic of the introduction of straight-through channels in GO membrane by ion irradiation [120].(i) Schematic of pore generation in a GO nanosheet via heating [116].[122].Kim et al. modulated the degree of interlocking of GO nanosheet by different stacking methods and found the prominent effect of interlocking on gas transport [116].Li et al. compared the gas permeance of 18 nm-thick GO membranes before and after the GO reduction and found no obvious change in gas permeance, suggesting that interlayer did not serve as the primary pathway [117].Therefore, gas transport can be regulated by stacking methods that result in different flow resistance of channel entrance.
In addition, gas flow can also be regulated by different spacing distances.For example, Ji et al. prepared polymer-hybridized GO membranes with intercalation of polymers into the interlayer channels of GO (Figure 8(f)) [118].The intercalated polymer could not only enlarge the interlayer distance from 8.83 Å to 10.4 Å and hence accelerate H 2 permeance (7108 Barrer; 1 Barrer = 1 × 10 −10 cm 3 (STP) cm/(cm 2 s cmHg)), but also impede CO 2 permeation due to the strong polymer-CO 2 interaction, leading to a H 2 /CO 2 selectivity of 10.8.The significance of chemical environment for gas transport manifested in this work has also been demonstrated by other researches.Zhou et al. introduced piperazine as a carrier-brush into the GO nanochannels with chemical bonding, which could facilitate CO 2 transport and hence resulted in a high CO 2 /N 2 selectivity of 680 with CO 2 permeance of 1020 GPU under wet condition (Figure 8(g)) [119].Notably, the presence of water in hydrophilic GO interlayer nanochannel would greatly hinder gas transport except CO 2 due to its high solubility, making GO membranes promising for application under wet conditions.Besides introduction of functional groups into GO interlayers, the intrinsic carboxylic acid groups of GO also provide adsorption site for CO 2 and impede CO 2 transport by strongly trapping it [116].
Moreover, gas transport can also be modulated by introducing nanopores on the basal planes.Yang et al. utilized swift heavy ion irradiation to introduce additional straightthrough channels to minimize transport resistance (Figure 8(h)), leading to a significantly increased H 2 permeance [120].The irradiation process also generated fresh oxygen functional groups around the newly created channels, which further reduced the interlayer distance of GO due to cross-linking between layers and thereby improved the H 2 / CO 2 selectivity.In addition, simple heat treatment was also utilized to create irreversible pores (Figure 8(i)), and could control the permeation and selectivity by various heating temperature and resulted pore density [116].
Attractive prospects of gas separation also appear in other lamellar nanosheets such as MXene [123][124][125], black phosphorene [126], and MoS 2 [127,128].MXene nanosheets with atomic thickness consist of transition metal carbides, nitrides, or carbonitrides [129].For lamellar stacked MXene membranes, the free spacing between face-to-face MXene nanosheets can be narrowed to 0.35 nm and there exist abundant functional groups on the channel surface (Figure 9(a)) [123].Ding et al. first demonstrated exceptional gas separation capabilities of lamellar MXene gas membranes, with H 2 permeability exceeding 2200 Barrer and selectivities of H 2 /CO 2 and H 2 /N 2 surpassing 160 and 90, respectively (Figure 9(b)) [123].These remarkable results arose from size exclusion and surface-functional groups-induced CO 2 adsorption [123].Shen et al. functionalized MXene layers with CO 2 -philic borate and polyethylenimine to convert the diffusion-controlled pristine MXene membranes into solution-controlled membranes, which selectively permeated CO 2 through enhanced CO 2 solubility (Figure 9(c)) [124].Besides MXenes, black phosphorene, a layered semiconducting allotrope of phosphorus, also shows attractive exploration.Liu et al. reported a novel black phosphorene membrane which showed H 2 permeance > 1000 GPU and H 2 /CO 2 selectivity > 100 for mixed gas measurement [126].In this study, the minimal distance between adjacent black phosphorene nanosheets was calculated to be 0.32 nm, right between the kinetic diameters of H 2 and CO 2 [126].DFT simulation further confirmed that the interlayer channels facilitated easy H 2 transport while effectively blocking larger gases, consistent with the experimental results [126].For the laminar MoS 2 membrane, Achari et al. achieved the regulation of gas transport by MoS 2 phase transition from 1T to 2H (Figure 9(f) and (g)) [127].When temperature increased from room temperature to 160°C, the proportion of 2H phase increased significantly from 28% to 91%, which tended to form few layer bundles (Figure 9(f)) [127].Consequently, the increased proportion of bundles led to a larger interlayer space and further increased gas permeability by about 30% (Figure 9(g)) [127].
channel heights in the range of 2.5-250 nm with angstrom-scale precision via controlling deposited tungsten film thickness.Measured gas flow under various Knudsen numbers (0.2-20) showed excellent agreement with theoretical predictions [133].
Recently, the fabrication of slit channels with heights down to several angstroms has been achieved through the van der Waals assembly of 2D materials [21,134].As a few layers of 2D materials are used as spacers between two crystals, the height resolution can be down to the thickness of 2D materials, while the micrometer-sized width and length of the channel are determined by electron beam lithography.Since then, the as-prepared angstrom-scale slit enables the exploration of gas transport at the atomic level, and many intriguing phenomena have appeared at this scale.For example, Keerthi et al. demonstrated ballistic molecular transport through atomically smooth graphene and h-BN slits, while for MoS 2 slits, instead, the gas transport followed the traditional Knudsen theory and showed two orders of magnitude lower flow rates than graphene and h-BN slits (Figure 10(d)) [21].Such difference highlighted the significant influence of fine details of the atomic landscape on gas reflection behaviors (Figure 10(e) and (f)) [21].The MoS 2 surface exhibited relatively strong corrugations (~0.1 nm), which could be 'seen' by He atoms and thus contributed to diffusive reflections in gas-wall collisions and friction in gas flow [21,22].In contrast, the much flatter surfaces of graphene and h-BN suggested more specular reflections and minimal loss of momentum during transport [21,22].In addition, despite their nearly identical kinetic diameter, shape, and thermodynamic properties, deuterium exhibited a slower flow rate compared to hydrogen through graphene channels [21].This finding indicated the remarkable contribution of matter-wave effects to reflection behaviors, where heavier atoms (deuterium) displayed more diffusive reflection due to their shorter de Brogile wavelength and more sensitivity to atomic landscape [21].However, when the channel height increased to 4-8 nm, the surface was no longer atomically smooth due to hydrocarbon contamination and ballistic transport transitioned to diffusive transport [21].Furthermore, the above investigations concentrated on He, H 2 , and D 2 , with consideration given only to collision interactions between gas molecules and the wall.Exploring the transport for CO 2 , H 2 S, and other gases would provide intriguing insights into the impact of molecular configurations and adsorption/desorption behaviors on ballistic Knudsen transport.

Smart gas membranes
In nature, the adaption of cells to external environment is indispensable for the survival and execution of biological processes in living organisms.For instance, in the drought conditions, land plants have two main strategies to maintain water balance [135,136].One is the increase of osmotic pressure in the cell to prevent further water loss, which can be achieved by the production of osmotically active compounds, such as sugars [135,136].Another is the reduction of water permeation through the plasma membrane aquaporins by altering the modification status of proteins (e.g.reduced phosphorylation) [135,136].Drawing inspiration from the self-regulation mechanisms observed in bio-channels, a number of smart gas membranes have been designed to modulate both permeability and selectivity during gas transport [137][138][139][140], which is highly desired in efficient gas separation.The stimuli-responsive gas transport mostly relies on conformational changes of membrane components triggered by external factors, including light, temperature, electric field, and other stimuli.In this section, we will discuss these aspects and how they work.

Light-responsive membranes
Recently, light has attracted extensive interest in smart membranes owing to its environmentally friendly nature, easy accessibility and manipulation, as well as controllable irradiation time and wavelength.The light-responsive gas membranes are founded upon photoisomerization, photothermal effect, and photoelectric effect.
The process of photoisomerization involves the conversion between isomers by light.Azobenzene is a widely employed photoisomerization-induced regulator of gas permeation, renowned for its reversible change of cis/trans configurations upon exposure to UV/VIS light (Figure 11(a)) [141][142][143][144][145][146][147].The transition from trans to cis results in a decrease in molecular size from 0.9 to 0.55 nm and an increase in dipole moment from 0.5 to 3.1 Debye [141].Therefore, the proposed strategy involves the integration of azobenzene molecules as side groups or linkers within host materials, facilitating control over gas adsorption [141][142][143][144][145] and pore size [141,146].Wang et al. reported dipole moment-dependent gas adsorption of azobenzene-containing MOFs of the type Cu 2 (BDC) 2 (AzoBipyB), where UV-induced cis structure behaved more gas adsorption and the disparity in gas uptake amounts between two structures increased with the increment of gas dipole moment (Figure 11(b)) [143].This can be explained by the dipole-dipole interaction between azobenzene and gas molecules, while molecular size has no impact [143].Subsequently, Wang et al. firstly reported photo-switchable MOF [Cu 2 (AzoBPDC) 2 (AzoBiPyB)] membrane (Figure 11(c)), which exhibited stepless and The ratio (m cis :m trans ) and normalized ratio ((m cis :m trans ) normalized ) of gas uptake amounts by Cu 2 (BDC) 2 (AzoBipyB) in the cis and trans states versus the dipole moment of gas molecules.The dotted line shows the predicted relationship of ratio and dipole moment by molecular dipole-dipole (keesom) interaction [143].(c) Schematic of reversible transition of Cu 2 (AzoBPDC) 2 (AzoBiPyB) configurations upon exposure to UV/VIS light [144].(d) The regulation of H 2 :CO 2 separation factor via extending UV exposure time [144].(e) Photoswitchable membrane separation factors [144].(f) Photoswitchable gas permeances at trans-cis transition of two kinds of zeolitic membranes [141].(g) Schematic of control of CO 2 adsorption by azobenzene photoisomerization [145].(h) Infrared thermal image of a Zr-Fc MOF supported ionic liquid membrane and its PMMA holder under a simulated sunlight irradiation (0.3 W cm −2 ).Inset is the related schematic [148].(i) Photoswitchable permeance and selectivity of CO 2 and H 2 with and without the simulated sunlight irradiation [148].(j) Schematic of photoinduced switch of surface charge [149].(k) The permeance decrease upon irradiation versus gas polarizability [149].
reversible adjustment in separation factors of H 2 /CO 2 (between 3 and 8) and N 2 / CO 2 (between 5.5 and 8.5) (Figure 11(d) and (e)) [144].During trans/cis transitions, the permeance of N 2 and H 2 remained almost unchanged, while only CO 2 permeance exhibited a significant change (Figure 11(e)) [144].This observation suggested that dipole-dipole interactions, rather than steric hindrance, played a dominant role in the switching of permeance.Specifically, the enhanced attractive interaction between cis azobenzene's dipole moment and CO 2 's quadrupole moment was expected to decelerate carbon dioxide diffusion after trans-to-cis transition [144].However, this switching affected negligibly on hydrogen permeation [144].In addition to MOF-based materials, zeolite-azobenzene membranes and their photoresponse were also investigated [141].After trans-to-cis transition, almost all measured gases (e.g.CO 2 , N 2 , CH 4 , and SF 6 ) exhibited obviously decreased permeance (Figure 11(f)) [141].Both gas adsorption and pore size were found to influence the permeance, which was also predicted by Monte Carlo simulations [141].Another effective way to regulate gas adsorption is by the interaction between adsorption sites and azobenzene molecules (Figure 11(g)).
In this process, photoisomerization changes the surface electrostatic potential of materials, which then modifies the adsorption behavior [142,145,].
The potential of photothermal and photoelectric effects in smart gas membranes has been demonstrated [148,149].Deng et al. employed Zr-Fc MOF nanosheets as efficient photothermal agents to convert solar energy into heat and enhance gas transport (Figure 11(h)) [148].Under a simulated sunlight irradiation of 0.3 W cm −2 , the permeance of CO 2 and H 2 increased by 35% and 45%, respectively, resulting in a slight decrease in CO 2 /H 2 selectivity (Figure 9(i)).A recent research utilized photoelectric effects to achieve faster response times compared with the switching event involving conformational changes [149].By exploiting the photo-induced surface charge of pCN and additional gas-charge interactions, polymeric carbon nitride (pCN) was coated on AAO membranes (with the channel diameter of tens of nanometers) as a functional layer for tunable gas selectivity (Figure 11(j)).Increasing the light power level led to decreased permeance for all gases due to enhanced gas-surface interactions, with the highest decrease observed for CO 2 attributed to its highest polarizability (Figure 11(k)) [149].However, due to the large nanochannel diameter, the influence of surface diffusion on total permeance was attenuated by Knudsen flow.Thus, for the optimal utilization of photoelectric effects, structures with dimensions in the range of several nanometers or angstroms are preferable, wherein gas transport is dominated by surface adsorption or molecular interactioninduced energy barrier.

Temperature-responsive membranes
Self-regulation in response to temperature changes is a prevalent and vital phenomenon in the natural world.For example, cactus survives temperature changes by regulating the rate of water transpiration through the opening or closing of adaptive stomata [150].Consequently, the development of artificial thermo-responsive membranes is of significance for the advancement of biomimetic nanofluids and their subsequent applications.Current studies on temperature-responsive gas membranes are based on adaptive channel sizes for gas transport [151][152][153].
Wang et al. explored temperature-responsive gas flow through 2D MAMS-1 (Mesh Adjustable Molecular Sieve) (Figure 12(a)) [152].For a 40-nm-thickness membrane, when temperature ranged from 20°C to 120°C, H 2 permeance initially increased from 20°C to 40°C but unexpectedly started to drop at 60°C.However, CO 2 measurements did not show any reversible temperature-related permeance fluctuation.This phenomenon can be attributed to the temperature-regulated interlayer distance in MAMS-1 and intensive thermal vibration of the tert-butyl group in the interface (Figure 12(b)).At room temperature, tert-butyl groups exhibit unrestricted rotational motion to allow H 2 molecules to pass through.But at a higher temperature, the movement of tert-butyl groups will be restricted as a result of decreased interlayer distance and steric impedance, causing a much higher transport barrier.Another research utilized crystallinity of liquid crystalline polymers (LCP) to modulate O 2 permeability (Figure 12(c)) [151].When LCP was heated above clearing temperature, LCP membrane was switched from a highly crystalline smectic phase ("close" state) to an amorphous isotropic phase ("open" state), resulting in a ten-fold increase in oxygen transport.
Tan et al. achieved continuous and reversible tuning of the effective aperture size of a highly robust Al-MOF via grafting thermally responsive methoxy groups (Figure 12(d)) [153].The aperture size ranged from 0.36 to 0.52 nm with the resolution of 0.01-0.05nm [153].As a result, this smart MOF enabled highly efficient separation for various gas mixtures (e.g.N 2 /CH 4 , C 2 H 4 /C 3 H 6 , and C 3 H 6 /C 3 H 8 ) at different temperature.Notably, this membrane exhibited excellent selectivity for C 3 H 6 /C 3 H 8 at room temperature (Figure 12(d)).In addition, Huang et al. reviewed other temperature-responsive materials [137], which have great potential in smart membranes.

Electrical-field-responsive membranes
Electrical-field-responsive membranes that deform or redistribute components in response to an electric field have garnered significant attention [154][155][156][157][158], due to the extensive utilization of electrical energy.
One approach for the fabrication of electrical-field-responsive membranes is integrating responsive materials into nanochannels [154][155][156][157]. Recently, poly(vinylidene fluoride) (PVDF), particularly β-phase PVDF, has garnered great attention as a responsive material due to its notable piezoelectric properties and affinity toward CO 2 [154,155].Widakdo et al. investigated the electrical-field-responsive transport through PVDF-graphene composite membranes (Figure 13(a)) [154,155].Upon application of an electrical field, the permeability of CO 2 increased from 214 to 492 × 10 −2 Barrer while there was no significant change observed for O 2 and N 2 (Figure 13(b)) [154].This phenomenon can be explained by two factors: alteration in gas pathway from PVDF-graphene interface to the free volume of β-PVDF plus more attraction and adsorption of CO 2 .Hybrid membranes with nanoconfined ionic liquid (IL) also exhibited effective electrical field-controlled gas permeance (Figure 13(c)) [156,157].In GO-supported IL membrane (GO-SILM), when a positive electrical field was applied, the CO 2 permeance increased from 117 to 260 GPU while selectivity values for CO 2 /H 2 , CO 2 /CH 4 , and CO 2 /N 2 enhanced by 2, 4, and 5 times, respectively, compared to those without an electrical field (Figure 13(d)) [157].This regulation was attributed to the redistribution effects on anions and cations within the IL under an electrical field (Figure 13(c)), which impacted gas solubility and diffusivity within the IL especially for CO 2 .Furthermore, it was discovered that the synergistic effect between solubility and diffusivity led to asymmetric CO 2 permeance under positive versus negative field.
Tunable gas transport by electrical field can also be realized in MOF ZIF-8 [158].ZIFs represent a category of soft MOF crystals where linker rotation matters, enabling their pores to accommodate larger molecules beyond the size expected from structural data, which impedes sharp molecular sieving [159].Knebel et al. applied an external electric field of 500 V mm −1 on ZIF-8 membranes, inducing crystal transitions from cubic to more restricted monoclinic and triclinic polymorphs [158].Although the pore size in these polymorphs is larger (0.36 nm) than in the cubic structure (0.34 nm), the restricted linker resulted in reduced gas flow (approximately 70%) and enhanced gas selectivity (from 6 to 8) (Figure 13(e) and (f)).

Other stimuli-responsive membranes
In addition to the aforementioned smart membranes, there exist various other potential types of stimuli-responsive membranes that merit further investigation, encompassing pressure-responsive and magnetically responsive membranes.The gas pressure-responsive membranes were investigated by Ying et al., where functional MOF nanosheets (MONs) were confined between GO nanosheets (Figure 14(a)) [160].It was found that as the CO 2 partial pressure increased from 0.1 to 1.4 bar (with a constant total pressure of 2.0 bar), there was a sudden jump in CO 2 permeance at approximately 0.5 bar, with values increasing from 173.8 to 1076.7 GPU for the CO 2 /N 2 mixture and from 188 to 1051 GPU for the CO 2 /CH 4 mixture (Figure 14(b)).However, the increase in N 2 and CH 4 was significantly lower, leading to increased permselectivity for CO 2 /N 2 and CO 2 /CH 4 .This intriguing phenomenon can be attributed to the phase transition of MOF nanosheets induced solely by CO 2 adsorption.Notably, hysteresis loops were observed in terms of CO 2 permeance due to the stabilizing effect of adsorbed CO 2 molecules on the "open" form.Takasaki et al. utilized stress-induced martensitic transition in a microporous single-crystal material, [Cu(II) 2 (bza) 4 (pyz)] n (bza: benzoate; pyz: pyrazine), to regulate gas flow [161].As shown in Figure 14(c), gases permeated the crystal surface of {100} α but were effectively blocked on {001} α .Upon applying controllable stress on the crystal surface with a glass needle, a stress-induced daughter (α') phase grew within the mother (α) phase, and the crystal surfaces of daughter phase exhibited distinct gas permeation behaviors.Consequently, a reversible and rapid gas flow switch can be achieved by manipulating the applied stress on the crystal (Figure 14(d)).
Several studies have demonstrated the magnetically responsive gas transport through attaching magnetic nanoparticles or materials into membranes [162,163].Raveshiyan et al. introduced carbonyl iron powders (CIPs) into polysulfone (PSf) membranes to manipulate O 2 /N 2 separation through different magnetic gas-channel interactions (Figure 14(e)) [162].For neat PSf membrane, when applying magnetic field from 0 to 570 mT, due to the paramagnetic property of O 2 and diamagnetic property of N 2 , external magnetic field accelerated O 2 transport but slowed down N 2 transport, leading to increased O 2 /N 2 selectivity from 5.27 to 6.56.It is noted that the addition of CIPs caused reduced selectivity from 4.75 to 3.26, arising from the formation of nonselective channels.However, under the influence of a magnetic field, these channels became magnetic and acted selectivity owing to different magnetic interactions of O 2 and N 2 .For instance, for the PSf membrane with 10 wt.% CIP loading, when subjected to a magnetic field strength of 570 mT, the membrane exhibited increase in both the O 2 permeability and O 2 /N 2 selectivity by 436% and 41% respectively compared with neat PSf membrane without magnetic field.Similar result has also been reported by Rybak et al. [163].

Conclusion and outlook
Investigating gas transport under (sub)nano scale plays vital roles for understanding various physiological activities in biological gas channels, and imparts the ability to tailor the transport process at the smallest scales.Based on this, this review summarizes significant progress in the field of nanoconfined gas transport, as well as the remarkable advancement in the fabrication of low-dimensional materials-based nanoconfined spaces.We start with the mechanisms of confined gas transport as the scale progressively reduces.Subsequently, we discuss gas transport properties of diverse low-dimensional materials, with a focus on the influence of specific structures on intriguing phenomena.Inherent from their structural characteristics, 0D nanopores in two-dimensional materials are supposed to offer the highest permeability theoretically due to the atomic thickness of the transport pathway, while in comparison, 1D nanotubes, 2D nanochannels, and nanopores in MOFs, COFs and zeolites possess more definite sizes and more interaction sites for gas molecules that have the potential for a higher selectivity beyond molecular sieving.Finally, we categorize smart gas membranes according to various environmental stimulations.With the rapid development of low-dimensional materials and nanofluidic gas transport, new opportunities and challenges arise as the next frontier in this field: (1) The mechanism of confined transport requires further refinement.As previously mentioned, the coupling effects of different pathways on the transport properties remain incompletely understood.Additionally, for activated transport in extreme crowding space, the impact of complex molecular interactions and entropic effects remains ambiguous.Although theoretical studies have made significant progress in understanding mechanisms in idealized structures, experimental explorations are still in its infancy.Fortunately, the past few decades have witnessed a dramatic change in advanced characterization tools, such as aberration corrected TEM, and single defect spectroscopy, which offers opportunities to reveal the structure of confined molecules as well as their interactions with confined spaces.Further interdisciplinary cooperation between different disciplines such as fluid mechanics, materials, chemistry, and computer science is needed to uncover the underlying mechanisms of confined transport.(2) Further advancements in fabrication techniques are needed to meet demands of scientific research and practical application by achieving controllable and uniform structure size with desired density.For instance, while nanoporous graphene has achieved controllable pore sizes with sub-nanometer resolution in single pore system, its log-normal pore size distribution limits gas selectivity when expanding to multi-pore system for practical applications.Furthermore, precise modifications of the formed nanopore are hampered currently, as a result of the difficulties to accurately control functionalization sites and rates of pore edge under extreme confinement, which present a promising avenue for future research.(3) For smart gas membranes, anti-interference properties, responsive time, and other factors should be considered for practical applications.First, the investigation of responsive behaviors of smart membranes primarily focuses on a single variable in laboratory, which overlooks the interference of other environmental factors.For instance, azobenzene, a photoresponsive molecule, can transform from cis to trans configuration by heating [164].Besides, a large part of regulations relies on conformational changes and usually takes several minutes or even hours, limiting their efficiency in applications.
Despite the above challenges, low-dimensional materials-based gas membranes exhibit fascinating transport behaviors, and thereby pave a novel pathway for future applications, such as high-efficient separation, energy reservation, precision chemical sensing, and medical physiology.

Figure 1 .
Figure 1.Mechanism of gas transport.(a) Length-scale dependence of gas transport mechanism.Kn, Knudsen number; l 0 , characteristic dimension of the structure; λ, gas mean free path; D k , gas kinetic diameter; Q, flow rate; μ, fluid viscosity; m, the molecular mass; ∆H ads , heat of adsorption; E, interaction energy (potential energy) between a single gas molecule and an aperture; E a , energy barrier of translocation; ∆S, the entropy difference; ε, adsorption potential depth; E 0 , zero-point energy; σ, molecular hard core radius; r, pore radius.(b) A schematic of gas flow through a channel and generalized flow resistances.R E , resistance of effusion; R S,A , resistance of surface diffusion to the aperture; R a , resistance of activated transport; R K , resistance of Knudsen diffusion; R S,C , resistance of surface diffusion in the channel.

Figure 2 .
Figure 2. Impermeability of pristine graphene lattice and molecule sieving of angstrom-sized pores in graphene.(a) Schematic of a graphene sealed silica microcavity (top) and atomic force microscope(AFM) image of multilayer graphene with higher gas pressure in the microcavity (bottom)[45].Inset is the optical image of a suspended single-layer graphene.(b) Deflection-time curves of 12 different single-layer graphene nanoballoon caused by permeation of H atoms in molecular hydrogen[46].Insets are representative changes of deflection with time taken by AFM (top) and illustration of the flipping process of hydrogen atoms permeation (bottom).(c) Measured gas leak rates of bi-layer graphene before and after etching.Inset is schematic of molecule sieving of a porous graphene[48].

Figure 3 .
Figure 3. Gas transport through atomically thin materials with multiple pores and the influence of functional groups on transport.(a) Comparison of the H 2 /CH 4 separation performance from the singleor few-pores and multi-pores membranes[26,48,51,[53][54][55].The black line shows the upper bound of 1-μm-thick polymer membrane[38].Considering that permeance is not applicable for few-pores system, the horizontal dash line is used to represent selectivity with green dash line for ref. 41 and blue dash line for ref. 24.(b) Aberration-corrected high-resolution transmission electron microscopy (AC-HRTEM) images of ozone-induced graphene nanopores and corresponding lattice-fitted structures (dots indicate missing carbon atoms) [53].(c) Distribution of the number of missing carbon atoms in the graphene nanopores based on the AC-HRTEM (top) and the reaction kinetics model (bottom) [53].(d) N 2 permeance through apertures with different diameters (red circles) and the predicted permeance by modified Sampson's model and effusion model (dash lines)[57].Inset is the scanning electron microscope (SEM) image of array of 50-nm-wide apertures in the suspended graphene (scale bar, 500 nm).(e) Comparison of normalized permeance of irradiated samples and controls, with the Knudsen predictions[58].Inset is aberration-corrected high-angle annular dark-field (AC-HAADF) image of ion-irradiated monolayer WS 2 flake and bright spots indicate W atoms. (f) CO 2 per-porepermeance of pores with different functionalization[59].Insets are schematics of graphene pores with oxygen edge atoms (up) and hydrogen edge atoms (down).The red, white, and dark gray balls are oxygen, hydrogen, and carbon separately.
Figure 3. Gas transport through atomically thin materials with multiple pores and the influence of functional groups on transport.(a) Comparison of the H 2 /CH 4 separation performance from the singleor few-pores and multi-pores membranes[26,48,51,[53][54][55].The black line shows the upper bound of 1-μm-thick polymer membrane[38].Considering that permeance is not applicable for few-pores system, the horizontal dash line is used to represent selectivity with green dash line for ref. 41 and blue dash line for ref. 24.(b) Aberration-corrected high-resolution transmission electron microscopy (AC-HRTEM) images of ozone-induced graphene nanopores and corresponding lattice-fitted structures (dots indicate missing carbon atoms) [53].(c) Distribution of the number of missing carbon atoms in the graphene nanopores based on the AC-HRTEM (top) and the reaction kinetics model (bottom) [53].(d) N 2 permeance through apertures with different diameters (red circles) and the predicted permeance by modified Sampson's model and effusion model (dash lines)[57].Inset is the scanning electron microscope (SEM) image of array of 50-nm-wide apertures in the suspended graphene (scale bar, 500 nm).(e) Comparison of normalized permeance of irradiated samples and controls, with the Knudsen predictions[58].Inset is aberration-corrected high-angle annular dark-field (AC-HAADF) image of ion-irradiated monolayer WS 2 flake and bright spots indicate W atoms. (f) CO 2 per-porepermeance of pores with different functionalization[59].Insets are schematics of graphene pores with oxygen edge atoms (up) and hydrogen edge atoms (down).The red, white, and dark gray balls are oxygen, hydrogen, and carbon separately.

Figure 4 .
Figure 4. Pore structures and gas separation properties of MOFs.(a) The single crystal structure with hierarchical pores and sod topology of a representative MOF, ZIF-8, depicted as a stick diagram (top) and as a tiling (center) [62].The largest cage of ZIF-8 (bottom) is shown with ZnN 4 tetrahedra in blue.H atoms are omitted for clarity.(b) Structural variations of flexible MOFs, including breathing, swelling and linker rotation[39].(c) Corrected diffusivities of ZIF-8 for various probe molecules at 35°C (squares represent the measured diffusivities from membrane permeation and circles represent the estimated diffusivities from kinetic uptake rate measurements)[63].Dash line: pore size of ZIF-8 determined by XRD.Shadow: effective pore size range of ZIF-8.(d) Top:: reduction of effective ZIF-8 membrane thickness by postsynthetic linker exchange with 2-imidazolecarboxaldehyde[65].Bottom: corresponding permeance of propylene and propane[65].(e) Isosteric heats of adsorption and permeances at 288 K of H 2 , CH 4 , N 2 and CO 2 for NH 2 -MIL-53(Al)[28].

Figure 5 .
Figure 5. Stacking of 2D COF nanosheets for narrowed pore size and improved gas separation performances.(a) Schematic of compact staggered stacking of two ionic covalent organic nanosheets with different pore sizes and opposite charges [79].(b) Improved H 2 /CO 2 separation factor of hybrid TpEBr@TpPa-SO 3 Na membrane compared to the individual COF components [79].(c) Schematic of preparation of COF membranes by assembling ionic COF nanosheets with PEI [82].(d) Schematic of facilitated CO 2 transport in the presence of amine groups [82].

Figure 6 .
Figure 6.Structures and gas transport properties of zeolites, bilayer silica and graphdiyne.(a) Permeability of gases and water through NaA zeolite membrane (solid red symbols) compared with results from other materials (open symbols) [31].(b) Pore structure of NaA zeolite with three Na + sites in the dehydrated crystal structure and DFT simulation results for the passage of H 2 O, CO 2 and H 2 molecules entering zeolitic channels of NaA [31].(c) Top: gas permeances of various gases through zeolite FAU membranes prepared on Al 2 O 3 substrate with and without APTES (3-aminopropyltriethoxysilane) modification[87].Bottom: H 2 /CO 2 separation performances of FAU membrane versus temperature[87].(d) Schematics of gas selectivity of bilayer silica (top) and atomic structure of bilayer silica (bottom)[88].(e) Permeances of tested gases through vitreous bilayer silica[88].(f) Schematic of monolayer graphdiyne's structure (top) and TEM image of quasi-2D graphdiyne layer[89].(g) Gas permeance through graphdiyne layer[89].Blue line shows the best fit by Knudsen dependence using data for light gases from3 He to Ne.

Figure 8 .
Figure 8. Lamellar GO membranes and their gas transport properties.(a) Schematic of lamellar nanosheet-based membranes for molecular separation[112].(b) Schematic of graphene oxide structure[114].(c) Permeability of water and other small molecules through GO membrane[115].(d and e) selective gas transport through few-layer GO membranes in comparison with other reported membranes[116,117].Black lines indicate the upper bound of polymeric membranes.(f) Schematic of gas permeation mechanism through graphene oxide nanoribbons (Gonr)/poly(ethylene oxide) (PEO) membrane[118].(g) Schematic of GO-brush membrane[119].The blue and red brushes represent the grafted agents on the top and bottom surface of GO, separately.(h) Schematic of the introduction of straight-through channels in GO membrane by ion irradiation[120].(i) Schematic of pore generation in a GO nanosheet via heating[116].

Figure 10 .
Figure 10.2D slit channels and their gas transport properties.(a) Schematic of 2-nm-height channels fabricated by anodic bonding [131].(b) Schematic of 2D slit channels in ref [133].μCh in/out and nCh represent micrometer-sized inflow/outflow channel and nanometer-sized channel that dominates gas transport, respectively.(c) TEM cross-section images of channels of different heights [133].(d) Comparison of He permeation through slit nanochannels (1.7 nm height) with walls fabricated from different materials.The Knudsen diffusion-predicted flow is shown by the solid black line.Inset is the measurement set-up with the arrow indicating the He flow direction [21].(e) Dependence of He transport on channel length [21].Insets are diffusive scattering on MoS 2 surface (top) and specular scattering on graphite surface (bottom).(f) Intrinsic roughness of atomically flat surfaces of graphene and MoS 2 by DFT [21].The grey scale represents the electron density near graphene and MoS 2 surfaces and red curves indicate the depth accessible for helium atoms with thermal energies.

Figure 11 .
Figure 11.Light-responsive membranes.(a) Schematic of reversible transition of azobenzene cis/trans configurations upon exposure to UV/VIS light [141].(b)The ratio (m cis :m trans ) and normalized ratio ((m cis :m trans ) normalized ) of gas uptake amounts by Cu 2 (BDC) 2 (AzoBipyB) in the cis and trans states versus the dipole moment of gas molecules.The dotted line shows the predicted relationship of ratio and dipole moment by molecular dipole-dipole (keesom) interaction[143].(c) Schematic of reversible transition of Cu 2 (AzoBPDC) 2 (AzoBiPyB) configurations upon exposure to UV/VIS light[144].(d) The regulation of H 2 :CO 2 separation factor via extending UV exposure time[144].(e) Photoswitchable membrane separation factors[144].(f) Photoswitchable gas permeances at trans-cis transition of two kinds of zeolitic membranes[141].(g) Schematic of control of CO 2 adsorption by azobenzene photoisomerization[145]. (h) Infrared thermal image of a Zr-Fc MOF supported ionic liquid membrane and its PMMA holder under a simulated sunlight irradiation (0.3 W cm −2 ).Inset is the related schematic[148].(i) Photoswitchable permeance and selectivity of CO 2 and H 2 with and without the simulated sunlight irradiation[148].(j) Schematic of photoinduced switch of surface charge[149].(k) The permeance decrease upon irradiation versus gas polarizability[149].

Figure 12 .
Figure 12.Temperature-responsive membranes.(a) Reversible thermal-regulated gas permeance and H 2 /CO 2 separation factors of the 40-nm MAMS-1 membrane [152].(b) Schematic of the thermally responsive change of interlayer distance in MAMS-1 and its influence on the rotation of tert-butyl groups [152].(c) Schematic of phase-switching upon temperature change in LCP polymer film and its influence on gas permeability [151].(d) Schematic of smart molecular gate in MOF (left) and C 3 H 6 / C 3 H 8 selectivity for the equimolar mixture at 248-323 K (right) [153].

Figure 14 .
Figure 14.Smart gas membranes responsive to the stimulation of pressure and magnetic field.(a) Schematic of CO 2 pressure-responsive membrane[160].(b) Two-cycle CO 2 permeance, N 2 permeance, and CO 2 /N 2 perm-selectivity of MON@GO membranes as a function of CO 2 partial pressure[160].(c) Schematic of gas permeation through single-crystal membrane (top) and the influence of crystal orientations on gas permeation[161].(d) Amount of permeated CO 2 and estimated permeability through the crystal in H (blue line) and V (red line) directions[161].Inset is the schematic of gas flow switch under the two directions.(e) Schematic of the magnetically responsive gas separation module (top) and separation factors of O 2 /N 2 of PSf membrane under different loading of CIP and magnetic field[162].