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DOI: 10.1039/D1QM00595B (Review Article) Mater. Chem. Front., 2021, 5, 6392-6412

Graphynes as emerging 2D-platforms for electronic and energy applications: a computational perspective

Tianwei He *ab, Youchao Kong b, Alain R. Puente Santiago c, Md Ariful Ahsan c, Hui Pan *bd and Aijun Du *a
aCentre for Materials Science and School of Chemistry and Physics, Queensland University of Technology, Garden Point Campus, Brisbane, QLD 4001, Australia. E-mail: he.tianwei@hdr.qut.edu.au; aijun.du@qut.edu.au
bInstitute of Applied Physics and Materials Engineering, University of Macau, Macao SAR, 999078, P. R. China
cDepartment of Chemistry, University of Texas at El Paso, 500 West University Avenue, El Paso, Texas 79968, USA
dDepartment of Physics and Chemistry, Faculty of Science and Technology, University of Macau, Macao SAR, 999078, P. R. China. E-mail: huipan@um.edu.mo

Received 18th April 2021 , Accepted 21st June 2021

First published on 28th June 2021

Abstract

Among all the 2D-carbon materials, graphyne is currently one of the most interesting carbon allotropes besides graphene. It has potential applications in a wide variety of scientific fields owing to its unique sp–sp2 hybrid network, which endows desirable electronic properties towards energy-related applications. In this review, we summarize the recent progress in graphynes for electronic and energy applications from a theoretical point of view. The intrinsic electronic structure of graphyne and its chemical and mechanical properties are comprehensively described. It is hoped that this review could provide a strong theoretical understanding of graphynes, thus accelerating the design of robust and efficient graphyne-based advanced energy and electronic devices in the future.

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Tianwei He

Tianwei He received his PhD degree in Physical Chemistry in 2020 from the Queensland University of Technology, Australia. He is working as a postdoctoral researcher at the University of Macau. He has published over 30 articles in very prestigious journals such as Journal of the American Chemical Society, Advanced Materials, Small Methods, Journal of Catalysis, Journal of Materials Chemistry A and Nano Research. The main goal of his research is the computational discovery and design of catalysts that are active, efficient, selective, stable, and cheap which ultimately enable them for large-scale applications.

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Youchao Kong

Youchao Kong received his bachelor's degree in Materials Physics from Northwestern Polytechnic University (NWPU) in 2012. He is currently pursuing a PhD program at the University of Macau under the supervision of Prof. Shuangpeng Wang. His research interest is the promotion of electrocatalysis through surface engineering.

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Alain R. Puente Santiago

Alain R. Puente Santiago received his PhD degree in Physical Chemistry with distinction (July 2017) from the University of Cordoba, Spain. He is working as a senior postdoctoral researcher in the Echegoyen Group at The University of Texas at El Paso, USA. He has published 53 articles in very prestigious journals such as Journal of the American Chemical Society, Angewandte Chemie, Chemical Society Reviews, Renewable and Sustainable Energy Reviews, Journal of Materials Chemistry A and Green Chemistry. The main goals of his research are based on the development of low-dimensional hybrids for electrocatalytic, sensing and energy storage applications.

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Md Ariful Ahsan

Md Ariful Ahsan received his MSc from the Department of Chemistry, Tuskegee University, in 2015, under the supervision of Prof. Michael L. Curry. Currently, he is doing his PhD at The University of Texas at El Paso, working with Prof. Juan C. Noveron. He has published over 35 articles in peer-reviewed prestigious journals, including Journal of the American Chemical Society, Angewandte Chemie, Green Chemistry, Communications Materials, etc. His research focuses on multi-functional nanomaterials for wastewater treatment and clean energy conversion technologies.

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Hui Pan

Dr Hui Pan is a professor in the Institute of Applied Physics and Materials Engineering, and the founding head of the Department of Physics and Chemistry in the Faculty of Science and Technology at the University of Macau. He got his PhD degree in Physics from the National University of Singapore in 2006. In his research, a combined computational and experimental method is used to design and fabricate novel nanomaterials for applications in energy conversion and storage (such as electrocatalysis, photocatalysis, water splitting, N2/CO2 reduction, supercapacitors, hydrogen storage, and fuel cells), electronic devices, spintronics, and quantum devices.

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Aijun Du

Aijun Du received his PhD from Fudan University of China in 2002. He is currently a full professor at the School of Chemistry and Physics at the Queensland University of Technology, Australia. His research lies at the interface of chemistry, physics and engineering, focusing on the design and development of innovative materials for energy, electronic and environmental applications using advanced theoretical modelling approaches.

1. Introduction

Owing to its unique mechanical, physical and chemical properties, graphene is the most widely explored two-dimensional (2D) carbon material since its discovery in 2004.1–5 Recently, a new emerging 2D carbon allotrope, graphyne, has currently sparked tremendous attention as a rising competitor, thus demonstrating comparable or even better potential applications than graphene.6 The main difference between graphene and graphyne is the types of hybridized carbon atoms in their networks. In all-carbon materials, there are three kinds of C–C hybridization states including C(sp2)–C(sp2), C(sp)–C(sp2) and C(sp)–C(sp). The typical examples in various carbon allotropes for these three types of C–C hybridization states are carbyne(sp),7 0D fullerene(sp2),8 1D carbon nanotube(sp2),9 2D graphene(sp2)1 and diamond(sp3). The common point they share is the single species of hybridized carbon atoms in their networks. Nevertheless, the graphyne structure contains more than one type of carbon–carbon bonds in the networks, which greatly benefits the electronic/chemical properties of 2D carbon materials.10

In 1987, Baughman and Eckhardt completed the first theoretical prediction of a new kind of carbon allotrope containing both sp and sp2 carbon atoms in its planar sheet, namely, graphyne.11 Li's group first prepared γ-graphene (GDY) on a copper surface using hexamethylene benzene (HEB) via a Glaser–Hay cross-coupling reaction. [Chem. Commun., 2010, 46, 3256–3258]. Due to the mixed sp and sp2 hybridized carbon atoms in its network, graphyne shows four types of carbon–carbon bonds including C–C double bonds (sp2–sp2) in the hexatomic benzene rings, C–C single bonds (sp–sp2) between the benzene ring and C[triple bond, length as m-dash]C triple bonds, another type of C–C single bonds which connects the two C[triple bond, length as m-dash]C triple bonds, and the C–C triple bonds. The lengths of the bonds are 1.43, 1.40, 1.23 and 1.33 Å,12 respectively. According to the number of –C[triple bond, length as m-dash]C– triple bonds, the different lengths of acetylenic linkages can lead to different graphyne structures, called graphyne-n, where n refers to the number of –C[triple bond, length as m-dash]C– bonds in the linkage, as shown in Fig. 1(a–d). Apart from graphyne-n structures, there are three other graphyne derivatives including 6,6,12-graphyne, 12,12,12-graphyne and 18,18,18-graphyne that were also predicted by Baughamn et al., shown in Fig. 1(e–g). They are characterized by diverse sp and sp2 hybridized carbon atom ratios in their networks. The concept of graphynes is not confined to a particular symmetry or structure, instead they can be formed by different combinations of carbon–carbon bonds. The different kinds of hybridized carbon atoms into the graphene network promote a high degree of π-conjunction. In addition to the 2D one-atom-thick structure, graphynes present other different morphologies such as 1D nanotubes/nanowires/nanoribbons13–16 and 3D nanoarchitectures.17,18 The graphyne network also exhibits robust mechanical properties, thus preserving its structure under uniaxial strain and exhibiting bigger Poisson ratios than graphene.7,19–22 More interestingly, graphynes exhibit tunable electronic properties with bandgap values oscillating from 0.44 to 2.23 eV that could be potentially used towards the fabrication of semiconductor materials.12,16,23–26 The layered and uniformly distributed 2D porous geometry structures, nonzero direct bandgap nature and flexible mechanical properties lead to promising applications of graphynes in energy conversion,27–29 electronic/optical devices30 and biomedicine.31 Among the graphyne family, graphyne-1 (γ-GY)32 and graphyne-2 (graphdiyne, i.e. GDY)33 are the most popular ones, which have currently been experimentally implemented. Although great progress has been achieved in the past decade since their first successful synthesis,6,34–37 the deep and extended applications of γ-GY and GDY are still in their infancy and facing great challenges that need further endeavors in both theoretical and experimental aspects.


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Fig. 1 Different structures of graphyne-n nanosheets. The index “n” in (a)–(d) indicates the number of carbon–carbon triple bonds in a link between two adjacent hexagons. Copyright 2016 Nature Publishing. Structures of α-graphyne (e), β-graphyne (g) and 6,6,12-graphyne (f). Copyright 2012 American Physical Society.

The giant advances in the development of more effective theoretical simulation techniques are triggering faster pathways towards the prediction and discovery of new-generation computational energy materials and their fascinating properties. Unlike other recent reviews that focus on the experimental synthesis and characterization analysis of graphyne-based materials, we will deeply discuss the recent advances of graphynes and their applications in electronics and energy conversion areas from a computational perspective. Additionally, we will tackle potential opportunities, challenges and plausible suggestions in the development of graphynes for new promising applications. We hope this review could not only give in-depth insights to theoretical scientists into the rational design of new functional graphyne-based materials, but also provide powerful tools to synthetic chemists in order to minimize conventional trial-and-error synthesis processes during their future endeavors.

2. Application of graphynes in electronic devices

To design efficient energy-related devices, the development of highly tunable bandgap nanostructures is of paramount importance. In contrast to graphene, graphynes have shown a natural nonzero bandgap ranging from 0.44 to 1.22 eV, depending on the selected calculation method.18,24 Moreover, the bandgap can be modulated by several strategies, including tuning the number of layers, applying strain,38 tailoring the architectures of graphynes39 and doping heteroatoms.40,41 Zheng et al.42 investigated for the first time the effect of different layers and stacking modes on the bandgap of GDY by using the DFT-GGA method. They calculated various stacking arrangements for bilayer and trilayer GDY, thus determining the most stable configurations, which are shown in Fig. 2a. The results revealed that the bandgap of the GDY network is reduced as a function of the number of layers. Very recently, Zhang's group43 studied another stacking mode (see Fig. 2(a–d)) by employing the HSE06 method, and the trends of the bandgap changed with the number of layers following the same trend as Zheng's results. These theoretical predictions were also verified through subsequent experiments.43,44 In 2013, Li et al.45 proposed to apply various strain approaches to tune the bandgaps of graphynes as shown in Fig. 2e. They found that the bandgaps of graphynes can be controlled by applying different loading types. The results indicated that homogeneous tensile strain can lead to a steady increase in the bandgaps, while upon the application of uniaxial tensile, and compressive or homogeneous compressive strain, the bandgaps will decrease (Fig. 2f). The intrinsic reason for this behavior is explained based on the energy states near the Fermi level, which can be shifted under strain environments.
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Fig. 2 (a) Most stable bilayer GDY configuration AB (β1) and (b) its energy band structure. (c) Most stable trilayer GDY (γ1) configuration and (d) its energy band structure. Copyright 2012 The Royal Society of Chemistry. Band structures of (e) graphyne and (f) graphdiyne nanosheets under biaxial strain (H-strain) and uniaxial strain along the armchair (A-strain) and zigzag (Z-strain) directions. Copyright 2013 American Chemical Society.

Similar to graphene, graphynes can also exhibit a variety of morphologies by structural engineering, such as nanoribbons,46–48 nanotubes49,50 or cages.51 Through tailoring the 2D graphyne nanosheets into zigzag or armchair edges of nanoribbons (Fig. 3a), the bandgap values can be largely regulated. The bandgaps of GDY nanoribbons can be adjusted by controlling the ribbon widths. As shown in Fig. 3b, both zigzag and armchair edges show semi-conductive characteristics. It was found that with the increase of ribbon widths, the band gaps of GDY nanoribbons are decreased because of the quantum confinement effect.16 In addition, the calculation results indicated that by increasing the width of GDY nanoribbons, the charge mobility will be enhanced.52 Heteroatom doping can also greatly change the electronic properties of graphynes.53 Gamallo et al.54 systematically studied the role of N and B atom doping on the electronic properties of graphynes by DFT calculations, as shown in Fig. 3(c–f). When the sp and sp2–C atoms were substituted by different types and concentrations of impurities, the electronic properties of doped graphynes are precisely switched from semiconductor-to-metal transition. The N and B atoms acted as n-type and p-type doping species that can transfer extra electrons to the conduction band and introduce holes into the valence band, respectively. Besides, the presence of doped atoms in the networks of graphynes will also affect the in-plane stiffness, giving rise to tunable mechanical properties.


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Fig. 3 (a) Structures of three different types of GDY nanoribbons: (I) divan-like, (II) zigzag-like and (III) zigzag-like with different widths. (b) Band structures of various GDY nanoribbons. Copyright 2011 American Chemical Society. (c) Structures of α-, β-, and γ-graphyne maintaining the armchair direction along the x-axis and the zig-zag direction along the y-direction. Band structures of (d) non-doped α-graphyne and α-graphyne doped with 2N and 2B. (e) Non-doped β-graphyne and β-graphyne doped with 2N and 2B. (f) Non-doped γ-graphyne and γ-graphyne doped with 2N and 2B. Copyright 2017 Elsevier B.V.

Overall, the intrinsic nonzero and tunable bandgap of graphynes pave the way towards their applications in the fabrication of a myriad of flexible and wearable electronic devices. In addition, due to its small effective mass, graphene is expected to have a greater carrier mobility than silicon at room temperature. Next, we will review the application of graphynes in optoelectronic, spintronic, magnetic and other electronic devices.

2.1 Optoelectronic devices

Owing to the finely tunable natural bandgap, graphynes possess broad light absorption and superior ambipolar carrier transport properties which can be potentially used in photonic and optoelectronic applications.24,30,55–57 In 1987, Baughman et al.11 theoretically predicted the nonlinear optical properties of graphynes. Due to the narrow bandgap and linear sp-hybridized carbon atoms of GDY, a large third-order susceptibility was found. Li et al.58 investigated the electronic and nonlinear optical (NOL) properties of γ-GY and GDY by doping single alkali metal atoms (Li, Na and K) using DFT calculations. They confirmed the most stable site of alkali metals (AM: Li, Na, and K) adsorbed on the triangular holes through van der Waals interactions as shown in Fig. 4a and b. The static polarizability (α0) and first hyperpolarizability (β0) of the AM doped γ-GY and GDY were calculated. The results show that the polarizabilities can be greatly increased when doped with Li, Na and K atoms. For AM@GDY, they further found that the increase of the atomic number of alkali metal atoms could dramatically increase the polarizabilities (Fig. 4c). Moreover, with the decrease of the electronegativity for Li, Na and K atoms, the βtot values of AM@GDY will gradually increase. As we can see in Fig. 4d, K@GDY exhibits the highest first hyperpolarizability which shows great performance for designing NOL devices. Mahmood et al.59 further investigated the NOL properties of GDY by doping with novel superalkalis. They designed a series of superalkali-modified GDY composites, named M2X@GDY (M = Li, Na, K and X= F, Cl, Br), as shown in Fig. 4e. The unique intramolecular electron donor–acceptor behavior in the delocalized π-conjugated framework promotes the effective chemisorption of superalkalis onto the GDY network. The first hyperpolarizability values of different superalkali-doped GDY complexes were calculated and analyzed (Fig. 4(f–h)). They concluded that all these doped GDY complexes show excellent NLO response with remarkably increased first hyperpolarizability values compared to pristine GDY. Thereafter, Li et al.60 also investigated tetrahedral alkali-metal nitride-decorated GDY as nonlinear optical materials by TDDFT calculations and revealed that Li3NK@GDY exhibits enhanced first hyperpolarizabilities. All these theoretical investigations61 highlight the promising application of alkali metal-doped GDY materials in the optoelectronic field.
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Fig. 4 Selected adsorption sites on (a) GY and (b) GDY nanosheets. Calculated (c) polarizability and (d) static first hyperpolarizability of AM@GY and AM@GDY (AM = Li, Na, K). (e) Optimized structures of M2F@GDY, M2Cl@GDY and M2Br@GDY complexes. Copyright 2019 The Royal Society of Chemistry. (f)–(h) Relationship of hyperpolarizability with the oscillator strength and crucial excitation energy of the superalkali-doped complexes. Copyright 2019 Elsevier B.V.

The broadband spectrum (300 to 800 nm) and high carrier mobility of graphynes make them appealing candidate materials for photodetection platforms.62–64 At room temperature, Shuai's group16 theoretically predicted an in-plane intrinsic electron mobility of 105 cm2 V−1 s−1 for GDY nanosheets which can boost the conversion of photons to voltages or electrical currents.24 More recently, Li's group65 reported graphdiyne-based flexible photodetectors by depositing its nanosheets onto a substrate which shows high responsivity and detectivity. They calculated the characteristics of H and OH adsorption on GDY to explore the photo-response behavior under an alkaline environment. As shown in Fig. 5a, the flat layered structure combined with vdW force in the interlayer can provide perfect adsorption sites for both H+ and OH− ions. Due to the small energy barrier (Fig. 5b), H+ can easily diffuse from the surface to the in-plane B region through the triangle hollows, and the chemically bonded H could give rise to large ab in-plane distortions of the structure. However, the OH− species will cross the first layer by overcoming a very small barrier (47 meV) and will be encapsulated into the interlayer C region, giving rise to ab out-of-plane structural distortions. They calculated the bandgap of the OH-/O-adsorbed GDY and found that the bandgap of the H-adsorbed GDY is smaller than that of the OH-adsorbed GDY (Fig. 5c). The larger bandgap of the OH-adsorbed GDY demonstrates stronger optical absorption than that of the H-absorbed and pristine GDY that can increase the generation of intrinsic photo-induced carriers (Fig. 5d). They concluded that the OH-adsorbed GDY can enhance the photo-response behavior, thus providing promising applications in the development of GDY heterojunction-based photodetector devices.


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Fig. 5 (a) Calculations of the diffusion of OH− or H+ ions on GDY under acidic, alkaline and neutral conditions. (b) Ion diffusion process with the chemical absorption of OH- and H-adsorbed GDY. (c) Band structures of GDY with chemically adsorbed OH and H. (d) Absorption spectra of pristine GDY and GDY with OH and H adsorption. Copyright 2020 John Wiley & Sons.

2.2 Spintronic devices

As is well-known, 2D carbon materials with sp3-type defects or vacancy can break the delocalized pi electronic system and prevent sp3-type functional group clustering, which is the main reason to induce magnetism. The clustering of sp3-type functional groups can be avoided into the GDY structure, placing them as excellent candidates for spintronics. He et al.66 first used DFT+U calculations to systematically investigate the magnetic properties of single transition metal atom-decorated graphynes. To accurately describe the electron correlation, they adopted linear response methods to obtain the Ueff values for all the TM (TM = V, Cr, Fe, Mn, Co and Ni) adatoms. They found that TM atoms can effectively change the magnetic properties of γ-GY and GDY. When doping with TM atoms on a γ-GY/GDY film, charge transfer between them was triggered (Fig. 6a). The magnetic properties of TM@γ-GY/GDY differ from each other. All the TM-doped γ-GY and GDY induce magnetism except for Ni. As we can see in Fig. 6b, Cr- and Co-doped γ-GY/GDY exhibit the largest and smallest magnetic moments, respectively. The adopted TM atom also modified the bandgaps of γ-GY and GDY, making V/Mn/Co@γ-GY and Co@GDY behave as spin-polarized half-semiconductors, while Cr/Fe@γ-GY and V/Cr/Mn/Fe@GDY behave as metals (Fig. 6c). The excellent magnetic properties induced by TM were attributed to the charge transfer that redistributed the electrons of the s, p, and d orbitals in the TM atom. Unlike transition metal atoms, nonmetal atoms are also important dopants.67,68 Dai et al.69 investigated the single X nonmetal atom (X = B, N, O, P and S) doped GDY monolayers. There are three different doped sites in GDY, as shown in Fig. 6d. The calculation results show that the B and S atoms prefer to occupy the sp2-hybridized C atoms, while the O, N, and P atoms are energetically favored to substitute the sp-hybridized C atoms at the acetylene linkage. The calculated spin charge density is depicted in Fig. 6e. We can see that the polarized charges mainly appeared at the C–N bond with the magnetic moments of 0.58 and 0.31μB for B-1 and B-2 doped GDY, respectively. For O-1/2, P-1/2 and S-1/2 doped GDY, the polarized charges mainly appeared at the acetylene linkage. Thus, the magnetic properties of GDY can be modulated by chemical doping. Besides the TM doping strategy, Huang et al.70 investigated the magnetic states of edge-modified γ-GDY. They found that the armchair and zigzag γ-GDY nanoribbons show the nonmagnetic state with a direct bandgap and the antiferromagnetic state with a very small bandgap (0.156–0.245 eV). The intrinsic magnetism71 combined with the aforementioned modulation strategies suggests promising potential in graphyne-based spintronic devices.
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Fig. 6 (a) Charge transfer between the TM atom and GDY/GY sheet. (b) Magnetic moment and spin-polarized energy. (c) Spin-polarized charge density distribution and magnetic moments for Co and Mn adsorbed GDY. Copyright 2012 American Chemical Society. (d) Geometrical structures of X (B, N, O, P, S) doped GDY with different doping sites. (e) Spin charge density of the B, O, P and S doped GDY nanosheets. Copyright 2019 Elsevier B.V.

2.3 Other electronic devices

The highly tunable electronic properties enable graphynes to be used either as semiconductors or semimetals with Dirac cones.38,72–74 Many theorists predicted the application of graphynes in quantum transport.52,75,76 Yao's group77 conducted first-principles quantum transport calculations and showed that zigzag α-graphyne nanoribbons can be used as a dual spin filter diode, a molecule signal converter and a spin caloritronic device. Zhang et al.78 systemically calculated the configuration and transport properties of zigzag graphyne nanoribbons. The graphyne demonstrated controllable conductivity, tunneling behavior and drain voltages which can be potentially used in several electronic devices. Graphynes can also be good candidates for thermoelectric devices. Liu's group79 theoretically predicted a ZT value of 3.0 and 4.8 for p-type holes and n-type electrons, respectively, at room temperature by using DFT calculations and MD simulations. These ZT values are superior to most of the current thermoelectric materials, indicting promising applications in high-powered thermoelectric devices.

3. Application of graphynes in energy conversion

The unique natural atomic-thick layered structure of graphynes exhibits uniformly distributed in-plane pores, large surface area, good mechanical properties, high conductivity and very good affinity with external atoms, thus qualifying as promising low-dimensional materials for energy conversion.80–82 Moreover, the tunable architectures of graphynes range from 1D to 3D structures, such as 1D nanotubes/nanoribbons/nanowires, 2D nanowalls/nanosheets and 3D nanostructure arrays, which further reinforce their energy-related applications. In the following part, we will review the energy applications of graphyne-based materials for the fabrication of high-performance catalysts, batteries, hydrogen storage nanosystems and other energy devices.

3.1 Catalytic applications

Currently, 2D materials are widely used as catalysts in various chemical reactions due to their flexible and designable structures, such as graphene, Mo/Co/CeS2 and g-C3N483 based catalysts. For pristine graphynes, the carbon atoms are catalytically inert. Some researchers have developed lots of methods, such as adding functional groups or supports and doping with different heteroatoms, to enhance the catalytic properties of the modified graphynes.84 The modified graphyne-based materials are predicted to be promising highly efficient candidates for a wide variety of catalytic applications such as the hydrogen evolution reaction (HER), oxygen evolution reaction (OER), oxygen reduction reaction (ORR), nitrogen reduction reaction (NRR), carbon dioxide reduction reaction (CRR), selective hydrogenation reaction and so on.
3.1.1 Hydrogen/oxygen evolution reaction and oxygen reduction reaction. The graphyne-based materials for the HER/OER/ORR are classified into metal atom and nonmetal atom modified catalysts.85–87 For metal-free graphyne-based catalysts, there are two methods to activate pristine inert carbon atoms.88 Lan et al.89 developed a novel heterojunction material composed of graphdiyne and molybdenum disulfide nanosheet (GDY–MoS2) as efficient hydrogen evolution electrocatalysts. As shown in Fig. 7a, when the GDY is incorporated with the MoS2 nanosheet, the carbon atoms become active for the HER, which is accompanied by the drastically decreasing ΔGH from 1.15 to 0.78 eV. The interaction between the GDY and MoS2 facilitates the electron transfer, thus improving both the electrical conductivity and the catalytic performance of the composite. Xue's group90 designed a new metal-free amino-graphdiyne catalyst, which delivered excellent electrocatalytic activities toward the HER under acidic conditions. The amino-decorated benzene rings induced charge redistribution among the carbon atoms, which makes the charge mainly localized at the C2 site (Fig. 7b). This functionalization strategy made the C2 site the most active site for the HER. Graphynes doped with nonmetal atoms are another strategy to activate inert carbon atoms. Chen's group91 systematically investigated the nonmetal X-doped (X = B, N, P, S) graphdiynes as the metal-free OER and ORR catalysts by DFT computations. They doped the X atom into different kinds of carbon atoms in the GDY network as shown in Fig. 7(c–e). They discovered that substituting different carbon atoms can generate different kinds of active sites. The graphitic S-doped(S1), sp-N-doped(N3) and P-doped(P1) GDY demonstrated excellent OER and ORR activities which are comparable or even better than Pt/C and RuO2. The huge variety of carbon atoms into the graphyne network notably favors their multiple catalytic functionalities. Chen et al.92 further studied the mechanism for different kinds of nitrogen-doped GDY as effective ORR electrocatalysts. They compared the catalytic activities of three types of N doping including grap-N, sp–N(I) and sp–N(II) and revealed that the doped N atom can activate the neighboring carbon atoms. They also explained the O2 dissociation and association reaction mechanisms on different types of N-doped GDY and concluded that the sp–N(II) GDY showed the best ORR performance. Feng et al.93 studied the B,N co-doped GDY monolayer and noted heat when the B atom was positioned in the benzene and the N atom was positioned in the acetylene linkage. Therefore, the B,N co-doped GDY exhibited the lowest overpotential of 0.57 V. Besides GDY, the N-doped β-graphynes are also very good ORR catalysts. Lee et al.94 found that N doping can not only increase the positive charge of the adjacent C atom but can also increase the work function of graphynes, thus promoting O2 decomposition during the ORR process.
image file: d1qm00595b-f7.tif
Fig. 7 (a) Optimized GDY–MoS2 heterostructure and the free-energy profile of the HER for pristine MoS2, GDY and different sites in GDY–MoS2. Copyright 2019 Elsevier B.V. (b) Structure of TAGDY and the HER energy diagram of H adsorbed on different sites. Copyright 2021 Elsevier B.V. Structures of (c) pristine and (d) N, (e) B, P, and S doped GDY in three possible active sites. Copyright 2019 John Wiley & Sons.

The uniformly distributed hierarchical pore structures of graphynes provide abundant anchor sites for heteroatoms.95 Yan et al.96 conducted a comprehensive mapping investigation of doping transition metal (TM) atoms on GDY nanosheets (Fig. 8(a–d)). They investigated 26 TMs from IIIB to IB of 3d to 5d in the periodic table anchored on GDY to screen out the zero-valence state of M@GDY catalysts. They found that Co-, Pt- and Pd-doped GDY possess the stability of zero-valence via calculating the energy barrier difference between the gaining and the losing electrons, which place them as novel high-performance zero-valence atomic catalysts. He et al.97 systematically investigated the HER, OER and ORR catalytic performances of 11 transition metal (from Sc to Zn and Pt) supported GDY nanosheets by high-throughput DFT calculations. In their work, they first checked the stability of the TM atoms on the GDY and found that the TM atoms prefer to anchor on the corner of the acetylenic ring (Fig. 8e). The TM atom-doped GDY catalysts show multifunctional catalytic activities towards the HER, OER and ORR. The Sc-, Ti-, V-, Fe- and Pt-doped GDY exhibited excellent HER performance (Fig. 8f). For Ti@GDY and V@GDY, both the carbon and TM atoms are the active sites. The Pt@GDY was found to perform bifunctional catalysis for the HER and OER which can be used for the construction of overall water splitting devices (Fig. 8g). The Ni@GDY displayed high activities for the OER and ORR, making them great nanohybrids for metal-air-battery devices (Fig. 8h).


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Fig. 8 (a) The formation energies of the TM atoms anchoring on GDY. (b) The zero-valence anchoring ability of TM. The decomposition of mapping into (c) oxidation and (d) reduction reactions. Copyright 2019 Elsevier B.V. (e) The three possible anchoring sites for single atoms. The energy diagrams for the (f) HER, (g–h) OER and ORR. Copyright 2019 John Wiley & Sons.
3.1.2 Nitrogen reduction reaction. Metal atom-doped graphyne-based catalysts are also very active materials for nitrogen fixation. Among all the TM atoms, the Mo-doped GDY catalyst was highly investigated. Li et al.98 theoretically screened the suitable Mo (from a single atom to a cluster) doped GDY for the N2 reduction reaction as shown in Fig. 9a. Based on the designed screening criteria, they found that Mo3@GDY showed the best catalytic performance with the highest selectivity and stability. By calculating the electron transfer between the metal atoms and the GDY, the GDY can serve as the electron reservoir during the NRR process (Fig. 9b). The oxidation state of the Mo atom on the GDY will change the catalytic properties of the Mo-doped GDY. Hui et al.99 proposed a bifunctional zerovalent Mo atom on the GDY catalyst (Mo0/GDY) which showed excellent catalytic activities and selectivities toward the NRR and HER. Ma et al.100 systematically investigated the catalytic performances of TM (TM = Mn, Fe, Co, Ni) single-, double-, triple-atom doped GDY catalysts for the NRR. The results showed that most of the single- and dimer-anchored GDY show better activities than those of the Ru(0001) stepped surface. The Co2@GDY exhibited the best catalytic performance with the lowest onset potential of −0.43 V and good selectivity to the HER. Feng et al.101 studied 30 kinds of TM@GDY (TM = Sc-Zn, Y-Cd and La-Hg) catalysts and found that Ti-, V-, Fe-, Co-, Zr-, Rh- and Hf-doped GDY could be very good candidates for the NRR. Unlike the CO2@GDY, the transition metal heteronuclear dimer can be the highly active site for the NRR.102 The unique structure of GDY provides the perfect anchor sites for metal atoms. Ma et al.103 screened the heteronuclear dimer-decorated GDY for the NRR. They calculated the heteronuclear 3d transition metal dimers, including FeM@ and NiM@ GDY (M = Ti, V, Cr, Mn, Fe, Co, Ni and Cu) NRR catalysts, thus determining that FeCo@GDY and Ni Co@GDY showed higher catalytic performance than Fe2@GDY and Co2@GDY counterparts with the onset potential of −0.44 and −0.36 V, respectively. The superior catalytic performance was associated with the synergy effect of the heteronuclear atoms.
image file: d1qm00595b-f9.tif
Fig. 9 (a) The most stable configurations of Mox (x = 1–4) anchoring on a GDY nanosheet. (b) The top and side views of Mo3–N2 and the charge density difference of the Mo3–N2@GDY system. Copyright 2020 American Chemical Society. The NRR energy profiles (c) and reaction pathways (d) on the W@N-GY catalyst. (e) The bond structures of the pristine GY and the N-GY. Copyright 2019 The Royal Society of Chemistry.

β-Graphyne, which has many small pores in its network, can be a better substrate for supporting single atoms than GDY.87 He et al.104 designed a single tungsten atom-decorated β-graphyne (W@GY) as an active and low-cost electrocatalyst for nitrogen fixation. The single W atom on the GDY can efficiently activate the inert triple bond, especially when coordinated with a N atom (an sp-hybridized carbon atom substituted by a N atom). The distal mechanism is identified as the main catalytic pathway and the onset potential can be as low as 0.29 V as shown in Fig. 9c and d. Moreover, the W and N co-doped β-graphyne exhibited better electrical conductivity compared to the pristine β-graphyne (Fig. 9e) which could enhance the electron transfer efficiency during the N2 reduction process.

3.1.3 Carbon dioxide reduction reaction. The diverse products of the CRR make it difficult to search for both active and selective CRR catalysts. He et al.105 first investigated the active-site dependent activity/selectivity for the reduction of CO2 on a precise number of Fe atom anchored GDY as shown in Fig. 10a. They observed that the number of Fe atoms supported on GDY can change the selectivity and activity of the CRR. The binding strength of the intermediaries can be tuned by varying the number of Fe atoms. Fe@GDY and Fe2@GDY prefer to generate CH4, while Fe3@GDY and Fe4@GDY can efficiently catalyze CO2 into HCOOH. Dai's group106 studied the precise number of copper atoms supported on GDY and found that Cu2@GDY can efficiently convert CO2 into CH4 with a very low limiting potential of −0.42 V owing to the spin magnetism of the catalyst. They further investigated the single alkali metal atom-doped GDY (AM@GDY) as efficient CRR catalysts (Fig. 10b), thus concluding that the size of the alkali metal atoms had a huge effect on the catalytic performances. Smaller alkali metal atoms such as Li- and Na-doped GDY can easily activate the CO2 molecule and promote the CO2 reduction to HCOOH. Fu et al.107 constructed a Cr-embedded graphyne (Cr-GY) electrocatalyst for a highly selective conversion of CO2 into CH4 with an ultralow limiting potential of −0.29 V and good inhibition of the HER. Recently, graphyne-based metal-free catalysts, for the conversion of CO2 into hydrocarbon products, have been investigated by Dai's group.108 They systematically studied the CO2RR catalytic activity of boron nitrogen cluster-doped GDY (BN-doped GDY) catalysts. As we can see in Fig. 10c, the bandgap of BN-doped GDY was calculated to be 0.902 eV which showed a photothermal effect under visible and infrared light irradiation (Fig. 10d). The most stable sites for BN pair in GDY are the two carbon atoms in the –C[triple bond, length as m-dash]C– chain. The designed BN-doped GDY catalyst enables the generation of different products at different onset potentials as follows: HCOOH (−0.57 V), CH4 (−0.62 V), CH3OH (−0.57 V) and C2H4 (−0.82 V), as shown in Fig. 10e.
image file: d1qm00595b-f10.tif
Fig. 10 (a) The structures of single-, double-, triple- and Fe clusters supported on a GDY monolayer. Copyright 2020 Elsevier B.V. (b) The CO2 and H2 adsorption and the different reaction pathways of CO2RR on alkali metal-decorated GDY. Copyright 2020 Elsevier B.V. The band structures (c) and light adsorptions (d) of pristine and B,N-doped GDY. (e) The CO2RR energy diagrams of B,N-doped metal-free GDY catalysts. Copyright 2020 IOP Publishing Ltd.
3.1.4 Other catalytic reactions. The wide structural variety of graphynes endows their broad potential applications in other catalytic reactions87,109 such as the selective hydrogenation reactions and CO oxidation. Lin110 investigated the single Sc and Ti atoms supported on GDY as high-efficient CO oxidation catalysts. The results show that the Sc and Ti atoms can be firmly anchored on the GDY surface and the high migration barrier could avoid the aggregation of the single atoms. Xu et al.111 reported a new reaction pathway to catalyze CO oxidation on single Ir-doped GDY catalysts by comparing different reaction mechanisms. They reported that the CO oxidation reaction more energetically occurred in the new Eley–Rideal (NER) mechanism with a very low rate-limiting step of 0.37 eV. Li's group112 designed a kind of single-cluster catalyst anchoring on a metal cluster on the 18-member ring hexagon of the GDY substrate (Fig. 11a). The designed triatomic cluster MxM′3−x/GDY (M, M′ = Ru, Os) catalysts can selectively hydrogenate acetylene to ethylene as shown in Fig. 11b. They also simulated the turnover frequencies (TOFs) and selectivity map by using microkinetic modeling under 420 K and pressures (Fig. 11c). Wang's group systematically investigated the different kinds and numbers of metal atom-doped GDY catalysts by taking advantage of the pores and flexible structures of a GDY network. They stated that the catalytic performances of PdxMy/GDY (M = Cu, Ag, Au, Ni; x + y = 1–3) catalysts for semi-hydrogenation of C2H2 to C2H4 depend on the composition and size of the doped metal atoms.113 Additionally, they studied the PdxCuy/GDY (x = 1, 2, 3, 4; x + y ≤ 4) catalysts for CO oxidative coupling to dimethyl carbonate (DMC).114 By tuning the ratio of Cu:Pd on the PdxCuy/GDY catalysts, both the activity and selectivity can be greatly improved. The Pd1Cu1/GDY and Pd1Cu2/GDY were screened out to be the best electrocatalysts for CO oxidative coupling. Li et al.115 found that the Cr-doped graphyne (Cr-GY) can be a promising catalyst for the oxidation and reduction of NO to N2, N2O and NO2. The calculation results show that the metal 3d orbital close to the Fermi level played a significant role in adsorbing and initiating the adsorbates during the reaction process.
image file: d1qm00595b-f11.tif
Fig. 11 (a) The side and top views of Mo3-doped GDY. (b) The reaction energy profile of hydrogenation steps of acetylene and ethylene on Os3/GDY. (c) The simulated TOF of ethylene and ethane through microkinetic modeling. Copyright 2019 American Chemical Society.

3.2 Rechargeable batteries

The typical layered and porous structures as well as the excellent electronic properties make graphynes ideal materials for energy storage devices.116,117 The large surface area and uniformly distributed porous channels provide perfect accommodations for metal ions. Sun et al.118 first calculated the adsorption and diffusion of Li atoms on GDY monolayers. Li atoms can either be adsorbed on the 6-C hexagon sites or on the 18-C hexagon sites as shown in Fig. 12(a–d). The calculated diffusing barriers were 0.18 to 0.84 eV, indicating that Li atoms can easily diffuse on the GDY surface. The storage capacity of GDY for Li atoms can reach to LiC3. To further enhance the performance of GDY as Li-ion battery anodes, Zhang et al.119 investigated the strained monolayer and bilayer GDY (Fig. 12(e–h)). The applied strain can improve the capacity of Li atoms and the monolayer GDY can tolerate as much as 12% biaxial strain. They discovered that under an external 6% biaxial strain, the capacity of GDY can be boosted to 1985 mA h g−1, which greatly outperforms the graphite performance. Searles's group120 calculated the storage and mobility of Na atoms on a single GDY layer and bulk GDY layers. The results show that the maximum capacity for single- and bulk-layer GDY is NaC2.57 and NaC5.14, respectively, without the expansion of the unit cell. However, the capacity can increase to NaC2.57 when we allow the expansion.
image file: d1qm00595b-f12.tif
Fig. 12 The optimized geometries for two Li atoms adsorbed on the (a) 6-C hexagon and (b) 18-C hexagon in a GDY network. The in-plane Li diffusion pathways (c) and (d) diffusion barriers. Copyright 2012 American Chemical Society. Top view and side view of the optimized Li adsorbed GDY nanosheet (e) without strain and (f) under 6% strain; (g) under 8% strain and (h) under 10% strain. Copyright 2019 Elsevier B.V.

Other than pristine graphynes, heteroatom-doped graphyne-based materials are predicted to be versatile candidates for rechargeable batteries. Singh et al.121 theoretically investigated the N-doped GDY nanosheets as the anode materials for Li/Na/Mg storage devices. The results suggested that Li and Na atoms can be absorbed on the N-GDY monolayer with a high storage capacity of 623–2180 mA h g−1, outperforming most of the recently discovered 2D phosphorene and borophane materials. Currently, a novel GDY material, nitrogenated-triphenylene (N-TpG) monolayer, was systematically studied as an anode material for Na, K, Mg and Ca storage.122 There are mainly three most stable adsorption sites for the metal atoms over an N-TpG monolayer as shown in Fig. 13a. The S1 and S3 were inside the plane hollow sites and the S2 was on top of the hexagonal. Then, they investigated the maximum capacity of these metal atoms by calculating their average adsorption energies. As we can see in Fig. 13b, the maximum storage of Na, K, Mg, and Ca over N-TpG was 30, 26, 10 and 30, respectively. The calculated corresponding capacities are 2159, 1871, 1439 and 4319 mA h g−1, respectively. The capacity of GDY can be improved from 744 to 872.68 mA h g−1 by doping B atoms. The different kinds of N doping on GDY will also affect the capability of GDY-based batteries. Huang et al.123 studied pyrimidine–graphdiyne (PM–GDY) and pyridine–graphdiyne (PY–GDY) by doping quantitative N atoms. As shown in Fig. 13c, the adsorbed Li atoms are more stable when they remain close to the N atom due to the higher electronegativity of N than C. They concluded that the pyridine-like N-doped GDY are beneficial to store Li-ion via increasing the binding energy. Besides, by controlling the N type and content in GDY, the PY–GDY (Li18–C22N2H4) and PM–GDY(Li20–C20N4H2) showed very good electrochemical performances delivering superior capacities of 1168 and 1165 mA h g−1, respectively, as well as excellent long-term cycling stability properties. Vafaee et al.124 investigated B-doped GDY (BGDY) nanosheets for sodium storage. They reported that the inclusion of B into the GDY structure is an efficient path to lower the activation barriers for Na atom diffusion between the active adsorption sites, thus boosting the mobility of the Na atom in the charge and discharge processes.


image file: d1qm00595b-f13.tif
Fig. 13 (a) The most stable adsorption sites for Na, K, Mg and Ca atoms on N-TpG. (b) Top and side views of the content of Na, K, Mg and Mg adatoms for the most energy-minimized monolayer N-TpG. Copyright 2019 Elsevier B.V. (c) Geometries and calculated Eb of Li–C22N2H4 and Li–C20N4H2 complexes. Copyright 2019 American Chemical Society.

3.3 Hydrogen storage

The layered and porous structures of graphynes are also very good hydrogen storage systems. Recently, Wang et al.125 investigated the newly synthesized 2D trophenylene–graphdiyne (TpG) as potential hydrogen storage materials. They explored different strategies to improve the hydrogen storage capacity of the pristine TpG, such as decorating with Li, Ca and B. The calculation results show that Li-decorated TpG had a hydrogen storage gravimetric capacity of 8.17 wt% with an average H2 adsorption energy of 0.18 eV/H2. When doped with B atoms, the Li-decorated B-doped TpG can store as many as 20 H2 molecules with an average adsorption energy of 0.24 eV/H2. Hussain et al.126 conducted the spin-polarized DFT-D3 calculations to investigate the H2 storage properties of B-doped GDY (BGDY) by decorating with Li, Na, K and Ca atoms. For each BGDY unit cell, the maximum accommodation of each type of atom is four and the dopants can uniformly distribute over the BGDY without clustering which is confirmed by AIMD under 400 K as shown in Fig. 14a. These BGDY decorated by alkali metal atoms can adsorb as much as 16 H2 molecules (Fig. 14b) exhibiting an ideal binding energy range from 0.17 to 0.40 eV. They also analysed the thermodynamics of H2 adsorption of these alkali-metal-doped BGDY under different temperatures and pressures of H2 gas (Fig. 14c). The results revealed that the adsorbed H2 molecules could be released under practical conditions of temperatures and pressures, making the metal functionalized BGDY a promising material for storing H2.
image file: d1qm00595b-f14.tif
Fig. 14 (a) Top and side views of the BGDY@4Li, BGDY@4Na, BGDY@4K and BGDY@4Ca. (b) BGDY@4Ca and BGDY@4Li loaded with 4H2, 8H2, 12H2 and 16H2. (c) The thermodynamics of adsorbed H2 molecules on alkali-metal-doped BGDYs as a function of the temperature and the pressure of H2 gas. Copyright 2019 Elsevier B.V.

3.4 Other energy applications

The large number of different sizes of pores makes graphynes ideal materials for serving as membranes. Jiao et al.127 theoretically studied the application of GDY as the membranes for H2 purification (Fig. 15a). The GDY exhibited excellent performance in the H2 selective permeation over different gas molecules, such as CH4 and CO, as shown in Fig. 15b. Zhao et al.128 investigated the aqueous proton-selective behavior on different sizes of 2D graphynes. They reported that when the side length of a 2D graphyne is less than 1.45 nm, it can effectively prevent the methanol crossover. Kou et al.129 explored the water desalination on different kinds of graphynes by using molecular dynamics simulation. The results show that graphyne-3 and graphyne-4 not only possess high salt rejection but also exhibit remarkable water permeability, making the graphynes great potential applications in water purification. Cranford indicated that graphdiyne could be a promising membrane for H2 purification.130 More recently, Yuan et al.131 reported that the special triangle pores in a GDY network can selectively adsorb different metal ions. As shown in Fig. 15c, Th4+, Pu4+, Am3+, Cm3+ and Cs+ can exist on GDY, while UO2+, La3+, Eu3+, Tm3+ and Sr2+ can hardly be adsorbed on GDY. The ion-size selective binding behaviors can efficiently separate the actinides and lanthanides in the nuclear fuel cycle.
image file: d1qm00595b-f15.tif
Fig. 15 (a) The schematic of hydrogen purification on GDY. (b) The interaction energies of CH4, CO and H2 molecules on a GDY monolayer. Copyright 2011 The Royal Society of Chemistry. (c) The interaction between GDY and different ions. Copyright 2020 John Wiley & Sons.

4. Conclusion and outlook

In this review, we have given a comprehensive computational perspective overview of graphynes and graphyne-based materials for electronics and energy conversion applications. The excellent intrinsic electronic, chemical and mechanical properties of graphynes have been attracting increasing attention and becoming a rising star among 2D materials. The graphyne family, GDY and GY, has been successfully synthesized, inspiring both theorists and experimentalists to extend their deeper and wider range of applications. However, compared to graphene, graphyne-based electronic and energy devices are still in their initial studies.

Up to now, only GDY and GY have been realized in experiments. The synthesis of other members in the graphyne family is necessary and urgent for basic applications. GDY was first synthesized on a Cu surface, and the growth mechanism on metal surfaces is sorely lacking and should be further investigated by theory modeling, which could lead to the realization of other group members. The stacking pattern has been proved to influence the electronic properties of layered 2D materials. Exploring how the different stacking structures affect the properties of graphynes is meaningful. The various morphologies of graphynes, including nanowires, nanotubes and nanosheets, can be used to construct different kinds of heterojunctions with other 2D materials.132 The diverse sp and sp2 carbon atoms and the uniformly distributed different sizes of pores in graphynes render them perfect platforms for supporting metal atoms. Although single atom-doped graphyne catalysts have been widely investigated, the investigation on a few precise number of metal atoms (double, triple and few metal clusters) supported on graphynes as efficient catalysts for different chemical reactions is still far behind.133 Moreover, most of the theoretical studies mainly focus on the catalytic performance of metal-doped graphynes, and the basic stability of the designed catalysts under real reaction conditions (temperature, pH, pressure, solvent effect, etc.) should be taken into consideration in theoretical modeling. Thus, a set of more realistic computational methods needs to be developed to simulate the in situ reaction process. In addition, the chemical instability of double and triple carbon bonds in graphynes is also of much interest for further investigations both experimentally and theoretically. The stability of graphynes could be further enhanced by the functionalization of triple carbon bonds to single ones, such as different doping approaches and forming composites with other materials. The design of heterogeneous diatomic metal atom catalytic centers is identified as the efficient method to greatly improve the catalytic performances for many reactions.102,134 Graphynes can provide abundant anchor sites for loading different kinds of metal atoms which could be used to develop novel low-cost and highly efficient heterogeneous dimer-/triple-metal-atom catalysts. Nonmetal elements such as B-, N-, O-, P- and S-doped graphynes have been successfully synthesized. The adsorption of transition metal (TM) atoms on graphynes is a promising strategy to modify their electronic and magnetic properties, and therefore improve their performances towards molecular storage, sensing, electrocatalysis, spintronics and nanomagnetism. Extensive computational studies on the structures and electronic properties of metal-doped graphynes have been performed to elucidate the most energetically favorable doping configurations of metallic centers into a GY network. Among the most insightful results, Kim et al. investigated the adsorption of 3d, 4d and 5d TM atoms on GY.135 They determined that except for the d10 group XII TMs, the TM atoms were solid chemisorbed over graphyne acetylenic rings, which appears to be the suitable anchored sites for TM atoms owing to their huge adsorption energies and high diffusion energy barriers. These computational findings have been recently verified. Lu and colleagues have computationally demonstrated using electron localization function and charge density difference the covalent bonding between TM atoms (Co, Fe, Cu and Mn) and the six C atoms in the acetylene chain.136 Therefore, the computational study of different coordination effects on the metal atom-doped graphynes could be a new topic of interest for the rational design of new catalysts with novel structural and electronic properties.

The high structural tailorability, well-controlled cavities, robust mechanical strength and large surface areas are converting graphynes as emerging platforms towards applications beyond electronics and energy conversion, such as drug delivery137 and DNA detection.31,138,139 It is believed that graphynes will continue to attract more research interest in many ways. However, opportunities and challenges always coexist. There are still many problems that need to be solved to promote this kind of material for broader and practical applications.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors acknowledge the generous grants of high-performance computing resources provided by the Queensland University of Technology, NCI National Facility, the Pawsey Supercomputing Centre through the National Computational Merit Allocation Scheme supported by the Australian Government, the Government of Western Australia. A. D. greatly acknowledges the financial support from the Australian Research Council under the Discovery Project (DP170103598). H. P. acknowledges the support from the Science and Technology Development Fund (FDCT) of Macau SAR (0102/2019/A2, 0035/2019/AGJ, 0038/2019/A1, 0154/2019/A3, and 0081/2019/AMJ).

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