The use of differential equilibrium functions for interpretation of metal binding in complex ligand systems: Its relation to site occupation and site affinity distributions

Abstract

This paper compares the capabilities of site affinity distribution functions (SADF) (also called affinity spectra) and differential equilibrium functions (DEF) for interpreting metal complexation by natural heterogeneous complexants using simulated data. The various steps and factors that influence the transformation of an experimental titration curve into SADF or DEF functions are discussed in detail and both practical and theoretical limitations are emphasized. Although an SADF enables one, in principle, to extract concentration and equilibrium constants of actual sites, the concentration and K values given by experimentally determined SADF always correspond to average values resulting from the influence of several sites at a given point in a titration. The averaging process depends on experimental errors and on the characteristics of the analytical method used (in particular the “width” of the analytical window). Consequently the concentrations and intensity parameters obtained by a SADF curve cannot be related, by rigorous mathematical expressions, to the individual concentration and equilibrium constants of actual sites. The Differential Equilibrium Function, on the other hand, can be defined by rigorous mathematical expressions without reference to experimental errors. Its exact meaning is discussed in detail with regard to the concentrations and complexation constants of the actual sites present. The effects of the relative concentrations of the various site types, the difference in their log K values, and the distribution shape of continuously distributed sites are studied in detail. The particular case of a linear logarithmic distribution (leading to the Freundlich isotherm followed by many natural complexing agents) and Sips distribution are also considered. The DEF for such continuous distributions is shown to be a promising means of approximating the underlying cumulative site distribution.