A Ti-decorated boron monolayer: a promising material for hydrogen storage

Abstract

A promising Ti-decorated boron monolayer (BM) system for hydrogen storage is proposed through the use of density functional theory. We find that the Ti decoration on the BM system is more stable, and the charge transfer between atoms will result in a more active system. The thermodynamic analysis showed that the doped Ti atoms reduced the thermodynamic stability of the BM sheets, but are suitable for a hydrogen storage system. One Ti atom-decorated BM can adsorb up to 5 H₂ molecules, and the orbital interaction is mainly due to H 1s, Ti 3d and B1 2p orbital hybridization. The LST/QST calculation shows that cluster formation can be excluded due to the high energy barrier. Therefore, 16 Ti atoms can be decorated on the double faces of the H1_t positions and the corresponding capacity of the system for H₂ storage is calculated to be approximately 10.44 wt%. Our results suggest that the Ti-BM will be a promising material system for hydrogen storage.

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1. Introduction

Hydrogen has been recognized as an attractive energy carrier, as it provides a renewable and clean energy source, and is abundant in nature. However, the application of H₂ is still limited due to the great challenges of transportation and efficiency of storage. Hydrogen storage in solid-state materials has been attracting widespread interest. For the past decade, metal or chemical hydride materials have been considered as hydrogen storage media. However, these materials have common shortcomings, like slow kinetics and poor reversibility.^1,2 Recently, carbon-based materials have been explored as a hydrogen storage medium because of the possibility of good reversibility, fast kinetics, and a high capacity (large surface area).^3–5 However, the storage capacity in these materials is significantly decreased at room temperature and ambient pressure,^6,7 because the binding energy of H₂ is low and because of the possible clustering problem of the decorated materials.

Boron is the nearest neighbor to carbon at the left of the periodic table. Carbon’s natural ground state structure is graphite, and its monolayer is the well-known graphene. However, boron tends to form networks of icosahedral clusters, not planar sheets. Recently, Sohrab Ismail-Beigi et al.⁸ performed theoretical calculations on a new class of two-dimensional boron sheets and found a sheet that is lower in energy than any structures previously considered. Xiaojun Wu et al.⁹ have reported that the β₁ boron monolayer (BM) is the most stable structure of all the heterostructures, and speculated that BM sheets may find applications such as specialized electrodes in batteries or as lithium storage components. Inspired by their work, BMs may be promising hydrogen storage media due to their low weight and large specific surface area. Of note, the BM possesses a typically porous structure, which can provide a patterned decorating/doping structure that can greatly enhance the capacity for hydrogen storage.

The light transition-metal atoms, such as Sc, Ti, and Co, are widely applied to be decorated on various kinds of hydrogen storage materials. Previous experimental¹⁰ and theoretical¹¹ results show that Ti atoms decorated on carbon nanotubes can improve their hydrogen storage capacity. The decoration of Ti on a SiC monolayer can lead to a 5.0 wt% H₂ storage capacity.¹² Ti-decorated boron–carbon–nitride monolayers and graphene can even store up to 7.6 wt% and 7.8 wt% in the H₂ molecular form, respectively.^13,14 Inspired by previous reports, we hypothesised that Ti-decorated BMs may lead to a high hydrogen capacity. Therefore, further investigations about hydrogen storage with Ti decorated β₁ BMs are desirable.

In this paper, we carry out a study on the hydrogen storage properties of a Ti-decorated BM (Ti/BM) using density functional theory. The interaction of both Ti decorated on a BM and H₂ adsorbed onto a Ti/BM were analyzed using computing charge population, projected electronic density of states, and electron density distribution. The Ti clustering problem was investigated by calculating the diffusion energy barriers at the transition state of Ti decorated atoms on the diffusion pathway. We concluded that the Ti-decorated BM will be a promising material for hydrogen storage applications.

2. Computational details

The DFT calculations were performed using the DMOL3 code.¹⁵ The generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) function was employed as the exchange–correlation function.¹⁶ A double numerical plus polarization basis set (DNP) was employed to expand the Kohn–Sham electronic eigen states with an orbital cutoff radius of 4.4 Å. The energy convergence tolerance was taken to be 2 × 10⁻⁵ Ha (1 Ha = 27.21 eV) with the allowed maximum force of 0.002 Ha/Å and displacement of 0.005 Å. The reciprocal space was represented via a Monkhorst–Pack special k-point scheme with 6 × 6 × 1 k-points for structural optimization and electronic structure calculations. We considered a boron monolayer with the vacuum width of 30 Å as a computational model system. The H₂ molecule was optimized in a large periodic cubic box with a cell parameter of 10 × 10 × 10 ų with a H–H bond length of ∼0.75 Å.

To investigate the possible clustering problem of Ti atoms on the BM, we performed the linear synchronous transition/quadratic synchronous transit (LST/QST)¹⁷ calculation in the DMOL3 code. Those methodologies have been demonstrated as useful tools to search for the structure of the transition state (TS) and the minimum energy pathway. The diffusion energy barrier of the Ti atom was defined as the difference between the energy at the TS and that at the initial state (before diffusion to the neighboring sites) of the Ti/BM system.

In order to evaluate the possibility of cluster formation and the stability of the BM sheet after Ti doping, thermodynamic calculations were performed. The thermodynamic parameters, including the enthalpy H, Gibbs free energy G, entropy S and heat capacity C_p were calculated at constant pressure. The calculation formula is shown below:^18,19

E(T) = E_vib(T) + E_rot(T) + E_tra(T) + RT (1)

where the subscripts stand for vibration, rotational, and translational contributions, respectively, and R is the ideal gas constant. For the enthalpy correction H, the contributions are given by:

H_rot(linear) = RT (3)

For entropy S, the contributions are given by:

As for the heat capacity C_p, the contributions are given by:

C_rot(linear) = R (11)

In the above formulas, k is Boltzmann’s constant, h is Planck’s constant, v_i is the individual vibrational frequencies, w is the molecular weight, I_x is the moment of inertia about axis x, and σ is the symmetry number.

3. Results and discussion

3.1 Decoration of Ti atoms on a boron monolayer

When we considered the possible decoration sites of the Ti atom on a BM, there are five different sites: the top of the hexagonal rings (H1_t), the top of the B1 atoms (B1_t), the top of the B2 atoms (B2_t), the top of the bridge sites between the B1 atoms (B_r1) and the top of the bridge sites between the B1 and B2 atoms (B_r2), as shown in Fig. 1. There are two kinds of B atoms: the first kind are the B atoms in the hexagonal rings (B1), which are surrounded by 5 neighboring B atoms; the second kind are the B atoms surrounded by six neighboring B atoms (B2). The adsorption energy of the Ti atom adsorbed on H1_t, B1_t, B2_t, B_r1 and B_r2 sites was calculated to be −4.37, −4.15, −4.13, −4.03 and −3.98 eV, respectively. Thus, the Ti atom prefers to reside over the H1_t position, which is the most stable position.

Fig. 1 (a) The side view of the BM: the triangular N pore (H1_t), the hexagonal rings (H2_t), the top of N1 (N1_t), the top of N2 (N2_t), and the top of C (C_t). (b) The top view of the BM and possible Ti decorating sites: the top of hexagonal rings (H1_t), the top of B1 atoms (B1_t), the top of B2 atoms (B2_t), the top of bridge sites between B1 atoms (B_r1) and the top of bridge sites between B1 and B2 atoms (B_r2). The green and pink spheres denote B1 and B2 atoms, respectively.

After finding the stable decoration site of the Ti atom, we investigated the charge transfer between Ti and B atoms by calculating the charge population, as shown in Table 1. To be noted is that the charge population of the system represents the charge transfer between atoms. The values of charge in the pristine BM are −0.05 and 0.16|e| for the B1 and B2 atoms, respectively. Ti decoration on the BM leads to a significant modification of the charge populations of the B atoms on the monolayer. The negative charge on every B1 atom around the Ti atom increased to be −0.01|e|, while the B2 atom charge increased to be 0.28|e|. The charge on the Ti atom was 0.54|e| after Ti decoration. As a result, the atoms in the Ti/BM system became more active. Moreover, the positive charge accumulation around the Ti atoms induced an electrostatic field, which probably enhanced the adsorption ability of the H₂ molecules.

Table 1 The Mulliken charge population of the layer in the (H₂)_n/Ti/BM system, where the unit of the atom charge is one electron charge |e|, n is the number of the adsorbed H₂

Atom	BM	n = 0	n = 1	n = 2	n = 3	n = 4	n = 5
Ti	—	0.54	0.37	0.30	0.06	−0.34	−0.39
B1	−0.05	−0.01	−0.06	−0.05	−0.01	0.03	0.03
B2	0.16	0.28	0.03	0.03	0.07	0.14	0.15

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Fig. 2 shows the thermodynamic properties of the pristine BM sheet and Ti-doped BM. In all cases, S, C_p and H increased gradually with the temperature increase, while G decreased with the temperature increase. At the same time, the thermodynamic properties were also affected greatly by the Ti doping concentration. The S, C_p and H increased quickly with the increase of the Ti doping concentration, while the G value decreased slowly with the increased Ti doping amount. This result indicates that the doped Ti atom can weaken the thermodynamic stability of boron monolayer sheet. The higher the Ti doping concentration, the more unstable the BM. However, the Ti doped BM system is stable as the G is positive below 600 K. Therefore, the Ti doped BM is stable and can be applied for hydrogen storage.

Fig. 2 Calculated thermodynamic properties of the pristine BM and Ti/BM material: (a) enthalpy H, (b) heat capacity C_p, (c) entropy S and (d) Gibbs free energy G.

3.2 H₂ adsorption and desorption on Ti-decorated BM

Firstly, we investigated single H₂ adsorption and interaction with the Ti/BM. The adsorption sites of H₂ on the Ti/BM were considered. As the H₂ adsorption originates due to the electrostatic field around the Ti atom, H₂ was mainly adsorbed around the top of the Ti. The calculated adsorption energy of the H₂ adsorbed around the Ti atom is similar (around −0.47 eV/H₂). After H₂ adsorption, the adsorption energy range is −0.47 eV/H₂, and the H–H bond length is 0.81 Å, as tabulated in Table 2. Of note is that the bond length of the adsorbed H₂ increases to 0.82 Å compared with the original bond length of 0.75 Å. This phenomenon can be explained by the following process. As the electric field exists around the positive charged Ti, H₂ is polarized and approaches Ti. H₂ interacts with Ti to accept some positive charge from the Ti/BM. Then, the additional positive charge in H₂ will enhance the repulsion interaction between the positive charges. Consequently, the H₂ bond is elongated.

Table 2 The adsorption energy (E_a), bond length (r_H–H), and Mulliken charge population of H₂ for more than one H₂ molecule adsorbed on the Ti/BM system, where the unit of the atom charge is one electron charge |e|

Model	Ti	1^st H2	2^nd H2	3^rd H2	4^th H2	5^th H2	Ea (eV/H2)	rH–H (Å)
Ti/BM	0.54
H2/Ti/BM	0.37	0.06					−0.47	0.81
(H2)2/Ti/BM	0.30	0.07	0.05				−0.36	0.82
(H2)3/Ti/BM	0.06	0.10	0.07	0.08			−0.26	0.80
(H2)4/Ti/BM	−0.34	0.12	0.12	0.10	0.09		−0.21	0.80
(H2)5/Ti/BM	−0.39	0.13	0.13	0.11	0.11	−0.02	−0.20	0.79

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The interaction between atoms can also be intuitively verified by analysis of the electron density distribution. Fig. 3 illustrates the electron density distribution of the Ti/BM systems before and after H₂ adsorption. The blue regions represent electron deletion, while the red regions represent electron enrichment. The white regions mean that the electron density does not change obviously. Before H₂ adsorption, the electrons mainly exist in the regions between the B and Ti atoms, as shown in Fig. 3(a). After H₂ adsorption, some electron distribution was found in the regions between the H and Ti atoms (Fig. 3(b)), indicating that the adsorption of H₂ on the Ti/BM was a weak chemisorption. It was worthwhile to note that the interaction between the H₂ and Ti/BM mainly took place between the H₂ and Ti atoms. The adsorbed H₂ molecules tended to tilt toward the Ti atoms because of charge redistribution.

Fig. 3 Illustrations of electron density distribution for (a) Ti/BM and (b) H₂/Ti/BM systems. The (a′) and (b′) are the corresponding top views. The red, gray and green spheres denote Ti, C, and N atoms, respectively. The green and gray spheres denote B and Ti atoms, and the yellow spheres are the nearest B atoms beside Ti.

To investigate the orbital interaction between the H₂ molecules and Ti/BM, we analyzed the projected electronic density of state (PDOS) of the H₂-adsorbed Ti/BM system. Fig. 4 displays the PDOSs of the H, Ti and B atoms before and after H₂ adsorption on the Ti/BM. Before H₂ adsorption, there is a hybridization area in the PDOS among the Ti 3d, B1 2p, and B2 2p orbitals at a range of −1.60 and 2.60 eV (dotted lines in Fig. 4(a)). After the H₂ is adsorbed on the Ti/BM, there are two new peaks of Ti 3d at 0.20 eV and −9.01 eV, which is due to the hybridization between the Ti 3d and H 1s, as shown in Fig. 4(b). At the same time, there is a resonance between the H and Ti, B1 and B2 atoms at −9.01 eV. Those results suggest that Ti interacts with both H₂ and BM, and plays an important role for hydrogen storage. After electrostatic adsorption of H₂, a charge transfer between atoms and orbital hybridization take place and forms a more stable adsorption system. Therefore, H₂ adsorption on the Ti/BM is suggestive of a weak chemisorption, which is consistent with the results deduced from the adsorption energy analysis.

Fig. 4 The PDOS of the Ti/BM (a) before and (b) after H₂ adsorption. The Fermi energy is set to be 0 eV.

Next, we investigated how many H₂ molecules can be adsorbed on one Ti decorated BM. We constructed an adsorption configuration with more than a single H₂ molecule adsorbed on the different positions. Table 2 tabulates the adsorption energies (E_a) and charge population of H₂ with different molecule adsorption numbers. As the number of the adsorbed H₂ molecules increased, E_a changed in the range from −0.20 to −0.47 eV/H₂. It is known that the ideal E_a between the host material and adsorbed H₂ molecules should be an intermediate between physisorption and chemisorption energy (week chemisorption), ranging from −0.20 to −0.80 eV.²⁰ It was noted that a single Ti atom decorated on the BM can adsorb up to 5 H₂ molecules with an adsorption energy of −0.20 eV/H₂, which is in the range of the ideal adsorption energy levels. The bond length of the fifth H₂ is 0.79 Å and the charge on the molecule is −0.02|e|, which means that the fifth H₂ is polarized and adsorbed around Ti. At the same time, the charge on the fifth H₂ changed from positive to negative, indicating that electron back-donation occurred. H₂ molecules are distributed almost symmetrically around the Ti atoms. Similar phenomena were observed on graphene decorated with rare earth elements (Y, Eu).^21,22 The sixth H₂ escaped without forming a bond with Ti which could be explained as the interaction between H₂ would weaken the adsorption and the electron back-donation would decrease the Coulomb force between the Ti and H atoms. Therefore, the saturated number of H₂ adsorption is 5.

After thoroughly understanding the adsorption behavior of H₂ on one Ti atom decorated BM, we turned to adjusting the number of decorated Ti atoms to evaluate the maximum hydrogen storage ability of this system. The possible clustering problem of metal atoms adsorbed on supports (such as graphene, silylene) is a typical bottleneck for many proposed hydrogen storage materials. Thus, we carefully computed the energy barrier for Ti diffusion on the BM. Firstly, we consider one Ti atom migrating from a H1_t position to its nearest neighboring one. The atomic structures of the initial state (IS), the transition state (TS) and the final state (FS) during Ti atom migration are shown in Fig. 5(a). We can calculate the diffusion energy barrier, E_bar = E_TS − E_IS, where E_TS and E_IS are the energies of the TS and the IS, respectively. Regarding TS, after the bonds between Ti and the surrounding B atoms are broken, Ti atom can diffuse and reach to the top of the B_r1 (TS site) between two H1_t sites. Eventually, Ti can diffuse to the neighboring H1_t site, and then forms bonds with the B atoms on that site. The energy barrier, E_bar, of Ti for diffusing from the H1_t to its neighboring one on the BM is calculated to be 1.40 eV. Noting that, the distance between two Ti atoms in the nearest H1_t site is 2.58 Å, which is smaller than the distance between the Ti atoms in the Ti metal phase (∼2.80 Å). Therefore, a Ti dimer formed between the two nearest neighboring Ti atoms. But, the structure will be more stable as the adsorption energy and energy barrier are doubled due to the special dimer structure. On the other hand, we consider one Ti atom migrating from the H1_t position to its secondary nearest neighboring H1_t position, as shown in Fig. 5(b). The E_bar of Ti for diffusing from H1_t to its neighboring one on the BM is calculated to be 2.75 eV, indicating that the migration in this pathway is very difficult. Therefore, it is difficult to form a cluster on pristine BM. 16 Ti atoms can be decorated on the double faces of H1_t positions in the β₁ BM with a value of η = 1/8, as shown in Fig. 6(a). η is the global density parameter, which is defined as the ratio of the number of hexagon holes to the number of atomic sites in the pristine triangular sheet within a unit cell of the decorated boron sheet.⁹ In this particular geometry, ten H₂ molecules can be adsorbed around every Ti dimer, as shown in Fig. 6(b). Eventually, 80 H₂ molecules could be adsorbed on the 1/8-boron monolayer system and the corresponding capacity of the system for H₂ storage is calculated to be about 10.44 wt%. Jiling Li et al.²³ have reported Li decorated BM for reversible hydrogen storage, corresponding to a hydrogen uptake of 15.26 wt%. Comparing with their work, we also choose the most stable boron monolayer (1/8-boron monolayer) and meet the hydrogen storage capacity target of DOE (9.0 wt%). However, there are many differences between our works. In their report, the binding energy of Li on the BM is 2.18 eV/Li, which is a little higher than the cohesive energy of bulk Li (1.63 eV/Li). In our work, the adsorption energy of one Ti decorated on the BM is −4.37 eV. Of note, a Ti dimer formed between the two nearest neighboring Ti atoms, which means that the adsorption energy is double. The Ti decorated BM system is more stable than the Li decorated BM. On the other hand, one Li decorated BM can adsorb 4 H₂ molecules, while 5 H₂ molecules can adsorb around each Ti atom. The positive charge on Li is less than 0.10|e|, while the charge on Ti decreased from 0.54 to −0.39|e|. The hydrogen adsorption ability of each Ti is obviously higher than the Li case.

Fig. 5 Diffusion energy barrier as a function of diffusion coordinate and detailed diffusion pathway of the Ti atom on the BM, where IS, TS, and FS are the structure of the initial state, transition state, and the final state, respectively. (a) For the single Ti atom, a single Ti atom migrates from the H_1t position to its nearest neighboring one (b) One Ti atom migrating from the H1_t position to its secondary nearest neighboring H1_t position. The green and gray spheres denote B and Ti atoms, respectively.

Fig. 6 The relaxed adsorption of H₂ molecules on the Ti/BM. (a) Side view of the BM structure possibly adsorbing up to 18 Ti atoms on both faces. (b) Ti/BM structure adsorbing up to 80 H₂ on the double face, respectively. (a′) and (b′) are the top views corresponding to (a) and (b), respectively. The green, gray and white spheres denote B, Ti and H atoms, respectively.

4. Conclusions

In conclusion, the adsorption behavior of H₂ molecules on the Ti/BM system was studied using density functional theory. We find that the Ti decoration on the BM system to be stable with an adsorption energy of −4.37 eV. The thermodynamic analysis showed that the doped Ti atoms reduced the thermodynamic stability of the BM sheets, but the Ti doped BM system is suitable as a hydrogen storage system. The charges transfer between atoms, which make the atoms in the Ti/BM system become more active. One Ti atom-decorated BM can adsorb up to 5 H₂ molecules with the adsorption energies from −0.20 to −0.47 eV/H₂. The orbital interaction exists mainly between H₂, Ti, and B1, which is mainly due to H 1s, Ti 3d and B1 2p orbital hybridization. Then, the possible clustering problems were investigated with a LST/QST calculation. The energy barrier of one Ti atom migrating from the H1_t position to its nearest neighboring H1_t position is 1.40 eV. However, a Ti dimer formed between the two nearest neighboring Ti atoms, and the adsorption energy and diffusion energy barrier are doubled due to the special dimer structure. The energy barrier of one Ti atom migrating from the H1_t position to its secondary nearest neighboring H1_t position is 2.75 eV. The cluster formation can be excluded due to the high energy barrier. Therefore, 16 Ti atoms can be decorated on the double faces of the H1_t positions and the corresponding capacity of the system for H₂ storage is calculated to be about 10.44 wt%. We can conclude that the Ti-decorated BM exhibits better stability, dispersity, and chemical reactivity compared with other 2-dimensional materials. Our results suggest that the Ti-decorated BM will be a promising material system for hydrogen storage, suggested by the DOE for commercial applications.

Acknowledgements

This work was supported by the National Natural Science Foundation of Shaanxi Province (Grant No. 2014JM2-5058), the Scientific Research Program of Yan’an (Grant No. 2013-KG03), the Science Innovation Training Program (Grant No. 2014107191081), the Science Foundation of Yan’an University (Grant No. YD2014-02) and the Special Research Funds for Discipline Construction of High Level University (Grant No. 2015SXTS02).

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