Theoretical calculation based on DFT is widely used to study the reaction mechanism of the hydrogen storage system. Because this study involves microwave field and H⁻ ion, it is difficult to carry out experiments at this stage. Therefore, the crystal structure and energy change of the reaction system are calculated by simulation calculation in the first place. Based on the DFT calculations, the change in thermodynamic properties of the reaction before and after the introduction of the microwave field could be deduced. It is essential to study the activation mechanism of microwave plasma to improve the thermodynamics of Mg-based hydrogen storage from the theoretical aspect.

Before the calculations of energy and properties, the geometry optimization of the unit cell should be first performed to achieve the most stable structure of the crystal. The projection augmented wave method (PAW) was employed to describe the interaction between ions and electrons in the simulation calculation. The iteration stops when the force on all atoms during the ion relaxation process is less than 0.02 eV  / Å, and the total energy variation between the two iterations in the electron relaxation process is less than 10^–5 eV. For the calculation of MgH₂ and H₂ energy, the cut-off energy is 400 and 350 eV, respectively.

As for free hydrogen molecules, the gas molecule is put into a huge cubic unit cell (a = b = c = 10 Å) under the periodic boundary condition for isolating these molecules. As a result, the interaction between different unit cells of the H₂ molecules could be ignored. Moreover, the Monkhorst-Pack mesh k-point for the free gas molecules was set as 3 × 3×3.

The structure models of magnesium and magnesium hydride are constructed as shown in Figure 4. Figure 4A is the crystal structure of Mg, whose space group is P1(#1–1) with the lattice constant of a = b = c = 3.186 Å, α = β = γ = 60°. Figure 4B shows the crystal structure model of magnesium hydride with 2 Mg atoms and 4 H atoms in the cell, whose space group is P42/mn (#136–1) with lattice constant of a = b = 4.517 Å, c = 3.02 Å, α = β = γ = 90°.

Mg and hydrogen molecular generally react in the process of storage as shown in the following equation: Mg + H 2 → MgH 2 + Δ H r 1. (1)

The reaction enthalpy change ( Δ H r 1 ) is calculated by analyzing the energy of reactants and products. Based on the previous DFT energy calculation results, the energies of all the species involved in the hydrogen storage reaction are calculated and summarized in Table 2. Therefore, the reaction enthalpy Δ H r1 of the conventional heating/MgH₂ process could be calculated as follows: Δ H r 1 = E ( Mg H 2 ) − [ E ( Mg ) + E ( H 2 ) + Z P E ( H 2 ) ] , (2) where E ( Mg H 2 ) represents the total energy of MgH₂, E ( Mg ) and E ( H 2 ) represent the energies of Mg and H₂, respectively. Z P E H 2 represents the zero-point energy of hydrogen molecule. This is because the energy of light elements in DFT calculation is inaccurate due to ignoring the contribution of vibration. The ZPE for H₂ is calculated to be 0.27 eV in the previous study (Wu et al., 2018). Accordingly, the reaction enthalpy Δ H r 1 is 79.6 kJ/mol H₂, which agrees well with the reported data of 73–85 kJ/mol H₂ (Sun et al., 2016; Hirscher et al., 2020).

As is well known, the reaction could happen and reach the equilibrium when the Gibbs free energy change is ∆G = 0. The relationship between ∆H and reaction temperature T is expressed in the following equation: Δ G = Δ H − T S , (3) T = Δ H Δ S . (4)

The corresponding value of reaction entropy change ∆S is 130 J/(mol∙K) (Bogdanović et al., 1999). As a result, the reaction temperature of conventional Mg-based hydrogen storage without the microwave plasma is calculated to be about 339°C, which is also close to the reported reaction temperature of 350°C (Bogdanović et al., 1999). The calculation error is approximately 3.2%, indicating that the prediction results by DFT are reasonable to evaluate the thermodynamic properties of the MgH₂ hydrogen storage system.

Figure 5 shows the detailed mechanism of the MW/MgH₂ -AHSP system. When the microwave works, the reactant is stimulated to produce high-energy electrons and other high-activity particles. Next, high-energy electrons in the plasma collide with the vibration-state hydrogen molecules, thus producing the excited H⁻ ions and H atoms (Janev et al., 1987). The produced H atoms further capture low-energy electrons in plasma to generate H⁻ ions. That is to say, H⁻ ions are provided in two ways. Finally, H⁻ ions spread along the gap in the lattice, and combine with Mg²⁺ ions freely.

In this case, the hydrogen storage in plasma is channeled by vibrational and electron excitation as follows: Step   1 :                                                     Mg + MW → Mg 2 + + 2 e (5) Step   2 :                                                     e + H 2 ( v ) → H + H - (6) Step   3 :                                                     e + H → H - (7) Step   4 :                                                     Mg 2 + + 2 H - → Mg H 2 (8)

Microwave irradiates on nano-scale magnesium particles with sharp tips, giving rise to a large energy focus in the microwave region. At the same time, the nano-scale surface roughness further enhances the plasma effect, making Mg convert into Mg²⁺ and releasing active electrons. Subsequently, H₂ and H are ionized as H⁻ via vibrational and active electron excitation.

That is to say, the active components produced in the atmosphere of microwave plasma change the reaction path. Accordingly, the overall reaction equation under microwave plasma is deduced as follows: Mg 2 + + e + H + H − + E A → Mg H 2   + Δ H r 2 , (9) where e is a low-energy electron and E _A is external energy to overcome energy potential barriers, whose value is 0.75 eV. Species activated by microwave plasma require different energy levels to overcome the different barriers of ion hop during diffusion. Furthermore, when electrons combine with the hydrogen atom, the surface electrons need to break through a potential barrier. It is considered that microwave provides energy (E _A) to overcome this potential barrier.

The reaction enthalpy Δ H r2 of MW/MgH₂ - AHSP could be calculated in the following formula: Δ H r 2 = E ( Mg H 2 ) − [ E ( Mg 2 + ) + 1 2 E ( H 2 ) + E ( H - ) + E ( e ) + E A ] . (10)

It is noteworthy that the energy of the low-energy electron is assumed to be -0.1 eV (Janev et al., 1987). In addition, the hydrogen anion is difficult to obtain energy values directly by DFT calculations. Hence, the energy of hydrogen anion is calculated by the following formula: E ( H − ) = E ( H ground-state - Reference ( H ) , (11) where E(H_ground-state) represents the ground state energy of hydrogen atom, Reference(H) is the value of H in POTCAR file, which is calculated as -1.96 eV.

As a result, the reaction enthalpy Δ H r2 of Mg-based hydrogen storage with the help of microwave plasma is significantly reduced to 49.4 kJ/mol H₂. The comparison of reaction enthalpy between the Mg-based hydrogen storage with and without the use of microwave plasma is illustrated in Figure 6. Accordingly, the hydrogenation temperature is also reduced to about 109°C, which is close to the vehicle-mounted hydrogen release temperature requirement of DOE. Figure 7 also compares the reaction temperature of Mg-based hydrogen storage between different enhancing methods, such as MgH₂+LiBH₄+C (Zhong et al., 2016), graphene + MgH₂ (Cho et al., 2016), MgH₂+2Ni₉₀ (Yang et al., 2010), Ti + MgH₂ (Setijadi et al., 2013), and Mg₂Ni (Hanada et al., 2005). It can be clearly seen that the microwave plasma activating hydrogen storage method has the lowest reaction temperature, which strongly indicates that this new modification method is feasible to reduce the hydrogen storage temperature of magnesium hydride.

Based on the previous analysis, it can be seen that a high ionization and dissociation are needed to ensure the production of active particles. It was reported the microwave power of 6 kW is stable for methane transformation (Zamri et al., 2021). Since the dielectric constant of hydrogen is 0.5 MW/m only, which is much lower than that of methane, hydrogen will be more easily ionized by microwave to produce plasma, so the microwave power of 5 kW is supposed to be enough for completing the reaction of producing high-energy hydrogen species.

In the Mg-based hydrogen storage system, the supply of heat is indispensable for the release of hydrogen. Therefore, it is necessary to provide thermal energy for the whole system with the help of external heat sources. Generally, heat is generated by steam via the boiler. Such heat sources need a long-term operation to ensure the stability of the reaction. Usually, the annual operation number is about 8,000 h. By comparison, the process of microwave plasma activating reaction does not require so much time. Specific time is ascertained based on reaction systems, microwave power, and other factors in experiments.

Therefore, it is hard to accurately calculate the reaction time. Some systems need several minutes (Ricard et al., 2001), while some need a few hours (Wongjaikham et al., 2021). But it is certain that the microwave plasma takes much less time than the conventional heating type. In a project funded by DOE, a pulsed microwave catalytic reactor was mentioned, which did not continuously supply energy. Only when the catalyst and reaction need an energy supply, does the microwave work. It was concluded that the pulsed microwave reactor almost doubles the reaction conversion and the product yield (Hu, 2018). This shows that the microwave can achieve a good cost-performance ratio of input to output.

In addition, the microwave promotes the generation of plasma owing to its own thermal effect. The existence of hot spots caused by microwave plasma makes the reactants vulnerable to activation. Microwave energy can be selectively transmitted between the active site and the reaction intermediate, and will not lose to the surrounding environment, thus improving the energy utilization efficiency (Tiwari et al., 2020).

The hydrogen storage system mentioned in this article is a magnesium hydride reactor coupled with a 300 kW SOFC for a heat and power co-generation system. The difference is that the conventional heating/MgH₂ system employs the boiler steam heated by natural gas or coal as the external heat source to provide energy for the whole reaction process. However, the microwave plasma is employed to activate and heat the hydrogen storage reaction as the external energy supply. On one hand, the thermal effect of microwave is used to make the reactants quickly reach the reaction temperature. On the other hand, the generated plasma activates the hydrogen ion and improves the reaction thermodynamics.

In the following analysis, system 1 represents the conventional hydrogen storage system without microwave plasma (conventional heating/MgH₂ system), while system 2 is the proposed microwave plasma activating hydrogen storage system (MW/MgH₂ -AHSP system). For the two reactor systems, it is assumed that the target hydrogen production is 100 kg. The hydrogen production rate of the magnesium hydride reactor is 40 NL/min (de Rango et al., 2016). The steam boiler generating hot fluid by combustion of natural gas fuel (0.33 $/m³) is used to supply energy for system 1. The efficiency of combustion converting to heat is usually 30%. The energy supply of generating microwave for system 2 is consuming electric energy with the price of 0.15 $/kWh. The reaction time of the pulse microwave reactor is assumed to be half of the conventional reaction time.

Figure 8 shows the comparison of energy consumption between conventional heating/MgH₂ system and MW/MgH₂ -AHSP system when coupling with SOFC for heat and power co-generation. It can be seen that the energy consumption cost per unit hydrogen mass of system 1 is approximately3.20 $/kg H₂, which is almost twice as large as that of system 2 (1.71 $/kg H₂). The comparison indicates that the microwave is cost-optimal and energy-saving for the large-scale hydrogen storage system.

Sensitivity analysis is further carried out with the change of electricity unit price and natural gas fuel unit price as the conditions. Assuming that the fluctuation range of fuel unit price is −20%∼+20%, the corresponding change range of total fuel cost is −8.7%∼ +8.7%. For the same fluctuation range of unit price of electricity, the total electricity cost changes from −21% to +21%. By comparison, the sensitivity of fuel or electricity price on the energy consumption cost of systems 1 and 2 could be illustrated as shown in Figure 9. It can be seen that the electricity price is more sensitive for system 2 compared with the fuel price for system 1. Therefore, for the application of microwave plasma enhancing hydrogen storage systems, the decision-makers should pay attention to the impact of the fluctuation of electricity prices on the economic benefits of the project.