Current-Potential Transients

The invention of polarography by Heyrovsky in 1920 s as a new experimental method followed by detail theoretical treatment in 1930 s which led to quantitative interpretation of the polarographic current-potential transients marked a milestone in electrochemistry (8,9). This technique permitted the electrochemist to interpret mass transfer electrode processes in terms of diffusion or convection it was subsequently applied in studies of reaction kinetics. Although the technique was limited to dropping mercury electrodes, its impact on electrochemistry and development of novel electroanalytical techniques was so tremendous that the inventor was awarded a Nobel Prize in Chemistry in 1959. 

Figure 13.6 Potential-step electro-oxidation of formaldehyde on a Pt/Vulcan thin-film electrode (7 p,gpt cm, geometric area 0.28 cm ) in 0.5 M H2SO4 solution containing 0.1 M HCHO upon stepping the potential from 0.16 to 0.6 V (electrolyte flow rate 5 pL at room temperature). (a) Solid line, faradaic current transients dashed line, partial current for HCHO oxidation to CO2 dotted line, difference between the net faradaic current and that for CO2 formation, (b) Solid line, m/z = 44 ion current transients gray line potential-step oxidation of pre-adsorbed CO derived upon HCHO adsorption at 0.16 V, in HCHO-free sulfuric acid solution, (c) Current efficiency transients for CO2 formation (dashed line) and formic acid formation (dotted line).

Fig. 19. Sampled-current voltammogram constructed from the current-time transients that resulted from a series of potential-step experiments at a stationary Pt electrode in a 35.0 x 10 3 mol L-1 solution of Ni(II) in the 66.7 m/o AlCl3-EtMeImCl melt ( ) total current, ( ) partial current for the electrodeposition of Ni, (O) partial current for the electrodeposition of Al. The total current was sampled at 3 s after the application of each potential pulse. Adapted from Pitner et al. [47] by permission of The Electrochemical Society. 

These equations cannot be used at higher overpotentials 77 > kT/e0. If the reaction is not too fast, a simple extrapolation by eye can be used. The potential transient then shows a steeply rising portion dominated by double-layer charging followed by a linear region where practically all the current is due to the reaction (see Fig. 13.2). Extrapolation of the linear part to t = 0 gives a good estimate for the corresponding overpotential. 

Forced convection can be used to achieve fast transport of reacting species toward and away from the electrode. If the geometry of the system is sufficiently simple, the rate of transport, and hence the surface concentrations cs of reacting species, can be calculated. Typically one works under steady-state conditions so that there is no need to record current or potential transients it suffices to apply a constant potential and measure a stationary current. If the reaction is simple, the rate constant and its dependence on the potential can be calculated directly from the experimental data. 

For the investigation of charge tranfer processes, one has the whole arsenal of techniques commonly used at one s disposal. As long as transport limitations do not play a role, cyclic voltammetry or potentiodynamic sweeps can be used. Otherwise, impedance techniques or pulse measurements can be employed. For a mass transport limitation of the reacting species from the electrolyte, the diffusion is usually not uniform and does not follow the common assumptions made in the analysis of current or potential transients. Experimental results referring to charge distribution and charge transfer reactions at the electrode-electrolyte interface will be discussed later. 

Cyclic voltammetry (CV) curves were recorded on a Kipp and Zonen BD91 X-Y recorder and the current-time transients resulting from the potential step experiments were recorded digitally. The apparatus used included a PAR Model 173 potentiostat and an IBM XT computer... 

Figure 6. A plot of the logarithm of the square root of the initial slope of the current time transients determined in the double step experiments against the final potential for the three single crystal surfaces investigated.

In cyclic voltammetry, simple relationships similar to equations (1.15) may also be derived from the current-potential curves thanks to convolutive manipulations of the raw data using the function 1 /s/nt, which is characteristic of transient linear and semi-infinite diffusion.24,25 Indeed, as... 

Deactivation of the Mediator Deactivation of the mediator is a commonly encountered event in the practice of homogeneous catalysis. Among the various ways of deactivating the mediator, the version sketched in Scheme 2.10 is particularly important in view of its application to the determination of the redox characteristics of transient free radicals (see Section 2.7.2).14 The current-potential responses are governed by three dimensionless parameters, 2ei = /F)(ke Cjl/v), which measures the effect of the rate-determining... 

Figure 13. Plot of current against time, (a), (b), and (c) Current-time transients on Pt(l 11) in 0.5M H2SO4, when CO was endorsed at potentials of 0.08.0.3, and 0.5 V(RHE) of curve 3 of (d), respectively. When CO was ptesent in the solution, curves I and 2 were observed. The sweep rate was 50 mV s". (From Ref. 24.)...

For example, if Qi = 50 tF/cm and R = 2 fi, t = 4.6 X 10 " s (0.46 ms). Thus, in the galvanostatic transient technique, the duration of the input current density pulse is on the order of milliseconds. From a series of measurements of for a set of i values, one can construct the current-potential relationship for an electrochemical process. For example. Figure 6.20 shows the current-potential relationship for the electrodeposition of copper from acid CUSO4 solution. 

Potential Sweep Method, In the transient techniques described above, a set of measurements of the potential for a given current or the current for a given potential is measured in order to construct the current-potential function, i = f(E). For example, the Tafel lines shown in Figure 6.20 were constructed from a set of galvanostatic transients of the type shown in Figure 6.18. In the potential sweep technique, i = f(E), curves are recorded directly in a single experiment. This is achieved by sweeping the potential with time. In linear sweep voltammetry, the potential of the test electrode is varied linearly with time (Fig. 6.23a). If the sweep rate is... 

It blocks inactivated sodium channels. It also decreases calcium current and transient outward, delayed rectifier and inward rectifier potassium currents. It is a potent inhibitor of abnormal automaticity. It prolongs duration of action potential, refracto-... 

Metal deposition or stripping and capacitance under constant current, (a) What is the potential transient in the case of metal deposition under constant current (/ = 10 mA/cm ) Derive its transition time x. Consider silver deposition on a silver substrate as an example ( Ag = 0.799 V, DAg - 1.65 x 10-5 cm2/s at room temperature), (b) If this process is reversed (i.e., silver is stripped from the silver substrate electrode), what should the expression be Suppose the initial solution does not contain silver salt, (c) What will the potential be at t = 0 ... 

Diffusion control constant flux mode. Table P.3 contains the potential transient data obtained on a platinum working electrode (against SHE) immersed in an aqueous solution of 0.1 M ferric perchlorate and 1.0 M ammonium perchlorate. The experiment was carried out at a constant current of 10 mA/cm2, and the diffusion coefficient of both reactant and product is assumed to be 10 5 cm2/s. 

For high values of k°r, very sharp decays of the current-time transients are observed, indicating the almost immediate electrochemical conversion of oxidized species (see solid lines corresponding to k°r = 100). Indeed, for k°t > 100, the faradaic conversion is so fast that the oxidized species disappears at the very first instants of the experiment and under these conditions 0p = 0. When k°r decreases, the observed currents also decrease, since the rate constant modulates the whole faradaic current. For k°t < 1, the current transients appear as quasi-linear, with current-time profile being shifted toward more negative potentials. Under these conditions, general equation (6.130) becomes identical to Eq. (6.134), corresponding to irreversible processes. 

Recently a series of dialkylpyrrolidinium (Pyr+) cations have been studied in our laboratory 7-9). These cations are reduced at relatively positive potentials and could be investigated electrochemically as low concentration reactants in the presence of (C4H9)4N+ electrolytes. Using cyclic voltammetry, polarography and coulometry, it was shown that Pyr+ react by a reversible le transfer. The products are insoluble solids which deposit on the cathode and incorporate Pyr+ and mercury from the cathode. Both the cation and the metal can be regenerated by oxidation. Quantitative analysis of current-time transients, from potential step experiments, showed that the kinetics of the process involve nucleation and growth and resemble metal deposition. 

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