Current-potential-time

Almost all kinetic investigations on azo coupling reactions have been made using spectrophotometric methods in very dilute solutions. Uelich et al. (1990) introduced the method of direct injective enthalpimetry for such kinetic measurements. This method is based on the analysis of the zero-current potential-time curves obtained by the use of a gold indicator electrode with a surface which is periodically restored (Dlask, 1984). The method can be used for reactions in high (industrial) concentrations. 

The real power of digital simulation techniques lies in their ability to predict current-potential-time relationships when the reactants or products of an electrode reaction participate in some intervening chemical reaction. These kinetic complications often result in a fairly difficult differential equation (when combined with the conditions for diffusion or convection encountered in electrochemical problems) that resists solution by ordinary means. Through simulation, however, the effect of any number of chemical steps may be predicted. In practice, it is best to limit these predictions to cases where the reactants and products participate in one or two rate-determining steps each independent step adds another dimensionless kinetics parameter that must be varied over the range of... 

Upon evaluating the convolution integral from the experimental current-potential (time) curve and its limiting values (Eq. 77), kinetic analysis can be performed with the help of Eq. (76). Conversely, Eq. (76) or similar equations can be used to calculate the theoretical current-potential curve, e.g., for the linear potential sweep voltammogram, provided that the values of all the parameters are known. Some illustrative examples were provided by Girault and coworkers [183]. 

Generally speaking the mathematical problems tackled in voltammetry involve the resolution of partial differential equation systems by means of analytical, semi-analytical or numerical methods. The solutions of the problem are the concentration profiles of the different species, and from them the current-potential-time response of the system to a given electrical perturbation can be calculated. 

Fig. II.1.3a, b Schematic drawing of a 3D plot with characteristic current-potential-time relationships for chronoamperometric and steady-state responses. The trace following the intersecting plane shows approximately the peak characteristics of a Mnear sweep voltammognun...

Voltammetry under transient (e.g., cyclic voltammetry) or steady-state (e.g., rotated disk or microelectrode) conditions which requires the interpretation of current-potential-time (I-E-i) curves. 

Most symbols concerning currents, potentials, time-intervals, concentrations and abbreviations for experimental techniques are summarized in Appendix A of chapter 2 of this volume. Abbreviations of substances dealt with in chapter 3 (e.g., MV, BQI, AA, DA) are explained in the text. 

It is convenient to describe the theory of voltammetry by considering the oxidation form of the half-cell reaction given in Equation (2.1). A current-potential-time (I-E-t) relationship under these conditions, which constitutes a description of a voltammogram, can be given by the expression ... 

In order to allow the widest possible flexibility in the basic electro-analytical variables of current, potential, time, and concentration the ideal potentiostat should have the following characteristics ... 

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

The change in current as a function of time in controlled-potential coulometry is approximated by an exponential decay thus, the current at time t is... 

A second approach to coulometry is to use a constant current in place of a constant potential (Figure 11.23). Controlled-current coulometry, also known as amperostatic coulometry or coulometric titrimetry, has two advantages over controlled-potential coulometry. First, using a constant current makes for a more rapid analysis since the current does not decrease over time. Thus, a typical analysis time for controlled-current coulometry is less than 10 min, as opposed to approximately 30-60 min for controlled-potential coulometry. Second, with a constant current the total charge is simply the product of current and time (equation 11.24). A method for integrating the current-time curve, therefore, is not necessary. 

Fig. 6. Discharge behavior of a battery where is the open circuit voltage (a) current—potential or power curve showing M activation, ohmic, and M concentration polarization regions where the double headed arrow represents polarization loss and (b) voltage—time profile.

Coulometry. If it can be assumed that kinetic nuances in the solution are unimportant and that destmction of the sample is not a problem, then the simplest action may be to apply a potential to a working electrode having a surface area of several cm and wait until the current decays to zero. The potential should be sufficiently removed from the EP of the analyte, ie, about 200 mV, that the electrolysis of an interferent is avoided. The integral under the current vs time curve is a charge equal to nFCl, where n is the number of electrons needed to electrolyze the molecule, C is the concentration of the analyte, 1 is the volume of the solution, and F is the Faraday constant. 

Figure 20-13 shows current and potential time curves for a stainless steel 500-liter tank with cathodic protection by impressed current and interrupter potentiostat. 

Fig. 20-13 Current and potential-time curves for a 500-liter stainless steel water tank. Impressed current protection with an interrupter potentiostat X (20 C) = 2250 IJ.S cm-i c (CF) = 0.02 mol L" 60 C.

Electrical methods of analysis (apart from electrogravimetry referred to above) involve the measurement of current, voltage or resistance in relation to the concentration of a certain species in solution. Techniques which can be included under this general heading are (i) voltammetry (measurement of current at a micro-electrode at a specified voltage) (ii) coulometry (measurement of current and time needed to complete an electrochemical reaction or to generate sufficient material to react completely with a specified reagent) (iii) potentiometry (measurement of the potential of an electrode in equilibrium with an ion to be determined) (iv) conductimetry (measurement of the electrical conductivity of a solution). 

FIGURE 3-1 Chronoamperometric experiment (a) potential-time waveform (b) change of concentration profiles with time (c) the resulting current—time response. 

FIGURE 3-11 Potential-time waveform used in alternating current (AC) voltammetry. 

Fig. 2. Common potential-time profiles used for the investigation of organic electrode processes. In each case the current response to the potential change is recorded.

In such a synthesis the lengths of the pulses are variable as well as the potentials of the square wave. Recently a potential-time profile has been used to maintain the activity of an electrode during the oxidation of organic compounds (Clark et al., 1972) at a steady potential the current for the oxidation process was observed to fall, but a periodic short pulse to cathodic potentials was sufficient to prevent this decrease in electrode activity. 

A method based on the oseillographie observation of the response after current interruption or tuming-on suitable for its interpretation taking into account the effect of side reactions on potential-time curves has been deseribed [59Khe, 61Zin]. (Data obtained with this method are labelled OCS.)... 

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