Competitive Adsorptive Mechanism of H₂/N₂ in LTA/FAU Zeolites by Molecular Simulations and Experiments

Abstract

For industrial tail gas to be converted into high-purity hydrogen, the H₂-N₂ mixture needs to be separated efficiently. This work examined the adsorption characteristics and competitive mechanisms of H₂ and N₂ on LTA- and FAU-type zeolites, at 77 K, 298 K, and 0.1–10 bar by thoroughly analyzing results of adsorption capacity experiments and molecular simulations. In the Grand Canonical Monte Carlo (GCMC) simulations, the force field causing a molecular dipole of H₂ and the polarization force field of N₂ are first applied. The accuracy of the force field was experimentally verified. The findings indicate that N₂ and H₂ loading on Ca-FAU (Ca-LTA) are higher than Na-FAU (Na-LTA). On NaX at 77 K, the highest adsorption selectivity (N₂/H₂) is observed; on NaA at 298 K, it is the opposite. The GCMC data findings demonstrate that H₂ and N₂ have remarkably similar adsorption sites, with framework oxygen atoms and non-framework cations serving as the main adsorption sites for adsorbate molecules. Furthermore, the rate at which H₂ diffuses is higher than that of N₂. The study of redistribution charge before and after adsorption demonstrated that N₂ has a greater affinity for the framework oxygen atoms than H₂. This study provides a molecular theoretical foundation for the adsorption behavior of H₂-N₂ mixture in zeolites.

1. Introduction

H₂ is a green and clean energy source with advantages of cleanliness, no pollution, zero emissions, and wide applications. The heat of the combustion of hydrogen is higher than that of most fuels based on the same mass, making it an ideal substitute for fossil fuels. According to sources, hydrogen can be divided into gray hydrogen [1,2,3], blue hydrogen [4,5], green hydrogen [6], and hydrogen-rich tail gas [7,8]. Currently, over 95% of hydrogen generation occurs through steam methane reforming (SMR), resulting in what is commonly referred to as “gray hydrogen”, or via coal gasification, which produces “brown hydrogen”. A promising approach toward decarbonized hydrogen involves combining SMR or gasification with carbon capture and sequestration (CCS), resulting in “blue hydrogen”. If renewable or nuclear power is used to supply the electricity for this process, the resulting hydrogen would be decarbonized and recognized as “green hydrogen” [9]. While gray hydrogen production currently accounts for a high proportion, it does result in significant pollution due to the discharge of harmful gasses. Furthermore, although environmentally friendly, green hydrogen can be costly, and its application rate is currently limited. However, the recovery of hydrogen-rich tail gas offers significant benefits for the comprehensive utilization of hydrogen and carbon neutrality. Currently, there is significant interest in the industrial exhaust effect caused by processes such as steam methane reforming (H₂/N₂/CO₂) [10,11], ammonia production (H₂/N₂/NH₃) [12], and coke oven gas (H₂/N₂/CH₄) [13]. These processes result in the production of a substantial amount of H₂-N₂ mixture. As a result, many researchers have focused on binary or ternary mixtures containing richer impurities such as CO₂/CH₄ [14]. According to Carbajo’s study on the adsorption and separation behavior of gas mixtures such as H₂/N₂/CO₂/CH₄/CO in zeolites, H₂ or N₂ had a lesser interaction with zeolite framework atoms [15]. This made it harder to separate them from other gasses compared to those gasses with higher polarizability. The associated physical properties of N₂ and H₂ gasses are shown in

Table 1. The physical parameters of H₂ and N₂.

Molecular	Kinetic Diameter (Å)	Polarizability (Å)	Dipole Moment (D)	Quadruple Moment (D Å)
H2	2.89	0.8	0	0
N2	3.6	1.74	0	1.18

.

Yaremov et al. investigated the effects of microporous zeolites’ pore parameters and surface characteristics (at 77, 197, and 253 K; 760 torr) on the adsorption of H₂, N₂, CO, and CH₄. According to this study, the adsorption inertia of H₂ helped in gas separation from other gasses [16]. There is research on the separation of H₂-N₂ mixture predominantly using MOFs [17], activated carbons [18,19,20], membranes [21,22], and zeolites [23]. A zeolite is a kind of porous material widely used in industry. It can selectively adsorb molecules based on their size, shape, and polarity. Li et al. studied N₂ adsorption in Linde Type A (LTA) and truncated octahedron (FAU)-type zeolites at 1 bar and 300 K [24,25]. The results indicated that N₂ had superior adsorption performance in FAU-type zeolites, with an adsorption capacity of up to 16.26 mol/kg. Then, the N₂ adsorption capacity of the LiX zeolite was twice that of the Type A zeolite with extra-framework cations of Ca (CaA) zeolite [26]. The results highlighted the benefits of FAU- and LTA-type zeolites for adsorptive H₂ or N₂. However, the study of the competitive adsorption mechanism of H₂-N₂ mixture in FAU- and LTA-type zeolites is not clear. Most researchers have utilized molecular simulation techniques employing classical force fields to investigate the adsorption of H₂ or N₂ in zeolites. In general, simulations employing classical force fields fail to replicate experimental findings. To address the inaccuracy of classical force fields, we examined the accuracy of hydrogen force field parameters, specifically dipole moments, and incorporated polarization correction in the nitrogen force field parameters. The simulation results for single-component adsorption isotherms exhibit strong agreement with experimental test results, confirming the credibility of the force field parameters and the models. This paper analyzes the effects of cation type (Na⁺ and Ca²⁺), adsorption temperature (77 K and 298 K), and pressure (0–10 bar) on the adsorption capacity of H₂ and N₂ in LTA- and FAU-type zeolites using the force field parameters. In addition, it examines the competitive diffusion behavior of adsorbate molecules and investigates the law of competitive diffusion. Furthermore, the competitive adsorption mechanism of H₂ and N₂ in zeolites is examined in terms of the adsorption sites and the charge density.

2. Results and Discussion

2.1. Adsorption Isotherm

The adsorption isotherms of H₂ and N₂ on LTA- and FAU-type zeolites were measured at 77 K (0.1–1 bar) and 298 K (0.1–10 bar). We conducted experimental H₂ and N₂ adsorption isotherms in the zeolite at 298 K, and the H₂ isotherms at 77 K were obtained from the works of Kotoh [27], Du [28], Langmi [29], and Kazansky [30], while the N₂ isotherm at 77 K was obtained from Sircar [31]. First, the one-component computed isotherms of H₂ and N₂ were compared with the available experimental data. It was observed that the simulated isotherms using the previously developed force field do not fit the experimental data shown in Figure 1 and Figure 2, and Evagelia used Feynman–Hibbs to explain the H₂ quantum effect involving dispersion-type interactions in their force field [32]. However, all the adsorption isotherms from this study’s force field, as shown in Figure 1 and Figure 2, exhibit reasonable agreement between experiments and simulations, and using experience, the values of relative average deviation (RAD) lower than 30% are acceptable, as shown in Table S1. The simulated isotherms of H₂ and N₂ at 77 K slightly over-predict the adsorption isotherms for NaX. Nevertheless, the simulated isotherms of H₂ and N₂ at 298 K slightly under-predict the adsorption isotherms below 60 kPa for NaA. By fitting the adsorption isotherms results with Langmuir model, the Langmuir model parameters for H₂ and N₂ were estimated, and they are presented in Table S2. The adsorption isotherms depicted in Figure 1 and Figure 2 conform to the Langmuir isotherm, indicating that the adsorption of H₂ and N₂ on the LTA- and FAU-type zeolites follows a microporous adsorption behavior. In the 0–1 bar range at 77 K, the N₂ loading on the LTA- and FAU-type zeolites is approximately twice the value of H₂ loading, as shown in Figure 1a,b. However, in the 0–10 bar range at 298 K, the N₂ loading on the LTA- and FAU-type zeolites exceeds ten times the H₂ loading values shown in Figure 2a,b. It is observed that the adsorption value of H₂ is greater in the FAU zeolite than in the LTA-type zeolite at 298 K. Furthermore, for FAU- and LTA-type zeolites at 77 K, the H₂ and N₂ adsorption capacities of Ca-FAU (Ca-LTA) are greater than those in Na-FAU (Na-LTA). In most cases, the adsorption affinity of H₂ in Ca-FAU (Ca-LTA) is stronger than that of Na-FAU (Na-LTA), which can be attributed to the smaller radius of Na⁺ and the shorter interaction distance with adsorbent molecules. When Na⁺ is exchanged with Ca²⁺ in the zeolite, the non-framework cation decreases, therefore expanding the pore volume of the zeolite framework and allowing for an increase in the space available for H₂ adsorption.

2.2. Adsorption Selectivity and Heat

Adsorption selectivity is a vital indicator used to evaluate the adsorption performance of adsorbent materials. In order to explore the H₂ and N₂ adsorption properties in LTA- and FAU-type zeolites, we apply the ideal adsorption solution theory (IAST) to predict the selectivity of H₂-N₂ mixture. The selectivity is calculated using Equation (1):

$$S=\frac{q_1/q_2}{p_1/p_2}$$

(1)

where q₁ and q₂ are the adsorption capacities, and p₁ and p₂ are the partial pressures.

In this study, the selectivity of N₂/H₂ was predicted at 77 K within the range of 0–1 bar, and at 298 K within the range of 0–10 bar. Using the same molar fractions of H₂ and N₂, we can easily investigate the competitive adsorption behavior of the H₂-N₂ mixture. All calculations were performed using the PyIAST package (3.12.4) [33]. As shown in Figure 3, the selectivity of N₂/H₂ in the FAU-type zeolite is higher than that in the LTA-type zeolite at 77 K. Additionally, the selectivity of N₂/H₂ in Ca-FAU (Ca-LTA) is lower than that in Na-FAU (Na-LTA) at 298 K. The greatest selectivity of N₂/H₂ is observed in NaX at 77 K, while the greatest selectivity of N₂/H₂ is observed in NaA at 298 K. The adsorption selectivity from the binary N₂-H₂ mixture via GCMC simulations is shown in Figure S1. The results indicate that the selectivity values obtained from binary mixture GCMC simulation are consistent with those predicted using the IAST.

In Figure 4, we present contributions from different interactions to the energy of adsorption of H₂ and N₂ in FAU- and LTA-type zeolites at high loadings though MC calculations. It is evident that the primary contribution to the energy of adsorption for H₂ and N₂ is the significant host–guest interaction, which consists of a dispersive and an electrostatic component. The main difference is that N₂ exhibits higher electrostatic interaction energies compared to H₂, while they have similar dispersive contributions. In the simulations of the FAU- and LTA-type zeolites, the calculated energy of adsorption is primarily influenced by the adsorption site binding energy, with only a minor contribution from the guest–guest interaction. However, the guest–guest interaction is approximately zero since we used a one-site guest model. To investigate the effect of temperature on adsorption, we conducted the calculation using single-component gas equilibrium adsorption isotherms at 77 K and 298 K, according to the Virial Method [34]. The heat of adsorption at infinite dilution is provided in

Table 2. Heats of adsorption at infinite dilution of H₂ and N₂ on zeolites.

Molecular	Zeolite	Experiment Adsorption Heat (kJ/mol)		Simulation Adsorption Heat (kJ/mol)
		77 K	298 K	77 K	298 K
H2	NaA	−10.59	−4.47	−9.23	−4.50
	CaA	−7.40	−4.32	−8.12	−5.51
	NaX	−10.54	−4.30	−9.47	−4.94
	CaX	−6.39	−4.51	−5.25	−5.99
N2	NaA	−17.07	−16.71	−17.16	−18.65
	CaA	−18.06	−15.01	−21.87	−17.23
	NaX	−18.98	−14.19	−17.29	−15.07
	CaX	−11.73	−11.05	−15.51	−11.69

.

2.3. Adsorption Sites

To investigate the H₂ and N₂ adsorption mechanism on the zeolites employed, we performed MC simulations in an NVT ensemble (with one H₂ or N₂ molecule per unit cell) under 1 bar at 77 K and 298 K. Figure 5 shows the interaction between H₂ (N₂) and the LTA-type zeolite at 77 K, and Figure 6 shows the interaction between H₂ (N₂) and the FAU-type zeolite at 77 K. The optimized geometry reveals a minimal O_NaA-H distance of 0.97 Å and the minimal O_NaA-N distance of 0.6736 Å. In Figure 6, we can observe the interaction of H₂ (N₂) with the FAU-type zeolite. The optimized geometry reveals a minimal O_CaX-N distance of 0.37 Å and a minimal O_NaX-N distance of 0.21 Å. In the preferred sites, the behavior of H₂ is similar to that of N₂. With similar adsorption sites, N₂ and zeolites are closer to each other, resulting in better adsorption. The binding interaction between H₂ and N₂ is observed to be stronger in the FAU-type zeolite compared to the LTA-type zeolite. This observation holds true at 298 K as well, as shown in Figures S2 and S3. The adsorption site is consistent with the adsorption density pattern (Figures S4–S7). From the adsorption density figures, it is evident that H₂ exhibits stronger adsorption density at 77 K in the vicinity of oxygen atoms in the zeolite. The adsorbate molecules interact more strongly with zeolites, and as the temperature increases, the H₂ molecules disperse to binding sites with lower binding energies, resulting in weaker interactions with the zeolite. On the other hand, N₂ adsorption behaves in the opposite manner, exhibiting stronger adsorption densities with the zeolite at 298 K. Significant density changes were observed in the CaA and NaX zeolites.

To investigate the interaction of H₂ and N₂ with zeolite atoms, we employed AIMD to examine the behavior of the H₂-N₂ mixture (H₂/N₂, 50/50, v/v) within the zeolite under the NVT ensemble. The radial distribution function (RDF) was obtained by calculating the molecular trajectories of H₂ and N₂. Figure 7 and Figure 8 present the zonal and average densities of H₂ and N₂ based on O, Si, Al, and non-framework cations in LTA- and FAU-type zeolites at 1 bar and 77 K. The shape and intensity of the peaks provide evidence of the interaction sites and adsorption capacities of H₂ and N₂ on the zeolites. It is evident that the zeolite exhibits a stronger interaction preference for N₂, as indicated by the local of the primary peak. In Figure 7, the initial peak occurs at 0.75 Å, indicating the highest likelihood of H₂ being present at 0.75 Å. Similarly, in Figure 8, the radial distribution function of N₂ displays the highest peak at 0.5 Å, indicating the highest probability of N₂ being present at 0.5 Å. These findings clearly show that the main peaks representing the interactions between N₂ and zeolites are higher than those of H₂. The intensity of the main peak for H₂ is 6, while that for N₂ is 8, which aligns with the observation in Figure 4 regarding the larger adsorption energy for the interaction of N₂ and zeolites. The initial peaks observed in Figure 7 and Figure 8, respectively, correspond to the oxygen atoms of framework. This suggests that the oxygen atoms of the framework assume the closest positions to the unrestricted movement of H₂ and N₂. Consequently, this finding supports the notion that the interaction energy between the H₂ (N₂) and the oxygen atoms of the framework accounts for a significant portion of the adsorption energy between the host and guest. The same principle applies at 298 K; please refer to Figures S8 and S9 for supporting evidence.

Because the dynamic diameters of H₂ and N₂ are similar to the effective pore diameter of the LTA- and FAU-type zeolites, diffusion plays a key role in the absorption and separation processes of H₂ or N₂. The diffusion of the adsorbate molecules in the zeolite is influenced not only by their dynamic diameter but also by their interaction with the oxygen atoms of the framework.

We analyzed the dynamic behavior of a H₂-N₂ mixture (H₂/N₂, 50/50, v/v) in FAU- and LTA-type zeolites at different temperatures by calculating the mean square displacements (MSDs) and the self-diffusion coefficients. Figure 9 and Figure 10 depict the relationship between the adsorbate molecular motion and equilibrium time. It is observed that the diffusion of H₂ is greater in FAU-type zeolite than in LTA-type zeolite at 298 K. Additionally, for both FAU- and LTA-type zeolites at 298 K, the H₂ and N₂ diffusion capacities of Ca-FAU (Ca-LTA) are greater than those of Na-FAU (Na-LTA). During the free movement of adsorbate molecules, H₂ diffuses more easily than N₂ in the pores of LTA- and FAU-type zeolites. Karger conducted a diffusion study on H₂ in NaX and NaA zeolites and found that the type of zeolite influences the diffusion process of H₂, with the diffusion rate decreasing as the size of the zeolite pores decreases [35,36]. The linear nature of the MSD indicates the reliability of the simulation process. The self-diffusion coefficients of H₂ and N₂ are calculated using the Einstein relation, as shown in Equation (2):

$$D={\displaystyle \frac{\mathbf{1}}{\mathbf{6}}}\underset{\mathit{n}\to \infty }{\mathbf{lim}}{\displaystyle \frac{\mathit{d}}{\mathit{d}\mathit{t}}}\left\{{\displaystyle \frac{\mathbf{1}}{{\mathit{N}}_{\mathit{i}}}}{{\displaystyle \sum }}_{\mathit{i}=\mathbf{1}}^{{\mathit{N}}_{\mathit{i}}}\langle {\left|{\mathit{r}}_{\mathit{i}}\left(\mathit{t}\right)-{\mathit{r}}_{\mathit{i}}\left(\mathbf{0}\right)\right|}^{\mathbf{2}}\rangle \right\}$$

(2)

where the average is taken over time t for the mean square displacement of the center of mass position vectors r of all the molecules N in the system; and ‹› indicates the overall average.

The calculated results are shown in

Table 3. Computed self-diffusion coefficients of H₂-N₂ mixture (H₂/N₂, 50/50, v/v) in LTA- and FAU-type zeolites at 77 K.

Zeolites	NaA	CaA	NaX	CaX
H2 (Å2/ps)	10.1	19.6	20.3	19.3
N2 (Å2/ps)	3.8	2.8	2.7	3.0
H2/N2	2.6	7.0	7.6	6.4

and

Table 4. Computed self-diffusion coefficients of H₂-N₂ mixture (H₂/N₂, 50/50, v/v) in LTA- and FAU-type zeolites at 298 K.

Zeolites	NaA	CaA	NaX	CaX
H2 (Å2/ps)	52.8	46.0	32.2	57.9
N2 (Å2/ps)	10.4	7.0	12.2	10.1
H2/N2	5.1	6.5	2.7	5.7

. Among the four types of zeolites, NaX zeolites exhibit the highest self-diffusion coefficients for H₂ and N₂ at 77 K, with a ratio of 7.6 (H₂/N₂). Similarly, CaX zeolites show the largest self-diffusion coefficients for H₂ and N₂ at 298 K, with a ratio of 6.54 (H₂/N₂). The self-diffusion coefficients of H₂ and N₂ in Na-FAU (Na-LTA) are lower than those in Ca-FAU (Ca-LTA).

2.4. Investigation of Charge Density

To investigate the effect of H₂ and N₂ on the chemical environment within the zeolite pores during adsorption at the atomic level, DFT calculations were performed to explore the redistribution of charge density in this system after adsorbing H₂ or N₂ molecules. The charge density analysis of LTA- and FAU-type zeolites is shown in Figures S10 and S11. It is clear from the figures that before the adsorption of gases, the electron cloud is concentrated around the zeolite pores. After the adsorbate molecules are adsorbed onto the zeolites, the electron density is transferred to the adsorbate molecules. The adsorption properties of the adsorbate molecules within the framework are determined using the oxygen atoms of the framework and the non-framework cations. As shown in Figure S10, due to the strong electron withdrawing ability of the zeolite atoms, the electrons of the H atoms in H₂ molecules migrate to the framework atoms, especially the oxygen atoms. Similarly, in Figure S11, the N atoms in N₂ donate some charges, leading to the interactions with the zeolite atoms. In comparing Figure 11 and Figure 12, it can be observed that the charge density transfers between oxygen atoms, and N₂ is more pronounced, which is likely due to the denser electron cloud distribution of N₂ molecules. The adsorbate molecules show an increased charge density on one side of the oxygen atoms of the zeolite framework and a decreased charge density on the other side in Figure 11 and Figure 12. H₂ and N₂ exhibit a blue area near the side of the oxygen atoms of the framework, indicating a decrease in charge density, while the framework atoms show a red area, indicating an increase in charge density. The electrostatic potentials of N₂ and H₂ in Ca-FAU (Ca-LTA) demonstrate larger values than those in Na-FAU (Na-LTA). A comparison of the analyses in Figure 11 and Figure 12 reveals that the charge transfer in the pores of LTA- and FAU-type zeolites after the adsorption of N₂ is more pronounced than that of H₂ and that N₂ is more affected by the chemical environment in the zeolite pores.

3. Methods

3.1. Framework and Adsorbate: Models and Force Fields

The zeolite flexible framework has little impact on the simulation of small-molecule adsorption. In this study, the rigid structure model was employed for simulation [26]. The atoms were considered “frozen”, neglecting interatomic interactions between framework atoms to significantly shorten the simulation time [37]. The zeolite structures used in this study were taken from crystallographic files (CIFs) of the IZA database, with additional framework cations inserted for structural optimization [38]. The geometric structure was optimized using Density Functional Theory (DFT). The overall unit cell maintains a rigid structure. We analyzed the geometric structure with the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation functional, associated with the third-generation dispersion correction (DFT-D3) to avoid weak interaction, implemented in the CP2K package (8.2.0) [39,40,41]. The density cut-off was set to 500 Ry, and the overall energy converged to within 10⁻⁶ eV. The physicochemistry characteristics of the investigated LTA and FAU samples in this study are shown in

Table 5. Physicochemistry characteristics of LTA and FAU Systems.

	NaA	CaA	NaX	CaX
Accessible pore volume (cm3/g)	0.28	0.3	0.261	0.31
Supercage pore size (Å)	4	5	7.4	8
Cation	Na	Ca	Na	Ca
Number of cations (N)	96	48	88	44
Si/Al	1	1	1	1

.

The accuracy of the force field is essential for GCMC simulations. In order to validate the accuracy of our GCMC simulations, we compared the specific force field parameters of Vujić [42], General [43], Evagelia [32], Kowsari [44,45], Pantatosaki [46], and Huang [47]. The force field previously described by J. Marcos takes into consideration the influence of the dipole moment of the H₂ molecule and the polarization of the electric field generated by the local structure of the zeolite. For hydrogen, we used a one-site point charge model, while for N₂, we used the parameters reported by Xuan [48]. There are strong Coulomb interactions between adsorbates and non-framework cations as well as mobility of these cations. So, the location and density of the non-framework cations influence the adsorption behavior of H₂ and N₂ in zeolite structures [49]. The cation Ca²⁺ parameters reported by Du and the cation Na⁺ parameters reported by Farida were employed to describe interactions in this work [45,50]. The force field parameters and partial charges are presented in

Table 6. Lennard-Jones interactions and partial charges.

Atom Types	ε (K)	σ (Å)	Q (e)	CITE
H2	38	2.92	-	[48]
N2	95.2	3.75	-	[49]
H2-Si	39	2.8	2.234	[48]
H2-Al	42.5	2.95	2.089	[48]
H2-O	47	3.08	−1.307	[48]
Na	8	3.5	0.8	[50]
Ca	78	2.98	2	[45]

.

The simulation accuracy of classical force fields is not sufficient when the polarization effect of N₂ is neglected. To enhance the simulation accuracy, the polarization force field is introduced by scaling the Lennard-Jones (L-J) interaction between N₂ and zeolite atoms with a parameter λ ∈ [0, 1] [51,52]. The atomic polarizabilities used in this study were obtained from the literature using Equation (3). For this study, λ was set to 0.4 by fitting the experimental data to the simulation results.

$${\epsilon }_i^{scaled}={\epsilon }_i·\frac{\left(1+\lambda \right)-\frac{{\alpha }_i}{{\alpha }_{max}}}{\left(1+\lambda \right)-\frac{{\alpha }_i}{{\alpha }_{max}}·\lambda }$$

(3)

where λ is a scaling factor between 0 and 1 used for rescaling the Lennard-Jones energy parameters; α_i means the polarizability of atom_i; α_max means the max polarizability; and ε_i means the initial force field parameter. λ = 1 means that N₂ has the same interaction potential energy function with other molecules, and λ = 0 means that N₂ does not interact with other molecules.

3.2. Simulation Details

The separation of H₂ and N₂ adsorption in LTA- and FAU-type zeolites was performed using the RASPA code [53,54]. The cut-off radius was set to half the length of the cell edge in the simulation box, without considering tail corrections, and by applying periodic boundary conditions to maintain a three-dimensional spatial structure. Only cations and adsorbate molecules were allowed to move, while the zeolite structure remained rigid. In these simulations, the following trial moves were used for the cations: translation (50%) and random (50%). For the H₂ and N₂ molecules, the trial moves were carried out: translation (20%), rotation (20%), insertion (20%), and random (40%). The total number of cations remained constant during the simulations, and only translation movements and regrow were considered for this type of particle. Based on the reported crystallographic locations of Na⁺, Na⁺ molecules were expected to enter the sodality cages in FAU-type zeolites, but not in LTA-type zeolites [55]. Therefore, blocking spheres were exclusively used for LTA-type zeolites in our investigation, with the ionic radius of Na⁺ (r_Na⁺ = 1.16) serving as the probe size. The simulations were performed for 5 × 10⁵ cycles, with 25,000 initialization cycles and 20,000 equilibration cycles. The final simulation result was obtained by averaging the results of the two simulation processes. The excess adsorption data were used for investigation [56]. The excess adsorption capacity (n_exc) was obtained by relating the absolute adsorption capacity (n_abs) to the pore volume of the adsorbent (V_g) and the molar density of the native gas phase (ρ_g), using Equation (4):

$$n_{exc}=n_{abs}-V^g{\rho }^g$$

(4)

In the He-void (ϕHe) calculations, the particle method with the Rosenbluth algorithm was used [57]. The largest cavity diameter (LCD), pore volume, and accessible surface area (ASA) were determined using Zeo⁺⁺ software packages (0.3) [58]. The interaction between the adsorbates and the zeolite atoms was calculated based on electrostatic and van der Waals force interactions. The electrostatic interactions were computed using the Coulomb force, while the interatomic interaction parameters were determined using Lorentz–Berthelot mixing rules [59]; Equation (5) was used for this calculation:

$${\epsilon }_{ij}=\sqrt{{\epsilon }_i{\epsilon }_j},{\sigma }_{ij}=\frac{{\sigma }_i+{\sigma }_j}{2}$$

(5)

where σ_ij and ε_ij are the L-J potential parameters.

Van der Waals interactions were described using the 12-6 Lennard-Jones (L-J), and the Ewald method was employed to calculate long-range electrostatic interactions with a relative accuracy of 10⁻⁶ [60]; Equation (6) was used for this calculation:

$$E_{LJ}\left(r_{ij}\right)=4{\epsilon }_{ij}\left[{\left({\displaystyle \frac{{\sigma }_{ij}}{r_{ij}}}\right)}^{12}+{\left({\displaystyle \frac{{\sigma }_{ij}}{r_{ij}}}\right)}^6\right]$$

(6)

where r_ij is the interatomic distance between the i and j atoms.

An MD simulation was performed using the RASPA code. Molecular dynamic runs of H₂-N₂ (H₂/N₂, 50/50, v/v) molecules were conducted in a 25 × 25 × 25 Å box at 77 and 298 K, with periodic boundary conditions imposed in all directions. The MD simulation was run for 1 ns with a time step of 0.5 fs in the NVT ensemble. The simulations included 2 × 10⁶ cycles, with 2000 initialization cycles and 20,000 equilibration cycles.

To explore the distribution of H₂ and N₂ molecules in zeolites, the ab initio molecular dynamic (AIMD) simulation was employed using the CP2K program (8.2.0). The simulations employed the Gaussian plane wave method, implemented in the Quickstep module [61], with the input file using the Multiwfn code [62]. The simulation was performed in the NVT ensemble using the BASIS_MOLOPT basis set [63] and GTH_POTENTIALS pseudopotential [64]. The employed density functional was the PBE with the DFT-D3 dispersion corrections. The CSVR thermostat with a temperature relaxation time of 0.5 ps was used to keep the temperature at 298 K during the simulations [65]. All reported properties were averaged over at least 500 ps, and the time step was set to 0.5 fs.

4. Conclusions

This study investigated the adsorption of H₂ and N₂ single components in Na⁺/Ca²⁺ ion-exchanged LTA- and FAU-type zeolites using GCMC and MD simulations. The adsorption isotherms obtained by the simulations correspond well with the experimental results. It is observed that the Ca²⁺ zeolites display a higher H₂ and N₂ adsorption capacity. The IAST predicts the adsorption selectivity of H₂-N₂ mixture in LTA- and FAU-type zeolites. The findings indicate that the selectivity of N₂/H₂ is greater for NaX at 77 K and NaA at 298 K. Additionally, the kinetic simulation of H₂-N₂ mixture diffusion demonstrated that H₂ exhibits the fastest diffusion rate in NaX.

This study on adsorption sites for H₂ and N₂ on LTA- and FAU-type zeolites shows that major adsorption sites are located near framework oxygen atoms and non-framework cations. For the non-framework cations, Na⁺/Ca²⁺, the findings regarding adsorption energy and radial distribution function suggest that the Ca²⁺ zeolites exhibit a stronger interaction energy with H₂ and N₂. Moreover, there is an apparent interaction between the zeolite and N₂ from the redistribution of charge density. This results in a relatively large charge transfer, leading to a stronger adsorption capacity.