AGNES (absence of gradients and Nernstian equilibrium stripping) is a stripping technique consisting of two conceptual steps: (i) application of a potential program (e.g. a step at a fixed potential) generating a known concentration gain between the outer and inner concentrations of the metal at the mercury electrode surface together with null gradients of the concentration profiles (inside and outside the mercury electrode) and (ii) determination of the concentration of reduced metal inside the amalgam in a stripping step. In the present implementation, the stripping step under diffusion limited conditions leads to a measured current just proportional to the free metal ion concentration. In this paper we present the basic principles of the technique, analytical expressions for a simplified model of its voltammetric implementation and a numerical study for a more refined model together with preliminary experimental results in the Cd(II)/nitrilotriacetic acid system showing how this technique can be used as an alternative to other techniques (such as ion selective electrodes) in order to determine free metal activities or concentrations in the presence of complex mixtures avoiding complications such as electrodic adsorption or complexation kinetics.

The size of a microelectrode can have a dramatic impact on the relative importance of the diffusional and kinetic contributions to the voltammetric current of an electroactive metal ion in a complexing medium. Decreasing the radius enhances the diffusional contribution and, as a consequence, the complex system tends to move away from labile behaviour (where an equilibrium relationship holds). Therefore, sufficiently small microelectrodes (either or not combined with short measuring times) should be able to directly sense free metal concentration for not too fast association/dissociation kinetics.The particular case of steady state spherical (or hemispherical) diffusion under ligand excess (pseudo-first order kinetics) is solved analytically. The ensuing lability criterion is shown to be in accordance with a geometrical derivation based on an analysis of the Published in Journal of Electroanalytical Chemistry 2001, vol 505, p 85-94 Voltammetric lability.. 2/25random walk of the free metal ions produced by dissociation of the complex. It is shown that, for a generated metal ion, the probability of reaching the microelectrode surface can be quite different from the planar case. Alternatively, the classical reaction layer concept can be used in the derivation of the lability criterion for spherical geometry as it is shown in this work. All treatments quantitatively show how the lability of metal complexes is reduced with decreasing the dimension of the microelectrode. [85][86][87][88][89][90][91][92][93][94] Voltammetric lability.. inert total kin J J J + ,The thickness of the reaction layer µ is a kinetic parameter [34][35][36][37][38][39], defined such that:

The bipolar faradaic depolarization of the interface metal/solution is examined for the situation in which the transversal electron transfer is limited by mass transfer of the components of a reversible redox couple. Transversal diffusion of the electroactive species to and from the surface and lateral convective mass transport, resulting from a pressure gradient applied along the surface, are taken into account. The analysis first focuses on the case in which the lateral electric field required for bipolar behavior is externally applied through the solution. Numerical analysis of the intrinsic nonlinear coupling between the convective-diffusion equation and the Poisson equation for finite currents allows derivation of the spatial distribution of the potential and the concentration profiles of the electroactive species. The corresponding distribution of the local faradaic current density along the metallic surface and the ensuing overall bipolar current are obtained. Characteristics of the conductivity curves, bipolar current versus applied field, are given for different sets of electric and hydrodynamic parameters. Then, on the basis of these results, the analysis of bipolar faradaic depolarization process is extended to electrokinetic phenomena, in particular streaming potential.

Analytical solutions for the steady-state flux arriving at an active surface from a mixture (in which one active species reacts with non-active ligands in the medium) can be helpful in a variety of problems: voltammetric techniques, heterogeneous processes in reactors, toxic or nutrient uptake, techniques of diffusive gradients in thin films (DGT), etc. Under any geometry that sustains steady-state, a convenient combination of the reaction-diffusion equations leads to a simpler formulation of the problem for arbitrary diffusivities of the species and arbitrary rate constants of the first order conversion between the active species and the non-active species. The resulting problem can be characterised in terms of a list of dimensionless parameters involving the kinetic and mobility properties of each species. A lability degree for each 1:1 complex in terms of the surface concentrations leads to: i) a lability criterion specific for each complex in the mixture and ii) the assessment of the relative contribution of each complex to the resulting flux. Semi-infinite spherical diffusion (as in the Gel Integrated MicroElectrode, GIME, biouptake modelling of microorganisms , etc.) is specifically considered and some consequences of its full analytical solutions are discussed.

Absence of gradient and Nernstian equilibrium stripping (AGNES) senses the free ion concentration of Zn(II) in solutions containing different ligands, being unaffected by the lack of reversibility of the Zn 2+ /Zn 0 couple under the conditions assayed. In the presence of oxalate, the determination of [Zn 2+ ] agrees with the stability and solubility constants of this sparingly soluble salt, once the precipitation kinetics are taken into account. Different strategies have been analysed and implemented in order to reduce the preconcentration time with the standard electrode of the polarographic stand (smallest drop radius around 0.141 mm): (i) using a lower preconcentration factor when there is no need of enhanced limit of detection; (ii) splitting the deposition stage into two, with a first potential step under diffusion limited conditions; (iii) the analysis of the chronoamperometric response in the deposition stage allows its duration to be adjusted, especially if non-inert complexes contribute to the arriving flux of metal to the mercury electrode. The two-potential-steps strategy is assessed as the most suitable in a general case.

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.

A quantitative theory is presented for the bipolar behavior of conducting planar surfaces in a thin-layer cell of a type commonly used in electrokinetic studies. The lateral current density distribution in the cell, as dictated by the externally applied field in the solution, is formulated for the situation in which depolarization of the interface arises from transversal electron-transfer processes that occur at the two sides of the conducting surface. The treatment explicitly analyses the two limiting cases of bipolar electrodic behavior, i.e., totally irreversible electron transfer and Nernstian (mass-transfer-limited) electrodics. The spatial distribution of the electric field is calculated by means of Poisson's equation under conditions of a finite current. The results allow for a rigorous estimation of the overall bipolar faradaic current. Analytical expressions are given for the electric parameters (potential, field, local current, and bipolar faradaic current) in the case of irreversible electron transfer, and numerical analysis is performed for the reversible, Nernstian case. Deviations of the conductivity curves from the trend expected on the basis of a linear potential profile are discussed in terms of the local ohmic and faradaic contributions to the total current. The theory is supported and illustrated by experimental data for gold and aluminum surfaces in KNO 3 solution, in the absence and presence of the electroactive species Fe(CN) 6 3-/Fe(CN) 6 4-.

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.