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Effects of a Carbon Surface Environment on the Decomposition Properties of Nanoparticle LiBH4: A First-Principles Study Tim Mason and E. H. Majzoub* Center for Nanoscience, and Department of Physics and Astronomy, University of Missouri−St. Louis, St. Louis, Missouri 63121, United States ABSTRACT: We present a first-principles study of small clusters of LiBH4 supported on graphene sheets in order to address the experimentally observed effects of the nanoconfinement of LiBH4 in hard carbon nanoframeworks prepared from low-temperature pyrolysis of phenolic resins, where a fullerenerelated structure with significant sp2 character is known to exist. Our results indicate that the wetting of carbon by LiBH4, as observed in experiments, is not energetically favorable without the introduction of boron substitution defects in the graphene sheet. The simplest defect, consisting of a carbon vacancy, introduces favorable wetting energies via the partial decomposition of LiBH4. Heteroatom boron in place of the carbon vacancies interacts with lithium and small clusters of the remaining LiBH4, making wetting of these clusters favorable. It is also predicted that the desorption product LiH will be ejected from the framework, in agreement with recent in situ TEM work. imately 100−150 °C from confining LiBH4 in a porous carbon with a surface area of 500 m2 g−1 as measured by Brunauer− Emmett−Teller (BET). Reversibility is significantly improved by the nanoconfinement with the composite sample releasing 5.8 wt % H2 after being recharged at relatively mild conditions of 320° and 40 bar for 120 min. When combining the scaffolding with the Ni catalysts, reversible releases of 9.2 wt % H2 were reported.4 The work of Liu et al.5 sheds further light on how the decomposition pathways of LiBH4 may be altered by nanoconfinement. In that experimental study, highly ordered nanoporous carbons (NPCs) were prepared by organic− organic assembly of copolymers PEO−PPO−PEO with resols via an evaporation-induced self-assembly technique. Lowtemperature pyrolysis, around 1000 °C, of these resins results in a carbon material with highly ordered pores featuring a very narrow pore size distribution with a diameter of approximately 2 nm. LiBH4 was melt-infiltrated into the carbon pores at 300 °C and 60 bar of H2 without needing to functionalize the carbon. This composite material reversibly absorbs and desorbs hydrogen at temperatures lower than that of bulk LiBH4. Recent in situ TEM work shows that, upon heating of the hydride-containing NPC, lithium hydride crystals begin to form outside of the pores.6 To understand why LiBH4 wets the carbon, and why LiH forms outside the NPC on decomposition, we use firstprinciples calculations that model LiBH4 in the nanoporous carbon environment as small clusters of LiBH4 on the simplest carbon template: a graphene sheet. We will justify the use of

I. INTRODUCTION With a theoretical hydrogen storage capacity of 18.5% by mass, LiBH4 has garnered much attention from researchers as a potential hydrogen storage material with the capacity requirements suitable for light-duty vehicles. It has many possible desorption pathways depending on whether the reaction proceeds in bulk or nanoparticle form. Two possible reactions are listed below. We neglect other possibilities, such as the formation of Li2B12H12, seen in the decomposition of LiBH4,1 that are outside the scope of this work.2 The reaction in eq 1 is observed above the melting temperature (about 550 K) in bulk samples and proceeds with an enthalpy of 74 kJ mol−1 H2.3 LiBH4 → LiH + B +

3 H2 2

LiBH4 → Li + B + 2H 2

(1) (2)

Unfortunately, in its bulk form, it is too stable for practical automotive use, releasing hydrogen only after heating above 400 °C. Further, reversibility is very poor as bulk LiBH4 rehydrogenates to only 8.3% after 200 min at 600 °C under 155 bar of H2. Two primary strategies have been attempted to engineer composite materials around LiBH4 with more practical properties. The first approach is to introduce catalysts, such as Pt, Ni, and carbon nanomaterials. This has yielded some success in lowering the desorption temperature. Ball-milling with Ni, for example, has been shown to lower the desorption temperature to 300 °C but does not adequately improve the recharging conditions (600 °C, 100 bar for 30 h to charge to 12 wt % H2).4 The second approach has been to confine the particle size of the metal hydride in order to utilize surface kinetics and thermodynamics more favorable to hydrogen release. Ngene et al. report a decrease in desorption temperature of approx© 2014 American Chemical Society

Received: October 2, 2013 Revised: April 3, 2014 Published: April 4, 2014 8852

dx.doi.org/10.1021/jp409819g | J. Phys. Chem. C 2014, 118, 8852−8858

The Journal of Physical Chemistry C

Article

extra carbon layers beyond the first had no effect on their results.16 This makes intuitive sense given the weak interaction between each carbon sheet in graphite, in which the carbon layers interact only through van der Waals forces. A study by Valencia et al. on lithium adsorption on graphite reports that, while geometries are not significantly affected by the number of layers used, binding energies do increase by about 0.1 eV when a second layer is included, but a third layer adds no significant change.17 We can thus presume that, for the relatively strongly reacting adsorbates (lithium and boron), excluding the sheet will cause us to slightly underestimate the binding energies. Rigid Lattice Approximation for the Graphene Substrate. The same study also finds significant effects from the number of k-points used on the bonding energy of lithium adsorption. They note a change in bonding energy from 0.76 eV for a single Γ k-point to 1.55 eV when using a 9 k-points grid on their 32 atom system surface. They show that this is due to the fact that, in the Γ calculation, the first excited state is far above the Fermi level, which raises the resulting energy of the charge transferred from the lithium atom. In the present work, beginning geometries were found by relaxing candidate structures with only a Γ k-point. The resulting configurations with the lowest energies were then recalculated with a 2 × 2 × 1 Γ-centered Monkhorst sampling grid. The final 2 × 2 × 1 results were used to calculate the wetting energies discussed herein. We also assume that the graphene sheet itself is not perturbed by the active material. To validate this assumption, VASP selective dynamics was used on selected samples to allow the 50 closest carbon atoms to the adsorbate to fully relax. In the case of a single boron adsorbate relaxed directly above a carbon atom in the sheet (see Figure 1.), relaxing the neighboring carbon atoms resulted in calculated C−C bond lengths of 0.146 nm, only 4 pm above unperturbed 0.142 nm of C−C bonds in graphene. The next-nearest bond length was 0.144 nm, and the next after that was 0.142 nm, the same as in unperturbed graphene. The total relaxation resulted in a total decrease in energy of 115 meV.

such a model, based on characterization of nanoporous carbons prepared using low-temperature pyrolysis of phenolic resins.

II. COMPUTATIONAL METHODS We calculate total energies of Li−B−H adsorbate clusters of varying size on a graphene surface using first-principles density functional theory (DFT). The VASP package7−10 was used with the interaction between the ion cores and the valence electrons represented with the projector augmented wave method (PAW),11,12 in combination with the correlationexchange functional of Perdew and Wang.13 A plane-wave energy cutoff of 600 eV was used, and because the unit cells for these calculations are very large, only one k-point at Γ was used for most calculations. Selected runs were refined with a 2 × 2 × 1 Γ-centered Monkhorst−Pack grid. We used a 98 atom (7 × 7 × 1) graphene supercell for our adsorbate calculations, and convergence tests using higher k-point densities indicate that our total energies are converged to within 4 meV. All structural parameters were relaxed until the forces on the ions were below 0.005 eV/Å. Justification of a Graphene Substrate for the Carbon Surface. The structure of disordered carbons depends on the synthesis technique. The NPC carbons prepared by Liu et al.5,14 are X-ray amorphous. They are prepared from pyrolysis of phenolic resins at around 800−1000 °C. Low-temperature pyrolysis (around 1000 °C) of phenolic resins results in no obvious graphitic domains in TEM, and although they are characterized as “glassy carbons”, higher pyrolysis temperatures of around 3000 °C are required to produce large-scale fullerene-like structures.15 The NPC carbons may be loosely characterized as “glassy”, but are pyrolyzed at a lower temperature (around 1000 °C), and consist of smaller fullerene domains with edge termination dangling bonds. Finally, modeling amorphous carbons with a large amount of disorder is computationally expensive, and simulations of disordered carbon networks would be difficult to justify given the lack of adequate structural characterization of the atomic arrangements. As an approximation, we model the carbon environment as a single graphene sheet (this is a 7 × 7 × 1, 98atom supercell, as shown in Figure 1.) and place nanoclusters of

III. RESULTS AND DISCUSSION Adsorption Energies. To isolate size effects, energies were calculated for isolated nanoparticles of Li, B, LiH, and LiBH4 for one to four formula units. The PEGS method was used to generate prototype geometries for the ionic LiBH4 and LiH.18 In this method, a simplified Hamiltonian involving only the electrostatic interaction is used to search configuration space for minimum energy configurations using Monte Carlo methods. For the simpler Li and B clusters, it was possible to generate several candidate geometries by hand. For all clusters, multiple prototype configurations were relaxed in DFT and the geometry with the lowest energy was chosen for comparisons in this study. The adsorption energies were obtained using the following method. First, a single primitive cell of graphene was relaxed. For this step only, the cell size was also allowed to relax until stresses were less than 0.1 GPa. The unit cell c axis was set to 16 Å to provide a vacuum layer sufficient to minimize the effects of periodic image interaction. From this relaxed structure, a (7 × 7 × 1) supercell was created, resulting in a sheet of 98 carbon atoms as seen in Figure 1. Calculations were then accomplished by placing adsorbed materials on the sheet at chosen locations and orientations and allowing ions to relax. In the relaxation, the dimensions of the supercell are static and only the adsorbed materials are allowed to move within the cell

Figure 1. A 7 × 7 × 1 (98 atom) supercell of graphene (left panel) was used for adsorption calculations. Cyan atoms represent carbon atoms that were allowed to relax to determine the effect of the rigid sheet approximation. Relaxing the rigid lattice approximation (right panel) introduces minor bond length changes.

adsorbate above the surface. The adsorbate is then allowed to relax to a local minimum energy configuration. This was done for each component of the reaction: Li, LiH, B, and LiBH4 at a varying number of formula units. We neglect the effect of the graphene layers below the surface of the pore. In their DFT study of platinum nanoparticles adsorbed on graphite, Wang et al. report that 8853



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while the carbon atoms are kept fixed. The energy of the absorbed material Ead is then calculated as follows

Ead =

(Eas − Es) f.u.

Table 1. Lowest-Energy Configurations and Their Wetting Energies (eV) for Each Member of LiBH4 Desorption Reactions for One to Four Formula Units on a Perfect Graphene Sheeta

(3)

where Eas is the total DFT energy for the adsorbate relaxed onto the sheet, Es is the total energy of the sheet in isolation, and f.u. is the number of formula units. Charge density plots of a single formula unit of LiH or LiBH4 revealed very little charge transfer from the clusters to the graphene sheet. This suggests that, for the case of the ionic compounds on a perfect sheet, van der Waals forces are important. The VASP package offers a semiempirical van der Waals pair potential following the method of Grimme,19 hereafter referred to as the VdW correction. For comparative purposes, many calculations in this effort were performed in duplicate, once with, and once without, this empirical correction. We will see, however, that very little qualitative effect was found beyond a small number of slight variations in the ionic configurations described below. Low-Energy Configurations. Table 1 shows the results of the lowest-energy configurations of adsorbed clusters of Li, B, LiH, and LiBH4. This was accomplished by placing the nanoparticles in differing orientations above each of the three sites in graphene (see Figure 2.), either directly above a carbon bond (A site), directly above a hexagon center (B site), or directly above a carbon atom (C site), and allowing the system to relax onto the sheet. The final lowest-energy configurations achieved are discussed below. Lithium. One notes that the lowest-energy configuration for a single lithium atom is a B-site in the center of a hexagon, as is the case for a LiC6. Bader analysis20 indicates 89% charge transfer from the lithium atom to the graphene sheet, over which it appears to be evenly distributed. At two formula units, when the lithium atoms are placed on neighboring carbon atoms or even two carbon atoms separated by a common neighbor, the lithium relaxes to a position slightly off center from the carbon atom in opposing directions, a symptom of the fixed carbon lattice not allowing a natural lithium separation distance. Here, we note a difference in the ground-state geometry when the VdW dispersion energy is included. When the dispersion term is not included, the lowest energy occurs when the two lithium atoms are stacked vertically above the sheet. With dispersion included, the system prefers the horizontal layout in which the two atoms are pushed out almost to the hexagon center. The two geometries are separated by 170 meV with dispersion enabled and 191 meV with dispersion disabled, indicating that the two states are not degenerate, and that this is a case in which including the VdW correction yields significantly different results. This is somewhat surprising because the significant charge transfer to the carbon atoms suggests that ionic bonding would dominate when compared to dispersion forces. At three formula units, both with and without dispersion forces, a vertical triangle above the sheet is preferred to a horizontal triangular arrangement. The four-formula-unit system also finds agreement with both methods preferring a pyramid structure. The single lithium atom results agree well with the Valencia study that also finds preferential geometry with the lithium atom on top of the hollow center of the hexagon. That work also shows charge density plots that clearly show charge transfer from the lithium s shell to the π bonds closest to the lithium atom as well as some decrease in charge from the σ bonds of the same atoms. Our bonding energies are within 10

a

Except for the case of two formula units of lithium, including Grimme’s VdW correction does not affect minimum energy configurations.

meV of theirs at Γ and our 2 × 2 × 1 bonding energy is within 20 meV of their 9 k-point system, finding good agreement with and supporting our choice of approximations. Boron. In contrast with lithium, a single atom of boron preferred residing directly above a carbon atom, consistent with p shell bonding, instead of over a hexagon center. Switching the boron atom with the carbon atom in the lattice was found to increase the energy by more than 2 eV, ruling out the possibility of boron displacing carbon atoms in a perfect sheet. With two boron atoms, two stable configurations were found. In the first, boron atoms are placed on consecutive carbon atoms, and in the second, boron is stacked vertically on a carbon atom. Initial configurations of spaced boron atoms on the sheet relaxed to a stacked configuration. As was the case for lithium, stacking above the sheet was preferred to layering by 350 meV. At three and four formula units, the preference for forming boron clusters, instead of a monolayer on the sheet, persisted with triangular and square planar configurations. Lithium Hydride. For many different configurations of LiH at one formula unit, very little charge is transferred from the 8854



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Figure 3. Wetting energies, defined as Eads − Ebulk/f.u., of defect-free graphene sheet as compared to Ebulk: the van der Waals term was omitted (black), the van der Waals term was included (red), and for the nanoparticles in isolation with no graphene sheet present (green). Figure 2. Positions of initial configurations for nanoclusters on the carbon: (A) on top of the carbon−carbon bond, (B) on top of the hexagon center, and (C) directly above a carbon atom.

and for the ionic clusters, it raises the energy. While these offsets are somewhat large, including dispersion does not alter the conclusions of our analysis. The result of increased wetting energies suggests that the VdW term introduces artifacts that increase the total electronic energy. The plot also reveals that there are only minor differences between the adsorbed and isolated nanoparticles, which indicates the weakness of the surface interaction. Only lithium shows a lowering of the energy (370 meV/f.u. at four f.u.), consistent with the large amount of charge transferred to the sheet seen in the Bader analysis.21 Boron, LiH, and LiBH4 have nearly identical energies when compared to their isolated particle counterparts, indicating almost no surface interaction. Effect of Carbon Vacancies. As seen in Figure 3, none of the compounds involved in LiBH4 desorption appear to wet a pure defect-free sheet of graphene as determined by the energies Eadsorbate and Ebulk. We, therefore, alter our model to include the simplest possible defect in the sheet to represent the amorphous nature of the carbon that will invariably include dangling bonds from vacancies, and grain boundaries for very small fullerene-like domains. Specifically, we introduce a single vacancy by removing a carbon atom from the supercell sheet and allowing the resulting system to relax to an equilibrium configuration, as shown in Figure 4. This vacancy is of type V from the work of Mochida et al.22 on lithium trap sites in hard carbons. These defects result from

ionic unit to the sheet, suggesting that van der Waals forces will be important. Indeed, without Van der Walls forces being considered, large energetic changes are only found by inverting the ionic unit, resulting in a 220 meV preference for the lithium atom facing the sheet. Shifting the unit in this configuration from the hexagon center to directly over a carbon atom results in a change of only 21 meV. Including the empirical van der Waals correction, however, results in the hexagon center being a favorable position by 140 meV. Energies at higher formula units were accomplished by placing clusters generated via PEGS18 onto the sheet with a lithium atom facing the hexagon center. For two, three, and four formula units, the favorable energy state was found to be a planar ring of alternating atoms, again with small amounts of surface interaction. Lithium Borohydride. The LiBH4 study was accomplished in a similar fashion to LiH with similar results and negligible charge transfer to the graphene. A configuration with the positive lithium cation facing the sheet favored the inverted configuration by 178 meV. Placement above the hexagon center was favored over the top of a carbon atom by 15 meV. Clusters generated from PEGS were all planar, similar to that of LiH, and were also the lowest-energy structures found when placed on the sheet, consistent with a small amount of interaction with the graphene. Wetting Energies. Wetting energies are defined in this work as Ewet = (Ead − Ebulk)/f.u. to convey the energy gained or lost from bulk material entering the pores and adsorbing onto the surface. We emphasize that our thermodynamic reference state is bulk material. These are plotted in Figure 3 for both the cases of the dispersion correction being included or omitted. Also plotted, for reference, are the energies of the isolated nanoparticles relative to bulk defined as (Enano − Ebulk) per formula unit, which were calculated without the van der Waals correction. One first observes that all configurations yield positive wetting energies, in contradiction with the experimental observation that LiBH4 naturally wets the carbon, indicating that the model of a pure graphene sheet is not entirely correct. We also note that, for all four materials, the wetting curves follow almost identical trends when enabling and disabling the van der Waals correction. For lithium, the only metallic cluster, the VdW term lowers the wetting energy,

Figure 4. A graphene sheet with a single vacancy as the simplest model for the introduction of dangling bonds. 8855



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Table 2. Wetting Energies of Various Compounds for One Formula Unit of Adbsorbate on Both a Perfect Graphene Sheet and One with a Vacancy Defecta adsorbate

wetting of perfect slab Ead − Ebulk

wetting of vacancy Ewv

LiBH4

0.98

−0.86

0.90

LiH lithium boron

2.07 1.05 6.06

−0.79 −0.75 −5.80

1.66 −1.13 3.61

wetting of boron−lithium in vacancy

wetting of boron-filled vacancy (on boron−bulk)

1 fu: 4 fu: 0.16 0.56 4.65

−0.52 −0.20

a

Columns 4 and 5 show the wetting energies for boron substituted in the vacancy, and an additional Li atom at the boron defect, respectively. Note the positive energies for all compounds on the perfect sheet showing the need for vacancies to account for wetting. All energies are in eV.

downhill, which may indicate why a large amount of capacity is immediately lost with respect to bulk as much of the boron becomes immediately trapped by strong bonding with unsaturated carbon. A lithium atom relaxes to a minimum 1.6 Å above the vacancy with roughly the same amount of charge transfer according to Bader analysis but with an energy 1.8 eV lower than that on the pure sheet. Lithium hydride is seen to react strongly with the vacancy by way of the hydrogen atom disassociating and bonding to one of the carbon atoms that borders the vacancy, lowering the energy by 2.86 eV and achieving a strong wetting energy of −0.79 eV. LiBH4 achieved the weakest wetting energy of only −0.86 eV as the result of a simple relaxation where two hydrogen atoms disassociate from the [BH4] unit to unite with the dangling carbon bonds in the vacancy. This configuration still leaves two H atoms bonded to the boron atom. An even lower energy can be obtained by manually moving a third hydrogen atom to the vacancy, achieving a wetting energy of −1.48 eV with a single hydrogen atom remaining attached to the boron atom. VASP linear response25 was used to calculate phonon frequencies for the B− H bonds. These are listed in Table 3, and compared with those

the calcination of heteroatoms in the hexagonal plane, leaving a vacancy. With respect to lithium insertion, they have a near equal chemical potential to the more abundant sites that arise from voids between the hexagonal planes of two adjacent graphitic domains. This implies a strong chemical similarity between these types of defect sites and justifies the single vacancy as an efficient means of modeling the dangling bonds that approximates the edge defects that would be more computationally costly. Further, the density of dangling bonds in amorphous carbons is well-known and is large, about 2 × 1020 cm−3.23 Given this density, a thickness of 10 Å (this is reasonable and perhaps conservative considering micropores) would contain roughly 1 × 1013 cm−2 dangling bonds. Graphene has a unit cell area of 0.051 nm2; therefore, we expect 1 in 100 unit cells to have boron filling the vacancy. One hundred unit cells of graphene has a radius of about 12.7 Å, so there should be roughly 25 Å between neighboring boron defects. This distance is the length of four unit cells of LiBH4 in the Pnma structure. Further, it is known that, upon decomposition of bulk LiBH4, the reaction products contain boron in a phase that is usually X-ray amorphous.1 It is plausible that this boron will interact with the dangling bonds in the framework during melt infiltration. Finally, carbons prepared from phenolic resins, pyrolyzed at temperatures of 1000 °C, are purposely doped with boron for use as supercapcitors.24 This directly supports our assertion that boron will dope NPC carbons and strongly supports our conclusions. We argue that the wetting energy is dominated by boron substitution in the carbon framework. This is most efficiently and convincingly demonstrated by using the most simple defect and structure possible. That our model provides agreement with the experiment6 lends further validity to our approach. To investigate the effects of the vacancy in the lattice on wetting energies, single formula units of the compounds were placed above the vacancy and allowed to relax while keeping the carbon fixed. Wetting energies for sheets with a single vacancy are then defined as Ewv =

Eav − (E bulk + Ev ) f.u.

Table 3. B−H Stretching and Bending Mode Frequencies Calculated by VASP Linear Response at Γ for Bulk LiBH4 and Various Configurations of BH4 in the Vacancy system LiBH426

experimental bulk experimental LiBH4 in carbon5 bulk LiBH4 BH4 in vacancy with 1 H on boron BH4 in vacancy with 2 H on boron

bending (cm−1)

stretching (cm−1)

1090−1099 1100 1066−1304 1056 1037, 1243

2157−2177 2200−2300 2348−2439 2149 2027, 2211

of the B−H bonds in bulk LiBH4. One would suppose that, if this configuration indeed occurs, it would disappear permanently after the first dehydrogenation in which, with the hydrogen desorbed, the boron atom would take full occupancy of the vacancy, as the energetics prefer boron in the vacancy instead of hydrogen by about 5 eV. Boron-Doped Graphene Sheets. Placing the single formula unit nanoparticles directly above boron doping sites was also attempted to evaluate whether boron doping might explain the wetting of LiBH4 observed in experiments. Given the favorable energetics of boron doping, it is plausible that, after hydrogen cycling, many of the vacancies are filled with boron atoms. The results in Table 2 for LiBH4 indicate that, in this state, there is no LiBH4 wetting. However, since lithium does exhibit considerable wetting energies on the boron-doped surface, we can consider a new surface in which

(4)

where Ewv is the wetting energy, Eav is the DFT energy of the adsorbate in the vacancy, and Ev is the energy of the vacancy defined as the DFT energy of the isolated graphene sheet in which one carbon atom is missing. Table 2 summarizes the wetting energies. As expected, boron finds a natural place in the lattice participating fully in the sp2 bonding skeleton, yielding a dramatic 6 eV reduction in energy as compared to the boron αbulk phase. This causes desorption reactions to be strongly 8856



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Figure 5. LiBH4 on a boron dopant that has been wetted with lithium (stereoscopic image for cross-eyed viewing).

IV. CONCLUSIONS We have examined the wetting properties of small clusters of Li, LiH, and LiBH4 in contact with a carbon substrate to gain an understanding of some of the underlying physical processes that occur in a carbon-based nanoframework material. Using a graphene sheet as a simple model of amorphous carbon successfully reproduces several experimental results of nanoconfined LiBH4 if one also introduces vacancies in the graphene, without which even simple wetting cannot be explained. Our results suggest a wetting mechanism for LiBH4 in which partial decomposition of molten LiBH4 produces Li−B defect centers that provide the necessary lowering of LiBH4 cluster/surface energies to result in wetting of the pores. This model also predicts the ejection of small clusters of LiH after desorption, which is observed in in situ TEM experiments.

lithium atoms are located adjacent to the boron dopants. Calculating DFT results for LiBH4 placed on this new surface (see Figure 5) results in a favorable wetting energy of −0.52 eV for a single formula unit. When this calculation is performed with the four-formula-unit cluster as the adsorbate, a wetting energy of −0.2 eV (−0.05 eV/f.u.) results. This is reasonable because the Li−B defect will see less of the adsorbate for a growing cluster. It will help to explain our results by considering a figure from an earlier publication of ours. See Figure 3 in ref 27. This figure shows the energy of small free clusters in the Na−Al−H system and the ratio of their energies with their corresponding bulk solid phases. Small metallic Na and Al clusters have energies much higher than their bulk energies (per formula unit), and they deviate a great deal from E/Ebulk = 1, corresponding to the energy per formula unit for full bulk solid. The high energy of free metallic nanoparticles is well-known.28 What is more interesting are the relative energies, E/Ebulk, for either NaH, or NaAlH4 nanoclusters. A one- or two-formula-unit cluster of NaAlH4 is nearly at the bulk energy per formula unit (within a few %), while NaH still requires eight or more formula units to be within 10% of the bulk energy. For small clusters of LiH and LiBH4, the results are nearly identical, with the total energy ratio E/Ebulk for one formula unit equal to 0.61 and 0.94, respectively. Our wetting results are easily understandable in this context. We take our thermodynamic reference state as bulk, and there is a smaller energy penalty to remove one LiBH4 cluster from bulk, compared to one formula unit of LiH from its bulk. Therefore, the binding energy for one formula unit of LiBH4 is favorable (with the defected sheet), whereas, for LiH, it is not. One could speculate that, during the melt-infiltration process, LiBH4 reacts with the dangling carbon bonds to partially decompose the molten LiBH4, releasing H2, in agreement with the loss of capacity seen in experiment.5 The new Li−B defect centers then provide the necessary lowering of surface energies to result in wetting of the pores with the remaining LiBH4. Strikingly, LiH exhibits positive wetting energies, suggesting that it would be ejected from the carbon after hydrogen desorption. This is indeed observed in in situ TEM experiments by House et al.6 Finally, we note that, while a single hydrogen atom will bond with the boron defect, adding a second hydrogen atom in the vicinity and allowing the system to relax via DFT causes both of them to separate from the sheet and form an H2 molecule. This result suggests that the trapped boron atoms may even act as catalytic centers for hydrogen desorption, perhaps improving kinetics, and explaining, in part, the lowered observed desorption temperatures.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially supported by the U.S. Department of Energy in the Hydrogen, Fuel Cells, and Infrastructure Technologies Program through the office of Energy Efficiency and Renewable Energy under Contract DE-AC04-94AL85000, and the Research Board of the University of Missouri.

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REFERENCES

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