Thermodynamic Insights into the Characteristics of Unary and Mixture Permeances in Microporous Membranes

Abstract

The primary objective of this article is to gain fundamental insights into the dependences of component permeances Π i in microporous membranes on the operating conditions (upstream partial pressures, temperature, and feed composition). It is argued that the permeances Π i for unary systems and mixtures need to be compared on the basis of the adsorption potential π A / RT , a convenient and practical proxy for the spreading pressure π that is calculable using the ideal adsorbed solution theory for mixture adsorption equilibrium. The use of π A / RT as a yardstick serves to elucidate and rationalize a wide variety of published experimental Π i data on unary and mixture permeances in microporous membranes. For cage-type host structures such as SAPO-34, DDR, and ZIF-8, the Π i values are uniquely dictated by the magnitude of π A / RT , irrespective of the partner species in the mixture. For MFI membranes, the tardier species slows down the more mobile partners due to correlated molecular motion within the channels; the degree of correlation is also a function of π A / RT .

Using Molecular Simulations to Unravel the Benefits of Characterizing Mixture Permeation in Microporous Membranes in Terms of the Spreading Pressure

“…As a consequence, the diffusion selectivity S diff is also uniquely dependent on Φ. When compared at the same Φ, the component permeabilities, Π i , for CO 2 , CH 4 , and N 2 , determinable from CBMC/MD data using eq , are found to be largely independent of the partners in the various mixtures investigated and have practically the same values as the values for the corresponding unary permeabilities. This simple result, verified in a number of experimental investigations, has important consequences for membrane process development. In all investigated mixtures, the permeability of H 2 falls significantly below the values of the unary permeabilities. As exemplified in Figure for CO 2 /CH 4 separation, the hierarchy of S ads versus Φ data are found to be precisely opposite to the hierarchy of S diff versus Φ data. This underscores the fact that adsorption and diffusion do not go hand-in-hand.…”

“…Experimental verification that the data such as these illustrated in Figures 4, 5, and 6 are available for a wide variety of guest/host combinations; see earlier work. 44 For CO 2 /H 2 permeation in MFI, for example, a fundamental reanalysis 44 of the experimental data of Sandstrom et al 10 provides confirmation that the permeability of H 2 in mixtures with CO 2 is significantly lowered by about an order of magnitude below the value for unary H 2 permeation. For permeation of various mixtures across the SAPO-34 membrane, the same set of experimental data in Figure 2, is plotted in Figure 7 as functions of Φ, determined at the upstream membrane face.…”

“…Consequently, Φ is also the thermodynamically appropriate parameter to describe the loading dependence of diffusivities in microporous materials, as has been established in earlier publications. 27 , 44 Further background on the wide variety of loading dependences of guest molecules in nanoporous materials is available in the published literature. 45 − 49 The presence of surface barriers has also been demonstrated to have a significant influence of the guest diffusivities.…”

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

“…Equation 6 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 …”

Thermodynamically Consistent Methodology for Estimation of Diffusivities of Mixtures of Guest Molecules in Microporous Materials

“…23,25,33,34 SAPO-34 has the same structural topology as CHA zeolite, consisting of cages of volume 316 Å 3 , separated by 8-ring windows of 3.8 × 4.2 Å size. 23 Compared at the same value of π A / RT , the magnitude of ρ Đ i /δ for a binary mixture is comparable to that for the corresponding pure component. Also noteworthy, from the data in Figure 1 is that the dependence of ρ Đ i /δ on π A / RT is distinctly different for each guest molecule.…”