Electrochemical analysis of metal complexes

H.G. de Jong

    Research output: Thesisinternal PhD, WU


    The present study is concerned with the electroanalytical chemistry of complexes of metals with large ligands. The main purpose was to develop quantitative descriptions of the voltammetric current-potential relation of metal complex systems with different diffusion coefficients of the species involved and of the conductometric response of metal/polyelectrolyte systems at various metal-to-ligand ratios. A further goal was to illustrate the theoretical treatments with some experiments on model systems.
    In chapter 1 the general background of this study is discussed. After a brief review of some environmental aspects of heavy metals, the importance of reliable analytical techniques for their speciation is advanced. The particular potentialities of electroanalytical techniques in this field are outlined.
    In chapter 2 a rigorous theoretical treatment is given of the voltammetric limiting current for metal complex systems in which the diffusion coefficents of the species Involved are different. The equation for the limiting current is formulated in the Laplace domain and is rigorous with respect to the values of the association and dissociation rate constants as well as to the ratio of the diffusion coefficients of the species. It is valid for an excess of ligand and a stationary planar electrode. In some limiting cases analytical expressions in the time domain have been obtained. In the degenerate case of equal diffusion coefficients the limiting current can be described by a series expansion of confluent hypergeometric functions. Another limiting case is the situation where the diffusion coefficient of the ligand is infinitely small. Here, the use of a perturbation technique leads to a satisfactory approximation in the form of a series of confluent hypergeometric functions, for the case where the diffusion coefficient of the ligand is at least one order of magnitude smaller than that of the uncomplexed metal ion. Where analytical inversion of the Laplace transformed limiting current expression falls, transients are obtained by a numerical procedure. The results are identical with what may be obtained from the time-consuming fully numerical solution of the differential equations using the explicit finite difference algorithm.
    In chapter 3 the behaviour of the limiting current is investigated as a function of the electrolysis time, the ratio of the diffusion coefficients of the species and the association/dissociation rate constants. New qualifications to specify the voltammetric behaviour of metal complex system are introduced. Depending on the mean life-times of the species, the system can be static, semi-dynamic and dynamic. When the mean life-times are large compared to the electrolysis time, the system is static and the limiting current is proportional to the concentration of uncomplexed metal. In the opposite case where the life-times are small compared to the electrolysis time, the system is dynamic. A dynamic system can be further subdivided in labile and nonlabile. The lability concept unambiguously follows from considering the limiting cases in the theory. A new lability criterion is formulated, which is, compared to earlier tentative formulations, generalized to the metal complex system as a whole. In the non-labile regime the limiting current is found to follow exactly the classical reaction layer model, provided there is a large excess of complex over free metal. In order to facilitate practical use of the various results, some Cottrell plots and working curves are given.
    In chapter 4 a rigorous treatment of the complete current-potential relation of the metal complex systems from the previous chapters is given. The general relation is again formulated in the Laplace domain. Besides its limitation to reversible electrode processes, it has the same range of validity as the limiting current equation of chapter 2. The half-wave potential is obtained numerically from the general current-potential relation and its dependence on the electrolysis time, the ratio of the diffusion coefficients of the species and the association/dissociation rate constants is discussed. In the case of equal diffusion coefficients of the species, the current- potential relation can be analytically transformed from the Laplace- to the time domain. The result is given as a series expansion of confluent hypergeometric functions. In the dynamic regime the current-potential relation is described by an experfc type of function. An analytical expression for the half-wave potential is then obtained. In the case of a labile system and a large excess of complex this expression reduces to the well-known DeFord-Hume equation.
    In chapter 5 experimental data from earlier work on the voltammetry of heavy metal/polyelectrolyte systems are reconsidered. A procedure for solving a voltammetric speciation problem for a given set of values of the electrolysis time and the ratio of the diffusion coefficients is presented. Under the given experimental conditions the Zn/PMA system was found to be labile. Here the speciation is straightforwardly performed using the mean diffusion coefficient concept. The Cd/PMA data are substantially affected by induced adsorption of the metal ion. Until this is eliminated, interpretation is not possible. The Pb/PAA system seems to be dynamic and not labile. Here, the speciation is involved and performed by fitting the experimental data to the rigorous equations of the chapters 2 and 4 and as a result the order of magnitude of both the stability constant and the dissociation rate constant are obtained. Anticipating future presentations the correctness of the stability constant evaluated under the assumption of an excess of ligand, is estimated.
    In chapter 6 a procedure is described for the analysis of the conductivity of solutions of polyions in which both mono- and divalent counterions are present. The method is based on analysis of the relation between the overall conductivity of the system and the conductivity of the monovalent cations and assumes that the latter are electrostatically bound. The system is described in terms of the two state approach, implying that the counterions are considered to be either in some kind of bound state or are completely free. The potentialities of the proposed method are explored by studying solutions of alkali polyacrylates with and without added zinc nitrate at several alkali nitrate concentrations The results give a picture of the composition of the counterionic atmosphere around the polyion. Up to a certain Zn/polyacrylate ratio, the zinc ions were found to be bound quantitatively by the polyion. The composition of the counterionc atmosphere was largely independent of the alkali nitrate concentration if the latter was not in too large excess with respect to both the zinc ions and the charged monomers.

    Original languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • Lyklema, J., Promotor, External person
    • van Leeuwen, H.P., Promotor, External person
    Award date9 Dec 1987
    Place of PublicationWageningen
    Publication statusPublished - 9 Dec 1987


    • heavy metals
    • analytical methods
    • electrochemistry
    • double salts
    • electroanalytical analysis


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