2.2 Thermodynamics

Thermodynamic properties for the M-H2 systems are usually characterized by measuring pressure-composition-isotherms (PCIs). Figure 3A shows ideal PCIs (without slope and hysteresis), where the x-axis is the hydrogen concentration (CH) expressed as the ratio between atomic hydrogen and metal (H/M), and y-axis is the hydrogen pressure (pH2). The procedure to measure a PCI consist in introducing the hydride forming metal or material in a sealed vessel connected to hydrogen supply and increase steeply the hydrogen pressure at a constant temperature. There are different steps involved during the hydrogen absorption process in a metal under equilibrium conditions. For example, taking the PCI at T2 (Figure 3A), a detailed description of the process during PCI characterization can be done as follows [4, 21]:


$$\mathbf{M}\_{\mathbf{(s)}} + \left(\mathbf{Y}/\mathbf{2}\right)\mathbf{H}\_{\mathbf{2}\left(\mathbf{g}\right)} \leftrightharpoons \mathbf{M}\mathbf{H}\_{\mathbf{Y}\left(s\right)}\left(\mathbf{a}\text{ phase}\right)\tag{2}$$

Figure 3C that the equilibrium pressure for the hydrogenation process is lower than the equilibrium pressure for the dehydrogenation process. This phenomenon is called hysteresis and it is ascribed to localized defects in the metallic lattice and inhomogeneity on the metal's surface [21–23]. Therefore, different equilibrium pressures for

The dependence of the equilibrium pressure (Peq.) on the temperature (T) is

RT � <sup>Δ</sup><sup>S</sup>

where ΔH and ΔS are the enthalpy and entropy changes for the chemical reaction of the hydride phase formation, respectively, and R is the ideal gas constant. Values for ΔH and ΔS can be obtained from the slope and intercept of the linear correlation between the ln(Peq) and 1/T, as shown in Figure 3B. This linear correlation is built from the equilibrium pressures determined by the PCI measurements (pH2 during the plateau region—Figure 3A—from point (b) to point (d)) at each temperature (T1, T2, etc.). ΔS indicates the entropy change for hydrogen, i.e., from molecular gas hydrogen to hydrogen in the hydride phase. For metal-hydrogen systems, the standard entropy change for hydrogen is 130 kJ/K mol, but it can have a different value for other kind of hydride systems as for example for hydrides composed of boron, aluminum, or nitrogen and alkaline or alkaline earth metals [4, 21]. ΔH of the hydride compound or system characterizes the stability of the metal-hydrogen bond (M–H) and it takes a negative value for the exothermic hydrogenation and a positive value for the endothermic dehydrogenation. These two thermodynamic parameters, i.e., ΔH and ΔS, are quite important for hydride forming material design and hence for practical applications. They allow calculating the temperature for the hydrogen release from hydride phase under atmospheric pressure (�1 bar), which refers to the minimum temperature for the dehydrogenation process without any kind of kinetic restriction. Additionally, the thermodynamic properties of the hydride phase provide information about the range of temperature and pressures at which the hydride system works. Table 2 shows the experimental enthalpy, entropy values, and decomposition temperature under 1 bar

R

, (4)

Tdecomposition = ΔH/ΔS at 1bar [°C]

Ref.

the hydrogenation and dehydrogenation processes are usually reported.

Tailoring the Kinetic Behavior of Hydride Forming Materials for Hydrogen Storage

ln Peq <sup>¼</sup> <sup>Δ</sup><sup>H</sup>

ΔH [kJ/mol H2]

(1) The values are reported as an average of the two steps reaction from NaH and Al to NaAlH4 [28].

Dehydrogenation thermodynamic parameters and decomposition temperature under 1 bar H2 for some hydride

(2) Values obtained from hydrogenation PCIs, assuming one reaction step [30]. (3) Entropy calculated from the reported van't Hoff plot [31]. n.a. = not available.

ΔS [J/K mol H2]

LaNi5H6 31.8 110.0 16 [24] MgH2 74 135 275 [25] Mg2FeH6 80 137 311 [26] LiBH4 74 115 370 [27] (1)NaAIH4 42 124 66 [28] LiNH2 45 n.a. - [29] (2)2LiBH4+MgH2 40.5 81.3 255 [30] Mg(NH2)2+2LiH 38.9 107(3) 90 [31]

given by the van't Hoff Eq. (4):

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

Hydride compound/ Hydride system

Table 2.

131

compounds and systems.

4.Increasing the hydrogen pressure, the solid solution (α phase) reaches a hydrogen saturation concentration at H/M = 0.1. From this hydrogen concentration, the hydride phase (β phase) starts to form as shown in Figure 3A—point (b). Significant expansions of the metal's lattice causes strong H–H interactions which result in the nucleation and then further growth of the hydride phase. In an ideal case, the overall process of formation of the hydride phase occurs under constant pressure and is called plateau region in the PCI curve, Figure 3A—from point (b) to point (d). In this region, the solid solution (α phase) and the hydride phase (β phase) co-exist in equilibrium conditions, Figure 3A—point (c). The pressure associated to the plateau region is called equilibrium pressure (Peq.). Reaction (3) describes the process:

$$\mathbf{MH}\_{\mathbf{Y}(\mathbf{s})} \left( \mathbf{a} \text{ phase} \right) + \left[ \left( \mathbf{X} - \mathbf{Y} \right) / 2 \right] \mathbf{H}\_{\mathbf{2}(\mathbf{g})} \leftrightharpoons \mathbf{MH}\_{\mathbf{x}(\mathbf{s})} \left( \boldsymbol{\upbeta} \text{ phase} \right) \tag{3}$$

5. Once the formation of the hydride phase is finished, the hydrogen pressure increases again, as shown in Figure 3A—from point (d). This phenomenon is ascribed to the atomic hydrogen dissolution in the hydride phase.

Under experimental conditions, the equilibrium pressure during the "plateau region" is not perfectly constant, as shown in Figure 3C. The sloppy plateau is attributed to expansions of the lattice of the hydride and relaxations of the metallic matrix, which causes a slight increase of the equilibrium pressure during the chemical reaction of the hydride phase (β phase) formation. Furthermore, it is also observed in

#### Figure 3.

(A) Ideal PCIs for the description of the hydrogen absorption-desorption process through hydride compound formation in equilibrium conditions. (B) van't Hoff plot built from PCIs. (C) PCIs showing the real behavior with slope and hysteresis.

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

Figure 3C that the equilibrium pressure for the hydrogenation process is lower than the equilibrium pressure for the dehydrogenation process. This phenomenon is called hysteresis and it is ascribed to localized defects in the metallic lattice and inhomogeneity on the metal's surface [21–23]. Therefore, different equilibrium pressures for the hydrogenation and dehydrogenation processes are usually reported.

The dependence of the equilibrium pressure (Peq.) on the temperature (T) is given by the van't Hoff Eq. (4):

$$
\ln P\_{eq} = \left[\frac{\Delta \mathbf{H}}{\mathbf{RT}}\right] - \left[\frac{\Delta \mathbf{S}}{\mathbf{R}}\right],\tag{4}
$$

where ΔH and ΔS are the enthalpy and entropy changes for the chemical reaction of the hydride phase formation, respectively, and R is the ideal gas constant. Values for ΔH and ΔS can be obtained from the slope and intercept of the linear correlation between the ln(Peq) and 1/T, as shown in Figure 3B. This linear correlation is built from the equilibrium pressures determined by the PCI measurements (pH2 during the plateau region—Figure 3A—from point (b) to point (d)) at each temperature (T1, T2, etc.). ΔS indicates the entropy change for hydrogen, i.e., from molecular gas hydrogen to hydrogen in the hydride phase. For metal-hydrogen systems, the standard entropy change for hydrogen is 130 kJ/K mol, but it can have a different value for other kind of hydride systems as for example for hydrides composed of boron, aluminum, or nitrogen and alkaline or alkaline earth metals [4, 21]. ΔH of the hydride compound or system characterizes the stability of the metal-hydrogen bond (M–H) and it takes a negative value for the exothermic hydrogenation and a positive value for the endothermic dehydrogenation. These two thermodynamic parameters, i.e., ΔH and ΔS, are quite important for hydride forming material design and hence for practical applications. They allow calculating the temperature for the hydrogen release from hydride phase under atmospheric pressure (�1 bar), which refers to the minimum temperature for the dehydrogenation process without any kind of kinetic restriction. Additionally, the thermodynamic properties of the hydride phase provide information about the range of temperature and pressures at which the hydride system works. Table 2 shows the experimental enthalpy, entropy values, and decomposition temperature under 1 bar


(1) The values are reported as an average of the two steps reaction from NaH and Al to NaAlH4 [28].

(2) Values obtained from hydrogenation PCIs, assuming one reaction step [30].

(3) Entropy calculated from the reported van't Hoff plot [31]. n.a. = not available.

#### Table 2.

Dehydrogenation thermodynamic parameters and decomposition temperature under 1 bar H2 for some hydride compounds and systems.

1. At the beginning of the process, molecular hydrogen (H2) near the metal's surface suffers van der Waals interactions. This H2-M interaction process is

2. Molecular H2 dissociates on the metal's surface (H2 ! H + H) and forms a M-H bond. This process is called chemisorption and the required energy for it

exothermically dissolves to form a solid solution (α phase). This process occurs in the low hydrogen concentration zone (H/M < 0.1), as shown in Figure 3A

Mð Þ<sup>s</sup> þ ð Þ Y=2 H2 gð Þ ⇆ MHY sð Þ ð Þ α phase (2)

3. Chemisorbed H diffuses to the interstitial site of the metal's lattice and

4.Increasing the hydrogen pressure, the solid solution (α phase) reaches a hydrogen saturation concentration at H/M = 0.1. From this hydrogen concentration, the hydride phase (β phase) starts to form as shown in Figure 3A—point (b). Significant expansions of the metal's lattice causes strong H–H interactions which result in the nucleation and then further growth of the hydride phase. In an ideal case, the overall process of formation of the hydride phase occurs under constant pressure and is called plateau region in the PCI curve, Figure 3A—from point (b) to point (d). In this region, the solid solution (α phase) and the hydride phase (β phase) co-exist in equilibrium conditions, Figure 3A—point (c). The pressure associated to the plateau region

is called equilibrium pressure (Peq.). Reaction (3) describes the process:

5. Once the formation of the hydride phase is finished, the hydrogen pressure increases again, as shown in Figure 3A—from point (d). This phenomenon is

Under experimental conditions, the equilibrium pressure during the "plateau region" is not perfectly constant, as shown in Figure 3C. The sloppy plateau is attributed to expansions of the lattice of the hydride and relaxations of the metallic matrix, which causes a slight increase of the equilibrium pressure during the chemical reaction of the hydride phase (β phase) formation. Furthermore, it is also observed in

(A) Ideal PCIs for the description of the hydrogen absorption-desorption process through hydride compound formation in equilibrium conditions. (B) van't Hoff plot built from PCIs. (C) PCIs showing the real behavior

ascribed to the atomic hydrogen dissolution in the hydride phase.

MHY sð Þ ð Þþ α phase ½ � ð Þ X–Y =2 H2 gð Þ ⇆ MHx sð Þ ð Þ β phase (3)

depends on the elements on the metal's surface.

—point (a) and is described by reaction (2):

called physisorption.

Gold Nanoparticles - Reaching New Heights

Figure 3.

130

with slope and hysteresis.

H2 for some hydride compounds and systems, which have been under intensive research [24–31].

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

Tailoring the Kinetic Behavior of Hydride Forming Materials for Hydrogen Storage

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

a. Physisorption: The hydrogen molecule approaches to the metal and interacts

b.Chemisorption: On the metal's surface, the hydrogen molecules dissociate and

c. Penetration through the α phase surface: Hydrogen atoms penetrate the

e. Diffusion through the β phase: Hydrogen atoms diffuse through the β phase

f. Nucleation and growth: The β phase (hydride phase) starts to nucleate and

The dehydrogenation process proceeds in the opposite way, as described above. In Figure 5, the involved steps during the hydrogenation and dehydrogena-

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

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

kinetic curve runs until reaching saturation, i.e., α = 1.

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

with the metal's surface through van der Waals forces.

the atomic hydrogen forms chemical bonds with the metal.

d.Hydrogenation: Formation of the β phase (hydride phase).

described as follows:

3.1 Hydrogenation process

metal's surface.

(hydride phase).

grows with α/β interface movement.

tion processes in dynamic conditions are shown.

dynamic and heat transfer restriction.

133

decomposition, can be described by Eq. (5) [32, 33]:

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