An Efficient Way To Suppress the Competition between Adsorption of

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Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

An Efficient Way To Suppress the Competition between Adsorption of H2 and Desorption of nH2−Nb Complex from Graphene Sheet: A Promising Approach to H2 Storage Omar Faye* and Jerzy A. Szpunar Department of Mechanical Engineering, College of Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, S7N 5A9 Saskatchewan, Canada

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S Supporting Information *

ABSTRACT: We performed first-principles calculations to investigate the electronic structure and hydrogen storage capacity of bare niobium (Nb) and niobium-decorated graphene (GR@Nb). The results predict that bare Nb can bind 6 H2 molecules in the quasi-molecular form to reach saturation with the binding energy of hydrogen in the range 0.2−0.7 eV. In addition, the maximum temperature of desorption was 466 K. We demonstrated that the most favorable site for Nb atoms is the hollow site of graphene with a binding energy of 1.783 eV. Moreover, we analyzed the stability of Nb dopant on the graphene surface by means of reaction barriers calculations and an ab initio molecular dynamics simulation. Our calculations reveal that an energy barrier of 0.435 eV is required for a Nb atom to move from one hollow site to the adjacent hollow site, which is far greater than the energy of thermal vibration of Nb at 300 K. We show that Nb-decorated graphene doped with nitrogen atoms at 7.25% can absorb 12 H2 molecules in the quasi-molecular form with an average binding energy of 0.410 eV at an average desorption temperature of 520 K. Our results predict that desorption of nH2−Nb complex from a graphene sheet can be suppressed by increasing the concentration of nitrogen atoms to 7.25%. Finally, the storage capacity of 2NGR@2Nb is about 8 wt %. These results clearly demonstrate that Nb-decorated graphene with a 7.25% concentration of nitrogen atoms is a promising candidate for H2 storage for mobile applications. applications like energy storage, gas sensing, and others.10−17 Specifically, carbon-based nanostructures have been found to be promising in hydrogen storage. However, for pristine materials such as fullerenes,18 carbon nanotubes,19 and graphene,20 the binding energy with H2 molecules is too low to realize storage under the moderate aforementioned conditions. Therefore, enhancing the interaction of H2 with these materials is necessary for obtaining a suitable hydrogen storage medium under the guidelines proposed by the DOE.21 Functionalizing carbon nanomaterial with transition metals (TM) is one way to improve the H2 storage capacity, as reported earlier.22 Recent reports also show that promising storage capacity can be obtained by doping carbon-based nanomaterials with transition metals.23−33 Large surface area and light weight favor graphene, among several carbon-based nanostructures, as a potential H2 storage medium because both sides can be utilized for adsorption. In our earlier work, we reported that Pd-functionalized graphene reached a gravimetric density of 3.622 wt %,28 and the competition between H2 adsorption and the desorption of Pd atoms can be suppressed by doping the graphene sheet with NH radicals. According to Wang et al., Li-decorated porous graphene can reach a H2 storage capacity of 10.89 wt % at T = 300 K with no external pressure.32 Asha et al. also predicted a gravimetric density of 11

1. INTRODUCTION Increasing energy consumption, depletion of fossil fuel supplies, and environmental concerns related to global warming necessitate a continuous search for an alternative fuel that is clean and sustainable in supply. Among various alternatives, hydrogen (H2) is one of the most promising candidates because it is the most abundant element on Earth and a clean energy carrier with water and heat as byproducts. However, at this stage, the main challenge is to develop reliable materials and systems for hydrogen storage. Current methods use high-pressure tanks as well as liquid and solidstate storage. Liquid-state and high-pressure tanks are problematic due to the cost of liquefaction, excessive loss of hydrogen, risk of explosion at high pressure, and the great weight of high-pressure containers. Solid-state storage of hydrogen is the most promising method.1 In this view, the U.S. Department of Energy (DOE)2 has established the criteria for a sorbent to be considered for mobile application. First, it should be able to store at least 6.5 wt % in gravimetric capacity and have 70 g/L of volumetric capacity at ambient temperature (−40 to 85 °C) and moderate pressures (less than 100 atm).3 Second, the adsorption energy window must be in the range of 0.2−0.7 eV to be used for mobile applications.4 In addition, storing H2 in a safe and lightweight container is also required for on-board automobile application.5,6 Due to their large surface area and light weight,7−9 twodimensional (2D) nanomaterials have been investigated in a wide range of experimental and theoretical research for Published XXXX by the American Chemical Society

Received: September 28, 2018 Revised: November 11, 2018

A

DOI: 10.1021/acs.jpcc.8b09498 J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Atomic (A) and molecular (M) state of H2 adsorption on a bare Cu atom. The white and green atoms represent H and Nb, respectively.

wt % for zirconium-doped graphene,1 which is much higher than the DOE target. Ao et al.33 claimed that Al-doped graphene has a high H2 storage of 13.19 wt % with an average H2 binding energy of −0.193 eV/H2. In addition, some earlier experiments demonstrated that during H2 cycling on Mg catalyzed with Nb and V the Nb can enhance the process of hydrogen cycling on Mg.34 Saba et al. reported that C2H4 doped with Nb atoms has a gravimetric density of 18.92 wt %.35 Despite the high gravimetric densities reported earlier in the literature related to the positive effect of Nb in functionalizing different structures for hydrogen storage, the H2 storage capacity on bar niobium (Nb) and niobium-functionalized graphene (GR@Nb) has not been addressed. To bridge this void, we report here a detailed DFT investigation of hydrogen storage capacity on bar niobium (Nb) and Nb-functionalized graphene (GR@Nb). First, we tested the H2 interaction with bar Nb. Second we looked into the physical and chemical properties of the interaction of Nb on graphene. Finally, we investigated H2 storage on single and double-sided Nbfunctionalized graphene with different concentrations of nitrogen atoms (N) at 3.625% (NGR@Nb) and 7.25% (2NGR@2Nb) and the presence of oxygen (O2) as a contaminant.

graphene plane and c is the interlayer distance between two adjacent graphene layers. The energy minimization was done with the convergence tolerance energy of 10−5 Ha. The atomic positions were relaxed such that the force acting on each atom was less than 0.002 Ha/Å. To check the effect of clustering of Nb atoms on a graphene surface, a transition state (TS) connecting two stable structures through a minimum energy path was examined based on the complete linear synchronous transit (LST) and quadratic synchronous transit (QST) methods.43 In this method, we performed the LST maximization followed by the energy minimization in the direction that conjugated to the reaction pathway to obtain an approximated TS. We used the approximated TS to perform QST maximization, followed by another conjugated gradient minimization. We repeated the cycle until a stationary point was located. The reaction energy (Ereaction) and the activation energy (Ea) are defined by these two sets of equations:

2. COMPUTATIONAL METHODS We performed a first-principles calculation by using spinunrestricted plane-wave density functional theory with the selfconsistent field method implemented in the Dmol3 module.36,37 The exchange correlation effect on electron−electron interaction was approximated by the generalized gradient approximation (GGA) using Perdew Burke and Ernzerhof (PBE)38 throughout this work. We used the semicore pseudopotential to represent the core electrons as a single effective potential.39,40 The double numerical plus polarization (DNP) used as a basis set included the vdW interaction approximated by Grimme’s DFT-D41 scheme, and this added a contribution of ϵ−6 in the DFT total energy for each pair of

3. RESULTS AND DISCUSSION 3.1. Hydrogen Interaction with Bare Niobium. Understanding the interaction of H2 with free Nb is an important step for Nb testing before using it as a catalyst on graphene. Cui et al. reported44 that the dissociation of H2 molecules decreases the hydrogen storage capacity. Therefore, it is necessary to first address the interaction of bare Nb with the two possible states of hydrogen: the atomic state (A) and the molecular (M) state. Their optimized structures are shown in Figure 1. The strength of the interaction between the H2 and Nb atoms was evaluated using the following equation:

R

atoms separated by a distance R. Our choice of

ϵ R−6

Ereaction = E(P) − E(R)

(1)

Ea = E(TS) − E(R)

(2)

where E(p) is the energy of the product of each reaction, E(R) is the corresponding energy of reactant in each step, and E(TS) is the energy of the transition state in each elementary reaction.

Eb =

is based on

E(Pd) + E(nH2) − E(Pd + nH2) n

(3)

where E(Pd).is the total energy of bare Nb, E(nH2) is the total energy of nH2 molecules, E(Pd + nH2) is the total energy of nH2 + Pd complex, and n represents the number of added H2 molecules. Using eq 3 for n = 1, the binding energy of the H2 molecule is 0.228 eV. Its equilibrium parameters are the average distance between H atoms (daveH−H) is 0.861 Å, the average distance between Nb and H atoms (daveNb−H) is 1.952 Å, and it is nonmagnetic. These results show that the interaction of the first H2 molecule with bare Nb is weaker

its simplicity and the low computational cost that this pairwise scheme offers. To model our system, we used a supercell of 4 × 4 × 1 containing 32 atoms with periodic boundary condition used along the x and y directions. The Brillouin zone was sampled using a 10 × 10 × 2 Monkhorst−Pack mesh of special kpoints.42 The optimized lattice of the supercell was a = b = 9.840 Å and c = 15 Å, where a and b are the distances along the B



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than the binding of H2 with bare copper (Cu), Ebave = 0.287 eV, as stated in our previous work,27 and bare palladium (Pd), Ebave = 1.11 eV, as reported by Contescu et al.45 On the other hand, in the chemisorption case, we found that the binding energy of H2 with free Nb atoms is 0.563 eV compared to 0.642 eV in the case of H2 on bare palladium (Pd)46 and 3.09 eV for free platinum (Pt) atoms.47 These values reveal that the interaction of hydrogen with bare Nb is more pronounced in the atomic state (A) rather than in the molecular state (M). The average distance between H and Nb atoms decreased from 0.861 Å for M state compared to 0.794 Å in the case of A state. The potential energy diagram that links these two states is depicted in Figure 2. By means of eqs 1 and 2, we noticed

of bare Nb is reached at six H2 molecules. We plotted in Figure 4 the change of the equilibrium parameters to better visualize them. We also represented the changes of the binding energy with respect to the number of H2 molecules in Figure 4b. We noticed here an increase of Ebave from 0.228 to 0.630 eV after the addition of the six H2 molecules and a decrease for an additional H2 molecule to 0.552 eV. We also plotted the changes of daveH−H and daveNb−H distances in Figures 4c and 4d for a different number of added H2 molecules. The shape of the plot line clearly indicates an increase of daveH−H for the first two H2 molecules from 0.861 to 0.895 Å and a decrease to 0.835 Å for the seventh H2 in Figure 4c. However, the opposite trend is observed for daveNb−H in Figure 4d where there is a decrease from 1.952 to1.898 Å for the first two H2 molecules and then a gradual increase in distance to a maximum value of 2.05 Å. Furthermore, another key issue for using hydrogen fuel in automobile transportation is the kinetics of H2 desorption. Therefore, to assess the temperature of desorption of H2 we used the Van’t Hoff method given by the following equation: ji P zyyz ji E zyij ΔS TD = jjj bave zzzjjjj − lnjjj zzzzzzz j KB z KB j P0 z k {k k {{

−1

where Ebave is the binding energy, KB represents Boltzmann’s constant (8.61733 × 10−5eV /K), P denotes the pressure (P = 1 atm), the reference pressure Po = 1 atm, R is the universal gas constant (8.314 JK−1 mol−1), and ΔS is the entropy change as H2 moves from gas to liquid phase. Using the value of P = 1 atmosphere pressure and taking the value of ΔS = 130.7J K−1 mol−1 from the literature,48−50 we calculated the desorption temperature for the corresponding binding energy as listed in Table 1. Figure 4a shows that the desorption temperature varied linearly with the binding energy and the existing correlation can be approximated by the relationship TD = 744 Eb − 2.28. We already learned that the binding energy of H2 with bare Nb increased as the number of H2 molecules rose from one to six. However, their adsorption energy is the energy windows identified by the DOE.51 Therefore, our predictions suggested that Nb be included as a potential candidate for a H2 storage system. 3.2. Interaction of Nb with Graphene. Knowing the interaction mechanism of Nb atoms with graphene is an important step toward its use as a H2 storage medium. Therefore, we probed this interaction at three points of high symmetry, namely the hollow (H), top (T), and bridge (B) sites. To assess the strength of binding energy, we used the following equation:

Figure 2. Potential energy diagram that showed the energies of the chemical species and transition state (TS) from the molecular (M) to the atomic (M) configuration.

that the transition from state A to state M is an endothermic process with 0.340 eV as the energy of reaction and 0.432 eV as the energy required to overcome the barrier between these two states. Even though the atomic form (A) is chemically more stable than the molecular form (M), the M state is more suitable for mobile applications.10 Therefore, the rest of this section will be devoted to the interaction of H2 in the molecular form with free Nb. We noticed a linear increase of the binding energy of H2 on free Nb atoms from 0.230 to 0.630 eV as we increased their numbers from one to six H2 molecules. The results of the reaction between H2 and Nb are summarized in Table 1, and their optimized structures are shown in Figure 3. A similar energy trend was also observed in our previous work.27 Moreover, the addition of a seventh H2 leads to a sudden decrease of Ebave to 0.552 eV with daveNb−H = 2.05 Å and daveH−H = 0.835 Å. This means that saturation

E b = E(G) + E(Nb) − E(G + Nb)

daveH−H (Å)

daveNb−H (Å)

TD (K)

Ebave (eV)

1 2 3 4 5 6 7

0.861 0.895 0.865 0.851 0.858 0.849 0.835

1.952 1.898 1.938 1.956 1.939 1.946 2.050

168 293 366 394 442 466 408

0.228 0.396 0.495 0.533 0.598 0.630 0.552

(5)

where E(G) and E(Nb) are the total energies of pristine graphene and an isolated Nb atom, respectively, and E(G+Nb) is the total energy of Nb-functionalized graphene. After geometry optimization, we found that Nb atoms prefer to bind in the hollow site with a binding energy of 1.783 eV at an average binding distance of 2.1 Å. This value is much higher than the binding energies of Pd and Cu on graphene, which are 0.8 and 0.7, respectively, as reported in our earlier works.28,27 Also, Modak et al.52 predicted a binding energy of 0.76 eV for Nbdecorated SWCNTs; 2.20 eV for Y-decorated single-walled carbon nanotube was calculated by Chakraborty et al.53 We also found that upon the adsorption of Nb on graphene, there was an elongation of the C−C bond of the C atoms in graphene from 1.40 to1.60 Å. The Nb-functionalized graphene

Table 1. Average Binding Energy (Eb) of the Successive H2 Addition on Bare Nb along with Their Equilibrium Distances between H−H Atom (daveH−H) and Nb and H Atom (daveNb−H) and the Desorption Temperature (TD) no. H2

(4)

C



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Figure 3. Optimized structures of the successive addition of H2 molecules on a bare Nb atom along with their average binding energy (Ebave). The green and white balls denote Nb and H atoms, respectively.

Figure 4. Physical and chemical parameters of the successive addition of H2 on bare Nb. Case (a) corresponds to the variation of the desorption temperature (Td) with respect the average binding energy (Ebave), case (b) represents the variation of the Ebave with the number of H2 molecules, case (c) the changes of daveH−H with respect to the number of H2, and case (d) the variation of daveNb−H with respect to the number of H2 molecules.

Figure 5. Potential energy diagram showing the energies of the chemical species and transition state (TS) involved in the migration of Nb on graphene surface. The green balls denote Nb, and the gray balls represent carbon atom of graphene.

storage as reported,53,54,55 finding an alternative way to avoid it is important in order to improve the H2 adsorption capacity. To check the clustering effect of Nb atoms, we analyzed their diffusion over the graphene surface. The diffusion was evaluated by performing a transition-state calculation of Nb

has a nonmagnetic behavior. We investigated the chargetransfer mechanism by means of Mullikan analysis, and it showed that Nb accepts +0.347e compared to the C atom directly attached to it where they have −0.043e each. Since clustering of metal atoms on graphene is a major issue for H2 D



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energy diagram that connects the two possible states of H2 is shown in Figure 6. The potential energy curve depicted in

atoms on two adjacent hollow sites of graphene. The potential surface energy is portrayed in Figure 5. We noticed that an energy barrier of 0.435 eV was required for Nb atoms to move between two adjacent hollow sites. In addition we performed an ab initio MD molecular dynamic simulation to measure the strength of the thermal vibration at room temperature (T = 300 K). According to the equipartition theorem, the average thermal energy of a molecule in three-dimensional space is given by Eave =

3KBT 2

(6) −5

where KB = Boltzmann’s constant (8.61733 × 10 eV /K) and T = temperature in Kelvin. Since Nb atoms vibrate only along the x and y axes in the graphene plane, eq 6 becomes Eave = KBT and the thermal vibration energy at T = 300 K is found to be 0.025 eV, which is very small compared to the 0.435 eV energy required to overcome the barrier. Yadav et al.1 also reported earlier that the energy barrier that prevents zirconium atoms from aggregating on pristine graphene is 1.23 eV. Comparing these energy barriers, we can speculate that Zr atoms have a stronger interaction with graphene than Nb atoms. In short, the small value of the vibration energy of Nb at T = 300 K and the high-energy barrier required to move between two adjacent hollow sites on graphene showed that the clustering of Nb atoms on graphene is not likely. Therefore, the required H2 storage capacity of Nb-functionalized graphene could be achieved. The following section will be devoted to H2 storage on Nb-functionalized graphene (GR@Nb). 3.3. H2 Adsorption on Graphene Decorated by Niobium Single-Sided (GR@Nb) and Double-Sided (GR@2Nb). To tackle this adsorption problem, we first investigated the interaction of H2 molecules on graphene decorated with niobium atoms on single-sided (GR@Nb) before moving to double-sided (GR@2Nb) storage. As predicted earlier by Cui et al.,44 the dissociation of H2 molecules is a key issue for H2 storage capacity. Therefore, before any serious study, it is important to investigate the dissociation of H2 molecules on GR@Nb. To address this problem, we studied the interaction of GR@Nb with two possible states of hydrogen. The calculated binding energy of GR@Nb with H2 in the molecular state is 0.640 eV compared to 0.471 eV for the atomic state. These values suggested that the interaction of GR@Nb with H2 is more favorable in the molecular form than in the atomic form. These results suggested that further studies must be conducted on GR@ Nb in order to test if it can be regarded as a promising sorbent for storage for mobile applications.10 To do so, the equilibrium parameters of the resulting reaction were determined, and we found a stretching of the H−H bond length from 0.749 Å for free H2 to 0.848 Å for the H2 + GR@Nb complex. On the other hand, the optimized structure of the atomic state of H2 + GR@Nb reveals that the distance between H−H is 2.997 Å compared to 1.86 Å in the case of Pt-functionalized single-wall carbon nanotubes.47 We also reported that the average distance between Nb and H atoms (d-Nb−H) is 1.805 Å for the complex H2 + GR@Nb as compared to 1.57 Å for H2− SWNT.47 Since the interaction of H2 molecules with GR@Nb can occur in two different configurations, to better visualize the reaction path, we connected these two stable configurations. To do so, we used a transition state (TS) search to find the intermediate point between these two states. The potential

Figure 6. Potential energy diagram showing the energies of the chemical species and transition state (TS) from the atomic to molecular configuration of H2 adsorbed on GR@Nb. The green balls denote Nb, the white balls represent H atom, and the gray balls represent carbon atom of graphene.

Figure 6 reveals that the reaction path from atomic state to the quasi-molecular state for the interaction of H2 with GR@Nb is endothermic with an energy of reaction of 0.169 eV and it has 0.233 eV as the energy barrier. These values suggested that additional investigations were needed on the successive addition of H2 molecules on GR@Nb in order to assess the storage capacity. This next section is focused on that research. The optimized structures are provided in the Supporting Information (see Figure S1). The binding energy of nH2-GR@ Nb (n = 1−7) along with their equilibrium parameters (the average distance between H atoms and Nb atoms (daveNb−H), the average bond length of H2 (daveH−H), and their corresponding bandgap) are summarized in Table 2. We Table 2. Average Binding Energy (Ebave) of the Successive Addition of H2 Molecules on GR@Nb Complex along with Their Equilibrium Distances between H−H Atom (daveH− H) and Nb and H Atom (daveNb−H) and Bandgap (Eg) no. H2

Ebave (eV)

dave H−H (Å)

daveNb−H (Å)

Eg (eV)

1 2 3 4 5 6 7

0.656 0.680 0.637 0.528 0.500 0.475 0.398

0.861 0.860 0.847 0.831 0.838 0.839 0.827

1.943 1.934 1.947 1.962 1.955 1.974 2.123

1.066 1.330 1.069 1.070 1.080 1.405 0.805

observed an increase of the binding energy for the first two additions of H2 on GR@Nb, where the adsorption energy changes from 0.646 to 0.674 eV. The corresponding parameter daveNb−H goes from 1.943 Å for the first H2 addition to 1.934 Å for the second H2. In addition, we observed a shortening of H2 bond length (daveH−H) for the second H2 addition, where daveH−H was 0.861 Å for the first H2 and 0.859 Å for the second one. However, for n = 3 to n = 7 the average binding energy decreased gradually from 0.630 to 0.390 eV, the average daveH−H fluctuated between 0.827 and 0.847 eV, and the average daveNb−H increased from 1.947 to 2.123 Å. We further explored the thermodynamic kinetic stability by E



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Figure 7. Side and top views of theee relaxed structures of H2 adsorption on GR@2Nb. The green balls represent the Nb atom, gray balls represent the C atoms, and the white balls represent H atoms.

consider that graphene decorated with niobium on a single side can absorb 6H2 molecules before reaching saturation. Since graphene can be decorated on both sides, the remaining part of this discussion is on double-sided Nb-decorated graphene (GR@2Nb). In order to determine its adsorption capacity, we examined the interaction of H2 with Nb-functionalized graphene (GR@ 2Nb). To begin with, we studied the electronic and physical properties of the successive addition of H2 molecules on a GR@2Nb complex. Figure 7 displays the optimized structures of this process. The average binding energies (Ebave) of nH2 molecules on GR@2Nb and their equilibrium parameters, the average distance between H atoms (daveH−H), the average distance between Nb and H atoms (daveNb−H), and the

calculating the energy difference between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), which represents the bandgap energy defined as Eg = (E LUMO − E HOMO)

(7)

Using eq 7, the bandgap energy (Eg) was determined, and the results are summarized in Table 2. The fifth column of Table 2 reveals that the kinetic stability reached its maximum for the first six H2 additions at Eg = 1.4050 eV and decreased to a minimum value of Eg = 0.805 eV as the seventh H2 molecule was added. Since the kinetic stability is related to the highest value of Eg, we can say that the system reached its maximum stability after the adsorption of the sixth H2 molecule. We can F



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energy gap (Eg), are summarized in Table 3. From Figure 7, we can assume that the interaction of H2 with GR@2Nb complex

molecules. However, from 6 to 14 H2 we observed a gradual decrease of Ebave with the increasing number of H2 molecules to a minimum value of 0.390 eV. The variations of daveH−H and daveNb−H are displayed in Figures 8c and 8d, respectively. Figure 8c shows some fluctuation of daveH−H; however, it varies in a small window from 0.839 to 0.854 Å. From 8 to 14 H2 molecules, a smooth decrease of daveH−H is observed (from 0.849 to 0.816 Å) as depicted in Figure 8c. The distance daveNb−H changed slightly from 1.948 to 1.991 Å for the addition of up to 12 H2 molecules and increased to 2.370 Å for the addition of the 14th H2 molecule Figure 8d. In addition, we calculated the distance between Nb atoms and the nearest carbon atom of the graphene sheet (d-C−Nb). This distance increased from 2.376 to 2.680 Å by increasing the number of adsorbed H2 molecules from 2 to 14 H2, and a complete desorption of the nH2−Nb was observed at n = 10. Furthermore, the correlation between the binding energy and the desorption temperature for the successive addition of H2 molecules was found to be approximated by the equation TD = 738Eb + 1.5 that was derived based on the data presented in Figure 8a. These results predict that GR@2Nb can be a promising H2 storage medium if we can eliminate the desorption of the complex nH2−Nb from the graphene sheet that occurs at 10 H2 molecules at d-C−Nb = 2.520 Å on GR@ 2Nb. To elucidate the competition between adsorption and desorption of the adatom from the graphene sheet, different approaches were adopted. As we reported earlier, the monovalence defect can prevent the desorption of sulfur atoms from a graphene sheet.56 We also predicted the complete dissociation of H2S by increasing the concentration of NH radicals on graphene.57 In this work, we introduce nitrogen atoms (N) to the graphene surface as a defect. The present study reveals that by increasing the concentration of N atoms on graphene from 3.6% to 7.25%, the desorption of nH2−Nb complex from GR@2Nb can be suppressed. The optimized structures of the H2 interaction with graphene

Table 3. Average Binding Energy (Ebave) of the Successive Addition of H2 Molecules on GR@2Nb Complex along with Their Equilibrium Distances between H−H Atom (daveH− H) and Nb and H Atom (daveNb−H), the Desorption Temperature (TD), and the Energy Gap (Eg) no. H2 molecules

daveH−H ( Å)

daveNb−H( Å)

TD (K)

Eb (eV)

Eg (eV)

2 4 6 8 10 12 14

0.848 0.854 0.839 0.849 0.833 0.819 0.816

1.974 1.948 1.962 1.951 1.970 1.991 2.370

446 508 476 392 387 303 288

0.603 0.687 0.643 0.530 0.523 0.410 0.390

0.323 0.860 0.141 0.832 1.352 2.122 0.859

occurs layer-by-layer where the first eight H2 molecules represent the first layer. The second layer starts from 10 to 12 H2 molecules and the last layer from 14 H2 molecules. We can say that the number of H2 molecules adsorbed decreased by a factor of 2 when we move from one layer to the nearest one. Moreover, kinetic stability was measured by using eq 7, and the results are summarized in column six of Table 3. The calculated value of Eg predicted that, as the number of available adsorption sites decreased, the kinetic stability of nH2 + GR@ 2Nb increased from 0.323 to 2.122 eV. The saturation level of GR@2Nb was reached at 12 H2 molecules. We observed some instability at Eg = 0.850 eV, which corresponds to 14 H2 molecules. To better represent the changes of equilibrium parameters during the interaction of H2 with GR@2Nb, we plotted Figure 8. We observed an increase in the adsorption energy for the first four H2 molecules from 0.603 to 0.687 eV as we show in Figure 8b where we plotted the change of the average binding energy with the increasing number of H2

Figure 8. Physical and chemical parameters of the successive addition of H2 on GR@2Nb complex. Case (a) corresponds to the variation of the desorption temperature (Td) with respect the average binding energy (Ebave), case (b) represents the variation of the Ebave with the number of H2 molecules, case (c) the changes of daveH−H with respect to the number of H2, and case (d) the variation of daveNb−H with the number of H2 molecules. G



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Figure 9. Side and top views of the relaxed structures of H2 adsorption on 2NGR@2Nb at 7.25% concentration of N atoms. The green balls represent the Nb atom, gray balls represent the C atoms, blue represent N atoms, and the white balls represent H atoms.

is a linear relationship between the desorption temperature (TD) and the binding energy (Ebave) given by TD = 741Eb − 0.751. We also illustrate the change of Ebave with the number of adsorbed H2 molecules on Figure 10b where Ebave fluctuated slightly in the range 0.583−0.611 eV before reaching a minimum for the two last additions of H2 at 0.465 eV. Furthermore, the variations of daveH−H and daveNb−H are represented in Figures 10c and 10d, respectively. These results show that daveH−H ranged from 0.810 to 0.852 Å, while daveNb−H ranged from 1.944 to 2.435 Å. Moreover, the distance between Nb atoms and the nearest carbon atom of 2NGR@2Nb surface (dC−Nb) was also determined. Based on

functionalized with Nb at 3.6% concentration of N atoms (NGR@2Nb) are provided in the Supporting Information (see Figure S2), and at 7.25% concentration of N atoms (2NGR@ 2Nb) are depicted in Figure 9. The calculated physical and chemical parameters are summarized in Table 4 along with their corresponding energy gaps. In addition, the densities of state of pristine graphene, Nb-decorated graphene (GR@Nb), and nitrogen-doped (at 7.25%) Nb-decorated graphene (2NGR@Nb) are given in the Supporting Information (see Figure S3). To better visualize the relationship between the equilibrium parameters, we plotted them as a function of the number of H2 molecules in Figure 10. Figure 10a shows there H



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Snapshots of MD simulations of 7H2−2NGR@Nb and 7H2−Nb are also provided in the Supporting Information (see Figure S5). To monitor the effect of air contamination in our system, we explored the interaction of GR@Nb with oxygen molecules (O2). Since O2 interferes strongly with H2 on the metal adsorption site, as reported by Sigal et al.59, for practical purposes it is important to investigate the interaction of O2 with the GR@Nb system. To calculate the strength of the binding of O2 with GR@Nb and the coadsorption of H2 and O2 on GR@Nb, we used the following three equations:

Table 4. Average Binding Energy (Ebave) of the Successive Addition of H2 Molecules on 2N GR@2Nb Complex along with Their Equilibrium Distances between H−H Atom (daveH−H) and Nb and H Atom (daveNb−H), the Desorption Temperature (TD), and the Energy Gap (Eg) no. H2

daveH−H (Å)

daveNb−H (Å)

TD (K)

Eb (eV)

Eg (eV)

2 4 6 8 10 12 14

0.850 0.852 0.842 0.854 0.835 0.820 0.810

1.976 1.956 1.968 1.944 1.962 2.337 2.435

431 451 452 426 450 388 344

0.583 0.610 0.611 0.576 0.608 0.524 0.465

0.375 0.367 0.452 0.351 1.069 1.072 1.050

our calculation, dC−Nb ranged between 2.353 and 2.375 Å for the 2NGR@2Nb system compared with 2.376 and 2.680 Å for the GR@2Nb complex. In addition, the computed bandgap is also shown in the last column of Table 4. We observed that the doping of N atoms on GR@2Nb does not affect the trend we observed earlier for Eg. We obtained the highest value of Eg at 12 H2 with Eg = 1.072 eV, and this value decreased to 1.050 eV for 14 H2, which means it reached a kinetic instability point. These results confirm what was earlier stated by Li et al.58 In addition, the thermal stability of the 2NGR@2Nb system was also calculated at T = 800 K, and the final structure is illustrated in the Supporting Information (see Figure S4). Even at T = 800 K, the system 2NGR@2Nb remained stable, which means that H2 storage on 2NGR@2Nb is feasible. Moreover, a MD simulation was also performed at T = 600 K for hydrogen adsorption on single-sided Nb-decorated graphene doped with nitrogen at 7.25% (7H2−2NGR@Nb) and H2 adsorption on bare niobium (7H2−Nb) at T = 500 K in order to compare these results with those obtained by using the Van’t Hoff equation. The obtained results show that at T = 500 K all the H2 of 7H2−Nb are desorbed; the same is also observed at T = 600 K for the 7H2−2NGR@Nb system, which is closer to the values of temperatures using the Van’t Hoff equation.

EO2 = EO2 + EM − EM + O2

(8)

Eads + H2 = E H2 + EM + O2 − EM + O2 + H2

(9)

Eads + O2 = EO2 + EM + H2 − EM + O2 + H2

(10)

In eq 8, EO2 is the energy of an isolated O2 molecule, EM the energy of GR@Nb in the case of the GR@Nb complex, and EM+O2 the total energy of the O2 + GR@Nb system. Equation 9 represents the adsorption energy of H2 in the presence of O2 for the system GR@Nb, and eq 10 defines the binding energy of O2 in the presence of H2 for these same systems. The relaxed structures are presented in Figure 11 along with their binding energies. By using eq 8, we found that the adsorption energy of an O2 molecule on GR@Nb was EO2 = 3.051 eV compared to the 3.16 eV for Ni-doped graphene (GR@Ni), 2.14 eV for Pd-doped graphene (GR@Pd), and 2.35 eV for Ptdoped graphene (GR@Pt) as stated by Sigal et al.59 As calculated earlier, the binding energy of H2 on GR@Nb was 0.656 eV compared to −1.12 eV for GR@Ni, −0.66 eV for GR@Pd, and −1.65 eV for GR@Pt complexes. The displacement energy (Edis), which is the energy necessary to substitute one oxygen molecule with one H2 molecule, is defined as the energy difference between the adsorption energy of O2 and H2 molecules on GR@Nb as (Edis = EO2 − EH2). We predicted that Edis = 2.395 eV compared to 2.04 for Ni-doped graphene; it is

Figure 10. Physical and chemical parameters of the successive addition of H2 on 2NGR@2Nb complex. Case (a) corresponds to the variation of the desorption temperature (Td) with respect the average binding energy (Ebave), case (b) represents the variation of the Ebave with respect to the number of H2 molecules, case (c) the changes of daveH−H with respect to the number of H2, and case (d) the variation of daveNb−H with respect to the number of H2 molecules. I



Article

Figure 11. Represents the optimized structure of the interaction of O2 molecule with GR@Nb and the coadsorption of H2 and O2 on GR@Nb complex where red atom stands for O atom, gray atom represents carbon atom C, the green atom stands for Nb atom, and the white ball for H atom.

emphasizing that increasing the concentration of N atoms on graphene can enhance considerably the binding of Nb metal on a graphene sheet and may suppress the desorption of nH2− Nb complex on graphene as we increase the number of H2 molecules. The O2 interference with H2 on the active site is not a very big issue for our system compared to what was reported earlier by Sigal et al.59 The binding energies also lie in the energy interval for a promising mobile H2 storage system.4

1.48 eV for Pd-doped graphene and 0.70 eV for Pt-doped graphene as reported by Sigal et al.59 We also evaluated the binding energy of H2 in the presence of an O2 molecule for the GR@Nb complex. Using the eq 9, we estimated that the adsorption energy of H2 in the presence of O2 is Eads+H2 = 0.217 eV and that can be compared to 0.18 eV for Ni-doped graphene, 0.22 eV for Pd-doped graphene, and 0.33 eV for Ptdoped graphene as calculated by Sigal et al.59 Since this is a reversible process, the adsorption of O2 in the presence of H2 on the GR@Nb system was also assessed by means of eq 10, and we found that Eads+O2 = 2.628 eV. This value can be compared to 2.23 eV for Ni-doped graphene, 1.69 eV for Pddoped graphene, and 1.03 eV for Pt-doped graphene as reported earlier by Sigal et al.59 To better visualize the interactions of O2 with GR@Nb matrix, we summarize the above results in Table 5. These results show that the presence

4. CONCLUSION In summary, to pursue the search for material for storage of hydrogen for mobile applications, we used first-principles calculations based on density functional theory (DFT) to study the interaction of H2 with free Nb and Nb-decorated graphene (GR@Nb) complex. We predicted that free Nb atoms can bind six H2 molecules in the binding energy interval (0.228− 0.630 eV) in the quasi-molecular form, and the maximum temperature to desorb all the absorbed H2 would be 466 K. Furthermore, our study of the interaction between Nb atoms and graphene demonstrated that the clustering of Nb atoms on graphene is probably unlikely since the diffusion of Nb on graphene between two adjacent hallow sites requires an energy barrier of 0.432 eV, much higher than its thermal vibration energy, which is 0.025 eV at room temperature. Moreover, we show that our complex GR@Nb can absorb six H2 in the energy window of 0.398−0.680 eV in the quasi-molecular form. We also predicted that the successive addition of H2 molecules on Nb-decorated doubled-sided graphene induced the desorption of the nH2−Nb complex from the graphene sheet when the number of H2 molecules was higher than 10 at a distance dC−Nb = 2.680 Å. We also demonstrated that the desorption process of the nH2−Nb can be suppressed by increasing the concentration of N atoms on the graphene surface. In addition, the interference between O2 and H2 on the adsorption site of GR@Nb indicates that the energy required to replace one H2 with O2 was 2.395 eV. Finally, we predict that the desorption of nH2−Nb complex can be suppressed when 7.25% of N atoms are doped on graphene and the storage capacity of 2NGR@2Nb is 8 wt %. Due to the high weight of niobium compared to carbon, we can easily say that 2NGR@Nb is more promising than bar niobium for mobile applications. Even though O2 is a drawback for

Table 5. Adsorption Energy of Hydrogen (EH2), Oxygen (EO2), Their Displacement Energy (Edis), the Adsorption Energy of O2 in the Presence of H2 (Eads+H2) and the Adsorption Energy of H2 in the Presence of O2 (Eads+O2) for Nb-Doped Graphene (GR@Nb), Ni-Doped Graphene (GR@Ni), Pd-Doped Graphene (GR@Pd), and Pt-Doped Graphene (GR@Pt) Complexes binding energies

GR@Nb (eV)

ref 59 (GR@ Ni) (eV)

ref 59 (GR@ Pd) (eV)

ref 59(GR@ Pt) (eV)

EH 2

0.656

−1.12

−0.66

−1.65

EO 2

3.051

3.16

2.14

2.35

Edis Eads+O2

2.395 2.628

2.04 2.23

1.48 1.69

0.70 1.03

Eads+H2

0.217

0.18

0.22

0.33

of O2 contamination in our sample diminished the storage capacity of H2 in the GR@Nb complex by interfering with H2 on the active site. Even though the binding energy of O2 on GR@Nb is higher than that of H2 on GR@Nb, oxygen molecule displacement energy and adsorption energy are very close to Ni-doped graphene; therefore, one can solve this issue by pressurizing the sample at the vacuum level before any hydrogen testing. We can partially conclude this section by J



Article

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hydrogen storage, the results obtained predicted that Nbdecorated graphene doped with at least 7.25% of nitrogen atoms is a promising medium for hydrogen storage in mobile applications. Experimental studies are required in order to verify this prediction.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b09498. Figures S1−S5 (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. ORCID

Omar Faye: 0000-0003-0520-6238 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Engineering Research Council of Canada and the Canada Research Chair program. For useful comments we thank Dr. Tanveer Hussain (School of Molecular Sciences, The University of Western Australia, Perth, WA 6009, Australia).

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