Voltammetric currents for any ligand-to-metal concentration ratio in fully labile metal-macromolecular complexation. Easy computations, analytical properties of the currents and a graphical method to estimate the stability constant

Abstract

In order to enable a wider use of voltammetric methods in speciation analysis, it is convenient not to be restricted by ligand excess conditions. This work assumes labile ideal complexation of a metal ion by a ligand, planar electrode, no electrodic adsorption and equal diffusion coefficients for the complex and the ligand, but very different from the metal ion. It is shown that the system of non-linear equations describing the diffusion of the species in a potentiostatic experiment for any ligand to metal ratio can be reduced to only one ordinary differential equation by means of a change of variable. Standard numerical methods can then be used in the computation of the solution with a great saving of computational time and resources in comparison with other existing methods. Some properties of the currents are also proved: (i) Cottrellian behaviour for any current in normal pulse polarography (NPP) and for limiting currents in reverse pulse polarography (RPP), (ii) the dependence of the normalised limiting current (φ) on just three parameters, and (iii) the equality of limiting NPP and RPP currents. The normalised current for high stability constant values depends on just two parameters, one of which is the ratio of total metal/total ligand concentrations, and can be found from an implicit algebraic equation. A new representation for the normalised limiting currents is suggested: the iso-φ diagram, which for each ratio of diffusion coefficients, e, describes the currents for any stability constant in a unique drawing. A new graphical procedure arising from this diagram is suggested and then applied to data corresponding to Zn/poly(methacrylic) acid at pH 6 and fixed ionic strength.