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J. Phys. Chem. C 2007, 111, 1584-1591
Predicting Reaction Equilibria for Destabilized Metal Hydride Decomposition Reactions for Reversible Hydrogen Storage Sudhakar V. Alapati,† J. Karl Johnson,‡,§ and David S. Sholl*,†,§ Department of Chemical Engineering, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213, Department of Chemical and Petroleum Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15261, and National Energy Technology Laboratory, Pittsburgh, PennsylVania 15236 ReceiVed: August 8, 2006; In Final Form: October 13, 2006
Reversible storage of hydrogen still remains one of the biggest challenges for widespread use of hydrogen as a fuel. Light metal hydrides have high hydrogen content but are typically too thermodynamically stable. Destabilization of metal hydrides is an effective way to improve their thermodynamics. First principles calculations have proven to be effective for screening potential destabilized reactions, but these calculations have previously been limited to examining approximations for reaction enthalpies. We have used density functional theory calculations to calculate the reaction free energy and van’t Hoff plots for a variety of potential destabilized metal hydride reactions. Our calculations suggest a multistage approach for efficiently screening new classes of metal hydrides prior to experimental studies.
Introduction Hydrogen is one possible energy carrier for storage and transport of energy that could one day replace fossils fuels. Large scale deployment of vehicular fuel cells will require relatively light weight, low-cost and high capacity hydrogen storage devices.1,2 Current U.S. Department of Energy (DOE) guidelines call for a system storage density of greater than 9 wt % H2 and a volumetric density of 81 kg H2/m3 to enable fuel cell powered vehicles to replace petroleum-fueled vehicles on a large scale.3-5 This volumetric target is considerably higher than the density of compressed H2 at 1000 bar and 0 °C.2,6 In addition to these capacity requirements, the storage system must operate reversibly under relatively mild conditions of temperature and pressure. One of the most promising classes of materials for reaching the storage capacity targets mentioned above are complex metal hydrides such as alanates, amides, and borohydrides of period 2 and 3 metals.7,8 A serious thermodynamic limitation of these materials is that high temperatures are often required to release H2. Stated more precisely, the reaction free energy for decomposition of these materials must lie in a narrow range of values to allow reversible hydrogenation/dehydrogenation at practical temperatures and pressures. A prerequisite for using complex metal hydrides in practical schemes for reversible H2 storage is to identify materials with suitable reaction thermodynamics. Reilly and Wiswall9,10 have shown that the thermodynamics of metal hydride dehydrogenation reactions can be modified by using additives to form compounds or alloys in the dehydrogenated state that are energetically favorable with respect to the products of the reaction without additives. This concept is known as destabilization. This method was first applied toward modifying the thermodynamics of light metal hydrides by Vajo et al.11,12 On the basis of their work, other * Corresponding author. Email:
[email protected]. † Carnegie Mellon University. ‡ University of Pittsburgh. § National Energy Technology Laboratory.
researchers also have predicted destabilization schemes for hydrogen storage applications. The destabilization of LiNH2 using LiH was studied by Chen et al.13,14 This material has shown to have a reversible capacity of 6.5 wt % H2. Pinkerton et al.15 and Aoki et al.16 studied the destabilization of the LiBH4 using LiNH2, a combination of compounds that can release 11.9 wt % H2 on completion. It was reported that this reaction leads to the formation of an intermediate hydride, Li3BN2H8 (later corrected to Li4BN3H10),17 dehydrogenation of which is exothermic at room temperature. Destabilization reactions of Mg(NH2)2 and LiH have also been studied.18-21 The lack of thermodynamic data for many of the compounds that could potentially participate in destabilized metal hydride reaction schemes has greatly limited the number of these reactions that has been considered. We recently showed that plane wave density functional theory (DFT) can be used to estimate thermodynamic data for large numbers of possible compounds.22 In that work, we used DFT to approximate the reaction enthalpy at 0 K in the absence of zero-point energy corrections, ∆H ≈ ∆U(T ) 0 K), where ∆U is the change in the total electronic energy per mole of H2. These calculations identified five new destabilized reactions that have high gravimetric and volumetric densities and also have reaction enthalpies close to the range necessary for reversibility at mild conditions. These five reactions are listed in Table 1. To examine the reactions listed in Table 1, or other promising reactions, in more detail, it is clearly desirable to characterize the free energy of reaction rather than the approximate reaction enthalpy used in our earlier work. The aim of this paper is to present an analysis of this kind. The temperature-dependent enthalpic and entropic contributions to the free energies of solids can be predicted from first principles calculations by computing the phonon density of states for the materials of interest.23 The phonon density of states approach also has been used by researchers to analyze the structural stability of H-containing compounds and more recently to study the temperature dependent formation enthalpy of NaH.24-26 We have performed these calculations for four of the reactions listed in Table 1. Once
10.1021/jp065117+ CCC: $37.00 © 2007 American Chemical Society Published on Web 01/10/2007
Reversible Hydrogen Storage
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TABLE 1: Reactions with 15 e ∆U(T ) 0K) e 75 kJ/mol H2 and Gravimetric Densities >6.5 wt % Identified Using DFT Calculations22 a reaction 3 LiNH2 + 2 LiH + Si f Li5N3Si + 4 H2 4 LiBH4 + MgH2 f 4 LiH + MgB4 + 7 H2 7 LiBH4 + MgH2 f 7 LiH + MgB7 + 11.5 H2 6 LiBH4 + CaH2 f CaB6 + 6 LiH + 10 H2 LiNH2 + MgH2 f LiMgN + 2 H2
energy of each solid can be written as
G ) U - TS + PV = U0 + Uvib(T) - TSvib(T) + PV
wt.% H2 ∆U(T ) 0 K) 7.16 12.46 12.99 11.69 8.19
34.2/23.3 69.2 71.5 62.7 31.9
a The first reaction lists results for materials with varying Si content in the reaction products.
the free energy of reaction has been determined in this way, van’t Hoff plots showing the equilibrium H2 pressure as a function of temperature can be constructed. Results of this type of presented for four of the reactions from Table 1. We also present analogous results for several complex metal hydrides for which experimental data are available. These examples are useful in discussing the accuracy of our DFT calculations. It is important to note that we are limited by the availability of structural information for predicting the reaction enthalpies. It is possible that one or more of the reactions we have identified can proceed via a multistep pathway involving reactants that are not included in the set of known structures we have considered. In such cases, the thermodynamics of each decomposition step would be distinct from the overall reaction examined in our analysis. Our calculations make it possible to separate the contributions of zero-point energy, entropy, and other contributions to the reaction free energies of destabilized metal hydrides. We have used this information to consider how DFT calculations may most efficiently be used to screen potential reaction schemes. Our results show that our initial calculations based on using ∆U(T ) 0 K) as a screening parameter are considerably more accurate than might be expected based on the approximations inherent in this quantity. The observed accuracy is the result of a fortuitous cancellation of errors in the calculations. We show below that using this parameter, which is much easier to calculate with DFT than a reaction free energy, is a good choice for initial examinations of new reactions. The initial calculations can be supplemented by more detailed free energy calculations if the reaction has promising thermodynamics. The work presented in this paper is limited to identifying materials for reversible H2 storage with acceptable reaction thermodynamics. Once materials with acceptable storage capacity and thermodynamics have been found, other considerations such as reaction kinetics will become crucial in examining these materials for practical applications. Our focus on thermodynamics is motivated by the observation that the reaction kinetics of metal hydrides can, at least in principle, be significantly accelerated by using catalysts27 or by controlling the particle size of reactants.28,29 These techniques, however, do not have a significant effect on the overall system’s thermodynamics, except possibly in extreme situations such as in nanoclusters containing
