Lability and mobility effects on mixtures of ligands under steady-state conditions

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 micro-organisms, etc.) is specifically considered and some consequences of its full analytical solutions are discussed.

[1]  W. Davison.  Defining the electroanalytically measured species in a natural water sample , 1978 .

[2]  F. W. Kellaway,et al.  Advanced Engineering Mathematics , 1969, The Mathematical Gazette.

[3]  J. Galceran,et al.  Voltammetric lability of metal complexes at spherical microelectrodes with various radii. , 2001 .

[4]  J. Buffle,et al.  Voltammetry of heterogeneous metal complex systems: Theoretical analysis of the effects of association/dissociation kinetics and the ensuing lability criteria , 1990 .

[5]  D. L. Olson,et al.  Kinetic spectrum method for analysis of simultaneous, first-order reactions and application to copper(II) dissociation from aquatic macromolecules , 1983 .

[6]  M. H. Back,et al.  Effect of metal/fulvic acid mole ratios on the binding of Ni(II), Pb(II), Cu(II), Cd(II), and Al(III) by two well-characterized fulvic acids in aqueous model solutions , 1999 .

[7]  D. Turner,et al.  The reversible electrodeposition of trace metal ions from multi-ligand systems , 1979 .

[8]  K. B. Oldham,et al.  Steady-State Voltammetry , 1989 .

[9]  Josep Galceran,et al.  Evaluation of the Koutecký-Koryta approximation for voltammetric currents generated by metal complex systems with various labilities , 2002 .

[10]  J. Pinheiro,et al.  Lability criteria for metal complexes in micro-electrode voltammetry , 1999 .

[11]  T. Carofiglio,et al.  Microelectrode voltammetry for studying host-guest complexation equilibria. An analysis of the possibilities of the method , 1994 .

[12]  H. P. Leeuwen,et al.  Voltammetry of metal complex systems with different diffusion coefficients of the species involved. II. Behaviour of the limiting current and its dependence. , 1987 .

[13]  H. Stone,et al.  Theoretical calculation of collection efficiencies for collector-generator microelectrode systems , 1997 .

[14]  D. Turner,et al.  The reversible electrodeposition of trace metal ions from multi-ligand systems: Part II. Calculations on the electrochemical availability of lead at trace levels in seawater , 1979 .

[15]  G. Grime,et al.  Dissolved metals in surface sediment and a microbial mat at 100-μm resolution , 1997, Nature.

[16]  J. Buffle,et al.  Complexation reactions in aquatic systems : an analytical approach / J. Buffle, translators S.P. Kounaves, A. Kounaves and R.S. Altman , 1990 .

[17]  Irma Lavagnini,et al.  Ultramicroelectrodes in kinetic investigations supported by simulation. A review with some additional examples , 1995 .

[18]  R. Hudson.  Which aqueous species control the rates of trace metal uptake by aquatic biota? Observations and predictions of non-equilibrium effects , 1998 .

[19]  H. Berg.  Random Walks in Biology , 2018 .

[20]  H. P. Leeuwen.  Revisited: The Conception of Lability of Metal Complexes , 2001 .

[21]  Peter Schuster,et al.  A principle of natural self-organization , 1977, Naturwissenschaften.

[22]  J. Galceran,et al.  Theoretical and analytical characterization of a flow-through permeation liquid membrane with controlled flux for metal speciation measurements. , 2003, Analytical chemistry.

[23]  Hao Zhang,et al.  In Situ Measurements of Dissociation Kinetics and Labilities of Metal Complexes in Solution Using DGT , 2003 .

[24]  H. P. Leeuwen.  Voltammetric titrations involving metal complexes: Effect of kinetics and diffusion coefficients. , 1987 .

[25]  H. Jannasch,et al.  Marine scavenging: The relative importance of mass transfer and reaction rates , 1996 .

[26]  Christopher G. Phillips,et al.  The long-time transient of two- and three-dimensional diffusion in microelectrode chronoamperometry , 1992 .

[27]  P. Bartlett,et al.  Application of Danckwerts' expression to first-order EC′reactions. Transient currents at inlaid and recessed microdisc electrodes , 1999 .

[28]  H. P. van Leeuwen,et al.  Voltammetry of metal complex systems with different diffusion coefficients of the species involved. I. Analytical approaches to the limiting current. , 1987 .