Ligand Mixture Effects in Metal Complex Lability

Numerical Simulation of Non-Linear Models of Reaction—Diffusion for a DGT Sensor

In this work, we present a novel strategy for the numerical solution of a coupled system of partial differential equations that describe reaction–diffusion processes of a mixture of metals and ligands that can be absorbed by a sensor or a microorganism, in an aqueous medium. The novelty introduced in this work consisted of an adequate database management in conjunction with a direct iterative schema, which allowed the construction of simple, fast and efficient algorithms. Except in really adverse conditions, the calculation is converging and satisfactory solutions were reached. Computing times showed to be better than those obtained with some commercial programs. Although we concentrate on the solution for a particular system (Diffusive Gradients in Thin Films [DGT] sensors), the proposed algorithm does not require major modifications to consider new theoretical or experimental configurations. Since the quality of numerical simulations of reaction–diffusion problems often faces some drawbacks as the values of reaction rate constants increase, some additional effort has been invested in obtaining proper solutions in those cases.

In situ measurements of micronutrient dynamics in open seawater show that complex dissociation rates may limit diatom growth

In this first in situ study of the dynamic availability of phytoplankton micronutrients, a SeaExplorer glider was combined with Diffusive Gradients in Thin Films and deployed in the Mediterranean Sea. On the basis of their labile metal complex pools, we discovered that Fe and Co can be potentially limiting and Cu co-limiting to diatom growth, contrary to the generally accepted view that phosphorus (phosphate) is the growth limiting element in the Mediterranean Sea. For flagellates and picoplankton, phosphorus remains the main element limiting growth. Our in situ measurements showed that organic complexes of Fe and Cu (>98% of total dissolved concentration), dissociate slower than inorganic complexes of Co, Cd and Ni (>99% of total dissolved concentration being free ions and inorganic complexes). This strengthens the potential growth limiting effect of Fe and Cu versus phosphate, which is present as a free ion and, thus, directly available for plankton.

Key role of the resin layer thickness in the lability of complexes measured by DGT

Analysis of the dynamic features of diffusion gradients in thin film devices (DGT) indicates that the penetration of complexes into the resin layer dramatically increases their lability. This should be taken into account when interpreting DGT measurements in terms of the dynamics of solution speciation. The experimental accumulation of Cd by DGT sensors in Cd-NTA systems confirmed these theoretical analyses. A computational code, which allows a rigorous digital simulation of the diffusion-reaction processes in the gel and resin layers, was used to model the results and to demonstrate the effect of the complex penetration into the resin layer on the lability degree. These findings suggest that DGT renders all complexes much more labile than if the resin-diffusive gel interface was considered as a perfect planar sink, explaining why DGT often measures a high proportion of the metal in a natural water. This information is relevant since some studies have stressed the importance of labile complexes as a source of bioaccumulated metal.

Interfacial metal flux in ligand mixtures. 3. Unexpected flux enhancement due to kinetic interplay at the consuming surface, computed for aquatic systems

Understanding the processes controlling metal biouptake in a mixture of ligands is a requirement for making predictions on dynamic risk assessment in ecotoxicology. In ligand mixtures, the metal uptake flux, due to the dissociation of non labile complexes, can be significantly enhanced by the presence of ligands forming labile complexes, even when the proportions of the latter are very small in the bulk solution. The flux enhancement results from a peculiar kinetic interplay, at the interface, between the labile and non labile species, which influences the lifetime of free metal ion and the reaction layer thickness. An extension of the concept of reaction layer, to multiligand systems, is used here, to explain the physicochemical basis of this flux enhancement and to compute the flux of trace metals in a simple way. This phenomenon is exemplified with four environmentally relevant systems including: (i) simple ligands (Pb-NTA-diglycolate; Cu-OH(-)-CO3(2-)), (ii) fulvic substances (Cu-fulvics-citrate), and (iii) aggregate complexants (Pb-aggregate-CO3(2-)). These examples are typical cases in laboratory experiments, in natural freshwaters and in soil-waters. They show that the flux enhancement effect may occur with all major inorganic and organic environmental complexants. It may be ubiquitous in natural waters or in biological systems and might play an important role in biouptake of toxic or vital metals.

Outer-sphere and inner-sphere ligand protonation in metal complexation kinetics: the lability of EDTA complexes

A generic framework, based on the Eigen mechanism, is formulated to describe the formation/dissociation kinetics of inner-sphere metal complexes that may undergo protonation. In principle, all protonated forms of the ligand contribute to the formation of the precursor outer-sphere complexes, but only the sufficiently stable ones effectively contribute to the overall rate of inner-sphere complex formation. The concepts are illustrated by experimental data for Cd(II)-EDTA complexes. Up to pH 8 the dissociation flux in this system is dominated by the protonated inner-sphere complex, even though it is a very minor component of the equilibrium speciation in bulk solution. The results highlight the importance of distinguishing between the thermodynamically predominant species versus the kinetically relevant ones in considerations of dynamic speciation analysis and bioavailability in natural and engineered systems.

Metal flux and dynamic speciation at (bio)interfaces. Part III: MHEDYN, a general code for metal flux computation; application to simple and fulvic complexants

Metal flux at consuming interfaces (e.g., sensors or microorganisms) is simulated in environmental multiligand systems using a new numerical code, MHEDYN (Multispecies HEterogeneous DYNamics), based on the lattice Boltzmann method. The attention is focused on the computation of the maximum flux of Cu(II), that is, the flux controlled by diffusion-reaction in solution, irrespective of processes occurring at the interface. In parts III and IV of this series, three types of typical environmental complexants are studied: (a) simple ligands (OH- and C03(2-)), (b) fulvic or humic substances including many sites with broadly varying rate constants, and (c) aggregates including a broad range of sizes and diffusion coefficients. Part III focuses on computations in the presence of simple ligands and fulvic/humic substances separately, and part IV discusses the case of aggregate complexes alone and the mixtures of all ligands in typical natural waters. These papers describe the dynamic contribution of the various types of sites for fulvic and aggregate Cu(II) complexes for the first time. Whenever possible, the metal fluxes computed by MHEDYN are compared with those given by another code, FLUXY, based on a fully different mathematical approach, and very good agreement between these codes is obtained. In all cases, MHEDYN computes the concentration profile of each complex and its time evolution, as well as the steady-state flux and the corresponding contribution of each complex to the flux. The metal fluxes can be computed at a planar consuming surface such as an organism or a sensor surface, in presence of an unlimited number of complexation reactions of the metal M, and for any metal/ligand concentration ratio, with values of the physicochemical parameters ranging over many orders of magnitude.