The energies of reactants, productions, transition state, dissociation barriers and reaction energies for the reaction of a H2 molecule with pristine graphene or with N-doped graphene and 2 H atoms bond on pristine graphene or on N-doped graphene in the presence of different electric fields.
Hydrogenation of carbon materials has been attracting a wide range of interests as an application of hydrogen storage materials in hydrogen-powered automobile as well as a methodology to manipulate the electric properties of carbon materials. Graphene with unique electronic, thermal and mechanical properties has been investigated as one of the most promising candidates for the next generation of electronic materials (Geim, 2009). However, several major challenges have to be tackled before the widespread application of graphene. For example, the absence of a band gap in the electronic spectrum of intrinsic graphene and the Klein paradox as a consequence of the Dirac-type nature of the charge carriers (Novoselov et al., 2004; Rao et al., 2009). The most efficient way to overcome these problems is hydrogenation of graphene (Luo et al., 2009). The graphane (Sofo et al., 2007), a fully hydrogenated single layer of graphene, was suggested to possess the promising semiconductor properties with a band gap of around 3.5 eV theoretically. Very recently, Elias et al. (Elias et al, 2009) experimentally demonstrated the formation of graphane through the exposure of a graphene membrane to hydrogen plasma. Subsequently, the rate of hydrogenation process of multilayer graphene was found to strongly depend on the number of layers (Luo et al., 2009; Ryu et al., 2008). These discoveries open important perspectives for the application of graphene-based devices because the electronic gap in those graphanes could be controlled by the degree of hydrogenation (Elias et al., 2009; Zhou et al., 2009).
The hydrogenation process of graphene in above experiments occurs through the exposure of graphene to the hydrogen plasma, which contains H+, H3 +, H atoms and H2 molecules (Elias et al., 2009; Luo et al., 2009). One generally assumes that H atoms form covalent bonds with the carbon atoms in the graphene (Luo et al., 2009). In this chapter, alternative approaches to hydrogenate graphene will be proposed theoretically based on density functional theory (DFT) calculations. It suggests that the hydrogenation process can be realized through the exposure of graphene to molecular hydrogen gas in the presence of a strong perpendicular electric field. It has been demonstrated that an electric field can modify the chemical activity of materials (Liu et al., 2009). For example, the dissociation activation energy of molecular oxygen on Pt (111) is tunable by an applied electric field (Hyman et al., 2005). To understand the mechanism of graphene hydrogenation with molecular hydrogen, the pathway of the dissociation of a H2 molecule and the subsequent atomic adsorption on graphene in the presence of an electric field will be investigated.
On the other hand, it is believed that graphene nanoribbons (GNRs) offer the possibility to achieve tunable electronic properties. This is because their properties are highly dependent on their width and also the orientation of edges, for example, the GNRs can be turned from semiconducting to metallic by manipulating the structural parameters (Han et al., 2010; Jiao et al., 2010). Unfortunately, to manipulate the edge structure and width of freestanding GNRs is a very challenging experimental task (Han et al., 2010; Jiao et al., 2010). Both experimental data and the corresponding
In this chapter, in order to enhance the hydrogen storage capacity in graphene and also to manipulate the electronic properties of graphene, the hydrogenation of graphene with and without an applied electric field, as well as the stability of the graphene/graphane interface in the hybrid nanoribbons are studied through DFT calculations. The energy barriers for the hydrogenation reaction and the diffusion of H atoms located at the graphene/graphane interface are simulated using DFT. All the possible reaction and diffusion pathways are analyzed to find the minimum reaction and diffusion barriers.
2. Hydrogenation of graphene
2.1. Hydrogenation of pristine graphene
In the simulation, all DFT calculations are implemented in the DMOL3 code (Delley, 2000). The local density approximation (LDA) with the PWC functional is employed as the exchange-correlation functional (Perdew & Wang, 1992). A double numerical plus polarization (DNP) is employed as the basis set. The convergence tolerance of energy is taken 10-5 Ha (1 Ha = 27.21 eV), and the maximum allowed force and displacement are 0.002 Ha and 0.005 Å, respectively. To investigate the minimum energy pathway for the hydrogen dissociative adsorption on graphene, linear synchronous transition/quadratic synchronous transit (LST/QST) (Halgren & Lipscomb, 1977) and nudged elastic band (NBE) (Henkelman & Jonsson, 2000) tools in DMOL3 code are used, which have been well validated to find the structure of the transition state (TS) and the minimum energy pathway. In the simulation, three-dimensional periodic boundary conditions are taken. The computer simulation cell consists of a 2×2 graphene supercell with a vacuum width of 18 Å to minimize the interlayer interaction. The
The adsorption energy of a molecular H2 on a pristine graphene layer
For the case of molecular hydrogen adsorbed on graphene, previous DFT reports showed that the H2 molecule is weakly physisorbed at the hollow site of graphene as shown in Fig. 1(a) (Ao et al., 2009, Arellano et al., 2000). The distance between the H2 molecule and the graphene layer
The energy minimum pathway for a H2 molecule dissociative adsorption on graphene is from the structure depicted in Fig. 1(a) to the structure in Fig. 1(b), which agrees with the reported minimum pathway (Miura et al., 2003). Here, this dissociative adsorption pathway is shown in Fig. 2(a). From Fig. 2(a), the dissociative adsorption reaction barrier
Next the effect of an electric field
The pathways for this reaction under different electric fields are given in Fig. 2. The energy minimum atomic structures of both reactant and product change in the presence of an electric field (Ao et al., 2008b). As shown in Fig. 2(b) at
The origin of the changes in
2.2. Hydrogenation of N-doped graphene
As shown in the last section, the process of hydrogenation in pristine graphene is divided into two steps: molecular hydrogen dissociation under the electric field and the formation of covalent bonds between the dissociated H atoms and C atoms after removing the electric field. This two-step hydrogenation process prevents the efficiency of graphene hydrogenation, and it is desirable to propose a direct hydrogenation approach, i.e. to find a way to reduce both the reaction barrier and reaction energy.
Doping of graphene is usually used to functionalize graphene (Rao et al., 2009). For example, Al-doped graphene was theoretically found to significantly enhance CO adsorption, where CO is found to be chemically adsorbed on the doped Al atom (Ao et al., 2008a). The gas adsorption properties of graphene with other elements, such as N, B and S, were systemically investigated using density functional theory (Dai et al., 2009). Recently, an
2.2.1 The adsorption of hydrogen on N-doped graphene
As reported, the H2 molecule is weakly adsorbed on pristine graphene, which is the reason why many people paid a lot of attention to modify graphene through doping or using the other methods to enhance the interaction between hydrogen and graphene (Ao et al., 2009; 2010a; Ataca et al., 2009). The energetic favorable adsorption configurations of one H2 molecule and two H atoms on pristine graphene surface are given in Fig. 1, and the corresponding discussion on the structure changes before and after hydrogenation are also shown in section 2.1. The band structures of pristine graphene, the system of a H2 molecule physi-adsorbed on graphene, and the system of graphene with 2 H atoms chemically adsorbed are shown in Figs. 4(a),
4(b) and 4(c), respectively. One can clearly see that pristine graphene has a zero band gap as expected (Elias et al., 2009; Rao et al., 2009; Shevlin & Guo, 2009; Sofo et al., 2007). After H2 molecular adsorption, there is almost no change in the band structure and the zero band gap remains. In fact, it is a simple combination of the band structure of pristine graphene and the H2 molecule. However, for the band structure of 2 H atoms chemically adsorbed on graphene, the significant changes are found near the Fermi level. It has an indirect band gap of 3.4 eV where the top of the valence band is located at the M point and the bottom of the conductive band is at the Γ point. The band gap is consistent with that of 3.5 eV for fully hydrogenated graphene—graphane (Sofo et al., 2007). Note that all C atoms are fully bonded and there are no unpaired electrons. Therefore, no net spin extists in this system. For half-hydrogenated graphene as shown in Fig. 3(a) of the Ref. (Zhou et al., 2009b), strong σ-bonds are formed between C and H atoms and the π-bonding network formed by
Doping graphene by both electrons and holes changes its electronic structure significantly (Rao et al., 2009). Recently, the nitrogen doped graphene was prepared by arc discharge of graphite electrodes in the presence of H2, He, and NH3 (Panchakarala et al., 2009), chemical vapor deposition (Wei et al., 2009), or through the electrothermal reaction with ammonia (Wang et al., 2009). Furthermore, using
In the arc discharge doping process, the vacancy defects in graphene were induced, thus allowing the N atoms from NH3 to adsorb at the vacancies and forming the covalent bonds with C atoms (Panchakarla et al., 2009). In this case, the binding energy
The favorable atomic structure of a H2 molecule physi-adsorbed on the N-doped graphene is shown in Fig. 5(b). The result shows that the planar structure remains and the adsorbed H2 molecule is located on the hollow site of the carbon hexagon. The distance
Different from the aforementioned physic-adsorbed H2, the favorable atomic structure of 2 H atoms chemically bonded on the C atoms is given in Fig. 5(c). Similar results for the case of pristine graphene are obtained, where the average binding energy for the C-H bonds
Fig. 6 shows a H2 molecule dissociative adsorption pathway on the N-doped graphene. Following the reaction coordinate, the reaction energy barrier is 2.522 eV, which is a little smaller than 2.734 eV for the H2 molecule dissociative adsorption on pristine graphene. The result is consistent with the report that N doping into CNTs would reduce the energy barrier of molecular hydrogen dissociative adsorption (Zhang & Cho, 2007). Besides the initial and final structures of the reaction, the atomic structure with the minimum energy state, State 1, and the transition state are also given in Fig. 6. For State 1, the H2 molecule diffuses from the hollow site of the carbon hexagon to a site near the doped N atom before the transition state. For the transition state, the H2 molecule is already dissociated into 2 H atoms but only H5 is adsorbed on C1 and H6 is a free atom near C4. Subsequently, H6 is also adsorbed as shown in the final structure. Such a reaction pathway explains why the two H atoms are not adsorbed onto two C atoms with symmetry, since the adsorption of the two H atoms does not occur at the same time. The adsorption of the first H atom would change the electronic distribution and also the chemical reactivity of each C atom.
The band structures of N-doped graphene, the system with a H2 molecule physi-adsorbed on N-doped graphene, and the system with 2 H atoms chemically adsorbed on N-doped graphene are given in Figs. 4(d), 4(e) and 4(f), respectively. It is clearly shown in Fig. 4(d) that there is an energy gap between the valence and conduction bands at the K point with N doping. The direct band gap is about 0.7 eV. As clarified by the others (Martins et al., 2007), the doping atoms enter into the lattice of graphene, form covalent bonds with the C atoms and change the atomic structure of graphene. This would largely modify the electronic structure of graphene and suppress the density of states near the Fermi level, thus a gap is opened between the valence and conduction bands. After a H2 molecule is adsorbed, the band structure of the system is not fundamentally changed. However, for the system of 2 H atoms adsorbed on N-doped graphene, the band structure changes a lot and an indirect band gap of around 3 eV is found. The top of the valence band is located at the K point and the bottom of the conduction band is at the Γ point. Therefore, doping N into graphene has no significant effect for the H2 molecule physisorption and only slightly reduces the dissociation energy barrier. However, for the band structure of graphene, doping N would induce a band gap energy of ~0.7 eV. Thus, similar to the N-doped CNTs (Zhou et al., 2006), N-doped graphene exhibits semiconductor behavior, which leads to a decreased conductivity, an improved on/off ratio and a Schottky barrier when electrodes are added.
2.2.2. The effect of an applied electric field on the dissociative adsorption
As a perpendicular electric field
It is interesting to notice that the reaction barrier is negative, i.e. -0.895 eV, for a H2 molecule dissociative adsorbed on N-doped graphene under a 0.009 a.u. electric field. Therefore, this reaction pathway is shown in Fig. 7. As shown in this figure, there are two transition states TS1 and TS2, and two minimum energy states: State 1 and State 2. For State 1 and State 2, the two dissociative H atoms bond on C1 and C4, which are closest to the doped N atom. For TS1 and TS2, the H2 molecule is dissociated and only one H atom is bonded with C1, which is closest to the doped N atom. Another H atom is free. However, the positions of the free H atom are different for the two transition states. The configurations of the two transition states are similar to that in the N-doped graphene system without electric field, where there is also one H atom bonded on C1 and another is free.
The reaction barrier -0.895 eV is the energy difference between IS and TS2. In this reaction process, there are two barriers that should be overcome, State 1 to TS1 with a barrier of 0.966 eV, and State 2 to TS2 with a barrier of 0.801 eV. However, the energy from the exothermic process of IS to State 1 is sufficient to support the endothermic process from State 1 to TS2. In the other words, the dissociative adsorption reaction can occur automatically if the energy created from IS to State 1 can be used to provide the energy needed from State 1 to TS2. Further increasing the electric field beyond 0.009 a.u., no transition state is found and the final structure can be obtained directly even by the geometry optimization method. Therefore, the electric field can induce molecular hydrogen dissociative adsorption in the N-doped graphene system, and the process changes from an endothermic to an exothermic reaction. It means that the electric field and N doping act as the catalyses of H2 dissociation.
The origin of the differences in the energy barrier of hydrogen dissociative adsorption on graphene can be understood through the analysis of the partial density of states (PDOS). Fig. 8 shows the PDOS of the hydrogen and carbon atoms which the H2 molecule dissociates and is adsorbed on for different electric field. The interaction between the hydrogen and graphene atoms is mainly determined by the bonding and antibonding interactions between
the σg and σu states of hydrogen and the
The hydrogenated graphene, i.e. graphane, was first synthesized in 2009 by exposing graphene to a hydrogen plasma (Elias et al., 2009). Here, a new promising approach is proposed to hydrogenate graphene. With this technique, the hydrogenation can be realized automatically. The hydrogenated N-doped graphene has two very attractive properties for applications. It has a very high volumetric and gravimetric hydrogen density if fully hydrogenated, and has a band gap around 3 eV. The gravimetric capacity of 7.5 wt% hydrogen is higher than the 6 wt% hydrogen target indicated by the Department of Energy U.S. (DOE), and the volumetric hydrogen capacity of 0.12 kg H2/L is higher than the DOE target of 0.081 kg H2/L. Alternatively, the band gap of N-doped graphene is increased to 3 eV after 2 H atoms are adsorbed, i.e. in the range of UV light. This is comparable to TiO2, graphitic C3N4 materials and porous graphene, which have shown the potential applications in photocatalyzed splitting of water into hydrogen (Du et al., 2010; Sum et al., 2002; Wang et al., 2008). These results suggest that the hydrogenated N-doped graphene may solve the band gap problem of graphene for nanoelectronic applications and display photocatalytic activity.
3. Diffusion of hydrogen on graphene/graphane interface
As aforementioned, manipulating the edge structure and width of GNR is a way to tuning the electronic properties of graphene, such as opening its band gap. High quality GNRs can be fabricated by selectively hydrogenating graphene or by carving GNRs on a graphane sheet. However, the hydrogen diffusion has a strong influence on the stability of the graphene/graphane interface and such a phenomenon needs to be clarified.
Similar to the studies above, the hydrogen diffusion behavior on the graphene/graphane interface is investigated with DFT calculation and all the DFT calculations were performed using the DMOL3 code (Delley, 2000). The generalized gradient approximation (GGA) with revised Perdew-Burke-Ernzerhof (RPBE) functional was employed as the exchange-correlation functional (Hammer et al., 1999). A double numerical plus polarization (DNP) was used as the basis set, while the DFT semicore pseudopotentials (DSPP) core treatment was employed for relativistic effects that replaces core electrons by a single effective potential. Spin polarization was included in all our calculations. The convergence tolerance of energy was set to 10-5 Ha (1 Ha = 27.21 eV), and the maximum allowed force and displacement were 0.02 Ha and 0.005 Å, respectively. To investigate the diffusion pathways of hydrogen atoms at the graphene/graphane interface, linear synchronous transition/quadratic synchronous transit (LST/QST)(Halgren & Lipscomb, 2000) and nudged elastic band (NEB) (Henkelman & Jonsson, 2000) tools in DMOL3 code were used, which have been well validated in order to search for the structure of the transition state (TS) and the minimum energy pathway. In the simulations, three-dimensional periodic boundary conditions were imposed, and all the atoms are allowed to relax.
The supercells used for the zigzag and armchair graphene/graphane nanoribbons are shown in Figs. 9(a)and 9(b), respectively. The interlayer interaction was minimized by allowing a vacuum width of 12 Å normal to the layer. For both type of nanoribbons, the C atoms are displaced from the C plane by about 0.29 Å due to the bonded H atoms. This value is similar to the shift of 0.32 Å that C atoms experience when a H2 molecule is dissociative adsorption on graphene (Ao & Peeters, 2010a). In both cases, this is a consequence of the change in the hybridization of the C atoms from
Now the stability of the two types of interfaces is analysed by calculating the diffusion barriers for hydrogen atoms. For the case of a zigzag interface, there are two different types of C and H atoms, which are indicated in Fig. 9(a) as sites A and B. For the diffusion of the H atom bonded to the C atom at site A, there are two possible diffusion paths labeled as 1 and 2 in Fig. 9(a). At the site B, there are three possible diffusion pathways for the H atom that we label as 3, 4 and 5. In the case of an armchair interface, all the C atoms at the interface are equivalent from a diffusion point of view. So there are five different diffusions pathways that are labeled as 6-10 in Fig. 9(b). When analysing the diffusion paths, it is found that all the diffusions are along linear pathways, and also that the H atom is free without directly binding to any C atom at the transition state.
The diffusion barriers for the different paths and for both types of graphene/graphane interfaces are summarized in Table 3. For the zigzag interface, it is found that the barriers are 3.83, 4.48, 2.86, 3.64 and 3.86 eV for the pathways 1−5, respectively. Thus, the minimum diffusion barrier for the zigzag GGNRs involves H diffusion from the carbon atom at site B along the C−C bond to its nearest carbon atom with an energy barrier of 2.86 eV. For the armchair interface, energy barriers for pathways 6−8 and 10 are 3.17, 4.07, 4.20 and 4.05 eV, respectively. The pathway number 9 involves H diffusion to the nearest C atom at site P. However, it is found that this diffusion cannot occur because during the geometry optimization, the H atom at site P diffuses back to the C atom at site I. Thus, the energy barrier for H diffusion in armchair interfaces can be minimized to 3.17 eV to the second nearest C atom along Path 6.
Recently, it was reported that the diffusion barrier for a single hydrogen atom on pristine graphene layer is about 0.3 eV, which was obtained by DFT calculation using a similar method to this work (Boukhvalov, 2010). Furthermore, the diffusion barriers of transition-metal (TM) atoms on graphene were reported in the range of 0.2−0.8 eV (Krasheninnikov et al., 2009). If the TM adatoms are coupled to a vacancy, the diffusion barrier would increase substantially, reaching to the range of 2.1−3.1 eV. Thus, it was claimed that adatoms with the barrier in such a magnitude are stable at room temperature (Krasheninnikov et al., 2009), supporting the notion that the stability of H atoms at GGNRs interfaces are enhanced greatly and rather stable at room temperature.
From above analysis, one can see that the minimum diffusion barriers for both of armchair and zigzag interfaces are about one order of magnitude larger than the energy barrier for H diffusion on pristine graphene. From Table 3, one can also see that all the aforementioned H diffusion processes imply increases of several electronic Volts in the energy of the system. At the same time, this indicates that after the diffusion the energy needed for recovering the system back to the initial perfect thermodynamic state is always lower than the energy needed for distorting the interfaces. The barriers for backward diffusion are defined as the difference of energy between the final and the transition states (EF-ET), and can be obtained from Table 3 as the difference between the values of EF-EI and the diffusion barrier (ET-EI). These demonstrate that the graphene/graphane interfaces are rather stable in both types of hybrid nanoribbons.
Such stability enhancement can be understood by calculating the binding energy of the H atoms in the different conditions, which is proportional to the strength of the C-H bonds. The binding energies (Eb) were calculated by Eb=Ei-(Ef+EH), where Ei is the initial energy of the system, Ef is the energy of the system after removing the H atom, and EH is the energy of an isolated H atom. For the zigzag interface, we found that the binding energy of the C-H bond at sites A and B are -4.59 and -2.80 eV, respectively. While for an H atom at site I of the armchair interface, the binding energy is -3.35 eV. All these values are larger than the binding energy of an isolated H atom on a graphene supercell containing 32º C atoms that is equal to -0.88 eV. This indicates the stability enhancement of the H atoms at graphene/graphane interfaces. The results of the binding energies also explains why for the zigzag interface it is easier to move the H atoms from site B (Eb=-2.80 eV) than from site A (Eb=-4.59 eV). This explanation is also applicable for us to understand why moving the atoms at site B (Eb=-2.80eV) in the zigzag interface is easier than moving the H atoms at site I (Eb=-3.35eV) in the armchair interface. In addition, the C-H bond length at site A (1.108 Å) is smaller than that at site B (1.112 Å). It is believed that if one bond breaks, the remaining coordinated ones would become shorter and stronger (Sun et al., 2009; Zhang et al., 2009). As shown in Fig. 9(a), the C atom at site F binds with other three C atoms, while the C atoms at both sites A and B are bonded with three C atoms and one H atom. Therefore, Eb of C-C bond between sites B and F is greater than that between sites A and B. Such a strong C-C bond weakens the others bonding at site B including the C-H bond (Aizawa et al., 1990). Hence, the C-H bond at site B is weaker than that at site A. The same explanation can be applicable to the case of armchair GGNR. On the other hand, C-C bond between sites R and I in Fig. 9(b) is weaker than that between sites A and B due to the effect from both C-C bonds between R and M as well as I and P. Thus, the Eb of C-H bond at site I is between those at sites A and B, which is consistent with the DFT result above. Therefore, the H atom at site B can diffuse easier and the GGNR with the armchair interface is more stable than the one with the zigzag interface.
To further understand the mechanism behind of the higher stability of the H atom at site A, the atomic charges are analysed through the Mulliken method. Table 4 gives the atomic charges of atoms near the interfaces. One can see that atoms at both interfaces (i.e. at sites A, B, and I) are more charged than other atoms. At the interface, C atoms are more negative and the corresponding H atoms are more positive. Furthermore, it also shows that the both interfaces mainly affect the charge distribution of the first row of atoms at interfaces, while there is slight effect on the atoms of the second row at the armchair interface. This result agrees with the fact that an interface influences mainly the atoms of the first two rows (Sun, 2007). It is known that the atomic charge is mostly affected by the atoms belonging to the same carbon ring, especially the nearest atoms. For the carbon and hydrogen atoms at the site A, they have similar nearest atoms as the sites in graphane region far apart from the interface, where the three nearest C atoms are bonded by
stronger than that on the site A. On the other hand, for both sites A and B, there are three C atoms bonded by
In summary, the reaction pathways of a H2 molecule dissociative adsorption on the pristine graphene and the N-doped graphene layer were investigated under a perpendicular applied electric field using DFT calculations. The corresponding atomic and electronic structures of the reactants, productions and transition states were analysed. The results show that the N doping and electric field facilitate the hydrogen dissociative adsorption. The energy barrier for hydrogen dissociative adsorption on N-doped graphene is suppressed by a positive electric field normal to the graphene surface, and the reaction can automatically occur when the electric field is increased above 0.005 a.u.. The origin of the differences in the energy barrier can be understood through the analysis of PDOS. N doping and the applied electric field are considered to diminish the third interaction band between C and H, which mainly determines the barrier height. Based these results, a promising approach to hydrogenate graphene is proposed. It can be used to enhance the hydrogen storage capacity, and also to manipulate the physical properties of graphene for the applications of nanoelectronic devices. Such an exotic phenomenon is associated with its photocatalytic activity due to the band gap opening caused by the applied electric field and doping effects.
On the other hand, the stability of graphene/graphane nanoribbons with both zigzag and armchair interfaces is studied by calculating the diffusion barriers of H atoms using DFT method. It is found that the H atoms can be firmly stabilized by the graphene/graphane interfaces effects. This is resulted by the increase of the C-H bond strength at the graphene/graphane interfaces. The results demonstrate that both zigzag and armchair graphene/graphane interfaces in hybrid nanoribbons are rather stable, thus increasing the feasibility for future technological applications of these systems.
This study was financially supported by the Vice-Chancellor’s Postdoctoral Research Fellowship Program of the University of New South Wales (SIR50/PS19184), the ECR grant of the University of New South Wales (SIR30/PS24201) and ARC Discovery project of DP1096769.
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