Detecting Binary Solid-Phase Interactions in Ternary Ion-Exchange Data (Methods in Modeling Ion-Exchange Selectivity, #1‪)‬

Many modelers of ion-exchange thermodynamics have assumed that the selectivity of two ions within a ternary system could be modeled from data gained from the associated binary systems.  The heart of this assumption is that the third ion has no synergistic interactions with the other ions in the solid phase, but rather influences the exchange solely by diluting the concentration of other ions on the solid.  Here, a method to detect synergism between solid-phase ions is reported.  The method developed employs Log Contrast models and the statistical F Test.  The Log Contrast models use mole ratios rather than mole fractions as inputs because mole ratios are not subject to the mixture constraint.  The Log Contrast models are fit to Vanselow selectivity coefficient (Kv) versus solid-phase mole fraction data, with or without the third ion in the model (but with the third ion on the exchanger).  If the model fit is statistically significantly better with the third ion in the model than without it, then the third ion actively influence the selectivity of the two exchanging ions. The method was tested against NH4+-Ca2+-K+ exchange selectivity data for the clay mineral vermiculite.  The results showed that NH4+ had insignificant synergistic effect on the Kv for Ca2+-K+ exchange and that Ca2+ had insignificant effect on the Kv for K+/NH4+ exchange.  The model fits were found to be consistent with the Triangle Rule.