Voltammetry of heterogeneous labile metal–macromolecular systems for any ligand-to-metal ratio

Binding Curve from Normalized Limiting Currents of Labile Heterogeneous Metal‐Macromolecular Systems. The Case of Cd/Humic Acid

“…This discrepancy can be explained by the dependence of the accuracy of the first order approximation on the total metal and total ligand concentrations. As shown elsewhere [13], the first order approximation always produces fractions of free metal higher than the actual ones and underestimates the coverage. Accordingly, it has been suggested that in case of overlapping of recovered binding curves corresponding to different c à T;L -titrations, the best value to be taken corresponds to the highest coverage.…”

“…The mathematical assumptions leading to Equation 2 as well as its physical interpretation have been discussed elsewhere [12,13]. …”

“…An early approach to analyze limiting currents from polarographic measurements used the homogeneous excess ligand expression to obtain an average stability constant at each metal to ligand ratio [10,11]. A very simple procedure, valid for any ligand to metal ratio and explicitly considering the heterogeneity of the ligand [12,13], was suggested and used in the analysis of Cd, Cu and Pb [14]. Let us refer to such procedure as the first order approximation, which can be easily implemented with a polynomial expression.…”

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

“…In our previous papers [1][2][3][4], the influence of the heterogeneity on the limiting currents has been analysed. From this analysis, the inverse problem, i.e., the determination of the binding curve from a titration experiment when the complex behaves as fully labile has been considered.…”

“…In addition, the rigorous procedure developed to recover the binding curve from the limiting currents requires some elaborate numerical tools to consider properly both the transport processes and the large variation of the average affinity function along the diffusion layer. Two levels of complexity and accuracy were considered: in the most simple approximation, the so-called first order approximation, the variation of the average equilibrium function along the diffusion layer is considered in an approximate way (a first order expansion of the average equilibrium function in terms of the metal concentration is used) [1,2]. Numerical simulation has shown that this approximation leads to very accurate results in most cases.…”