Lability of a mixture of metal complexes under steady-state planar diffusion in a finite domain

The rigorous analytical solution for the fluxes from a mixture of 1:1 metal complexes toward an active surface under steady-state planar diffusion in a finite domain and excess ligand conditions allows for the computation of the global degree of lability of the system as well as particular degrees of lability of each complex in the mixture. This kind of system is found in a variety of fields ranging from electrochemical techniques (such as stripping chronopotentiometry at scanned deposition potential, SSCP) to analytical devices (such as diffusion gradients in thin-film gels, DGT). Among the specific effects arising from the presence of a mixture of ligands competing for the metal we highlight the following: (i) The degree of lability of a complex in the mixture differs from its degree of lability in an unmixed system with the same ligand concentration, and (ii) the degree of lability of one complex depends on (i.e., can be modified with) the concentrations of the ligands in the mixture. The impact of these characteristics on the metal flux crossing the active surface reaches the highest value when both complexes are partially labile. The complex contribution to the metal flux goes through a maximum when the thickness of the diffusion domain is varied. Thus, the thickness of the diffusion domain can be chosen to enhance the contribution of one particular complex. Lability criteria for each complex of the mixture within the reaction layer approximation are also reported. In particular, the reaction layer formulation for a complex is discussed in detail for two limiting cases: the rest of complexes are all nonlabile or the rest of complexes are all labile.     

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.     

Impact of ligand protonation on higher-order metal complexation kinetics in aqueous systems

The impact of ligand protonation on the complexation kinetics of higher-order complexes is quantitatively described. The theory is formulated on the basis of the usual situation for metal complex formation in aqueous systems in which the exchange of water for the ligand in the inner coordination sphere is rate-determining (Eigen mechanism). We derive expressions for the general case of lability of ML(n) species that account for the contributions from all outer-sphere complexes to the rate of complex formation. For dynamic complexes, dissociation of ML is usually the rate-determining step in the overall process ML(n) --> M. Under such conditions, it is the role of ligand protonation in the step ML --> M that is relevant for the kinetic flux. 1:2 complexes of Cd(II) with pyridine-2,6-dicarboxylic acid fall into this category, and their lability at a microelectrode is reasonably well predicted by the differentiated approach. For non-dynamic systems, the kinetic flux arising from dissociation of higher-order complexes contributes to the rate-determining step. In this case, the weighted contribution of protonated and unprotonated outer-sphere complexes in all contributing dissociation reactions must be taken into account. The kinetic flux arising from the dissociation of 1:2 complexes of Ni(II) with bicine at a conventional electrode was quite well described by this combined approach. The results establish the generic role of ligand protonation within the overall framework of metal complexation kinetics in which complexes may be dynamic to an extent that depends on the operational time scale of the measurement technique.     

Computing steady-state metal flux at microorganism and bioanalogical sensor interfaces in multiligand systems. A reaction layer approximation and its comparison with the rigorous solution

In complicated environmental or biological systems, the fluxes of chemical species at a consuming interface, like an organism or an analytical sensor, involve many coupled chemical and diffusion processes. Computation of such fluxes thus becomes difficult. The present paper describes an approximate approach, based on the so-called reaction layer concept, which enables one to obtain a simple analytical solution for the steady-state flux of a metal ion at a consuming interface, in the presence of many ligands, which are in excess with respect to the test metal ion. This model can be used for an unlimited number of ligands and complexes, without limit for the values of the association/dissociation rate constants or diffusion coefficients. This approximate solution is compared with a rigorous approach for the computation of the fluxes based on an extension of a previously published method (J. Galceran, J. Puy, J. Salvador, J. Cecília, F. Mas and J. L. Garcés, Phys. Chem. Chem. Phys., 2003, 5, 5091-5100). The comparison is performed for a very wide range of the key parameters: rate constants and diffusion coefficients, equilibrium constants and ligand concentrations. Their combined influence is studied in the whole domain of fully labile to non-labile complexes, via two combination parameters: the lability index, L, and the reaction layer thickness, mu. The results show that the approximate solution provides accurate results in most cases. However, for particular combinations of metal complexes with specific values of L or mu, significant differences between the approximate and rigorous solutions may occur. They are evaluated and discussed. These results are important for three reasons: (i) they enable the use of the approximate solution in a fully reliable manner, (ii) when present, the differences between approximate and rigorous solution are largely due to the coupling of chemical reactions, whose importance can thus be estimated, (iii) due to its simple mathematical expression, the individual contribution of each metal species to the overall flux can be computed.     

Lability criteria in diffusive gradients in thin films

The penetration of metal complexes into the resin layer of DGT (diffusive gradients in thin films) devices greatly influences the measured metal accumulation, unless the complexes are either totally inert or perfectly labile. Lability criteria to predict the contribution of complexes in DGT measurements are reported. The key role of the resin thickness is highlighted. For complexes that are partially labile to the DGT measurement, their dissociation inside the resin domain is the main source of metal accumulation. This phenomenon explains the practical independence of the lability degree of a complex in a DGT device with respect to the ligand concentration. Transient DGT regimes, reflecting the times required to replenish the gel and resin domains up to the steady-state profile of the complex, are also examined. Low lability complexes (lability degree between 0.1 and 0.2) exhibit the longest transient regimes and therefore require longer deployment times to ensure accurate DGT measurements.     

Metal flux through consuming interfaces in ligand mixtures: boundary conditions do not influence the lability and relative contributions of metal species

In a mixture of metal ions and complexes, it is difficult to predict ecological risk without understanding the contribution of each metal species to biouptake. For microorganisms, the rate of uptake (internalization flux) has not only a major influence on the total metal flux but also on the bioavailability of the various metal species and their relative contributions to the total flux. In this paper, the microorganism is considered as a consuming interface, which interacts with the metal ion, M, via the Michaelis-Menten boundary conditions. The contribution of each metal complex to the overall metal flux, in relation to its lability, is examined for a number of important boundary parameters (the equilibrium constant K(a) of metal with transport sites, internalization rate constant k(int) and total transport sites concentration {R}(t)). Computations were performed for Cu(II) complexes, in a multicomponent culture medium for microoganisms. For a one-ligand system, results were acquired using rigorous mathematical expressions, whereas approximate expressions, based on the reaction layer approximation (RLA) and rigorous numerical computations (computer codes MHEDYN and FLUXY), were employed for ligand mixtures. Under the condition of ligand excess, as often found in the natural environment, the relative contribution of each metal species to the total flux is shown to be independent of the boundary conditions. This finding has important implications, including an improved basis for relating the analytical signals of dynamic metal speciation sensors to metal bioavailability.     

Determination of Dynamic Metal Complexes and their Diffusion Coefficients in the Presence of Different Humic Substances by Combining Two Analytical Techniques

The combined use of a competing ligand exchange (CLE) method and a diffusive gradient in thin films (DGT) technique in a quasi-labile system provides a better understanding of dynamic metal (Cu and Ni) complexes in the presence of humic substances of different origins. The CLE and DGT techniques provide total labile (dynamic) metal complexes (Cu and Ni) and their dissociation rate constants in environmental systems. DGT was found to estimate lower concentrations of labile metal complexes than CLE. These discrepancies were caused by diffusion controlled metal flux (towards the binding resin gel) in the diffusive gel of DGT. The interactions of Cu and Ni with humic acids are stronger than their interactions with fulvic acid and natural organic matter. Changes in the lability of Ni and Cu complexes (complexed with humic substances of different origins) with the changing analytical detection window indicate that the complexes of these metals were formed with different binding sites with diverse binding energies in the humic substances. The combination of these two techniques was found to be very useful in determining diffusion coefficients of labile metal-humate complexes in quasi-labile systems. The values of diffusion coefficients of labile Ni and Cu complexes determined in this study are in good agreement with limited results from the literature. This finding is novel and can be very useful in further improving our understanding of the metal-humate interactions in natural environments.     

Kinetics of metal ion binding by polysaccharide colloids

The dynamics of metal sorption by a gel-like polysaccharide is investigated by means of the electrochemical technique of stripping chronopotentiometry (SCP). The measured response reflects the diffusive flux properties of the metallic species in the dispersion. The colloidal ligand studied here is a functionalized carboxymethyldextran. Its complexation with Pb(II) reveals a time dependence that identifies strong differences in the dynamic nature of the successive metal complexes formed. Apparently, the formation of intramolecular bidentate complexes requires a slow conformational reorganization of the macromolecule that becomes the rate-limiting step in the complexation reaction. The relevant parameters for metal binding and release kinetics are computed and thus provide knowledge of the time-dependent stability and lability of metal polysaccharide complexes.     

Application of permeation liquid membrane and scanned stripping chronopotentiometry to metal speciation analysis of colloidal complexes

The potential of permeation liquid membrane (PLM) to obtain dynamic metal speciation information for colloidal complexes is evaluated by measurements of lead(II) and copper(II) complexation by carboxyl modified latex nanospheres of different radii (15, 35, 40 and 65 nm). The results are compared with those obtained by a well characterized technique: stripping chronopotentiometry at scanned deposition potential (SSCP). Under the PLM conditions employed, and for large particles or macromolecular ligands, membrane diffusion is the rate-limiting step. That is, the flux is proportional to the free metal ion concentration with only a small contribution from labile complexes. In the absence of ligand aggregation in the PLM channels, good agreement was obtained between the stability constants determined by PLM and SSCP for both metals.     

In situ differentiation of labile/inert metal species in Brazilian tropical rivers by means of a time-controlled batch-procedure based on TEPHA resin

The present study deals with a new analytical procedure based on a cellulose diffusion membrane and immobilised tetraethylene-pentamine-hexaacetate chelator (DM-TEPHA) for an in situ differentiation of labile and inert metal species in aquatic systems. The DM-TEPHA system was prepared by placing TEPHA chelator in pre-purified cellulose bags and in situ applied immersing the system in two Brazilian rivers to study the relative lability of metal species (Cu, Pb, Fe, Mn and Ni) as a function of the time and the quantity of exchanger, respectively. The procedure is simple and enables a new perspective for understanding the complexation, transport, stability and lability of metal species in aquatic systems rich in organic matter.     

New analytical procedure based on a cellulose bag and ionic exchanger with p-aminobenzoic acid groups for differentiation of labile and inert metal species in aquatic systems

A new procedure was developed for the in situ characterization of the lability of metal species in aquatic systems by using a system equipped with a diffusion membrane and cellulose organomodified with p-aminobenzoic acid groups (DM-Cell-PAB). To this end, the DM-Cell-PAB system was prepared by adding cellulose organomodified with p-aminobenzoic acid groups (Cell-PAB) to pre-purified cellulose bags. After the DM-Cell-PAB system was sealed, it was examined in the laboratory to evaluate the influence of complexation time, mass of exchanger, pH, metal ions (Cu, Cd, Fe, Mn, and Ni), and concentration of organic matter on the relative lability of metal species. It was found that the pH and kinetics strongly influence the process of metal complexation by the DM-Cell-PAB system. At all pH levels, Cd, Mn, and Ni showed lower complexation with Cell-PAB resin than Cu and Fe metals. Note that relative lability of metals complexed to aquatic humic substances (AHS) in the presence of Cell-PAB resin showed the following order: Cu≅Fe≫Ni>Mn=Cd. The results presented here also indicate that increasing the AHS concentration decreases the lability of metal species by shifting the equilibrium to AHS–metal complexes. Our results indicate that the system under study offers an interesting alternative that can be applied to in situ experiments for differentiation of labile and inert metal species in aquatic systems.     

Copper and nickel speciation in mine effluents by combination of two independent techniques

To control potentially toxic metals in water resources it is necessary to know metal speciation and changes in the metal speciation that occur after aqueous effluents containing metals are discharged into freshwaters. This work explores the speciation of nickel and copper in metal-mining aqueous effluents. Diffusive gradients in thin films (DGT) technique and competing ligand exchange (CLE) method have been applied to determine the speciation of nickel and copper. The results of this investigation demonstrate that combination of two analytical techniques having complementary analytical capabilities can provide a better physicochemical picture of metal speciation than either one of the analytical technique can do alone. The combined use of these techniques revealed that copper formed labile complexes having slow diffusion coefficient along with the presence of small labile copper complexes. Nickel-dissolved organic complexes (DOC) complexes in the aqueous effluent have been found to have fast diffusion coefficient. The results are likely to have environmental significance for providing a link between the metal species in mine aqueous effluent and their bioavailability by determining the characteristics of copper and nickel complexes in metal-mine aqueous effluents. This knowledge is expected to promote a better understanding of the lability of DOC complexes of copper and nickel in mining effluents.     

Lability of nanoparticulate metal complexes in electrochemical speciation analysis

Lability concepts are elaborated for metal complexes with soft (3D) and hard (2D) aqueous nanoparticles. In the presence of a non-equilibrium sensor, e.g. a voltammetric electrode, the notion of lability for nanoparticulate metal complexes, M-NP, reflects the ability of the M-NP to maintain equilibrium with the reduced concentration of the electroactive free M²⁺ in its diffusion layer. Since the metal ion binding sites are confined to the NP body, the conventional reaction layer in the form of a layer adjacent to the electrode surface is immaterial. Instead an intraparticulate reaction zone may develop at the particle/medium interface. Thus the chemodynamic features of M-NP complexes should be fundamentally different from those of molecular systems in which the reaction layer is a property of the homogeneous solution (μ?=?(D _M/k _a ^′)^1/2). For molecular complexes, the characteristic timescale of the electrochemical technique is crucial in the lability towards the electrode surface. In contrast, for nanoparticulate complexes it is the dynamics of the exchange of the electroactive metal ion with the surrounding medium that governs the effective lability towards the electrode surface.     

Roles of dynamic metal speciation and membrane permeability in metal flux through lipophilic membranes: general theory and experimental validation with nonlabile complexes

The study of the role of dynamic metal speciation in lipophilic membrane permeability in aqueous solution requires accurate interpretation of experimental data. To meet this goal, a general theory is derived for describing 1:1 metal complex flux, under steady-state and ligand excess conditions, through a permeation liquid membrane (PLM). The theory is applicable to fluxes through any lipophilic membrane. From this theory, fluxes in the three rate-limiting conditions for metal transport are readily derived, corresponding, namely, to (i) diffusion in the source solution, (ii) diffusion in the membrane, and (iii) the chemical kinetics of formation/dissociation of the metal complex in the interfacial reaction layer. The theory enables discussion of the reaction layer concept in a more general frame and also provides unambiguous criteria for the definition of an inert metal complex. The theoretical flux equations for fully labile complexes were validated in a previous paper. The general theory for semi- or nonlabile complexes is validated here by studying the flux of Pb(II) through PLMs in contact with solutions of Pb(II)-NTA and Pb(II)-TMDTA at different pHs and flow rates.     

Heterogeneity and liability of Pb(II) complexation by humic substances: practical interpretation tools

The complexation of Pb(II) by natural organic matter (NOM) is better described by taking into account the dependence of the strength of binding on metal loading conditions. The utility of a linear differential equilibrium function for interpretation of metal ion binding data is demonstrated. This approach considers the binding intensity (log K*) as a function of metal ion loading (theta = bound metal/binding site concentration). Three methods for calculating this function are presented: -direct calculation from metal titration curves, -direct calculation from polarograms, and -compilation of data derived from interpretation of complexation in terms of one- or two- binding sites (e.g. Scatchard analysis), i.e. Cc (complexation capacity = effective site concentration)-K pairs. Heterogeneity also impacts on the apparent lability of complexes; complexes formed at the lowest metal loadings are the least labile.     

A simple transient approach to dynamic metal speciation: Can independent of time complex voltammetric lability criteria be used?

In this paper, a simple approximated transient solution for dynamic metal speciation is discussed. From this, the validity of the extensively used time-independent solution to study metal complexation is checked, proving that it is restricted to the case of very high stability constants, long times or small radius values.Moreover, the linear diffusion and reaction layer thicknesses are defined and used to study complex lability, pointing out that the latter depends on kinetic parameters but also on geometrical ones, which is not considered in a wide literature.     

In situ application of a cellulose bag and an ion exchanger for differentiation of labile and inert metal species in aquatic systems

This work involved the development and application of a new analytical procedure for in-situ characterization of the lability of metal species in aquatic systems by using a system equipped with a diffusion membrane and cellulose organomodified with p-aminobenzoic acid groups (DM-Cell-PAB). To this end, the DM-Cell-PAB system was prepared by adding cellulose organomodified with p-aminobenzoic acid groups (Cell-PAB) to pre-purified cellulose bags. After the DM-Cell-PAB system was sealed, it was examined in the laboratory. The in-situ application involved immersing the DM-Cell-PAB system in two different rivers, enabling us to study the relative lability of metal species (Cu, Cd, Fe, Mn, and Ni) as a function of time and quantity of exchanger. The procedure is simple and opens up a new perspective for understanding environmental phenomena relating to the complexation, transport, stability, and lability of metal species in aquatic systems rich in organic matter.     

ASV determination of cadmium complexation in seawater. Methodology evaluation

The methodology for using DPASV to study cadmium complexation in seawater is evaluated using EDTA as a model ligand and by analysing natural samples. The results show that the methodology gives an accurate evaluation of metal complexation when inert complexes are studied, both as regards the ligand concentration and the conditional stability constant; the error for both the parameters is lower than 10% at a ligand concentration of about 10(-8) M and a conditional stability constant of 10(9) M-1. Cadmium complexes with ligands present in natural seawater show an evident kinetic lability that may lead to underestimation of the conditional stability constant when a working electrode characterised by a very thick diffusion layer is used. The conditional stability constant in one water sample of the Adriatic coast ranged between 0.14 and 1.4 l/nmol using a rotating disk electrode at rotation rates of 300 and 6000 rpm. The results of cadmium complexation obtained for samples collected in coastal seawater show that the ligands present low specificity for the metal.     

Development of a new analytical approach based on cellulose membrane and chelator for differentiation of labile and inert metal species in aquatic systems

A new procedure was developed in this study, based on a system equipped with a cellulose membrane and a tetraethylenepentamine hexaacetate chelator (MD-TEPHA) for in situ characterization of the lability of metal species in aquatic systems. To this end, the DM-TEPHA system was prepared by adding TEPHA chelator to cellulose bags pre-purified with 1.0 mol L⁻¹ of HCl and NaOH solutions. After the MD-TEPHA system was sealed, it was examined in the laboratory to evaluate the influence of complexation time (0-24 h), pH (3.0, 4.0, 5.0, 6.0 and 7.0), metal ions (Cu, Cd, Fe, Mn and Ni) and concentration of organic matter (15, 30 and 60 mg L⁻¹) on the relative lability of metal species by TEPHA chelator. The results showed that Fe and Cu metals were complexed more slowly by TEPHA chelator in the MD-TEPHA system than were Cd, Ni and Mn in all pH used. It was also found that the pH strongly influences the process of metal complexation by the MD-TEPHA system. At all the pH levels, Cd, Mn and Ni showed greater complexation with TEPHA chelator (recovery of about 95-75%) than did Cu and Fe metals. Time also affects the lability of metal species complexed by aquatic humic substances (AHS); while Cd, Ni and Mn showed a faster kinetics, reaching equilibrium after about 100 min, and Cu and Fe approached equilibrium after 400 min. Increasing the AHS concentration decreases the lability of metal species by shifting the equilibrium to AHS-metal complexes. Our results indicate that the system under study offers an interesting alternative that can be applied to in situ experiments for differentiation of labile and inert metal species in aquatic systems.     

Heterogeneity and lability of Pb(II) complexation by humic substances: practical interpretation tools

The complexation of Pb(II) by natural organic matter (NOM) is better described by taking into account the dependence of the strength of binding on metal loading conditions. The utility of a linear differential equilibrium function for interpretation of metal ion binding data is demonstrated. This approach considers the binding intensity (log K*) as a function of metal ion loading (ı = bound metal/binding site concentration). Three methods for calculating this function are presented: – direct calculation from metal titration curves, – direct calculation from polarograms, and – compilation of data derived from interpretation of complexation in terms of one- or two- binding sites (e.g. Scatchard analysis), i.e. Cc (complexation capacity = effective site concentration)–K pairs. Heterogeneity also impacts on the apparent lability of complexes; complexes formed at the lowest metal loadings are the least labile. Received: 28 December 2000 / Revised: 23 February 2001 / Accepted: 28 February 2001