Effect of Heterogeneous Kinetics on Chronocoulometric Responses

Chronocoulometric responses may be governed wholly or partially by the charge transfer kinetics. It has been reported that, in some cases, the diffusion-limited situation cannot be reached, e.g., due to the insufficient power of the potentiostat and the inherent properties of the system, especially at the beginning of the potential step. On the other hand, in many cases, potential steps of smaller magnitudes than that required for diffusion control are applied in order to study the electrode kinetics. 

If the potential amplitude of the step is less than 2 - E, i.e., the step is made to any potential in the rising portion of the voltammogram, either charge transfer control or mixed kinetic-diffusional control prevails, i.e., the concentration of the reactant is not zero at the electrode surface. Still, cr (x = 0) c, so R does diffuse to the electrode surface where it is oxidized. Since the difference between the bulk and surface eoncentration is smaller than in the case of mass transport control, less material arrives at the surface per unit time, and the currents for corresponding times are smaller than in the diffusion-limited situation. Nevertheless, the concentration gradient for R still increases, which means that the current still decreases with time, albeit to a smaller extent. The current-time curves when the potential is stepped from 2 E2 E22 are shown in Fig. II.4.6. 

If we sample the current at some fixed time (U), then, by plotting 7(4) vs. Til, 22, 21, 2, etc., a current-potential curve is obtained that resembles the waveshape of a steady-state voltammogram. This kind of experiment is called sampled-current voltammetry. In fact, it serves as the basis for the theoretical description of dc polarography and several other pulse techniques. For the mathematical description, the flux equations [see Chap. 1.3, Eq. (1.3.30)] should be combined with the respective charge transfer relationships [see Chap. 1.3, Eqs. (1.3.5), (1.3.12), and (1.3.13)]. 

When initially only R is present, the following expression can be derived  

E2 E21 E22 E, and E2 and E22 correspond to potentials in the rising portion of the voltammogram where mixed charge transfer-mass transport control prevails 

If the potential amplitude of the step is less than E2- E, i. e., the step is made to any potential in the rising portion of the voltammogram, either charge transfer control or mixed kinetic-diffusional control prevails, i.e., the concentration 

If we sample the current at some fixed time (tg), then, by plotting I vs Ej, 

If both O and R are present, an even more complex equation is obtained  

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