Transition time chronopotentiometry

Fig. 3.53 shows the effect of an electroactive species such as an acid or a more active depolarizer that undergoes cathodic reduction in one ac half-period and anodic oxidation in the next ac half-period (see also Fig. 3.54) x is the so-called transition time, well known from chronopotentiometry (see later), i.e., in Fig. 3.53 the transition time of reduction. 

A more usual procedure for overcoming the disturbances from contaminants is current reversal chronopotentiometry here the current is reversed at the initial transition time tf of the forward reaction and the next transition time xb of the backward reaction is measured as a rule the reversal wave will not be influenced by the contaminant because it will react either before the forward or after the backward reaction of the analyte (see Fig. 3.60a) the entire procedure can be even repeated as cyclic chronopotentiometry (see Fig. 3.60b), which may provide a further check on the reliability. The reversal technique can be applied to initial reduction followed by re-oxidation and also to initial oxidation followed by re-reduction79. 

Chronopotentiometry has also been used to determine chloride ions in seawater [31]. The chloride in the solution containing an inert electrolyte was deposited on a silver electrode (1.1 cm2) by the passage of an anodic current. The cell comprised a silver disc as working electrode, a symmetrical platinum-disc counter-electrode and a Ag-AgCl reference electrode to monitor the potential of the working electrode. This potential was displayed on one channel of a two-channel recorder, and its derivative was displayed on the other channel. The chronopotentiometric constant was determined over the chloride concentration range 0.5 to 10 mM, and the concentration of the unknown solution was determined by altering the value of the impressed current until the observed transition time was about equal to that used for the standard solution. 

Chronopotentiometry. Paunovic and Oechslin (8) measured the adsorption of peptone on lead-tin alloy electrodes using chronopotentiometric and double-layer measurements. This case is different from the adsorption of HCOOH because peptone is not an electroactive species in the conditions smdied but only blocks the surface used for the electrodeposition of lead-tin alloys from solutions containing Sn and Pb ions. Chronopotentiometric analysis is based on the following principles (7). In the absence of adsorption, the relationship between the transition time r (for reduction of Sn and Pb in this case), the bulk concentration c° of the substance reacting at the electrode, and the current I is given by the equation... 

In chronopotentiometry, conditions are chosen so that transport in the solution is rate controlling. A solution contains 0.001 M Cd(N03) (with 1M KN03) and the constant current applied is 0.10 A cm-2. The quarter-time potential is (L57 V vs. standard calomel. Use Sand s equation to calculate the transition time, x, and plot the electrode potential as a function of time. (Bockris)... 

Controlled-current voltammetry generally involves either a sinusoidal waveform (see Chap. 4) or a constant current [Fig. 18(a)]. Constant-current voltammetry, or chronopotentiometry [64, 65], generates a potential—time signal, as in Fig. 18(b), characterized by a transition time r. 

Chronopotentiometry suffers from difficulty in experimentally determining the transition time and the fact that the charging current is not easily resolved from the faradaic response, since the electrode potential is varying throughout the experiment. Various extrapolation procedures have been devised, but usually without rigorous theoretical justification [1-5]. 

If the polarity of the applied current in an ordinary chronopotentiometry experiment is reversed during the recording of the chronopotentiogram, the product R of the initial electrochemical reaction may now undergo the reverse reaction to give a current-reversal chronopotentiogram, as shown in Figure 4.5 [1-5]. A reverse transition time xr will result when the concentration of R becomes zero at the electrode surface (see Fig. 4.2C). Such reverse potential-time curves can be treated quantitatively for reversible and irreversible couples. 

In cyclic chronopotentiometry, the current is continually reversed at potentials corresponding to the forward and reverse transition times as shown in Figure... 

In derivative chronopotentiometry, the potential response signal of a normal chronopotentiometry experiment is electronically differentiated, and this rate of change of potential with time, dE/dt, is recorded as a function of time, as shown in Figure 4.9 [12]. The minimum in a derivative chronopotentiogram is quantitatively related to the transition time. Thus for a reversible couple,... 

In general, chronopotentiometry consists of the application of a programmed current function to an electrode, the potential of which is measured as a function of time [13]. Thus the current program may be any function that is electronically feasible. Examples of potentially useful current functions (in addition to those described in preceding sections) are ramp current chronopotentiometry for the elucidation of adsorption mechanisms, and square-root-of-time current chronopotentiometry for which concentration is directly proportional to the transition time ... 

B. Chronopotentiometry (Formerly called Voltammetry at Constant Current). These terms were applied by Delahay et al (Refs 4 5) to measurements in which the course of polarization of an electrode (immersed in an unstirred soln) under forced constant current was followed potentiometrically as a function of time. The potential-time curve recorded in the presence of a depolarizer is characterized by a transition time, during which the rate of change of potential is relatively small. This... 

This term denotes a potential whose nature depends on the technique used. Typical characteristic potentials are the half-wave potential in polarography, the quarter-transition-time potential in chronopotentiometry, and the peak or half-peak potential in stationary-electrode voltammetry. Regardless of its nature, the characteristic potential always depends on the identity of the electroactive substance, on the kinetics or thermodynamics of the electron-transfer process, and of course on the experimental conditions for any particular technique and under any completely defined set of experimental conditions the value of any characteristic potential is a reproducible property of the electroactive substance. 

Transition time (for chronopotentiometry) — Electrolysis time required before the surface concentration of a redox species drops to zero in - chronopotentiometry. In constant-current chronopotentiometry (see also -> constant-current techniques), the transition time r is given by the - Sand equation ... 

This would suggest that chronopotentiometry could be a sensitive electroanalytical technique. It is rarely used in this context, however, since it is often difficult to determine the transition time accurately, because of double-layer charging at short times and competing reactions at long times. The same limitations apply when one attempts to use Eq. 49K to measure the diffusion coefficient. On the other hand this equation can be used as a quick method of obtaining n,... 

Fig. I8K Current—reversal chronopotentiometry, for the oxidation of 1 niM PAP to PQl in 0.1 M H SO, at a platinum electrode, followed by hydrolysis to PBQ. i = 0.10 niAlcm. x is the transition time on the reverse pulse, following a forward pulse of duration t. From Gileadi, Kirowa-Eisner and...

Chronopotentiometry has found only little use in mechanistic organic electrochemistry. This is primarily due to experimental difficulties in the accurate evaluation of the transition time. A solution to this problem includes the application of a convolution procedure [230]. Another extension includes the application of exponential current-time functions and theoretical data for this method are now available for a number of mechanisms [231]. 

When applied to the analysis of kinetic data, chronopotentiometry is most often used in the current-reversal mode, in which the direction of the current is changed after some time tf (Fig. 29). When only the direction, but not the magnitude, of the current is changed, the reverse transition time is given by Eq. (73) [232]. 

Theory for chronopotentiometry of reversible channel electrode reactions under the Levich approximation has been presented by Aoki and Matsuda [73]. The transition time in flowing solution, tc, was found to be related to that in stationary solution, t0, via the approximations... 

For example, for the special case tiiOf Cf = n Oy Cf, = 3ti. Thus, while in controlled-potential voltammetric methods two substances at equal concentration with equal diffusion coefficients show two waves of equal height, in chronopotentiometry unequal transition times arise. The long second transition results from the continued diffusion of Oi to the electrode after ti, so that only a fraction of the applied current is available for reduction of O2 (Figure 8.5.1). 

For current reversal chronopotentiometry involving the forward reduction of a species O under conditions of semi-infinite linear diffusion, the reverse transition time can be made equal to forward... 

This equation applies to the totally mass-transfer-limited condition at the RDE and predicts that //c is proportional to Cq and One can define the Levich constant as which is the RDE analog of the diffusion current constant or current function in voltammetry or the transition time constant in chronopotentiometry. 

Consider a chronopotentiometric experiment dealing with two components that are reversibly reduced in waves separated by 500 mV. Derive an expression for the second transition time in an experiment carried out in a thin-layer cell. Compare and contrast the properties of multicomponent systems in thin-layer chronopotentiometry with those of the semi-infinite method. 

For simple reversal chronopotentiometry, the ratio of reversal transition time T2 to the forward time t is 1/3, just as in the diffusion-controlled case, independent of the rate constants. However, for cyclic chronopotentiometry the transition times for the third (73) and subsequent reversals differ from those of the diffusion-controlled case (31). 

The equations governing r, the E-t curve, and single reversal experiments are given in Section 12.2.2. Cyclic chronopotentiometry shows a continuous decrease in the relative transition times on repeated reversals because of the irreversible loss of R during the course of the experiment (22). 

Figure 5.4 Chronopotentiometry, concentration depletion in a cathodic reduction process, potential plotted as function of time, and determination of the transition time...

For chronopotentiometry, a good choice for the observation time is the transition time itself, and this has the interesting consequence that the constant current reduces to constant G — 2,Jn, the... 

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