General analytical solution for a reversible i/t response to a double potential step at spherical electrodes in the absence/presence of amalgamation effects

Abstract

, 2378 (1994).The general rigorous theory corresponding to double potential step chronoamperometry for a reversible charge transfer reaction in a spherical electrode whose area increases with t', where z > 0, is presented. The static mercury drop electrode (z = 0) and the dropping mercury electrode ( z = 213) are addressed specifically. The explicit equations for the current versus time response assuming unequal diffusion coefficients for the oxidized and reduced species are valid when the product is soluble in both the electrolytic solution and the electrode. Comparisons with previous general treatments in the literature are made. The theory is applied to the detection of amalgamation in RP and DNP techniques.Moreover, in this work we show the origin of errors appearing in some general treatments in the literature, these errors lead to physically meaningless results when amalgamation takes place. 2378 (1994). On prCsente la thCorie gCnCrale rigoureuse correspondant 2 la chronoampkromCtrie avec une Ctape h double potentiel d'une rCaction rCversible de transfert de charge dans une Clectrode sphCrique dont la superficie augmente comme t Z , oh z > 0. On examine d'une f a~o n spCcifique les cas des Clectrodes avec goutte de mercure statique (z = 0) et avec goutte de rnercure tombante (z = 213). Les Cquations explicites pour le courant en fonction du temps de rCponse, en supposant des coefficients de diffusions diffkrents pour les espbces oxydCes et rkduites, sont valides lorsque le produit est soluble dans le solution Clectrolytique ainsi que dans 1'Clectrode. On prCsente des cornparaisons avec les traitements gCnCraux rapportCs antCrieurement dans la littkrature. On applique la thCorie ii la dCtection d'arnalgamation dans les techniques de RP et de DNP.De plus, dans ce travail, on rnontre l'origine des erreurs qui apparaissent des quelques traftements gCnCraux rapportks dans la littkrature et qui, lorsqu'une amalgamation se produit, rendent les risultats physiquement sans signification.[Traduit par la rCdaction] Introduction In this paper we study the application of a double potential pulse to a reversible charge transfer process at stationary and nonstationary spherical electrodes. We consider the general case when the diffusion coefficients of the oxidized and reduced species are different, and the reduced species can dissolve in the electrolytic solution as well as in the electrode. In order to obtain an exact expression for the response corresponding to the second potential pulse, it is essential to consider the perturbation of the second pulse on the concentration profiles generated by the first potential pulse. Previous investigators (1, 2) have neglected this perturbation.The difficulties in the calculation of the response to the second potential step for a spherical electrode arise from surface concentrations which are dependent on potential, diffusion co-

Theoretical and experimental study of Differential Pulse Voltammetry at spherical electrodes: Measuring diffusion coefficients and formal potentials

“…Moreover, it is worth highlighting that under these conditions, the expression for DPV curves contains the function Fðn 0 1 Þ an infinite power series of n 0 1 (sphericity parameter), while previous solutions [14][15][16][17], which contain only a few terms, are approximate solutions, not valid for small electrodes.…”

Reciprocal Derivative Chronopotentiometry with Programmed Current: Influence of the Reversibility

“…In order to evaluate these errors we have compared Equations 12 and 17 for an SMDE considering spherical diffusion and amalgam formation of references [13,14] corresponding to the i vs. E and E vs. t curves, respectively, with Equations 1 and 17 in this article. The influence of the electrode sphericity on the peak potentials was negligible.…”

Theory for double potential step chronoamperometry for any potential values at spherical electrodes

“…We showed the importance of the proposed mathematical procedure [1,2] against those existing in the literature [3][4][5][6] that lead to partial solutions with more complex forms and even to physically meaningless results. Moreover, the mathematical method proposed permits to easily consider that both species are initially present in the system.…”