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

Te 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 afected by the ambient temperature, humidity, and pressure. Compared with traditional porous materials, metal-organic frameworks (MOFs) have outstanding features such as low densities, large specifc surface areas, high crystallinities, and fexible structures. Cr-MIL-101 (MIL: Mat´erial 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 clarifcation. Terefore, this study constructed a molecular model of Cr-MIL-101, simulated the adsorption equilibrium of N 2 and O 2 molecules on this material using the grand canonical Monte Carlo (GCMC) method, and obtained their adsorption isotherms and densities. At 298K and 100kPa, the maximum adsorption capacities of Cr-MIL-101 for N 2 and O 2 were 0.94 per cell and 0.23 per cell, respectively. While at 238K and 100kPa, the maximum adsorption amounts of Cr-MIL-101 for N 2 and O 2 were 5.10 and 1.07 per cell, respectively. Te thermodynamic parameters and adsorption equilibrium parameters during the adsorption process were analyzed. Te conclusion of this study provides theoretical support for optimizing the N 2 /O 2 separation performance of Cr-MIL-101 in high-altitude environments.


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 afected 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.
Tere 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.Terefore, 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].Tis method should be promoted at plateau in the future.
Te adsorption and separation performance of molecular sieve and organic membranes under high-altitude conditions is greatly afected by environmental factors such as temperature, humidity, and air pressure.Te characteristics of membranes seriously afect the oxygen production efciency.Terefore, 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].Tey are still developing rapidly.
MOFs are new types of organic-inorganic hybrid materials with highly ordered structures.Tey 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 specifc surface, high crystallinities, fexible structures, and adjustable pores [7].
MIL-101 (MIL: Matérial Institut Lavoisier), an MOF material containing unsaturated Cr, outperforms Li lowsilica X-type (Li-LSX) molecular sieves in O 2 and N 2 separation.Also, it has an excellent N 2 adsorption capacity.Hence, it is applicable for O 2 production through air separation [8].Since high-altitude conditions are harsh with a complex and changeable climate, the applicability of Cr-MIL-101 for O 2 production in high-altitude environments must be studied.Terefore, 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 O 2 production in high-altitude areas.

Cr-MIL-101 Model Construction.
Te original structure of Cr-MIL-101 was downloaded from the Cambridge Crystallographic Data Centre (CCDC) database.Te 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 diferent sizes of windows.Te regular pentagons are 12 Å, while the regular hexagons are 14.7 Å. Te corresponding pore sizes are 29 Å and 34 Å, with a ratio of 2 : 1. Te 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 simplifed to a primitive cell.
Te structural optimization calculation was performed using the Forcite module of Materials Studio with the Universal force feld.Generally, in such calculations, a force feld is used to describe the interactions between the adsorbent and adsorbate molecules and the interactions between the adsorbate molecules.Te quality of the force feld greatly afects the accuracy of the simulation results.Universal force feld 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.Te model after structural optimization is shown in Figure 2(b).

Adsorbate-Adsorbent Interaction Potential.
In this study, N 2 and O 2 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.Te models of N 2 and O 2 molecules (adsorbate molecules) are shown in Figures 3(a Te 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.Te 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][11][12].

Simulation Method
Te 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 2 Journal of Chemistry summation method with a set precision of 10 −5 kcal/mol.Te van der Waals forces were calculated using the atombased summation method with a cutof radius of 18.5 Å.In the grand canonical Monte Carlo (GCMC) simulations, the initial confguration was obtained using Metropolis rules.Te adsorption isotherm of N 2 and O 2 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.According to Figure 5, the adsorption loadings of N 2 and O 2 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 N 2 is obviously greater than that for O 2 , which indicates that Cr-MIL-101 had higher N 2 adsorption capacity and lower O 2 adsorption capacity.Tat is benefcial for equilibrium selectivity-based N 2 and O 2 separation.

Results and Discussion
Figure 6 shows the adsorption densities of N 2 and O 2 , respectively, at 238 K and 100 kPa.Te maximum adsorption capacities of Cr-MIL-101 for N 2 and O 2 are 5.10 and 1.07 per cell.
Figure 7 shows the adsorption densities of N 2 and O 2 , respectively, at 298 K and 100 kPa.Te maximum adsorption amounts of Cr-MIL-101 for N 2 and O 2 are 0.94 per cell and 0.23 per cell.Te adsorption capacities for N 2 at 238 K is 5.42 times that at 298 K, and the adsorption capacity of Cr-MIL-101 for O 2 at 238 K is 4.64 times that at 298 K. Terefore, the efect of the temperature diference in highaltitude environments on adsorption cannot be ignored.

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 difcult.Te 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 ft the obtained pure-component adsorption isotherm data to make it functional.
Te 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 ftting 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.
Te Langmuir adsorption isotherm equation is as follows: 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 refect the relative afnity of the adsorbate for the adsorbent surface.
Te Langmuir equation was used to perform regression analysis on the adsorption isotherm data for N 2 and O 2 on Cr-MIL-101 from 238 to 298 K. Te results are shown in Table 2. S is the selectivity coefcient of the single-component gas N 2/ O 2 , which has the following expression at diferent temperatures [16]:   Journal of Chemistry Te variation curve of Cr-MIL-101 shows in Figure 8(a) that the selectivity coefcient S value increases gradually with decreasing temperature at 0.1 kPa and 100 kPa.Interestingly, the selectivity coefcient gradient of Cr-MIL-101 is −0.75%, compared to 5 A zeolite (0.11%), and Li-LSX(5.43%)[5].Tis indicates that Cr-MIL-101 has more stable relationship with temperature fuctuation.Also, it is suitable for O 2 and N 2 separation material at highaltitude areas.
Figure 8(b) shows the selectivity coefcient 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 N 2 /O 2 selectivity increases with the pressure increased.In addition, the selectivity also increase with the temperature decreased, indicating that the adsorption process is exothermic.Te slope of curve is an indicator to illustrate the correlationship between variables.Tough linear ftting the curvature, the slope is 0.00479 at 298 K and 0.00810 at 238 K. Tis 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.Tis indicates that the pressure stability frst increases and then decreases with temperature rises.

Adsorption Termodynamic Properties.
Te isosteric heat of adsorption is a crucial parameter in the adsorption process, and its magnitude refects 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 afected by temperature.Terefore, we can defne ∆H � −Q st , where Q st is the desorption enthalpy or isosteric heat of adsorption, which has a positive value [17].Te isosteric heat will change with loading increase because it is greatly afected by the uneven energy distribution on the surface of the adsorbent, and the interactions between adsorbate molecules in the pores cannot be ignored.Terefore, to obtain the Q st -N curve, it is necessary to calculate the values of Q st corresponding to diferent values of adsorption loading (N).For each adsorption loading (N), its Q st must be calculated [18].

6
Journal of Chemistry At a certain adsorption capacity, the relationship between pressure P and temperature T can be expressed by the following virial equation [19]: where N is the adsorption loading, and a i and b j are empirical parameters independent of temperature.Te following expression [20] can be used to calculate the isosteric heat of adsorption (Q st ): When the temperature range is sufciently small, Q st can be assumed to be independent of temperature.Ten, adsorption isotherms measured by two or more sets of experiments can be used to calculate Q st .Here, two sets of temperature data, 238 K and 248 K, were used to calculate the isosteric heat of N 2 and O 2 on Cr-MIL-101 at 238 K.
Figure 9 shows the simulated isosteric heat of N 2 and O 2 on Cr-MIL-101 at 238 K. Obviously, the adsorption process belongs to physical adsorption.Te 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.Te decrease rate for N 2 and O 2 are 18.6% and 16.9%, respectively.Tat means when temperature and pressure decrease, both the adsorption amounts of N 2 and O 2 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.
Trough GCMC simulation calculations, the potential energy distributions of N 2 and O 2 on Cr-MIL-101 at 238 K and 298 K were obtained, as shown in Figure 10.Te diference of quadrupole moment makes N 2 and O 2 selectively adsorbed on Cr-MIL-101.Te electrostatic interactions between N 2 molecules and metal cations are stronger than that of O 2 .Te potential energy distributions of N 2 and O 2 molecules adsorbed on Cr-MIL-101 are greatly afected by the distribution of adsorption sites in the interior space of the adsorbent.Te 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 N 2 by Cr-MIL-101 occurs mainly in two concentrated regions, the potential energy distribution of N 2 has two peaks, and the O 2 molecules are distributed in regions with lower potential energy.Notably, the peak intensities of the potential energy distributions of N 2 at 238 K and 298 K difer greatly, which indicates that the adsorption sites of N 2 in the pores have a weaker binding capacity for N 2 at 298 K than at 238 K.As shown in Figure 11, to obtain more intuitive structural information on diferent adsorption sites in the pores of Cr-MIL-101, the three-dimensional potential energy surfaces of N 2 and O 2 at 238 K were superimposed on the equaladsorption density planes.N 2 and O 2 molecules distributed closer to red areas have higher adsorption interaction energies, and those distributed closer to blue areas have lower adsorption interaction energies.Trough this method, the active adsorption sites of N 2 and O 2 molecules can be identifed directly on the map.Te color contrast between N 2 and O 2 is clearly large.On Cr-MIL-101, the absolute value of the potential energy of N 2 is higher than that of O 2 .Tese results are consistent with the simulated adsorption isotherms.

Conclusions
In this study, a molecular model of Cr-MIL-101 was constructed, the adsorption equilibrium of N 2 and O 2 on this material was calculated by the GCMC simulation method, and the adsorption isotherms and adsorption densities were determined.Termodynamic 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.Te fndings of this study provide theoretical support for optimizing the N 2 /O 2 separation performance of Cr-MIL-101 in high-altitude environments.
) and 3(b).Te charge on each N atom in the N 2 molecule model is −0.509, and the charge on the virtual atom in the N 2 molecule model is +1.018.Also, the charge on each O atom in the O 2 molecule model is −0.112, and the charge on the virtual atom in the O 2 molecule model is +0.224 [9].
12,000 m to 0 m.Te adsorption isotherms of N 2 and O 2 are shown in Figures 5(a) and 5(b).

Figure 4 :
Figure 4: Comparison of simulated N 2 and O 2 adsorption isotherms and experimental results.

Figure 10 :
Figure 10: Potential energy distributions of N 2 and O 2 on Cr-MIL-101 at 238 and 298 K.

Table 1 :
Parameter settings of the Lennard-Jones potential function and atomic charges.