Tracing Experimentally Compatible Dynamical and Structural

Article pubs.acs.org/JPCC

Tracing Experimentally Compatible Dynamical and Structural Behavior of Atmospheric N2/O2 Binary Mixtures within Nanoporous Li−LSX Zeolite: New Insights to Influence of Extra-Framework Cations by MD Simulations Mohammad H. Kowsari* Department of Chemistry and Center for Research in Climate Change and Global Warming (CRCC), Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran S Supporting Information *

ABSTRACT: Along with available adsorption isotherms and uptake kinetic data, microscopic knowledge of the guest self-diffusion and intracrystalline movement of the simple air binary mixture of nitrogen (N2) and oxygen (O2) within Li−LSX zeolite is needed to optimize the design and to reach a breakthrough high-efficiency of air separation process based on the selective adsorption in this zeolite. In the current work for the first time, an all-atom molecular dynamics (MD) simulation is used to study the average single-particle dynamics, self-diffusion, and microscopic structure of the atmospheric binary gaseous mixtures of N2 and O2 in Li−LSX zeolite at temperatures between (260 and 700) K. The common order of magnitude of the computed guest self-diffusion coefficients at different temperatures is in the range of 10−9 - 10−8 m2·s−1 and corresponding activation energies obtained using the Arrhenius equation varied in the range of ∼0.6 for O2 to 1.6−3.3 kcal·mol−1 for N2 in simulations with mobile and with fixed extra-framework Li+ on SIII sites (Li−III), respectively. Present results provide some new molecular-level insights into the link between the behaviors of the pendulum-like motion of Li−III with the guest molecules. Results show that O2 guest molecules freely move into the supercages and channels of the zeolite without any attachment to the key sorption cationic sites and the behavior of O2 is independent of the fixed or mobile Li−III situation during of simulations. In contrast, the oscillatory motion or immobility of the Li−III cation is found to have a surprisingly large influence on the intracrystalline N2 self-diffusion, the local (N2−Li−III) structural correlation, and the mean time of attachment of N2 to Li−III. The different observed adsorption behavior of two guest components was previously connected to the difference in their relative values of permanent quadrupole moments which causes different guest−Li−III affinities. These are well explained by a microscopic structural and dynamical analysis in current study. O2 component diffuses faster than N2 within the nanoporous Li−LSX zeolite, especially with a greater relative diffusivity difference for simulations with fixed Li−III at relatively low temperatures which correspond to favorable selective adsorption conditions. The computed O2/N2 diffusion selectivity ratio increases with decreasing temperature.

1. INTRODUCTION Nowadays, tracing dynamical behavior, diffusion coefficient, mass transfer, microscopic structure, and physical adsorption/ trapping process of guest molecules inside nanoporous solids such as zeolites, metal organic frameworks (MOFs), clathrate hydrates, and carbon-based materials, under microscopic equilibrium and macroscopic nonequilibrium conditions, is the main subject of many industrial and academic projects. These studies can lead to widespread practical opportunities from drug release to catalysis, adsorption, ion-exchange, storage, and separation processes.1−11 The efficient design and improved performance of such processes requires a detailed understanding of the basic adsorption, diffusion, and transport mechanisms of guest molecules within the nanoporous materials. For example, the differences in the flux rates of the different guest species resulting from differences in their intracrystalline diffusion coefficients basically control the separation process. Another possible effective feature for © 2017 American Chemical Society

separation is the dissimilar size of different guest species relative to the pores dimensions.4,12,13 Advance techniques and challenges in the study of diffusion in nanoporous materials from both experimental and molecular modeling have been previously reviewed.14−16 Typical zeolites with open three-dimensional (3D) aluminosilicate framework structures have SiO4 and AlO4− tetrahedra as the primary building units. These tetrahedra are linked through sharing all the oxygen bridges (−O−) to form regular intracrystalline cages, cavities, and channels, as the secondary building units which are big enough (from nearly 3 Å to over 10 Å) to allow small guest molecules to enter.12,17 The negative electrostatic charge of the framework composed of these primary building units must be compensated with the Received: November 17, 2016 Revised: January 4, 2017 Published: January 18, 2017 1770

DOI: 10.1021/acs.jpcc.6b11611 J. Phys. Chem. C 2017, 121, 1770−1780

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The Journal of Physical Chemistry C

cations.19,31,36 Hence, the extra-framework cation plays an important role in the N2/O2 selectivity. Li+ has a relatively small ionic radius and polarizability, and high ionic charge density compared to other alkali metal cations, consequently, PSA and VSA using Li−LSX zeolite results in highly efficient and operative technology for air separation.37 However, during the 1990s new generations of highly selective adsorbents, such as LiX or Li−LSX type zeolites contributed to significant O2 air separation by PSA-based processes. In 2010−2011 Zanota et al.38,39 reported the experimental adsorption isotherms of pure and binary mixtures of air compounds on LSX zeolites with alkali metal cations. Sircar et al. recently focused on adsorption and mass transfer of pure N2, O2, and Ar in Li−LSX.33,40−44 They published extensive equilibrium adsorption data for pure N2, O2, and their binary mixtures on a commercial sample of Li−LSX zeolite at temperatures of 0, 30, and 65 °C, and in the pressure range 0− 6 atm.40−42 Sircar et al. also summarized the corresponding sporadic published equilibrium adsorption isotherm data in the literature on the same systems.40 The literature shows continual active research on the adsorption properties of Li−LSX for production of O2 from air.33,34,44 In addition to the study of related air separation applications of Li−LSX zeolite, previous experimental and computational reports also investigated H2 adsorption and diffusion within Li−LSX zeolite.26,27,45 Stuckert and Yang used Li−LSX and K− LSX zeolites in comparison with the NaX zeolite and aminegrafted SBA-15 for CO2 capture from the atmosphere and simultaneous concentration by cyclic adsorption−desorption processes. They reported a breakthrough performance for Li− LSX with double the capacity of NaX at dry atmospheric conditions.46 In general, performance and capacity of zeolites as adsorbents are reduced under moist conditions. Several previous experimental reports and/or Monte Carlo simulations emphasize the inhibitor role of water impurity on the adsorption performance of N2 gas on Li−LSX zeolite.37,47−50 Therefore, before air separation, the Li−LSX zeolite must be thermally dehydrated and air needs to be dried.37,47 From a computational point of view, there are several Monte Carlo simulations of air separation by the Li−LSX zeolite.31,36,51,52 These simulations are generally performed with the aim of predicting the adsorption isotherms, isosteric heat of sorption, and preferred sorption sites for N2 and O2 gases, both as single components, and as binary mixtures in Li− LSX. The above literature review shows a number of groups reported extensive experimental measurements and little Monte Carlo research, especially with the subject of the equilibrium adsorption data for pure N2, O2, and their binary mixtures within hydrated and dehydrated Li−LSX zeolites. However, to our knowledge, there is no previous MD study of the diffusion and microscopic structural details of N2−O2 air binary mixture within Li−LSX zeolite. Molecular simulation is a powerful tool which complements experiments to obtain molecular level details about behavior of guest molecules inside zeolites53,54 if the crystal structure of the target zeolite is available.12,30,36,55 The type and location of cations in the zeolite framework affect the adsorption properties considerably.12,30,36 In this work, the dynamics, self-diffusion coefficients, and microscopic structure of the binary mixtures of N2 and O2 as the simple model of air, in two designed states of Li−LSX

introduction of extra-framework cations, such as alkali or alkaline-earth metals. These microporous materials are largely used as commercial heterogeneous catalysts and precise gasseparation adsorbents. This is mainly due to the fact that these frameworks have active extra-framework cationic sites, adjustable composition, high thermal and chemical stabilities.18 The identification and characterization of sorption sites in zeolites, like extra-framework cations, can be performed by IR spectroscopy, in particular using diffuse reflectance infrared Fourier transform (DRIFT).19−22 One of the most well-known and industrially important synthetic zeolite families which is the most commonly used commercial adsorbent and has the most highly heterogeneous surface known among porous materials, is the aluminum rich or “low-silica” type X zeolites (LSX) based of faujasite (FAU) framework, with Si/Al ≈ 1. The LSX framework represents an optimum in pore volume, channel structure, and the golden composition formula with the highest possible Al content, and consequently, the maximum number of charge-balancing cation exchange sites. The internal surface of LSX zeolites results in high electrical field gradients at active sites which have an effective role in highly selective adsorption of water, polar, and polarizable molecules. This is useful in many applications.23 The size and ionic charge density of exchangeable cations, along with their location and their number density in the LSX frameworks can control the diameter of the pores, the internal surface area, and the guest-framework interactions. These features have significant contributions to the effective physisorption of gases for purification and drying, storage, and separation purposes.24−31 The determination of extra-framework lithium cation locations in Li+ exchanged LSX (Li−LSX) zeolite, the target zeolite in this study, were reported by Feuerstein and Lobo using a combination of neutron diffraction and magic-angle spinning (MAS) NMR spectroscopy.30 Figure S1 in the Supporting Information clarifies how the FAU type zeolite structure contains three different Li+ sites. The SI′ positions are in the center of the six-membered rings located between sodalite cages and hexagonal prisms. The SII positions are in the center of the six-membered rings located between a sodalite cage and a supercage. The third SIII position is near the four-membered ring inside the supercage. Feuerstein and Lobo found much larger temperature factors for Li+ in SIII than for Li+ in SI′ and SII locations which is the same as earlier neutron diffraction structure of Li−LSX reported by Plevert et al.32 They concluded that the SIII Li+ cations are mobile. A total of 96 Li+ cations per unit cell was determined by chemical analysis.30 Air is a mixture of gases, mainly N2 and O2 with mole fractions of 0.78 and 0.21, respectively. Both of these abundant gases in the atmosphere have important uses in industry and medicine. Air is readily available and the cheapest source of N2 and O2, and air separation by zeolites with the aim of obtaining both the N2 and O2 is one of the main commercial/industrial approaches in this field.33,34 Li−LSX zeolite has been used for a long time in chemical industry for the effective separation of N2 from air in dry conditions33−35 by cyclic pressure or vacuum swing adsorption (PSA/VSA) processes, and particularly for ∼90% O 2 production from ambient air. Previous studies emphasize the selective adsorption of N2 due to the larger permanent quadrupole moment of N2 compared to that of O2. This causes stronger interaction of N2 with extra-framework 1771


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The Journal of Physical Chemistry C zeolite, with fixed or mobile Li−III, were studied by MD simulations. One of the purposes of this study is to compare the details of dynamical behavior of N2 and O2 in Li−LSX zeolite by computing of the mean square displacement (MSD), velocity autocorrelation function (VACF), and self-diffusion for the center of mass of these simple guest molecules through the zeolite medium. Another purpose is to determine microscopic structural details of guest molecules by calculating of partial site−site radial distribution functions (RDFs), the molecular animations of MD trajectories, and the snapshots visualization of molecular structure of simulation boxes. We also determine the effect of temperature and the influence of the mobile or the fixed Li−III situation on the structure, dynamics, self-diffusion value, activation energy for diffusion process, and diffusion selectivity of guest species of studied air binary mixtures inside of the Li−LSX framework.

Table 1. Partial Atomic Charges and Lennard-Jones Parameters for Atoms of the Li−LSX Zeolite Framework, N2, and O2 Gas in the MD Simulations51−54 (CoM: Center of Mass of a Guest Molecule) atom

q (e)

ε (kcal·mol−1)

σ (Å)

Si Al O Li: I, II, III N N(CoM) Og Og(CoM)

1.525 1.525 −1.000 0.950 −0.405 0.810 −0.112 0.224

0.037 0.0384 0.3342 0.0087 0.0723 0.000 0.108 0.000

0.677 1.016 2.708 1.090 3.318 0.000 3.050 0.000

are considered separately in both fixed and mobile form to better illuminate the different intracrystalline behaviors of two molecular guest species and to determine the role of the Li−III cation motion on the selective guest gas adsorption and diffusion. N2 and O2 were modeled as rigid three-site molecules where the absolute value of the partial charge in the center of mass site is equal to twice the partial charges of each atom site. Guest molecules are inserted randomly in the free space of the supercages using the Mercury program.59 The bond distance of N2 and O2 molecules has assumed 1.10 and 1.21 Å, respectively.51 Reports of guest behavior in flexible (vibrating) and rigid frameworks from previous reviews,12,60 show that diffusion coefficients of guest molecules at low loading, within the flexible and nonflexible frameworks are similar when the sizes of guest molecules are smaller than the critical dimensions of the micropores. Hence, we concluded that the influence of the flexible framework on the diffusion of N2 and O2 guest molecules at relatively low loading is not noticeable. However, our current results show the important effect of considering motion for Li−III extra-framework sorption sites, located in the internal surfaces of the supercages, on the local structure and dynamics of N2 (the inverse of O2) within Li−LSX zeolite. In this study to simplify zeolite framework force field and to reduce computing run-times, it was decided to assume the atoms of Li−LSX zeolite framework do not move during the current simulations of air binary mixtures in this nanoporous material. A future simulation study with a flexible framework force field will need to be carried out to determine the effect of the mobility of the internal framework atoms on the guest behavior. The initial structure was equilibrated by performing a NVT simulation at 700 K for 2000 ps in which the total energy of simulated system has stabilized with time. This configuration was used for submitting additional runs to collect data averages. The final structure of each higher temperature is used as the initial structure for a lower temperature. In each temperature, after similar equilibration stages, the final MSD results for N2/ O2 are taken by averaging five sample NVT trajectories with the production run-times of 300 ps to improve reproducibility and the statistical accuracy of reported dynamical results. Afterward, a similar procedure is used for computing of the VACF from five short runs, each with the run-time of 10 ps. As a test to investigate the effect of applied run-time length on the calculated results, a longer simulation run with 2000 ps was also performed for the “mix 16−4” configuration at 400 K. Comparison of the results of two runs with different run-times of 300 and 2000 ps showed no significant difference for the

2. COMPUTATIONAL METHODS Extensive canonical (NVT) MD simulations at 260, 298, 400, 500, 600, and 700 K are performed using the DL_POLY program,56 version 2.18, to study the dynamical and structural details of binary gaseous mixtures of N2 and O2 inside of Li− LSX zeolite. Periodic boundary conditions were employed, the SHAKE algorithm was used for rigid N2 and O2 molecule motion, and the equations of motion were integrated using the Verlet leapfrog scheme.57 The time step of the simulations was 1 fs and cutoff distance of short-range potentials was chosen as Rcutoff = 20 Å. The simulation box was chosen as a 2 × 2 × 2 replica of the cubic unit cell (Fd3)̅ of Li−LSX,30 with |Li96|[Si96Al96O384] formula unit and a lattice constant a = 25.6957 Å. The guest loading per unit cell for each component was chosen to roughly give the molar ratio of N2/O2 in air and previously reported adsorption isotherm data from grand-canonical Monte Carlo simulations or experimental measurements. The maximum possible reported guest loadings per unit cell of Li−LSX for N2 and O2 at atmospheric pressure were around 16 and 4, respectively.47 We simulated a simple model of two air mixtures, one with (16N2 + 4O2) loading per unit cell of Li− LSX zeolite (“mix 16−4”) and another with (8N2 + 2O2) loading per unit cell of Li−LSX zeolite (“mix 8−2”). The results for two loadings show the same trends and we present our findings mostly for the statistically preferred “mix 16−4” simulations. The pairwise van der Waals interactions between the guest− guest, guest−zeolite, and zeolite−zeolite atomic sites were represented using Lennard−Jones (LJ) potentials. The electrostatic (Coulombic) interactions were calculated using the Ewald summation method.57 All of partial atomic charges and the main LJ (12−6) parameters are derived and used in references [51−54]. We summarize the force field parameters in Table 1. The LJ parameters between different atom types were obtained from the Lorenz−Berthelot mixing rules, εij = εiiεjj and 1

σij = 2 (σii + σjj). Experimental studies on Li−LSX zeolite reported that Li cations on SIII sites (Li−III) are mobile at temperatures above 233 K.58 Hence, considering mobile Li−III cations at temperatures higher than 233 K is a more accurate representation than considering fixed Li−III cations. In the current simulations, all the atoms of the zeolite, except of Li− III cationic sites, are fixed at the rigid crystallographic structure obtained by Feuerstein and Lobo.30 The Li−III cationic sites 1772


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3. RESULTS AND DISCUSSION 3.1. Dynamical Details, Self-Diffusion Coefficients, Diffusion Selectivities, and Activation Energies. MD simulations of guest mixtures through zeolites improves the understanding of multicomponent diffusion in zeolites which is important for technological applications.16 To better recognize the role of Li−III cations in the N2 and O2 separation/adsorption process in Li−LSX zeolite and to clarify the Li−III selective interaction with these guest molecules, two parallel sets of all-atom mixture simulations, ones with mobile and the other ones with fixed extraframework Li−III cations were carried out at all different temperatures. Although the previous spectroscopic experimental evidence58 showed the Li−III sites are mobile, the simulations with mobile and fixed Li−III models can help to clarify the effect of (absence of) dynamics of extra-framework sorption sites of similar nanoporous materials, on the microscopic details of selective adsorption/diffusion process. The fixed Li−III simulations are of practical interest in cases where it is possible to reduce the dynamics of adsorbing metal sites up to extremely fixed situation, while the accessibility of the sorption sites are not changed. Figure 2 compares the calculated MSDs for N2 and O2 in the “mix 16−4” at different temperatures when the Li−III cations

both dynamical and structural properties. Thus, it can be said that the applied production run-time of 300 ps is sufficient for calculating the properties (see Figure S2 of the Supporting Information for details). Figure 1 shows the final snapshot of the simulation box viewed along the [110] direction by Rasmol program61 for “mix

Figure 1. Sample snapshot of the simulation box of “mix 16−4” at 298 K within the framework of Li−LSX zeolite with mobile Li−III sites (yellow color) viewed along [110]. It includes the distribution of N2 (blue color) and O2 (red color) guest at 298 K and a close-up view of a supercage of the Li−LSX zeolite. The red, white, and cyan colors represent O, Al, and Si sites of zeolite, respectively.

Figure 2. Comparison of the computed center of mass MSD of N2 and O2 within nanopores of Li−LSX zeolite from “mix 16−4” simulations with mobile Li−III cationic sites at different temperatures. High temperature conditions cannot be used for separation of N2 from air by Li−LSX zeolite.

16−4” at 298 K and allowing mobile Li−III sites. A close-up view of a supercage of Li−LSX zeolite is also shown. The distribution of N2 and O2 guest molecules (blue and red color, respectively) in the framework of Li−LSX zeolite is shown. It can be observed that the N2 molecules are localized near the mobile Li−III sites of the supercages. To simplify the view, the center of mass sites of the guest molecules are not shown. The corresponding snapshot of the simulation box with fixed Li−III sites for the “mix 16−4” simulation is shown in Figure S3 of the Supporting Information for comparison. The basic computational relations and applied methods for computing the different quantities are presented and summarized in the end of the Supporting Information.

are mobile during of simulations. The corresponding result for the fixed Li−III situation is shown in Figure S4. The results show that the motion of guest species is in the sufficiently linear diffusive regime of MSD over time. The temperature dependency of self-diffusion coefficients for the two guests of the binary mixtures in the Li−LSX zeolite considering both the fixed and mobile Li−III ions during the simulation are reported in Table 2. The self-diffusion coefficients, D, are calculated from the slope of MSD curves in the long-time linear regime (in the range of 100−250 ps) which corresponds to the β value, β = d[log MSD]/d[log t], close to 1.62 As seen in Table 2 and also in Figures 2, 3, and S4, O2 diffuses significantly faster than N2 inside Li−LSX especially with a greater relative MSD and/or self-diffusion difference for 1773


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Table 2. Calculated Self-Diffusion Coefficients, Di, of N2 and O2 Molecules in Li−LSX Framework from Two Binary Mixture Simulations Using the Mobile Li−III Model (in Comparison with Those Self-Diffusion Values Using the Fixed Li−III Model in Parentheses) at Different Temperatures from the Linear Regime (100−250 ps) of MSD Plots DN2 (in 10−8 m2·s−1) T (K)

(8N2 + 2O2)/uc

a

260 298b 400 500 600 700

0.75 1.18 2.64 3.80 4.51 5.20

DO2 (in 10−8 m2·s−1)

(16N2 + 4O2)/uc

(0.002) (0.07) (0.65) (1.65) (2.90) (3.71)

0.62 1.01 2.35 3.40 4.07 4.84

(0.016) (0.11) (0.80) (1.79) (2.96) (3.66)

(8N2 + 2O2)/uc 2.34 2.74 3.75 4.18 4.68 5.16

(2.63) (2.94) (4.22) (4.57) (5.01) (5.72)

(16N2 + 4O2)/uc 2.33 2.82 3.66 4.06 4.54 5.05

(2.56) (2.68) (3.95) (4.32) (4.70) (5.28)

Experimental diffusion value at 260 K for N2 in Li−LSX is 0.35 × 10−8 m2·s−1 obtained by QENS.65 bThe PFG NMR intracrystalline N2 selfdiffusivities in NaX zeolite in the temperature range of 135−300 K is about ∼10−11 up 10−9 m2·s−1.66 a

If the uptake kinetic criteria are also satisfied at the low temperature conditions, using the Li−LSX zeolite will give good performance in the separation process of N2 from its binary mixture with O2 at these conditions. This finding is in good agreement with the previous experimental study of inverse temperature effect on the adsorption capacity of LSX zeolites.38 Figure S5 compares the MSDs of N2 guest molecules obtained from the separate similar simulations of “mix 16−4” with fixed and with mobile Li−III cations at different temperatures. The corresponding results for O2 component are showed in Figure S6. As seen in Table 2 and Figures S5 and S6, the self-diffusion and the MSD of N2 shows a strong dependence on the mobility of Li−III cations, while translational motion of the guest O2 molecules do not depend appreciably on the mobility of Li−III cations. Another useful guideline for future design of zeolitic structures can be extracted by comparing the results of fixed and mobile Li−III simulations which are summarized in Table 2 and Figure 3. The calculated self-diffusion values of guests at the same temperatures indicate that the probable lowering of Li−III dynamics (up to extremely fixed situation), corresponding to access higher O2/N2 diffusion selectivity due to the suppression of the diffusion of N2. Therefore, it is possible to increase the selective adsorption of N2 in Li−LSX if it is practically possible to reduce the dynamics of accessible Li−III sorption sites. Parts a and b of Figure 3 clearly show the temperature dependence of the N2 and O2 self-diffusion coefficients of the two studied air binary mixtures, “mix 16−4” and “mix 8−2”, in the pores of Li−LSX zeolite when the Li−III extra-framework cations are mobile or fixed during of separate simulations, respectively. The diffusion selectivity, Sdiff, can be taken from the MD simulation of a binary guest mixture by computing the ratio of the self-diffusivities of species in the mixture.63 Figure 3c involves the temperature dependence of the diffusion selectivity, Sdiff = Dself,1/Dself,2. As shown in Figure 3a,b and Table 2, the self-diffusion of O2 in the two air binary mixture loadings through Li−LSX is higher than that of N2 at the same conditions. The self-diffusion coefficients of both guest components increase with increasing temperature. The calculated self-diffusion coefficients of both N2 and O2 in the “mix 16−4” do not show a quantifiable difference compared with those of in the “mix 8−2”. Ruthven and Post have proposed a classification of intracrystalline diffusion mechanisms of general guest molecules in pores of porous materials on the basis of the pore diameter into three different regions: Molecular, Knudsen, and

Figure 3. Effect of temperature and mixture loading on the computed self-diffusion coefficients of N2 and O2 inside the nanopores of Li− LSX zeolite with (a) mobile Li−III and (b) fixed Li−III. (c) Temperature dependency of diffusion selectivity for two studied binary mixtures with fixed and mobile Li−III situation.

simulations with fixed Li−III at low temperatures. As the temperature increases, the difference in the MSDs and selfdiffusions of N2 and O2 decreases. This trend indicates that the activation energy for diffusion process of N2 within the nanopores of Li−LSX zeolite is higher than that of O2, see Table 3. It can also be concluded that the relatively low temperatures, corresponding to greater differences in the selfdiffusion, are optimal to access high O2/N2 diffusion selectivity. Table 3. Calculated Arrhenius Activation Energies (in kcal· mol−1) for the Diffusion Process of N2 and O2 Molecules in the Li−LSX Framework from Two Binary Mixture Simulations Using Fixed and Mobile Li−III Models fixed Li−III

mobile Li−III

mixture component

8−2) E(mix a

16−4) E(mix a

8−2) E(mix a

16−4) E(mix a

N2a

3.29 0.63

2.88 0.61

1.61 0.64

1.70 0.60

O2

Experimental Eact value for N2 in Li−LSX zeolite is ∼ 2.6 kcal·mol−1 for the low temperature range between 260 and 293 K.65 a

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around 0.6 kcal·mol−1 and show no quantifiable dependency on the fixed or mobile Li−III situation during of simulations. The calculated Eact for the N2 diffusion process through Li−LSX zeolite is around 3−5 times higher than that of the calculated Eact for O2. These numerical Eact values do not show a meaningful difference between “mix 16−4” and “mix 8−2” loadings, but they are in good agreement with the limited experimental Eact value65 (2.6 kcal·mol−1 for N2 in Li−LSX zeolite for low temperature range between 260 and 293 K) and compatible with the common relation of the pore diameter of typical zeolite with guest activation energy. The explicit MSD components in the x, y, and z directions are calculated for the centers of mass of N2 and O2 molecules within the pores of Li−LSX zeolite from trajectory averaging of five short NVT simulations of “mix 16−4” at 260, 400, and 700 K as shown in Figure S8. The approximately same values of three MSD components for each of guest species show that the translational motion of guest molecules in this zeolite is isotropic. The calculated VACFs for the center of mass of N2 and O2 guest molecules at 298, 500, and 600 K for “mix 16−4” from simulations with fixed and mobile Li−III are shown and compared in Figures 5 and 6. The short time average single-

Configurational.64 The diffusion mechanism is in the Molecular (Fickian) regime when the diameter of guest molecule is much smaller than the diameter of the pores in the macroporous materials. Under these conditions, the collisions between molecules occur more frequently than collisions with the macropore wall, causing approximately free movement and resulting in relatively high self-diffusion of guests in the range between ∼10−5 and 10−4 m2·s−1. The number of guest collisions with pore walls increases with decreasing pore diameter. The Knudsen diffusion regime occurs when the pore diameter becomes comparable to or smaller than the mean free path of guest gas molecules. In this regime, diffusion starts to depend on the pore diameter and decreases with decreasing pore diameter due to molecule−pore wall interactions. The self-diffusion of the guest at the end of Knudsen regime is ∼10−8 m2·s−1. Finally, in the microporous materials likes zeolites and MOFs with the pore diameter of less than 2 nm and comparable to the diameters of the guest molecules, the diffusion mechanism is in the Configurational regime. The pore sites and guest molecules will continuously interact in the Configurational regime, causing significant restrictive movement. The self-diffusion coefficients of both the guest molecules, N2 and O2, are in the range of ∼10−9 - 10−8 m2·s−1 as reported in Table 2. This order of guest self-diffusion occurs at the end of the Knudsen and beginning of the Configurational regime with respect to the pore diameter of Li−LSX zeolite, which changes from 7.4 Å in the 12-membered ring up to 12 Å in the internal cavity. The calculated guest self-diffusion values from the current simulations are in good agreement with the limited experimental diffusion data for N2 and O2 in Li−LSX zeolite reported in 2005 by Jobic et al.65 which were based on quasielastic neutron scattering (QENS) techniques; see Table 2. The guest activation energies, Eact, for intracrystalline diffusion process of N2 and O2 from mixture simulations at different temperatures are calculated by linear least-squares fits of the Arrhenius plots (ln D versus (1000/T)) which are shown in Figures 4 and S7 for mobile and fixed Li−III, respectively. The slope of Arrhenius plot gives −Eact/R. The calculated Eact values of N2 and O2 are reported in Table 3. For instance, the Eact values for N2 from “mix 16−4” with fixed and mobile Li−III situation were 2.88 and 1.70 kcal· mol−1, respectively. While, the calculated Eact values for O2 were

Figure 5. Effect of simulations with fixed or mobile Li−III cationic site on the normalized center of mass VACFs of N2 and O2 within Li−LSX zeolite from short MD simulation runs of “mix 16−4” at different temperatures. In contrast of N2, the VACF of O2 is not sensitive to the fixed/mobile Li−III situation.

particle dynamics of guest molecules can be obtained from the VACF plots. As seen in Figure 5, the first zero time in the VACF plot represented a mean collision time which occurs for N2 at the shorter time than that of O2 in both simulations with the fixed and mobile Li−III situations. The mean collision time for N2 in the simulation with fixed Li−III situation occurs at shorter time than that of the simulation with mobile Li−III situation (see the left panels of Figure 5). This first zero time is roughly equal for O2 in both simulations with fixed and mobile Li−III. However, it occurs at few shorter time when the Li−III considered mobile in the simulation. Figure 5 shows the VACF of N2 is very sensitive to the mobile/fixed Li−III situations which indicates a strong association between the adsorption and short single-particle dynamics behavior of N2 and the Li−III situation. In contrast, the VACF of O2 is not sensitive to the mobile/fixed Li−III

Figure 4. Arrhenius plots of the natural logarithm of the self-diffusion coefficient of N2 and O2 versus the inverse temperature 1/T, for determining activation energy of diffusion within Li−LSX zeolite for two studied binary mixtures with mobile Li−III situation. 1775


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Figure 6. Comparison of normalized center of mass VACFs of N2 and O2 within Li−LSX zeolite from “mix 16−4” simulations with fixed and mobile Li−III cationic sites at different temperatures. Sharper VACF of N2 with clear oscillations are obtained from simulations with fixed Li−III.

Figure 7. Comparison of the (Li−III−N2) and (Li−III−O2) RDFs from “mix 16−4” simulations with mobile Li−III cationic sites at different temperatures. The structural correlation between O2 molecules and Li−III cations is significantly weaker than that of N2 molecules. The height of (Li−III−N2) RDF decreases with increasing temperature.

situations. When neighboring N2 molecules collide with each other (especially after being in contact with fixed Li−III for a long time) or, with lower probability collide with the atoms of framework, backscattering occurs which results in negative velocity correlations. The effect of fixed Li−III sites as strongly associated sorption sites of N2 molecules on the velocity relaxation is to cause some shortening of the crossover time and enhance the region of negative and positive correlation, causes the sharper oscillatory behavior in the calculated VACF of N2 from the simulations with fixed Li−III at all studied temperatures.60 Indeed, the molecular animations of the related MD trajectory show the high probability of presence of N2 molecules around the Li−III sites and solid-like vibrational motion of guest N2 molecules which are adsorbed around Li− III cationic sites of Li−LSX zeolite at these conditions (see molecular animation files in the Supporting Information for more understanding). The simulated VACFs of N2 in the mobile Li−III situation are not showed the mentioned oscillation behavior which represents higher N2 translational motion in the simulations with mobile Li−III (Figure 5, left panels). As shown in the left panels of Figure 6, the VACF pattern of N2 is rather similar to the VACF of O2 for the simulation with the mobile Li−III. While, the uneven sharper VACF pattern of N2 is very different with the smoother VACF of O2 for the simulation with the fixed Li−III model. As shown from the smoother VACF of O2 in the right panels of Figure 6, the collisions involve this guest type cause softer backscattering60 because of significantly lower structural correlations of O2 guest molecules with fixed Li−III sites; see the RDF analysis in section 3.2 for more detail. 3.2. The Structural Analysis of the “Mix 16−4” on the Basis of the RDFs. In Figures 7−9 and S9−S11, microscopic structural details of guest molecules inside Li−LSX zeolite are studied mainly by calculating the partial site−site RDFs from MD simulations of “mix 16−4” at different temperatures for both mobile and fixed Li−III situation. We particularly focus on the RDF between the center of mass of guest molecules (N2 or O2) and Li−III cationic sites as the active centers of Li−LSX

Figure 8. Comparison of the (Li−III−N2) and (Li−III−O2) RDFs from “mix 16−4” simulations with fixed Li−III cationic sites at different temperatures. Sorption of N2 with Li−III cations is much higher than that of O2. The height of (Li−III−N2) RDF decreases with increasing temperature.

zeolite for gas adsorption process. In addition, molecular animations were extracted from MD trajectories to visualize the microscopic molecular structural behaviors. Figure 7 shows the comparison of the calculated RDFs between the Li−III and the center of mass of N2 or O2 from the “mix 16−4” simulations with the mobile Li−III situation at different temperatures. The corresponding result for the fixed Li−III situation during of simulations is shown in Figure 8. As seen in both Figures 7 and 8, the strongest structural association is between the Li−III extra-framework cationic sites and the guest N2 molecules. While, there is no structural correlation between the Li−III and the guest O2 molecules. The contribution of Coulombic interactions between O2 molecules and Li−III cations is relatively weaker than that of 1776


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mobile Li−III at 298 K (see two animation files as Supporting Information). O2 has fairly uniformed distribution within supercages without any significant association with both fixed and mobile Li−III cationic sites. While, N2 molecules adsorb around Li−III sites and undergo a short ranged periodic oscillating motion around the fixed Li−III and experience transiently attached to the mobile Li−III. The video files visually show that indeed the N2 molecules spend shorter times around the mobile Li−III cations compared with around the fixed ones (see also Figures S3 and 1). The mobility of the Li− III cations does indeed decrease the mean time of association of the N2 molecules with the cation. This observation is also partly included in the (N2−Li−III) RDF plots of Figure S9 at different temperatures. These plots indicate that the N2 association with mobile Li−III is lower than that of fixed Li− III and this association is weakened at higher temperatures as expected. Figure 9 shows the comparison of the structural correlations between the three different extra-framework Li+ sites of the Li− LSX zeolite and the center of mass of the two guest components of the “mix 16−4” which is represented by the (N2--Li) and (O2--Li) RDFs. The effect of the selected mobile or fixed Li−III sites on these RDFs can also be observed. In the RDFs between N2 and Li−I or Li−II, and also in RDFs between each of three different Li+ sites and O2, there are no significant peaks, indicating that the probability of presence of N2 molecules around the sites I and II Li+ and the probability of presence of O2 molecules around three different Li+ sites is negligible. This observation from Figure 9 is in very good agreement with previous experimental adsorption reports19,37,47 which showed only Li−III sites in the supercages of Li−LSX zeolite framework are available to interact with guest gases such as N2 and H2. The accessible Li−III cationic sites are in a high energy, low coordination environment in the supercages, while other Li+ cations further imbedded in the framework and are sterically inaccessible to guest molecules.35 Figure S11 shows the RDF curves between center of mass of N2 or O2 and oxygen, aluminum, and silicon atoms of the rigid framework of Li−LSX zeolite for “mix 16−4” at 400 K. Both guest molecules show similar behavior and do not have strong structural correlations with O, Al, and Si framework sites.

Figure 9. Computed RDFs between the center of mass of N2 or O2 molecules with the different extra-framework Li+ sites of Li−LSX zeolite from “mix 16−4” simulations with fixed and mobile Li−III cations at 400 K.

N2 molecules (see partial charges in Table 1) and as a result, sorption of N2 by Li−III cations is much stronger than that of O2. A strong RDF peak between N2 and Li−III appears in short distances around 2.3 Å with high intensity at all temperatures as seen in Figure 7. There are strong electrostatic and van der Waals interactions between the center of mass of N2 molecules and the Li−III cationic sites as key adsorption sites of Li−LSX zeolite. Recent gas chromatography studies for the guest N2, O2, and Ar molecules within the zeolite X with alkali or alkaline-earth metals, indicate that the extra-framework cations are the principle sites for selective interactions with the N2 sorbate molecules.67 Increasing the temperature decreases the intensity of the (N2−Li−III) RDF peak and broadens it as expected (see Figures 7 and 8). At lower temperatures, the first coordination layer is bound more tightly to the Li−III and a sharper peak in the (N2−Li−III) RDF will be observed. Furthermore, increasing temperature does not have quantifiable influence on the (O2−Li−III) RDF peaks, as shown in Figures 7 and 8. Figure S9 shows the comparison of the calculated (N2−Li− III) RDFs in the “mix 16−4” from the separate simulations with the fixed or mobile Li−III cationic sites at different temperatures. The corresponding (O2−Li−III) RDFs are shown in Figure S10. At each temperature, in the calculated (N2−Li−III) RDF from the simulation at the mobile Li−III condition, there is relatively weaker and broader peak when compared to the corresponding strong sharper RDF peak from the simulation at fixed Li−III condition. In the simulation with the mobile Li−III sites, the first neighbor layer of N2 around Li−III is less compact and includes a smaller number of molecules in the first coordination layer than the fixed Li−III condition as seen in Figure S9. Grand-canonical Monte Carlo (GCMC) of propane adsorption in the FAU type zeolites by Zhang et al.68 showed that the number density of extra-framework cations has a principle role in the amount of adsorption. There are no differences in the intensity of the calculated (O2−Li−III) RDFs from the separate simulations with the fixed or mobile Li−III cationic sites at different temperatures (Figure S10). There is strong dynamical correlation between the N2 guest molecules and Li−III cationic sites, as we discuss in the MSD analysis part. Figures S5, S9, 5, 7, and 8 show strong dynamical and structural correlations between N2 molecules and Li−III sorption sites. We can clarify the microscopic behavior of Li− III cationic sites interacting with guest molecules by focusing on the molecular animations constructed from the short parts of MD trajectories of “mix 16−4” simulations with fixed and

4. CONCLUSIONS Understanding dynamical properties, self-diffusion, and microscopic structure of guest mixtures in nanoporous zeolites that include extra-framework cations is essential to efficient design and improved performance of different technological applications. Because of commercial application of Li−LSX zeolite in the air separation process at dry conditions and to better understand this process at the molecular level, extensive allatom MD simulations at different temperatures are performed for atmospheric N2/O2 binary mixtures within Li−LSX zeolite in both fixed and mobile designed states of extra-framework Li−III sorption cationic sites. The details of dynamical behavior of N2 and O2 in the Li− LSX zeolite are compared by computing the MSD, VACF, selfdiffusion, the activation energy of the diffusion process and the diffusion selectivity. The microscopic structural details of guest molecules are determined by calculating of partial site−site RDFs, constructing molecular animations of MD trajectories, and from snapshots visualizing the molecular structures of simulation boxes. In particular, we determine the influence of the mobile or the fixed state of Li−III cations and temperature 1777



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on the intracrystalline behavior of guest species. It is important to emphasize the critical role of performing trajectory averaging on several production runs to improve reproducibility and the statistical accuracy of dynamical results of guest molecules. O2 diffuses significantly faster than N2 through zeolite, especially with a greater relative diffusivity difference at low temperatures. Temperature dependence of the guest MSDs and corresponding self-diffusions indicates that the Arrhenius activation energy for the diffusion process of N2 within the pores of Li−LSX zeolite is around 3−5 times higher than that of O2. The dynamical results confirm the strong dependence of N2 guest molecule dynamics (the inverse of O2 case) to the fixed or mobile state of Li−III sites in the simulation runs. The order of magnitude of the calculated guest self-diffusion coefficients are in the range of ∼10−9−10−8 m2·s−1 which places the diffusion mechanism at the end of the Knudsen and beginning of the Configurational regime with respect to the pore diameter of Li−LSX zeolite, which varies from 7.4 Å up to 12 Å. The mean collision time (first zero point) in the VACF plot occurs for N2 at a shorter time than that of O2 in both simulations with the fixed and mobile Li−III. The VACF of N2 is very sensitive to the mobile/fixed Li−III state which is related to a strong association between the adsorption of N2 and the Li−III site. In contrast, the VACF of O2 is not sensitive to the mobile/fixed Li−III situations. RDF analysis shows the strongest structural association is between the Li−III extra-framework cationic sites and the guest N2 molecules. While, there is no structural correlation between the Li−III and the guest O2 molecules. The intensity of the (N2−Li−III) RDF peak decreases with increasing temperature and the peak broadens as expected. At lower temperatures, the first coordination layer has greater structure, and sharper (N2− Li−III) RDF peaks are observed. Furthermore, increasing temperature or performing separate simulations with mobile and with immobile Li−III do not have quantifiable influence on the (O2−Li−III) RDF peaks. Comparison of constructed molecular animations from MD trajectories of simulations with both fixed and mobile Li−III situation shows that the attached N2 molecules to Li−III are much more readily stripped off from mobile cations than from fixed ones. Thus, the N2 attachment time is notably enhanced with fixed Li−III cations and with decreasing temperature. Existing simulations show the major role of Li+ cations in site III in sorption of N2 guest molecules and indicate Li+ cations in sites I and II are not accessible for effectively interacting with guest molecules, and consequently, they do not participate in the sorption process. This observation is in good agreement with experimental and computational findings. Current simulation analyses emphasize the fact that many interesting N2 guest behaviors vary significantly with considering internal surface motion for Li−III extra-framework cationic sites. Hence, a future comprehensive study of guest behavior in the all-atom flexible (vibrating) framework seems to be more realistic than that of with rigid framework. In future work, the quantitatively characterization of the details of N2 attachment to Li−III sites will be studied and the influence of considering mobile or immobile Li−III states and temperature on the scale of mean associated time of guest molecules to key Li−III sorption sites will be determined.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b11611. Figure showing the main types of cation positions in the framework of faujasite, the effect of simulation run-time on the calculated (guest−Li−III) RDFs and the MSDs of guest molecules from binary air mixture simulations in Li−LSX zeolite with mobile Li−III at 400 K, a snapshot of the equilibrated simulation box of “mix 16−4” at 298 K within the framework of Li−LSX zeolite with fixed Li− III sites, effect of simulations with fixed or mobile Li−III cationic site on the computed center of mass guest MSDs and also on the (Li−III−guest) RDFs, Arrhenius plots for simulations with fixed Li−III, computed explicit center of mass MSD components of guest species, the RDF between the center of mass of N2 or O2 and O, Al, and Si atoms of Li−LSX zeolite framework, and finally the applied basic relations for computing the different quantities (PDF) Molecular animation file constructed from short (2 ps) parts of MD trajectories of “mix 16−4” in Li−LSX zeolite with fixed Li−III cationic site at 298 K (MPG) Molecular animation file constructed from short (2 ps) parts of MD trajectories of “mix 16−4” in Li−LSX zeolite with mobile Li−III cationic site at 298 K (MPG)

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +98 24 3315 3207. Fax: +98 24 3315 3232. Email: [email protected]; [email protected] (M.H.K.). ORCID

Mohammad H. Kowsari: 0000-0003-4391-194X Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The support for this work by the Department of Chemistry and the Center for Research in Climate Change and Global Warming (CRCC) of the Institute for Advanced Studies in Basic Sciences (IASBS) are gratefully acknowledged. The author thanks Dr. Mahmud Ashrafizaadeh for introduction to Li−LSX zeolite, helpful suggestions, and discussions on the initial stages of this project. Helpful discussions and comments by Dr. Saman Alavi are also gratefully acknowledged.

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REFERENCES

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