Cottrell region

Definition of symbols AEp = peak potential difference, Epa = peak potential at cathodic peak current, Epc = peak potential at anodic peak current, tpa = anodic peak current, ipc = cathodic peak current, s = scan rate, t = time after peak (the Cottrell region), n = number of electrons involved in redox reaction. Rate parameters (acn ) and heterogeneous rate constant can be found from irreversible wave. 

First, there is no Cottrell region during the entire lithium intercalation/deintercalation, which is substantiated by no region with constant value of in the/(t)-/ v. In f plots of Figures 13(b) and 14(b). Moreover, Figures 13(b) and 14(b) show shoulders and more than one local maxima at the potential drops where the electrode... 

The above is still valid for CTs of other transition metal oxides and carbonaceous material (graphite). For instance, the I t)- vs. In t plots from graphite electrode (Figure 3b) do not show any Cottrell region, similarly to the case of LiNiOj in Figure 2(b). The appearance of shoulders and of more than one local maxima in Figures 2(b) and 3(b) will be addressed again in Section 111.3. 

Concentration Profiles. Cottrell Equation. As previously mentioned, the region close to the electrode surface where the concentrations... 

The current is now controlled solely by the mass transfer to the electrode (region c in Fig. 36) and the equation reduces to the so-called Levich equation, Eq. (88), which may be used together with the Cottrell equation, Eq. (64), in the experimental determination of S [252]. 

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... 

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. 

In a potential-step experiment, the potential of the working electrode is instantaneously stepped from a value where no reaction occurs to a value where the electrode reaction under investigation takes place and the current versus time (chronoamperometry) or the charge versus time (chronocoulometry) response is recorded. The transient obtained depends upon the potential applied and whether it is stepped into a diffusion control, in an electron transfer control or in a mixed control region. Under diffusion control the transient may be described by the Cottrell equation obtained by solving Tick s second law with the appropriate initial and boimdary conditions [1, 2, 3, 4, 5 and 6] ... 

Deviations from the strictly geometrical lattice structure (Schmid and Boas 1950). Alternatively, an interfacial region whose advance causes a fully slipped region to grow at the expense of an unslipped region (Cottrell 1967). 

In the case of a step to the diffusion-limited current region, the integrated Cottrell equation is obtained ... 

A program, written in FORTRAN, for the simulation of a simple potential step experiment in the diffusion controlled region is included at the end of this Appendix. Translation to other languages should prove easy. This program also compares the simulated value of Z with the corresponding analytical value obtained from the Cottrell equation. For the A th iterations this is given by... 

The technique is simple in concept (see Fig. 1.63). A series of potential pulses is applied to the polymer-coated electrode, each of increasing amplitude but always starting from the same base potential at which negligible reaction occurs. The normal pulse (NP) voltammogram then consists of a plot of current, measured toward the end of the pulse as a function of pulse amplitude. The form of the current/potential response is sigmoidal. A plateau region is observed at large values of pulse amplitude (see Fig. 1.63). In essence each pulse is a Cottrell potential step experiment, so we can write... 

We introduce here the diffusion-controlled potential-step experiment, hereafter called the Cottrell experiment [15], Consider Fig. 2.3, showing a long thin tube representing an electrochemical cell, bounded at one end by an electrode and filled with electrolyte and an electroactive substance initially at concentration c (the bulk concentration). We place the electrode atx = 0 and the other, counter-electrode (not shown), at a large distance so that what happens there is of no consequence to us. We apply, at f = 0, a potential such that our electroactive substance reacts at the electrode infinitely fast—that is, its concentration cq at the electrode (x = 0) is forced to zero and kept there. Clearly, there wiU be flow of substance towards the electrode by diffusion (we assume no convection here) and we will gradually cause some depletion of material in the solution near x = 0 this depletion region will grow out from the electrode with time. Mathematically, this is described by the diffusion equation... 

Thus, in the Nernstian regime, a plot of / vs. / - will be linear, and useful information about the parameters n and Dr can be obtained from its slope for the electrode process of interest. (Double potential step experiments similarly afford information about the reverse process, reduction.) Likewise a plot of it vs, (Fig. 20.7c) yields kinetics information for a non-Nernstian process. The horizontal region at large values of it - corresponds to the Cottrell regime, whereas the short-time data are... 

With increasing electrode surface temperature, the stationary diffusion layer thickness is decreasing very rapidly and reaches a limiting value of about 8 pm at a temperature larger than 20-30 K compared to the bulk temperature. In this region the limiting current is proportional to the real diffusion coefficient. This result has been confirmed by chronoamperometric experiments where the Cottrell decay was evaluated [6]. 

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