Particle Distribution in a Microporous Material: Experiments with Zeolite A

Abstract

The theory on particle distribution and exchange equilibria in a microporous material is applied to experimental ion-exchange data involving zeolite Na-A and zeolite K-A, with silver ions as the exchanging species. The presented method enables direct evaluation of the measured data and consideration of nonequivalent particle sites. The isotherms of the K+ versus Ag+ exchange in zeolite K-A rise much more steeply, at low exchange degrees, than those of the Na+ versus Ag+ exchange in zeolite Na-A. This result implies a different course of the ion-exchange reactions. Spectroscopic measurements on dehydrated, partly silver-exchanged zeolites Na-A and K-A do indeed show that in zeolite Na-A, the Na+ ions occupying four-ring positions are exchanged faster for Ag+ than the Na+ ions occupying eight- and six-ring positions, while in zeolite K-A the exchange does not start with the four-ring ion but with six-ring ions, followed by the four-ring ion. These findings are consistent with the results obtained from evaluation of the ion-exchange data. The resulting thermodynamic quantities significantly differ from published reference values, which we suggest should be revised.

Entropy in Multiple Equilibria, Systems with Two Different Sites

“…This is a simplification which allows studying systems quantitatively by experimental and theoretical means which otherwise might be difficult to handle. A numerical analysis of experimental data for a system with 5 different types of sites has been carried out based on this reasoning and has allowed to correct earlier reports on the reaction entropy of silver zeolite A [16]. We improve the physical insight by discussing a simple Xm{AB}Xn system in detail.…”

“…Instead of inventing adsorption models, it might make sense to describe a system in such terms. The system may consist of one set of equivalent sites [1], two sets, as reported here, or even of several sets of equivalent sites [16].…”

“…The same holds for K2, K5, and K8 and also for K3, K6, and K9. From this follows a further simplification from the application of the particle distribution function f(n,r) [1,16,30], where n is the total number of equilibria of a set and r counts the individual equilibria in a set; r = 0, 1, …, n − 1:…”

Particle Distribution in a Microporous Material: Theoretical Concept

“…The theory can be used to evaluate ion-exchange experiments, since the inequivalence of cation sites can be accounted for in the evaluation of experimental results. [5] The common result of three different derivations of the distribution formula is reported, and we derive formulae for the free-energy, the enthalpy, and the entropy of ion-exchange reactions, based on the particle exchange theory. We intentionally choose a different approach than found in important literature on the statistical-mechanics-based analysis of sorption thermodynamics in zeolites and other crystalline nanoporous solids, because the goals are also different in some aspects.…”

“…Nevertheless, we can show that in spite of its simplicity, the results can be used for the excellent evaluation of measured ion-exchange isotherms. [5] We initially assume that all cation sites in the host are equivalent. The inequivalence of host sites can be taken into account in a second step.…”