Diffusion limitation region

When solving for the apparent activation energy in the diffusion limited region we obtain... 

Fig. 3.3 Zinc blende (111) XRD reflections vs. deposition potential, for 2 xm thick CdSe films electrodeposited from a pH 2 bath on Ni cathode, at the indicated potentials within the diffusion-limited region. (With kind permission from Springer Science+Business Media [60])...

The plateau in Fig. 13.9 corresponds to the diffusion-limited region where the rate of electron transfer is faster than the rate of diffusion. According to the Marcus theory of electron transfer, the observed rate constant of an intermolecular electron transfer is given by [23]... 

Of course, the influence of magnetic field appears to be restricted to the diffusion-limited regions. During electrolysis under parallel fields, the Lorentz force induces convective flow of the electrolyte close to electrode surface. A magnetically stimulated convection leads to a decrease of the diffusion layer thickness thus increasing the diffusion-limited current density.39 As a rule, it was adopted that the limiting diffusion current density depends on magnetic field, as z l oo 51/341 Anyway, the increase of the... 

This relation is the general response function for a step experiment in a reversible system. The Cottrell equation, (5.2.11), is a special case for the diffusion-limited region, which requires a very negative E — so that 0. It is convenient to represent the... 

Since staircase voltammetry does not involve periodic renewal, each cycle inherits its initial conditions from the preceding cycle, and the response from any sample is generally affected by the prior history of the experiment. The most common manifestation is found in the diffusion-limited region of a voltammogram, where samples in successive cycles do not produce a plateau, as they do in polarography, but instead decline as the depletion of electroactive species near the electrode becomes cumulatively greater. Thus the typical staircase voltammogram of a simple system is peak-shaped, rather than wave-shaped. 

In the normal pulse experiment, the usual practice is to select a base potential E in a region where the electroactive species of interest does not react at the electrode. The scan is made by allowing pulses in successive cycles to reach first into the potential range surrounding and eventually into the diffusion-limited region. If we take the usual reversible case of O + R, with O present in the bulk and R absent, then Ey would be set perhaps 200 mV more positive than E, and the pulses would be made in a negative... 

For a reversible system, the shape of the RPV wave can be derived from the general double-step response given in (5.7.14). We confine our view to the situation where the forward electrolysis always takes place in the diffusion limited region, so that 0 = Qxp[nf(E -E )] 0. Then we have for the current sampled in a reverse pulse to any value of E ... 

Derive the equation for the large-step coulostatic response in the diffusion limited region, analogous to (8.7.14), for a spherical indicator electrode. 

The cell in Figure 17.1.2a is designed for experiments involving semi-infinite linear diffusion of the electroactive species to the electrode surface (6). It is normally used for experiments in which one applies large-amplitude steps in order to carry out electrolysis in the diffusion-limited region, and one then records the change in absorbance, si, versus time. From an electrochemical standpoint, the result is the same as that of the Cottrell experiment described in Section 5.2.1. 

The activation energy for diffusion was about 6 to 10 kcal/mol (25-42 kJ/mol) and so in the strong pore diffusion limitation region with d, = 0.17 mm., the predicted falsified activation energy is... 

At low frequencies, a diffusion-limited region appears, which, if fitted to a Warburg impedance, can be used to determine diffusion coefficients of charge carriers in the conducting polymer. At... 

The two reactions proceed eventually at an equal rate to determine a mixed potential of the electrode, which is given as an intersection of the polarization curves for and O2 as shown in Fig. 36.2. It is noted that reaction (36.5) enters into the diffusion-limited region under low concentrations, and this fact provides a basis for the Hj-concentration dependent e.m.f of the present sensor. The observed Nernst slope of c. 140 mV decade" is understood as originating from the polarization curve for reaction (36.6). 

Besides the oxidation of ethylene we also paid attention to the combustion of 1-butene. This reaction was found to be 1.3 order in 1-butene and has an activation energy of 6.7 kJ/mole (500-713K), indicating that the reaction runs also in the film diffusion limitation region. Like in the case of ethylene oxidation the relative situation of the curves in the c/c vs L/RPe plane is solely determined by the value of Da. Also here the Leveque equation proves to be a good description of the experimental results. 

Figure 6. Verification of the Leveque equation for the oxidation of ethylene in the diffusion limitation region...

It is seen that given the intrinsic kinetics, the actual rate of the reaction in the diffusion-limited region can be used to determine the effective diffusivity. 

When the Thiele modulus is large, say > 3, tanh approaches unity. In this diffusion-limited region, the effectiveness factor is approximated by ... 

---