Tracing the origins of transient overshoots for binary mixture diffusion in microporous crystalline materials

Abstract

Separation of mixtures using microporous crystalline materials is normally achieved by exploiting differences in the adsorption strengths of the constituent species. The focus of the current investigation is on diffusion-selective separations that exploit differences in intra-crystalline diffusivities of guest molecules. A number of experimental investigations report overshoots in intra-crystalline loadings of the more mobile species during transient mixture uptake. Analogous overshoots in fluxes occur for mixture permeation across thin microporous membrane layers. The attainment of supra-equilibrium loadings is a common characteristic of diffusion-selective separations; this allows the over-riding of adsorption selectivities. The primary objective of the current investigation is to demonstrate that the Maxwell-Stefan diffusion formulation, using chemical potential gradients as driving forces, is capable of providing a quantitative description of the temporal and spatial overshoots found in diverse experimental studies. The origins of the overshoots can be traced to thermodynamic coupling effects that emanate from sizable off-diagonal contributions of the matrix of thermodynamic correction factors. If thermodynamic coupling effects are neglected, the overshoots are not realized. It is also demonstrated that while the transport of the more mobile partner is uphill of its loading gradient, its transport is downhill the gradient of its chemical potential. The deliberate exploitation of uphill diffusion to achieve difficult separations is highlighted.

Highlighting the Influence of Thermodynamic Coupling on Kinetic Separations with Microporous Crystalline Materials

“…29 If thermodynamic coupling effects are ignored and the assumption Γ ij = δ ij is invoked, no overshoots in CO 2 uptake are experienced, and the simulations show poor agreement with experiments during the early transience. 29…”

“…The attainment of supraequilibrium loadings of N 2 during the early transience signals the phenomena of uphill diffusion, which can be exploited to achieve kinetic separations in fixed-bed adsorption devices. 7,20,29…”

“…3,36−38 The experimental data of Majumdar et al 43 on transient uptake of N 2 /CH 4 mixtures in Ba-ETS-4 show overshoots in N 2 loading, confirming the manifestation of uphill diffusion and thermodynamic coupling effects. 18,29…”

“…At any time t , the component loadings at the surface of the particle q i ( r c , t ) = q i * is in equilibrium with the bulk phase gas mixture. 29 The loadings q i * are determined by the IAST or mixed-gas Langmuir model, as appropriate. 30…”

Application of microimaging to diffusion studies in nanoporous materials

“…of the concentration gradient of component j on the diffusive flux of component i. This behavior as following with the Maxwell-Stefan formalism of irreversible thermodynamics (Kärger et al 2012;Krishna 2015Krishna , 2016Krishna , 2019Kärger and Ruthven 2016) has now, with the potentials of microimaging, become accessible by direct monitoring.…”