Two-Dimensional Carbon-Based Auxetic Materials for Broad

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Energy Conversion and Storage; Plasmonics and Optoelectronics

Two-Dimensional Carbon-Based Auxetic Materials for Broad-Spectrum Metal-Ion Battery Anodes Shuaiwei Wang, Yubing Si, Baocheng Yang, Eli Ruckenstein, and Houyang Chen J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00905 • Publication Date (Web): 29 May 2019 Downloaded from http://pubs.acs.org on May 30, 2019

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The Journal of Physical Chemistry Letters

Two-Dimensional Carbon-based Auxetic Materials for Broad-Spectrum Metal-Ion Battery Anodes Shuaiwei Wanga, Yubing Sia, Baocheng Yanga, Eli Ruckensteinb, Houyang Chenb*

a Henan

Key Laboratory of Nanocomposites and Applications, Institute of Nanostructured Functional

Materials, Huanghe Science and Technology College, Zhengzhou 450006, China b Department

of Chemical and Biological Engineering, State University of New York at Buffalo,

Buffalo, New York 14260-4200, USA

________________ * To whom correspondence should be addressed. Email: [email protected]

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Auxetic materials possess special applications due to their unique negative Poisson’s ratios (NPRs). As a classic two-dimensional (2D) carbon material, the NPR of graphene is still deliberated. Introducing NPR in graphene would increase its extraordinary properties, and the NPR together with other properties would bring more significant applications for graphene. In this paper, based on first-principles calculations, we reconfigure the structure of graphene, and, as an example, we propose a new 2D planar carbon allotrope, xgraphene, which is constructed by 5-6-7 carbon rings. Our theoretical calculations indicate that xgraphene has a NPR and constitutes a broadspectrum of metal ion battery anodes with high performance. Its maximum storage capacities are 930/1302/744/1488 mA h/g for Li/Na/K/Ca-ion batteries. They have low metal-ion diffusion energy barriers (≤ 0.49 eV) and low average open circuit voltages (≤ 0.53 V). Our density functional theory results also showed that it is intrinsically metallic, and possesses dynamic, thermal, and mechanical stabilities. Its intrinsic NPR, which stems from the weakness of coupling of carbon-carbon bonds, is found upon loading the uniaxial strain along the armchair direction. This work would not only open up a new direction for the design of the next-generation broad-spectrum energy storage materials with low cost and high-performance, but also offer a class application for auxetic materials. Keywords: 2D carbon material; negative Poisson’s ratio; metal-ion battery; anode material; broad-spectrum

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Graphical Abstract

A new 2D carbon allotrope xgraphene possesses negative Poisson’s ratios and can be used as broad-spectrum and low-cost metal-ion battery anodes.

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Carbon can generate numerous allotropes1-7 with extraordinary physical and chemical properties and wide engineering applications. As a typical example, the twodimensional (2D) material graphene acquires a giant success in both science community and industrial field owing to its extraordinary properties such as the unusual electronic89

and thermal properties10-11 as well as the quantum Hall effect12. Thus, researchers are

motivated to design and innovate new 2D carbon allotropes. Massive 2D carbon materials with various geometric structures, containing tetragons, pentagons, hexagons, heptagons, octagons, and linear chains, have been predicted and prepared by experiments and theories, such as planar C4 sheet13-14, penta-graphene15, phagraphene16, ψ-graphene17, phographene18, popgraphene19, Θ-graphene20 and graphdiyne21-22. They possess a diversity of electrical properties and other superior properties such as thermal conductivity5 and magnetic properties6. Recently, the carbon-based 2D auxetic materials, which possess negative Poisson’s ratios (NPRs), including penta-graphene15, black phosphorus23-24, tungsten carbide W2C25, and δ-phosphorene26, are studied. Among these materials, not all of their atoms are in the same plane. Thus, their NPR behaviors are mainly originated from their puckered configurations. In addition, the NPR behavior of the single-atomic layer graphene is also deliberated by both classical molecular dynamics (MD) simulations27 and first principles calculations28. Although some carbon-based 2D auxetic materials are reported, they are rare. Due to their unique properties, they have some special applications, such as in the fields of aircraft and automobiles. However, searching and designing a single-atomic layer of carbon-based 2D materials with NPR behaviors 4


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remains a challenge. On the other hand, unique properties of materials play a crucial role in their applications, such as gas capture29, catalysis30, and metal-ion battery (MIB)17, 19-20. One of the great potential prospects of 2D carbon materials is the MIB, which is a sufficiently advanced technology in modern clean energies. For example, the low cost graphite anode with good stability has been successfully prepared in commercial applications31-32. However, its maximum storage capacity is only 372 mA h/g for lithium-ion batteries (LIBs) and it cannot be used in sodium-ion batteries (SIBs)33, which limit its applications in the future. Later, other carbon-based 2D materials were employed for use in electrode materials. As LIB anodes, popgraphene19, pentagraphene34, phagraphene35, -graphene17, and -graphene29 have capacities between 372 and 1489 mAh/g, whereas, as SIB anodes, penta-graphene34 and -graphene29 possess capacities from 1275 to 1489 mAh/g. Most of carbon-based 2D materials are tested for LIBs and/or SIBs, and other metal-ion batteries (except LIBs or SIBs) are rarely reported. For example, -graphene is adopted for use in potassium-ion batteries (KIBs) with a capacity of 956.34 mA h/g, however, it cannot be used for magnesiumion battery (MgIB) anodes29. Compared with the lithium (Li), the sodium (Na), potassium (K), calcium (Ca), magnesium (Mg) and zinc (Zn) are abundant elements in the earth. With the development of technologies, it is necessary and possible to explore new anode materials for broad-spectrum MIBs with low cost and high performance. In this work, with the idea of combining the extraordinary properties of both auxetic materials and single-atomic layer of 2D materials, we reconfigure the structure 5



of graphene. As an example, we propose a new planar 2D carbon allotrope, xgraphene, by using the state-of-the-art density functional theory (DFT), and determine that xgraphene possesses NPR properties. The theoretical method is achieved by the Vienna ab-initio Simulation Package (VASP)36-37 (the computational method is provided in section S1 of the supporting information). The single-atomic thickness carbon allotrope xgraphene contains pentagons, hexagons and heptagons of carbon atoms (5-6-7 rings), forming an hourglass shape in its unit cell. Our DFT results reveal that it is stable and has a metallic character. The NPR mechanism is investigated at both atomic and electronic levels. More interestingly, it is an anode for broad-spectrum MIBs. Our theoretical calculations illustrate that the reconfigured graphene is a promising electrode material for LIBs, SIBs, KIBs, and especially for the low cost calcium-ion batteries (CaIBs). This work provides a significant insight for the innovation of a promising family of 2D auxetic materials for the next-generation low cost and high performance metal-ion batteries, and also open up a new avenue for the application of auextic materials. Structure and stability. The optimized structure of the new 2D carbon allotrope is shown in Fig. 1a. It is composed of two 5-6-7 rings in a unit cell, which looks like an hourglass shape, and is named xgraphene. It contains 24 carbon atoms per unit cell. Similar to graphene, it is a one-atom-thick planar nanosheet. The optimized lattice constants are 4.81 and 13.53 Å in the x (zigzag) and y (armchair) axes. The bond lengths are approximately 1.37~1.52 Å, which are in agreement with the experiment data38 of bond lengths (1.14~1.63 Å) of 5-7 rings. It is energetic stability and the total energy is 6


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-9.03 eV per atom, which is lower than those of popgraphene19, Θ-graphene20, and penta-graphene15 (between -8.98 and -8.32 eV per atom), a little higher than those of graphene16 and ψ-graphene17 (between -9.23 and -9.07 eV per atom), and the same as that of phagraphene16 (-9.03 eV per atom). As provided in Fig. 1b, no imaginary mode is detected in the Brillouin zone (BZ), indicating that its structure is dynamically stable. The ab initio molecular dynamics (AIMD) results with a 1 × 4 × 1 supercell reveal that the structure remains its original configuration at 300 K (Fig. 1c) and a little distortion at 1500 K (Fig. 1d) for 5 ps. Thus, xgraphene has high thermal stability. The elastic constants C11, C12, C22, and C66 are 426, 93, 439, and 167 GPa, respectively, which satisfy the criteria39 C11C22 ― C212 > 0 and C66>0, showing that xgraphene is mechanically stable. Electronic Properties. The electronic band structure of xgraphene is calculated by the PBE functional (Fig. 2a). No bandgap is found between the conduction and valence bands, suggesting that xgraphene has a metallic character. To reveal the origin of band structure, the partial density of states (PDOS) for different orbitals of C atoms are presented in Fig. 2b. One can find that the non-zero value of total DOS is found near the Fermi level, again confirming its metallic state. The total DOS around Fermi level (-3~3 eV) are mainly contributed by the pz orbitals of C atoms, and the contributions of s, px and py orbitals can be neglected. Mechanical Properties. Apart from electronic properties, the mechanical properties of xgraphene are also investigated. From the stress-strain curves of xgraphene (Fig. 3a), the linear relationship between stress and strain was obtained for 7



xgraphene at small strains in both armchair and zigzag directions. The stress undergoes a plastic region with the strain increases until cracking in both armchair and zigzag directions. The tensile strength (strain) are 31.4 and 29.8 N/m (0.22 and 0.18) along the armchair and zigzag directions, respectively. The calculated tensile strength are lower than those of graphene (32.9 and 36.2 N/m for the armchair and zigzag directions, respectively)

40,

but are much higher than those of graphyne (17.8 and 18.8 N/m in

armchair and zigzag directions, respectively)41, penta-graphene (23.5 N/m in both armchair and zigzag directions) , and phagraphene (25.6 and 25.4 N/m in both armchair and zigzag directions, respectively)42. The Young’s moduli along the armchair and zigzag directions are 281.6 and 268.3 N/m, respectively. The different Young’s moduli in the two directions indicated the mechanically anisotropic. The Young’s moduli are lower than those of graphene43 (342.2 N/m), but they are close to those of ψ-graphene17 (298 N/m) and penta-graphene15 (263.8 N/m). The high tensile strength and Young’s modulus suggest its good applications in nanodevices. Fig. 3b demonstrates the correlation between strains εx and εy at the range from 0% to 25% for xgraphene subjected to the uniaxial tensile test in the armchair direction. It clearly indicates that a transition from positive Poisson’s ratio to negative Poisson’s ratio occurs at ~16.8%. The data are fitted by the 4th polynomial regression. Taking the first derivative of this function, the corresponding Poisson’s ratios, which are shown in Fig. 3c, are obtained. The Poisson’s ratio decreases from approximately 0.18 to –0.05 when the strain εy increases from 0% to 20%. The calculated NPR of xgraphene is comparable to those of single-layer black phosphorus23 (–0.027) and graphene (–0.03)44, but it is lower than 8


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that of W2C25. Interestingly, we cannot observe the NPR phenomenon with the tensile loading along the zigzag direction. It is important to highlight that the one-atomthickness structure xgraphene exhibits an auxetic behavior under uniaxial tensile conditions. To understand the mechanism of NPR in xgraphene, the evolution of bond lengths (b1, b2, b3, and b4) and angle (θ) were investigated during a uniaxial loading (Fig. 4). With the strain increases along the armchair direction, bond lengths b3 and b4 along this direction increase, while lengths b1 and b2 change a little (Fig. 4b). At small strains, the bond angle (θ) decreases quickly, and the lattice constant 2(b1sin(θ1)+b2sin(θ2)) (where θ = θ1+ θ2) along the zigzag direction decreases. In this process, the bond angle dominates the variation of the lattice constant along the zigzag direction, and no NPR occurs. At large strains, the increasing ratio of the bond length b4 is larger than that of bond length b3, weakening the C-C interaction in b4. Thus, with increasing strain, the bond angle (θ) increased quickly, while tiny variations occur for lengths b1 and b2, increasing the lattice constant 2(b1sin(θ1)+b2sin(θ2)) and inducing the NPR phenomenon. In short, for large strains, the different increases in b3 and b4 amplifies the bond angle, resulting in the increase of the lattice constant and finally forming NPR with the tensile loading along the armchair direction of xgraphene. To reveal the underlying mechanism at the electronic level, we further study the electron localization functions (ELF) in xgraphene with the strain applied along the armchair direction. Fig. 4c demonstrates the evolution of ELF, which would provide the patterns of bonding and electron pair probability based on the electronic level45, at the strains from 0.0% to 17% to 22%. Electrons are localized on the neighboring carbon bonds, 9



generating strong σ bonding states. The bond angle (θ) increasing at large strains along the armchair direction at the atomic level can be further explained at the electronic level (i.e. by ELF). The ELF of b4 becomes more decentralized than that of b3, resulting in weaker coupling of b4 than that of b3. Thus, the ELF coupling of b4 leads to the generation of NPR. In short, based on both atomic and electronic levels, the simultaneously increasing bond length b4 results in the ELF decentralization and weakens the coupling of carbon-carbon in bond b4, inducing the NPR phenomenon. Promising application as a broad-spectrum metal-ion battery anode. The metallic and high surface-to-mass properties of xgraphene suggest that it would have a potential application in metal ion batteries. To determine the anode for broad-spectrum MIBs, we investigated the adsorption abilities of multiple metal ions (i.e. Li/Na/K/Ca/Zn/Mg atoms) on the surface of xgraphene. We define the adsorption energy Eads = (EnM-xgra Exgra - n EM)/n, where EnM-xgra, Exgra and EM are the total energies of xgraphene with and without metal atoms adsorption, and of a single metal atom in bulk. n is the number of metal atoms. Adsorption behaviors of a single Li/Na/K/Ca/Zn/Mg atom were considered on the hollow, top, and bridge adsorption sites (Fig. 5a). Adsorption energies of a Li/Na/K/Ca/Zn/Mg atom are shown in Table 1. The Li, Na, and K atoms prefer to be located on sites A-E, while the Ca atom tends to stay at sites A-C and E-F. However, both Zn and Mg atoms cannot be adsorbed on those sites. The stability of the preferred adsorbed configurations follows the order of K > Li > Na > Ca. The Bader charge was calculated to better analysis the adsorption properties of Li/Na/K/Ca on the surface of xgraphene. The Li/Na/K atoms transfer approximately 0.89/0.88/0.90, 10


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0.89/0.90/0.91, 0.89/0.90/0.91, 0.91/0.90/0.71, and 0.90/0.90/0.90 e- to A-E sites of xgraphene, respectively, while the Ca atom transfers approximately 1.38, 1.38, 1.37, and 1.38, 1.38 e- to A-C and E-F sites. The mobility of metal ions is also a key factor of an anode material. The diffusion of Li/Na/K/Ca was studied by using the climbing-image nudged elastic bond method46. Three possible migration pathways are considered from one adsorption site A to another adsorption site A along the crystal axes (Fig. 5b-c), and their corresponding diffusion energy profiles are shown in Fig. 5(d-g). The maximum diffusion barriers of all paths for Li/Na/K/Ca are 0.49/0.33/0.18/0.39 eV. These barriers are close to those in ψgraphene17 (0.31 eV in LIBs), Θ-graphene20 (0.48/0.39/0.37 eV in LIBs/SIBs/KIBs, respectively), and popgraphene19 (0.55 eV in LIBs). It should be noted that paths I~III are available for Li/Na/K. The path II works well for Ca, however, paths I and III for Ca ions shift to paths I’ and III’. Interestingly, the diffusion barrier for K atoms is approximately one half of those of Ca, Li, and Na atoms. The lower barrier led to the higher metal-ion mobility, indicating the faster charge-discharge rates in xgraphene for its application as an anode material in MIBs. In the practical applications, it is important to investigate the storage capacity of batteries. We then determine the maximum capacity of the anode material. Only one and two layers of Li/Na/K/Ca on one side and both sides of xgraphene were considered using a 2 × 2 supercell. For a single layer adsorption, the maximum capacities of xgraphene are 930/744/558/1116 mA h/g for Li20C48/Na16C48/K12C48/Ca12C48 with the corresponding adsorption energies of –0.07/–0.08/–0.12/–0.09 eV. After the first layer 11



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adsorbed fully, the second layer was considered to add subsequent metal atoms on both sides of an xgraphene monolayer. The maximum capacities for Li/Na/K/Ca become 744/1302/744/1488 mA h/g and their adsorption energies are –0.06/–0.04/–0.39/–0.05 eV. It should be mentioned that (1) these capacities are higher than that of graphite47 (372 mA h/g for LIBs) and are close to other 2D carbon allotropes for LIBs19-20, 34-35; (2) a high storage capacity of 1302/1488 mA h/g was found for the Na/Ca-ion battery; and (3) the considerable storage capacities for K and Ca were obtained which were rarely reported. Finally, values of the open-circuit voltage (OCV) for Li20C48, Li16C48/Na16C48/K16C48/Ca16C48,

Li14C48/Na14C48,

Li12C48/Na12C48/K12C48/Ca12C48,

Li10C48/Na10C48/K10C48/Ca10C48,

Li8C48/Na8C48/K8C48/Ca8C48,

Li6C48/Na6C48/K6C48/Ca6C48, Li2C48/Na2C48/K2C48/Ca2C48

Li4C48/Na4C48/K4C48/Ca4C48, are

0.07,

0.10/0.08/0.39/0.03,

and 0.10/0.12,

0.12/0.23/0.12/0.05, 0.15/0.25/0.31/0.07, 0.24/0.25/0.48/0.11, 0.30/0.26/0.54/0.10, 0.50/0.35/0.78/0.13, and 0.73/0.59/1.10/0.13 V, respectively. The corresponding average OCVs are 0.28/0.27/0.53/0.09 for Li/Na/K/Ca, which are larger than that of graphite48 (0.11 V for LIBs), are comparable to those of popgraphene19 (0.30/0.29/0.60 V for LIBs/SIBs/KIBs), and are also lower than that of ψ-graphene17 (0.64 V for LIBs). The results of low OCVs suggest that xgraphene provides more benefits than the currently used anode materials in MIBs, especially in Na- and Ca-ion batteries. In summary, by employing first-principles theory, we reconfigure the structure of graphene, and as an example, we propose a new metallic auxetic allotrope of 2D carbon material xgraphene, which is composed of 5-6-7 carbon rings. Its structure has a lower 12


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energy than most of 2D carbon allotropes, and is intrinsically metallic. Through the calculated phonon spectra, AIMD simulations, and elastic constants, we confirmed that this new structure possesses dynamic, thermal and mechanical stabilities. The NPR phenomenon, which is rare for a single-atom-thick layer of planar materials, of the planar xgraphene occurs by uniaxial loading along the armchair direction. At the atomic level, by analyzing the evolution of bond lengths and bond angles with increasing strain, the origin for NPR occurrence in xgraphene is the different increase of the bond lengths. At the electronic level, ELF results indicate that the weakness of ELF coupling of bond b4 is the driving factor for the NPR formation. Thus, this study would light on the further applications of xgraphene in modern nanoscale devices. We also found that the 2D xgraphene monolayer could be a high performance anode material for broad-spectrum metal-ion batteries such as LIBs, SIBs, KIBs and CaIBs. However, it cannot be used as ZnIB and MgIB anodes. The maximum theoretical specific capacities for Li/Na/K/Ca are 930/1302/744/1488 mA h/g, which are larger than that of graphite for LIBs. More excitingly, low energy barriers (≤ 0.49 eV) and low average OCVs (≤ 0.53 V) were determined for the Li, Na, K, and Ca diffusion on the surface of xgraphene, indicating its excellent charge-discharge capability. The present results suggest that xgraphene can be a broad-spectrum metal-ion battery anode, and possesses potential advantages in Naion batteries and the low-cost Ca-ion batteries. This work may provide new insights for the innovation of 2D anode materials for broad-spectrum and low-cost metal-ion batteries.

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Conflicts of interest There are no conflicts to declare.

Acknowledgements This work was supported by the University at Buffalo and the National Natural Science Foundation of China (NSFC) (Grant Nos. 21206049, 21703077), the Innovation Scientists and Technicians Team Construction Projects of Henan Province (Grant No. CXTD2017002), the College Students' innovation and entrepreneurship training program of Henan Province (No. 201711834019), the International Cooperation Project of Zhengzhou Science and Technology Bureau (No. N2014SX0167). We thank the High performance Computing Center of Huanghe Science and Technology College for the computational time provided.

Supporting Information Available Computational methods.

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Table 1. Adsorption energies for Li, Na, K, Ca, Zn, and Mg atoms at various adsorption sites (A–F). “–” means that the atom cannot be adsorbed on such site.

Li Na K Ca Zn Mg

A

B

C

D

E

F

–0.84 –0.79 –1.36 –0.51 – –

–0.71 –0.65 –1.29 –0.26 – –

–0.67 –0.58 –1.26 –0.17 – –

–0.35 –0.48 –1.20 – – –

–0.42 –0.53 –1.27 –0.26 – –

– – –

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–0.27 – –

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Figure 1. (a) The optimized structure (top and side views) of xgraphene. The x and y axes are along the zigzag and armchair directions, respectively. The red dashed rectangle is the unit cell of xgraphene. (b) The phonon spectrum of xgraphene. The equilibrium structures of xgraphene at (c) 300 and (d) 1500 K during AIMD simulations. Insets in (c) and (d) are snapshots of AIMD simulations at 5000 fs.

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Figure 2. (a) Electronic band structure of xgraphene. The inset shows the shape of the Brillouin zone (BZ), and the energy at Fermi level was set to zero. (b) The projected DOS of xgraphene.

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Figure 3. (a) Stress–strain curves of xgraphene with uniaxial tensile along the armchair and zigzag directions, (b) strain εy as a function of εx, and (c) the Poisson’s ratios of xgraphene in the armchair direction.

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Figure 4. (a) The schematic of the bond lengths and the bond angle  of xgraphene. (b) The evolution of bond lengths and the angle  of xgraphene with the strain along the armchair direction. (c) The evolution of the electron localization functions (ELFs) of xgraphene with the strain of 0.0, 0.17, and 0.22 along the armchair direction.

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Figure 5. (a) The possible adsorption sites A-F for Li/Na/K/Ca/Zn/Mg on the surface of xgraphene. Three possible migration paths for Li/Na/K (b) and Ca (c) atoms, and (d-g) their corresponding diffusion energy profiles.

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Two-Dimensional Carbon-Based Auxetic Materials for Broad

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