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Graphdiyne and graphyne: from theoretical predictions to practical construction Yongjun Li,a Liang Xu,ab Huibiao Liua and Yuliang Li*a Flat carbon (sp2 and sp) networks endow the graphdiyne and graphyne families with high degrees of p-conjunction, uniformly distributed pores, and tunable electronic properties; therefore, these materials are attracting much attention from structural, theoretical, and synthetic scientists wishing to take advantage of their promising electronic, optical, and mechanical properties. In this Review, we summarize

Received 29th October 2013

a state-of-the-art research into graphdiynes and graphynes, with a focus on the latest theoretical and

DOI: 10.1039/c3cs60388a

experimental results. In addition to the many theoretical predictions of the potential properties of graphdiynes and graphynes, we also discuss experimental attempts to synthesize and apply graphdiynes in

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the areas of electronics, photovoltaics, and catalysis.

1. Introduction Although living a low-carbon life is important to many people, carbon appears everywhere in our daily lives. Carbon-rich molecules and materials [e.g., graphene,1 graphite,2 diamond, fullerenes,3 nanostructured and amorphous carbon4,5 (Fig. 1)] display a wide range of mechanical, electronic, and electrochemical properties, leading to many advanced applications, including photovoltaic cells, organic light-emitting diodes (OLEDs), field-e ect transistors, and chemical sensors.6 8 There are only two major naturally existing carbon allotropes: diamond and graphite; they feature extended networks of sp3- and a

Beijing National Laboratory for Molecular Sciences (BNLMS), CAS Key Laboratory of Organic Solids, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P.R. China. E-mail: [email protected]; Fax: +86-10-82616576; Tel: +86-10-62588934 b Graduate University of Chinese Academy of Sciences, Beijing 100190, P.R. China

sp2-hybridized carbon atoms, respectively.9 The discovery of fullerenes,3 nanotubes,10 and graphene1 expanded the categories of available zero-, one-, and two-dimensional (0D, 1D, and 2D, respectively) sp2-hybridized carbon materials. Theoretically, carbon allotropes can be constructed by changing the periodic motifs within networks of sp3-, sp2-, and sp-hybridized carbon atoms due to the versatile flexibility of carbon atoms.11,12 Graphyne (GY), which features assembled layers of sp- and sp2-hybridized carbon atoms, has been proposed to be a synthetically approachable carbon allotrope.13 This planar, layered material, containing both hexagonal rings and acetylenic linkages, was named for its relationship to graphite and its acetylenic components. Haley et al. proposed the preparation of graphdiyne (GDY),14 which contains two diacetylenic linkages between repeating patterns of carbon hexagons. The networks of GDY and GY both contain sp- and sp2-hybridized carbon atoms; they can be thought of as hybrid systems of graphene (sp2-like carbon atoms) and carbyne (sp-like carbon atoms)15 (Fig. 2). The flat (sp2- and sp-hybridized)

Yongjun Li was born in 1975 in Sichuan, China. He received his Master s degree in Chemistry from Sichuan University in 2001, and he earned his PhD in organic chemistry in 2006 at ICCAS. He is currently an associate professor in Prof. Yuliang Li s group, ICCAS, working on the design and synthesis of functional molecules. Yongjun Li

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Liang Xu was born in 1987 in Shanxi, China. He is now studying at ICCAS as a Master Doctor combined program graduate student under the supervision of Prof. Yuliang Li. His research interest focuses on the design and synthesis of functional molecules.

Liang Xu

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Fig. 1

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Naturally existing and man-made carbon allotropes.

anode materials in batteries in some cases, their utility has been realized experimentally. Because of their promising electronic, optical, and mechanical properties, the members of the GDY and GY family have attracted much attention from many structural, theoretical, and synthetic scientists.11,12 It is believed that 0D, 1D, and 2D forms of GDYs and GYs can compete in various potential applications with conventional sp2-hybridized carbon systems, namely fullerenes, nanotubes, and graphene, and meet the increasing demand for carbon-based nanomaterials. In this Review, we summarize and discuss the state-of-the-art research into GDYs and GYs, with a focus on the latest theoretical and experimental results. In addition to the many theoretical predictions of the potential properties of GYs, we also discuss experimental attempts to synthesize and apply GDYs in the areas of electronics, photovoltaics, and catalysis.

2. Theoretical predictions of GDYs and GYs 2.1

Fig. 2 Hybridization classification. A mixed configuration of carbon atoms can be classified as sph, according to the fraction of sp- and sp2-hybridized carbon atoms, where 1 o h o 2. [Reproduced with permission from the Royal Society of Chemistry (ref. 15).]

carbon networks endow the members of the GDY and GY family with high p-conjunction, uniformly distributed pores, and tunable electronic properties. They have possible applications as gas separation membranes, energy storage materials, and

Structural predictions and investigations of stability

The equilibrium atomic structures of 2D one-atom-thick networks of hexagonal GYs have been investigated using several computational approaches. Table 1 provides a summary of the computed bond lengths. For GYs, the predicted bond lengths are 1.48 1.50 ¯ for aromatic bonds (i.e., sp2), 1.46 1.48 ¯ for single bonds, and 1.18 1.19 ¯ for triple bonds (i.e., sp). The single bonds are contracted and the aromatic bonds extended relative to typical values (ca. 1.54 and 1.40 ¯, respectively19) because of weak conjugation between the alkyne units and the benzene rings, reflecting the hybrid effects of the sp- and sp2-hybridized carbon atoms. The mean bond lengths have been used to quantitatively ascertain the lattice spacing; first principles20 and molecular dynamics (MD)21 calculations have revealed homogeneous increases in the lattice spacing of extended GYs. For example, full atomistic first-principles-based ReaxFF MD analysis has indicated a regular increase in the lattice

Huibiao Liu was born in 1970 in Jiangxi, China. He received his PhD degree in 2001 at the Nanjing University. He is currently a professor in Prof. Yuliang Li s group, ICCAS, working on inorganic organic hybrid nanomaterials.

Huibiao Liu

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Yuliang Li

Yuliang Li (Qingdao, China, 1949) is a professor at the Institute of Chemistry, Chinese Academy of Sciences. His research interests lie in the fields on design and synthesis of functional molecules, selfassembly methodologies of low dimension and large size molecular aggregations structures, chemistry of carbon and rich carbon, with particular focus on the design and synthesis of photo-, electro-active organic inorganic hybrid materials and nanoscale and nano-structural materials.

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Calculated equilibrium bond lengths (Å) [Reproduced with permission from the Royal Society of Chemistry (ref. 15)]

Work 15,43

Cranford and Buehler Baughman et al.16 Yang and Xu21 Narita et al.20 Bai et al.22 Mirnezhad et al.17 Peng et al.32 Pei18

Aromatic

Single

Triple

Note(s)

1.48 1.50 1.428 1.405 1.406 1.419 1.440 1.423 1.426 1.431

1.46 1.48 1.421 1.341 1.396 1.401 1.341 1.400 1.404 1.407 1.337 1.395

1.18 1.19 1.202 1.239 1.240 1.221 1.239 1.219 1.223 1.231

MD, ReaxFF potential; extended GYs MNDO; canonical (1987); GYs MD, AIREBO potential; extended GYsa DFT, LSDA; extended GYs DFT, GGA-PBE; GDY onlya DFT, GGA-PBE; GY only KS-DFT; GY only VASP, GGA-PBE; GDY onlya

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a

Range of single bond lengths, due to di erentiation between interior single bonds (connecting two sp-hybridized carbon atoms) and exterior single bonds (connecting sp- and sp2-hybridized carbon atoms).

spacing of approximately 2.66 ¯,15 whereas quantum level analysis has given an increase of approximately 2.58 ¯, upon addition of a single acetylene linkage (with slight variations as a result of discrepancies in bond lengths of the implemented atomic orbital method20). These results indicate that the addition of extended acetylene linkages does not lead to large structural variations. The diversity of C C bonds results in the structural flexibility of GYs being greater than that of graphene, thereby offering the opportunity to form curved structures, such as nanotubes, but with the disadvantages of weakened mechanical stiffness and decreased chemical stability. A low formation energy and high thermal stability is predicted for GY, although the formation energy is higher than that for graphite. The presence of acetylenic (diacetylenic) linkages in these 2D carbon networks decreases their stability relative to those of graphene and some other sp2-like graphene allotropes. Baughman et al.16 first predicted from modified-neglect-of-diatomic-overlap (MNDO) quantum chemical calculations that GY would have a high temperaturestability of 12.4 kcal mol 1 per carbon atom; the energy per atom was used to assess the relative stability of each GY. Qiao et al. calculated22 the energy (E) for GDY to be 0.803 eV per atom (with respect to graphene); the corresponding values for diamond, graphite, (6,6)-nanotubes, C60, and carbyne are approximately 0.022, 0.008, 0.114, 0.364, and 1.037 eV per atom, respectively. Density functional theory tight-binding (DFT-TB) calculations have been used to systematically study the stability and structural properties of 2D planar carbon networks (such as GY and GDY),23 where the difference in total energy between the allotrope (En-yne) and pristine graphene (Egraphene) was defined as dE (per carbon atom). Based on the fraction of sp- and sp2-hybridized carbon atoms, the energies of GYs can be predicted well in terms of the number of acetylene linkages (n) or the hybridization (h) (Fig. 3A and B). Their stability decreases upon increasing the number of acetylenic linkages ( CRC ) in the GY-like networks. Similar predictions23 of the values of E for a series of (sp2 + sp)-like 2D carbon networks have been obtained through the DFT-TB approach, leading to the conclusion that the stability decreases upon increasing the ratio of sp- to sp2-hybridized carbon atoms. 2.2

Electronic properties

First-principles calculations have indicated that GY allotropes have a natural band gap, in contrast to the zero band gap of graphene.20 The existence of a direct band gap facilitates the

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Fig. 3 Using differential energy per atom (dE) to assess the relative stability of GYs. The energy of GYs can then be predicted theoretically through (A) the number of acetylene groups (n) or (B) the hybridization (h) (solid lines). For comparison, previous first-principles results5,16 are plotted along with the current computational results (black crosses). The energy of carbyne (dEmax = 1.17 eV per atom) provides an asymptotic limit; the GY structures are less stable as they approach pure sp-hybridization. [Reproduced with permission from the Royal Society of Chemistry (ref. 15).]

application of GYs in photoelectronic devices. Both GY and GDY are semiconductors with direct transitions at the M and G points of the Brillouin zone, respectively. The minimal band gaps of these GYs have been predicted to exist in the range from 0.46 to 1.22 eV, depending on the applied methods and exchange correlation functionals.24 Baughman et al.11 estimated

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Dirac cones, and their associated transport properties, had originally been considered as a unique feature of graphene, ¤rling et al.28 demonstrated related to its hexagonal symmetry. Go that Dirac points and cones not only exist in a- and b-GY, which have hexagonal symmetry, but also in 6,6,12-GY, which has rectangular symmetry (Fig. 5). These phenomena reflect the extreme charge-transport properties in GY materials. Novel direction-dependent electronic properties, such as novel conductivities, are predicted in these GY structures. The intrinsic mobilities of holes and electrons in 6,6,12-GY at room temperature (4.29 105 and 5.41 105 cm2 V 1 s 1, respectively) are

Fig. 4 (A) Geometrical structure, unit cell (red dashed diamond), coordinate bases, and first Brillouin zone (green hexagon) of GDY. (B) Band structures and density of states (DOS) of GDY at the LDA and GW levels. Optical transitions between the first two Van Hove singularities are indicated. (C) Experimental absorbance (blue circle) of GDY film and theoretical absorbance at the GW+RPA (green dotted line) and BSE (red solid line) level of GDY. [Reproduced with permission from the American Physical Society (ref. 25).]

¤ckel level of the band gaps to be 0.79 eV using the extended Hu theory; Narita et al.20 obtained a band gap of 0.52 eV using the local spin density approximation (LSDA) within the framework of DFT. Employing the GW many-body theory, Lu et al. obtained a value for the band gap of a GDY monolayer of 1.10 eV, increased from a value of 0.44 eV obtained using local density-approximation (LDA) (Fig. 4B).25 The optical absorption spectrum obtained from calculations using the Bethe Salpeter equation (BSE) is in good agreement with the experimental result: three absorption peaks obtained experimentally at 0.56, 0.89, and 1.79 eV correspond to the BSE excitonic peaks at 0.75, 1.00, and 1.82 eV, respectively (Fig. 4C). Smith et al.26 predicted that the band gap of 1.22 eV, similar to that of silicon, would render GYs as possible replacements in silicon electronic devices; for example, GY is a better candidate than graphene for use in field effect transistors. Froudakis investigated the possibility of using hydrogenation to tailor the electronic properties of GDY.27

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Fig. 5 (A) Chemical structures of GYs. (B) Electronic structures of b-GY: (a) Band structure. (b) DOS. (c) First Brillouin zone with letters designating special points and with the lines along which the band structure is displayed. (d) Dirac cone formed by the valence and conduction band in the vicinity of the Dirac point. (C) Electronic structures of 6,6,12-GY: (a) band structure; the two different Dirac points are labeled I and II. (b) DOS. (c) First Brillouin zone, with letters designating special points (d and e) Dirac cones (d) I and (e) II; gray planes indicate the Fermi level. [Reproduced with permission from the American Chemical Society (ref. 29).]

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larger than those in graphene (ca. 3 105 cm2 V 1 s 1).29 Cao et al.30 obtained concrete analytical expressions for the energy dispersion relations in the vicinity of the Dirac points in these three GYs. Furthermore, they found an unusual phenomenon in b-GY: the quantum Hall e ect diminishes when its Dirac points are all located at the M points. The strain-induced semiconductor semimetal transition in GDY was discovered through first-principles calculations combined with the tight-binding approximation. The band gap of GDY can increase from 0.47 to 1.39 eV upon increasing the biaxial tensile strain, while it can decrease from 0.47 eV to nearly zero upon increasing the uniaxial tensile strain, with Dirac cone-like electronic structures being observed. Su et al. ascribed the uniaxial straininduced changes of the electronic structures of GDY to the breaking of the geometrical symmetry that lifts the degeneracy of the energy bands.31 2.3

Mechanical properties

E orts have also been devoted to characterize the mechanical properties of GY and other structures in the GY family. GY has a relatively low in-plane Young s modulus (162 N m 1) and a large Poisson ratio (0.429) relative to that of graphene. Calculations have indicated that GY can sustain large nonlinear elastic deformations up to an ultimate strain of 0.2, followed by strain softening until failure.32 Buehler et al.33 also used full atomistic first-principles-based ReaxFF MD to characterize the mechanical properties of single-atomic-layer GY sheets. The c-GY is strongly anisotropic; its fracture strain ranges from 8.2 to 13.2%, while its fracture stress ranges from 48.2 to 107.5 GPa. Compared with graphene, the combination of the sparser carbon arrangement and the directionality of the acetylenic groups in GY leads to internal sti ening depending on the direction of the applied load, leading to a nonlinear stress strain behavior. Buehler et al.15 developed simple scaling laws for the stiffness, strength, and fracture of extended GYs; they found that the introduction of acetylene links (sp-hybridized carbon atoms) resulted in effective decreases in stability, elastic modulus, and failure strength, all of which could be predicted as a function of the number of acetylene repeats or the lattice spacing (Fig. 6). Zhang34 also found that the presence of the acetylenic linkages in the GY structures influenced their Young s moduli, fracture strains, and fracture stresses. The fracture strains and ultimate stresses for different networks depend strongly on the type of applied load (armchair- or zigzaglike); this effect can be explained21 by considering the unique bond elongations and atomic stress distributions among the various conformations of the acetylenic groups. First-principles calculations have been performed to reveal the elastic constants and strain-tunable band gaps of the GY family.35 The in-plane sti ness decreases gradually upon increasing the number of acetylenic linkages from 166 to 88 N m 1 upon proceeding from graphyne to graphyne-4; in contrast, their Poisson s ratios vary by only a small amount. The relationship between in-plane sti ness and number of acetylenic linkages follows a simple scaling law. Upon application of strain, the band gaps of graphyne and its family can be tuned through di erent loading types (Fig. 7). The band gaps increase steadily under

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Fig. 6 Fracture mechanics of GYs. Each GY sheet was subjected to mode-I fracture via the introduction of a crack/wedge. (A) Stress–strain results for each model. Near-linear stress versus strain behavior was observed for each model, supporting the purely elastic results. In terms of critical stress (onset of fracture), failure events are observed that are consistent with those predicted using the linear spring model (with ultimate stresses decreasing from ca. 30 GPa for GY to less than 10 GPa for graphtriyne/graphtetrayne). (B) Visualizations of failure, indicating that, as anticipated, fracture initiates at the crack and propagates along a plane defined by the single C–C bonds of the acetylene links (indicated by arrows). A pronounced shifting (e.g., geometric alignment) of the finite samples is observed in the higher allotropes (n = 3, 4), facilitating the observed ‘‘two-tier’’ effect. [Reproduced with permission from the Royal Society of Chemistry (ref. 15).]

homogeneous tensile strain, but decrease under uniaxial tensile, compressive, and homogeneous compressive strains. Most interestingly, although the band gaps of graphyne and graphyne-3 are direct and located at either M or S points depending on the type of applied tensile strain, graphdiyne and graphyne-4 always maintain their direct band gaps at the G point regardless of the strain. The changes in these band structures are ascribed to the shift in energy states near the Fermi level under the strain. The results suggest that GYs are promising candidate materials for strain-tunable nanoelectronics and optoelectronics.35 2.4

Functionalization of GY

The presence of carbon carbon triple bonds in GYs and GDYs provides the opportunity to introduce adatoms (e.g., hydrogen, fluorine, oxygen) to prepare newly proposed 2D carbon compounds.36 In-plane pattern reactions prefer to occur at these sites, due to the intrinsic characteristics of sp-hybridized

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Fig. 7 (A): (a) Geometric structure of a GY sheet; the primitive cell is denoted by the yellow parallelogram. r-1 and r-2 symbolize the in-plane lattice vectors, which are defined as ( a/2, O3a/2, 0) and (a/2, O3a/2, 0), respectively. Green and blue arrows indicate the deformation directions of Z- and A-strain. (b) Schematic representation of the units of the GY family constructed by acetylene linkages between hexagons. (c–e) Brillouin zone with highsymmetry points labeled under (c) H-strain, (d) A-strain, and (e) Z-strain. (B): (a) Band structure of unstrained GDY calculated with GGA-PBE (solid line) and HSE06 (filled circle) functionals. Gv1 and Gv2 represent the highest (doubly degenerate) valence states; Gc1 and Gc2 correspond to the lowest (doubly degenerate) conduction state at the G-point; Fermi level has been set at zero. (b and c) Variations of band gap versus strain, calculated using (b) GGA-PBE and (c) HSE06 functionals. Open triangles, squares, and circles correspond to the direct band gaps under H-, A-, and Z-strain, respectively. [Reproduced with permission from the American Institute of Physics (ref. 35).]

carbon atoms; the planar network of carbon atoms is preserved upon converting the carbon atoms from sp to sp2 hybrids. The extended p-conjugation system is influenced slightly by such in-plane addition reactions. Depending on the species and distributions of adatoms, the resulting 2D carbon compounds can be semiconductive or metallic, provided a good opportunity to modify the properties of the pristine GDs and GDYs for use in electronic and optoelectronic devices, chemical sensors, or energy storage. Computational investigations considering both thermodynamic and kinetic aspects have revealed that GY favors unprecedented homogeneous in-plane addition reactions. The addition of dichlorocarbene to the regioselective C(sp) C(sp) bond in GY occurs through a stepwise mechanism.37 Additions at C(sp) C(sp) bonds generate structurally ordered 2D carbon compounds because of the homogeneous nature of GYs.

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The electronic band structures of 2D carbon compounds are near the Fermi level, similar to those of graphene; these novel materials are either electrically semi-conductive or metallic, depending on whether the reactions break the hexagonal symmetry. More importantly, 2D carbon compounds can be further functionalized through substitution reactions with little damage to the extended p-electron conjugation system. 2D carbon compounds derived from GY possess physical properties comparable with those of graphene and chemical properties superior to those of graphene; thus, 2D carbon compounds are expected to be better candidates for practical applications.37 2.5

Structural and size-based properties

Understanding the structural and size-based properties of carbon materials should lead to new design principles for producing benign, high-performance carbon-based nanoscale materials.

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Fig. 8 (A) Optimized configuration of the bilayer GDY AB(b1) and the band structure at E> = 0 V Å 1; (B) ABA configuration of the trilayer GDY and related band structure at E> = 0 V Å 1. [Reproduced with permission from the Royal Society of Chemistry (ref. 38).]

Variations of, for example, the ribbon width, edge morphology, and edge functionalization should open up new and e ective ways of tailoring their electronic, chemical, mechanical, and magnetic properties. Lu et al. reported that it is possible to tune the electronic structures and optical absorptions of bilayer and trilayer GDYs under an external electric field (Fig. 8).38 In the most-stable bilayer and trilayer GDYs, the hexagonal carbon rings are stacked in a Bernal manner (AB- and ABA-style configurations, respectively). Bilayer GDYs in the most-stable and second-most-stable stacking arrangements have direct band gaps of 0.35 and 0.14 eV, respectively; trilayer GDYs with stable stacking styles have band gaps of 0.18 0.33 eV. The band gaps of semiconducting bilayer and trilayer GDYs generally decrease upon increasing the external vertical electric field, irrespective of the stacking style. The electronic band structure of bilayer a-GY is qualitatively di erent from its monolayer form and depends crucially on the stacking mode of the two layers. Two stable stacking modes are found: the AB stacking mode, a configuration featuring a gapless parabolic band structure, similar to AB-stacked bilayer graphene; and the Ab stacking mode, which exhibits a doubled Dirac-cone spectrum and a band structure around the Fermi-level exhibiting a linear dispersion that can be tuned by an electric field with a gap opening rate of 0.3 eV ¯ 1 (Fig. 9).39 A systematic study of 1D nanoribbons (NRs) of GDY layers would aid our understanding of the possible structural characteristics and electronic properties of this novel carbon allotrope. Cutting the GDY along the direction of the nearest-neighbor carbon hexagons (AfB) results in divan-like edges of the graphdiyne nanoribbon (DGDNR, Fig. 10A I); cutting the sheet along the direction of the next-nearest-neighbor carbon hexagons (AfC) results in zigzag-like edges of the GDNR (ZGDNR, Fig. 10A II). There are two possible types of ZGDNRs obtained by cutting at different sites: those having uniform width (Fig. 10A II) and those having non-uniform width (Fig. 10A III). Fig. 10B F illustrates examples of such structures. First-principles calculations have been used to study the electronic structures of GDY sheets and NRs.40,41 Using first-principles DFT and the Boltzmann transport equation with the relaxation time approximation, Shuai et al.40 calculated the intrinsic charge carrier mobility of GDY sheets (Fig. 11) and GDNRs scattered by the longitudinal acoustic phonon. They found that the electron mobility in a single GDY sheet could reach 2 105 cm2 V 1 s 1 at room temperature,

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Fig. 9 (A) Six different stacking configurations for bilayer a-GY. (B) Binding energy of bilayer a-GY plotted against the relative shift of the upper layer with respect to the lower layer. (C) A single Dirac cone of Ab-stacked bilayer a-GY in the (a) absence and (b) presence of an electric field (0.1 V Å 1). [Reproduced with permission from the American Institute of Physics (ref. 39).]

whereas the hole mobility was an order of magnitude lower. The room-temperature electron mobility of GDNRs could also reach 104 cm2 V 1 s 1 significantly greater than the hole mobility. The charge carrier mobility was found to increase upon increasing the width of the GDNRs, with the mobility of the divan-edged GDNRs being larger than that of the zigzag-edged GDNRs. From a study of more than 20 GY and GDY NRs of various widths, Du et al.41 found that all of these ribbons remained semiconductors. Their band gaps decreased upon increasing the ribbon width. The band gaps of GDY NRs can be tuned by applying transverse electric fields,42 with the band gap decreasing upon increasing the electric field strength; at some values of electric field strength, which also depends on the width and orientation of the NRs, a semiconductor-to-metal transition is predicted. The band gap reduction under an electric field is caused by localization of the near-Fermi states induced by the field; that is, by a giant Stark e ect. Huang et al.22 performed a theoretical investigation of 1D GDY NRs using the self-consistent field crystal orbital (SCF-CO)

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Fig. 10 (A) Schematic representation of three GDY NR building blocks: (I) a divan-like edged GDNR, (II) zigzag-like edged GDNR with uniform width, and (III) a zigzag-like GDNR with alternating width. (B–F) Schematic representations of various building blocks. Structures (B) and (C) are divan-like GDNRs having widths of two and three carbon hexagons, respectively. Structures (D) and (E) are zigzag-like GDNRs having widths of two and three carbon hexagons, respectively. Structure (F) is a zigzag GDNR having two carbon hexagons at its narrowest width and three at its broadest. (G) Band structures of two divan-like edged GDNRs (D1, D2) and three zigzag-like edged GDNRs (Z1, Z2, Z3). The structures of these GDNRs are given in (B)–(F), with D2 wider than D1 and Z2 wider than Z1; Z3 has an edge width alternating between those of Z1 and Z2. [Reproduced with permission from the American Chemical Society (ref. 40).]

Fig. 11 Schematic representation of a single GDY sheet. Band structure and density of states for a single GDY sheet, obtained from DFT calculations. The Brillouin zone is also shown. [Reproduced with permission from the American Chemical Society (ref. 40).]

method under the periodical boundary conditions. The 1D GDY NRs they investigated were all more stable than the 2D GDY slab in terms of energy, with the stability of the GDY NRs decreasing upon increasing their widths. The mobilities of the GDY NRs were also predicted to be in the range from 102 to 106 cm2 V 1 s 1 at room temperature, based on the DP theory and e ective mass approach. Thus, GDY NRs appear to be candidate materials displaying high mobility. The mechanical properties of GYs are also size-dependent. The calculated Young s moduli for most GDY NRs are about half of those for graphene NRs and single-walled carbon nanotubes (SWCNTs), indicating that the GDY NRs are softer materials. Coluci et al. presented a theoretical study of the electronic and mechanical properties of GY-based nanotubes (GNTs). Their investigation of the e ect of charge injection on the dimensions of GNTs indicated that low levels of electron injection should cause qualitatively di erent responses for armchair- and zigzag-type GY nanotubes. Although the behavior is qualitatively similar to that of the usual carbon nanotubes (CNTs), the charge-induced strains are predicted to be smaller for GNTs than for ordinary SWCNTs.43

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Li et al.44 studied the spontaneous magnetization of GY NRs. They found that all divan-like edged GDNRs behave as nonmagnetic semiconductors. In contrast, zigzag-like NRs become magnetic and adopt a ground state with ferromagnetic spin ordering at each edge and the opposite spin orientation between the edges, with magnetic moments depending on the width of the zigzag-like ribbons. First-principles calculations have been performed to investigate the transport properties of zigzag a-GY NRs (ZaGNRs). The results suggested that asymmetric ZaGNRs behave as conductors with linear current voltage relationships, whereas symmetric ZaGNRs have very small currents under finite bias voltages, similar to those of zigzag-like graphene NRs. The symmetrydependent transport properties are ascribed to different coupling rules between the p and p* sub-bands around the Fermi level; they are dependent on the wave-function symmetry of the two sub-bands. The bipolar spin-filtering effect in the symmetric ZaGNRs has also been investigated based on the coupling rules. A spin-polarized current of nearly 100% can be generated and modulated by the direction of the bias voltage and/or the magnetization configuration of the electrodes. In addition, a

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magneto-resistance effect having an order larger than 500 000% is also predicted. Our calculations suggest that ZaGNRs are promising candidate materials for spintronics.45 Theoretical investigations of thermal conductance in GY NRs have indicated that the thermal conductances of GY NRs are approximately 40% of those of graphene NRs, indicating that GY NRs are attractive materials for potential thermoelectric applications.46,47

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2.6

Potential applications

Gas separation. An abundance of pores of various sizes makes GYs ideal molecular sieves for gas separation applications directed toward various separation needs and objectives. From a structural view, GDYs possess uniform and repeating triangular atomistic pores, having van der Waals (vdW) openings with areas on the order of approximately 6.3 ¯2, suggesting their potential use as, for example, superthin separation membranes for the purification of H2 from syngas (a mixture of H2, CH4, and CO). Smith,26 Buehler,48 and Luo49 performed further theoretical studies on the applications of GDY as superior separation membranes for H2 purification an important aspect of the clean energy economy. Buehler et al.48 predicted the mass flux of H2 molecules through a GDY membrane to be on the order of 7 to 10 g cm 2 s 1 (at temperatures between 300 and 500 K), allowing the isolation of CO and CH4 molecules (Fig. 12B). Variations in pressure can trigger the required filtering of H2, CO, or CH4 through a GDY sheet; for example, addition of a driving force (50 100 pN molecule 1) can allow the selective filtering of CO or CH4. Luo49 performed first-principles calculations to determine the H2 separation characteristics of GYs (GY, GDY, and rhombic-GY). The selectivity toward H2 over other gas molecules (e.g., CO, N2, CH4) was sensitive to the pore sizes and shapes. The penetration barriers normally decrease exponentially upon increasing the pore sizes. They found that GY having small pores was unsuitable for H2 separation. GDY, with its larger pores, displays high selectivity (109) for H2 over relatively large gas molecules (e.g., CH4), but relatively low selectivity (103) over small molecules (e.g., CO, N2) (Fig. 12C). In the case of a rhombic-GY monolayer, which

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possesses pore sizes between those of GY and GDY, large di erences appear in the di usion barriers for the penetration of gas molecules through the monolayer; accordingly, high selectivities (>1016) are predicted for the separation of H2 from the other gases. The great advantages of using GYs for gas separation is that they provide unique, chemically inert, and mechanically stable platforms for selective gas separation under nominal pressures through homogeneous material systems there is no need for chemical functionalization or the comprehensive introduction of molecular pores. Water desalination through pristine GY nanowebs. Water desalination through nanoporous membranes has been suggested as an energy-e cient method that might outperform existing commercial technologies, such as reverse osmosis. Buehler et al.50 demonstrated that a carbon nanoweb allowing both barrier-free permeation of water molecules and perfect rejection of salt ions would be an ideal candidate for water desalination. A carbon nanoweb can be fabricated from a monolayer of pristine GY, a 2D allotrope of carbon that is highly inert, robust, and porous, with well-defined triangular atomic pores and oneatom-thick web strings. Through MD simulations and simple kinetic models, Buehler investigated the water permeabilities, salt ion rejections, and associated free energy barriers with respect to the length of the web string (N-acetylenic linkage, which dictates the pore size and porosity of the membrane) and the applied hydrostatic pressure (Fig. 13). The results indicated that graphtriyne (with an e ective pore diameter of 3.8 ¯) would provide the optimal desalination performance. Overall, GY nanowebs outperform existing desalination membranes for water permeabilities by a few orders of magnitude. One important advantage of using GY for water purification is that no chemical functionalization or defects need to be introduced, thereby maintaining long-term device performance. Metal-doped GYs for H2 storage and Li-ion batteries. Metaldoped GYs exhibit fascinating properties. Because of their additional in-plane p states, which do not exist in sp2-bonded graphene and fullerenes, GYs display enhanced binding energy to Ca, allowing them to be optimized as H2 storage materials.51,52 Liu et al. predicted that Li-decorated GY could also serve as a promising candidate

Fig. 12 (A) Schematic illustration of the separation of H2 through GDY membrane. (B) MD simulation snapshot (T = 500 K; t = 30 ps) of the permeation of H2 across a GDY membrane. (C) Energy profiles for the passage of H2, CO, N2, and CH4 through the pores of GDY as a function of adsorption height; the energies of the respective equilibrium adsorption configurations have been set to zero. [Reproduced with permission from the Royal Society of Chemistry (ref. 48), the American Chemical Society (ref. 49).]

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Fig. 14 (A) In-plane and (C) out-of-plane diffusion pathways of Li in bulk GY; (B and D) corresponding energy profiles as a function of intercalation sites. [Reproduced with permission from the American Chemical Society (ref. 54).] Fig. 13 (A) Nanoweb structure (left, in vdW volume-filling view) and simulation unit cell (right, in bond view) of a 2D GY membrane with atomic pores and one-atom-thick strings. Graphtriyne is displayed as a representative case; its chemical structure is displayed in the dashed red rectangle. The vdW area of the triangular nanopore is represented by the dotted green triangle. The effective pore diameter (D) is displayed for the green circle that is tangential to the triangle. (B) Simulation snapshots showing hydrogen bonds as water passes through the nanopores. Snapshot taken for the graphtriyne (N = 3) membrane under DP = 50 MPa. (C)–(F) Simulation snapshots showing contaminants passing through the nanopore: (C) CuSO4, (D) NaCl, (E) CCl4, and (F) C6H6. Snapshots taken for N = 4 under DP = 50 MPa. The red dashed lines represent hydrogen bonds (criteria: cutoff distance, 3 Å; cutoff angle, 201). Color code: purple, C; red, O; white, H; blue, Na; green, Cl; yellow, S; orange, Cu. [Reproduced with permission from the Royal Society of Chemistry (ref. 50).]

for H2 storage, with a storage capacity of up to 18.6 wt%.53 The high mobility and high capacity of Li in multilayered GY suggests potential applications for GY in Li ion batteries.53 56 Unlike graphite, where Li diffusion is limited in the interlayer space (in-plane diffusion), the unique atomic arrangement and electronic structures of GY enable both in-plane and out-of-plane diffusion of Li ions with moderate barriers of 0.53 0.57 eV. The highest Li intercalation density in GY would be LiC4, exceeding the upper limit of LiC6 found in the commonly used graphite54 (Fig. 14). First-principles calculations have indicated that the atomic arrangement of GDY enables a unique Li triangular occupation pattern: each pore accommodates three Li atoms located at three symmetric sites (Fig. 15). The energy barrier of 0.52 eV for the continuous di usion of Li atoms across a single GDY layer has been predicted. These Li atoms can easily penetrate the GDY plane, overcoming an energy barrier of 0.35 eV, resulting in Li atoms being well dispersed on both sides of single-layer GDY. Because of the alternating distribution of triangular-patterned Li atoms on both sides of the GDY plane, the maximum Li storage capacity of GDY monolayers has been predicted to reach as high as LiC3, twice the capacity of graphite and multilayered GDY. With its considerably high mobility and high Li storage capacity, GDY should function as an e cient anode material for Li ion batteries.56

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GDY and GY systems featuring a single adsorbed 3d transition metal atom (V, Cr, Mn, Fe, Co, Ni) are excellent candidates for spintronics. Calculations have indicated that the electronic structures of transition metal GDY/GY systems are sensitive to the on-site Coulomb energy for the transition metal 3d orbital. The adsorption of the transition metal atom not only modulates the electronic structures of GDY/GY systems but also introduces excellent magnetic properties, such as those of a spin-polarized half-semiconductor (Fig. 16). The modulation is generated through charge transfer between the transition metal adatom and the GDY/GY sheet, as well as the electron redistribution of the transition metal intra-atomic s, p, and d orbitals.57

Fig. 15 (A and B) Top and side views of the optimized configurations of GDY occupied by Li atoms with (A) one and (B) three A sites in a single triangle-like pore. (C and D) Electrostatic potentials projected on (C) a parallel plane containing a GDY layer and (D) a perpendicular plane containing h, H, and one of the three A sites. The rainbow is in units of au Å 3. [Reproduced with permission from the American Institute of Physics (ref. 56).]

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Fig. 16 Magnetic moments (M) of transition metal–GDY/GY systems and spin-polarized charge density (SCD) distributions for Co-adsorbed GDY and Mn-adsorbed GY. Dark (red) and light (green) isosurfaces denote spinup and -down charge densities, respectively. [Reproduced with permission from the American Chemical Society (ref. 57).]

Narita et al.58 predicted from LSDA band calculations that K-doped GY should behave as a metal. The presence of the acetylenic linkages in GYs also leads to a significant decrease in thermal conductivity, as a result of the associated low atom density in the structures and weak single bonds in the acetylenic linkages.59 Cai reported that GY is a good, metal-free electrocatalyst for oxygen reduction reactions in acidic fuel cells.60

3. Experimental efforts to synthesize and apply GDY To fulfill the potentially fascinating applications of GY-based materials, GYs must be available in large quantities. The accessibility of novel molecular (e.g., cyclocarbons) and regular polymeric (e.g., GY and GDY) carbon allotropes has greatly

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benefited from the development of new synthesis methodologies over the past decades, such as metal-catalyzed cross-coupling reactions, alkyne metathesis, and templated synthesis. Many monomeric and oligomeric substructures of GY and GDY have been prepared. Dehydrotribenzo[12]annulenes and dehydrotribenzo[18]annulenes61,62 and perethynylated expanded radialenes63 are sections or fragmental model systems of GY and GDY (Fig. 17); they serve as targets for theoretical modeling to gain further insight into the aromaticity and spectroscopic and electronic properties of these materials.64,65 Dehydrobenzo[n]annulenes, which exhibit two-photon absorption properties66 and good electronic conductivities when doped,67 can also be used as photochromic,68,69 highly spin-magnetic,70 and liquid-crystalline71 materials. The details of the syntheses of these GY fragments have already been stated in excellent recent reviews.12,62 The high-yield direct preparation of GDY remained a challenge until Li et al. recently developed an in situ cross-coupling reaction on Cu foil to fabricate large-area ordered films of GDY from hexaethynylbenzene (Fig. 18).72 The Cu foil acts as not only the catalyst for the cross-coupling reaction but also the substrate, providing a large, flat space for directional polymerization when growing the GDY film; accordingly, the polymerization on the flat Cu surface drives the reaction toward the formation of a diyne-polymer.72 The prepared GDY films are uniform and are composed of GDY multilayers. The conductivity has been calculated to be 2.516 10 4 S m 1, comparable with that of Si, and demonstrates that the GDY film exhibits excellent semiconducting properties. Understanding the electronic structure of GDY is necessary if we are to investigate and apply it further. The electronic structure of GDY exposed to air has been investigated using X-ray absorption spectroscopy and scanning transmission X-ray microscopy (Fig. 19). The feature A has been assigned to p*

Fig. 17 Synthesized benzannellated and perethynylated dehydroannulene-derived substructures and perethynylated expanded radialenes for the construction of GY sheets. [Reproduced with permission from Wiley-VCH Verlag GmbH & Co. (ref. 12).]

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Fig. 19 (A) GDY structure. (B) Comparison of C K-edge XANES spectra of SWNTs, graphene oxide, and GDY exposed to air for 1 week (GD-1w) and 3 months (GD-3m). [Reproduced with permission from the American Chemical Society (ref. 73).]

Fig. 18 (A and B) Structures of the (A) hexaethynylbenzene monomer and (B) GDY film. (C) AFM image of GDY film. (D) Tapping-mode 3D height AFM image. (E) Profile of the GDY film height taken along the line marked in C. (F) Current AFM image. (G) I–V curve of GDY film; inset: I–V curve of the GDY film measured on the device. [Reproduced with permission from the Royal Society of Chemistry (ref. 72).]

excitation of aromatic carbon carbon bonds in a carbon ring structure; feature C to s* excitation of carbon carbon bonds; and feature B to the interlayer states or transitions to sp3-hybridized states, due to the presence of oxygenated functional groups (e.g., carboxylate). For GD that had been stored for one week, feature A clearly broadened, relative to those of SWNTs and graphene oxide, because of the contribution of a new feature (A00 ) that is higher in energy than feature A by 0.3 eV. Whereas feature A near 285.5 eV is attributed to p* excitation of unsaturated carbon carbon bonds in a carbon ring structure, feature A00 has been assigned to p* excitation of carbon carbon triple bonds.9,20 Therefore, these features confirm the existence of carbon carbon triple bonds in GDY. The six-membered carbon ring will also contribute to the C spectrum with the p* and s* excitations described as features A and C in Fig. 19B, respectively. Carbon carbon triple bonds at defect sites in GDY have been observed to change into double bonds after 3 months of exposure to air.

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Experimental analyses have revealed the existence of oxygen and nitrogen functional groups, with oxidation occurring throughout the aged GDY and nitrogen contamination occurring mainly on its surface. Bond length changes, due to opening of the triple bonds, resulted in buckling of the aged GDY. Notably, annealing at high temperature (e.g., 800 1C) may remove most of the functional groups from the aged GDY.73 Almost 10 years after the theoretical prediction of the GDY nanotube,74 graphdiyne nanotube (GDNT) arrays were fabricated through an anodic aluminum oxide template, catalyzed by Cu foil (Fig. 20). The as-grown nanotubes had a smooth surface with a wall thickness of approximately 40 nm; after annealing, the wall thickness of the GDNTs was approximately 15 nm. The morphologydependent field emission properties of GDY arrays have been measured; these materials display high-performance field emission properties.75 The turn-on field and threshold field of annealed GDNTs 4.20 and 8.83 V mm 1, respectively are lower than those of many semiconductor nanomaterials. GDNTs also exhibit lower work functions and greater stability than those of CNTs. A novel aggregate structure of graphdiyne nanowires (GDNWs) having a very-high-quality, defect-free surface has also been constructed through a vapor liquid solid growth process using ZnO nanorod arrays on a silicon slice as the substrate (Fig. 21).

Fig. 20 SEM images of annealed GDY-NTs: (A and B) top views and (C and D) side views of a GDY-NT array at (A and C) low and (B and D) high magnification. [Reproduced with permission from the American Chemical Society (ref. 75).]

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Fig. 21 SEM images of GDY NWs of various lengths (L) and diameters (D): (A) L, 550 nm; D, 46 nm; (B) L, 780 nm; D, 23 nm; (C) L, 1070 nm; D, 20 nm; (D) L, 1700 nm; D, 33 nm. Insets (in blue): schematic representations of their shapes. [Reproduced with permission from the Royal Society of Chemistry (ref. 76).]

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These results suggest that GDNWs are promising materials for use in the fields of electronics and photoelectrics.76 An alternative way of developing GY chemistry would be to assemble supramolecular analogues in which some of the carbon carbon covalent bonds in the network have been replaced by noncovalent bonds.77 Successful doping of GDY enables the fabrication of various potentially useful GDY-based materials. For example, isoelectronic doping of GDY with B and N atoms can provide stable configurations with modified band gaps.78 After hydrothermal reactions, the diacetylenic linkage of GD can transform in part into a 2D p-conjugated structure favorable for electronic transmission, thereby enabling its use as an electron-transport material in photodegradation processes. Accordingly, GD has been used to further improve the photocatalytic performance of TiO2.79 The complicated phases and facets of loaded P25 samples have made it di cult to understand the charge transfer mechanism at the interface of TiO2 and GDY (Fig. 22A). Wang et al.80 used first-principles DFT to calculate the chemical structures and electronic properties of TiO2 GD and TiO2 GR composites featuring different TiO2 facets. They found that the TiO2(001) GD composite exhibited greater performance in terms of electronic structure, charge separation, and oxidation ability relative to pure TiO2(001) or the TiO2(001) GR composite (Fig. 22B). Therefore, the TiO2(001) GD composite was recognized as an excellent candidate for use as a high-efficiency photocatalyst. In the photocatalytic degradation of methylene blue, the rate constant when using the TiO2(001) GDY composite was 1.63 times that of the pure TiO2(001) and 1.27 times that of the TiO2(001) graphene composite. Thus, GDY should become a superb competitor among other types of 2D carbon materials for applications in photocatalysis and photovoltaics. The doping of GDY can improve the short circuit current ( Jsc) and power conversion e ciency (PCE) of P3HT/PCBM solar cells,

Fig. 22 (A) Schematic representation of the proposed photodegradation of Methylene Blue (MB) over the P25/GDY composite. The presence of C 2p states leads to narrowing of the band gap of titania; in addition, GDY can act as an acceptor of the electrons photogenerated from P25 and, thereby, ensure fast charge transportation, owing to its high conductivity. (B) Schematic representation of the photodegradation of dyes in the presence of TiO2–GD and TiO2–GR composites. In the TiO2–carbon composite materials, the electrons photogenerated from TiO2 can be captured by the p-conjugated carbon structure via a percolation mechanism. Both GD and GR act as electron acceptors in the TiO2–carbon system, effectively suppressing charge recombination and leaving more holes to form the reactive species that promote the degradation of dyes. [Reproduced with permission from Wiley-VCH Verlag GmbH & Co. (ref. 79) and the American Chemical Society (ref. 80).]

The GDNWs produced are excellent semiconductors, having a conductivity of 1.9 103 S m 1 and a mobility of 7.1 102 cm2 V 1 s 1.

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Fig. 23 Chemical structures of P3HT, PCBM, and GDY and the structure of a GDY-containing photovoltaic device. [Reproduced with permission from Elsevier B.V. (ref. 81).]

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due to high charge transport capability of GDY and the formation of e cient percolation pathways in the active layer (Fig. 23).81 The incorporation of 2.5 wt% GDY has enhanced the value of Jsc of a device by 2.4 mA cm 2, providing a highest PCE (3.53%) that is 56% higher than that of the corresponding device prepared without GDY.

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4. Conclusions and perspectives This Review discusses recent advances in the predicted and experimental behavior of GYs and GDYs. Several 0D, 1D, and 2D GYs and GDYs have been examined theoretically and prepared experimentally, allowing investigations of their structural, mechanical, and electronic properties. Studies of structural and size-based properties have indicated that variations of such factors as the ribbon width, edge morphology, and edge functionalization are e ective means of tailoring the electronic, chemical, mechanical, and magnetic properties. Several promising applications such as use as gas separation membranes, energy storage materials, or anode materials in batteries have been predicted; indeed, experimental e orts have revealed that GDY composites should be competitive with other types of 2D carbon materials for applications in photocatalysis and photovoltaics. Nonetheless, research in the application of GY- and GDYbased materials is in its infancy, with many challenges and opportunities remaining. Although potential uses in electronics, energy storage, and separation technologies have been predicted, appropriate experimental and practical data remain to be obtained. Reaching these goals will require the development of new strategies for preparing GY and GDY sheets in large quantities with high quality, as well as methods for controlling the hierarchical structures formed through the aggregation and assembly of these GYs and GDYs.

Acknowledgements Our contributions to this Review were realized with support from the National Nature Science Foundation of China (21031006, 21290190, 21322301), the NSFC-DFG joint fund (TRR 61), and the National Basic Research 973 Program of China.

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