Article pubs.acs.org/JPCC
Lithium Storage on Graphdiyne Predicted by DFT Calculations Chenghua Sun*,† and Debra J. Searles†,‡ †
Australia Institute for Bioengineering and Nanotechnology and ‡School of Chemistry and Molecular Biosciences, The University of Queensland, QLD 4072, Australia ABSTRACT: Graphdiyne (GD) is a new carbon allotrope, consisting of an sp- and sp2-hybridized carbon network. In this work, density functional theory calculations are carried out to investigate the adsorption and diffusion of lithium (Li) atoms on GD monolayers, and the results are compared with those for graphyne and graphene monolayers. High-capacity Li storage, as LiC3, has been predicted, and the preferred adsorption sites for Li have been identified computationally. Moreover, it is found that Li can easily diffuse on the GD monolayer with moderate barriers of 0.18 to 0.84 eV. The predicted high capacity and mobility indicate that GD may offer excellent performance as the anode of lithium batteries.
1. INTRODUCTION Carbon structures have been extensively studied over the last decades as energy storage materials.1−5 One of the industry applications is as the anode of lithium(Li)-ion batteries. Currently,graphite, a layered material consisting of sp2-bonded carbon sheets, is the predominant anode material and offers a theoretical capacity of 372 mA•h/g with Li stored as LiC6 and inserted between two graphene layers.6−8 Typically, Li adsorbs over the 6-C hexagons with a distance from the neighboring Li more than 4 Å, as determined by the repulsive Li−Li interaction.9,10 To achieve higher capacity, many carbon allotropes have been explored, such as fullerenes,11 disordered carbon,12 graphene,13−15 carbon nantoubes,16−18 and so on. For sp2-dominated carbon structures, like graphene, graphite and carbon nanotubes, Li-atoms are captured by the 6-C hexagon with a maximum loading of LiC6, and the space for further improvement of the capacity is limited. To achieve higher storage capacity, sp-sp2 hybrid allotropes may be an option. Computational studies of its formation energy have indicated that graphyne (GP), a planar sheet with 6-C hexagon connected by acetylenic chains (−CC−), is stable.19 In fact, acetylenic chains can be used to connect benzene rings flexibly and form various hybrid structures.20 In recent years, numerous monomeric and oligomeric compounds have been successfully synthesized,21,22 supporting early theoretical predictions on the stability of sp-sp2 hybrid structures. With respect to graphene, GP introduces acetylenic linkages (−CC−) to form 12-C hexagons and leads to a lower atom density; as a result, higher Li storage capacity (LiC4) and excellent mobility may be achievable.23 Currently, the major challenge for GP is its synthesis. On the basis of GP, incorporating another −CC− into the acetylenic linkages can generate another sp-sp2 hybrid carbon allotrope, graphdiyne (GD), which is even more stable than GP.19,24 GD substructures were first synthesized by Haley et al,24 and very recently Li et al. achieved the large-scaled synthesis of GD films25 and their tubular aggregations.26 It has © 2012 American Chemical Society
been found that the GD monolayer presents unique electronic structures and excellent conductivity according to first-principle calculations.27−29 Moreover, both Li-decorated GD and GP are promising for hydrogen storage, with moderate adsorption energies of 0.15 to 0.27 eV/H2.30 Therefore, it is reasonable to expect that those sp-sp2 hybrid planar structures are also promising for energy storage.31 Given that the atom density in GD is even lower than that in GP, higher storage capacity may be achievable. In this work, density functional theory (DFT) calculations have been carried out to investigate the adsorption and diffusion of Li atom on the GD monolayer. As shown below, high capacity (LiC3) and excellent mobility can be offered by GD.
2. COMPUTATIONAL METHODS All spin-polarized calculations were carried out using the DFT scheme, as implemented in the DMol3 package.32,33 The generalized gradient approximation with the Perdew−Burke− Ernzerhof functional,34,35 together with effective core potentials with double-numeric quality basis sets, was utilized for all geometric optimization and single-point energy calculations. During the calculations, a global cutoff radius of 4.5 Å was employed, and the convergence criteria for structure optimizations were set with an energy tolerance of 0.27 × 10−4 eV per atom and maximum displacement tolerance of 1.0 × 10−3 Ǻ . K-space was sampled by the Γ point. Along the z direction, a vacuum space of 20 Å was employed to avoid the interaction between neighboring images. The strength of the Li-GD interaction was described by the average adsorption energy, Eads, which is defined by Eads = (nE(Li) + E(GD) − E(Li n‐GD))/n Received: September 28, 2012 Revised: November 9, 2012 Published: November 28, 2012 26222
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Figure 1. Optimized geometries for the adsorption of two Li atoms on GD. Li and C are shown as purple and gray spheres. (a) Li in 6-C hexagon (two Li atoms distribute on the two sides of carbon network) and (b) Li in 18-C hexagon (both Li atoms are on the same side of the carbon network).
Figure 2. Optimized geometries for the adsorption of Li atoms on GD with different capacities. (a) LiC3, (b) LiC1.29, and (c) LiC.
Figure 3. High Li-loading as LiC2.57. (a) Optimized adsorption geometry. (b) Energy profile for Li-atoms throughout the SCF process. The inset shows the Li atoms spontaneously moving from one side to another. Side views for four intermediate steps 1, 30, 50, and 67 are shown in the inset. The energy for the final geometry is set to zero.
where n is the total number of adsorbed Li atoms and E(Li), E(GD), and E(Li-GD) are total energies of a single Li, the clean GD slab, and the interacting Li-GD system, respectively. By this definition, a positive Eads indicates that the interacting Li-GD system is stable. The transition state (TS) for Lidiffusion was located in two stages: (i) the initial TS guess was obtained via a combination search using the linear synchronous transit (LST) maximization and quadratic synchronous transit (QST) maximization36,37 and (ii) the LST/QST result was further examined by the nudged elastic band (NEB)38 method until the TS is confirmed to connect the reactant and the product. In the above setting, the van der Waals (vdW) interaction is not considered by standard DFT and may have impact on the results. Therefore, DFT-D calculation39 has been carried out to examine the effect of vdW on the bonding of LiGD and the Li-diffusion. Because of the addition term of vdW interaction, the adsorption energies of both Li and the Lidiffusion barrier are slightly higher compared with those from DFT, but the difference is not significant, typically ∼0.1 eV/Li according to our tests. (A DFT-D barrier is shown for the out-
of-plane Li-diffusion in a triple layer model; see below.) For the investigation of GD multiple layers and highly compact Liadsorption, DFT-D is recommended to take the vdW interaction into the consideration.
3. RESULTS AND DISCUSSION 3.1. Li Adsorption on GD Unit Cell. Li adsorption was first tested using a (1 × 1) unit cell for GD, as shown in Figure 1. The optimized lattice constant is 9.55 Å, which is consistent with previous experimental25 and theoretical reports.27,28 In principle, the Li atoms can be absorbed by both the 6-C hexagon and the 18-C hexagon, and thus to determine the optimal absorption site various starting geometries were tested and the minimum energy configuration identified. As shown in Figure 1a, two Li atoms can absorb above and below the center of each 6-C hexagon, with Eads = 2.24 eV/Li and a distance above/below the plane of the GD of 1.72 Å. Figure 1b shows the configuration with Li adsorbed on the 18-C hexagons, with Eads = 2.63 eV/Li, and the typical atom distances are shown in units of angstroms. In this case, a higher Eads was obtained 26223
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Figure 4. In-plane Li diffusion. (a) Diffusion paths 3→1 and 3→5(7), with Li and C presented as purple and gray spheres and 2, 4, 6 indicating the TS states. (b) Energy profile in units of electronvolts.
Figure 5. Out-of-plane Li diffusion. (a) Model for GD triple layers with ABA stacking and (b) energy profile for Li diffusion from IS to FS shown in panel a. Energy barrier is indicated in units of electronvolts. The number in the parentheses is obtained with vdWs correction.
3.2. Li-Diffusion on GD Unit Cell. With respect to graphene, the major merit brought by the acetylenic chain is the high mobility for Li in-plane and out-of-plane diffusion. Previous work23 shows that the in-plane diffusion in GP is dominated by the immigration from the 12-C hexagon to the 6C hexagon, with a barrier of 0.92 eV, which is slightly higher than that for Li-hoping in graphene (0.32 to 0.48 eV40,41). In the case of GD, the Li atom was initially adsorbed by 18-C hexagon (site 3), as shown in Figure 4a, which is the most preferred adsorption, and it is found that the Li atom needs to cross a barrier of 0.84 eV to reach the 6-C hexagon (site 1) or 0.18 eV to the neighboring site (site 5) in the same 18-C hexagon or 0.70 eV to another 18-C hexagon (site 7). These barriers are slightly smaller than those obtained in GP (0.72 eV for 14-C to 14-C and 0.92 eV for 14-C to 6-C diffusion). As shown in Figure 2a, the 18-C hexagon can offer a capacity of LiC3, and Li atoms prefer to adsorb in the 18-C hexagons, and thus the in-plane diffusion is dominated by the diffusion in the same 18-C hexagon and between neighboring 18-C hexagons. The barriers for these two are small at 0.18 and 0.70 eV, respectively. Therefore, it is reasonable to expect that GD can provide excellent in-plane mobility. For out-of-plane diffusion, Li atoms can easily pass through the 12-C hexagon in GP, with a small barrier of 0.18 eV for outof-plane diffusion,23 which is much smaller than that for passing through the 6-C hexagon in graphene.9,23 Essentially, such improvement is due to the larger size of 12-C hexagon. With no doubt, the barrier for Li passing through the 18-C hexagon in GD will be further reduced due to the larger pore size, as indicated in Figure 3b. Figure 5 shows the out-of-plane with a model of triple layers for GD. Because of interlayer interaction, there are several stacking possibilities, indicated as ABA, ABC, and AAA. Following Lu et al.,42 ABA stacking is employed as a model of triple layered GD, and the top view and side view are shown in Figure 5a,b, with A and B shown as gray and blue colors. Figure 5c shows the energy barrier for Li diffusion to pass through the middle layer, with a barrier as small as 0.17 eV.
when both Li atoms were on the same side of the GD plane. From this test, it appears that Li prefers to adsorb on the 18-C hexagon, which is similar to what occurs in GP. To examine the maximum adsorption capacity, more Li atoms are introduced on GD. In each case, at least 20 different initial sites for the Li atoms were selected randomly, and the structure of the Li-GD system was optimized. Figure 2a−c shows the optimized geometries for 6, 14, and 18 Li atoms on GD, leading to LiC3, LiC1.29, and LiC and with Eads = 2.38, 2.06, and 1.72 eV/Li, respectively. For the latter two, however, the acetylenic chain was found to be distorted, indicating that heavy Li loading can impair the stability of the carbon network. This might be problematic if a rechargeable battery is required. Furthermore, only in the first case were all Li atoms on the same side of the carbon network, giving a storage capacity of LiC3. Given that the 6-C hexagon is capable of storing Li and no Li atoms are located on the 6-C hexagon in Figure 2a, it was expected that another Li atom could be introduced on the 6-C hexagon, leading to LiC2.57. This gave a structure with a positive E, which when optimized gave a structure with no obvious distortion over the whole GD network, as shown in Figure 3a. However, to achieve such high capacity is difficult because the Li atoms captured by 18-C hexagon prefer to adsorb on the other side to avoid the repulsion with Li adsorbed over the 6-C hexagon. As shown in Figure 3b, although all Li atoms first are adsorbed on the same side (see image 1), as the geometry is optimized the 6 Li atoms surrounded by 18-C hexagons move to the opposite side, leading to a final stable adsorption shown in Figure 3a and as image 67 in Figure 3b. This out-of-plane diffusion is spontaneous, indicating that Li atoms can easily diffuse between different layers, and thus GD may offer excellent mobility, as confirmed later. According to the above calculations, the maximum capacity can be up to LiC3, which is higher than both GP (LiC4) and graphene (LiC6), confirming our hypothesis that extending the acetylenic chain helps to improve the capacity for Li storage. 26224
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Figure 6. Structural models for (a) graphene, (b) GP, and (c) GD. All three contain 72 atoms.
maximum storage capacity for GD, GP, and graphene is essentially determined by the atom densities in the carbon network. In principle, further extending the acetylenic chains might be helpful in achieving higher capacity, but the stability of the carbon networks becomes lower, which should be taken into account, too.
With the vdW correction, the barrier increases by 0.10 eV, which is still small, confirming our speculation that 18-C hexagon offers excellent out-of-plane mobility. 3.3. Li-Adsorption on Graphene, GD, and GP Monolayers. To compare the adsorption of Li on graphene, GD and GP, supercells with the same number of atoms (72 atoms) have been employed to investigate Li-loading, as shown in Figure 6. Li adsorption on the three materials has been studied with different loadings: LiC72, Li7C72, Li12C72, Li18C72, and Li24C72. On the basis of our tests, the preferred adsorption sites for LiC72, Li7C72, Li18C72, and Li24C72 can be easily determined. In the case of Li12C72, there are many possible configurations with similar stabilities; therefore, it is essential to perform a comprehensive scan to identify the preferred geometries. In this work, more than 20 starting geometries have been tested by carrying out full optimizations, from which the favored adsorption sites are obtained. Figure 7a presents the calculated adsorption energy in units of electronvolts per Li. Clearly, the adsorption on GD and GP
4. CONCLUSIONS The adsorption and diffusion of Li atoms on GD have been studied within the DFT framework. It is found that GD can offer high storage capacity (up to LiC3) and excellent mobility (diffusion barriers 0.17 to 0.84 eV). Compared with GP and graphene, the above improvement is the result of the lower atom density provided by the acetylenic chains. Because GD has been synthesized readily, it is promising to be applied as Libattery anodes.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS C.S. thanks Prof. Y. L. Li and Dr H. B. Liu for sending their graphdiyne samples and thanks Prof. J. Lu for sharing an unpublished manuscript. Financial support from Australian Research Council through the Centre of Excellence for Functional Nanomaterials and the Queensland State Government (Smart Future Fellowship for C.S.) has been acknowledged. C.S also appreciates the generous grants of CPU time from both the University of Queensland and the Australian National Computational Infrastructure Facility.
Figure 7. Comparison for Li-adsorption on graphene, GD and GP. (a) Adsorption energies. (b) Geometry for the maximum capacity LiC3 by GD. (c) Geometry for the maximum capacity LiC4 by GP.
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is stronger than that on graphene for all loadings, which is mainly the results of two factors: (i) a single Li prefers to adsorb on an acetylenic chain in the case of GD and GP, because sp2- and sp-hybridized carbon atoms dominate the lowest unoccupied states, and (ii) with the increment in Liloading, the Li−Li repulsive interaction becomes important and it is weaker in GD and GP due to their lower atom density. Overall, the adsorption energies for Li-GD and Li-GP are similar, and the major difference comes from the maximum adsorption capacity. Two major differences between Li-GD and Li-GP can be summarized: (i) the maximum capacities are LiC3 and LiC4 for GD and GP, as shown in Figure 7b,c, respectively, and (ii) the high Li-loading achieved in GD does not rely on the contribution of 6-C hexagon, which is valuable in achieving high mobility. In the case of GP, each 12-C hexagon can only hold one Li atom to avoid the strong Li−Li repulsive interaction, whereas each 18-C hexagon in GD can store three Li-atoms. Therefore, the above difference in the
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