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

Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems

The limiting current density is one of to the most important indicators in electroplating for the maximal current density from which a metal can be deposited effectively from an electrolyte. Hence, it is an indicator of the maximal deposition speed and the homogeneity of the thickness of the deposited metal layer. For these reasons, a major interest in the limiting current density is given in practical applications. Usually, the limiting current density is determined via measurements. In this article, a simple model to compute the limiting current density is presented, basing on a system of diffusion–reaction equations in one spatial dimension. Although the model formulations need many assumptions, it is of special interest for screenings, as well as for comparative work, and could easily be adjusted to measurements.

Evaluation of the measurement of Cu(II) bioavailability in complex aqueous media using a hollow-fiber supported liquid membrane device (HFSLM) and two microalgae species (Pseudokirchneriella subcapitata and Scenedesmus acutus)

The environmental bioavailability of copper was determined using a hollow-fiber supported liquid membrane (HFSLM) device as a chemical surrogate and two microalgae species (Scenedesmus acutus and Pseudokirchneriella subcapitata). Several experimental conditions were studied: pH, the presence of organic matter, inorganic anions, and concomitant cations. The results indicated a strong relationship between the response given by the HFSLM and the microalgae species with free copper concentrations measured by an ion selective electrode (ISE), in accordance with the free-ion activity model (FIAM). A significant positive correlation was evident when comparing the bioavailability results measured by the HFSLM and the S. acutus microalga species, showing that the synthetic device may emulate biological uptake and, consequently, be used as a chemical test for bioavailability measurements using this alga as a biological reference.

Kinetic studies of Ni organic complexes using diffusive gradients in thin films (DGT) with double binding layers and a dynamic numerical model

In situ deployments of diffusive gradients in thin films (DGT) can provide direct information on complex dissociation rates in natural waters. Recent advances in understanding the dynamics of the interactions of metal complexes within DGT devices have highlighted the characteristics of the binding layer, but there are few data to complement these theoretical developments. In this work the penetration into the Chelex binding layer of complexes of Ni with nitrilotriacetic (NTA) and Suwannee River fulvic and humic acids (FA and HA) in solution at pH 7 was investigated by deployment of DGT devices with two sequential binding layers, a "front" and a "back" layer. In Ni-NTA experiments, the masses of Ni bound by the front and back binding layers were similar, as predicted for slowly dissociating complexes. For Ni-FA/HA solutions, a higher mass of Ni was taken up by the front binding layer, consistent with fast dissociation from a high proportion of the binding sites. The ratio of Ni in the front to back binding layers was significantly lower (p < 0.05) for solutions of Ni-HA compared to those of Ni-FA, indicating that Ni-HA complexes are less labile than Ni-FA complexes in similar solutions (FA = 10 mg L(-1) and HA = 8 mg L(-1)). A dynamic numerical model of the complexes in a DGT system was used to estimate the dissociation rate constants that provided the best agreement with the experimental data. Values obtained of 2 ± 0.5 × 10(-4) s(-1) for Ni-NTA and 2.5 × 10(-3) s(-1) for Ni-FA when FA = 20 mg L(-1) and 3.42 × 10(-4) s(-1) for Ni-HA when HA = 8 mg L(-1), could be rationalized with current knowledge of the dynamics of these systems. This approach can improve kinetic information obtainable using DGT and widen the range of considered complex labilities.

Chemodynamics of aquatic metal complexes: from small ligands to colloids

Recent progress in understanding the formation/dissociation kinetics of aquatic metal complexes with complexants in different size ranges is evaluated and put in perspective, with suggestions for further studies. The elementary steps in the Eigen mechanism, i.e., diffusion and dehydration of the metal ion, are reviewed and further developed. The (de)protonation of both the ligand and the coordinating metal ion is reconsidered in terms of the consequences for dehydration rates and stabilities of the various outer-sphere complexes. In the nanoparticulate size range, special attention is given to the case of fulvic ligands, for which the impact of electrostatic interactions is especially large. In complexation with colloidal ligands (hard, soft, and combination thereof) the diffusive transport of metal ions is generally a slower step than in the case of complexation with small ligands in a homogeneous solution. The ensuing consequences for the chemodynamics of colloidal complexes are discussed in detail and placed in a generic framework, encompassing the complete range of ligand sizes.

Sorption to humic acids enhances polycyclic aromatic hydrocarbon biodegradation

The hypothesis that humic acids (HA) can act as carriers of polycyclic aromatic hydrocarbon (PAH) compounds and provide bacteria with PAH fluxes beyond those obtained by diffusion of the water-dissolved fraction of these poorly soluble chemicals was tested. Controlled degradation experiments using microcrystalline phenanthrene and Sphingomonas sp. LH162 were performed without HA and in the presence of two HA concentrations. In the absence of HA, phenanthrene was steadily present at the maximum dissolved concentration, indicating that the phenanthrene dissolution flux compensated for the consumption. This was confirmed by dissolution experiments where phenanthrene dissolved roughly an order of magnitude faster than it was consumed in the degradation experiments. Interestingly, the presence of HA further increased the rates of phenanthrene degradation by factors up to 4.8 in an HA concentration-dependent manner. This can only be interpreted by an HA-mediated transport of phenanthrene to the cells, supplementing diffusive uptake from the freely dissolved phase. It is proposed that HA-sorbed phenanthrene is released directly to the cells upon their interaction with HA aggregates, increasing the total phenanthrene flux and also degradation.

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.

Metal flux and dynamic speciation at (bio)interfaces. Part IV: MHEDYN, a general code for metal flux computation; application to particulate complexants and their mixtures with the other natural ligands

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 (i.e.,the flux controlled by diffusion-reaction in solution) of Cu(II). Part III described flux computation in the presence of simple ligands and fulvic/humic substances. This paper (Part IV) discusses the case of metal complexes formed with aggregates including a broad range of sizes and diffusion coefficients and their mixture with simple and fulvic ligands under typical natural water conditions. This paper describes the dynamic contribution of the various size classes of aggregate Cu(II) complexes for the first time. In two typical waters containing mixtures of ligands, the contribution of aggregates is found to be small, whereas that of fulvics may play a major role, even under pH conditions where the lability of their Cu(II) complexes is low. These results point out the great usefulness of MHEDYN for dynamic speciation in very complex mixtures. In all cases, MHEDYN enables us to compute the concentration profile of each complex and itstime evolution, as well as the steady-state flux and the corresponding contribution of each complex to the flux. Thus, MHEDYN should be very useful for comparing theoretical predictions with experimental measurements of metal bioavailability or of dynamic sensor response in a complete aquatic medium.