Constraints upon Electrolyte Binding Constants in Triple-Layer Model Calculations and Consequences of the Choice of the Thermodynamic Framework

Abstract

We discuss parameter extraction procedures for electrolyte binding constants in the triple-layer model (TLM) involving constraint equations arising from common intersection points in titration curves for (hydr)oxide surfaces. In model parameter estimation within the triple-layer surface complexation model the constraint arising from the point of zero charge condition, when derived from the respective defining surface chemical reactions, is different for two limiting thermodynamic frameworks of the TLM. For the two frameworks, when the parameter estimation procedure proposed by K. F. Hayes, G. Redden, W. Ela, and J. O. Leckie (J. Colloid Interface Sci. 142, 448 (1991)) is used, the intrinsic acidity constants will be the same, and the intrinsic electrolyte binding constants very similar. Constraints on electrolyte binding as used in the paper by Hayes et al. have consequences arising from the TLM framework that should be rigorously respected. Literature model parameters for the TLM exhibit nonsymmetrical electrolyte binding in most cases. A reasonable use of the constraint equations must be expected to result in symmetrical electrolyte binding. For the data sets we investigated, it was possible to obtain fits to the data that were as good when symmetrical electrolyte binding was imposed as when the possibility of nonsymmetrical electrolyte binding was accepted. Therefore, it appears reasonable to impose symmetrical electrolyte binding, which is consistent with the constraint equations used.