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.

Effects of a mixture of ligands on metal accumulation in diffusive gradients in thin films (DGT)

“…Previous works on voltammetric sensors under steady state conditions have shown [13][14][15] that the addition of labile ligands to the system tends to increase the lability degree of the more inert complexes, whereas the addition of inert ligands tends to decrease the lability degree of labile complexes. Buffle and co-workers 16,17 reported that the metal fux can be orders of magnitude diferent from what expected when the flux in the mixture is computed with the lability degrees of single ligand systems. We refer to "mixture effect" to indicate a change in the flux contribution of one metal-ligand complex due to the presence of other ligands also complexing the same metal when the SLS and the mixture share identical concentrations of free metal, ligand and complex.…”

Experimental verification of the metal flux enhancement in a mixture of two metal complexes: the Cd/NTA/glycine and Cd/NTA/citric acid systems

“…6). The main result of this figure is that there is also a good convergence of the theoretical results of the mixture system (at the rigorous level, by using eqn (10) or by using the reaction layer approximation, eqn (15) in ref. 16) with the experimental ones, while the theoretical results given by eqn (4) that neglect the interaction between the complexes diverge yielding lower flux values.…”

“…3,12 Despite mixtures of ligands corresponding to the most common situation in natural media, mixture effects have only recently been described. [13][14][15][16][17] By rigorous simulation, it has been shown that the increase of the concentration of one ligand decreases the lability degree of its complex in the mixture as in the case of a single ligand system, but also influences the lability degree of the other complexes. Thus, interactions of the complexes in a mixture can play unexpected and relevant roles in the metal availability.…”

Electrochemical activity of various types of aqueous In(III) species at a mercury electrode

“…More rigorously, the formulation of the reaction layer thickness should also take into account the mobility of the fully hydrated form and its mean free lifetime, 1/kd,i, (governed by the rate of release of water). The expression for such a generalised reaction layer thickness, i, defined by both the associative and dissociative terms for a given species i, is given by [52,53]:…”