Re-examination of the potential-step chronoamperometry method through numerical inversion of Laplace transforms. I. General formulation and numerical solution

Re-examination of the potential-step chronoamperometry (PSCA) method through numerical inversion of Laplace transforms is proposed in this work. First, a general expression is derived in the Laplace domain for the current transient following the application of a potential step of arbitrary amplitude. The formulation applies to first-order electrochemical–chemical reactions (E, EC and CE reactions) with one-dimensional mass-transport processes of implicated species in the electrolytic solution or the electrode. Next, numerical inversion of the relevant Laplace transform is performed by the Gaver–Stehfest (GS), Fourier–Euler (FE) and ‘fixed’ Talbot (FT) methods. The so-called GS-, FE- and FT-PSCA algorithms in this work make it possible to investigate a wide range of electrode geometry and chemical, electrochemical and one-dimensional mass-transport processes by the PSCA method. Each algorithm provides a full explicit formulation of Faradaic current with respect to time, applied potential and electrochemical parameters (initial concentrations, geometrical parameter(s), standard potential, electrochemical and chemical rate constants and diffusion coefficients), which greatly simplifies the computation of potentiostatic current transients. Some application examples relative to diffusion equations with spherical electrode geometry will be presented in the second part of this work.     

New approach of electrochemical systems dynamics in the time domain under small-signal conditions: II. Modelling the responses of electrochemical systems by numerical inversion of Laplace transforms

In the first part of this work, we showed that numerical inversion of Laplace transform (NILT) methods could be readily applied to compute the responses of electrochemical systems to small input signals from any reasonable model of the system immittance that is the impedance for current-controlled techniques and the admittance for potential-controlled techniques. The aim of this second article is to provide some applications examples in different fields of electrochemical kinetics. The response of a polymer exchange membrane fuel cell to a small current pulse is computed. The responses of corrosion systems to small potential step/ramp signals are also dealt with. The response of electrochemical systems to a sinusoidal perturbation of electrode potential is investigated. Finally, both Faradaic and non-Faradaic components of the total current are computed by NILT methods under potential- and current-controlled conditions.     

Discussion of the potential step method for the determination of the diffusion coefficients of guest species in host materials: Part I. Influence of charge transfer kinetics and ohmic potential drop

Theoretical expressions are given for the output response of ion-insertion electrodes to a potential step assuming linear diffusion, restricted (blocking) diffusion conditions and possible limitations by insertion reaction kinetics. The effects of ohmic potential drop are also investigated. It is shown that slow interfacial charge transfer cannot be distinguished from ohmic drop effects, in contrast to impedance diagrams where ohmic drop and charge transfer effects can be separated. The influence of potential step amplitude is discussed. Chronocoulometric analysis is dealt with considering diffusion controlled processes as well as mixed control conditions. The error in the determination of the chemical diffusion coefficient of a guest species from chronoamperometric data, when using the limiting Cottrell equation in the short-time range or the exponential decay of current in the long-time domain, is evaluated in relation to insertion reaction kinetics and ohmic potential drop. Determination of the diffusion coefficients by curve fitting is also envisaged using the current versus time and charge versus time relationships. Finally, previous results in the electrochemical literature are discussed in the light of the theoretical derivations proposed in this paper.     

Investigation of potential inversion in the reduction of 9,10-dinitroanthracene and 3,6-dinitrodurene

In the case of two-electron reduction of a compound, potential inversion refers to the situation where introduction of the second electron occurs with greater ease than the first. That is E⁰₁?E⁰₂<0 where E⁰₁ and E⁰₂ are the standard potentials for the two steps of reduction. The extent of potential inversion in the reduction of 9,10-dinitroanthracene, 1, and 3,6-dinitrodurene, 2, has been assessed by steady-state microelectrode voltammetry, cyclic voltammetry under conditions of near-reversible behavior, cyclic voltammetry under conditions of quasireversible behavior and electrochemical impedance spectroscopy (EIS). The studies were conducted in acetonitrile at 298 K. Cyclic voltammetry under quasireversible conditions and EIS were most sensitive to small changes in E⁰₁?E⁰₂. The value of E⁰₁?E⁰₂ for 1 was found to be ?107 mV and that for 2 was ?280 mV.