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J. Phys. Chem. C 2009, 113, 14512–14517
Hydriding and Dehydriding Kinetics of Sodium Alanate at Constant Pressure Thermodynamic Driving Forces H. Yang, A. Ojo, P. Ogaro, and A. J. Goudy* Department of Chemistry, Delaware State UniVersity, DoVer, Delaware 19901 ReceiVed: March 7, 2009; ReVised Manuscript ReceiVed: June 17, 2009
A study was done to compare the hydriding and dehydriding kinetics of the first two decomposition steps in NaAlH4. In the first step, NaAlH4 decomposes forming Na3AlH6. In the second step, Na3AlH6 decomposes forming NaH. This comparison was made using a novel procedure in which the ratio of the equilibrium plateau pressure (Pm) to the opposing pressure (Pop), or the N-value, was the same. This represents the first time that such a comparison has been made in a complex hydride displaying two decomposition steps. Since the Gibbs free energy change is proportional to ln(Pm/Pop), it was concluded that these experiments were carried out under constant thermodynamic driving forces. It was found that, under these conditions, the first decomposition step occurs about an order of magnitude faster than the second decomposition step. Experiments were also done to compare absorption and desorption rates for the second decomposition step. It was found that, using the same N-value, the absorption rates were about 20 times faster than desorption. Modeling studies showed that the absorption kinetics are most likely controlled by reaction at a moving boundary. Desorption reactions displayed a more complex behavior in which no single model described the entire process. Indications are that nucleation and growth control the reaction rate in the early stages but that diffusion through a product layer may control the rate in latter stages. 1. Introduction Sodium alanate, NaAlH4, has attracted considerable interest in recent years because of its potential for hydrogen storage. It was demonstrated by Bogdanovic and coworkers1,2 that Ti-doped NaAlH4 can reversibly absorb and desorb hydrogen as described in the following mechanism:
1 2 NaAlH4 T Na3AlH6 + Al + H2 (3.7 wt %) 3 3
(1)
1 1 1 Na AlH6 T NaH + Al + H2 (1.9 wt %) 3 3 3 2
(2)
Since this material has 5.6 total weight percentage of hydrogen that is thermodynamically available at moderate temperatures, scientists have studied it extensively to determine its suitability for hydrogen storage. In recent years, many of these studies have focused on finding ways of improving the sorption characteristics of sodium alanate. Zaluska et al.3 were able to improve dehydrogenation kinetics by mechanical grinding both with and without the addition of carbon. Sandrock et al.4 measured the cyclic capacity, the charging and discharging rates, and the thermal effects over a wide temperature range and found that TiCl3 catalyst gave better results than the alkoxide-catalyzed materials that had been used previously. Zidan et al.5 reported that doping sodium alanate with titanium and zirconium precursors lowered the dehydriding temperatures of the reactions in eqs 1 and 2 thus resulting in greatly enhanced dehydrogenation kinetics. Bogdanovic et al.6 recently reported that rare earth elements such as cerium and praseodymium as * To whom correspondence should be addressed.
well as scandium may be even better catalysts for the hydrogenation of sodium alanate than titanium precursors. In other studies, investigators have done kinetics studies on sodium alanate in order to determine the mechanism that controls reaction rates. Since sodium alanate reacts in two steps, there have been some attempts to determine the relative rates of both reaction steps. Kircher and Fichtner7,8 did some kinetic studies on Ti-doped NaAlH4 and found that the decomposition kinetics of Na3AlH6 were slower than the first decomposition step of NaAlH4. On the basis of their results, they concluded that the first decomposition step of NaAlH4 could be best described by a nucleation and growth model. Sandrock et al.9 also performed kinetics studies and concluded that the discharge of hydrogen from NaAlH4 to Na3AlH6 was faster than the decomposition of Na3AlH6 to NaH. Kiyobayashi et al.10 however did a similar study and found that both NaAlH4 and Na3AlH6 undergo dehydrogenation at nearly equal rates. They concluded that the kinetics are probably influenced by processes such as nucleation and growth and/or long-range atomic transport phenomena. Thus, there appears to be some disagreement about the relative reaction rates of the first and second decomposition steps in NaAlH4. This is an example of the types of disagreements that are likely to result when investigators are not specific about the reaction conditions that have been used to collect data. Goudy and coworkers11-13 saw similar disagreements when they did some detailed kinetic studies on LaNi5 and its analogues. The reaction rates being reported by various investigators at that time differed by as much as 3 orders of magnitude. Goudy and coworkers were able to demonstrate that a number of conditions must be carefully controlled if different investigators are to make meaningful comparisons in kinetic results. It is important to control factors such as temperature, pressure, particle size, and thermodynamic driving force. They showed that, for desorption reactions, this thermodynamic driving force was directly proportional to the logarithm of the
10.1021/jp902073u CCC: $40.75 2009 American Chemical Society Published on Web 07/22/2009
Hydriding and Dehydriding Kinetics of NaAlH4
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Figure 1. Schematic diagram of the apparatus used for performing kinetics measurements.
ratio (midplateau pressure/applied pressure). For absorption reactions, the thermodynamic driving force was directly proportional to the logarithm of the ratio (applied pressure/ midplateau pressure). In the present research study, the methods developed in our laboratory by Goudy and coworkers have been used, for the first time, to compare the kinetics of the two decomposition steps in NaAlH4. 2. Experimental Methods The sodium alanate and titanium chloride used in this research were obtained from Sigma Aldrich. The materials were greater than 95% pure and were used without further purification. All samples were handled in a vacuum/atmospheres argon-filled glovebox to protect them from exposure to air and moisture. The glovebox was capable of achieving less than 1 ppm oxygen and moisture. Prior to analysis, the sodium alanate and 2.0 mol % titanium chloride were milled for an hour in a SPEX 8000 M mixer/mill that contained an argon-filled stainless steel milling pot. The ball-to-powder ratio in the pot was 5:1. The sample was then transferred into a stainless steel reactor and subjected to PCI analyses. PCI analyses were done in a gas reaction controller-PCI unit. This apparatus was manufactured by the Advanced Materials Corporation in Pittsburgh, PA. The unit was fully automated and was controlled by a Lab View-based software program. High purity hydrogen gas of 99.999% purity was used throughout the analyses. The experimental apparatus used to perform kinetics measurements is shown schematically in Figure 1. It consisted essentially of a stainless steel manifold with ports for adding hydrogen, venting, and evacuating. Pressure regulators were installed to control the hydrogen pressure applied to the sample and to allow hydrogen to flow to or from the sample into a remote reservoir. The sample was subjected to at least 10 absorption/desorption cycles prior to analysis to achieve a reasonably stable kinetic state. When comparing the kinetics of two or more samples, this apparatus could allow each sample to be measured at the same constant pressure driving force. 3. Results and Discussion It is known that, when hydrogen is added to or removed from sodium alanate under isothermal conditions, the resulting isotherm displays two plateau regions.2 The two plateaus correspond to the two reactions shown in eqs 1 and 2. Since one of the goals of this research was to perform absorption and desorption kinetics in each plateau region, it was necessary to construct the pressure composition isotherms. Figure 2 contains absorption and desorption isotherms for sodium alanate that were done at 160 °C. The higher pressure plateau, in each isotherm, corresponds to the reaction shown in eq 1, and the lower plateau
Figure 2. Absorption and desorption isotherms for NaAlH4 at 160 °C.
corresponds to the reaction in eq 2. Some hysteresis is also evident in these isotherms. Other researchers have also observed a similar amount of hysteresis in the NaAlH4 system.2 3.1. Kinetic Measurements. Absorption kinetic measurements were performed in the lower plateau region. This was done by evacuating the hydrogen from the sample then adjusting the hydrogen pressure in the sample reactor to a value just slightly lower than that of the midplateau pressure (Pm), to ensure that only the hydrogen deficient hydride phase was initially present. The reactor was sealed off, and the pressure in the remaining system (Pop) was then adjusted to a value such that the ratio of the opposing pressure to the midplateau pressure was a small whole number. This ratio (Pop/Pm) in the remainder of the text has been referred to as the N-value. The gas from the high pressure reservoir was allowed to flow through the pressure regulator and into the sample reactor. Absorption kinetic measurements were performed only in the lower plateau region because the equipment used in the research was not capable of achieving the very high pressures that would be required to achieve the desired N-values when analyzing the upper plateau region. Figure 3 contains plots of reacted fraction versus time for the absorption of hydrogen during the lower plateau reaction at 160 °C and N ) 2, 3, and 4. At this temperature, Pm was 8.33 atm. Therefore the Pop necessary for N ) 2, 3, or 4 was set at 16.66, 25.0, or 33.33 atm respectively. Figure 4 contains plots of the pressures in the sample reactor and in the remote pressure reservoir at N ) 2. The plots show that Pop remains virtually constant as hydrogen is absorbed by the sample whereas the pressure in the remote pressure reservoir decreases over time as hydrogen flows from it into the sample reactor. The rate of pressure decrease in this reservoir is a direct measure of the reaction kinetics. It is clear from the plots in Figure 3 that the
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Figure 3. Plots of absorption fraction (f) vs time (t) at 160 °C with N-values of 2, 3, and 4 for the lower plateau reaction.
Figure 4. Pressure in the reactor and reservoir for the absorption reaction at 160 °C and N ) 2.
Figure 5. Plots of absorption fraction (f) vs time (t) at 160, 170, and 180 °C with an N-value of 2 for the lower plateau reaction.
reaction rates increase as the N-value increases. This demonstrates that it is important to perform kinetics reactions at constant N-values. Figure 5 contains plots of reacted fraction versus time during the lower plateau reaction at several temperatures while keeping the N-value constant. In this case, the N-value was set at 2, and the temperatures were set at 160, 170, and 180 °C. This confirmed that, when the thermodynamic driving force is kept constant, the reaction rates increase with increasing temperature. Desorption kinetic measurements were performed in both of the plateau regions. This was done by adjusting the hydrogen pressure in the reactor to a value just slightly higher than that of the midplateau pressure (Pm), to ensure that only the hydrogen rich phase was initially present, and sealing off the reactor. The
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Figure 6. Absorption kinetic modeling measurements at 160 °C with 1 1 N-values of 2, 3, and 4, plotted as (1 - f) /3 vs t /2 for the lower plateau reaction.
pressure in the remaining system (Pop) was then adjusted to a value such that the ratio of the midplateau pressure to the opposing pressure was a small whole number. In the case of desorption, this was accomplished by using the same ratio of the equilibrium plateau pressure (Pm) to the applied hydrogen pressure (Pop). The N-value in the case of desorption is defined as the ratio Pm/Pop. In these experiments, hydrogen was allowed to flow out of the sample, through a regulator, and into a low pressure reservoir. As the sample released hydrogen, the regulator prevented any pressure change in the sample reactor by allowing the necessary amount of the hydrogen to flow out of the reactor and into the pressure reservoir. 3.2. Kinetic Modeling Studies. The hydriding reactions can possibly be described by any of several kinetics models. These include diffusion, moving boundary, and nucleation and growth. To determine which, if any, of these kinetics models describe these reactions, it was necessary to construct plots corresponding to the theoretical equations. The theoretical equations are summarized below:
(1 - f)1/3 ) 1 -
√kt R
(3)
(1 - f)1/3 ) 1 -
( Rk )t
(4)
f ) 1 - exp(-ktn)
(5)
Equation 3 corresponds to a diffusion-controlled process; eq 4 depicts a process that is limited by reaction at a moving boundary; eq 5 represents a nucleation and growth controlled process. In these equations, f is the reacted fraction, t is the time, k is a rate constant, R is the radius of the hydride particles, and n is a constant that depends on the geometry of the system. If diffusion were controlling the rates, then according to eq 3, 1 1 a plot of (1 - f) /3 versus t /2 should be linear. Figure 6 contains such plots for the absorption reaction at 160 °C and N ) 2, 3, and 4. The nonlinear nature of these plots shows that diffusion is not the rate-limiting process. On the basis of eq 4, a moving boundary controlled reaction should result in a linear plot of (1 - f)1/3 versus t. Figure 7 contains such plots, and they are indeed linear under the conditions used. Therefore, the moving boundary model is a plausible mechanism. Finally, according to the nucleation and growth model represented by eq 5, a plot
Hydriding and Dehydriding Kinetics of NaAlH4
Figure 7. Absorption kinetic modeling measurements at 160 °C with 1 N-values of 2, 3, and 4, plotted as (1 - f) /3 vs t for the lower plateau reaction.
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Figure 9. Pressure in the reactor and reservoir for the desorption reaction at 160 °C and N ) 2.
Figure 10. Plots of desorption fraction (f) vs time (t) at 160 °C with N-values of 2, 3, and 4 for the lower plateau reaction. Figure 8. Absorption kinetic modeling measurements at 160 °C with N-values of 2, 3, and 4, plotted as -ln(1 - f) vs t for the lower plateau reaction.
of -ln(1 - f) versus t should be linear, assuming that n ) 1. The plots based upon this model are shown in Figure 8. The slight curvature in each plot indicates that this model is not applicable in this case. An attempt was also made to model the desorption reaction in the lower plateau region. In the case of desorption, the lower plateau reaction is the forward reaction in eq 2. Any of three processes could control the rate: small nuclei of NaH and Al must form and grow as H2 is released; a chemical reaction must occur at the boundary between the various phases; and a hydrogen containing species must diffuse away from the interface to reach the surface of the solid. To determine what process controlled the reaction rate, it was necessary to perform the reaction at constant N-values, as was done with the absorption reaction. Figure 9 contains plots of the pressure in the reactor and the reservoir for a sample that desorbed hydrogen at 160 °C and N ) 2. At this temperature, Pm ) 4.5 atm. Therefore, the pressure regulator was set to maintain the reactor pressure at 2.25 atm. The kinetics were monitored by measuring the increase in reservoir pressure versus time. In order to describe what model best describes desorption kinetics, it was again necessary to construct plots of reacted fraction versus time. Figure 10 contains such plots for desorption at 160 °C and N ) 2, 3, and 4. As was the case for desorption, the reaction rate increases with increasing N-value. By using the data for these plots, it was then possible to test the models described by eqs 3-5 and determine which, if any, of them fit the experimental data. Figures 11-13 contain the plots corresponding to these equations. It can be seen that none of these
Figure 11. Desorption kinetic modeling measurements at 160 °C with 1 1 N-values of 2, 3, and 4, plotted as (1 - f) /3 vs t /2 for the lower plateau reaction.
plots are linear over the course of the reaction. This indicates that no single mechanism controls the rates over the entire course of the reaction. A closer examination of the plots shows that some of them display good linearity over certain stages of the reaction. The plots that particularly exemplify this are those in Figure 13. It can be seen that in the early stages of the reaction, nearly linear behavior is exhibited. There is a change in slope during midreaction that might be caused by a change in the rate-controlling process. Thus, the mechanism, in the case of desorption, is complex. To get a better determination of how the mechanism changes over time, -ln(1 - f) versus t plots were made using reaction fractions in the range 0-0.5. The plots are shown in Figure 14. Good linearity is displayed in each plot indicating that nucleation and growth is the likely rate-
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Figure 12. Desorption kinetic modeling measurements at 160 °C with 1 N-values of 2, 3, and 4, plotted as (1 - f) /3 vs t for the lower plateau reaction.
Figure 13. Desorption kinetic modeling measurements at 160 °C with N-values of 2, 3, and 4, plotted as -ln(1 - f) vs t for the lower plateau reaction.
Figure 14. Desorption kinetic modeling measurements for reaction fraction (0-0.5) at 160 °C with N-values of 2, 3, and 4, plotted as -ln(1 - f) vs t for the lower plateau reaction.
controlling process during the first 50% of the reaction. Plots 1 1 of (1 - f) /3 versus t /2 were constructed in the 0.7-0.9 range to determine if diffusion was perhaps the rate-controlling process during the latter stages of the reaction. These are presented in Figure 15. The good linearity that is displayed supports the idea that diffusion through a product layer may control the rates in this range. It should be noted that the modeling curves for desorption in the upper plateau region display nonlinearity similar to that seen for the lower plateau region. An analysis of these data indicated that a similar mechanism controls the desorption reaction rates in both plateau regions. 3.3. Comparison of Reaction Kinetics. It was also of interest to make comparisons of the reaction rates for absorption and desorption of hydrogen in the lower plateau region. Since
Yang et al.
Figure 15. Desorption kinetic modeling measurements for reaction fraction (0.7-0.9) at 160 °C with N-values of 2, 3, and 4, plotted as 1 1 (1 - f) /3 vs t /2 for the lower plateau reaction.
Figure 16. Plots of absorption and desorption fractions (f) vs time (t) at 160 °C with an N-value of 2 for the lower plateau reaction.
the absorption and desorption reactions corresponding to the lower plateau were performed at the same temperatures and the same N-values, it should be possible to make a valid comparison of the intrinsic absorption and desorption rates. Factors such as particle size, surface morphology, and so forth should not be an issue, since the same sample was used throughout. Figure 16 contains plots of reacted fraction versus time for the absorption and desorption reactions at N ) 2 and 160 °C. It can be seen that the absorption rate is about 20 times faster than the desorption rate. This is a further indication that the rate-controlling processes are different in these two cases. It was also possible to perform desorption kinetics of the reaction corresponding to the upper plateau. Desorption measurements were done at 160 °C and N ) 4 and 5. It was not possible to do runs at N ) 2 and 3 due to some limitations of the equipment that was used. Since a lower plateau desorption reaction kinetics measurement was also done at 160 °C and N ) 4, it was possible to compare the kinetics of the reactions corresponding to the two plateau regions at the same temperature and N-value. Figure 17 contains plots of reacted fraction versus time for the desorption reactions done at 160 °C and N ) 4 for the upper and lower plateau reactions. It is evident that the upper plateau reaction proceeds about an order of magnitude times faster than the lower plateau reaction under these conditions. Since higher plateau pressures generally denote lower stability, the observed differences in rates are most likely due to differences in stability of the reactants and products in each process. It should be noted that Goudy and coworkers did similar studies on ErCo3H414 and Dy2Co7H9.15 Each of these systems forms interstitial hydrides with isotherms that display two plateau regions. In each case, the upper plateau reaction reacted much faster than the lower plateau.
Hydriding and Dehydriding Kinetics of NaAlH4
J. Phys. Chem. C, Vol. 113, No. 32, 2009 14517 through a product layer may control the rate in latter stages. Additional modeling studies must be done on sodium alanate and related materials under various conditions to further test these models and determine if the mechanisms observed here are universal in nature. Acknowledgment. This work was financially supported by grants from the BP Foundation, the U.S. Department of Transportation, and the U.S. Department of Energy. References and Notes
Figure 17. Plots of desorption fractions (f) vs time (t) at 160 °C with an N-value of 4 for both lower and upper plateau reactions.
4. Conclusions This study has shown that it is possible to compare the intrinsic reaction rates of the hydriding and dehydriding reactions in titanium chloride catalyzed sodium alanate under equivalent reaction conditions. When this was done, it was demonstrated that the decomposition of NaAlH4 occurs about an order of magnitude faster than the decomposition of Na3AlH6. This is most likely related to higher bonding enthalpies in Na3AlH6. It was also demonstrated that the absorption reaction occurs about 20 times faster than the desorption reaction. The large difference in hydriding/dehydriding reaction rate is most likely due to the involvement of different rate-controlling processes. Modeling studies demonstrate that the moving boundary model best describes the absorption process but the desorption mechanism is more complex. Indications are that nucleation controls the reaction rate in the early stages but that hydrogen diffusion
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JP902073U
