Voltammetry of heterogeneous labile metal–macromolecular systems for any ligand-to-metal ratio: Part I. Approximate voltammetric expressions for the limiting current to obtain complexation information

We present approximate expressions and rigorous numerical simulations corresponding to the voltammetric limiting currents of a titration experiment of a heterogeneous macromolecular ligand with a metal ion under fully labile conditions. We highlight the accuracy of an approximate expression based on a polynomial expansion of the limiting current in terms of the fraction of the bound metal concentration in the bulk solution. Values of the coefficients of the polynomial expansion for macromolecular complexation are provided. The accuracy of this polynomial expression for systems exhibiting different degrees of heterogeneity together with its easy computation, suggests its application in the finding of the bulk value of the bound metal concentration from the limiting current for a given pair of total ligand and metal concentrations. Thus, straightforward calculations lead to the binding curve which can then be interpreted using the standard methods.