3. Fundamental concepts about hydrogenation-dehydrogenation kinetics

Most of the hydride compounds and hydride systems cannot work at the temperature predicted by the thermodynamics. This fact is related to kinetic constraints, leading to notable higher operative temperatures than that thermodynamically feasible. For this reason, enhancing the kinetic behavior of hydride compounds and hydride systems has been matter of intensive research. To start with a comprehensive development about the strategies to improve the kinetic behavior of the hydride compounds and systems, it is important to introduce fundamental concepts and details about the experimental method used to understand and to tailor the hydrogenation/dehydrogenation rates, respectively.

The kinetic behavior for the formation/decomposition of a hydride compound gives information about the time required for the material to uptake/release hydrogen in non-equilibrium (dynamic) conditions. Figure 4 shows experimental kinetic hydrogenation and dehydrogenation curves for Nb2O5-doped MgH2. These curves show hydrogen concentration as a function of time. For the sake of clarity, all the explanation and description is referred to a nominal metal hydride (MHx(s), M = metal, H = hydrogen). The absorbed/desorbed hydrogen concentration is expressed in terms of fraction (α), which is the ratio between the absorbed/ desorbed hydrogen concentration at each time during the process and the

Figure 4. (A) Hydrogenation kinetic behavior and (B) dehydrogenation kinetic behavior for metal-hydrogen system.

Tailoring the Kinetic Behavior of Hydride Forming Materials for Hydrogen Storage DOI: http://dx.doi.org/10.5772/intechopen.82433

maximum absorbed/desorbed hydrogen concentration. Under dynamic conditions, the hydrogenation reaction happens when the operative pressure (Pa) is over the equilibrium pressure (Peq) of the hydride phase at the operative temperature (T), Figure 4A. On the contrary, for dehydrogenation under dynamic conditions, the operative pressure (Pd) has to be below the equilibrium pressure (Peq) of the hydride phase at the operative temperature (T), Figure 4B. The procedure to measure a kinetic curve for the hydrogenation/dehydrogenation consist in introducing the hydride forming metal or material in a sealed vessel connected to hydrogen supply and suddenly increase/decrease the hydrogen pressure at a constant temperature, respectively. After the sudden pressure increase/decrease, the operative pressure is kept constant and higher/lower than the Peq for the hydrogenation/dehydrogenation dynamic processes, respectively. The measurement of the kinetic curve runs until reaching saturation, i.e., α = 1.

In order to clarify the complexity of the hydrogenation/dehydrogenation processes under dynamic conditions, the sequence of involving steps can be simply described as follows:

#### 3.1 Hydrogenation process

H2 for some hydride compounds and systems, which have been under intensive

do not meet this requirement at the time to work at low hydrogen pressure.

3. Fundamental concepts about hydrogenation-dehydrogenation

straints, leading to notable higher operative temperatures than that

Most of the hydride compounds and hydride systems cannot work at the temperature predicted by the thermodynamics. This fact is related to kinetic con-

The kinetic behavior for the formation/decomposition of a hydride compound gives information about the time required for the material to uptake/release hydrogen in non-equilibrium (dynamic) conditions. Figure 4 shows experimental kinetic hydrogenation and dehydrogenation curves for Nb2O5-doped MgH2. These curves show hydrogen concentration as a function of time. For the sake of clarity, all the explanation and description is referred to a nominal metal hydride (MHx(s), M = metal, H = hydrogen). The absorbed/desorbed hydrogen concentration is expressed in terms of fraction (α), which is the ratio between the absorbed/ desorbed hydrogen concentration at each time during the process and the

(A) Hydrogenation kinetic behavior and (B) dehydrogenation kinetic behavior for metal-hydrogen system.

thermodynamically feasible. For this reason, enhancing the kinetic behavior of hydride compounds and hydride systems has been matter of intensive research. To start with a comprehensive development about the strategies to improve the kinetic behavior of the hydride compounds and systems, it is important to introduce fundamental concepts and details about the experimental method used to understand and to tailor the hydrogenation/dehydrogenation rates, respectively.

Table 2 clearly indicates that the use of some hydride compounds and systems for solid-state hydrogen storage system working under mild temperature conditions is thermodynamically feasible. Moreover, other cases such as Mg2FeH6 are more suitable for energy storage because of its large enthalpy value. All efforts toward the design of hydride compounds, especially for mobile applications, have been focused on reaching enthalpy values ranging between 40 and 50 kJ/mol H2, leading to an operative temperature between 20 and 90°C. It seems that some materials such as room temperature hydride fulfill these requirements, but the thermodynamic stability is not the unique parameter that determines the practical application of the hydride compound, since the capacity plays a major role. For this reason, high gravimetric hydrogen capacities are required as well, and room temperature hydrides

research [24–31].

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kinetics

Figure 4.

132


The dehydrogenation process proceeds in the opposite way, as described above. In Figure 5, the involved steps during the hydrogenation and dehydrogenation processes in dynamic conditions are shown.

In the previous description (Figure 5), any fluid dynamic and heat transfer restrictions associated to large amounts of material are not taken into account. For instance, fluid dynamic restriction occurs when hydrogen can flow into the material's bed. For the case of the heat transfer restrictions, it is referred to the notable temperature increase or decrease during the exothermic or endothermic hydrogenation or dehydrogenation reaction, respectively. The heat transfer through the hydride bed is not efficient because the thermal conductivity of the hydride compounds is rather low. For these reasons, the analysis on the kinetic behavior and tailoring will be performed for a punctual mass of hydride bed without any fluid dynamic and heat transfer restriction.

There are functional dependences of the hydrogenation/dehydrogenation reaction rates on the temperature, pressure, and morphology of the material. The rates for gas-solid reactions, such as the ones occurring during the hydride formation and decomposition, can be described by Eq. (5) [32, 33]:


contracting models, (3) diffusion models, and (4) autocatalytic models. In Table 3, the integral form of the gas-solid kinetic models is described. There are more gas-solid models, but it is not the aim to perform exhaustive description of them. Among the steps involved in the hydrogenation/dehydrogenation processes (Figure 5), it is usually found a slowest one, which limits the overall reaction rate of the process. Thus, the slowest step is commonly called "rate-limiting step." The determination of the rate-limiting step depends on the kind of hydride and the experimental conditions. Identifying the rate-limiting step requires the application of gas-solid models shown in Table 3. The determination of the rate-limiting step is carried out by measuring kinetic curves under constant temperature and pressure, as the ones shown in Figure 4. Once, the hydrogen uptake and release against time is expressed in terms of hydrogen fraction, α, the integral models can be applied to

Tailoring the Kinetic Behavior of Hydride Forming Materials for Hydrogen Storage

A first approach to study which process limits the hydrogenation/dehydrogenation kinetic behavior is to find which model has the best linear fitting of the integral

build a graph of g(α) as function of time.

DOI: http://dx.doi.org/10.5772/intechopen.82433

Table 3.

135

Integral form of the gas-solid models [32, 33, 36].


#### Figure 5.

Steps involved in the hydrogenation and dehydrogenation processes under dynamic conditions.

$$\frac{da}{dt} = K(T) \times F(P) \times G(a),\tag{5}$$

where the overall reaction rate, dα/dt (α = hydrogen fraction and t = time) is function of the temperature, K(T), of the pressure, F(P), and of the intrinsic and morphological changes of the material occurring during the hydrogenation/dehydrogenation process, G(α), which is function of the hydrogen fraction (α). As shown by Eq. (5), the dependencies of the rate on the K(T), F(P), and G(α) can be investigated independently by keeping two of them constant. In the following sections, each dependence will be explained.
