Voltammetric lability of metal complexes at spherical microelectrodes with various radii

Kinetics of metal detection by luminescence-based whole-cell biosensors: connecting biosensor response to metal bioavailability, speciation and cell metabolism

Luminescent whole-cell metal biosensors are genetically engineered cells used for the detection of metals in e.g. aqueous solutions. Herein, we detail the quantitative connections between time-response of luminescent bacterial metal sensors and the bioavailability of free and complexed metal species. To that end, we formulate the biophysicochemical dynamics of metal partitioning at a biosensor/solution interface and integrate the required metabolism contribution to cell response. The formalism explains the ways in which cell signal depends on: coupled Eigen kinetics of metal complexation and diffusion of metal species to/from the interface; kinetics of metal excretion, Michaelis-Menten bioaccumulation and ensuing metal depletion from bulk solution; and kinetics of bioluminescence production following intracellular metal sequestration by regulatory metalloproteins. In turn, an expression is derived for the time-dependent cell signal as a function of interrelated (bioavai)lability of metal species and (thermo)dynamic descriptors of extra/intracellular metal complexation. Quantitative criteria are elaborated to identify scenarios where equilibrium modeling of metal speciation is incorrect, bulk metal depletion is operative, metal biouptake kinetics is governed by metal diffusion, or labile metal complexes fully contribute to cell response. Remarkably, in agreement with experiments, the theory predicts time-shifts of bioluminescence peaks with increasing concentration of biosensor and/or metal ligand in solution. We show that these shifts originate from the crosstalk between activation kinetics of cell photoactivity and speciation-dependent kinetics of bulk metal depletion. Overall, the work paves the way for the elaboration of new strategies to exploit the bioluminescence response of metal lux-biosensors at a dynamic level and evaluate metal bioavailability properties in environmental or biological aqueous samples.

Effect of Polymer Aging on Uptake/Release Kinetics of Metal Ions and Organic Molecules by Micro- and Nanoplastics: Implications for the Bioavailability of the Associated Compounds

The main driver of the potential toxicity of micro- and nanoplastics toward biota is often the release of compounds initially present in the plastic, i.e., polymer additives, as well as environmentally acquired metals and/or organic contaminants. Plastic particles degrade in the environment via various mechanisms and at different rates depending on the particle size/geometry, polymer type, and the prevailing physical and chemical conditions. The rate and extent of polymer degradation have obvious consequences for the uptake/release kinetics and, thus, the bioavailability of compounds associated with plastic particles. Herein, we develop a theoretical framework to describe the uptake and release kinetics of metal ions and organic compounds by plastic particles and apply it to the analysis of experimental data for pristine and aged micro- and nanoplastics. In particular, we elucidate the contribution of transient processes to the overall kinetics of plastic reactivity toward aquatic contaminants and demonstrate the paramount importance of intraparticulate contaminant diffusion.

Back Accumulation of Diffusive Gradients in Thin-Films Devices with a Stack of Resin Discs To Assess Availability of Metal Cations to Biota in Natural Waters

Determining species, concentrations, and physicochemical parameters in natural waters is key to improve our understanding of the functioning of these ecosystems. Diffusive Gradients in Thin-films (DGT) devices with different thicknesses of the resin or of the diffusive disc can be used to collect independent information on relevant parameters. In particular, DGT devices with a stack of two resin discs offer a simple way to determine dissociation rate constants of metal complexes from the accumulation of the target metal in the back resin disc. In this work, simple approximate expressions for the determination of the dissociation rate constant are reported and applied to a model Ni nitrilotriacetic complex as well as to Zn complexes in the Mediterranean Osor stream. Once the physicochemical parameters are known, one can plot the labile fraction of the metal complexes in terms of the thickness of the diffusion domain. These plots reveal a strong dependence on the nature of complexes as well as on the characteristics of the diffusion domain, and they are of high interest as predictors of availability to biota whose uptake is limited by diffusion.

Effective concentration signature of Zn in a natural water derived from various speciation techniques

The uptake of nutrients or toxicants by different organisms in aquatic systems is known to correlate with different fractions of the nutrient's or toxicant's total concentration. These fractions can be provided by different analytical techniques, from which the better correlation is expected to be found for those with a characteristic length comparable to that in the considered organism uptake. An effective concentration signature can be built up with the concentration values associated to the availability (i.e. fluxes in dynamic techniques) of the nutrient or toxicant measured by various analytical techniques with different characteristic lengths. Here, this new representation was obtained for the pool of Zn complexes in the Mediterranean stream Riera d'Osor (Girona, Catalonia, Spain) with a suite of four analytical techniques. Absence of Gradients and Nernstian Equilibrium Stripping (AGNES) and Polymer Inclusion Membrane (PIM) devices provided the free Zn concentration. Linear Anodic Stripping Voltammetry provided a labile fraction (defined here as c_LASV, higher than the free concentration), related to the diffusion layer scale. Diffusion Gradients in Thin-films provided higher labile fractions (known as DGT concentrations, c_DGT) connected to the different characteristic lengths of different configurations (e.g. one or two resin discs) longer, in any case, than that corresponding to LASV. The combination of the information retrieved by the techniques allowed to quantify lability degrees of the pool of Zn complexes and to build up the effective concentration signature for this water.

Availability of metals to DGT devices with different configurations. The case of sequential Ni complexation

The analytical technique DGT (Diffusive Gradients in Thin-films) is able to gain access to a wealth of information by carefully interpreting accumulation data from passive samplers with different configurations (i.e. different thicknesses of its constituent layers). A set of DGT devices were simultaneously deployed in solutions of Ni and nitrilotriacetic acid (NTA) of different concentrations to measure the availability of Ni in these solutions. Accumulations indicate that the availability of Ni depends on both the thickness of the resin and the thickness of the diffusive gel. In both cases, the lability degree increases as the thickness increases. As the formation of successive complexes (such as Ni(NTA)₂) proceeds, the availability of the metal decreases, which is quantitatively explained by reducing the formulation to a case with only one complex, but with an effective dissociation rate constant that decreases as the concentration of NTA increases. Simple analytical expressions are reported to quantify the lability degree in the different DGT configurations. These results indicate that a set of different DGT devices can characterize the availability of a cation in a natural sample with uptake processes at different spatial or time scales. Alternatively, and from a more fundamental point of view, information on speciation, mobilities and labilities of the species present in natural samples can be obtained with a set of DGT configurations.

Speciation of Inorganic Compounds in Aquatic Systems Using Diffusive Gradients in Thin-Films: A Review

The speciation of trace metals in an aquatic system involves the determination of free ions, complexes (labile and non-labile), colloids, and the total dissolved concentration. In this paper, we review the integrated assessment of free ions and labile metal complexes using Diffusive Gradients in Thin-films (DGT), a dynamic speciation technique. The device consists of a diffusive hydrogel layer made of polyacrylamide, backed by a layer of resin (usually Chelex-100) for all trace metals except for Hg. The best results for Hg speciation are obtained with agarose as hydrogel and a thiol-based resin. The diffusive domain controls the diffusion flux of the metal ions and complexes to the resin, which strongly binds all free ions. By using DGT devices with different thicknesses of the diffusive or resin gels and exploiting expressions derived from kinetic models, one can determine the labile concentrations, mobilities, and labilities of different species of an element in an aquatic system. This procedure has been applied to the determination of the organic pool of trace metals in freshwaters or to the characterization of organic and inorganic complexes in sea waters. The concentrations that are obtained represent time-weighted averages (TWA) over the deployment period.

Assessing the uranium DGT-available fraction in model solutions

The uranium speciation in humic acid (HA) and fulvic acid (FA) model solutions was investigated by diffusive gradients in thin films (DGT). A reference solution was used to normalize the DGT data from different samples. This approach was used to assess uranium DGT-available fraction (F_U), which was calculated from experimental data and reflect both the mobility and lability of uranium species. F_U decreased with increasing HA or FA concentrations, because more uranium was able to bind the strong binding sites of HA or FA. When copper was spiked, F_U increased due to the competition between copper and uranium. In HA model solutions, an increase of ionic strength could increase F_U, and when pH was greater than 7, F_U increased significantly. The DGT uptake factor (φ), which can be obtained from data fitting, is the ratio of the product of diffusion coefficient and lability degree of the unknown sample to that of the reference solution. In U-HA-NaHCO₃ solutions, UO₂(CO₃)₂^2- had a relatively high φ value and might be the most DGT-available species. This approach allows the comparison of DGT data from different samples, and combining with a data fitting procedure, it can be used to investigate the distribution of metal species.

Chemodynamics of Soft Nanoparticulate Metal Complexes: From the Local Particle/Medium Interface to a Macroscopic Sensor Surface

The lability of a complex species between a metal ion M and a binding site S, MS, is conventionally defined with respect to an ongoing process at a reactive interface, for example, the conversion or accumulation of the free metal ion M by a sensor. In the case of soft charged multisite nanoparticulate complexes, the chemodynamic features that are operative within the micro environment of the particle body generally differ substantially from those for dissolved similar single-site complexes in the same medium. Here we develop a conceptual framework for the chemodynamics and the ensuing lability of soft (3D) nanoparticulate metal complexes. The approach considers the dynamic features of MS at the intraparticulate level and their impact on the overall reactivity of free metal ions at the surface of a macroscopic sensing interface. Chemodynamics at the intraparticulate level is shown to involve a local reaction layer at the particle/medium interface, while at the macroscopic sensor level an operational reaction layer is invoked. Under a certain window of conditions, volume exclusion of the nanoparticle body near the medium/sensor interface is substantial and affects the properties of the reaction layer and the overall lability of the nanoparticulate MS complex toward the reactive surface.

Influence of the settling of the resin beads on diffusion gradients in thin films measurements

Binding resin beads used in DGT (diffusion gradients in thin films) tend to settle to one side of the resin during casting. This phenomenon might be relevant for metal accumulation when partially labile complexes dominate the metal speciation, especially after recognizing the important role played by complex dissociation in the resin domain. The influence of the inhomogeneity of the binding agent distribution on metal accumulation is here assessed by numerical simulation of DGT devices with binding beads in only one half of the resin disc, as a reasonable model of the standard resin discs. Results indicate that a decrease in mass accumulation of less than 13% can arise in these inhomogeneous devices (as compared with an ideal disc with homogeneous dispersion of the resin beads) when complexes with stability constant K<10(2)m(3)mol(-1) (K<10(5)Lmol(-1)) dominate the metal speciation. The loss increases as K increases, but the percentage of mass loss always remains lower than the volume fraction of resin disc without beads. For very labile or inert complexes, the impact of the inhomogeneous distribution of binding resin beads is negligible. As kinetic dissociation constants of complexes can be estimated from the distribution of the metal accumulation in a DGT device with a stack of two resin discs, the influence of the inhomogeneity on the recovered kinetic constant is also assessed. For the cases studied, the recovered kinetic dissociation constant, kd,recovered, retains the correct order of magnitude, being related to the true kd by kd≈f(-1)kd,recovered, quite independently of K and kd values, being f the fraction of volume of the resin disc where resin beads are dispersed.

Limits of the linear accumulation regime of DGT sensors

A key question for the practical application of DGT (Diffusive Gradients in Thin films) as dynamic sensors in the environmental monitoring of trace metals is the influence of pH and dissolved ligands over the linear accumulation regime. Protons compete with metal ions for the binding to the DGT resin sites at relatively low pH, whereas high affinity dissolved ligands compete with resin sites for the binding of metals. Any of the two phenomena can lead to a departure from the linear accumulation regime and an underestimation of the actual species concentration in solution. These effects are studied here through numerical simulation of the diffusion-reaction processes in both gel and resin domains using a detailed chemical model of metal ions and protons interacting with resin sites. Results were tested successfully against experimental data of the Cd-NTA representative system. Charts to delimitate the range of experimental conditions (pH, ligand concentration and strength) where the linear accumulation regime prevails, can be helpful for designing sampling strategies in field conditions. For example, it is foreseen that perturbations of linear regime within 10 h of deployment are negligible above pH 5 and weak complexation (log K' < 0) or above pH 7 and strong complexation (log K' < 3), where K' is the effective stability constant. These plots can also be approximately used for partially labile systems whenever the time is replaced with the product lability degree times t.

Influence of pH and Chloride Concentration on the Corrosion Behavior of Unalloyed Copper in NaCl Solution: A Comparative Study Between the Micro and Macro Scales

The effects of pH and chloride concentration on the electrochemical corrosion of copper in aqueous sodium chloride (NaCl) media were studied at the micro scale using a microcapillary droplet cell and at the macro scale using a conventional large scale cell. Using an experimental design strategy, electrochemical response surface models of copper versus pH and NaCl concentration were constructed with the minimum number of experiments required. Results show that the electrochemical behavior of copper under corrosive media shows significant differences between the micro and macro scale experiments. At the micro scale, the pit initiation of copper occurs at more negative potentials for high NaCl concentrations and alkaline pH values. Also, the micro scale potentiostatic measurements indicate higher stabilised passive currents at high NaCl concentrations and low (acidic) pH values. At the macro scale, the pH is shown to have a greater influence on the corrosion potential. The chloride concentration is the most significant factor in the passive current case while at the micro scale the effect of these two factors on the passive current was found to be the same. The surface morphology of the formed patina on the corroded copper in both micro and macro systems reveal a more significant role of the chloride concentration on the structure and the grain size of the patinas. Finally, micro and macro electrochemical impedance spectroscopy of copper at various NaCl concentrations and pH values demonstrates a different behavior of copper after several potentiodynamic polarization cycles.

Kinetic signatures of metals in the presence of Suwannee River fulvic acid

This work provides new information on the dissociation kinetics of metal-fulvic acid (FA) complexes. Diffusive gradients in thin-film (DGT) devices deployed in solutions containing metals and 30 mg L(-1) Suwannee River FA at pH 5 and 7, at two different metal-to-ligand ratios, were used to estimate an apparent diffusive boundary layer (ADBL) thickness at the gel-solution interface. The discrepancy between the ADBL thickness measured for metals that are known to dissociate from complexes quickly (e.g., Cd) and that of other trace metals was exploited to calculate the rate of complex dissociation. When the ADBL thickness is plotted for a suite of metals, a "kinetic signature" is created. There was a clear kinetic signature at pH 7, with substantial kinetic limitation for Cu, Pb, and Ni and none for Cd, Co, and Mn (i.e., Cu-, Pb-, and Ni-FA complexes dissociated more slowly). At pH 5, the kinetic signature was less distinct, due in part to slow association kinetics of Mn, and possibly Cd and Co, with the resin. The good sensitivity of the method to small changes in dissociation kinetics was able to show that the dissociation of most metal-FA complexes is sufficiently fast to not limit the DGT measurement.

Contribution of partially labile complexes to the DGT metal flux

Penetration of complexes into the resin layer can dramatically increase the contribution of complexes to the metal flux measured with a DGT (diffusive gradients in thin films) sensor, but equations to describe this phenomenon were not available. Here, simple approximate analytical expressions for the metal flux, the lability degree and the concentration profiles in a DGT experiment are reported. Together with the thickness of the reaction layer in the gel domain, the effective penetration distance into the resin layer that would be necessary for full dissociation of the complex (λ(ML)) plays a key role in determining the metal flux. An increase in the resin-layer thickness (r) effectively increases the metal flux and the lability degree until r ≈ 3λ(ML). For the usual DGT configuration, where the thickness of the gel layer exceeds that of the resin layer, the complex is labile if r > (D(ML)/k(d))½, where D(ML) is the diffusion coefficient of the metal complex and k(d) its dissociation rate constant. A general procedure for estimating the lability of any complex in a standard DGT configuration is provided.

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.

Protonation effects on dynamic flux properties of aqueous metal complexes

The degree of (de)protonation of aqueous metal species has significant consequences for the kinetics of complex formation/dissociation. All protonated forms of both the ligand and the hydrated central metal ion contribute to the rate of complex formation to an extent weighted by the pertaining outer-sphere stabilities. Likewise, the lifetime of the uncomplexed metal is determined by all the various protonated ligand species. Therefore, the interfacial reaction layer thickness, μ, and the ensuing kinetic flux, Jkin, are more involved than in the conventional case. All inner-sphere complexes contribute to the overall rate of dissociation, as weighted by their respective rate constants for dissociation, kd. The presence of inner-sphere deprotonated H2O, or of outer-sphere protonated ligand, generally has a great impact on kd of the inner-sphere complex. Consequently, the overall flux can be dominated by a species that is a minor component of the bulk speciation. The concepts are shown to provide a good description of experimental stripping chronopotentiometric data for several protonated metal–ligand systems.

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 binding by heterogeneous ligands: kinetic master curves from SSCP waves

Stripping chronopotentiometry at scanned deposition potential, SSCP, is shown to be a powerful tool for determination of the distribution of metal dissociation rate constants, kd, for heterogeneous ligands. SSCP effectively scans a range of metal-to-ligand ratios from the foot to the plateau of the wave, thus allowing a portion of the distribution of k(d) values to be determined for a given bulk solution composition. In particular, the nature of the measurement renders accessible very low metal-to-ligand ratios which are otherwise difficult to attain by a bulk solution methodology, such as a potentiometric titration. In the presence of kinetic currents, the shape of the SSCP wave is modified as compared to the labile case. A data interpretation framework is developed which well-describes the SSCP wave for heterogeneous complexes in the kinetic current regime. The analysis utilizes the Freundlich binding isotherm together with the Koutecký-Koryta approximation, i.e., assuming a spatially discontinuous transition from labile to nonlabile behavior. For the case of Pb(II) and Cu(II) complexation by a peat fulvic acid, the existing body of data is drastically expanded to the low to very low metal-to-ligand ratio domain, thereby greatly improving the quality of the derived distribution parameters.

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.

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.

Metal flux and dynamic speciation at (bio)interfaces. Part I: Critical evaluation and compilation of physicochemical parameters for complexes with simple ligands and fulvic/humic substances

In the computation of metal flux in aquatic systems, at consuming surfaces like organism membranes, diffusion processes of metal ions, ligands, and complex species, as well as the kinetic and thermodynamic aspects of their chemical interactions, must be considered. The properties of many natural ligands, however, are complicated (formation of successive complexes for simple ligands, polyelectrolytic properties and chemical heterogeneity for macromolecular ligands, large size distribution and fractal structure for suspended aggregates). These properties should be properly modeled to get the correct values of the chemical rate constants and diffusion coefficients required for flux computations. The selection of the most appropriate models and parameter values is far from straightforward. This series of papers discusses the various models and compiles the parameters needed for the three most important types of complexants found in aquatic systems: the small, simple ligands, the fulvic and humic compounds, and the colloidal "particles" or aggregates. In particular, new approaches are presented to compute the rate constants of metal complex formation, with both fulvics/humics and particles/aggregates. The method to include the site distribution of fulvics/humics and the size distribution of particles/aggregates in metal flux computation at consuming interfaces is also discussed in detail. These models and parameters are discussed critically and presented in the same framework, forthe computation of metal flux in presence of any of the above complexants or mixtures. Such parameters, largely spread in the literature, are gathered here and selected specifically for environmental applications. The focus in Part I of the series is on simple ligands and fulvic/humic compounds. Part II deals with particulate and aggregate complexants.

Metal flux and dynamic speciation at (bio)interfaces. Part II: Evaluation and compilation of physicochemical parameters for complexes with particles and aggregates

The computation of metal flux in aquatic systems at consuming surfaces like organism membranes must consider the diffusion processes of metal ions, ligands, and complex species, as well as the kinetic and thermodynamic aspects of their chemical interactions. Many natural ligands, however, have complicated properties (formation of successive complexes for simple ligands, polyelectrolytic properties and chemical heterogeneity for macromolecular ligands, large size distribution and fractal structure for suspended aggregates). These properties should be properly modeled to get the correct values of the chemical rate constants and diffusion coefficients required for flux computations. The selection of the most appropriate models and parameter values is far from straightforward. In this series of papers, models and compilations of parameters for application to the three most important types of complexants found in aquatic systems, the small, simple ligands, the fulvic and humic compounds, and the colloidal "particles" or aggregates, are discussed. In particular, new approaches are presented to compute the rate constants of metal complex formation for both fulvics/humics and particles/aggregates. A method to include the site distribution of fulvics/ humics and the size distribution of particles/aggregates in metal flux computation at consuming interfaces is also discussed in detail. These models and parameters are discussed critically and presented in a single consistent framework, applicable to the computation of metal flux in presence of any of the above complexants ortheir mixtures. Part I of the series focuses on simple ligands and fulvic/ humic compounds. Part II deals with particulate and aggregate complexants.

Ligand Mixture Effects in Metal Complex Lability

The degree of lability of a given metal complex species is modified in the presence of a mixture of ligands. This modification is a consequence of the coupling of the association and dissociation processes of all of the complexes according to the competitive complexation reaction scheme. We show that, because of the mixture effect, the lability of a given complex usually increases when another more labile complex is added into the system, while it decreases upon addition of a less labile one. Typically, complexes tend to adapt to the global lability of the mixture. A quantitative evaluation of these effects for diffusion-limited conditions in a finite domain by rigorous numerical simulation in a system with two complexes indicates that the lability degree of a complex can change by more than 100% with respect to that in the single ligand system. The impact of the mixture effect on the metal flux depends at least on two main factors: the respective abundance of the metal species and the particular values of their lability degrees. Dominant complexes (i.e., those most abundant when these complexes have equal diffusion coefficients) undergo smaller changes in their own lability degree, but these changes have the greater impact on the overall metal flux. Partially labile complexes are more easily influenced by the mixture than labile or inert ones. Some mixture effects can be qualitatively predicted by an analytical expression for the lability index derived using the reaction layer approximation. For a mixture of many complexes, the change in the lability degree of a complex due to the mixture effect can be understood as a combination of the changes due to all of the complexes present.