Thermodynamically Stable Calcium-Decorated Graphyne as a

Publication Date (Web): August 31, 2012 ... thermodynamics, we found that individual Ca-decorated graphynes are thermodynamically stable, unlike previ...
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Thermodynamically Stable Calcium-Decorated Graphyne as a Hydrogen Storage Medium Ho Jun Hwang, Yongkyung Kwon, and Hoonkyung Lee* Division of Quantum Phases & Devices, School of Physics, Konkuk University, Seoul 143-701, Korea ABSTRACT: Recently, carbon nanomaterials decorated with Ca atoms as attractors of H2 molecules have been suggested as room temperature hydrogen storage media because of their large surface area and low weight. However, clustering of Ca atoms was found to significantly reduce the hydrogen storage capacity of Ca−carbon nanostructures. Through the firstprinciples density functional calculations, we explored new carbon allotropes known as graphynes for hydrogen storage. Using equilibrium statistical thermodynamics, we found that individual Ca-decorated graphynes are thermodynamically stable, unlike previously studied Ca−carbon complexes. Up to five H2 molecules can be adsorbed on a Ca atom, each with a binding energy of ∼0.2 eV/H2 required for H2 filling and delivery under an achievable operation condition of temperature and pressure. We also show that Ca-decorated graphynes can serve as promising hydrogen-storage materials with a capacity of ∼7 wt %.

1. INTRODUCTION Over the past decade, allotropes of carbon have been discovered in a variety of forms: graphene (a honeycomb lattice of carbon atoms), carbon nanotubes (CNTs, rolled-up graphene with a finite width), and fullerenes. These nanomaterials, each of which has distinct electronic properties, have been of intense interest and have made significant contribution to the development of modern nanotechnology. For instance, graphene has Dirac cones (massless Dirac fermions) and pseudospins, leading to anomalous quantum Hall effects and pseudospintronics.1,2 Furthermore, much research has been done in terms of its potential application to transparent electrodes, replacing indium tin oxide,3 nanophotonics,4 and electron supercollimation in a graphene superlattice made by a periodic potential.5,6 Very recently, it was theoretically shown that, as with graphene, α-, β-, and 6,6,12-graphynes, which are two-dimensional structures consisting of sp2- and sp-bonded carbon atoms, have Dirac cones.7,8 Some graphynes are predicted to have very anisotropic Dirac cones, which could cause electrons to conduct only in a preferred direction. Therefore, similar to a graphene superlattice, electron collimation might be achieved in a graphyne without any external field. In recent years, various nanomaterials have been explored for reversible high-capacity hydrogen storage because of their large surface area (∼2600 m2/g).9−12 However, the hydrogen storage capacity of these materials is too low at room temperature due to low hydrogen binding energy (∼0.05 eV).13 For reversible room temperature hydrogen storage, the binding energy is required to be in the energy window of ∼0.2−0.6 eV.14 It was found that the so-called Kubas interaction, which results from a hybridization of transition metal d orbitals and H2 σ and σ* orbitals, could enhance the binding energy of hydrogen.15 This © 2012 American Chemical Society

has led to recent studies on various Kubas-type hydrogen storage nanomaterials such as Sc-decorated fullerenes, Tidecorated CNTs, Ti-decorated ethylene, Ti-decorated polymers, and Ti-decorated nanostructures. These materials adsorb H2 molecules with enhanced binding energies of ∼0.2−0.6 eV,16−23 and their hydrogen storage capacities are predicted to meet the gravimetric goal (6 wt %) set by the Department of Energy (DOE). As a matter of fact, some experiments have shown that Ti−silica complexes or Ti−ethylene complexes can bind H2 molecules with a binding energy of ∼0.2 eV/H2.24−26 It is, however, suspected that a clustering of Ti atoms may occur because of the large cohesive energy (∼4 eV) of bulk Ti, which significantly reduces the hydrogen storage capacity of these complexes.27,28 More recently, it has been found that calcium ions (Ca+ or Ca2+) also generate the Kubas interaction for H2 molecules because the unoccupied d orbitals of a calcium ion near the Fermi level are hybridized with H2 σ and σ* orbitals, similar to the case of H2 binding to transition metal atoms.29 Thus, Cadecorated nanomaterials, in which the charge state of the Ca atom is around +1, can bind multiple H2 molecules with a binding energy of ∼0.2 eV/H2 through the Kubas interaction.30−33 In terms of decorating metal atoms as attractors of H2 molecules, Ca could be the best candidate because Ca is a less aggregated (small cohesive energy) and abundant (low cost) element of low weight (high capacity). As in the case of transition metal atoms, however, the clustering issue of Ca atoms on graphene and CNTs32 still remains because the binding energies of Ca atoms on these carbon structures (0.48 Received: June 25, 2012 Revised: August 29, 2012 Published: August 31, 2012 20220

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eV/Ca on graphene34 and 0.88 eV/Ca on a (7,7) CNT32) are smaller than the bulk cohesive energy (1.84 eV/Ca). Even aggregation of two Ca atoms considerably reduces the binding energy of H2 molecules and hence the number of adsorbed H2 molecules, compared to the case with individual Ca-decorated structures. Recently, it was found that aggregation or clustering of Ca atoms can be suppressed on boron-doped CNTs32 or on zigzag graphene nanoribbons31 by enhanced selective attachment of Ca atoms to the B sites or the edges. However, high Bdoping concentrations or narrow zigzag graphene nanoribbons are required to achieve high-capacity hydrogen storage. Furthermore, the thermodynamics for Ca dispersion on these carbon structures has not been studied yet. Graphynes have structural properties that are distinct from those of graphene. Graphynes are “nanoporous sheets” that are permeable to H2 gas, whereas graphene is effectively an H2impermeable rigid two-dimensional sheet. The area of a hexagon of a graphyne is approximately eight times as large as that of a graphene; the length of a hexagonal side of graphyne is ∼4 Å, whereas that of graphene is ∼1.4 Å. Hence, graphynes may have a larger surface area than that of graphene and could be used for effective hydrogen storage. In this study, we explored the possibility of using graphynes decorated with Ca atoms for room temperature high-capacity hydrogen storage materials. We found that, unlike transition metal atoms, Ca atoms are thermodynamically dispersed on graphynes without any clusterings because the Ca binding energy is greater than the cohesive energy of bulk Ca. We also found that up to five H2 molecules can be adsorbed on each of these Ca atoms with a binding energy of ∼0.2 eV/H2, and that the hydrogen storage capacity is as large as ∼7 wt %. Our estimation of the practical capacity shows that Ca-decorated graphynes can serve as promising high-capacity hydrogen storage materials.

2. COMPUTATIONAL DETAILS The total energy electronic structure calculations with an energy minimization scheme35 based on density functional theory were performed. The exchange correlation energy functional was used with the generalized gradient approximation (GGA) in the Perdew−Burke−Ernzerhof scheme36 and the kinetic energy cutoff was taken to be 400 eV. Our calculated lattice constant of α-graphyne was 4.01 × √3 Å, which was consistent with the value predicted by Coluci et al.8 Our model α-graphyne system was a 2 × 2 hexagonal supercell containing 32 C atoms. The geometrical optimization of the Ca−graphyne complexes was carried out within a fixed 2 × 2 supercell obtained from the equilibrium lattice constant of the isolated graphyne until the Hellmann−Feynman force acting on each atom was less than 0.01 eV/Å. The first Brillouin zone integration was done by the Monkhorst−Pack scheme.37 The 4 × 4 × 1 k-point sampling was done for the 2 × 2 graphynes. To remove spurious interactions between neighboring structures due to periodic calculations, a vacuum layer of 10 Å was taken in each of all nonperiodic directions.

Figure 1. Atomic structures of Ca atoms attached on (a) 2 × 2 αgraphyne, (b) 2 × 2 β-graphyne, and (c) 2 × 2 γ-graphyne. The gray and green dots indicate carbon atoms and calcium atoms, respectively.

Ca atoms on the graphynes, i.e., on top of the C atoms and in the hollow sites of sp- and sp2-bonded hexagons and sp-bonded triangles. For the attachment of Ca atoms on α-graphyne, the most favorable adsorption site is located in-plane and slightly off the center of a hexagon, as shown in Figure 1a, where the distance between the Ca atom and the nearest C atom is 2.7 Å. On β-graphyne, a Ca atom prefers to be attached on a triangular hollow site (consisting of sp-bonded carbon atoms) with a binding energy of 3.22 eV/Ca rather than a hexagonal hollow site (see Figure 1b). The nearest Ca−C distance is 2.6 Å and the Ca atom is at a height of 1.5 Å above the graphyne sheet. On γ-graphyne, as with β-graphyne, a Ca atom binds to a

3. RESULTS AND DISCUSSION Figure 1 shows the atomic structures of α-, β-, and γ-graphynes decorated with Ca atoms. Calculations for a 2 × 2 supercell of the graphynes were performed. The molecular formulas of the structures for the α-, β-, and γ-graphynes are (C32·Ca)n, (C72·Ca)n, and (C42·Ca)n, respectively, where n is a large integer. Unlike graphene, there are several attachment sites for 20221

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triangular hollow site with a binding energy of 2.49 eV/Ca, as shown in Figure 1c. Here, the nearest Ca−C distance is 2.6 Å and the Ca atom is located at a height of 1.5 Å above the graphyne sheet. We also investigated the adsorption of H2 molecules on the Ca-decorated graphynes. A H2 molecule is bound to a Ca atom on α-graphyne with a binding energy of 0.34 eV, while the bond length of the H2 molecule is slightly elongated from 0.75 Å to ∼0.76 Å and the Ca−H2 distance is 2.7 Å. Up to five H2 molecules in succession can be bound to the Ca atom with a distance of ∼2.7 Å, as shown in Figure 2a. As the number of H2

Figure 2. The optimized atomic geometries of Ca atoms adsorbed on 2 × 2 (a) α- and (b) γ-graphynes with the maximum number of H2 molecules, respectively. The yellow dots indicate hydrogen atoms.

molecules increases, the binding energy of the H2 molecules decreases slightly (see Table 1). An attractive feature of the CaTable 1. Calculated Binding Energy (eV/H2) of H2 Molecules on Ca-Decorated α- and γ-Graphynes As a Function of the Number of Adsorbed H2 Molecules materials

1 H2

2 H2

3 H2

4 H2

5 H2

α-graphyne γ-graphyne

0.30 0.26

0.26 0.21

0.25 0.20

0.23 0.15

0.20

Figure 3. (a) The calculated binding energy of Ca atoms on 2 × 2 αgraphyne. The inset shows the optimized geometry of Ca-decorated graphyne with N = 4. The dotted line indicates the calculated cohesive energy (1.64 eV) of bulk Ca. (b) The optimized atomic geometries of maximum number of adsorbed H2 molecules for a Ca-decorated αgraphyne. The maximum capacity of H2 molecules is 6.9 wt %.

decorated α-graphyne is that even with in-plane Ca decoration, no steric hindrance is associated to accommodate H 2 molecules. The distance between the H2 molecules and the nearest carbon atoms is ∼3 Å, which is close to a typical equilibrium distance (∼3.4 Å) of the van der Waals interaction. For γ- or β-graphyne, up to four H2 molecules can be adsorbed on a Ca atom attached to a triangular hollow site, as shown in Figure 2b, and the binding energy of the H2 molecules decreases slightly as the number of H2 molecules increases. The calculated H2 binding energies to the Ca-decorated α- and γgraphynes are presented in Table 1. This energy range satisfies the binding energy requirement for reversible room temperature hydrogen storage. We further investigated α-graphyne as being representative of graphynes for Ca-decorated hydrogen storage systems. As the number of Ca atoms increases, we calculate the binding energy of the Ca atoms on a 2 × 2 α-graphyne, defined by N E bind (Ca) = (EC + N ·ECa − ECN− Ca)/N

corresponding values of 0.88 eV/Ca (GGA calculation) on a (7,7) CNT,32 0.99 eV/Ca (local density approximation calculations) on graphene,33 ∼0.5 eV/Ca (GGA calculations) on graphene,38 and 0.5−1.0 eV/Ca (GGA calculation) on CNTs with a diameter of ∼5−10 Å.38 Another important feature is that the Ca binding energy is greater than the cohesive energy of bulk Ca, whose theoretical and experimental values are 1.64 and 1.84 eV, respectively, until up to four Ca atoms are attached to the 2 × 2 α-graphyne. From this we conclude that Ca atoms can be adsorbed on the α-graphyne without any clustering. We also studied whether clusterings of Ti and Sc atoms take place on α-graphyne as they do on graphene and carbon nanotubes. The stable adsorption sites of both Ti and Sc atoms are in the in-plane hexagon, similar to those of Ca atoms. The calculated binding energy (2.49 eV/Ti) of a Ti atom on αgraphyne is smaller than the cohesive energy of bulk Ti but slightly larger than the binding energy of 2.20 eV/Ti on a (8,0) CNT17 and of 1.93 eV/Ti on graphene.39 On the other hand, the binding energy of a Sc atom on α-graphyne is 3.03 eV, which is smaller than the value of 3.75 eV/Sc on a C60 buckyball16 but larger than the value of 1.59 eV/Sc on graphene.40 However, unlike Ca atoms, the binding energy of Sc atoms on α-graphyne does not exceed the cohesive energy of bulk Sc. Hence, the clustering issue of transition metal atoms

(1)

ENC−Ca

where N is the number of attached Ca atoms per cell, is the total energy of the isolated 2 × 2 α-graphyne decorated with N Ca atoms, EC is the total energy of the 2 × 2 isolated αgraphyne, and ECa is the total energy of an isolated Ca atom in vacuum. As can be seen in Figure 3a, the calculated binding energies of Ca atoms on α-graphyne are much larger than the 20222

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This is ascribed to the Gibbs factor (e3(μ−ε3)/kT) for the binding of three H2 molecules, which dominates at 25 °C and 30 atm (adsorption conditions) and where μ is −0.21 eV and ε3 is −0.25 eV. The occupation number at 100 °C and 3 atm (desorption conditions) goes to zero because the Gibbs factors are negligible where μ is −0.36 eV. This shows that more or less three H2 molecules out of five are usable upon the change of conditions. Therefore, the usable capacity of the Cadecorated α-graphynes is ∼4.2 wt %. We note that for a usable hydrogen system that operates at the adsorption and desorption conditions described above, the H2 binding energy should be in the energy range from ∼0.20 to ∼0.35 eV. This suggests that the Ca−graphyne complexes can serve as efficient room temperature hydrogen storage mediums.

still remains for graphynes and Ca is expected to be the best element for decorating metal atoms. We then investigated how Ca atoms are dispersed on the graphyne. Figure 3a shows the binding energy of Ca atoms on the 2 × 2 graphyne as a function of the number of Ca atoms. To investigate the stability of the Ca-decorated structures, we calculated the formation energy per 2 × 2 cell defined by F(N ) = ECN− Ca − EC − N ·E b − Ca

(2)

where Eb−Ca is the total energy per Ca atom of bulk calcium. The formula for the formation energy can be reduced to F(N) N Ca = N(ECa cohesive − Ebind), where Ecohesive (≡ECa − Eb−Ca) is the cohesive energy of bulk Ca and ENbind is the Ca binding energy N of eq 1. When ECa cohesive < Ebind (F(N) < 0), the Ca-decorated αgraphyne is energetically more stable than the segregated phase between bulk Ca and α-graphyne. We found that the formation energy of the Ca-decorated α-graphyne is indeed negative until the number of Ca atoms is less than 7 (see Figure 3a). We then took into account the thermodynamics of the Ca dispersion on α-graphyne to determine the concentration of Ca atoms on α-graphyne. We assumed that the Ca atoms decorated on the 2 × 2 graphyne are in thermal and diffusive equilibrium with bulk Ca, in which the Gibbs factor e−N(μCa− EN)/kT of a N-calcium configuration can be determined with μCa N = −ECa cohesive and EN = −Ebind. It turns out that the N = 4 configuration, in which each hexagon of the graphyne accommodates exactly one Ca atom, as shown in the inset of Figure 3a, is the most probable and thermodynamically stable structure at room temperature, the Gibbs factor of which is dominant over all other configurations. Figure 3b shows the structure of the N = 4 Ca−graphyne complex when the maximum number of H2 molecules are attached on the complex and its molecular formula is (C8·Ca·5H2)n. Hence, the hydrogen storage capacity of this structure can reach up to 6.9 wt % of hydrogen. Another attractive feature of this structure is that no steric hindrance is associated with it when H2 molecules are adsorbed on each Ca atom. This means that individually dispersed Ca atoms attract H2 molecules as does a Ca atom on the 2 × 2 graphyne. To estimate the usable capacity of hydrogen at ambient conditions, we considered the thermodynamics of adsorption of H2 molecules on the Ca−graphyne complexes. The occupation number of H2 molecules as a function of the pressure and temperature from the grand canonical partition function is as follows:19 f=

4. SUMMARY We did total energy electronic structure calculations on the Cadecorated graphynes to explore the possibility of reversible room temperature hydrogen storage. An important finding was that individual Ca-decorated graphynes are thermodynamically stable and a Ca−α-graphyne complex can store as much as ∼7 wt % of hydrogen with a binding energy of ∼0.2 eV/H2 for a readily achievable H2 filling and delivery operation condition of temperature and pressure. According to ref 41, it is possible to make graphynes from carbon networks based on dehydrobenzoannulenes by using a bottom-up approach.41 Our study shows that graphynes have considerable potential as promising hydrogen storage materials. We believe that graphynes could also be used for energy storage lithium-ion battery anode materials owing to the large surface area of the graphynes. Our work should stimulate experimental efforts to synthesize the room temperature high-capacity hydrogen storage media.

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Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the WCU Program (Grant No. R31-2008-000-10057-0), and by the Basic Science Research Program (Grant No. KRF-2012013124) through the National Research Foundation of Korea, funded by the Ministry of Education, Science and Technology. The authors also acknowledge the support from KISTI under the Supercomputing Applications Support Program (KSC-2012-C2-52).

∑n = 0 ngne n(μ − εn)/ kT ∑n = 0 gne n(μ − εn)/ kT

AUTHOR INFORMATION

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(3)

where μ is the chemical potential of the H2 gas and −εn (>0) and gn are the average binding energy of the H2 molecules and the degeneracy of the configuration for a given adsorption number of the H2 molecules n, respectively. The occupation number of H2 molecules on the Ca-decorated α-graphyne is calculated as the pressure and temperature at which the experimental chemical potential of H2 gas19 and the calculated binding energy (−εn) were used. We chose the adsorption condition of 25 °C−30 atm and the desorption condition of 100 °C−3 atm to estimate the usable capacity of hydrogen at ambient conditions. These conditions may be readily achievable on board vehicles. The occupation number f of H2 molecules on the Ca-decorated α-graphynes at 25 °C and 30 atm is ∼3.

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