Voltammetry of heterogeneous labile metal–macromolecular systems for any ligand to metal ratio: part IV. Binding curve from the polarographic waves

The influence of the heterogeneity of the ligand on the polarographic wave recorded in a labile metal–macromolecule system at any metal-to-ligand ratio is discussed. Previous approximate expressions reported in the literature together with new analytical approximate expressions suggested in this work are tested with rigorous numerical simulation. The theoretical framework developed allows the solution of the inverse problem: the determination of the binding curve from the waves recorded in a polarographic titration. In particular, an approximate analytical expression for the computation of the fraction of bound metal at the bulk solution from the potential shift of the wave is provided. This procedure extends the classical De Ford Hume expression to heterogeneous ligands at any ligand to metal ratio. A good agreement between the recovered binding curve and the rigorous one is shown for different cases with a discrete number or a continuous distribution of kinds of affinities.