Ion exchange in porous crystals: Part II. The relationship between self- and exchange-diffusion coefficients

Abstract

It has been shown that, using chabazite as exchanger, no previous (1, 2) theoretical treatment allows one to calculate integral (and therefore differential) inter-diffusion coefficients, D A B , from the self-diffusion coefficients, D ∗ A and D ∗ B , for the ion-pairs Ca 2+ ⇋ Sr 2+, Ca 2+ ⇋, Ba 2+ and Sr 2+ ⇋ Ba 2+. In part the failure of the previous treatments arises from a strong dependence of the self-diffusion coefficients upon the cationic composition of the chabazites, as shown for Sr 2+ and Ca 2+. However, correction for this concentration dependence still left a substantial discrepancy between theoretical and experimental values of d A B . A second important factor is that the previously developed (1) expression relating the differential inter-diffusion coefficient D A B and D ∗ A and D ∗ B , i.e. D AB= D A ∗D B ∗(C AZ a 2+C BZ B 2) D A ∗C AZ A 2+D B ∗C BZ B 2 is over-simplified. The correct relationship has been derived, and a special case of this relationship has been used to recalculate the integral inter-diffusion coefficients for the Sr 2+ ⇋ Ca 2+ exchange. Although this improved the correspondence between measured and calculated inter-diffusion coefficients, the discrepancy remained considerable. Some possible reasons for this were discussed.