Potentiostatic current transient method

As mentioned in potentiostatic current transient method, when the fractal dimension is determined by using diffusion-limited electrochemical technique, the diffusion layer length acts as a yardstick length.122 In the case of cyclic voltammetry, it was... 

The potentiostatic current transient (PCT) technique has been known as the most popular method to understand lithium transport through an intercalation electrode, based on the assumption that lithium diffusion in the electrode is the rate-determining process of lithium intercalation/deintercalation [45]. By solving Eick s second equation for planar geometry with I.C. in Equation (5.28), impermeable B.C. in Equation (5.29), and potentiostatic B.C. 

Each of these two procedures can be varied by proceeding from a low to a high current density (or potential) or from a high to a low current density (or potential) the former is referred to as forward polarisation and the latter as reverse polarisation. Furthermore, there are a number of variations of the potentiostatic technique, and in the potentiokinetic method the pwtential of the electrode is made to vary continuously at a predetermined rate, the current being monitored on a recorder in the pulse method the electrode is given a pulse of potential and the current transient is determined by means of an oscilloscope. 

For the individual types of transient measuring techniques, special names exist but their terminology lacks uniformity. The potentiostatic techniques where the time-dependent current variation is determined are often called chronoamperometric, and the galvanostatic techniques where the potential variation is determined are called chronopotentiometric. For the potentiodynamic method involving linear potential scans, the term voltammetry is used, but this term is often used for other transient methods as well. 

The principle of this method is quite simple The electrode is kept at the equilibrium potential at times t < 0 at t = 0 a potential step of magnitude r) is applied with the aid of a potentiostat (a device that keeps the potential constant at a preset value), and the current transient is recorded. Since the surface concentrations of the reactants change as the reaction proceeds, the current varies with time, and will generally decrease. Transport to and from the electrode is by diffusion. In the case of a simple redox reaction obeying the Butler-Volmer law, the diffusion equation can be solved explicitly, and the transient of the current density j(t) is (see Fig. 13.1) ... 

The steady-state method has advantages in its freedom from double-layer charging and in the simplicity of light and current measurements. The transient method is mechanically simpler and does not require a dual potentiostat (Chap. 6). Moreover, the rate of electrolysis is smaller, and hence solutions may suffer more slowly from the buildup of contaminants arising from side reactions. 

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 was mentioned in Sects. 2.8.1 and 2.8.2, application of the Laplace transform to the transient potential and current permits determination of the operational impedance. Such a method was initially introduced by Pilla [90-93] and applied to studies using mercury electrodes. Using a fast potentiostat a small potential step was applied, and both voltage and current transients were measured. Of course, because of the nonideal potentiostat response, the potential increase was not a rectangular step but occiured more slowly. Examples of the measured potential and current transients are shown in Fig. 3.6. Such data acquisition was extended to longer times and then extrapolated as the integration had to be continued to inlinity. 

Potential or current step transients seem to be more appropriate for kinetic studies since the initial and boundary conditions of the experiment are better defined unlike linear scan or cyclic voltammetry where time and potential are convoluted. The time resolution of the EQCM is limited in this case by the measurement of the resonant frequency. There are different methods to measure the crystal resonance frequency. In the simplest approach, the Miller oscillator or similar circuit tuned to one of the crystal resonance frequencies may be used and the frequency can be measured directly with a frequency meter [18]. This simple experimental device can be easily built, but has a poor resolution which is inversely proportional to the measurement time for instance for an accuracy of 1 Hz, a gate time of 1 second is needed, and for 0.1 Hz the measurement lasts as long as 10 seconds minimum to achieve the same accuracy. An advantage of the Miller oscillator is that the crystal electrode is grounded and can be used as the working electrode with a hard ground potentiostat with no conflict between the high ac circuit and the dc electrochemical circuit. 

As explained earlier, in transient electrochemical methods an electrical perturbation (potential, current, charge, and so on) is imposed at the working electrode during a time period 0 (usually less than 10 s) short enough for the diffusion layer 8 (2D0) to be smaller than the convection layer (S onv imposed by natural convection. Thus the electrochemical response of the system investigated depends on the exact perturbation as well as on the elapsed time. This duality is apparent when one considers a double-pulse potentiostatic perturbation applied to the electrode as in the double-step chronoampero-metric method. 

Chromatography, spectroscopy, radiotracer, and other analytic procedures, coulombio efSciency (1) Stationary methods current density potential relations at constant composition and temperature Honstationary methods (i) galvano-static transients, (ii) potentiostatic transients, (Hi) superimposed ac methods, (iv) cyclic voltammetry... 

Chronoamperometry Chronoamperometry involves the study of the variation of the current response with time under potentiostatic control. Generally the working electrode is stepped from a potential at which there is no electrode reaction to one corresponding to the mass-transport-limited current, and the resulting current-time transient is recorded. In double-step chronoamperometry, a second step inverts the electrode reaction and this method is useful in analysing cases where the product of the initial electrode reaction is consumed in solution by a coupled homogeneous chemical reaction. 

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