Effect of chemical functionalization groups on Zr₆-AzoBDC to enhance H₂, CH₄ storage and CO₂ capture: a theoretical investigation

All grand canonical Monte Carlo (GCMC) simulations were carried out using MUSIC software package [4]. The interaction between the adsorbent (MOF) with methane (CH₄) and carbon dioxide (CO₂) were described mainly by van der Waals forces. The electrostatic forces in this case do not play an important role. We used the Lennard–Jones model with the parameters obtained from the transferable force fields (TraPPE) for molecular gas (adsorbate) and Dreiding force field [5] for the atoms in the MOF (adsorbent). The Lorentz–Berthelot rule was used to calculate the parameters for interaction between gas molecules and the MOF. The Lennard–Jones interactions of distances greater than 12.8 Å are ignored. In the simulation, a supercell 2 × 2 × 2 (i.e. 8 unit cells) of MOF was kept rigid, the molecular gas was considered a 'spherical molecule'. Each point of the isotherm was obtained by 15–20 million simulation steps. The authenticity of this methodology has been proven by reported literature [6]. In the view of adsorption theory, one needs to distinguish the nature of simulation with that of the experiment. While the result calculated by GCMC simulation is the amount of gas molecules in the pore of adsorbent, namely the total amount N^abs, current experimental techniques of are not able to characterize this absolute amount of adsorbed molecules. Fundamentally, these measurements just produce the difference in the amount of total adsorbed gas and the amount of bulk gas at same condition of measurement, namely N^ex. The equation to converse between two these quantities was given by [7]

$$\begin{eqnarray}&&{N}^{ex}={N}^{abs}-{V}_{g}{\rho }_{g},\end{eqnarray} \tag{ 1 }$$

where N^ex, N^abs excess and absolute amount, respectively, V_p is pore volume of the adsorbent and ρ_g is the fluid density in the bulk phase at the same temperature and pressure for adsorption, which is calculated by the Peng–Robinson equation of state [8]. At low pressure (lower than 1 atm) the difference between N^ex and N^abs is negligible.

Molecular mechanics (MM) is a practical technique to study atomistic systems containing thousands of atoms per unit cell. Total potential energy of the system is determined for each set of positions of the atoms by using intermolecular/intramolecular potential function in the classical force field. It helps to refine the repetitive geometry of a mechanical approach until some predetermined criterion of convergence is satisfied. Finally, the quality of geometrical optimization depends on the accuracy of the force field. Amongst the diversity of force fields developed, the UFF force field is probably the most versatile since its parameters are derived for most of the atoms in the periodic table. In addition, this force field can combine with the QEq method to study systems in which electrostatic interactions [9] are important. Moreover MM method possesses an advantage in optimizing systems, such as MOF-205, PCN-14, MIL-101(Cr) [10] since the implement of high computational-cost calculations are not reasonably practicable. In this study, MOF structures are optimized with Dreiding force fields and UFF using GULP software [11].

The isosteric heat of adsorption [12] (Q_st) is based on the thermochemical parameters of the adsorption process. Adsorption enthalpy (ΔH_ads) can be calculated from gas adsorption isotherms simulated at two or more different temperatures by means of fitting of the virial equation. The zero-coverage isosteric heat corresponds to the interaction energy between gas molecule and the strongest interaction site of the MOF. The virial equation

$$\begin{eqnarray}&&{\rm ln} \ P={\rm ln} \ N+\displaystyle \frac{1}{T}\displaystyle \sum _{i=0}^{m}{a}_{i}{N}^{i}+\displaystyle \sum _{i=0}^{n}{b}_{i}{N}^{i},\end{eqnarray} \tag{ 2 }$$

where P is pressure, N is the amount adsorbed CH₄ gas, T is temperature, m and n represent the numbers of coefficients required to adequately describe the isotherms. The virial equation consists of temperature-independent parameters a_i and b_i is used to fit the sorption data. Adsorption isotherms measured at 273 K and 298 K are used in this procedure by applying the statistical program Origin 8.5 (MicroCal Software Inc., Northampton, MA). ΔH_ads is then calculated by following equation

$$\begin{eqnarray}&&\Delta {H}_{ads}=-{Q}_{st}=-R\displaystyle \sum _{i=0}^{m}{a}_{i}{N}^{i},\end{eqnarray} \tag{ 3 }$$

where R is universal gas constant.

Adsorption-based separation is a physisorptive operation governed by thermodynamic equilibrium processes, which relies on the fact that guest molecules reversibly adsorb in nanopores at densities that far exceed the bulk density of the gas sources in equilibrium with the adsorbents [13].

It has been shown in numerous published papers [14–17] that the IAST can be used to estimate quite accurately adsorption equilibrium of mixtures from pure component isotherm data. For a binary gas mixture adsorption (A, B components), the predicted adsorption selectivity (S_A/B) was calculated by

$$\begin{eqnarray}&&{S}_{A/B}=\displaystyle \frac{{x}_{A}/{x}_{B}}{{y}_{A}/{y}_{B}},\end{eqnarray} \tag{ 4 }$$

where x_A, x_B and y_A, y_B are the mole fractions of A and B in the adsorbed and bulk phases, respectively.

Hydrogen (H₂) uptake of Zr₆AC5N, Zr₆AC4N2 and Zr₆AC4S are 24.06, 23.69 and 23.73 mg g⁻¹, respectively; these values are higher than those of unmodified Zr₆-AzoBDC (13.55 mg g⁻¹) and other MOFs at 77 K and 1 atm. This may be because Zr₆AC5N, Zr₆AC4N2 and Zr₆AC4S contain nitrogen phenyl group such as pyridine, pyrimidine and thiophene. The nitrogen and sulfur atoms possess a high affinity with gas, thereby improving their isosteric heat of adsorption. Furthermore, this may be due to the sulfonic acid group, corresponding to Zr₆ASO₃H, which significantly enhanced the isosteric heat of adsorption (8.39 kJ mol⁻¹) at 87 K and 1 atm (table 1) and this result is consistent with previous research [21, 22].

Similarly, the Zr₆ASO₃H, Zr₆AC4N2 and Zr₆AC4S (144.50, 131.31 and 125.43 c.c. c.c.⁻¹) show higher methane volumetric uptakes than unmodified Zr₆-AzoBDC (105.09 c.c. c.c.⁻¹) and other MOFs at 298 K and 38 atm (table 1). This is explained by the high affinity with the gas of nitrogen and sulfur atoms. Also the isosteric heats in methane adsorption of these materials are improved (Zr₆AC4N2: 18.82 kJ mol⁻¹ and Zr₆AC4S: 18.62 kJ mol⁻¹, compared with 13.13 kJ mol⁻¹ of Zr₆-AzoBDC). In contrast, Zr₆AC6 and Zr₆AC5 possess the lower capacity of methane adsorption, corresponding to the volumetric uptakes of 76.14 and 82.70 c.c. c.c.⁻¹, respectively.

For CO₂ adsorption, Zr₆ASO₃H shows the highest volumetric uptake (297.77 c.c. c.c.⁻¹ at 298 K, 38 atm) and Zr₆AC4N2 has the highest isosteric heat of adsorption (26.54 kJ mol⁻¹ at 298 K and 1 atm) (table 1). They have significantly enhanced volumetric uptake and absorption heat energy compared to unmodified Zr₆-AzoBDC (266.28 c.c. c.c.⁻¹ and 17.91 kJ mol⁻¹) as well as compared to other groups, since the sulphonic acid group increases both the heat of adsorption and total uptake for carbon dioxide.

According to gas selectivity studies, the initial slopes for CO₂ and CH₄ adsorption uptakes indicate noticeable affinities for CO₂/CH₄ of proposed structures at high pressure. We studied the selectivity adsorption by the ideal adsorbed solution theory (IAST), which calculates the system's gas selectivity capabilities of theoretical gas mixtures utilizing the pure component isotherms in figures 3 and 4, and the results are shown in figure 5. It should be noted that even though IAST calculations are performed using GCMC isotherm, their selectivity results represent theoretical values that might deviate from practical applications. The selectivity for CO₂/CH₄ of new MOFs is quite significant at 22 bar for 50/50 mixture of CO₂ and CH₄. The selectivity of MOFs that contain C4N2 and C5N (pyridine and pyrimidine) groups would increase with increasing pressure; while the Zr₆ACl and Zr₆AC6 decreased at high pressure. The validity of IAST calculations is dependent on the ideality of MOFs [23]. We confirm this result by calculating selectivity from the initial slopes of the isotherms (figure 6). The resulting selectivity for CO₂/CH₄ are in agreement with the IAST value. In summary, the pyridine and pyrimidine groups can enhance CO₂/CH₄ selectivity.

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