1. Introduction
Storage of hydrogen, as one of the clean alternative energy resources with highest energy content by weight [1], has been investigated in metal hydrides [2, 3], alloys [4-7], and porous substances [8, 9], and is found to be particularly promising in graphene [10–20], which has excellent electronic, mechanical, and thermal properties [21, 22], as well as the special characteristic of reversible hydrogenation–dehydrogenation reactions [23]. The hydrogen isotope tritium is one of the most important initial radiological activities of irradiated graphite waste after reactor shutdown [23] and therefore, tritium desorption from such phenomenon becomes one of the crucial targets of decontamination of nuclear graphite. Tritium has adsorption, diffusion, and desorption properties similar with hydrogen; for this reason, fundamental understanding of the adsorption/desorption of hydrogen molecules and the migration mechanism of H atoms on graphene surface is of particular importance [24].
Nevertheless, the dissociation rate of H2 molecules on pristine graphene is too low as it goes through to physisorption, while the dissociation energy barrier is very high (2.7-3.3eV) [25, 26]. Compared to pristine graphene (or graphene-like materials), adsorption and desorption of H2 are easier on graphene (or graphene-like materials) with defects [24, 27-37]. Nonetheless, such various defects, including the adsorption property of electromagnetic waves [38-40], dielectric property [41], and so on, affect the properties and performance of graphene. Studies have shown that the adsorbing capacity of toxic gases (NO, CO, HCN, and SO2) [42] and reactive gases (CO and O2) [43-46] on graphene (or graphene-like materials) can be regulated by doping, and that vacancies as common defects, reduces the adsorption energy of adsorbents, such as sodium [47] and H atoms [48], so that graphenes with vacancy defects have attracted considerable research attention [28-37]. Vacancy defects in graphene can enhance its reactivity and affect charge distributions, and are always found to be sites of chemisorption [24]; they are classified into single vacancy (SV), double vacancy (DV), among others [49-52].
SV is identified to promote the dissociation of H2 molecules with reduced activation barrier energy of 0.63 eV, as compared to 2.38 eV for pristine graphene [53]. An isolated SV in a graphene can bind four H atoms stably or even six, to form a metastable and magnetic structure at room temperature [53]. On one hand, successive adsorption reaction of H2 on SV has been studied [48, 54, 55], especially in Ref. [48], where a detailed map of the continuous process of hydrogenation was demonstrated systematically. On the other hand, the reversible hydrogenation–dehydrogenation reactions have been discussed in Sunnardianto et al., who reported on a reversible hydrogen-dissociative adsorption on a SV graphene that absorbs two H atoms [55]; they further stated minimum energy pathways and activation barriers for both adsorption and desorption of one H2 molecule on triple-hydrogenated vacancy graphene that suggests a potential application for hydrogen storage [56].
The focus of previous research to date was on SV graphene, while rare attention has been paid to DV graphene, which has better thermal stability and thus, is thermodynamically favored over the former, aside from its vacancies having even number of missing atoms being more stable than those with odd number of missing atoms [49-51]. In this paper, we utilized first-principles calculation to study the behaviors of hydrogen adsorption, diffusion, and desorption on both SV and DV graphenes, which could provide theoretical guidance for both hydrogen storage by use of graphene and thermal desorption of tritium from decommissioned nuclear graphite.
2. Computational methods
All calculations were performed via density functional theory method [57, 58] implemented in the Vienna Ab Initio Simulation Package (VASP) [59]. Exchange and correlation effects were treated self-consistently with a generalized gradient approximation (GGA) [60]. To describe the electron-ion interaction, the projector augmented wave (PAW) pseudo-potential [61] was employed. Cut-off energy for the plane wave basis was set at 450 eV to ensure good convergence. Geometry optimization was performed with force convergence criterion of 0.01 eV/Å, while energy convergence criterion was 10-6 eV. Diffusion and desorption energy barriers were estimated through the climbing image nudged elastic band (CI-NEB) method [62-64]. The Brillouin zone was sampled with a grid of 4×4×1 k-points, with the lattice constant of optimized graphene set to 2.462 Å, which is in good agreement with other theoretical and experimental values [65, 66]. A 6 × 6 hexagonal supercell containing 72 carbon atoms was used to model the graphene in all the calculations. Periodic boundary conditions were adopted in all three directions and the size of supercell in the z-axis (i.e. the thickness of the vacuum) was set at 18.75 Å.
The reaction energy for adsorbing n H atoms on the graphene is computed as [48]
where the three terms on the right are the total energy of the graphene supercell with n-times hydrogenated vacancy, the energy of the graphene supercell with bare vacancy, and the reference state of n H atoms, respectively. The reaction energy for sequential adsorption
where
As validation, we simulated the adsorption, migration, and desorption behaviors of H atoms on pristine graphene. Results showed an adsorption energy of 0.73 eV, which agrees well with the other theoretical values [67, 68], and desorption energy barrier of 2.55 eV, which also coincides with those of previous studies [26, 69].
3. Results and discussion
3.1 SV and DV graphene structures
The calculation model of the SV graphene was constructed from a carbon atom extracted from the 6 × 6 hexagonal supercell, then the bare vacancy underwent a Jahn–Teller distortion, with two of the three carbon atoms in it forming a C–C bond [50, 70-73]. Likewise, the DV graphene model was formed from the 6 × 6 hexagonal supercell by extracting two carbon atoms in different ways. Calculation models of SV, DV5-8-5, DV555-777, and DV5555-6-7777 graphenes [49-52] after structure optimization are shown in Fig. 1. The simplest DV graphene was DV5-8-5, which contains two pentagons and one octagon; the most stable was DV555-777 [74] with three pentagons and three heptagons and; DV5555-6-7777 had four pentagons, one hexagon, and four heptagons. No dangling bonds were present in these three DV structures unlike in the SV structure. Simulation results illustrated that the top site of the carbon atom in the DV structures was a stable adsorption site.
3.2 Hydrogen adsorption and desorption on SV graphenes
Figure 2 shows a detailed map of optimized hydrogenated SV graphene structures, in which the calculated energies were compared with the results in Ref. [48] (shown in blue inside parentheses in Fig. 2). Only the energetically favorable process of continuous hydrogenation in SV graphene is depicted in the figure.
In general, the resulting adsorption energies in Fig. 2 coincide with those in Ref. [48]. In the SV graphene, a first H atom was preferentially absorbed by the C atom with a dangling bond, i.e., C1 in the Fig. 1(a), which is strongly exothermic, and the adsorption energy was -4.35 eV, slightly higher than -4.42 eV [48], but significantly lower than -3.45 eV [53]. When adsorbing a second H atom, along with the initial atom they could be located either on the same or on different sides, with the most energetically favorable configuration labels of SV11(u-u) and SV11(u-d). After absorption of a third H atom, the most stable structure becomes SV111(u-u-d) (each of the three vacant C atoms bonding with one H atom and one of the three H atoms, are oriented differently).
From Fig. 2, the SV111(u-u-d) configuration could transform into SV211(ud-d-d) through adsorption of a fourth H atom at -2.42 eV, which again, agrees with Ref. [48]. Nevertheless, SV111(u-u-d) was also found to transform to SV211(uu-u-d) by adsorbing a fourth H atom at the energy of -2.71 eV, which is not found in Ref. [48] and which was even lower than that in SV211(ud-d-d) (-2.42 eV), so that SV211(uu-u-d) was as important as SV211(ud-d-d). Unfortunately, the SV211(uu-u-d) configuration is yet to be studied.
After absorption of the fifth H atom, SV221(ud-ud-u), SV221(uu-ud-d), and SV221(uu-uu-d) form, as demonstrated in Fig. 2. Desorption of hydrogen molecule from SV221(ud-ud-u) to form SV111, and in turn, adsorption of hydrogen molecule in SV111 to form SV221(ud-ud-u) have been investigated in Ref. [56], in which the energy barrier of these reactions was 1.3 eV, which means this storage and release concept has the potential to act as a hydrogen storage system. Furthermore, in this work, first-principles calculations were used to study the energy pathways and barriers of the reactions, i.e., SV111 + H2 ↔ SV221(uu-ud-d) and SV111 + H2 ↔ SV221(uu-uu-d).
Minimum energy pathways for SV221(uu-ud-d) ↔ SV111(u-d-d)+H2 and SV221(uu-uu-d) ↔ SV111(u-u-d)+H2 are shown in Fig. 3. The energy barriers of H2 desorption and adsorption for SV221(uu-ud-d) ↔ SV111(u-d-d)+H2 and for SV221(uu-uu-d) ↔ SV111(u-u-d)+H2 were 1.85 eV and 1.92 eV, and 2.17 eV and 2.26 eV, respectively. All energy barriers of these two reactions were apparently higher than those for SV221(ud-ud-u) ↔ SV111(u-u-d)+H2 (i.e., 1.30 eV [56]), but their desorption energy barriers were lower than those for SV2(u-u) → SV+H2 (i.e., 4.06 eV [53]) and their adsorption energy barriers were significantly higher than those for SV+H2 →SV2(u-u) (i.e., 0.63eV [53]). As a result, H2 desorption and adsorption were more difficult in SV221(uu-ud-d) ↔ SV111(u-d-d)+H2 and SV221(uu-uu-d) ↔ SV111(u-u-d)+H2 than in SV221(ud-ud-u) ↔ SV111(u-u-d)+H2, and these two reactions could not be identified as potential hydrogen storage reactions.
3.3 Adsorption, migration, and desorption of hydrogen on DV graphene
Figure 1 illustrates the stable adsorption sites with high symmetry in DV5-8-5, DV555-777 and DV5555-6-7777. Adsorption energies of hydrogen in these sites were calculated and are shown in Table 1, where the adsorption energies of H atoms observed on the DV region were mostly lower than those away from the region. For example, the adsorption energy of an H atom in T2 site of DV555-777 (i.e., -2.51 eV) was apparently lower than in the T6 site (i.e., -1.31 eV). This indicated that H atoms have an evident tendency to diffuse to the region of double vacancy from outside. The adsorption, migration, and desorption behaviors of H atoms in these DVs were studied and are shown in Figs. 4, 5, and 6.
| Substrates | Sites | Ead (eV) |
|---|---|---|
| DV5-8-5 | T1 | -1.22 |
| T2 | -2.31 | |
| T3 | -1.57 | |
| T4 | -1.23 | |
| T5 | -0.97 | |
| T6 | -1.23 | |
| T7 | -1.65 | |
| T8 | -1.18 | |
| DV555-777 | T1 | -1.18 |
| T2 | -2.51 | |
| T3 | -1.95 | |
| T4 | -1.86 | |
| T5 | -1.60 | |
| T6 | -1.31 | |
| DV5555-6-7777 | T1 | -1.40 |
| T2 | -2.14 | |
| T3 | -1.82 | |
| T4 | -1.51 | |
| T5 | -1.47 | |
| T6 | -1.83 | |
| T7 | -1.90 | |
| T8 | -1.53 | |
| T9 | -1.33 | |
| T10 | -1.12 |
In DV5-8-5, the region of double vacancies mainly had an octagon ring and two pentagon rings; in DV555-777, the vacancy region was made up of three octagon and three pentagon rings and; in DV5555-6-7777, the region was composed of four octagon and two pentagon rings, and one hexagon ring. Hence, the order of the vacancy size was DV5555-6-7777>DV555-777>DV5-8-5, which could influence the capacity of hydrogen adsorption on these structures.
According to the calculated adsorption energies in Table 1, the most stable site in DV5-8-5 was T2, as shown in Figs. 1(b) and 4, which was the top site of the carbon atom shared by a pentagon, a hexagon and an octagon ring. Hydrogen adsorption energy in this site was -2.31 eV, and the first adsorbed H atom was bound to occupy this site. The second most stable site in DV5-8-5 was not T1 in the octagon ring, but T3 with adsorption energy of -1.57 eV. It was clear from Table 1 that the adsorption sites (e.g., T2 and T3) in DV5-8-5 were more stable than those away from the vacancy (e.g., T8), which justified the tendency of H atoms to accumulate in the vacancy region of DV5-8-5.
Adsorption and desorption of H2 molecules on/from DV5-8-5 are shown in Fig. 4. Before the desorption process, two H atoms should gather together in the DV5-8-5; the first atom was adsorbed in T2, while the second was assumed to migrate along the path of T5→T4→T3 to T3, which is the second most stable site. Two steps occurred during this migration at energy barriers of 1.21 eV and 0.49 eV, as shown in Fig. 4. The possible desorption of H2 molecule from DV5-8-5 was investigated, where the system energy decreased by 0.21 eV after dehydrogenating; Nevertheless, the reaction energy barrier was found to be 2.10 eV, which means that desorption of H2 molecule was difficult. For the adsorption of H2 molecule on DV5-8-5, the energy barrier was 2.31 eV, close to the value on pristine graphene (i.e., 2.38 eV) [53], which is mainly induced by the absence of dangling bonds in both DV5-8-5 and pristine graphene.
From Table 1, the most stable site in DV555-777 was that of T2 at adsorption energy of -2.51 eV. Interestingly, T2 was not the center of DV555-777, as shown in Fig. 1; the center site T1, however, was the most energetically unfavorable energetically, as observed in Table 1, with adsorption energy of -1.18 eV.
Figure 5 shows the adsorption and desorption of H2 molecules on/from DV555-777. The first H atom was adsorbed in T2, while the second was supposed to diffuse along the path of T6→T4→T3 to T3, which was the second most stable site and was adjacent to T2. From the figure, the energy barriers of the two-step migration were 0.74 eV and 0.71 eV, respectively. The energy barriers of H2 desorption and adsorption were calculated at 2.23 eV and 2.55 eV, respectively. Hence, while migration for H2 molecule was relatively easy, desorption and adsorption from/on DV555-777 was otherwise difficult.
For the configuration of DV5555-6-7777 in Table 1, T2 was the most stable site with -2.14 eV energy of adsorption, and thus, the first H was adsorbed in this site. The second H was assumed to migrate through T10→T4→T3 to T3, which was a relatively stable site adjacent to T2, and where the corresponding energy barriers were 0.69 eV and 0.97 eV, respectively, as shown in Fig. 6. As in the cases of DV5-8-5 and DV555-777, H2 molecule adsorption and desorption from/on DV5555-6-7777 was also difficult, because the energy barriers for these processes were 2.10 and 2.76 eV, respectively, as in Fig. 6.
4. Conclusion
First-principles calculations were performed for investigation of adsorption and desorption processes of hydrogen from SV and DV graphenes. In SV graphene, continuous hydrogenation was an energetically favorable process, and the minimum energy pathways were calculated by SV221(uu-ud-d) ↔ SV111(u-d-d)+H2 and SV221(uu-uu-d) ↔ SV111(u-u-d)+H2. In DV graphene, adsorption energies of H atoms on the region of double vacancy were generally lower than those away from the region, and the corresponding energy barriers for H diffusion into the vacancy were relatively low as well. Based on these energy barriers, desorption and adsorption of H2 molecules from/on DV graphenes was difficult. This work provides a comprehensive understanding of adsorption and desorption of hydrogen on/from single-vacancy and double-vacancy graphenes, and can serve as theoretical guidance for both hydrogen storage on graphene and thermal desorption of tritium from decommissioned nuclear graphite.
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