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Calcium-decorated graphyne nanotubes as promising hydrogen storage media: A first-principles study
Journal of Solid State Chemistry 197 (2013) 323–328
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Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Calcium-decorated graphyne nanotubes as promising hydrogen storage media: A first-principles study Yu Sheng Wang a,b,n, Peng Fei Yuan a, Meng Li a, Wei Fen Jiang b, Qiang Sun a, Yu Jia a,n a b
Center of Clean Energy and Quantum Structures, and School of Physics and Engineering, Zhengzhou University, Zhengzhou, Henan 450052, China College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450011, China
a r t i c l e i n f o
abstract
Article history: Received 17 June 2012 Received in revised form 25 August 2012 Accepted 1 September 2012 Available online 12 September 2012
First principles calculations based on density functional theory are carried out to study the hydrogen storage properties of Ca-decorated graphyne nanotubes. The results show that Ca atoms can be adsorbed stably on the acetylenic ring of the graphyne nanotube (GNT) without Ca atom clustering. Both the polar interactions and the orbital hybridizations contribute to the adsorption of H2 molecules. The average adsorption energy is in the range of 0.13–0.33 eV/H2 which is almost independent of the tube diameter. Each Ca atom can adsorb up to four H2 molecules due to the steric hindrance of the H2 molecules. With a hydrogen uptake of 7.44–8.96 wt%, the Ca-decorated GNT is an optimal choice for hydrogen recycling at near ambient conditions. & 2012 Elsevier Inc. All rights reserved.
Keywords: Hydrogen storage Graphyne nanotube Nanostructure
1. Introduction The increasing need for clean and renewable energy has aroused growing research interest in hydrogen as a ‘‘green’’ energy carrier because of its abundance, pollution-free, and packing more energy per unit mass than any other fuel [1,2]. However, storing hydrogen efficiently and safely is still a major challenge to realize hydrogen economy. To perform hydrogen reversibly under ambient thermodynamic conditions for motor vehicles and other mechanical systems, the storage materials should store hydrogen with high gravimetric density and the binding energy of hydrogen molecules should lie between the physisorbed and the chemisorbed states ( 0.2 eV/H2) [3,4]. The U. S. Department of Energy (DOE) has set the gravimetric density of 9 wt% in 2015 for usable specific energy from H2. To achieve this goal, the storage materials should consist of only light elements. Instead of traditional storing modes such as compressed gas, liquefied hydrogen or metal hydride, it is suggested to store molecular hydrogen in metal-decorated carbon-based nanostructures owing to their light weights and large surface areas. Decorating atoms include alkaline metals (AM) [5–7], alkaline-earth metals (AEM) [8–10] and transition metals (TM) [11–13]. AM atoms decorated carbon nanostructures can give a high storage weight
n Corresponding authors at: Zhengzhou University, Center of Clean Energy and Quantum Structures, and School of Physics and Engineering, kexue road 100, Zhengzhou, Henan 450052, China. Fax: þ 86 371 67767758. E-mail addresses: [email protected] (Y.S. Wang), [email protected] (Y. Jia).
0022-4596/$ - see front matter & 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jssc.2012.09.004
percent, but the binding energy of AM metals to backbone nanostructures is usually small and the system can become unstable. It is well known that clustering is one of the major problems on the way to successful produce metal-decorated hydrogen storage nanomaterials [14]. Because of the large cohesive energy, TM atoms tend to form clusters on the surface of carbon nanostructures and consequently the hydrogen storage capacity drops dramatically after several cycles. The binding strength of Ca, the first AEM atom with empty 3d orbitals, to carbon-based nanostructures is between the too weak AMs and the too strong TMs. For this reason, Ca has recently emerged as an interesting element to improve the hydrogen storage in carbon-based materials and found that each Ca atom can adsorb several hydrogen molecules [15–19]. However, in the case of Ca-decorated carbon-based nanostructures, i.e., graphene, fullerene, nanotube, the binding energy of Ca is 1.14 [10], 1.3 [15] and 0.88 eV/Ca, [16], respectively. All these binding energies are less than the cohesive energy of bulk Ca. As a result, the Ca-cluster will form in practice which will lower the gravimetric density of H2. To solve this problem, we should find new backbone materials to increase the Ca binding energy beyond the Ca cohesive energy, thereby advancing the structural stability of the system without clustering. Graphyne, a carbon allotrope, which has the same symmetry as graphene and is obtained by replacing one third of the carbon–carbon bonds in graphene with acetylenic linkages [20] (see Fig. 1(a)), has been systematically studied due to promising electrical and optical properties [21–23]. With larger natural ‘‘holes’’ than graphene, graphyne can hold adatoms stably rather than metal aggregation. Li et al. suggest Ca decorated graphyne can adsorb 9.6 wt% of hydrogen molecules with an average binding energy of 0.2 eV/H2.
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The strong binding between Ca and s–p and s–p2 bonded graphyne is due to the additional in-plane p states which do not exist in graphene and fullerenes [24]. Here, instead of considering Ca-decorated graphyne, we focus on the case of individual Ca atoms dispersed on graphyne nanotubes (GNTs). Although the theoretically predicted GNT has not been synthesized, previous studies have shown that g-graphyne is the lowest-energy members of the graphyne family and the GNT formed by g-graphyne is the most likely to be synthesized [24,25]. Our study will concentrate on the hydrogen storage of this kind of GNT. Through first principles calculations, we show that the binding energy of Ca to GNT is much larger than the cohesive energy of bulk Ca leading to the prevention of metal clustering on the surface of GNT. The average adsorption energy of H2 is about 0.13–0.33 eV/H2, the hydrogen storage capacity can reach 7.44–8.96 wt% while the gravimetric density of H2 in the Ca-decorated B-doped carbon nanotubes is only 5–6 wt%. All the above results will place this system as one of the promising hydrogen storage materials.
2. Computational method All calculations are performed using a first-principles method based on density functional theory as implemented in the Vienna ab initio simulation package (VASP) [26]. Both generalized gradient approximation (GGA) [27] and local density approximation (LDA) [28] are used for exchange-correlation energy. For hydrogen binding, the GGA and LDA are known to provide a lower and an upper bound of a more accurate energy obtained with highly correlated methods such as MP2 or coupled-cluster with singles and doubles and perturbative triples correction [29,30]. A 450 eV cutoff energy is chosen for the plane-wave basis. Periodic boundary condition and vacuum space of 15 A˚ along x- and y-directions are applied in order to avoid interactions between two images of GNTs. The
Fig. 1. The optimized geometry of (a) graphyne, (b) GNT (4, 2).
Brillouin zone is sampled by 1 1 6 k-points within the Monkhorst–Pack scheme, where the convergence of total energy with respect to the number of k-points in Brillouin zone is carefully tested. Denser k-point meshes will affect the total energy within 0.002 eV. All the obtained structures are optimized without any symmetry constraints until the force on each atom is less than 10 2 eV/A˚ and the total energy changes are less than 10 4 eV.
3. Results and discussion The geometry structure of the graphyne is given in Fig. 1(a). The calculated bond lengths for C(sp2)–C(sp2), C(sp2)–C(sp), and ˚ respectively, which C(sp)–C(sp) are 1.425, 1.406, and 1.221 A, are in good agreement with previously reported results [21,25]. In this study, we consider zigzag GNTs that are rolled up from corresponding graphyne layers. To find the effect of the size of the GNTs on the hydrogen storage, we investigate three zigzag GNTs with different diameters labeled by (2, 1), (4, 2) and (6, 3), respectively. For simplicity, here we denote these GNTs as GNT1, GNT2 (see Fig. 1), and GNT3, respectively. Our discussions begin with the binding of a single Ca atom on the GNTs. There are five different adsorption sites as shown in Fig. 2(a), which are the hollow center of the hexagon (T1), the hollow center of the acetylenic ring (T2), and three different bridge sites of C–C (namely B1, B2, and B3, respectively). After varying the position of the Ca atom and relaxing all structures, we find that the T2 site is energetically favorable compared to other sites. The bridge sites are unstable adsorption sites, after full relaxation, the Ca atom will move to the most stable adsorption site (T2). To check the stability of our model, the binding energy between Ca and GNT is defined as Eb ¼ ½EðGNTÞ þnEðCaÞEðGNT þnCaÞ=n
ð1Þ
where E(GNT), E(Ca), and E(GNTþnCa) are the energy of the pristine GNT, the energy of a free Ca atom, and the total energy of the GNT with n adsorbed Ca atoms, respectively. The calculated binding energies of Ca adsorbed on T2 sites are much larger than that in Ca bulk (1.84 eV per Ca atom) for all the GNTs presented here, indicating that Ca atoms will be adsorbed stably on the T2 sites. The Eb of Ca adsorbed on T1 site are 1.92, 1.27, and 1.24 eV (LDA: 2.34, 1.90, and 1.92) for GNT1, GNT2 and GNT3, respectively, which are less than that of adsorbed on T2 site: 3.03, 2.39, and 2.32 eV (LDA: 3.69, 3.14, and 3.07 eV). We also find that the binding energy of Ca to GNT decreases as the tube diameter increases and converges to that of the corresponding Cadecorated graphyne. This is due to the reduction in the curvatures of the GNTs. Since previous studies have revealed that metal
Fig. 2. (a) Isolated and (b) clustered configurations of the 6Ca/GNT2 complex. The relative energy DE is evaluated referring to configuration (a). The five possible adsorption sites are shown in (a) where C (sp2) and C (sp) are denoted by CA and CB. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Y. S. Wang et al. / Journal of Solid State Chemistry 197 (2013) 323–328
atoms attached on some host materials can easy to form clusters as the number of metal atoms increases, one may wonder whether the attached Ca atoms reported here would like to aggregate together. As a prototype system we here test the total energy of six Ca atoms adsorbed on GNT2. As shown in Fig. 2, the configuration that Ca atoms form a cluster is 4.58 eV higher in energy than when they disperse evenly on T2 sites. It is worth noting that in the case of Ca atoms adsorbed on T2 sites the Ca–Ca ˚ Consequently, higher distances turn out to be larger than 4.40 A. Eb and larger Ca–Ca distance make Ca atoms adsorbed stably on T2 sites without clustering. To understand the nature of binding properties between the Ca and the GNT, we also calculate the charge transfer between metal Ca and GNT as the positive Ca ion is expected to polarize and bind the H2 molecules. The difference of charge density is calculated by using the following formula:
Dr ¼ rðGNT þCaÞrðGNTÞrðCaÞ
ð2Þ
where r(GNTþCa), r(GNT), r(Ca)are the charge density of the system of a Ca/GNT, the charge density of pristine GNT, and the charge density of a Ca atom, respectively. The three-dimensional charge density difference for a Ca/GNT is shown in Fig. 3 as an insert. The red and blue iso-surface indicates positive and negative charge density corresponding to electron accumulation and depletion, respectively. It is readily seen that charges are transferred from Ca to the GNT, and transferred charge is mainly located on the acetylenic ring just below the Ca atom. It is useful to make a Bader charge analysis to determine the charges on the Ca atom [31]. The Bader charge analysis shows that the Ca atom donates 1.77e to the GNT. To further understand the charge transfer and the nature of the binding, we plotted the partial density of states (PDOS) of GNT and Ca/GNT in Fig. 3. For the pristine GNT, the states near valence band maximum and conduction band minimum come from the pz of both CA and CB atoms (see Fig. 3(a) and (b)). For the CA atoms, two additional highly localized bonding px þpz states can be seen around 2.5 eV below
Fig. 3. (a) The PDOS of CA in pristine GNT, (b) The PDOS of CB in pristine GNT, (c) The PDOS of CA in Ca/GNT, (d) The PDOS of CB near Ca atom in Ca/GNT, (e) The PDOS of Ca atom in Ca/GNT. The Fermi level is set as zero. The isosurface of charge density difference with an isovalue of 0.0033e/A˚ 3 for Ca/GNT is shown as an insert. The red and blue iso-surface indicates space charge accumulation and depletion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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the Fermi energy. This bonding mechanism is similar to the previous studies about graphyne [24]. In the case of Ca/GNT, the hybridization of C 2p orbital and Ca 3d orbital is observed at the Fermi level and in the region between 5 and 2.5 eV. For the CA atoms, px, py and pz states all contribute to the bonding. For the CB atoms, px and pz states at the Fermi level and all three p orbitals between 5 and 2.5 eV participate in the hybridization. The bond between Ca and GNT leads to the s electrons of Ca transfer to GNT forming a Ca ion as shown in Fig. 3(d). GNT then back-donates some charges to the low-lying Ca 3d orbital that hybridize with GNT 2p orbitals between 5 and 2.5 eV. This bonding mechanism can also be observed in the case of Ca binding onto graphene and carbyne networks [10,18]. To further check the stability of the Ca decorated GNT system, we also calculate the migration energies of Ca on the surface of the GNT2. In the case of Ca atom diffusion from T2 to T1, we select two diffusion paths: (a) T2-1-T1; (b) T2-2-T1 as shown in Fig. 4. The corresponding diffusion barriers are 1.70 and 2.20 eV, respectively. In the case of Ca atom diffusion from T2 to another nearest T2, we also consider two diffusion paths: (a) T2-1-T2; (b) T2-2-T2 as depicted in Fig. 5. The diffusion barriers are 1.97 and 2.19 eV, respectively. Such high diffusion barriers indicate that the Ca atoms would rather disperse evenly on the surface of GNTs than form metal clusters. On the basis of the above investigation of the stability of Cadecorated GNT, in the following, we now turn to the discussion on the adsorption of hydrogen molecules on this complex. The average adsorption energy Ead per H2 to the system is defined as the following term: Ead ¼ ½EðCa=GNTÞ þ nEðH2 ÞEðnH2 þCa=GNTÞ=n
ð3Þ
where n indicates the number of the H2 molecules. E(Ca/GNT), E(H2) and E(nH2 þCa/GNT) are the energies of the Ca-decorated GNT, hydrogen molecules, and Ca-decorated GNT with adsorbed nH2 molecules, respectively. We first consider the system of a single Ca atom decorated on T2 site of the GNT2. After testing different H2 positions, it is found that the first H2 molecule is adsorbed in molecular form with the adsorption energy of 0.17 eV/H2 (LDA: 0.31 eV/H2). The H–H bond length is elongated slightly from 0.749 A˚ ˚ The average Ca–H of the isolated molecule to 0.764 A˚ (LDA: 0.795 A). distance is about 2.536 A˚ (LDA: 2.355 A˚ ). Through the PDOS analysis in Fig. 6, we can find that the peak of Ca 3d orbital around 5.83 eV hybridizes with the H2 s orbital. A similar hybridized interaction between H2 s states and Ca 3d orbitals also exists in H2 adsorbed on Ca-decorated carbon nanotubes and graphene [10,12]. From the different charge density inserted in Fig. 6, we can find that there is an induced dipole for the adsorbed hydrogen molecule, with electron density accumulation on the side close to the Ca and depletion on the side away from the Ca atom. As a result, two binding mechanisms contribute to the adsorption of H2, namely, the polarization of the H2 molecule under the electric field produced by the Ca/GNT dipole and the hybridization of the 3d orbitals of Ca with the s orbitals of H2. We add additional H2 molecules close to the Ca atom. The maximum number of adsorbed H2 per adsorbed Ca atom is six (LDA: five) for all the three GNTs studied here. The schematics of adsorption of H2 molecules on a single Ca atom decorated GNT2 and the average adsorption energies as a function of the number of adsorbed H2 molecules for different GNTs decorated with one Ca atom are plotted in Fig. 7. These values lie in the range of 0.11–0.17 eV/H2 calculated by using GGA and 0.25–0.33 eV/H2 by using LDA. Table 1 summarizes the average bond length of H–H ˚ (dH–H) (A), the average distance between Ca atom and H2 molecule dCa–H, and the average adsorption energy of the Cadecorated GNT2 with different numbers of H2 for both LDA and GGA methods. It is known that GGA tends to underestimate, whereas LDA tends to overestimate the adsorption energy.
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Fig. 4. (a) Schematic of the diffusion pathways of a Ca atom from T2 to T1. Variation in the total energy difference of a Ca atom moves along (b) T2-1-T1, (c) T2-2-T1. Atoms on the backside are not shown for visual clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. (a) Schematic of the diffusion pathways of a Ca atom from T2 to another nearest T2. Variation in the total energy difference of a Ca atom moves along (b) T2-1-T2, (c) T2-2-T2. Atoms on the backside are not shown for visual clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Thus the accurate adsorption energies should be probably in between the GGA and LDA values. It turns out that the H–H bond lengths of H2 molecules range from 0.757 to 0.764 A˚ (LDA: 0.783 to
˚ which are slightly stretched from the isolated H2 molecule. 0.795 A), As the number of adsorbed H2 molecules increases, the degree of the bond-length elongation of H2 molecules is slightly reduced while the
Y. S. Wang et al. / Journal of Solid State Chemistry 197 (2013) 323–328
average distance between H2 and the Ca atoms is increased. This is in accord with the fact that the average adsorption energies of H2 are slightly reduced, as the number of adsorbed H2 molecules increases. For different Ca-decorated GNTs, the average binding energies of H2 within GGA are all slightly reduced with increasing the number of adsorbed H2 molecules. This means that the binding energies of the H2 molecules are almost independent of the tube diameter. To evaluate the maximum hydrogen gravimetric density and the corresponding adsorption energy of Ca-decorated GNTs, we next only focus on fully Ca-decorated GNT2 where all the T2 sites are occupied by Ca atoms. After relaxation, all Ca atoms still bind separately on T2 sites without aggregation due to strong binding of Ca atoms and the GNT. The average binding energy is 1.87 eV/Ca (LDA: 2.63 eV/Ca). In order to probe the charge transfer from the Ca atoms to GNT, the charge density of 8Ca/GNT2 in the form of a 2D contour is plotted in Fig. 8(a). Furthermore, we calculated the difference of charge density of 8Ca/GNT2. The resulting isosurface is plotted in Fig. 8(b). It is readily seen that there is a significant charge accumulation around the C atoms near the Ca atoms. The substantial charge redistribution upon Ca decorating leads to a high electric field near the Ca atoms. Thus, the H2 molecules can be polarized and be adsorbed via the polarization mechanism. The clustering of adsorbed Ca atoms is hindered by the Coulomb
327
repulsion. Finally, we introduce H2 molecules onto the surface of the 8Ca/GNT2 system. Due to the steric hindrance of the H2 molecules, each Ca atom can adsorb up to four H2 molecules (LDA: five). It can be observed in Fig. 8 that H2 is adsorbed not only on Ca atoms, but also on T1 sites of the GNT. The distance between the GNT and the near hydrogen atom of H2 adsorbed on ˚ Therefore, 36H2 molecules (LDA: 44H2 T1 sites is about 2.10 A. molecules) can be adsorbed on 8Ca/GNT2 system. As shown in Fig. 8, with 32 hydrogen molecules binding to 8Ca atoms and 4 hydrogen molecules adsorbed on 4 T1 sites of GNT (LDA: 40H2 on 8Ca and 4H2 on 4 T1 sites), the Ca-decorated GNT gains a gravimetric density of H2 as high as 7.44 wt% (LDA: 8.96 wt%). The average adsorption energy of H2 is 0.13 eV/H2 (LDA: 0.33 eV/H2), which indicates that hydrogen storage can be achieved at near ambient conditions.
4. Conclusions In summary, we have studied the hydrogen storage properties of Ca-decorated GNT using density functional theory. Our calculations have indicated that Ca atom can bind strongly to the acetylenic ring (T2 site) of the GNT and the Coulomb repulsion between Ca adatoms can hinder metal clustering efficiently. In contrast, Ca atoms dispersed on fullerene or graphene are generally unstable, with its binding energy less than the Ca cluster cohesive energy. The polarization interaction and orbital hybridization between the H2 molecules and the Ca atoms lead to
Table 1 ˚ bond length between Ca and H2 molecule Average bond length of H–H (dH–H) (A), ˚ and the corresponding adsorption energy of H2 (Ead) (eV) for a single (dCa–H) (A), Ca atom decorated GNT2. GGA
Fig. 6. The PDOS of H2 molecule and the Ca atom in H2/Ca/GNT system. The Fermi level is set as zero. The isosurface of charge density difference with an isovalue of 0.001e/A˚ 3 for the system of H2/Ca/GNT is shown as an insert. Red and blue colors of the isosurface represent electron accumulation and depletion regions after H2 adsorption. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
1H2 2H2 3H2 4H2 5H2 6H2
LDA
dH–H
dCa–H
Ead
dH–H
dCa–H
Ead
0.764 0.762 0.760 0.758 0.757
2.536 2.579 2.604 2.673 2.675
0.17 0.16 0.15 0.14 0.12
0.795 0.789 0.782 0.784 0.782 0.783
2.355 2.405 2.401 2.438 2.527 2.513
0.31 0.29 0.27 0.28 0.25 0.25
Fig. 7. Schematics of adsorption of H2 molecules on a single Ca atom decorated GNT. The average adsorption energies as a function of the number of adsorbed H2 molecules for different Ca/GNT system are shown in the middle panel. Atoms on the back side are not shown for visual clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 8. (a) 2D contour of charge density of 8Ca/GNT2, (b) Charge density difference with an isovalue of 0.002 e/A˚ 3 for 8Ca/GNT2, (c) side view, and (d) top view of 44H2 molecules adsorbed on 8Ca/GNT2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
an average adsorption energy of 0.13 eV/H2 (LDA: 0.33 eV/H2) which falls within the ideal hydrogen storage binding range. The results also show that the adsorption energies of the H2 molecules are almost independent of the tube diameter. The storage capacity of H2 can reach 7.44 wt% (LDA: 8.96 wt%). This suggests that Ca decorated GNT can be used as a promising system for hydrogen storage.
Acknowledgements The work was support partly by the NSF of China (Grant Nos. 11274280, 10874154), partly by Innovation Scientists and Technicians Troop Construction Projects (ISTTCP) of Henan Province, and partly by Program for Science and Technology Innovation Talents in University (HASTIT) of Henan Province. The calculations were performed on the High Performance Clusters of Zhengzhou University. References [1] [2] [3] [4] [5]
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Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Calcium-decorated graphyne nanotubes as promising hydrogen storage media: A first-principles study Yu Sheng Wang a,b,n, Peng Fei Yuan a, Meng Li a, Wei Fen Jiang b, Qiang Sun a, Yu Jia a,n a b
Center of Clean Energy and Quantum Structures, and School of Physics and Engineering, Zhengzhou University, Zhengzhou, Henan 450052, China College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450011, China
a r t i c l e i n f o
abstract
Article history: Received 17 June 2012 Received in revised form 25 August 2012 Accepted 1 September 2012 Available online 12 September 2012
First principles calculations based on density functional theory are carried out to study the hydrogen storage properties of Ca-decorated graphyne nanotubes. The results show that Ca atoms can be adsorbed stably on the acetylenic ring of the graphyne nanotube (GNT) without Ca atom clustering. Both the polar interactions and the orbital hybridizations contribute to the adsorption of H2 molecules. The average adsorption energy is in the range of 0.13–0.33 eV/H2 which is almost independent of the tube diameter. Each Ca atom can adsorb up to four H2 molecules due to the steric hindrance of the H2 molecules. With a hydrogen uptake of 7.44–8.96 wt%, the Ca-decorated GNT is an optimal choice for hydrogen recycling at near ambient conditions. & 2012 Elsevier Inc. All rights reserved.
Keywords: Hydrogen storage Graphyne nanotube Nanostructure
1. Introduction The increasing need for clean and renewable energy has aroused growing research interest in hydrogen as a ‘‘green’’ energy carrier because of its abundance, pollution-free, and packing more energy per unit mass than any other fuel [1,2]. However, storing hydrogen efficiently and safely is still a major challenge to realize hydrogen economy. To perform hydrogen reversibly under ambient thermodynamic conditions for motor vehicles and other mechanical systems, the storage materials should store hydrogen with high gravimetric density and the binding energy of hydrogen molecules should lie between the physisorbed and the chemisorbed states ( 0.2 eV/H2) [3,4]. The U. S. Department of Energy (DOE) has set the gravimetric density of 9 wt% in 2015 for usable specific energy from H2. To achieve this goal, the storage materials should consist of only light elements. Instead of traditional storing modes such as compressed gas, liquefied hydrogen or metal hydride, it is suggested to store molecular hydrogen in metal-decorated carbon-based nanostructures owing to their light weights and large surface areas. Decorating atoms include alkaline metals (AM) [5–7], alkaline-earth metals (AEM) [8–10] and transition metals (TM) [11–13]. AM atoms decorated carbon nanostructures can give a high storage weight
n Corresponding authors at: Zhengzhou University, Center of Clean Energy and Quantum Structures, and School of Physics and Engineering, kexue road 100, Zhengzhou, Henan 450052, China. Fax: þ 86 371 67767758. E-mail addresses: [email protected] (Y.S. Wang), [email protected] (Y. Jia).
0022-4596/$ - see front matter & 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jssc.2012.09.004
percent, but the binding energy of AM metals to backbone nanostructures is usually small and the system can become unstable. It is well known that clustering is one of the major problems on the way to successful produce metal-decorated hydrogen storage nanomaterials [14]. Because of the large cohesive energy, TM atoms tend to form clusters on the surface of carbon nanostructures and consequently the hydrogen storage capacity drops dramatically after several cycles. The binding strength of Ca, the first AEM atom with empty 3d orbitals, to carbon-based nanostructures is between the too weak AMs and the too strong TMs. For this reason, Ca has recently emerged as an interesting element to improve the hydrogen storage in carbon-based materials and found that each Ca atom can adsorb several hydrogen molecules [15–19]. However, in the case of Ca-decorated carbon-based nanostructures, i.e., graphene, fullerene, nanotube, the binding energy of Ca is 1.14 [10], 1.3 [15] and 0.88 eV/Ca, [16], respectively. All these binding energies are less than the cohesive energy of bulk Ca. As a result, the Ca-cluster will form in practice which will lower the gravimetric density of H2. To solve this problem, we should find new backbone materials to increase the Ca binding energy beyond the Ca cohesive energy, thereby advancing the structural stability of the system without clustering. Graphyne, a carbon allotrope, which has the same symmetry as graphene and is obtained by replacing one third of the carbon–carbon bonds in graphene with acetylenic linkages [20] (see Fig. 1(a)), has been systematically studied due to promising electrical and optical properties [21–23]. With larger natural ‘‘holes’’ than graphene, graphyne can hold adatoms stably rather than metal aggregation. Li et al. suggest Ca decorated graphyne can adsorb 9.6 wt% of hydrogen molecules with an average binding energy of 0.2 eV/H2.
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The strong binding between Ca and s–p and s–p2 bonded graphyne is due to the additional in-plane p states which do not exist in graphene and fullerenes [24]. Here, instead of considering Ca-decorated graphyne, we focus on the case of individual Ca atoms dispersed on graphyne nanotubes (GNTs). Although the theoretically predicted GNT has not been synthesized, previous studies have shown that g-graphyne is the lowest-energy members of the graphyne family and the GNT formed by g-graphyne is the most likely to be synthesized [24,25]. Our study will concentrate on the hydrogen storage of this kind of GNT. Through first principles calculations, we show that the binding energy of Ca to GNT is much larger than the cohesive energy of bulk Ca leading to the prevention of metal clustering on the surface of GNT. The average adsorption energy of H2 is about 0.13–0.33 eV/H2, the hydrogen storage capacity can reach 7.44–8.96 wt% while the gravimetric density of H2 in the Ca-decorated B-doped carbon nanotubes is only 5–6 wt%. All the above results will place this system as one of the promising hydrogen storage materials.
2. Computational method All calculations are performed using a first-principles method based on density functional theory as implemented in the Vienna ab initio simulation package (VASP) [26]. Both generalized gradient approximation (GGA) [27] and local density approximation (LDA) [28] are used for exchange-correlation energy. For hydrogen binding, the GGA and LDA are known to provide a lower and an upper bound of a more accurate energy obtained with highly correlated methods such as MP2 or coupled-cluster with singles and doubles and perturbative triples correction [29,30]. A 450 eV cutoff energy is chosen for the plane-wave basis. Periodic boundary condition and vacuum space of 15 A˚ along x- and y-directions are applied in order to avoid interactions between two images of GNTs. The
Fig. 1. The optimized geometry of (a) graphyne, (b) GNT (4, 2).
Brillouin zone is sampled by 1 1 6 k-points within the Monkhorst–Pack scheme, where the convergence of total energy with respect to the number of k-points in Brillouin zone is carefully tested. Denser k-point meshes will affect the total energy within 0.002 eV. All the obtained structures are optimized without any symmetry constraints until the force on each atom is less than 10 2 eV/A˚ and the total energy changes are less than 10 4 eV.
3. Results and discussion The geometry structure of the graphyne is given in Fig. 1(a). The calculated bond lengths for C(sp2)–C(sp2), C(sp2)–C(sp), and ˚ respectively, which C(sp)–C(sp) are 1.425, 1.406, and 1.221 A, are in good agreement with previously reported results [21,25]. In this study, we consider zigzag GNTs that are rolled up from corresponding graphyne layers. To find the effect of the size of the GNTs on the hydrogen storage, we investigate three zigzag GNTs with different diameters labeled by (2, 1), (4, 2) and (6, 3), respectively. For simplicity, here we denote these GNTs as GNT1, GNT2 (see Fig. 1), and GNT3, respectively. Our discussions begin with the binding of a single Ca atom on the GNTs. There are five different adsorption sites as shown in Fig. 2(a), which are the hollow center of the hexagon (T1), the hollow center of the acetylenic ring (T2), and three different bridge sites of C–C (namely B1, B2, and B3, respectively). After varying the position of the Ca atom and relaxing all structures, we find that the T2 site is energetically favorable compared to other sites. The bridge sites are unstable adsorption sites, after full relaxation, the Ca atom will move to the most stable adsorption site (T2). To check the stability of our model, the binding energy between Ca and GNT is defined as Eb ¼ ½EðGNTÞ þnEðCaÞEðGNT þnCaÞ=n
ð1Þ
where E(GNT), E(Ca), and E(GNTþnCa) are the energy of the pristine GNT, the energy of a free Ca atom, and the total energy of the GNT with n adsorbed Ca atoms, respectively. The calculated binding energies of Ca adsorbed on T2 sites are much larger than that in Ca bulk (1.84 eV per Ca atom) for all the GNTs presented here, indicating that Ca atoms will be adsorbed stably on the T2 sites. The Eb of Ca adsorbed on T1 site are 1.92, 1.27, and 1.24 eV (LDA: 2.34, 1.90, and 1.92) for GNT1, GNT2 and GNT3, respectively, which are less than that of adsorbed on T2 site: 3.03, 2.39, and 2.32 eV (LDA: 3.69, 3.14, and 3.07 eV). We also find that the binding energy of Ca to GNT decreases as the tube diameter increases and converges to that of the corresponding Cadecorated graphyne. This is due to the reduction in the curvatures of the GNTs. Since previous studies have revealed that metal
Fig. 2. (a) Isolated and (b) clustered configurations of the 6Ca/GNT2 complex. The relative energy DE is evaluated referring to configuration (a). The five possible adsorption sites are shown in (a) where C (sp2) and C (sp) are denoted by CA and CB. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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atoms attached on some host materials can easy to form clusters as the number of metal atoms increases, one may wonder whether the attached Ca atoms reported here would like to aggregate together. As a prototype system we here test the total energy of six Ca atoms adsorbed on GNT2. As shown in Fig. 2, the configuration that Ca atoms form a cluster is 4.58 eV higher in energy than when they disperse evenly on T2 sites. It is worth noting that in the case of Ca atoms adsorbed on T2 sites the Ca–Ca ˚ Consequently, higher distances turn out to be larger than 4.40 A. Eb and larger Ca–Ca distance make Ca atoms adsorbed stably on T2 sites without clustering. To understand the nature of binding properties between the Ca and the GNT, we also calculate the charge transfer between metal Ca and GNT as the positive Ca ion is expected to polarize and bind the H2 molecules. The difference of charge density is calculated by using the following formula:
Dr ¼ rðGNT þCaÞrðGNTÞrðCaÞ
ð2Þ
where r(GNTþCa), r(GNT), r(Ca)are the charge density of the system of a Ca/GNT, the charge density of pristine GNT, and the charge density of a Ca atom, respectively. The three-dimensional charge density difference for a Ca/GNT is shown in Fig. 3 as an insert. The red and blue iso-surface indicates positive and negative charge density corresponding to electron accumulation and depletion, respectively. It is readily seen that charges are transferred from Ca to the GNT, and transferred charge is mainly located on the acetylenic ring just below the Ca atom. It is useful to make a Bader charge analysis to determine the charges on the Ca atom [31]. The Bader charge analysis shows that the Ca atom donates 1.77e to the GNT. To further understand the charge transfer and the nature of the binding, we plotted the partial density of states (PDOS) of GNT and Ca/GNT in Fig. 3. For the pristine GNT, the states near valence band maximum and conduction band minimum come from the pz of both CA and CB atoms (see Fig. 3(a) and (b)). For the CA atoms, two additional highly localized bonding px þpz states can be seen around 2.5 eV below
Fig. 3. (a) The PDOS of CA in pristine GNT, (b) The PDOS of CB in pristine GNT, (c) The PDOS of CA in Ca/GNT, (d) The PDOS of CB near Ca atom in Ca/GNT, (e) The PDOS of Ca atom in Ca/GNT. The Fermi level is set as zero. The isosurface of charge density difference with an isovalue of 0.0033e/A˚ 3 for Ca/GNT is shown as an insert. The red and blue iso-surface indicates space charge accumulation and depletion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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the Fermi energy. This bonding mechanism is similar to the previous studies about graphyne [24]. In the case of Ca/GNT, the hybridization of C 2p orbital and Ca 3d orbital is observed at the Fermi level and in the region between 5 and 2.5 eV. For the CA atoms, px, py and pz states all contribute to the bonding. For the CB atoms, px and pz states at the Fermi level and all three p orbitals between 5 and 2.5 eV participate in the hybridization. The bond between Ca and GNT leads to the s electrons of Ca transfer to GNT forming a Ca ion as shown in Fig. 3(d). GNT then back-donates some charges to the low-lying Ca 3d orbital that hybridize with GNT 2p orbitals between 5 and 2.5 eV. This bonding mechanism can also be observed in the case of Ca binding onto graphene and carbyne networks [10,18]. To further check the stability of the Ca decorated GNT system, we also calculate the migration energies of Ca on the surface of the GNT2. In the case of Ca atom diffusion from T2 to T1, we select two diffusion paths: (a) T2-1-T1; (b) T2-2-T1 as shown in Fig. 4. The corresponding diffusion barriers are 1.70 and 2.20 eV, respectively. In the case of Ca atom diffusion from T2 to another nearest T2, we also consider two diffusion paths: (a) T2-1-T2; (b) T2-2-T2 as depicted in Fig. 5. The diffusion barriers are 1.97 and 2.19 eV, respectively. Such high diffusion barriers indicate that the Ca atoms would rather disperse evenly on the surface of GNTs than form metal clusters. On the basis of the above investigation of the stability of Cadecorated GNT, in the following, we now turn to the discussion on the adsorption of hydrogen molecules on this complex. The average adsorption energy Ead per H2 to the system is defined as the following term: Ead ¼ ½EðCa=GNTÞ þ nEðH2 ÞEðnH2 þCa=GNTÞ=n
ð3Þ
where n indicates the number of the H2 molecules. E(Ca/GNT), E(H2) and E(nH2 þCa/GNT) are the energies of the Ca-decorated GNT, hydrogen molecules, and Ca-decorated GNT with adsorbed nH2 molecules, respectively. We first consider the system of a single Ca atom decorated on T2 site of the GNT2. After testing different H2 positions, it is found that the first H2 molecule is adsorbed in molecular form with the adsorption energy of 0.17 eV/H2 (LDA: 0.31 eV/H2). The H–H bond length is elongated slightly from 0.749 A˚ ˚ The average Ca–H of the isolated molecule to 0.764 A˚ (LDA: 0.795 A). distance is about 2.536 A˚ (LDA: 2.355 A˚ ). Through the PDOS analysis in Fig. 6, we can find that the peak of Ca 3d orbital around 5.83 eV hybridizes with the H2 s orbital. A similar hybridized interaction between H2 s states and Ca 3d orbitals also exists in H2 adsorbed on Ca-decorated carbon nanotubes and graphene [10,12]. From the different charge density inserted in Fig. 6, we can find that there is an induced dipole for the adsorbed hydrogen molecule, with electron density accumulation on the side close to the Ca and depletion on the side away from the Ca atom. As a result, two binding mechanisms contribute to the adsorption of H2, namely, the polarization of the H2 molecule under the electric field produced by the Ca/GNT dipole and the hybridization of the 3d orbitals of Ca with the s orbitals of H2. We add additional H2 molecules close to the Ca atom. The maximum number of adsorbed H2 per adsorbed Ca atom is six (LDA: five) for all the three GNTs studied here. The schematics of adsorption of H2 molecules on a single Ca atom decorated GNT2 and the average adsorption energies as a function of the number of adsorbed H2 molecules for different GNTs decorated with one Ca atom are plotted in Fig. 7. These values lie in the range of 0.11–0.17 eV/H2 calculated by using GGA and 0.25–0.33 eV/H2 by using LDA. Table 1 summarizes the average bond length of H–H ˚ (dH–H) (A), the average distance between Ca atom and H2 molecule dCa–H, and the average adsorption energy of the Cadecorated GNT2 with different numbers of H2 for both LDA and GGA methods. It is known that GGA tends to underestimate, whereas LDA tends to overestimate the adsorption energy.
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Fig. 4. (a) Schematic of the diffusion pathways of a Ca atom from T2 to T1. Variation in the total energy difference of a Ca atom moves along (b) T2-1-T1, (c) T2-2-T1. Atoms on the backside are not shown for visual clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. (a) Schematic of the diffusion pathways of a Ca atom from T2 to another nearest T2. Variation in the total energy difference of a Ca atom moves along (b) T2-1-T2, (c) T2-2-T2. Atoms on the backside are not shown for visual clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Thus the accurate adsorption energies should be probably in between the GGA and LDA values. It turns out that the H–H bond lengths of H2 molecules range from 0.757 to 0.764 A˚ (LDA: 0.783 to
˚ which are slightly stretched from the isolated H2 molecule. 0.795 A), As the number of adsorbed H2 molecules increases, the degree of the bond-length elongation of H2 molecules is slightly reduced while the
Y. S. Wang et al. / Journal of Solid State Chemistry 197 (2013) 323–328
average distance between H2 and the Ca atoms is increased. This is in accord with the fact that the average adsorption energies of H2 are slightly reduced, as the number of adsorbed H2 molecules increases. For different Ca-decorated GNTs, the average binding energies of H2 within GGA are all slightly reduced with increasing the number of adsorbed H2 molecules. This means that the binding energies of the H2 molecules are almost independent of the tube diameter. To evaluate the maximum hydrogen gravimetric density and the corresponding adsorption energy of Ca-decorated GNTs, we next only focus on fully Ca-decorated GNT2 where all the T2 sites are occupied by Ca atoms. After relaxation, all Ca atoms still bind separately on T2 sites without aggregation due to strong binding of Ca atoms and the GNT. The average binding energy is 1.87 eV/Ca (LDA: 2.63 eV/Ca). In order to probe the charge transfer from the Ca atoms to GNT, the charge density of 8Ca/GNT2 in the form of a 2D contour is plotted in Fig. 8(a). Furthermore, we calculated the difference of charge density of 8Ca/GNT2. The resulting isosurface is plotted in Fig. 8(b). It is readily seen that there is a significant charge accumulation around the C atoms near the Ca atoms. The substantial charge redistribution upon Ca decorating leads to a high electric field near the Ca atoms. Thus, the H2 molecules can be polarized and be adsorbed via the polarization mechanism. The clustering of adsorbed Ca atoms is hindered by the Coulomb
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repulsion. Finally, we introduce H2 molecules onto the surface of the 8Ca/GNT2 system. Due to the steric hindrance of the H2 molecules, each Ca atom can adsorb up to four H2 molecules (LDA: five). It can be observed in Fig. 8 that H2 is adsorbed not only on Ca atoms, but also on T1 sites of the GNT. The distance between the GNT and the near hydrogen atom of H2 adsorbed on ˚ Therefore, 36H2 molecules (LDA: 44H2 T1 sites is about 2.10 A. molecules) can be adsorbed on 8Ca/GNT2 system. As shown in Fig. 8, with 32 hydrogen molecules binding to 8Ca atoms and 4 hydrogen molecules adsorbed on 4 T1 sites of GNT (LDA: 40H2 on 8Ca and 4H2 on 4 T1 sites), the Ca-decorated GNT gains a gravimetric density of H2 as high as 7.44 wt% (LDA: 8.96 wt%). The average adsorption energy of H2 is 0.13 eV/H2 (LDA: 0.33 eV/H2), which indicates that hydrogen storage can be achieved at near ambient conditions.
4. Conclusions In summary, we have studied the hydrogen storage properties of Ca-decorated GNT using density functional theory. Our calculations have indicated that Ca atom can bind strongly to the acetylenic ring (T2 site) of the GNT and the Coulomb repulsion between Ca adatoms can hinder metal clustering efficiently. In contrast, Ca atoms dispersed on fullerene or graphene are generally unstable, with its binding energy less than the Ca cluster cohesive energy. The polarization interaction and orbital hybridization between the H2 molecules and the Ca atoms lead to
Table 1 ˚ bond length between Ca and H2 molecule Average bond length of H–H (dH–H) (A), ˚ and the corresponding adsorption energy of H2 (Ead) (eV) for a single (dCa–H) (A), Ca atom decorated GNT2. GGA
Fig. 6. The PDOS of H2 molecule and the Ca atom in H2/Ca/GNT system. The Fermi level is set as zero. The isosurface of charge density difference with an isovalue of 0.001e/A˚ 3 for the system of H2/Ca/GNT is shown as an insert. Red and blue colors of the isosurface represent electron accumulation and depletion regions after H2 adsorption. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
1H2 2H2 3H2 4H2 5H2 6H2
LDA
dH–H
dCa–H
Ead
dH–H
dCa–H
Ead
0.764 0.762 0.760 0.758 0.757
2.536 2.579 2.604 2.673 2.675
0.17 0.16 0.15 0.14 0.12
0.795 0.789 0.782 0.784 0.782 0.783
2.355 2.405 2.401 2.438 2.527 2.513
0.31 0.29 0.27 0.28 0.25 0.25
Fig. 7. Schematics of adsorption of H2 molecules on a single Ca atom decorated GNT. The average adsorption energies as a function of the number of adsorbed H2 molecules for different Ca/GNT system are shown in the middle panel. Atoms on the back side are not shown for visual clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 8. (a) 2D contour of charge density of 8Ca/GNT2, (b) Charge density difference with an isovalue of 0.002 e/A˚ 3 for 8Ca/GNT2, (c) side view, and (d) top view of 44H2 molecules adsorbed on 8Ca/GNT2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
an average adsorption energy of 0.13 eV/H2 (LDA: 0.33 eV/H2) which falls within the ideal hydrogen storage binding range. The results also show that the adsorption energies of the H2 molecules are almost independent of the tube diameter. The storage capacity of H2 can reach 7.44 wt% (LDA: 8.96 wt%). This suggests that Ca decorated GNT can be used as a promising system for hydrogen storage.
Acknowledgements The work was support partly by the NSF of China (Grant Nos. 11274280, 10874154), partly by Innovation Scientists and Technicians Troop Construction Projects (ISTTCP) of Henan Province, and partly by Program for Science and Technology Innovation Talents in University (HASTIT) of Henan Province. The calculations were performed on the High Performance Clusters of Zhengzhou University. References [1] [2] [3] [4] [5]
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