Highlighting the Anti-Synergy between Adsorption and Diffusion in Cation-Exchanged Faujasite Zeolites.

Using configurational-bias Monte Carlo simulations of adsorption equilibrium and molecular dynamics simulations of guest diffusivities of CO2, CH4, N2, and O2 in FAU zeolites with varying amounts of extra-framework cations (Na+ or Li+), we demonstrate that adsorption and diffusion do not, in general, proceed hand-in-hand. Stronger adsorption often implies reduced mobility. The anti-synergy between adsorption and diffusion has consequences for the design and development of pressure-swing adsorption and membrane separation technologies for CO2 capture and N2/O2 separations.

Introduction

Despite the burgeoning research and development activities on novel metal–organic frameworks (MOFs) in separation applications, cation-exchanged zeolites remain viable contenders for use as adsorbents in the industrial practice. For post-combustion CO2 capture, Na+ cation-exchanged FAU (faujasite) zeolite, NaX, also commonly known by its trade name 13X (with Si/Al ≈ 1.2), is considered to be the benchmark adsorbent, with the ability to meet government targets for CO2 purity and recovery.[1] NaX zeolites are also of potential use in natural gas purification,[2,3] alkane/alkene separations,[4−8] and hydrogen purification processes.[3,9−23] Coulombic interactions of CO2 and unsaturated alkenes with the extra-framework cations (e.g., Na+, Ca++, Li+, and Ba++) result in strong binding; the binding strength and selectivity can be tuned by the appropriate choice of the extra-framework cations and the adjustment of the Si/Al ratios.[9,11,20,24−26]

Li+ cation-exchanged FAU (faujasite) zeolite is commercially used for separation of N2/O2 mixtures.[23,27,28] For supplying medical grade oxygen to prevent hypoxemia-related complications related to COVID-19, portable medical oxygen concentrators commonly use LiLSX (LS = low silica; Si/Al ≈ 1) to achieve high N2/O2 adsorption selectivities, ensuring enhanced rejection of purified O2, the desired product.[29,30]

For separation applications using pressure-swing adsorption (PSA) technology, consisting of adsorption/desorption cycles, there is often a mismatch between the requirements of strong adsorption and ease of desorption.[31] For example, NaX has a very strong affinity for CO2, but the regeneration requires application of deep vacuum. For CO2 capture from flue gases, Prats et al.[25,26] have used molecular simulations of mixture adsorption in FAU to determine the optimum Si/Al ratio for PSA operations.

In the design and development of PSA technologies employing cation-exchanged zeolite adsorbents, we also require data on the intracrystalline diffusivities of guest molecules. Most commonly, diffusion limitations cause distended breakthrough characteristics and reduction in the purities of the desired products.[31−36] Diffusivity data are also of vital importance in the development of zeolite membrane constructs for mixture separations in which cation-exchanged zeolites are used as thin layers or as fillers in mixed-matrix configurations.[37−43]

The primary objective of this communication is to gain some fundamental thermodynamic insights into the adsorption and diffusion characteristics of a variety of guest molecules such as CO2, CH4, N2, and O2 in FAU zeolites with varying amounts of extra-framework cations: Na+ and Li+. The desired insights are obtained by performing configurational-bias Monte Carlo (CBMC) simulations of adsorption and molecular dynamics (MD) simulations of diffusion in Na- and Li-exchanged FAU zeolites with varying Si/Al ratios. The CBMC and MD simulation methodologies, along with details of the force field implementations, are detailed in the Supporting Information accompanying this publication. We aim to demonstrate the anti-synergy between adsorption and diffusion; the stronger the binding of a guest molecule, the lower is its mobility. Such insights are of vital importance in determining the optimum Si/Al ratio of zeolite for use in PSA technologies or in membrane constructs.

The Gibbsian Concept of Spreading Pressure

The spreading pressure, π, is related to the molar chemical potential, μ, by the Gibbs adsorption equation[44]where A represents the surface area per kg of framework, and q is the component molar loading in the adsorbed phase mixture. At thermodynamic equilibrium, the μ are related to the partial fugacities in the bulk fluid mixture

In developing the ideal adsorbed solution theory (IAST), Myers and Prausnitz[45] write the following expression relating the partial fugacities in the bulk gas mixtureto the mole fractions, x, in the adsorbed phase mixture

In eq , P0 is the pressure for sorption of every component i, which yields the same spreading pressure, π, for each of the pure components as that for the n-component mixture:

In eq , q0(f) is the pure component adsorption isotherm. Since the surface area A is not directly accessible from experimental data, the surface potential πA/RT ≡ Φ, with the units mol kg–1, serves as a convenient and practical proxy for the spreading pressure π.[46−49] As derived in detail in the Supporting Information, the fractional pore occupancy, θ, is related to the surface potential bywhere qsat, mix is the saturation capacity for mixture adsorption. Equation implies that Φ may also be interpreted as a proxy for the pore occupancy; it is the fundamentally correct yardstick to compare the adsorption and diffusion characteristics of different host materials.[41,48−50]

In view of eq , we may express the adsorption selectivity for the i–j pair as follows

Applying the restriction specified by eq , it follows that Sads is uniquely determined by the surface potential Φ, irrespective of the mixture composition and total fugacity, ft.

Results and Discussion

CO2 Capture Using Na-Exchanged FAU

Figure a plots the CBMC data on isosteric heats of adsorption, Qst, a measure of the binding energies, of CO2 and CH4 in FAU (0 Al, all-silica), NaY (54 Al uc–1), and NaX (86 Al uc–1) zeolites, plotted as a function of the surface potential Φ. For CO2, the hierarchy of Qst is NaX > NaY > FAU; this hierarchy reflects the strong electrostatic interactions with the extra-framework cations, engendered by the large quadrupole moment of CO2. For CH4, the differences in the Qst in the three different hosts are considerably smaller because the adsorption of CH4 is due to van der Waals interactions that also increase with increasing number of cations.

Figure 1

(a) CBMC simulations of the isosteric heats of adsorption, Qst, of CO2 and CH4 in FAU (0 Al, all-silica), NaY (54 Al uc–1), and NaX (86 Al uc–1) zeolites, determined at 300 K, plotted as a function of the surface potential Φ. (b) MD simulations of the self-diffusivities, D, of CO2 and CH4 in FAU, NaY, and NaX zeolites, determined at 300 K, plotted as a function of the surface potential Φ. All simulation details and input data are provided in the Supporting Information accompanying this publication.

Strong binding of guest molecules also implies a higher degree of “stickiness” and, consequently, lower mobility.[51,52] To demonstrate this, Figure b presents the MD simulations of the unary self-diffusivities, D, of CO2 and CH4 in FAU (0 Al), NaY, and NaX zeolites. Compared at the same surface potential Φ, the hierarchy of self-diffusivities is precisely reverse of the hierarchy of Qst. Noteworthily, CH4, the guest with the larger kinetic diameter of 3.8 Å, has a higher mobility than CO2, which has a smaller kinetic diameter of 3.3 Å. The fallacy of using kinetic diameters to anticipate hierarchies in the diffusivity values has been underscored in published works.[15,51]

CBMC simulations were carried out for equimolar (f1 = f2) CO2(1)/CH4(2) mixtures in FAU (0 Al), NaY, and NaX zeolites. The values of the adsorption selectivities, Sads, are plotted in Figure a as a function of Φ. The hierarchy of Sads values is NaX > NaY > FAU (0 Al), reflecting the stronger binding of CO2. The corresponding hierarchy of diffusion selectivities, Sdiff = D1, self/D2, self, is precisely the reverse of Sads; evidently, mixture adsorption and diffusion do not proceed hand-in-hand. This anti-synergy has important consequences of use of cation-exchanged zeolites in membrane constructs. If the partial fugacities of the components at the downstream face are negligibly small in comparison with those at the upstream face, the component permeabilities may be estimated from the following expression[41]

Figure 2

Comparison of CBMC/MD simulations of (a) adsorption selectivities, Sads, and (b) diffusion selectivities, Sdiff, of CO2/CH4 mixtures in FAU (0 Al), NaY, and NaX zeolites at 300 K. The selectivities are plotted as a function of the surface potential Φ. All simulation details and input data are provided in the Supporting Information accompanying this publication.

For FAU (0 Al), NaY, and NaX zeolites, Figure a,b compares the values of the CO2 permeabilities, Π1, and the permeation selectivity

Figure 3

Comparison of (a) CO2 permeability, Π1, and (b) permeation selectivity, Sperm, for CO2(1)/CH4(2) mixtures in FAU (0 Al), NaY, and NaX zeolites at 300 K; the x-axis represents the surface potential Φ. (c) Robeson plot of Sperm vs Π1 data at ft = f1 + f2 = 106 Pa and 300 K. All simulation details and input data are provided in the Supporting Information accompanying this publication.

The CO2 permeabilities, Π1, decrease with increasing values of Φ. The Sperm is a product of the adsorption selectivity and diffusion selectivity (cf. Figure a,b). While the Sdiff increases with Φ for all three hosts, the Sads increases with Φ until a maximum is reached for NaX and NaY and decreases on a further increase in Φ. Consequently, the Sperm also shows a maximum value for NaX and NaY. For the specific choice of upstream operating conditions, ft = f1 + f2 = 106 Pa, Figure c shows the Robeson[53] plot of Sperm vs Π1 for the three host structures. We note that the performances of both NaY and NaX lie above the line representing the Robeson upper bound.[53] Since both Sperm and Π1 are important metrics governing the choice of the appropriate membrane material, there is room for optimization of the Si/Al ratio depending on the relative weightage to be assigned to permeation selectivity and permeability. CBMC/MD data that are analogous to those presented in Figures and 3 are obtained for CO2/N2, CO2/H2, CH4/H2, CH4/C2H6, and CH4/C3H8 mixtures in FAU (0 Al), NaY, and NaX (see Figures S60–S64 of the Supporting Information).

N2/O2 Separations Using Li-FAU and Na-FAU

Figure a presents MD simulations of the unary self-diffusivities, D, for N2, at 300 K in Li-exchanged FAU zeolites, with different Al contents per unit cell: 0, 48, 54, 86, and 96, plotted as functions of the surface potential Φ; the contents of Li+ are equal to that of Al. The magnitudes of D decrease with increasing values of Φ, which also serves as a proxy for the pore occupancy. At any specified value of Φ, the values of the self-diffusivity, D, show the following trend: FAU (0 Al) ≫ FAU (48 Al) ≈ FAU (54 Al) > FAU (86 Al) ≈ FAU (96 Al). This hierarchy of D values correlates, inversely, with the corresponding values of the isosteric heats of adsorption of N2 (cf. Figure b). N2 has a significant quadrupole moment, and the electrostatic interaction potentials increase with increasing Al content, leading to increasing binding energies. The data in Figure a,b confirm that the diffusional mobility of N2 is reduced with increased binding energy.

Figure 4

(a) MD simulations of the unary self-diffusivities for N2 at 300 K in Li-exchanged FAU zeolites, with different Al contents per unit cell: 0, 48, 54, 86, and 96, plotted as a function of the surface potential Φ. (b) Isosteric heats of adsorption, Qst, plotted as a function of the number of Al atoms per unit cell. (c) MD simulations of the unary self-diffusivities for O2 at 300 K in Li-exchanged FAU zeolites, with different Al contents per unit cell: 0, 48, 54, 86, and 96, plotted as a function of the surface potential Φ. All simulation details and input data are provided in the Supporting Information accompanying this publication.

On the other hand, we note from Figure b that the isosteric heats of adsorption of O2 are practically uninfluenced by the addition of extra-framework cations due to the significantly lower quadrupole moment of O2. Therefore, we should anticipate that the mobility of O2 should be practically independent of the degree of Li exchange; this expectation is fulfilled by the MD simulations of the self-diffusivities of O2 in Li-FAU (see Figure c).

For 80/20 N2/O2 mixture adsorption, Figure a plots the adsorption selectivities, Sads, of Li-exchanged FAU zeolites, with different Al contents. We note that the Sads increases with increasing Al content. MD simulations of the N2/O2 diffusion selectivities, Sdiff, plotted in Figure b, demonstrate the anti-synergy between adsorption and diffusion; the higher the adsorption selectivity, the lower is the corresponding diffusion selectivity. Analogous CBMC and MD simulations with Na-exchanged FAU zeolites were also carried out; the results are provided in Figures S73–S81 of the Supporting Information.

Figure 5

(a) CBMC simulations of the adsorption selectivity, Sads, for binary 80/20 N2/O2 mixture adsorption in Li-FAU, with different Al contents per unit cell: 0, 48, 54, 86, and 96. (b) MD simulations of the N2/O2 diffusion selectivity, Sdiff, at 300 K in Li-FAU zeolites. All simulation details and input data are provided in the Supporting Information accompanying this publication.

For 80/20 N2/O2 mixture separations at a total fugacity of 100 kPa, Figure a compares the adsorption selectivities of Li-FAU and Na-FAU. For the same Al content, we note that the Sads values with Li-FAU are significantly higher than for Na-FAU. The interaction potential, engendered by the quadrupole moment, is inversely proportional to the cube of the center-to-center distance between nitrogen molecules and the extra-framework cation (see the detailed explanation provided in Chapter 2 of the Supporting Information). Due to the smaller ionic radius of Li+, compared to Na+, the N2–Li+ distances are smaller than the N2–Na+ distances; this is confirmed by radial distribution functions for N2–Li+ and N2–Na+ pairs for 80/20 N2/O2 mixture adsorption in Li-FAU(96Al) and Na-FAU(96Al) (see Figure ).

Figure 6

Comparison of the (a) adsorption selectivity and (b) diffusion selectivity for 80/20 N2/O2 separations using either Li-exchanged or Na-exchanged FAU zeolites, with different Al contents per unit cell: 0, 48, 54, 86, and 96. All simulation details and input data are provided in the Supporting Information accompanying this publication.

Figure 7

Radial distribution functions for N2–Li+ and N2–Na+ pairs for 80/20 N2/O2 mixture adsorption in Li-FAU (96Al) and Na-FAU (96Al) at 100 kPa and 300 K.

The N2/O2 diffusion selectivities for Na-FAU are only slightly higher than those of Li-FAU (see Figure b). The CBMC/MD data rationalize the use of LiX, with Al ≈ 96 uc–1, in the industrial practice.[29,30]

Figure shows a Robeson plot of Sperm vs N2 permeabilities of N2 for binary 80/20 N2/O2 mixture permeation across the Li-FAU zeolite membrane at an upstream total pressure of 100 kPa. We note that the separation performance increases monotonously with increasing degrees of Li+ exchange; the permeabilities are significantly higher than the values reported in the literature[54] for polymeric and mixed-matrix membranes.

Figure 8

Robeson plot of Sperm vs N2 permeabilities for binary 80/20 N2/O2 mixture permeation across the Li-exchanged FAU zeolite membrane, with different Al contents per unit cell: 0, 48, 54, 86, and 96. All simulation details and input data are provided in the Supporting Information accompanying this publication.

Conclusions

A combination of CBMC and MD simulations for adsorption and diffusion of guest molecules CO2, CH4, N2, and O2 in FAU zeolites with varying amounts of extra-framework cations (Na+ or Li+) was carried out to investigate the influence of varying Si/Al ratios on mixture separations. Stronger adsorption, with increasing amounts of extra-framework cations, results in lowered diffusivities. For CO2/CH4 and N2/O2 mixture separations, the adsorption selectivity, Sads, and diffusion selectivity, Sdiff, do not proceed hand-in-hand. The anti-synergy between adsorption and diffusion has important consequences for the choice of the extra-framework cation, Na+ or Li+, and the Si/Al ratio for use in PSA and membrane separation technologies.