Simulation Study of the Air Separation Performance of Cr-MIL-101 in High-Altitude Environments

Abstract

The most severe challenge for troops in a high-altitude environment is hypoxia. Pressure swing adsorption coupled with membrane separation is an ideal solution for oxygen production in high-altitude areas, but the molecular sieve membranes and organic membranes used in this technique are greatly affected by the ambient temperature, humidity, and pressure. Compared with traditional porous materials, metal-organic frameworks (MOFs) have outstanding features such as low densities, large specific surface areas, high crystallinities, and flexible structures. Cr-MIL-101 (MIL: Matérial Institut Lavoisier) and its derivatives are MOFs with high nitrogen adsorption capacities and can be used for oxygen production by air separation. However, since the plateau climate is complex, the applicability of Cr-MIL-101 for oxygen production in high-altitude environments awaits clarification. Therefore, this study constructed a molecular model of Cr-MIL-101, simulated the adsorption equilibrium of N₂ and O₂ molecules on this material using the grand canonical Monte Carlo (GCMC) method, and obtained their adsorption isotherms and densities. At 298 K and 100 kPa, the maximum adsorption capacities of Cr-MIL-101 for N₂ and O₂ were 0.94 per cell and 0.23 per cell, respectively. While at 238 K and 100 kPa, the maximum adsorption amounts of Cr-MIL-101 for N₂ and O₂ were 5.10 and 1.07 per cell, respectively. The thermodynamic parameters and adsorption equilibrium parameters during the adsorption process were analyzed. The conclusion of this study provides theoretical support for optimizing the N₂/O₂ separation performance of Cr-MIL-101 in high-altitude environments.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Oxygen is crucial for maintaining human life activities. After oxygen enters the human body, it combines with hemoglobin in the blood to form oxyhemoglobin and then circulates with the blood to various tissues and organs to generate energy for the normal operation of the tissues and organs [1]. As altitude increases, the partial pressure of oxygen in the atmosphere decreases apparently. When altitudes are higher than 2,700 meters, the human cardiovascular and central nervous systems are affected by hypoxia. Above 4,500 meters, the brain function deteriorates rapidly until loss of consciousness occurs completely.

Xizang Plateau covers an area of 2.5 million square kilometers, accounting for 26.9% of the total land area of China [2]. Most of the Xizang Plateau has elevations of more than 2,700 meters above the sea level, which easily causes altitude sickness. People living in low-altitude areas usually develop symptoms of altitude sickness, such as dyspnea. For hastily arrival at high-altitude areas, the incidence rate is approximately ranging from 25% to 85% [3]. At present, the main treatment methods for acute altitude sickness are oxygen inhalation and hyperbaric oxygen therapy.

There are two main methods for oxygen production in high-altitude areas as follows: cryogenic distillation and pressure swing adsorption combined with membrane separation. Cryogenic distillation techniques and processes are mature and can produce high-purity oxygen. Therefore, it is currently the most widely used oxygen production method in plain areas. However, this method is not suitable for plateau due to the high energy consumption in oxygen production and the challenges in transporting compressed oxygen cylinders [4]. Pressure swing adsorption combined with membrane separation is an ideal method for oxygen production at plateau due to its advantages, including short construction period for oxygen production equipment, low energy consumption, high degree of automation, and convenient equipment maintenance [5]. This method should be promoted at plateau in the future.

The adsorption and separation performance of molecular sieve and organic membranes under high-altitude conditions is greatly affected by environmental factors such as temperature, humidity, and air pressure. The characteristics of membranes seriously affect the oxygen production efficiency. Therefore, it is necessary to develop a new type of air separation material with high adsorption capacity, good environmental adaptability, and simple preparation process. In the past two decades, metal-organic frameworks (MOFs) have been successfully developed for air separation and received great attention [6]. They are still developing rapidly.

MOFs are new types of organic-inorganic hybrid materials with highly ordered structures. They have enormous development potential and attractive development prospects in gas storage, detection, adsorption- separation, catalysis, drug delivery, sensing, etc., especially in oxygen production through air separation [5], due to their advantages of low densities, large specific surface, high crystallinities, flexible structures, and adjustable pores [7].

MIL-101 (MIL: Matérial Institut Lavoisier), an MOF material containing unsaturated Cr, outperforms Li low-silica X-type (Li-LSX) molecular sieves in O₂ and N₂ separation. Also, it has an excellent N₂ adsorption capacity. Hence, it is applicable for O₂ production through air separation [8]. Since high-altitude conditions are harsh with a complex and changeable climate, the applicability of Cr-MIL-101 for O₂ production in high-altitude environments must be studied. Therefore, this study will simulate the air separation ability of this material under high-altitude conditions, aiming to provide a reliable theoretical basis for the practical application and optimization of MOFs for O₂ production in high-altitude areas.

2. Experiment

2.1. Cr-MIL-101 Model Construction

The original structure of Cr-MIL-101 was downloaded from the Cambridge Crystallographic Data Centre (CCDC) database. The Cr-MIL-101 topological structure is shown in Figure 1. Cr-MIL-101 consists of two cage structures.One is a regular pentagon, and another is a football structure with alternating pentagons and regular hexagons, where these two types of cages correspond to two different sizes of windows. The regular pentagons are 12 Å, while the regular hexagons are 14.7 Å. The corresponding pore sizes are 29 Å and 34 Å, with a ratio of 2 : 1. The model was imported into Materials Studio to construct the unit cell, as shown in Figure 2(a). To decrease the consumption resources, the unit cell was simplified to a primitive cell.

[figure(s) omitted; refer to PDF]

The structural optimization calculation was performed using the Forcite module of Materials Studio with the Universal force field. Generally, in such calculations, a force field is used to describe the interactions between the adsorbent and adsorbate molecules and the interactions between the adsorbate molecules. The quality of the force field greatly affects the accuracy of the simulation results. Universal force field contains interaction parameters for all elements in the periodic table and can be used to calculate interactions such as adsorption and separation of large systems. The model after structural optimization is shown in Figure 2(b).

2.2. Adsorbate-Adsorbent Interaction Potential

In this study, N₂ and O₂ three-point charge models of the adsorbate molecules were established. To maintain electrical neutrality, the center of each molecule is a virtual atom with only charge and no mass. The models of N₂ and O₂ molecules (adsorbate molecules) are shown in Figures 3(a) and 3(b). The charge on each N atom in the N₂ molecule model is −0.509, and the charge on the virtual atom in the N₂ molecule model is +1.018. Also, the charge on each O atom in the O₂ molecule model is −0.112, and the charge on the virtual atom in the O₂ molecule model is +0.224 [9].

[figure(s) omitted; refer to PDF]

The Lennard‒Jones potential function was used in the adsorption simulation process. Assuming that the framework of Cr-MIL-101 and the molecular conformation of the adsorbate remain unchanged during adsorption, only the interactions between frameworks and adsorbate molecules should be considered in the whole system. The interactions include van der Waals and electrostatic. Table 1 lists the parameter settings of the Lennard‒Jones potential function and the atomic charges in the framework of Cr-MIL-101 and in the adsorbate molecules [10–12].

Table 1

Parameter settings of the Lennard‒Jones potential function and atomic charges.

Molecule	Site	ε (kcal/mol)	σ (Å)	Charge
N2	N	0.072	3.724	−0.509
O2	O	0.068	3.624	−0.112
MOF	C_2	0.0951	3.898	−0.0481
	C_21	0.1467	3.983	−0.0481
	H	0.044	2.886	+0.37383
	O	0.0957	3.4046	−0.705
MOF cations	Cr	0.015	3.023	+3.000

3. Simulation Method

The Cr-MIL-101 model based on the minimum unit cell was used to simulate the energy and structure of the system. Electrostatic interactions were processed using the Ewald summation method with a set precision of 10⁻⁵ kcal/mol. The van der Waals forces were calculated using the atom-based summation method with a cutoff radius of 18.5 Å. In the grand canonical Monte Carlo (GCMC) simulations, the initial configuration was obtained using Metropolis rules. The adsorption isotherm of N₂ and O₂ on Cr-MIL-101 under conditions of temperatures from 238 to 298 K and pressures from 20 to 100 kPa were obtained for the subsequent derivation and analysis of thermodynamic properties. All simulations in this work were conducted using the Sorption and Forcite modules in Materials Studio.

4. Results and Discussion

4.1. Model Validation

Based on the model we constructed, the adsorption isotherms of N₂ and O₂ at 298 K were obtained and compared with experimental results from the literature [8]. The results are shown in Figure 4. The black curves represent simulation results, and red curves represent experimental results. The results shows that the numerical values and trends of the N₂ and O₂ molecules adsorbed on Cr-MIL-101 are close to the literature data, which demonstrate the accuracy of the model and force field parameters. The method can be used to simulate adsorption at a wider range of temperatures and pressures and to obtain thermodynamic properties such as adsorption isotherms and isosteric heat.

[figure(s) omitted; refer to PDF]

4.2. Adsorption Isotherm and Adsorption Density

To simulate the conditions of low temperature and low pressure in high-altitude areas, the temperature range was set to 238 K–298 K and the pressure range was set to 20 kPa–100 kPa, corresponding altitude range from 12,000 m to 0 m. The adsorption isotherms of N₂ and O₂ are shown in Figures 5(a) and 5(b).

[figure(s) omitted; refer to PDF]

According to Figure 5, the adsorption loadings of N₂ and O₂ on Cr-MIL-101 increase with temperature decreasing, opposite of pressure increasing, which are consistent with the basic adsorption theory. In addition, the adsorption capacity of Cr-MIL-101 for N₂ is obviously greater than that for O₂, which indicates that Cr-MIL-101 had higher N₂ adsorption capacity and lower O₂ adsorption capacity. That is beneficial for equilibrium selectivity-based N₂ and O₂ separation.

Figure 6 shows the adsorption densities of N₂ and O₂, respectively, at 238 K and 100 kPa. The maximum adsorption capacities of Cr-MIL-101 for N₂ and O₂ are 5.10 and 1.07 per cell.

[figure(s) omitted; refer to PDF]

Figure 7 shows the adsorption densities of N₂ and O₂, respectively, at 298 K and 100 kPa. The maximum adsorption amounts of Cr-MIL-101 for N₂ and O₂ are 0.94 per cell and 0.23 per cell. The adsorption capacities for N₂ at 238 K is 5.42 times that at 298 K, and the adsorption capacity of Cr-MIL-101 for O₂ at 238 K is 4.64 times that at 298 K. Therefore, the effect of the temperature difference in high-altitude environments on adsorption cannot be ignored.

[figure(s) omitted; refer to PDF]

4.3. Adsorption Equilibrium Parameters

Designing and developing porous materials with selective adsorption properties requires an understanding of the adsorption behavior of single components and mixtures. Although single-component adsorption isotherms are convenient to obtain, the accurate measurements of mixture adsorption isotherms are time consuming and difficult. The ideal adsorption solution theory (IAST), proposed by Myers and Prausnitz in 1965, is a method for deriving multicomponent adsorption isotherms from single-component adsorption isotherms [13, 14].

For IAST calculations, pure-component adsorption isotherm data for both gases are necessary. To obtain accurate results in subsequent calculations, the measurement of adsorption isotherm data should be as accurate as possible. Various adsorption models can be used to fit the obtained pure-component adsorption isotherm data to make it functional.

The adsorption equilibrium parameters, which characterize the equilibrium state between the bulk phase and the adsorbed phase, play an important role in the adsorption thermodynamic properties during the separation process. By fitting the adsorption isotherms in Figure 5 with the Langmuir adsorption isotherm equation, which is a model commonly used to explain adsorption isotherms [15], we deduced the adsorption equilibrium parameters.

The Langmuir adsorption isotherm equation is as follows:$$\begin{array}{}\text{(1)}& q_e=q_L\times \frac{K_L\times \text{Ce}}{1+K_L\times \text{Ce}},\end{array}$$where q_e is the adsorption capacity, q_L is the theoretical single-component saturated adsorption capacity, mg g⁻¹; K_L is the Langmuir constant, L mg⁻¹, and q_L and K_L reflect the relative affinity of the adsorbate for the adsorbent surface. The Langmuir equation was used to perform regression analysis on the adsorption isotherm data for N₂ and O₂ on Cr-MIL-101 from 238 to 298 K. The results are shown in Table 2.

Table 2

Isotherm fitting results of Cr-MIL-101 from 238 to 298 K.

T (K)	Gas	Langmuir model
		$q_L$	$K_L$	$R^2$
298	N2	41.13633	0.000125347	0.9875475
	O2	0.717732	0.005958928	0.9767753
288	N2	3.820489	0.001788996	0.9719318
	O2	0.8428591	0.005784134	0.9857251
278	N2	4.119924	0.002067344	0.9964676
	O2	0.9222731	0.006383623	0.9715641
268	N2	6.492107	0.001513454	0.9766884
	O2	0.879186	0.008685264	0.9797441
258	N2	3.863356	0.003380611	0.9952929
	O2	1.066382	0.00823606	0.967755
248	N2	4.38552	0.003717685	0.9951871
	O2	1.462952	0.00692409	0.9643031
238	N2	3.691746	0.00626844	0.991314
	O2	1.418926	0.009785687	0.9771911

S is the selectivity coefficient of the single-component gas N_2/O₂, which has the following expression at different temperatures [16]:$$\begin{array}{}\text{(2)}& S=\frac{q_{L1}\times K_{L1}}{q_{L2}\times K_{L2}}.\end{array}$$

The variation curve of Cr-MIL-101 shows in Figure 8(a) that the selectivity coefficient S value increases gradually with decreasing temperature at 0.1 kPa and 100 kPa. Interestingly, the selectivity coefficient gradient of Cr-MIL-101 is −0.75%, compared to 5 A zeolite (0.11%), and Li-LSX(5.43%) [5]. This indicates that Cr-MIL-101 has more stable relationship with temperature fluctuation. Also, it is suitable for O₂ and N₂ separation material at high-altitude areas.

[figure(s) omitted; refer to PDF]

Figure 8(b) shows the selectivity coefficient S decline with decreasing pressure from 100 kPa to 0 kPa. Apparently, S decreases in every temperature. Consistent with the trend of the isotherm, the N₂/O₂ selectivity increases with the pressure increased. In addition, the selectivity also increase with the temperature decreased, indicating that the adsorption process is exothermic. The slope of curve is an indicator to illustrate the correlationship between variables. Though linear fitting the curvature, the slope is 0.00479 at 298 K and 0.00810 at 238 K. This means that under room temperature Cr-MIL-101 is steadier than it under low temperature. However, at 248 K, the slope reaches the minimum value of 0.00456. This indicates that the pressure stability first increases and then decreases with temperature rises.

4.4. Adsorption Thermodynamic Properties

The isosteric heat of adsorption is a crucial parameter in the adsorption process, and its magnitude reflects the characteristics of the bond-broken and separation process. Since the physical adsorption of gases in porous materials is a spontaneous process, the Gibbs free energy decreases in this process ($∆G<0$). In addition, the entropy is also reduced during this process ($∆S<0$) since the disordered gas molecules are bound on the surface or in the pores of porous materials during this process. According to $∆G=∆H-T∆S$ and $∆H=∆G+T∆S<0$, the adsorption enthalpy ($∆H$) is negative and affected by temperature. Therefore, we can define $∆H=-Q_{st}$, where $Q_{st}$ is the desorption enthalpy or isosteric heat of adsorption, which has a positive value [17]. The isosteric heat will change with loading increase because it is greatly affected by the uneven energy distribution on the surface of the adsorbent, and the interactions between adsorbate molecules in the pores cannot be ignored. Therefore, to obtain the $Q_{st}$-N curve, it is necessary to calculate the values of $Q_{st}$ corresponding to different values of adsorption loading (N). For each adsorption loading (N), its $Q_{st}$ must be calculated [18].

At a certain adsorption capacity, the relationship between pressure P and temperature T can be expressed by the following virial equation [19]:$$\begin{array}{}\text{(3)}& \ln P=\ln N+\frac{1}{T}\times {\displaystyle \sum }_{i=0}^m{a}_i{N}^{i}i+{\displaystyle \sum }_{j=0}^n{b}_j{N}^j,\end{array}$$where N is the adsorption loading, and $a_i$ and $b_j$ are empirical parameters independent of temperature.

The following expression [20] can be used to calculate the isosteric heat of adsorption ($Q_{\text{st}}$):$$\begin{array}{}\text{(4)}& Q\text{st}=-R{\displaystyle \sum }_{i=0}^m{a}_i{N}^i.\end{array}$$

When the temperature range is sufficiently small, $Q_{\text{st}}$ can be assumed to be independent of temperature. Then, adsorption isotherms measured by two or more sets of experiments can be used to calculate $Q_{\text{st}}$. Here, two sets of temperature data, 238 K and 248 K, were used to calculate the isosteric heat of N₂ and O₂ on Cr-MIL-101 at 238 K.

Figure 9 shows the simulated isosteric heat of N₂ and O₂ on Cr-MIL-101 at 238 K. Obviously, the adsorption process belongs to physical adsorption. The isosteric heat gradually decreases with increasing adsorption loading, which indicates that low-temperature conditions are more favorable for the adsorption performance of Cr-MIL-101. The decrease rate for N₂ and O₂ are 18.6% and 16.9%, respectively. That means when temperature and pressure decrease, both the adsorption amounts of N₂ and O₂ decrease at the same time. But the drop in nitrogen is even greater, which leads to the decline of S, that is, consistent with the IAST results.

[figure(s) omitted; refer to PDF]

Through GCMC simulation calculations, the potential energy distributions of N₂ and O₂ on Cr-MIL-101 at 238 K and 298 K were obtained, as shown in Figure 10. The difference of quadrupole moment makes N₂ and O₂ selectively adsorbed on Cr-MIL-101. The electrostatic interactions between N₂ molecules and metal cations are stronger than that of O₂. The potential energy distributions of N₂ and O₂ molecules adsorbed on Cr-MIL-101 are greatly affected by the distribution of adsorption sites in the interior space of the adsorbent. The interaction energy between the adsorbate molecules and adsorbents increases with temperature decreasing, but its distribution does not change with temperature. Figure 10 shows that the adsorption of N₂ by Cr-MIL-101 occurs mainly in two concentrated regions, the potential energy distribution of N₂ has two peaks, and the O₂ molecules are distributed in regions with lower potential energy. Notably, the peak intensities of the potential energy distributions of N₂ at 238 K and 298 K differ greatly, which indicates that the adsorption sites of N₂ in the pores have a weaker binding capacity for N₂ at 298 K than at 238 K.

[figure(s) omitted; refer to PDF]

As shown in Figure 11, to obtain more intuitive structural information on different adsorption sites in the pores of Cr-MIL-101, the three-dimensional potential energy surfaces of N₂ and O₂ at 238 K were superimposed on the equal-adsorption density planes. N₂ and O₂ molecules distributed closer to red areas have higher adsorption interaction energies, and those distributed closer to blue areas have lower adsorption interaction energies. Through this method, the active adsorption sites of N₂ and O₂ molecules can be identified directly on the map. The color contrast between N₂ and O₂ is clearly large. On Cr-MIL-101, the absolute value of the potential energy of N₂ is higher than that of O₂. These results are consistent with the simulated adsorption isotherms.

[figure(s) omitted; refer to PDF]

5. Conclusions

In this study, a molecular model of Cr-MIL-101 was constructed, the adsorption equilibrium of N₂ and O₂ on this material was calculated by the GCMC simulation method, and the adsorption isotherms and adsorption densities were determined. Thermodynamic parameters such as the adsorption potential energy distribution and isosteric heat, as well as adsorption equilibrium parameters such as the adsorption energy and selectivity, were obtained. The findings of this study provide theoretical support for optimizing the N₂/O₂ separation performance of Cr-MIL-101 in high-altitude environments.

Disclosure

Ying-chao Wang and Yuan-zhe Li are the co-first authors.

Authors’ Contributions

Ying-chao Wang conceptualized the paper. Yuan-zhe Li drafted the manuscript. Chen-xu Zhang supervised the project. Ming-ming Zhai drafted a part of the manuscript. Cheng-cheng Zhao drew a part of the figures. Kang-ning Xie reviewed the manuscript and corrected the grammar error. Chi Tang and Er-ping Luo edited the manuscript finally. Ying-chao Wang and Yuan-zhe Li contributed to the work equally.

Acknowledgments

This research was funded by Medical Equipment Research Project (KJ2017A05193) and NSF of Shaanxi Province (2023-YBGY-163).

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