The effects of time-variance on impedance measurements: examples of a corroding electrode and a battery cell

When performing electrochemical impedance spectroscopy (EIS) measurements on a system, we must make sure it fulfills certain conditions. One of them is that it should be stationary that is to say, steady-state and time-invariant. Commonly studied systems are time-variant, for example a corroding electrode or a battery under operation. A corroding electrode sees its polarization resistance decrease with time. A passivating electrode sees its polarization resistance increase with time. These phenomena cause a deformation of the Nyquist impedance at low frequencies. This result was first simulated and validated by experimental measurements on a corroding steel sample undergoing uniform corrosion. The effect of performing impedance measurements on a discharging battery was also shown. Several methods are available to check and correct time-variance. The nonstationary distortion (NSD) indicator is used to separate valid and invalid data samples and the so called “4D impedance” method can easily produce instantaneous impedance data

Contribution à l'identification paramétrique du processus d'oxydation anodique du zinc en milieux basiques

One of the aims of electrochemical kinetics is to establish a reaction scheme that "explains" the behavior of an electrode. This diagram can be deduced from a reaction balance and a number of experimental relationships between electrical variables. As in chemical kinetics, it explains the reactions likely to take place in the overall electrochemical process, and specifies the nature of the species involved in the reactions. In general, it is not possible either to identify these intermediate species, or, a fortiori, to follow the spatial and temporal evolution of their concentrations, and direct confirmation of this reaction scheme is therefore not possible. To prove the validity of a reaction scheme, it is therefore necessary to compare the experimental responses of the object under study with the theoretical responses of the model that is supposed to represent it. This procedure can be placed within the framework of systems theory, and we will show in the first part of this thesis that the elaboration of a reaction scheme in electrochemical kinetics includes the steps of characterization, identification and verification.verification. We will then apply these concepts to the study of the electrochemical behavior of zinc in basic media. A preliminary experimental characterization will enable us to distinguish two different behaviors of zinc, depending on the pH of the electrolyte. We will develop a model describing the zinc oxidation process in a weakly basic medium. Its partial parametric identification will be carried out in intentiostatic mode. We will then study the operation of the zinc electrode as a first species. Application of the concept of system governability will enable us to reject a certain type of explanation of the "passivation-reactivation" processes of zinc in very basic media. The use of a new negative internal resistance regulator will demonstrate the existence of multiple stationary states of anodic zinc dissolution, and a mechanism that takes account of the influence of the ohmic drop will be characterized.Établir un schéma réactionnel qui "explique" le comportement d'une électrode, tel est l'un des buts que l'on peut se fixer en cinétique électrochimique. Ce schéma peut être déduit d'un bilan réactionnel et d'un certain nombre de relations expérimentales entre des variables électriques. Il explicite, comme en cinétique chimique, les réactions susceptibles d'intervenir dans le processus électrochimique global et précise la nature des espèces participant aux réactions. En général, il n'est possible, ni de mettre en évidence ces espèces intermédiaires, ni, a fortiori, de suivre l'évolution spatiale et temporelle de leurs concentrations et la confirmation directe de ce schéma réactionnel n'est donc pas possible. Il est donc nécessaire, pour prouver la validité d'un schéma réactionnel, de comparer les réponses expérimentales de l'objet étudié et celles, théoriques du modèle supposé le représenter. Cette procédure peut se replacer dans le cadre de la théorie des systèmes et nous montrerons dans la première partie de ce mémoire que l'élaboration d'un schéma réactionnel en cinétique électrochimique comprend les étapes de caractérisation, d'identification etde vérification. Nous appliquerons ensuite ces notions à l'étude du comportement électrochimique du zinc en milieux basiques. Une caractérisation expérimentale préalable nous permettra de distinguer, en fonction du pH de l'électrolyte, deux comportements différents du zinc. Nous élaborerons un modèle décrivant le processus d'oxydation du zinc en milieu faiblement basique. Son identification paramétrique partielle sera effectuée en mode intentiostatique. Nous étudierons ensuite le fonctionnement de l'électrode de zinc en première espèce. L'application du concept de gouvernabilité des systèmes permettra le rejet d'un certain type d'explication des processus de "passivation-réactivation" du zinc dans les milieux très basiques. L'utilisation d'une nouvelle régulation à résistance interne négative mettra en évidence l'existence d'états stationnaires multiples de dissolution anodique du zinc et un mécanisme tenant compte de l'influence de la chute ohmique sera caractérisé

Une étude des PEMFC et de leurs membranes

Dans la première partie, des électrodes métalliques recouvertes d'un ou de plusieurs films polymères pour piles à combustible (PAC)sont étudiées théoriquement et expérimentalement. On montre qu'il n'est pas possible de déterminer par spectroscopie d'impédance électrochimique (SIE) les paramètres clés de ces systèmes : coefficients de diffusion dans les films (D), épaisseurs des films (L) et coefficients de partage à chaque interface (gamma). Seuls les paramètres gamma D/L et L*L/D sont déterminables à l'aide de cette technique.Dans la seconde partie, une nouvelle méthode de mesure de l'impédance de chaque élément d'une PAC en cours de fonctionnement re el est proposée. On montre, pour une PAC directe au méthanol commerciale, que l'impédance de l'anode où a lieu l'electro-oxydation du méthanol est environ 20 fois plus petite que l'impédance de la cathode où a lieu l'electro-réduction du dioxygène. On montre aussi, pour un stack de PAC dihydrogène-dioxygène lui aussi commercial, que les quatre éléments de ce stack ne fonctionnent pas de manière identique selon leur position par rapport à l'arrivée des gaz.GRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

New approach of electrochemical systems dynamics in the time-domain under small-signal conditions. I. A family of algorithms based on numerical inversion of Laplace transforms

International audienceDynamic modelling of electrochemical systems in the time-domain generally requires the inversion of Laplace transforms. Unfortunately, many practical systems exist for which the inverse transforms cannot be derived analytically. A new approach of the dynamics of electrochemical systems, investigated under small-signal conditions, is proposed in this work. The method is based on numerical inversion of Laplace transforms and, more especially, on the Gaver–Stehfest (GS) inversion formula. General and explicit formulations of the time-domain responses of stable systems to a small potential step/ramp and to a small current step/pulse are derived in part I of this work from linear combinations of values of the system immittance that is the admittance for potential-controlled techniques and the impedance for current-controlled techniques. The GS approach of system dynamics is illustrated by taking the example of finite-space diffusion of electroactive species. Application to corrosion systems, polymer exchange membrane fuel cells and thin-film ion-insertion electrodes will be presented in the next parts of this work

Unusual concentration impedance for catalytic copper deposition

International audienceRecently a new mechanism for copper deposition has been proposed by Gabrielli et al. [C. Gabrielli, P. Moçotéguy, H. Perrot, R. Wiart, J. Electroanal. Chem. 572 (2004) 367]. In this mechanism cupric ions are supposed to be reduced by two different paths. The first path is a direct discharge of cupric ions in two steps, and the second follows a parallel path through a catalytic complexation with chloride ions and adsorption of copper (I) chloride onto the copper surface. In the second path, chloride ions are consumed in the first step and produced in the second step, therefore chloride ions act as catalysts. The rates of the two steps of the second path are equal under steady-state condition and the concentration of Cl- anion is constant in the electrolytic solution. In contrast the step rates are not equal under dynamic conditions causing a concentration impedance of chloride ions with a rather unusual expression. Such an impedance is calculated and thoroughly examined in this paper. Finally, decomposition of the Faradaic impedance into the sum of concentration impedances of adsorbed species and chloride ions makes it possible to determine the contribution of each concentration impedance to the global impedance of the electrode

Destabilizing role of the double layer for a dissolution–depassivation mechanism

International audienceA new dissolution–depassivation mechanism showing a non-trivial complex S-shaped polarization curve due to the Frumkin isotherm hypothesis has been studied. A potential domain exists for sufficiently low values of the Frumkin interaction parameter where a negative differential resistance is observed. For this mechanism, the electrode potential acts as an essential system variable due to the double layer capacitance. Harmonic and relaxation oscillations can be observed for the dissolution–depassivation mechanism under galvanostatic control (GC). Hopf bifurcation gives rise to oscillations under GC only for sufficiently high values of the double layer capacitance. Bifurcation diagrams are plotted

Diffusion-trapping impedance under restricted linear diffusion conditions

International audienceThe theoretical expression for the mass-transport impedance is derived considering diffusion-trapping controlled processes studied under restricted linear diffusion conditions (impermeable surface) and assuming uniform distribution of trapping sites in the electrode. The relevant expression applies to hydrogen diffusion-trapping in metals and alloys, as well as ion insertion-trapping in host materials provided the metallic type potential distribution is assumed in electrolyte/host material systems. The impedance diagram shape is discussed based on two dimensionless parameters, i.e. the ratio of the diffusion resistance to the trapping resistance and the ratio of the diffusion time constant to the trapping time constant. A case diagram is plotted to determine the validity conditions for the limiting expressions of the mass-transport impedance derived for diffusion and trapping control. The conditions for characterization of diffusion with trapping from EIS data are discussed depending on the system parameters and the frequency range accessible experimentally. The influence of non-uniform spacial distribution of trapping sites is also discussed. Distribution of trapping sites with different kinetic constants and concentrations is finally envisaged

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

International audienceIn 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

Problem of Kramers–Kroenig Transformation of EIS Data in Case of Instabilities

International audienceElectrodes presenting negative resistances or capacitances in their electrical model are often not consistent with Kramers–Kroenig transformations (KKT) due, in most cases, to violation of stability condition. Stability is related to the way of their electrical, either potential or control of the current, and it is determined by the form of the impedance expressed in terms of its zeros and poles. For KKT to be valid, the form of the transformed immittance has to represent stable control. For electrodes stable under potentiostatic and unstable under galvanostatic control, to get satisfying KKT it is adequate to transform data in their admittance representation and not as impedance. For unstable electrodes, to get the transformed spectrum identical as the original one, one may apply the expedient of changing the sign of the part of the electrical model responsible for instability. Two examples presenting problems with KKT compliance are presented here: (i) artificial electric circuit with negative resistance and (ii) the metal/metal ion electrode in the transpassive state. In both cases the expedient of the sign change of the low-frequency segment of the Voigt equivalent circuit was sufficient to reproduce the original electrochemical impedance spectroscopy data after KKT of its otherwise Kramers–Kroenig nontransformable impedance representation

Kramers-Kronig Transforms as Validation of Electrochemical Immittance Data Near Discontinuity

International audienceImmittance data was recorded for copper rotating disk in concentrated copper sulphate/sulphuric acid electrolyte, and its evolution under potential control (PC) was analyzed starting from the active state at rest potential, through active/passive transition up to the stable passivity. In the potential range corresponding to the passivity under PC, the transition was observed from the nonminimum phase (nmp)-type of immittance to the minimum phase (mp) one which corresponded to Hopf bifurcation under current control. This transition was manifested by a resonance-like peak on the amplitude characteristic and the phase change from apparently discontinuous as displayed in [–180°, +180°] range (nonminimum) to the continuous (minimum) one. In complex coordinates this was featured by scattered impedance points. Validation by Kramers-Kronig (KK) transformation of nmp-type immittance data failed for impedance representation used in transformation but was successful for admittance representation as the latter was the form actually recorded under PC. This finding validates both nmp and mp immittance data in agreement with earlier suggestions of other authors. [See, Gabrielli et al., in Electrochemical Impedance: Analysis and Interpretation, p. 140, ASTM, Philadelphia, PA (1993).] Transition from mnp to mp type of electrode dynamics can be attributed to appearance of conduction channels representing local depassivation of the electrode