Electrode kinetics relaxation methods

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

In electrode kinetics, however, the charge transfer rate coefficient can be externally varied over many orders of magnitude through the electrode potential and kd can be controlled by means of hydrodynamic electrodes so separation of /eapp and kd can be achieved. Experiments under high mass transport rate at electrodes are the analogous to relaxation methods such as the stop flow method for the study of reactions in solution. 

As this chapter is primarily dedicated to the study of electrode kinetics, we wish to deal only briefly with the fundamental consequences of reactant adsorption for the methodology of the relaxation techniques, again confined to the potential step and the impedance methods. In addition, we will review briefly the potentialities of these methods with regard to the study of adsorption itself in the case of the reversible electrode reaction. 

Thus, Thonstad et al. [135,136] used the relaxation method with galvano-static perturbation and electrochemical impedance spectroscopy to study the kinetics of the A1(III)/A1 electrode reaction in cryolite-alumina melts and found that the exchange current densities were of the order of 5-15 A cm 2. The general electrode reaction scheme may be written... 

The techniques for characterizing the kinetics of electrode reactions can be classified into steady-state and transient methods. The steady-state methods involve the measurement of the current-potential relationships at constant current (galvanoslatic control) or constant potential (potentiostatic control) conditions and measuring the response, which is either the potential or the current after a steady state is achieved. The non-steady-state methods involve the perturbation of the system from an equilibrium or a steady-state condition, and follow the response of the system as a function of time using current, potential, charge, impedance, or any other accessible property of the interface. Relaxation methods are a subclass of perturbation methods. 

As for the permeability measurements, most techniques based on the analysis of transient behavior of a mixed conducting material [iii, iv, vii, viii] make it possible to determine the ambipolar diffusion coefficients (- ambipolar conductivity). The transient methods analyze the kinetics of weight relaxation (gravimetry), composition (e.g. coulometric -> titration), or electrical response (e.g. conductivity -> relaxation or potential step techniques) after a definite change in the - chemical potential of a component or/and an -> electrical potential difference between electrodes. In selected cases, the use of blocking electrodes is possible, with the limitations similar to steady-state methods. See also - relaxation techniques. 

The development during the last three decades of laboratory methods for investigation of the kinetics of electrode reaction[44,45,46] e.g. of relaxation techniques (potential step, current step, A.C. impedance methods, etc.), of cyclic voltammetry and, most recently of the use of electrodes of very small dimensions, has led to a marked increase in our level of understanding of these processes. The value of these techniques has been greatly enhanced by the development of computer based methods of data analysis. 

There are in fact two slightly different types of non-steady state technique. In the first an instantaneous perturbation of the electrode potential, or current, is applied, and the system is monitored as it relaxes towards its new steady state chronoamperometry and chronopotentiometry are typical examples of such techniques. In the second class of experiment a periodically varying perturbation of current or potential is applied to the system, and its response is measured as a function of the frequency of the perturbation cyclic and a.c. voltammetry are examples of this type of approach. In both cases the rate of mass transport varies with the time (or frequency), and by obtaining data over a wide range of these variables and by using curve fitting procedures, kinetic parameters are obtainable. Pulse techniques will be discussed later in this chapter, whilst sweep methods are described in Chapter 6 and a.c. methods in Chapter 8. 

After having described one equilibrium method for the measurement of kinetics of rather fast electrode processes and two steady state methods for measurement of slow electrode processes, let us turn now to consider the so called transient or, sometimes, relaxation techniques, where time is a very important factor in the equations. 

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