Interfacial Metal Flux in Ligand Mixtures. 1. The Revisited Reaction Layer Approximation: Theory and Examples of Applications

Abstract

Understanding the physical chemical behaviors of each metal species in a solution containing a mixture of ligands is a prerequisite, e.g., for studying metal bioavailability or making predictions on dynamic risk assessment in ecotoxicology. For many years, the reaction layer concept has been used fruitfully due to its simplicity for understanding and making predictions on diffusion/reaction processes. Until now, it has been applied mainly to solutions containing one ligand. Here, we reconsider the fundamentals of this approach and extend it to multiligand systems. It is shown that each metal complex has its own reaction layer (so-called composite reaction layer), which results from the interplay of this particular complex with all the other complexes. Moreover, it is shown that the overall metal flux can be computed by assuming the existence of one single fictitious equivalent reaction layer thickness for the whole of the complexes. This equivalent reaction layer is a mathematical combination of all the composite reaction layers. Simple analytical equations are obtained, which make it possible to readily interpret the role of the various types of metal species in a mixture. The revisited reaction layer approach, denoted as the reaction layer approximation (RLA), is validated by comparing the total metal flux, the individual fluxes of each metal species, and their concentration profiles computed by the RLA with those obtained by a rigorous mathematical approach. The examples of Pb(II) in a modified Aquil medium and of Cu(II) in solutions of nitrilotriacetic acid and N-(2-carboxyphenyl)glycine are treated in detail. In particular, an original result is obtained with the Cu/NTA/N-(2-carboxyphenyl)glycine system, namely an unexpected flux enhancement is observed, which is specific to solutions with ligand mixtures. The corresponding physicochemical mechanism is not readily understood by the rigorous mathematical (either numerical or analytical) solutions due to their involved combination of parameters. On the other hand, we show that, due to the simplicity of the RLA concept, the RLA facilitates elucidation of the physicochemical mechanism underlying complicated processes.