Metal hydride hydrogen storage operates on well-defined thermodynamic principles that govern the absorption and desorption of hydrogen. These principles are critical in determining the efficiency, capacity, and operational conditions of metal hydride systems. The core thermodynamic aspects include pressure-composition-temperature (PCT) relationships, enthalpy of formation, and entropy changes during hydrogenation and dehydrogenation. Understanding these factors is essential for optimizing storage performance.

The pressure-composition-temperature (PCT) curve is a fundamental tool for analyzing metal hydride systems. It describes the equilibrium relationship between hydrogen pressure, hydrogen concentration in the metal lattice, and temperature. A typical PCT curve exhibits a plateau region where the metal hydride undergoes a phase transition from a solid solution (α-phase) to a hydride phase (β-phase). The plateau pressure corresponds to the equilibrium pressure at which hydrogen absorption or desorption occurs at a given temperature. The slope and length of the plateau provide insights into the homogeneity of the hydride and its reversible storage capacity. At higher temperatures, the plateau pressure increases, following the van't Hoff equation, which links equilibrium pressure with temperature thermodynamically.

The van't Hoff equation is expressed as:
ln(P_eq) = ΔH/(RT) - ΔS/R

Here, P_eq is the equilibrium plateau pressure, ΔH is the enthalpy of formation, ΔS is the entropy change, R is the universal gas constant, and T is the absolute temperature. This equation highlights the direct relationship between temperature and equilibrium pressure. A higher enthalpy of formation (ΔH) results in a steeper slope in the van't Hoff plot, indicating greater temperature sensitivity of the plateau pressure. The entropy term (ΔS) is primarily associated with the transition from gaseous hydrogen to hydrogen absorbed in the metal lattice and is often approximated as the standard entropy of hydrogen gas (130 J/mol·K for H₂ at standard conditions).

The enthalpy of formation (ΔH) is a key thermodynamic parameter that determines the heat released during hydrogen absorption and the heat required for desorption. Exothermic absorption means that heat must be removed to maintain efficient hydrogen uptake, while endothermic desorption requires heat input to release hydrogen. Metal hydrides are classified as low-temperature (ΔH < 30 kJ/mol H₂), medium-temperature (30–60 kJ/mol H₂), or high-temperature (ΔH > 60 kJ/mol H₂) based on their enthalpy values. Low-temperature hydrides operate near ambient conditions but may have weak binding, leading to lower stability. High-temperature hydrides require significant energy input for hydrogen release but offer stronger binding and higher stability. The choice of hydride depends on the application's thermal management capabilities and operating temperature range.

Entropy changes (ΔS) during hydrogen absorption and desorption are dominated by the loss of hydrogen gas entropy when it transitions into the solid metal lattice. Since gaseous hydrogen has high entropy, its incorporation into a more ordered solid phase results in a substantial entropy decrease. This entropy loss must be compensated by the enthalpy of formation to achieve a favorable Gibbs free energy change (ΔG = ΔH - TΔS). For absorption to occur spontaneously, ΔG must be negative, which is typically achieved through exothermic reactions at moderate temperatures. Conversely, desorption requires ΔG to become positive, facilitated by increasing temperature or decreasing pressure.

Thermodynamics also dictate the operational conditions for metal hydride storage systems. The equilibrium pressure must be carefully matched to the application requirements. For example, fuel cell vehicles often require hydrogen delivery pressures between 1–10 bar, necessitating hydrides with plateau pressures in this range at near-ambient temperatures. Stationary storage systems may prioritize higher capacities over precise pressure control, allowing for a broader selection of hydrides. Temperature management is equally critical since excessive heat during absorption can slow kinetics, while insufficient heat during desorption can limit hydrogen release rates. Thermal integration with waste heat sources or active cooling systems is often employed to maintain optimal conditions.

The reversibility of metal hydrides is another thermodynamic consideration. Ideal hydrides exhibit minimal hysteresis between absorption and desorption PCT curves, ensuring efficient cycling. Hysteresis arises from energy losses due to lattice strain, phase nucleation barriers, or interfacial effects, but its magnitude is constrained by thermodynamics. Systems with large hysteresis require higher energy input to reverse the hydrogenation process, reducing overall efficiency.

The maximum theoretical storage capacity of a metal hydride is determined by its stoichiometry and atomic weight. Lightweight metals like magnesium can store up to 7.6 wt% hydrogen (MgH₂), but their high ΔH (> 70 kJ/mol H₂) necessitates elevated temperatures for dehydrogenation. In contrast, intermetallic compounds like LaNi₅ (ΔH ≈ 30 kJ/mol H₂) offer lower capacities (~1.4 wt%) but operate at near-ambient conditions. Thermodynamics thus imposes a trade-off between capacity and operational practicality.

Practical systems must also account for the thermodynamic limitations of multi-component hydrides. Alloying or doping can modify ΔH and ΔS to tailor plateau pressures and temperatures, but these adjustments are bounded by the intrinsic properties of the constituent elements. For instance, destabilizing MgH₂ with additives can reduce ΔH, but the theoretical capacity inevitably decreases due to the inclusion of heavier elements.

In summary, the thermodynamics of metal hydride hydrogen storage are governed by PCT behavior, enthalpy of formation, and entropy changes. These factors collectively determine equilibrium pressures, temperature dependencies, and energy requirements for hydrogen uptake and release. Operational conditions must align with thermodynamic constraints to ensure efficient and reversible storage. While material selection and system design can optimize performance, the fundamental thermodynamic principles remain the foundation of metal hydride technology.