Selective Permeation Through One-Atom-Thick Nanoporous Carbon

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Selective Permeation Through One-Atom-Thick Nanoporous Carbon Membranes: Theory Reveals Excellent Design Strategies! Cheriyacheruvakkara Owais, Anto James, Chris John, Rama Dhali, and Rotti Srinivasamurthy Swathi J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b01117 • Publication Date (Web): 12 Apr 2018 Downloaded from http://pubs.acs.org on April 12, 2018

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The Journal of Physical Chemistry

Selective Permeation Through One-atom-thick Nanoporous Carbon Membranes: Theory Reveals Excellent Design Strategies! Cheriyacheruvakkara Owais, Anto James, Chris John, Rama Dhali and Rotti Srinivasamurthy Swathi* School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram (IISER-TVM), Vithura, Thiruvananthapuram 695551, India Email: [email protected]

ABSTRACT

Research on the permeation of various species through one-atom-thick nanoporous carbon membranes has gained an unprecedented importance in the last decade, thanks to the development of numerous theoretical design strategies for a plethora of applications ranging from gas separation, water desalination, isotope separation, and chiral separation, to DNA sequencing. Although some of the recent experiments have demonstrated successful performance of such carbon membranes in sieving, many of the suggested applications are yet to be realized in experiments. This review aims to draw the attention of the theoretical as well as the experimental researchers working on two-dimensional carbon materials towards the recent theoretical developments probing the permeation of various species such as atoms, ions, small molecules and biopolymers like DNA through carbon frameworks like graphynes, 1 Environment ACS Paragon Plus

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graphdiyne, graphenylenes and various forms of nanoporous graphene, including graphene crown ethers. The underlying guiding principles toward the design of carbon-based membranes for nanofiltration are established using estimates of the adsorption energies, barrier heights for permeation, rates of permeation, selectivities, permeances, etc. The crucial roles of tunneling, temperature effects, chemical functionalities and dynamical aspects of the nanopores are also highlighted, paving the way to a comprehensive description of the theoretical design strategies for tailoring the applicability of novel nanoporous carbon membranes in sieving and related aspects.

INTRODUCTION: DIVERSITY OF ONE-ATOM-THICK NANOPOROUS CARBON MEMBRANES Gas separation involves the separation of one or more desired gases from a mixture. The major processes used for gas separation are (i) absorption, (ii) adsorption, (iii) cryogenic distillation, and (iv) membrane separation.1 Absorption is a widely used process for gas separation, wherein one of the components of a gaseous mixture is contacted with a liquid in which it is preferentially soluble. Absorption can be purely physical or chemical or a combination of both. Since all solvents cannot be recycled back, this technique is not environment friendly. Another commonly employed industrial process for gas separation is adsorption. Selective adhesion of a component of a mixture onto the surface of a solid adsorbent is utilized to separate the gaseous component from the mixture. This is usually a physical process and is based on an equilibrium mechanism. In pressure swing adsorption, the desired gas species is desorbed from the adsorbent by lowering the partial pressure and the process is often carried out at high temperatures, resulting in reduced efficiency and sorbent selectivity. The third separation process, cryogenic distillation is employed at very low temperatures. This method uses the difference in the boiling points of the individual components of a mixture for its separation,

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requires a phase change and is therefore a very energy intensive process. Unlike the techniques discussed above, membrane separation is an energy efficient process that does not require extreme conditions and hence has become a topic of growing interest in the last few years. Membranes act as thin barriers that selectively transport various species through them depending on their permeability.2,3 Proper choice of a membrane material is crucial, as it enables control of the permeability and selectivity of a given species. Polymeric membranes are generally used for the bulk separation of gases. They are further classified into glassy and rubbery membranes.4,5 Glassy membranes are rigid with low permeability but high selectivity, whereas rubbery polymers are flexible with high permeability but low selectivity. Polymer membranes cannot withstand high temperature and extreme chemical environments and hence zeolites, silica and carbon-based membranes, which can withstand harsh conditions have evolved as alternatives. Among these, carbon membranes are especially studied in recent times because of their high selectivity, permeability and mechanical stability in aggressive conditions. Graphene, a two-dimensional (2D) one-atom-thick sheet of sp2 hybridised carbons was first synthesized by Geim and Novoselov and has ever since been extensively studied both theoretically and experimentally, because of its unique thermal, mechanical, electrical, electronic and optical properties, most of which are the result of long-range conjugation across the 2D framework.6 Over the last decade, numerous applications have evolved out of this wonder material made of carbon. With the exception of proton, graphene is impermeable to even the smallest atom, helium, since the electron density of the conjugated rings repels any atom or molecule attempting to permeate through the rings.7 The quest for the utilization of the highly robust graphene membranes for sieving applications has resulted in the emergence of various forms of nanoporous graphene as excellent platforms for membrane technology. Since pristine graphene is impermeable to various species, introduction of pores in graphene has



evolved as a practical strategy for achieving the selective permeation of various species through the 2D membrane.8-10 Besides, other forms of one-atom-thick carbon membranes possessing nanoporous architectures have also emerged. Two major approaches for realizing one-atomthick nanoporous carbon membranes, namely top-down method and bottom-up method have evolved over time.11-13 In the top-down approach, nanopores are created in a graphene sheet by irradiation with electron beam or ion beam, oxidative etching, block copolymer lithography etc.14-20 The main drawback of such top-down approaches is the difficulty in controlling the pore size distribution and the pore densities. Therefore, bottom-up approaches have emerged, wherein chemical synthesis of 2D membranes with well defined, regularly spaced intrinsic pores is attempted. The first successful synthesis of such a membrane via bottom-up approach was reported by Bieri et al. wherein a 2D polymeric network of uniform single-atom wide pores was synthesized using metal-assisted coupling of hexaiodo-substituted cyclohexa-mphenylene.21 By replacing the biphenyl-like bonding in the porous graphene (PG) synthesized by Bieri et al. with one, two or three stilbene-like groups (PG-ES1, PG-ES2 and PG-ES3, respectively) along the hexagonal directions, further variation in pore size was proposed. A study by Brockway et al. revealed that PG-ES1 has a higher permeance than PG and can be used for He separation from natural gas. PG-ES1 was also shown to have high selectivity and permeance for CO2, making it a promising membrane for CO2 separation from N2 and CH4.22 Guo et al. reported a new interesting class of chemically functionalized nanoporous graphene by embedding crown ethers in graphene frameworks.23 A series of crown ether architectures were embedded in graphene and a detailed experimental characterization of the nanopores was reported. Following this, Rohini and co-workers used such graphene crown ethers (GCEs) for ion separation by considering a set of GCEs with oxygen and nitrogen atoms as the heteroatoms.24 Alkali metal ions were shown to bind better to azacrown-based nanopores, rather than conventional oxygen-based nanopores. Further, selectivity in ion transmission


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through the nanomeshes of GCEs was also demonstrated. Various other nanopore configurations for achieving selective permeation are designed by functionalizing the pore rims of nanoporous graphene (NPG) using -H, -F, -OH etc. (a)

- H/F/OH

(b)

(c)

- O/N

(d)

(e)

(f)

(g)

(h)

(i)



Figure 1. Representative structural models of various one-atom-thick carbon membranes: (a) graphene nanopores passivated using -H, -F, -OH functionalization, (b) oxygen and nitrogen-based graphene crown ethers, (c) stilbene-based nanoporous graphene, (d) γ-GY, (e) rhombic-GY, (f) graphenylene, (g) nitrogen and hydrogen passivated γ-GY, (h) defective graphene nanopores (STW defect and divacancy defect), and (i) graphene oxide.

Presence of structural defects in graphene affects its electronic and mechanical properties.25-27 Even though structural defects can adversely affect some of the applications of graphene, their presence is a boon for processes like sieving. Stone-Thrower-Wales (STW) defect is an important class of topological defects in sp2-bonded carbon materials,28 arising due to an inplane 90° rotation of two π-bonded carbon atoms with respect to their bond centre, thereby changing four hexagons of the lattice into two heptagons and two pentagons. Lalitha et al. showed that selectivity in He isotope separation can be achieved by employing an STWdefective graphene membrane, since the defect structure considerably reduces the tunneling barrier.29 The larger heptagonal pore in a graphene layer containing STW defect was also shown to significantly decrease the energy barrier for proton permeation by Zhang and coworkers.30 The success of NPG in membrane-based separation applications has also brought significant interest in tailoring the properties of other derivatives like graphene oxide (GO) for gas separation.31 GO is a graphene derivative obtained by oxidizing graphite with strong oxidizers and is extremely hydrophilic.32,33 Interestingly, recent results indicate that GO in the dry state does not allow He atoms to pass through, whereas GO membrane exposed to humidified atmosphere allows the permeation of He.10,34 This is attributed to the increase in interlayer separation of GO due to the intercalated water molecules. The transport of gases through GO is therefore strongly facilitated by the stacked water molecules present in between the sheets.


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The ability of carbon to exist in various states of hybridization (sp, sp2 and sp3) creates numerous opportunities for novel 2D nanoporous carbon materials. Baughman and co-workers first predicted the structures and properties of a new class of planar sheets containing sp and sp2 carbon atoms, referred to as graphynes (GYs).35 Graphynes are 2D allotropes of carbon obtained by introducing uniformly distributed acetylenic units to connect the hexagons of graphene in different ratios. The most well studied form of GYs is γ-GY which consists of acetylenic linkages between the hexagons in graphene leading to triangular pores. Depending on the number of acetylenic units introduced in between the hexagonal rings, γ-GYs are denoted as GY1, GY2, GY3, GY4 and so forth. Among the family of γ-GYs, graphdiyne (GDY) is usually considered separately because of its rather interesting properties. The term “graphdiyne” is a result of the introduction of two acetylenic (diacetylenic) linkages between the hexagons in graphene. Owing to the presence of uniformly distributed pores, GYs are considered as potential candidates for sieving. Therefore, bottom-up syntheses of various forms of GYs are attempted. Successful synthesis of GDY was reported in 2010 by employing the cross-coupling reaction of hexaethynyl benzene on a Cu surface.36 In a theoretical study, GDY was shown to exhibit remarkable performance for hydrogen purification from syngas since the pore size of GDY networks is in between the kinetic diameters of H2 and CH4/CO.37 In contrast, the triangular pore of GY1 is too small to allow H2 molecules to pass through. Sang et al. found that introducing modifications in the γ-GY frameworks by rupturing the shared base and substituting the acetylenic groups with nitrogen (γ-GYN) or hydrogen (γ-GYH) atoms can make it potentially useful for hydrogen purification.38 Rhombic-GY is another member of the GY family, with a pore size in between that of γ-GY and GDY. Rhombic-GY is generated by replacing two-thirds of the carbon-carbon bonds in graphene by acetylenic linkages, leading to rhombus-like pores. The optimal pore size of rhombic-GY results in high selectivity for hydrogen separation from CO and N2.39 Yet another interesting class of one-atom-thick carbon



allotropes are graphenylenes, which were first theoretically predicted by Balaban et al. and recently synthesized by Liu and co-workers.40,41 Theoretical calculations showed that graphenylenes possessing well defined pores of 3.2 Å diameter are ideal for the separation of H2 from CO, N2, CO2, and CH4.42 Nanoporous membranes consist of a solid matrix with randomly or uniformly distributed pores, which act as permeable barriers through which various species can pass.43 The separation ability of a membrane depends on various factors like pore size, pore area, pore density, cohesive energy of the membrane, electron density of the membrane etc. Pore size of a membrane is indicative of the mean size of the pores in a membrane. Circular pores are characterized using the radius of the pore and rectangular pores are defined using either the length and the width, or using the diagonal distances in the pores. Optimal pore size of a membrane required for the selective transmission of a species depends on the kinetic diameter of the species.44 Kinetic diameter is the smallest effective diameter of a species. For non-polar molecules, kinetic diameter is defined from the Lennard-Jones (LJ) potential and for polar molecules, it is usually defined using the Stockmayer potential.45 The kinetic diameters are closely related to the quantum mechanical diameters defined by the molecular electronic densities derived from the quantum mechanical calculations.46 The pore size distribution gives a quantitative description of the different sizes of pores present in a membrane, leading to a better picture of the possible species that can be separated using the membrane. Pore area is also often used to characterize a pore’s ability to allow the permeation of a species. Another important feature that characterizes a membrane is the pore density, which is the number of pores per unit area of the membrane. Cohesive energy is indicative of the chemical stability of a membrane and is defined as the amount of energy required to disintegrate a membrane completely into its constituent atoms. Higher is the cohesive energy, stronger is the membrane framework. The electron density around the pores also plays an important role in the


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transmission of various species through the membranes. If the interaction of the electron cloud of the incoming species with the electron cloud of the membrane (pore region, in particular) is repulsive, then it restricts the permeation of the species through the pore. The two main factors that characterize the efficiency of a membrane for sieving are the permeability and the selectivity. Permeance is inversely proportional to the thickness of a membrane.47 Permeability coefficient or permeability is defined as the product of permeance and thickness. It is also defined as the membrane thickness multiplied by the gas flux per unit pressure difference across the membrane.48 The gas flux is the volume flowing through the membrane per unit area per unit time. Since permeance is inversely proportional to the membrane thickness, one-atomthick membranes are highly suited for the separation of gases.49 Membrane selectivity (SAB) is given by the ratio of permeability of the more permeable gas (PA) to that of the less permeable gas (PB) in a given binary gas pair.48 In gas separation studies, membrane selectivity is often used as a measure to compare the separating capacities of various membranes. (a)

(b)

(c)

(d)



(e)

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(f)

Figure 2. Role of various parameters affecting the permeation of gases through carbon membranes: (a) pore size: energy barriers for the passage of He atom through defect structures of nanoporous graphene of varying pore size, (b) kinetic diameter: permeation of gaseous species with different kinetic diameters through a graphene nanopore, (c,d) pore geometry: permeation of various gas molecules through pores of different eccentricity, (e,f) chemical affinity: exceptions to the size sieving effect revealed by the higher permeation of (e) larger-sized N2 over H2, and (f) larger-sized N2 over CO2. Structural models of the membranes are shown as insets. Figure a is adapted with permission from ref 50. Copyright AIP Publishing LLC. Figure b is adapted with permission from ref 51. Copyright Elsevier. Figures c and d are adapted with permission from ref 52. Copyright American Chemical


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Society. Figure e is adapted with permission from ref 53. Copyright John Wiley and Sons. Figure f is adapted with permission from ref 54. Copyright Royal Society of Chemistry.

In Figure 1, we depict the representative structural models of various kinds of one-atom-thick nanoporous carbon membranes that have been investigated in recent times for achieving selective permeation of various species through their porous architectures. Membrane separation utilizes either size sieving or selective surface diffusion mechanism.55-57 In size sieving, smaller species pass through the pores, leaving behind the larger-sized components. Therefore, there should be a size difference between the components of the mixture for achieving effective separation using size sieving. Chemical functionalization of nanopores allows selective adsorption of various species based on their chemical affinity with the pores. Using this method, one can separate weakly/non-adsorbing species from those that have high affinity towards the membranes, even when the components of the mixture are of the same size. Besides adsorption differences at the pore, the differential adsorption of various species on the membrane surfaces also results in an enhanced permeance of one species over the other.58,59 Although the conventional size sieving mechanism can be successfully employed to explain the sieving process in some contexts, transmission through porous membranes is a nontrivial problem (Figure 2), governed by a complex interplay of several factors such as nanopore geometries, kinetic diameters of the permeating species, electronic properties of the permeating species and the membranes, chemical affinities of the permeating species to the nanopores, quantum mechanical features such as tunneling, and so forth. In order to establish the theoretical principles behind the design of carbon-based membranes for nanofiltration and elucidate the role played by various factors such as pore size, pore geometry, chemical functionalization of the nanopores, kinetic diameters of the permeating species, temperature



etc. in governing the permeability and selectivity, this review provides a careful theoretical analysis of the transmission of noble gases, small gas molecules, ions, hydrocarbons, chiral molecules and biomolecules through carbon-based nanopores. Molecular dynamics (MD) simulations and density functional theory (DFT) are the most common computational methods adopted by researchers for investigating the permeation of various species through nanoporous membranes.60 MD simulations enable modeling of larger systems, including the effects of pressure, temperature, multiple species present in the system and solvation, while quantum mechanical calculations provide an opportunity to investigate site-specific interactions and estimate binding energies, quantify electronic and structural changes during the binding of the species and energetics for passage through the nanopores. To design new nanoporous architectures, specific structural motifs for site-specific interactions need to be introduced in the carbon membranes. First-principles calculations help us in designing new membranes with specific sites and structural parameters, while MD simulations can help us unravel the effects of pressure, temperature, electric field, interparticle interactions etc. Permeation through carbon membranes represents a classic example of a research problem wherein MD simulations and first-principles calculations can be synergistically employed to arrive at a comprehensive theoretical understanding of the underlying factors. SELECTIVE PERMEATION OF GASES THROUGH CARBON MEMBRANES Selectivity Aspects in Noble Gas Permeation. Noble gases are an important class of chemicals with various industrial and medical applications such as low temperature refrigeration, lighting, lasers, anesthetics, magnetic resonance imaging etc.61-64 Therefore, approaches for separation and purification of noble gases are widely investigated. Although cryogenic distillation is the most commonly used technique for noble gas separation, due to its high cost and energy requirements, membrane separation technology has evolved as an


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attractive alternative. Although He is found abundantly in the universe, the percentage of He on earth is only 0.0005.65 Thus, efficient separation of He is of utmost importance. Separation of He using a graphene membrane was first investigated by Leenaerts et al. wherein the authors studied the penetration of He through a defective graphene layer.50 Employing DFT and MD simulations, permeation of He through point defects in graphene like STW defect, di-, tetra-, hexa- and deca-vacancies that kept the sp2 framework of the carbon atoms intact was probed. The computed barrier heights (obtained as the energy differences between the transition states and the minimum energy configurations) decay exponentially with the increase in the size of the defect, as can be seen from Figure 2a. The STW and divacancy defects offer a large barrier for He penetration and only the deca-vacancy defect led to a sufficiently low barrier for He penetration. The variation of the permeation barriers with pore size is clearly a manifestation of the size sieving effect, one of the simplest mechanisms for explaining selective permeation through pores. Besides the pore size, pore geometry is another important factor that dictates permeation through pores. Schrier studied the permeability of He, Ne and CH4 through the PG membrane that was synthesized by Bieri et al. using the MP2/cc-pVTZ methodology.66 Optimal separation of He from Ne and CH4 is achieved by a combination of high temperature separation followed by a low temperature separation. The initial high temperature is used to maximize the total flux through the membrane and at this temperature, most of the He atoms, a small quantity of Ne atoms and none of the CH4 molecules get transmitted. Further separation at low temperature will completely remove Ne atoms, resulting in the transmission of He atoms alone. The diffusion of He, Ne, Ar, H2, O2, N2, CO, CO2 and NH3 through PG is probed by Blankenburg and co-workers using the PBE exchange-correlation functional.53 As earlier, the deep minima of noble gases were attributed to their large polarizability. Even though He has the smallest kinetic diameter, the diffusion barrier for H2 was found to be lower than that of He, because of the polarization effect of He near the membrane, as can be seen from Figure 2e.



The selectivity of the membrane towards various components was further studied using transition state theory (TST) and the membrane showed high selectivity for He and H2. The success of PG in noble gas separation fueled interest toward the design of similar porous structures that are better suited for separation. Brockway et al. investigated the permeation of noble gases through PG-ES1, PG-ES2, and PG-ES3.22 Use of a simple hard sphere van der Waals model indicated that repulsive interactions experienced by an atom passing through the pore decrease as the size of the pore increases since the overlap between the hydrogen atoms on the pore rims and the noble gas atoms at the pore centres decreases. The reduced overlap for the gas atoms in case of PG-ES1 compared to PG accounts for the lowering of energy barriers for the penetration of the atoms. On further increasing the pore size to PG-ES2, overlap of He and Ne are reduced to zero, while Ar, Kr, Xe and Rn still have overlaps with the rim atoms and in the case of PG-ES3, none of the noble gas atoms overlap with the hydrogen atoms at the rim. However, this simple model does not consider the attractive dispersion forces and hence does not provide an accurate picture. Therefore, one of the DFT functionals (the PBE functional) with and without dispersion corrections was used to probe the permeation process further. For PG and PG-ES1, dispersion-corrected PBE functional and the hard sphere model yielded qualitatively similar results. In case of PG-ES2, the van der Waals model is consistent with PBE results for He and Ne, both of which give rise to an attractive potential well for both the atoms, although the minima are further stabilized by including the dispersion-corrected terms. For Ar, the simple van der Waals model predicted the repulsive potential, but PBE and dispersion-corrected PBE results indicate an attractive well due to its polarizability, which is neglected in the hard sphere model. The results for the permeation of Kr, Xe, and Rn are nontrivial. Thus, in some cases, both PBE and hard sphere model predict repulsive interactions, overlooking the very large attractive dispersion interactions that arise due to the polarizabilities of these atoms. Therefore, introducing corrections by way of dispersion interactions can lead


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to an accurate estimate of the barriers and the large dispersion terms result in deeper wells for the more polarizable atoms. The efficiency of PG-ES1 as a membrane for He separation from natural gas was further probed using MD simulations. PG-ES1 showed (i) 90 times more permeance for He than PG and (ii) higher selectivity for He over CH4, Ar, CO2 and N2, making it a suitable membrane for He separation. Gas permeance is therefore not just dependent on the sizes of the gaseous species in a mixture, but is also affected by the chemical and physical interactions of the gaseous species with the membranes (Figure 2). Thus, in order to describe the gas permeation process accurately, it is rather important to employ high level electronic structure calculations. Success in theoretical design of optimal membranes for several gas separation processes in recent times can be primarily attributed to advancements in electronic structure theory. More recently, porous graphene and its derivatives are extensively researched as potential membranes for isotope separation. Consideration of quantum mechanical tunneling along with classical transmission results in an increase in the transmission probabilities for the atoms. Since tunneling is associated with an explicit mass dependence, this effect can be utilized for isotope separation. In case of the permeation of the He isotopes through PG, the classical transmission was found to be orders of magnitude lower than the tunneling transmission at very low temperatures because there are very few atoms with classical kinetic energy higher than the energy barrier at low temperatures.66 At low temperatures, the tunneling effect showed increased transmission of 3He over 4He, even though the total flux is low. For higher temperatures, the flux is improved at the cost of the 3He/4He transmission ratio. Schrier investigated the effects of tunneling and zero-point energy (ZPE) on isotope separation using two reservoirs kept at two different temperatures (TC and TH) separated by PG.67 The isotope concentrations were predicted using three different theories. In classical transmission, no relative isotopic enrichment is seen because there is no mass dependence. In case of quantum



transmission, the thermally-weighted transmission probability of 3He (t3He) is greater than that of 4He (t4He) at all temperatures, because lighter particles show significant tunneling. The compartment with TH has greater fraction of particles with energy greater than the potential barrier, whereas the compartment with TC has a higher fraction of particles with energy lower than the barrier. Hence, the probability of the hot and heavy particles to exit the hot reservoir and the light and cold particles to exit the cold reservoir is high. The ratio, t3He/t4He is observed to be a monotonically decreasing function of temperature with an asymptote of unity. The last approach is based on TST, where zero-point effects are taken into consideration. The two isotopes have different ZPE values and therefore the barrier heights become mass-dependent. The separation factor r is defined as

𝑟=

(𝑃𝐶,4 /𝑃𝐶,3 ) , (𝑃𝐻,4 /𝑃𝐻,3 )

where PT,i is the partial pressure of the isotope iHe at temperature T. When r is equal to one, the transmission is purely classical. When this factor deviates from one, it indicates isotope enrichment or depletion. As Figure 3a shows, quantum tunneling results in r > 1 for TC < TH. According to TST (Figure 3b), r < 1 for TC < TH, in contrast to the results from tunneling. Further, the tunneling effects were incorporated into TST and in this case if r > 1, it implies that there is tunneling (Figure 3c). However, if r < 1, it need not indicate the absence of tunneling. Largest isotope separation occurs when there is a maximum temperature difference between the compartments and this is better achieved by lowering the temperature of the cold compartment than increasing the temperature of the hot compartment because the separation ratio is inversely proportional to TH. As the pore size increases, the barrier height reduces rapidly whereas the barrier width increases gradually. Therefore, one can turn the tunneling on and off by controlling the pore size. While pristine graphene is impermeable to several species, presence of tiny pores can bring in both quantum and classical transmission. As pore size


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increases, the transmission becomes purely classical. Quantum size sieving effect thus offers an excellent handle to achieve isotope separation using carbon-based substrates (Figures 3d3f). For further finetuning the barrier heights, larger nanopores with nitrogen functionalization were suggested by Hauser et al.68 Initially, an optimum potential for achieving efficient 3He/4He separation was calculated and then graphene nanopores with nitrogen and hydrogen atom passivations were designed. The energy profiles for the passage of a He atom through three different functionalized pores are shown in Figure 4a. On comparing the different models, the nanopore with two-ring holes and nitrogen passivation on single side proved to be the best candidate for isotope separation. Transmission probability of 3He was greater than that of 4He at low temperatures and this trend reverses at high temperatures. Besides the higher 3He selectivity, higher transmission probabilities are observed at low temperatures. In case of thermally-driven isotope separation, best results were achieved when there is nitrogen passivation on both sides of the pore.69 The PG-ES1 structure was also studied for isotope separation because it provides low energy barriers for permeation, analogous to the nitrogenfunctionalized pores studied by Hauser.22 At high temperatures, the temperature-driven isotope separation calculated using PBE and dispersion-corrected PBE gave qualitatively similar results, indicating the dominance of ZPE effects on isotope separation. However, for low temperatures, various functionals employed gave varying results for the separation factor, making it impossible to pinpoint whether the actual dominating factor is ZPE or the tunneling effect. The nanopore configurations considered thus far enabled modeling the potential as a single barrier problem. Study of permeation through an appropriate double layered graphene nanostructure showed an improved isotope separation for temperature less than 12 K.70 The selectivity of 3He almost doubles when a graphene bilayer is used, although the flux rate remains the same. The enhanced selectivity of 3He over 4He is attributed to resonant tunneling.



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On employing an asymmetric double barrier, the flux of both the isotopes increased with enhancement of isotope selectivity in certain cases. The effect of defects and further functionalization of these defective graphene nanopores using hydrogen, nitrogen, oxygen or fluorine atoms on isotope separation was investigated by Lalitha and co-workers.29 The defective structures are created by incorporating three consecutive STW defects, followed by the removal of two pentagon rings of the central STW defect. The carbon atoms at the rims of the pore are then passivated with hydrogen, nitrogen, oxygen and fluorine atoms. The hybridization of the carbon atoms in the defect region is different from the surroundings, thus weakening the electron density around the pore. This results in lesser repulsions between the electron clouds of the nanopores and the He atom, thereby leading to higher tunneling probabilities.

Oxygen

functionalization

yields

smaller

pore

sizes

than

nitrogen

functionalization because of the higher electronegativity of oxygen. The largest pore is observed for double-sided nitrogen functionalization. Double-sided fluorine functionalization reduces the pore size such that He penetration is impossible. In the case of oxygen and fluorine, the potential barrier is asymmetric because of the steric repulsions between O-O and F-F atom pairs. The barrier heights are lower for double side passivation (D) than for single side passivation (S) because of the larger pore sizes. The computed energy barriers follow the order: pristine > S-nitrogen > D-nitrogen > hydrogen > S-oxygen > D-oxygen. The order of the transmission probabilities is: D-oxygen > S-oxygen > D-nitrogen > S-nitrogen > hydrogen > pristine. The double-sided oxygen passivated pore shows a preference for the lighter isotope up to 100 K, but it has relatively low selectivity for 3He compared to the double-sided nitrogen system. The lowest value of He flux is for the hydrogen-passivated pore, whereas maximum flux is obtained for the double-sided oxygen-passivated pore. (a)

(b)


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Figure 3. Selective permeation of various isotopes through carbon membranes due to quantum effects: Interplay of tunneling and ZPE on isotope separation: (a) effect of tunneling, (b) effect of ZPE, and (c) combined effect of tunneling and ZPE on the transmission ratio for the isotopes of He. (d) Transmission probabilities for the He isotopes calculated using classical and quantum approaches, (e) selectivity in the permeation of D2 over H2 through the pore center and exit barrier of Ti-N-PG, and (f) relative ZPE values of H+, D+, T+ bound at the center of coronene. Structural models of the membranes are shown as insets. Figures a, b, c and d are adapted with permission from ref 67. Copyright Elsevier. Figures e and f are adapted with permission from refs 71 and 72, respectively. Copyright American Chemical Society. Further to the successful investigations of PG and its derivatives for gas and isotope separation applications, many more nanoporous carbon membranes were probed for finetuning the separation capabilities. MP2C calculations revealed that GDY provides lower barrier for He penetration than PG.73 The computed barrier herein was comparable to the nitrogenfunctionalized graphene nanopores and PG-ES1 mentioned earlier. GDY exhibits much higher



permeability than PG for a large range of temperatures due to its optimal pore size. MD simulations using Improved LJ pair potentials showed high selectivity of GDY towards the separation of He/CH4 and Ne/CH4 mixtures.73 He/Ne selectivity of GDY is moderate but is in the industrially acceptable range. The thermally-weighted He tunneling calculations for the transmission of 3He and 4He through GDY revealed selective transmission of 3He over 4He. Hernandez et al. further investigated the quantum effects and analyzed the competition between ZPE and tunneling in governing the temperature dependence of the selectivity of He isotope transmission through GDY.74 As in the case of PG, the ZPE of 3He is appreciably larger than that of 4He and this difference in ZPE values of the two isotopes plays an important role in the transmission dynamics of the isotopes through GDY. When the ZPE is considered to be zero, there is a considerable decrease in the transmission rate coefficient values and this effect is more pronounced in the case of the lighter isotope, implying that the effect of ZPE is nonnegligible. On similar lines, the role of tunneling on the rate coefficients was studied.74 There is no appreciable change in the rate coefficients when tunneling is neglected, except at low temperatures. Therefore, the role of tunneling is significant only at very low temperatures. In contrast to the previous result where ZPE was not considered, transmission of 4He was found to be faster than 3He. This is due to the predominant contribution of ZPE selectivity of heavier isotope over the tunneling selectivity, which favors the lighter isotope. As temperature decreases, both the contributions increase, but the increase is slightly larger for the tunneling effect. Therefore, at temperatures lower than 20 K, GDY shows selective permeation of the lighter isotope. A recent study by Gijon and co-workers employs three-dimensional wave packet calculations for an improved understanding of the effects of ZPE and tunneling on He transmission through GDY and a holey graphene model.75,76 The GDY system yields a moderately small selectivity for the 3He/4He system, in contrast to the earlier one-dimensional tunneling calculations because these simpler models neglected the ZPE effects for the degrees


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of freedom along the perpendicular directions of the reaction path. In case of holey graphene, the rate coefficients and selectivity ratios computed using this method do not agree well with the values predicted using TST. Very recently, the isotope-separating capacity of graphenylene was investigated by Qu et al. and graphenylene showed remarkable permeance, along with good He isotope separation efficiency, when compared to the nitrogen-passivated PG, hydrogen-passivated PG and GDY.77 Therefore, it is clear that a systematic theoretical investigation of the isotope separation using a variety of carbon membranes such as PG, PGES1, various heteroatom-passivated nanoporous graphene, GDY, and graphenylene have enabled the design of superior carbon membranes that the authors believe could be realized in experiments. Selectivity Aspects in Gas Molecule Permeation. The discovery of various nanoporous carbon membranes has made a significant impact on gas separation technologies. Among these, graphene-based membranes are highly popular and extensively researched for industrially important processes such as H2 purification, CO2 separation, etc. The permeation process takes place in three steps: (i) the gas molecules approach the pores of the membrane, (ii) the gas molecules either pass through the pores or adsorb on the pores due to chemical affinity, and (iii) the adsorbed species diffuse through the pores. Employing DFT calculations, Jiang et al. studied the selectivity and permeability for the separation of H2/CH4 using subnanometer-sized porous graphene.78 The objective is to make pores with pore size closer to the size of the smallest molecule in a given gaseous mixture. Two kinds of pores are generated in graphene by removing carbon atoms followed by either (i) fully passivating the dangling bonds with hydrogen atoms (denoted as hydrogen-passivated pore), or (ii) by passivating four of the dangling bonds with hydrogen atoms and replacing four carbon atoms with nitrogen atoms (denoted as the 4N-4H pore). The hydrogen-passivated pores showed higher selectivity for the separation of H2/CH4 than the 4N-4H pore. The additional hydrogen atoms in the hydrogen-



passivated pores caused narrowness of the pore, leading to a drastic increase in energy barrier for the passage of CH4. The computed selectivities for the 4N-4H pores and the hydrogenpassivated pores are ~108 and 1023, respectively. Tao et al. used PG-ESX (X=1, 2, and 3) to find out the best possible porous membrane with optimal balance between selectivity and permeability for hydrogen separation from CH4.79 DFT as well as MD simulations indicated that PG-ES1 with pore size of 3.27 Å is the best candidate for the separation of H2. The higher energy barrier for CH4 compared to H2 was attributed to the large electron density overlap of CH4 with the electron density isosurface of the stilbene-based nanopore and the sieving process was explained based on the differential kinetic diameters of H2 and CH4. The 4N-4H nanopore was further employed for studying the permeation of H2, CO2, N2, Ar, and CH4. The effect of pressure on the permeation of these gases was investigated by Liu et al. using MD simulations.80 The flux variation is in accordance with the kinetic diameters of the molecules and follows the order H2>CO2>N2>Ar>CH4. The selectivity of gas permeation in each of the above cases could be easily explained based on the size sieving effect. However, gas permeation through membranes is also governed by several other factors such as chemical affinity of the permeating molecules to the nanopores, pore geometry, electronic properties of the molecules as well as the pores, etc. We now illustrate the role of each of these factors by considering a few examples. The pore geometry has a significant effect on the permeance of gases through porous graphene membranes. Li et al.52 investigated the effect of pore geometry on the permeation of coal gas by employing porous graphene denoted as g-n (n=1-4), obtained by removing various number of benzene rings from graphene. The g-3 membrane showed higher selectivity for H2. When pores with the same area are compared for their selectivity, it was found that the pores with deviation from circular geometry hindered the permeation of some molecules, thereby increasing the selectivity, as can be seen from Figures 2c and 2d. Further, the effect of


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eccentricity of various pores of constant area on gas permeation was studied.81 Pores with large eccentricity are expected to show lower permeance due to deviations from circular geometry. However, the authors argue that, if designed with right eccentricity, such pores can be excellent candidates for gas separation. (a)

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Figure 4. Gas permeation through carbon membranes: (a) effect of nitrogen passivation of PG on the energy barrier for He permeation, (b) energy barriers for the selective permeation of CO2 through fluorine-modified porous graphene, and (c) selective permeation of CO2 through nitrogen-doped carbon membrane. Energy barriers for the selective permeation of various gas molecules through (d) GDY, (e) nitrogen-doped GDY, and (f) rhombic-GY. Structural models of the membranes are shown as insets. Figures a, b, c and f are adapted with permission from refs 68, 82, 83 and 39, respectively. Copyright American Chemical Society. Figures d and e are



adapted with permission from refs 84 and 85, respectively. Copyright Royal Society of Chemistry. Increasing the pore size in order to obtain larger gas fluxes results in a decrease in selectivity. Chemical functionalization of the pores can be an effective strategy for achieving increased selectivity. Shan et al. studied the effect of chemical functionalization of the rims of nanoporous graphene with nitrogen atoms for the separation of CO2/N2.86 Pore-10 (the pores are named on the basis of the number of carbon atoms removed from the graphene sheet) selectively allows the permeation of CO2 molecules, while blocking N2 molecules. But, pore11 allows both the molecules to pass through. Selectivity of CO2/N2 was enhanced in case of pore-10 due to strong electrostatic interactions between CO2 molecules and the functionalized pore. Fluorine-functionalized graphene nanopores can also significantly affect the separation of CO2 from N2. Wang et al. investigated the role of chemically functionalized graphene nanopores54,87 by considering a series of hydrogen-passivated porous graphene membranes for CO2/N2 separation using DFT and MD simulations. The membranes are denoted as H-pore-n, where n represents the number of carbon atoms removed to form a pore. H-pore-13 was identified as the best candidate for effective N2/CO2 separation.54 Both CO2 and N2 bind strongly to H-pore-13 at distances of 2.0 Å and 1.6 Å, respectively, which makes it difficult for CO2 to penetrate through the pore even though the kinetic diameter of CO2 is less than that of N2. Figure 2f clearly indicates the higher selectivity of N2 over CO2. Wu et al. compared the selectivities of two different pores obtained by removing the same number of carbon atoms and saturating the carbons with hydrogen and fluorine atoms.83 The polarity of the C-F bond is expected to enhance the adsorption of polar gas molecules. Porous graphene without functionalization did not show any selectivity towards CO2/N2 separation. Hydrogenpassivated porous graphene showed no selectivity, whereas fluorine-passivated membranes showed high selectivity for CO2/N2 separation. This is attributed to the quadrupole moment of


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CO2, which exhibits stronger dispersion interactions with fluorine atoms. The interaction energy plot of CO2 and N2 with fluorine-passivated graphene nanopore is shown in Figure 4b. Further, Qu et al. demonstrated the quadrupole moment driven separation of CO2/N2 using nitrogen-rich membranes.82 The interaction energy between the gas molecule and the porous membrane is the sum total of the van der Waals and the electrostatic interaction terms. They found that the electrostatic interaction energy determines the selectivity of CO2/N2 separation. Figure 4c shows higher permeation as well as selectivity of CO2 over N2. Liu et al. studied the separation of a series of gases using the 4N-4H graphene nanopore by MD simulations to estimate the ideal selectivity.51 Due to the strong attraction between CO2 molecules and the functionalized pore, the barrier heights are in the order CH4 > Ar > N2 > H2 > CO2. However, the lower mass of H2 results in larger collision rates, leading to the following flux sequence: H2 > CO2 > N2 > Ar > CH4, as shown in Figure 2b. Schrier et al. employed differential surface adsorption mechanism to achieve the separation of CO2 from N2, O2, and CH4 using PG-ES1. Enhanced permeance arising due to stronger adsorption of CO2 to the PG-ES1 surface is traced to its large polarizability as well as to its quadrupole moment.88 Du et al. used nanoporous graphene with pores of various sizes and shapes for hydrogen purification from N2.58 N2 adsorbs on the surface of porous graphene very strongly, forming a single layer. Upon increasing the pore size, the N2 molecules diffuse and escape through the pores, resulting in enhanced permeance of N2 as well as enhanced N2/H2 selectivity. Such an exceptional behavior of the permeation of N2, leaving behind H2 through porous graphene can be interpreted based on the analytical model of Drahushuk and co-workers.59 According to the model, the permeation of gas through porous membrane can proceed through (i) direct gas phase pathway, wherein molecules in gas phase strike the pores and (ii) adsorbed phase pathway, wherein the permeation of gas involves adsorption and desorption of the gas molecules. The analytical calculations show that, in case of smaller pore, the energy barrier for the adsorbed phase



molecules is higher than the gas phase molecules whereas larger pores allow the passage of adsorbed phase molecules due to low barrier, accounting for the enhancement in selectivity for N2/H2 separation. Permeation of molecules through pores could be expressed in terms of contributions from direct flux as well as surface flux.89 In case of gas permeation through NPG, Sun et al. showed that the contribution from surface flux is of the order of direct flux.75 Wen and co-workers investigated the role of non-permeating gas (CH4) on the permeances of H2 and N2 by varying their partial pressures. The blocking effect and strong adsorption of CH4 on the porous membrane cause a reduction in the permeances of the permeating gases (H2 and N2).90 In all the above cases, permeation of the gas molecules through various nanopores is governed by the chemical interactions of the permeating species with the functionalized carbon membranes. Employing accurate electronic structure methods for modeling the electronic interactions of the gas molecules with the membranes, particularly the nanopore regions is therefore highly essential for the design of optimal nanoporous substrates to be employed in experiments. Selectivity in permeation through pores can also be achieved by (i) tuning the electronic structure of the nanopores by the introduction of charges as well as by (ii) introducing tensile strain in the nanopore. The effect of introduction of charges in the nanopore on the separation of H2S/CH4 was studied by Lei and co-workers using MD simulations.91 A graphene nanopore is generated by removing 12 carbon atoms from graphene and introducing charges in the pore. The generated pore size (4.05 Å) is larger than the kinetic diameters of H2S (3.6 Å) and CH4 (3.8 Å). The electrostatic interactions between the H2S molecules and the charged pore increase the permeation flux as well as the selectivity for H2S/CH4. Zhu et al. studied the effect of applying tensile strain across a graphenylene membrane on the gas permeance.42 Application of the tensile strain reduces the repulsive interactions between the membranes and the gases, facilitating the passage of the gas molecules. Jungthawan et al. discussed the effect of tensile


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strain on the permeation of gases through PG by employing DFT.92 On comparison with the uniaxial strain, application of a symmetrical strain stretches the PG equally in both the directions, resulting in decreased barrier height. Diffusion barriers of O2 and CO2 were found to decrease more rapidly than that of H2 on applying strain on PG, decreasing the selectivity in H2/CO2 and O2/CO2 separation. The decrease in diffusion barriers was ascribed to the increase in pore size on the application of strain. Currently, graphynes are extensively investigated for the design of optimal carbon membranes for gas separations. We now illustrate some of the design principles involving various forms of graphynes. Since hydrogen molecules cannot pass through γ-GY with a triangular pore size of 1.69 Å, Sang et al. designed a new set of pores38 by rupturing one of the acetylenic linkages and substituting the resultant dangling bonds with hydrogen and nitrogen atoms, resulting in γGYH and γ-GYN, respectively. The designed pores are further probed using DFT and MD simulations for hydrogen purification from other gases. The electron density isosurfaces show no electron overlap between H2 and γ-GYX (X=H and N), a consequence of the small kinetic diameter of H2, suggesting that the motion of H2 through γ-GYX may be barrierless. The computed energy barriers for passage through γ-GYH and γ-GYN reveal that the latter is the best candidate for H2 purification. Jiao et al. studied the separation of hydrogen gas from CH4 and CO using GDY.84 Since GDY has natural and uniformly distributed pores with pore size in between the van der Waals diameters of H2 and CH4/CO, it is considered to be a good candidate for H2 purification. Even though H2 permeates through GDY, its large pore size decreases the selectivity. Therefore, the authors further used nitrogen-modified GDY (NGDY), which is obtained by replacing three sp2 hybridised carbon atoms on the hexagon with nitrogen atoms, for achieving enhancement in the selectivity of hydrogen purification from CH4 and CO.85 The nitrogen modification decreases the barrier height for H2 by the modification of the transition state configuration, whereas it increases the diffusion barrier for



both CO and CH4. H2 purification from CO and CH4 using pristine GDY is purely based on the kinetic diameters of the molecules, but the selectivity can be further enhanced by the introduction of charges in the porous membrane. Tan et al. modelled the separation of H2 from CO and CH4 using one-electron positively charged triangular GDY pores.93 In case of H2, the decrease in the interaction energy of the transition state (TS) is larger than that of the initial state (IS), implying a decrease in barrier height. For CH4, a decrease in interaction energy was found for both IS and TS. However, the decrease in interaction energy of TS is less than that of IS, leading to enhanced barrier height. The barrier height of CO increases since the interaction energy in TS increases, whereas in IS, the interaction energy decreases. The advantage of this method is that, introduction of charges in carbon membranes does not rely on any complicated synthesis and can be easily achieved. Zhang et al. used rhombic-GY whose pore size is in between that of γ-GY and GDY to increase the selectivity in hydrogen purification.39 The selectivity of rhombic-GY for H2/CH4 (1016) was shown to be much higher when compared to that of GDY (109). Interestingly, the computed diffusion barriers are not in accordance with the kinetic diameters of the gas molecules, but follow the physical and chemical interactions between the gas molecules and the pores strongly. A depiction of the energy barriers for the purification of H2 using various graphynes is presented in Figures 4d-f. Graphene oxide, a functionalized derivative of graphene can also be used for gas separation.94,95 When compared to the interlayer separation of graphite, the interlayer separation in GO is large enough for the diffusion of gas molecules in between the layers. The selectivity of GO membrane for various pairs of gases was studied by Jiao et al. using MD simulations.94 Due to the presence of oxidative groups, CO2 strongly binds on the surface of graphene oxide, decreasing its permeance. The permeability of a set of gases was found to vary in the order: He, H2 > CH4 > O2 > N2, CO > CO2, in contrast to what one would have expected based on


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their kinetic diameters. This is clearly suggestive of the role of chemical interactions between the gas molecules and the membrane surface in governing permeation through pores. Hankel and co-workers studied the isotope separation of molecular hydrogen using quantum sieving effect of porous graphene.71 Two porous graphene membranes, namely PG and N-PG (a form of PG designed by removing some rings from pristine graphene and replacing the unsaturated carbon atoms with nitrogen atoms) were initially analyzed by employing fourdimensional quantum calculations. PG showed better selectivity for the heavier D2 isotope, but the small pore size of PG results in low flux of the isotopes. N-PG, however showed higher selectivity for D2 and resulted in sufficient gas flux for achieving optimal separation. Although N-PG provides good selectivity and barrierless permeation, the symmetry in the interaction potential can also cause a decrease in gas selectivity on the way out of the pore. An interesting way out of such a situation is to introduce asymmetry by metal decoration of the pores on the exit side of the membrane. The N-PG was therefore decorated with lithium on the backside and since molecular hydrogen and deuterium are attracted to the metal, the exit energies are lower than those in case of undecorated N-PG.71 The passage of the molecules is favored only in the forward direction, since on crossing the energy barrier, the molecules adsorb to Li and motion in the backward direction is unfavorable. The exit barrier for Li-doped N-PG is 0.1 eV, which is too high for low temperature separation and therefore to overcome this difficulty, effect of Ti doping was studied. Ti-doped N-PG has a very small barrier of 0.03 eV, leading to favorable kinetics for isotope separation even at low temperatures, making Ti-N-PG the best candidate for selective isotope separation. The selectivity of D2 permeation over H2 through the pore center and exit barrier of Ti-N-PG is shown in Figure 3e. The nanoporous membranes considered thus far possessed pores of definite sizes. It would be interesting to think of designing nanopores that can adjust themselves dynamically in order to facilitate the selective permeation of various species. This rather appealing idea was put 29 Environment ACS Paragon Plus


forward in a very recent report by Tian et al. using an ionic liquid (IL) to dynamically tune the pore size of a nanoporous graphene membrane.96 Using classical MD simulations, dynamic tuning of the pore size of a porous graphene membrane of 6.0 Å diameter by an IL, [emim][BF4] is employed for achieving the selective permeation of CO2, N2 and CH4. The nonvolatile monolayer of IL coated over the membrane helps in achieving good permeance for gas molecules passing through the nanopores. The IL attracts gas molecules towards the membrane as well as tunes the pore size, since the graphene membrane controls the structure of the IL layer through the graphene-IL interaction. Such a synergistic interaction between the graphene layer and the IL makes this system perfect for selective gas separation. It is the right combination of the pore size of the graphene membrane and the ion size that yields high selectivity and permeance. In the absence of IL, the membrane was permeable to all three gas molecules, thus offering zero selectivity. In contrast, in the presence of a monolayer of IL on the graphene layer, the membrane shows high CO2 selectivity and the permeation of CH4 is significantly lowered. The anions and cations of the IL stay on the feed side because the cations are too large to pass through the pore and the anions are held by the electrostatic interactions with the cations. The selectivity of CO2 over N2 is due to the stronger affinity of IL to CO2 compared to N2, while the selectivity of CO2 over CH4 is due to the size sieving effect. Further, the effect of the nature of the ion in controlling the pore size is analyzed by using the larger [PF6]- ion in place of the smaller [BF4]- ion. When the larger anion is used, permeances of both CO2 and N2 decrease, with a larger decrease for N2 thereby making the membrane more CO2/N2 selective. This increase in selectivity is attributed to the diffusivity selectivity, since the adsorption selectivity indeed decreases slightly on changing the anion. Therefore, it is clear that, by choosing a proper anion, the nanopore size can be dynamically tuned for achieving better selectivity. Besides, the effect of pore size is also investigated by considering a larger nanopore of size 9.6 Å and a smaller pore of size 4.2 Å. The use of a larger pore enables the


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passage of the ions, thereby decreasing the selectivity of CO2/CH4, whereas on using smaller pore, the flux of CO2 decreases. The investigated nanopores were terminated with hydrogen atoms and therefore attracted the anions. Instead, if electronegative atoms like nitrogen or fluorine were used for functionalization, the pore sizes could be modulated using cations. Studies on dynamic tuning of the pore sizes in nanoporous membranes are only beginning to appear and experiments along these lines can provide numerous opportunities for sieving applications in membrane technology. SELECTIVE PERMEATION OF IONS THROUGH CARBON MEMBRANES The permeability of ions through membranes has been studied for a long time for desalination of water, separation of ionic mixtures and mimicking biological membranes. One-atom-thick membranes with precise pore size and functionalities can help in selective ion passage and salt rejection. Selectivity of ion permeation through membranes is shown to depend on the size and shape of nanopores97, functionalization of nanopores98, ionic and hydrodynamic radii99, polarizability of the hydration shell, energetics of dehydration of the hydration shell100, electrostatic interactions as well as external factors such as applied electric field101 and pressure.99,102-104 Biological systems provide almost precise selectivity for the permeation of ions through protein channels. Mimicking biological systems by controlling the features of the nanopores of artificial membranes can provide excellent selectivity for various ions. Graphene nanopores can be functionalized in such a way that the permeation barriers arising due to dehydration can be compensated by the interactions with the functional groups flanking the nanopores for better passage of the ions.105 (a)

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Figure 5. Ion permeation through carbon membranes: Radial distribution functions for the passage of Na+ and K+ ions through (a) oxygen-based graphene crown ether and (b) graphene nanopore, (c) structural model of carboxylate-passivated graphene nanopore, (d) depiction of the permeation of the ions through the pore (K+ ion in green and Na+ ion in magenta), DFT scans for the permeation of the alkali metal ions, Li+, Na+ and K+ through (e-g) various nitrogenand oxygen-based graphene crown ethers, (h) graphenylene and -GY, and (i) electric field


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dependence of the rate of passage of Na+ and Cl- ions. Figures a and b are adapted with permission from ref 105. Copyright Royal Society of Chemistry. Figures c and d are adapted with permission from ref 97, figures e, f and g are adapted with permission from ref 24 and figure i is adapted with permission from ref 101. Copyright American Chemical Society. Figure h is adapted with permission from refs 106 and 107. Copyright American Chemical Society and Royal Society of Chemistry, respectively.

Biological proteins such as KcsA and NavAb with different ligands at the active sites bind to the alkali ions cooperatively. Kang et al. constructed three different kinds of oxygenfunctionalized graphene nanopores corresponding to different binding sites in the KcsA protein.105 As the length scales reach sub-nanometer regime, the pore edges deform the hydration layers of the ions, resulting in an increase of energy barriers for ion permeation. Nanopore shown in the inset of Figure 5a exhibits selective binding to the K+ ions with computed ratios of the number of the K+ ions to the number of the Na+ ions passing through the pores from 1.7 to 7.0, under different applied electric fields. All six oxygen atoms of the nanopore interact with the K+ ion and capture it to the pore, thus partially compensating for the hydration energy. As a result, the nanopore becomes selective for the potassium ions. This is evident from the radial distribution function (RDF) shown in Figure 5a, indicating that the K+ ions are found at the center of the nanopore. To prove that the mechanism of selectivity is based on dehydration energy, Kang and co-workers considered a hydrogen-terminated nanopore (inset of Figure 5b), structurally similar to the nanopore discussed above, through which both K+ ions and Na+ ions do not permeate, as is evident from its RDF (Figure 5b). Similarly, He et al. proposed three nanopores functionalized with carbonyl or carboxylate groups, analogous to the structures of the KscA and NavAb proteins. First nanopore with four CO groups has a pore diameter of around 0.65 nm, similar to that in KscA protein and showed a higher selectivity 33 Environment ACS Paragon Plus


towards K+ ions due to its better interactions with the carbonyl groups around the rims of the nanopore.97 Second nanopore (pore diameter of 0.79 nm), which has a structural similarity with the NavAb protein channel for Na+ ions, also showed selectivity towards K+ ions. This is attributed to the fact that the carboxylate groups at the pore rims are flexible and move out of the plane while binding with the ions. Na+ ions bind to the nanopore with a stronger affinity compared to the K+ ions and they remain bound to the pore, but are unable to block the pore from the K+ ions due to their small size. Thus, the nanopore gives better selectivity for K+ ion permeation. Smaller nanopore with three carboxylate groups as shown in Figure 5c shows a selectivity for the Na+ ions at low voltages and the selectivity switches towards the K+ ions at high voltages. Carboxylate groups at low voltage stay in the plane and Na+ ion fits in the pore to form a favorable complex, compared to the K+ ion. Na+ ion preferentially blocks the pore and can get replaced by only another Na+ ion through a knock-on mechanism (Figure 5d). At high voltage, carboxylate ion swings out of the plane and thus destabilizes the complex with the sodium ion. K+ ions can knock out Na+ ions to pass through the pore in this situation, while sodium ions remain bound to the pore. Achieving selectivity for ions by modification of the functional groups that can replace the water molecules in second hydration shell has also been explored recently.108 Functionalized graphene nanopores, containing either five carbonyl or five negatively charged carboxylate ions at the edges of the nanopores, have been proposed for achieving selective permeation of Mg2+ ions over Li+ ions.108,109 Potential of mean force (PMF) calculations show that the Mg2+ ions are allowed to pass through in a barrierless fashion, while Li+ has a finite barrier to cross through both the nanopores. The functional groups can replace water molecules from the second hydration shell. Both lithium and magnesium ions lose approximately the same number of water molecules from hydration shells. For Mg2+, the carbonyl or carboxylate oxygen atoms replace the lost water molecules. Thus, the coordination number of the ion in the second hydration shell remains the same at the pore and in the bulk.


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For Li+ ions, the functional groups do not completely replace the water molecules removed from the second hydration shell. The excess energy required for the dehydration of the Li+ ions accounts for the lower selectivity in permeation of the Li+ ions over the Mg2+ ions.108,109 GCEs are nanoporous structures similar to the nanopores designed by Kang et al.105 and have been studied in our research group for achieving selective ion permeation.24 We have employed electronic structure calculations to model six different crown ethers (conventional oxygenbased as well as nitrogen-based crown ethers), namely, 9-crown-1, 10-crown-2, 12-crown-3, 14-crown-4, 16-crown-5, and 18-crown-6 (insets of Figure 5e-g) embedded in graphene membranes.24 GCEs were shown to have better affinity towards alkali metal ions compared to the normal crown ethers. Alkali metal ions bind stronger to the N-based GCEs compared to the O-based systems due to stronger electrostatic interactions. Analysis of energy barriers for the transmission of the ions through the pores indicates that the 18-crown-6 embedded GCE allows barrierless passage of all the three alkali metal ions, as depicted in Figure 5g. Only Li+ ions pass through the smaller crown-4 GCE, while crown-5 GCE offers a very small barrier for the Na+ ions (Figures 5e and 5f). Other 2D carbon membranes like GYs and graphenylenes can also provide precise pore shape and size for the ions to interact and permeate through them without any chemical modifications on the membranes. MD simulations studying water desalination through GY nanopores reveal very high salt rejection efficiency and water flux compared to commercial reverse osmosis (RO) membranes.104,110 α-, β-GYs and GY3 have 100% salt rejection efficiency, while GY4 with larger pores allows the permeation of some of the ions.110 As these membranes are highly conjugated, cation- interactions play an important role in the permeation of the ions. Our group employed cluster-based model compounds such as dehydrobenzoannulenes and cyclohexaphenylenes for GYs and graphenylenes, respectively for estimating cation- interaction strengths and investigating selectivity in transmission of ions through the pores.106,107,111 We used dispersion-including density functionals for



computing the binding energies and energy barriers for transmission through the pores. -GY allows Li+ ions to pass through with a slight barrier (Figure 5h), while Na+ and K+ ions are not permeable through -GY due to large barriers. In contrast, GDY allows all the three alkali metal ions to permeate without any barrier. Graphenylene provides a barrierless passage for the Li+ ions through the pores. The barrierless passage of Li+ through the pores of GDY and graphenylene further suggested a potential role for GDY and gaphenylene in the context of energy storage in lithium ion batteries (Figure 5h). Contrary to the case of graphite, wherein only in-plane diffusion of lithium is possible, lithium in -GY, GDY and graphenylenes can undergo an out-of-plane diffusion in addition to the in-plane diffusion. The increased propensity for the out-of-plane diffusion of lithium in -GY, GDY and graphenylenes therefore provides an edge for these novel carbon-based materials over graphite as electrode materials in lithium ion batteries. Nanopores terminated by electronegative atoms like nitrogen and fluorine favor the passage of cations, while hydrogen-terminated nanopores allow the passage of anions.98,101 The binding affinities are dictated by the electrostatic interactions of the ions and the partial charges on the functional groups. Cohen-Tanugi et al. performed MD simulations to assess the salt rejection performance of hydroxylated and hydrogenated graphene nanopores.99 Permeabilities of water and alkali metal ions are shown to be higher for the hydroxylated nanopores compared to the hydrogenated nanopores, but hydrogenated pores exhibit better salt rejection efficiency. The hydroxylated pores can participate in hydrogen bonding interactions with water molecules as well as ions, thereby providing a smoother entropic surface for permeation, resulting in larger flux of molecules through the pores leading to lower salt rejection efficiency. In hydrogenated pores, simulations reveal that water is in more orderly arrangement near the pores and has a lesser propensity for hydrogen bonding. Ions like Li+ and F- are strongly hydrated due to their smaller radii and larger effective nuclear charge and hence show the lowest passage rates, 36 Environment ACS Paragon Plus

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whereas K+ and Br- ions pass through the pores relatively smoothly as their hydration shell can be removed easily when they interact with polar and charged nanopore regions.101 Application of electric field increases the permeability and selectivity for the ions (Figure 5i). Increase in permeability can be attributed to two effects: (i) electric field breaks the coulombic binding of the ions to the pore and polarises water molecules near the pore,100,101 and (ii) increased polarisation results in lowering of barrier heights and promotes ‘polarization-induced chaperoning of ions’.100 In contrast to the conventional diffusive RO membranes, salt rejection efficiency of a given nanoporous carbon membrane decreases with increase in applied pressure, since the permeability depends on the volume of the solvated ions.112 MD simulations on GY membranes for water desalination show that GY3 has complete salt rejection capability, while the salt rejection abilities of GY4 and GY5 decrease with increase in hydrostatic pressure.112 GY3 and GY4 membranes have a potential advantage over conventional RO membranes due to higher flow rate and salt rejection efficiency. Nanoporous carbon membranes are also proposed to be useful for the removal of heavy metal ions with better efficiencies compared to the RO membranes113. GO sheets are recently well explored for water desalination due to their ease of fabrication.114,115 In GO membranes, permeation occurs through the pores as well as the interedge spaces of the layers116 and can be controlled by a variation in porosity and edge area. GO sheets are hydrophilic in nature and interlayer separation between hydrated graphene oxide sheets is ~9 Å, implying that ions of hydrodynamic radii less than 4.5 Å pass through the membrane.115 Interlayer separation and ion rejection ability of GO can be modified by ion adsorption or metal coordination on sheets or by chemical reduction.103 Intercalated cations in GO membrane allow ions of similar or smaller size to pass through.114 First-principles calculations can also account for the quantum mechanical tunneling effects and isotopic separation of ions. Graphene membranes were recently shown to provide an isotopic separation



ratio of 10 for H+/D+.72 Difference in the permeances of the isotopic species arises due to differences in their isotope-dependent velocities, which in turn depend on the quantum ZPEs (Figure 3f). Graphene sheets containing defects like the STW defect increase the ratio of isotopic separation further.72 Thus, we can infer that nanoporous carbon membranes provide ample avenues for high-end technological applications in lithium ion batteries, water desalination, toxic metal removal,113 isotopic separation etc. It is interesting to note that, most of the above suggestions are based on theoretical design principles and are yet to be realized in experiments. With the current advancements in synthetic methodologies and device fabrication protocols, we believe that technologies employing carbon membranes would soon become a reality. SEPARATION OF HYDROCARBONS USING CARBON MEMBRANES Sieving techniques employing graphene nanomeshes are no longer restricted to the investigations on permeation of atoms, ions, and small molecules. Recent efforts are directed towards achieving hydrocarbon separation, an industrially relevant process, using graphene nanomeshes, wherein the permeability of hydrocarbons through nanopores depends on the area and the diameter of the pores, chemical functionalities on the nanopores, length of the hydrocarbon, geometry of the hydrocarbon, etc. Using MD simulations, Nieszporek and Darch have suggested the separation of a mixture of methane, ethane, propane, butane and isobutane by employing a series of hydrogen-passivated graphene nanopores with pore diameters in the range 0.32 - 0.76 nm.117 Permeation of methane dominates over butane for the smallest pore (diameter of 0.32 nm) when the bimolecular mixture is considered.117 However, for the larger pore of diameter 0.76 nm, reversal in selectivity occurs, i.e., butane permeates much faster than methane through the nanopore, as depicted in Figure 6a. This is referred to as the cork effect by methane, which exhibits attractive interactions with the nanopore, blocks the pore and does not permeate through the pore (inset of Figure 6a). The rate of translocation of alkanes through 38 Environment ACS Paragon Plus

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the nanopores is mainly related to the relative distance between the pore and the molecule and the average translocation time. Shorter alkanes can easily pass through the nanopores one by one with smaller average translocation time. Li et al. have studied the translocation of linear alkanes (CnH2n+2, n=10-50; in short Cn) through three different oxygen-passivated graphene nanopores of diameters 0.585 nm (pore-a), 0.789 nm (pore-b), and 1.287 nm (pore-c) using MD simulations.118 Initially, simulations were carried out at various temperatures ranging from 100 K to 400 K for a time period of 2 ns to study the passage of thirty C11 molecules through the pores. Pore-a is too small for the passage of the C11 molecules. Pore-c is wide and more than one molecule can pass at a time, making the translocation process more complex. Pore-b (inset of Figure 6b), therefore serves as an ideal nanopore allowing only one C11 molecule to pass at a time. At low temperatures (100-200 K), C11 possesses very less kinetic energy and at high temperatures, it undergoes dissociation. Therefore, pore-b and a temperature of 298 K were found to be ideal for further investigations of the permeation of various alkanes through the nanopores. Hence, simulations were performed at 298 K for the translocation of all alkanes ranging from C10 to C50 through pore-b. Radial distribution functions between carbon atoms of alkanes and carbon atoms of the pore reveal the relative positions of alkanes with respect to the pore. Chain length plays a significant role in the translocation process, and the authors have shown that the translocation time increases and the translocation rate decreases with increase in chain length (Figure 6b), in agreement with the experiments.119,120 Separation of isomers of alkanes is yet another aspect explored using graphene membranes. Zhang and co-workers have reported first-principles calculations on a series of single-layer porous graphene membranes, suggesting that porous graphene with appropriate pore sizes can separate isomers.121 Four graphene-based hydrogen-passivated nanopores (of diameters 5.7 Å, 6.8 Å, 6.9 Å, and 7.3 Å), possessing different pore sizes are considered for the separation of short alkane isomers. An appropriate control of the pore size can render separation of the di-



branched isomers from their mono-branched and linear counterparts. The nanopore of diameter 6.9 Å was suggested as the best nanopore for the separation of the isomers of pentane and this pore is further used to separate hexane and heptane. Investigations were also carried out for few higher order alkanes. From the analysis of the energy barriers for the permeation of the various isomers of pentane, hexane and heptane, the following inferences were made: (i) there is no barrier for the translocation of the linear and mono-branched forms, and (ii) the barriers observed for all the di-branched alkanes are of the same magnitude. Recent studies have highlighted the role of entropy in governing the selectivity in alkane separation through carbon membranes. The translocation of alkanes through nanopores is associated with an entropy cost and this aspect has been investigated by Solvik and co-workers using classical atomistic models.122 The effect of temperature and pressure on the transmission of a variety of hydrocarbons like ethane, ethene, propane, propene, n-butane, isobutane, isobutene, 1-butene, cis-2-butene, trans-2-butene, and 1,3-butadiene through nanometer-sized pores of a novel 2D polyphenylene network (denoted as PG-TP1) have been probed. Gas molecules need to pass through the center of the sheet to cross the PG-TP1 membrane and the calculations reveal zero probability density at the pore center for ethane, but not for ethene. Ethane therefore takes more time than ethene to pass through. Computed potential energy profiles obtained using MD simulations as well as nudged elastic band calculations show that the interaction is attractive, not repulsive throughout the entire barrier crossing process. Ethene and ethane both have comparable well depths, but the absence of probability density for ethane at the pore center indicates that it is not trapped in the well. Ethane therefore possesses an entropic barrier of the type described by Zwanzig,123 instead of the potential energy barrier, enabling high selectivity in hydrocarbon separation. The variation in entropy during translocation depends on the number of possible conformations and orientational configurations within a pore. Higher translocation rate for ethene than ethane could be attributed to a lower number of configurations


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for ethene in PG-TP1 nanopore (Figure 6c). On similar lines, the entropic contributions for the permeation of propene over propane, and 1,3-butadiene over other butanes could be accounted for. Alkanes with larger branches were completely rejected by the nanopores. An antiArrhenius behavior was observed since increase in temperature leads to a decrease in the number of crossings, directly affecting the entropy defined based on the microcanonical definition of the entropy, S = kBlnΩ. Here, Ω is the number of accessible microstates and kB is the Boltzmann constant. The entropy of activation, ΔS‡ = S‡ − S can be estimated as the difference between the entropy of the gas in the transition state (within the pore, S‡) and that of the free gas (S). Thus, the entropic contribution for the permeation of two molecules A and B is given by

‡

‡

e∆(SA −SB )/kB =

(Ω‡A ⁄ΩA ) (Ω‡B ⁄ΩB )

,

which is directly proportional to the Eyring-Polanyi reaction rate. For nanopores of small size, very few orientations of the gas molecules are allowed when compared to the orientations possible for the free gas molecules (Ω‡ ≪ Ω). Ethene has a faster transport rate than ethane because it is easier for the smaller ethene molecule to enter the pore from the gas phase since it has lesser entropic barrier than ethane. Thus, it is clear that, by a careful choice of the nanopore configurations, one can achieve selectivity in the separation of various isomeric forms of alkanes. (a)

(b)


(c)


(d)

(e)

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(f)

Figure 6. Hydrocarbon and chiral molecular separation using carbon membranes: (a) selective permeation of butane over methane through a graphene nanopore and potential of mean surface energy (PMF) for methane as inset, (b) effect of chain length on alkane permeability, (c) antiArrhenius behaviour of the crossing rate (rate decreasing with increase in temperature), (d) transition state structures for the permeation of chiral species with gatekeeper attached to a graphene nanopore, (e) (i) H-passivated hexagonal graphene nanoflake along with the (ii) nonhelical (mutual rotation angle is 0º) and (iii) helical flakes (mutual rotation angle is 60º); one of the carbons is highlighted in dark colour to show the angle, and (f) number of L- and Dleucine molecules permeated through the two types of flakes. Figure a is adapted with permission from ref 117. Copyright Royal Society of Chemistry. Figure b is adapted with permission from ref 118. Copyright Springer Nature. Figure c is adapted with permission from ref 122 and figures e and f are adapted with permission from ref 98. Copyright American


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Chemical Society. Figure d is adapted with permission from ref 124. Copyright John Wiley and Sons.

ENANTIOSELECTIVE PASSAGE THROUGH CARBON MEMBRANES Separation of the chiral enantiomers from racemic products is a viable alternative for expensive and complex enantioselective syntheses of drugs or natural products. Conventionally, chromatography-based separations are employed, wherein the nature of interactions between the chiral components and the racemic stationary phase governs the separation efficiencies. This process is costly, time-consuming and may produce harmful sub-products.125 Hauser and co-workers have therefore proposed an out-of-plane functionalized graphene nanopore that could be potentially used for chiral separation.124 In this process, separation of the chiral components occurs in terms of a yes-or-no decision, implying that the components either pass through the pore or not. Symmetry dictates chiral ineffectiveness for most of the general nanopores discussed thus far, as molecules can approach from either side of the pore. Out-ofplane functionalization is suggested as a viable solution to this problem, as the functionality can act as a gatekeeper or a molecular doorman for molecules of different chiralities. In their work, Hauser and co-workers considered a hydrogen-passivated trapezoidal pore consisting of 17 carbon rings, and an enantiomeric form of 1-aminoethanol is used as the gatekeeper to separate R- and S-1-aminoethanol.124 Gatekeeper molecules form dimers with the incoming chiral molecules, with a small difference in their binding energies between the two chiral components, insufficient to enable chiral separation. However, reasonable free energy differences for the permeation of the chiral components through the nanopore are obtained from subtle differences in sizes and orientations of the chiral components. As a result, one of the enantiomers fits into the pore, while the other one is blocked, as shown in Figure 6d. This



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model can be extended to various nanopore architectures and enantiomeric pairs by a rational choice of the gatekeeper molecules. If this approach becomes viable experimentally, it can be used as an alternative to the conventional chromatographic separation method for chiral molecules. Chiral molecules can also be separated by using multilayer graphene nanopores under an electric field. Recently, Yan and co-workers have proposed a new set of helical graphene nanoflakes which are capable of separating ionized L- and D-leucine.98 Flakes were prepared by placing six hydrogen-modified graphene layers with a mutual rotation of 0° and ±60° and at mutual distances of ~ 3.35 Å, giving rise to two kinds of multilayer flakes, namely non-helical and helical (Figure 6e). In MD simulations carried out under the presence of a 0.8 V/nm electric field, flakes were allowed to change their conformations. The dynamics during the last 150 ns of the 200 ns simulations clearly indicate that non-helical flakes (rigid as well as freely moving) and rigid nanoflakes in the helical structure are not selective towards any of the forms of leucine (Figure 6f). In the case of freely moving helical flakes, L-leucine had twice larger transport rate than D-leucine, suggesting enantioselectivity in permeation. Therefore, stacked porous graphene channels with helical profiles can show excellent enantioselectivity towards molecular transport and can be used in nanofluidic devices.126 TRANSLOCATION

OF

BIOMOLECULES

THROUGH

CARBON-BASED

NANOPORES Biomolecular translocation through carbon membranes is yet another very exciting area with potential implications in biology (Figure 7a). A new era in nanobiotechnology started with the first report of successful translocation of DNA through nanoporous graphene by Merchant et al.127 Graphene membranes have shown exceptional sensitivity towards reading both double and single stranded DNA.128,129 A voltage was applied across the chamber of an electrolyte solution, driving the DNA along with the electrolyte ions through a nanoscale-sized, atomically thin nanopore. The nucleobases of DNA show various affinities towards the ions of the 44 Environment ACS Paragon Plus

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electrolyte, which differentially block the current through the nanopores as the DNA translocates (Figures 7b and 7c). The differential fall in current when each of the nucleobases translocates enables DNA sequencing using graphene nanopores, which is a low-cost, high throughput DNA sequencing technique.130 One of the challenging aspects of using graphene to detect DNA is to decrease their translocation speeds. For a monolayer graphene nanopore, translocation speed is so high to be able to detect nucleobases under high voltage conditions. A plausible solution to this problem is to employ ionic liquids in order to elongate the translocation time and lower the translocation rate. Kulkarni et al. have investigated saltdependent ion transport during translocation and found that the presence of stronger positive ions near the pores lends strong interactions with nucleobases, leading to reduced translocation speeds.131 Another solution to decrease translocation speed is to use multilayer graphene (MLG) nanopores (Figure 7d), which increase the translocation time by a great amount.132 Employing bilayer OH-passivated graphene, Prasongkit et al., in their MD simulations and DFT calculations, have successfully deciphered the DNA sequences by reading the interlayer conductance during passage.133 Liang and co-workers have studied the effect of MLG nanopores made from 1, 3, 5, 7, and 9 layers with a pore radius of 1.5 nm and found that the translocation time is directly proportional to the number of layers until 7 layers are reached and decreases further on increasing the layers.134 There exists a critical number of layers for the optimal performance, as MLGs soon approach the three-dimensional limit of electrically conducting graphite, causing high noise in sequencing (Figure 7e). However, in experiments wherein very low electric field (30 mV/nm) is applied, the effect of thickness is hardly observable due to the long sticking times and trapping times for DNA. Theoretical calculations inferred that application of a high voltage (100 mV/nm) increases the translocation time, as can be seen from the estimation of translocation times for various MLGs as depicted in Figure 7f. As the number of layers increases, the nanopore resistance increases and therefore the average



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current for each nanopore decreases. The theoretical model elucidates the role of the number of layers in governing translocation and sequencing and lends good agreement with the experimental results. Bonome and co-workers studied the translocation of a protein, thioredoxin along with ions across a graphene nanopore of 1.5 nm diameter under voltagedriven condition.135 The pathway has been observed by integrating all dynamic pathways with a bioinformatic analysis that can assist in protein sequencing. Later, the authors have proposed a set of self-tunable class of single-layer graphene-based nanopore devices to control conductance for single biomolecular translocation.135 Using MD simulations, they have demonstrated detection of glycine, the smallest amino acid in aqueous water and saline solution, with high sensitivity and up to 90% change in conductance. In the case of the nitrogenpassivated device, sensitivity gets even more enhanced due to intramolecular electrostatics. Such devices are highly promising and can be used as potential tunable biosensors towards next generation single-biomolecule detection. (a)

(b)

(c)

(d)

(e)

(f)


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Figure 7. DNA translocation through carbon membranes: (a) various stages of

DNA

translocation through a graphene nanopore, (b) time variation of the ionic current through the nanopore for single-stranded DNA (ssDNA) translocation, (c) translocation time vs biased current profiles for ssDNA (blocked current plots are shown as insets), (d) DNA translocation through multi-layer graphene, (e) time variation of the current for DNA translocation through 9 layer graphene nanopores, and (f) variation in translocation time with the number of nanolayers under 100 mV/nm and 30 mV/nm, respectively. Figures b and c are adapted with permission from ref 129. Copyright American Physical Society. Figures e and f are adapted with permission from ref 134. Copyright Royal Society of Chemistry. CONCLUSIONS AND OUTLOOK Overall, theoretical investigations of permeation through one-atom-thick carbon membranes have been pursued with great interest, not just to decipher the fundamental aspects of the permeation process but to contribute to the design of intelligent membranes for applications like gas separation, isotope separation, energy storage, water desalination, hydrocarbon separation, chiral separation and DNA sequencing. The authors believe that molecular dynamics simulations and electronic structure calculations can be employed synergistically to elucidate the role of kinetic diameters of the permeating species, geometrical features of the nanopores, electronic interactions between the permeating species and the carbon membranes, quantum mechanical effects etc. in governing the selective permeation of various species. Studies on chiral separation and hydrocarbon separation are in their infancy and theory can open up numerous avenues by suggesting appropriate design strategies which can render effective separation protocols that can be tested in experiments. Strategies for tethering appropriate gatekeeper molecules that can render efficient chiral separation of pairs of enantiomers need to be evolved.



A very recent study by Borges et al. suggested the utility of GO membranes for alcohol dehydration.136 Size effect as well as faster water dynamics compared to the alcohol dynamics help in the selective permeation of water. In contrast, graphene/CNT membranes facilitate faster permeation of alcohol through the pores due to the stronger hydrophobic interactions between alcohol molecules and the carbon substrates.137 The employability of porous carbon networks for liquid separation is still an area to be widely researched, since most studies thus far have focused on gas separation. Experimental studies on nanoporous carbon membranes for separation applications are still largely limited due to the challenges faced in the syntheses of various membranes. For instance, although there are numerous theoretical studies on the use of GYs for separation purposes in last few years, their experimental realization has met with limited success due to lack of synthetic protocols. Only GDY sheets and nanotubes have so far been successfully synthesized.36 Therefore, research aimed at evolving synthetic strategies for achieving separation of molecules using one-atom-thick membranes is highly desired. Theoretical challenges involve the high computational cost of electronic structure calculations for obtaining an accurate description of the permeation of various species through membranes large enough for commercial applications. Improved theories and faster methodologies might help pave way for a better quantum mechanical understanding of these processes. The role of light in achieving selective permeation is yet another aspect that can be pursued by researchers in future. For instance, it is interesting to think of tethering functionalities to the nanopores that can respond to light in specific ways, thereby lending control on the selectivity in permeation via light as a stimulus. Although there are recent studies investigating photoswitching on surfaces138,139, employing photoswitching as a mechanism for achieving the selective permeation through nanopores has not yet been realized. Another emerging area of interest is separation using multilayer carbon membranes, as they can be more easily synthesised than single layers. By manipulating various configurational variables like number of layers, layer


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separation, pore alignment etc., it should be possible to tailor the design of desirable multilayer substrates for separation applications. ACKNOWLEDGMENT RSS acknowledges the Science and Engineering Research Board (SERB), Government of India for financial support through the SERB Women Excellence Award Scheme. CO, AJ and CJ thank IISER-TVM for financial support. RD thanks the Department of Science and Technology (DST), Government of India for financial support through the INSPIRE fellowship. The authors are grateful to P. P. Rafeeque for graphical support. REFERENCES (1)

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AUTHOR INFORMATIONS Cheriyacheruvakkara Owais is an Integrated PhD student pursuing his doctoral studies under the supervision of Dr R S Swathi at the School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram (IISER-TVM), India. His research focuses on


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employing continuum approaches for modeling carbon-based nanostructures such as graphene, carbon nanotubes and graphynes. Anto James is currently pursuing his doctoral studies under the supervision of Dr R S Swathi at IISER-TVM. His research is aimed at designing nano-oscillators by investigating the permeation of fullerenes through the pores of higher order graphynes. Chris John is an Integrated PhD student pursuing her doctoral studies under the supervision of Dr R S Swathi at IISER-TVM. Her research focuses on developing optimal parameters for model potentials governing the interactions of atoms and molecules with graphene, carbon nanotubes, as well as boron nitride sheets and tubes. Rama Dhali is a BS-MS student at IISER-TVM working under the supervision of Dr R S Swathi. She is currently a recipient of the INSPIRE fellowship. Her research is aimed at investigating the permeation of noble gases through nanoporous carbon membranes such as graphene crown ethers. R S Swathi obtained her PhD from Indian Institute of Science, Bangalore under the guidance of Prof. K L Sebastian in the area of theoretical chemistry. Subsequently, she joined as an Assistant Professor in School of Chemistry, IISER-TVM. Her research group employs analytical as well as computational approaches for modeling the interactions of atoms, ions and molecules with carbon-based and metal-based nanostructures. She is a recipient of the Young Scientist Awards from Indian National Science Academy, New Delhi, National Academy of Sciences, Allahabad and Kerala State Council for Science, Technology and Environment. She is an Young Associate of the Indian Academy of Sciences, Bangalore. Swathi has also been awarded the Distinguished Lectureship Award of the Chemical Society of Japan for her work in the area of theoretical chemistry. She is currently on the Editorial Advisory Board of the journal, ACS Applied Materials & Interfaces.




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ACS Paragon Plus Environment

Selective Permeation Through One-Atom-Thick Nanoporous Carbon

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