Electroactive species diffusion coefficient

The kinetic requirements for a successful application of this concept are readily understandable. The primary issue is the rate at which the electroactive species can reach the matrix/reactant interfaces. The critical parameter is the chemical diffusion coefficient of the electroactive species in the matrix phase. This can be determined by various techniques, as discussed above. 

Chronoamperometry is often used for measuring the diffusion coefficient of electroactive species or the surface area of the working electrode. Analytical applications of chronoamperometry (e.g., in-vivo bioanalysis) rely on pulsing of the potential of the working electrode repetitively at fixed tune intervals. Chronoamperometry can also be applied to the study of mechanisms of electrode processes. Particularly attractive for this task are reversal double-step chronoamperometric experiments (where the second step is used to probe the fate of a species generated in the first step). 

Here, n is the number of electrons of the half-reaction, F is the Faraday constant, A is the electrode area, D is the diffusion coefficient of the electroactive species, and x is the distance from the electrode. 

At high frequencies, a semicircle is expected as a result of a parallel combination of R and Cg. At low frequencies a Warburg impedance may be found as part of the interfacial impedance. In some cases it may dominate the interfacial impedance as in Fig. 10.13(a), in which case only the diffusion coefficient of the salt will be determinable. It should be noted that, in the absence of a supporting electrolyte, the electroactive species, in this case Li, cannot diffuse independently of the anions. 

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

The transition time in the galvanostatic mode is listed in Table El. The concentration of electroactive species is 0.1 M and the diffusion coefficient is 10-5 cm2/s. Find the number of electrons transferred and draw a current-time response in a potentiostatic mode. 

Here, A is the electrode area, C and D are the concentration and the diffusion coefficient of the electroactive species, AE and co(=2nfj are the amplitude and the angular frequency of the AC applied voltage, t is the time, and j=nF (Edc-Ei/2) / RT. For reversible processes, the AC polarographic wave has a symmetrical bell shape and corresponds to the derivative curve of the DC polarographic wave (Fig. 5.14(b)). The peak current ip, expressed by Eq. (5.24), is proportional to the concentration of electroactive species and the peak potential is almost equal to the half-wave potential in DC polarography ... 

This method is sometimes abbreviated to LSV. In this method, a static indicator electrode (A cm2 in area) is used and its potential is scanned at constant rate v (V s-1) from an initial value ( ) in the positive or negative direction (Fig. 5.18). A typical linear sweep voltammogram is shown in Fig. 5.19. In contrast to DC polar-ography, there is no limiting current region. After reaching a peak, the current decreases again.9 For a reversible reduction process, the peak current ip (A) is expressed by Eq. (5.26), where D and C are the diffusion coefficient (cm2 s 1) and the concentration (mol cm-3) of the electroactive species ... 

In the opposite case of a perfectly immobile equilibrium given by eqn. (178), its rate of establishment is low compared with the duration of the perturbation, so that, in the time scale of the experiment, no significant conversion of OLp to O or vice versa takes place. Then, the system behaves as if only the electroactive member of the two is present. Consequently, the first or the second version of eqn. (179) is to be employed and the electrochemical experiment can reveal the concentration of the electroactive species, OL, if its diffusion coefficient, DOLj> is known. 

Chronoamperometry has proven useful for the measurement of diffusion coefficients of electroactive species. An average value of it1/2 over a range of time is determined at an electrode, the area of which is accurately known, and with a solution of known concentration. The diffusion coefficient can then be calculated from it1/2 by the Cottrell equation. Although the electrode area can be physically measured, a common practice is to measure it electrochemically by performing the chronoamperometric experiment on a redox species whose diffusion coefficient is known [6]. The value of A is then calculated from it1/2. Such an electrochemically measured surface area takes into account any unusual surface geometry that may be difficult to measure geometrically. 

D = diffusion coefficient of electroactive species, cm2/s td = drop time, s... 

What is this parameter called the apparent diffusion coefficient, Dapp As indicated earlier, it is a measure of the rate of charge transport in a multilayer film at an electrode surface. What Dapp physically means depends on the type of film being investigated. If the electroactive species is free to diffuse through... 

It will be clear that cyclic voltammetry is a powerful tool for a first analysis of an electrochemical reaction occurring at the surface of an electrode because it will reveal reversibility. Depending on whether the system is reversible, information will be obtained about half wave potential, number of electrons exchanged in the reaction, the concentration and diffusion coefficient of the electroactive species. However, these data can also be obtained for an irreversible system1113 but, in this case, the equations describing the current-potential curves differ somewhat from Equations 2.21 to 2.27. 

The well-known equation i = 4nFDCr (i limiting current, n number of electrons implied in the electrochemical process, F Faraday constant, D diffusion coefficient, C electroactive specie concentration and r radius of the disk) describes the theoretical steady-state limiting currents of the disk UMEs. This equation is useful to determine the effective radius of a disk UME and to estimate diffusion coefficients. In this sense, the above-mentioned polished carbon disk UMEs have been characterised through the limiting currents obtained in solution with known parameters, i.e. ferrocyanide aqueous solutions (0.05 M and 2M KC1) [118]. The experimental limiting currents were fairly accurately described by this equation ( + 10%). When the effective radius is determined, this equation can be employed to obtain unknown diffusion coefficients. In this way, we have estimated the diffusion coefficients for /i-carotene in several aprotic solvents with different electrolytic concentrations [123]. 

The addition of the inert electrolyte affords other advantages. The most important point is that the conductivity of the solution increases (and thus the ohmic drop decreases through a decrease of the resistance of the cell, Rccw see Sect. 1.9). Moreover, the diffuse double layer narrows, being formed mainly by the ions of the inert electrolyte (with a sharp potential drop over a very short distance from the electrode surface). This makes the capacitance more reproducible and the Frumkin effects less obtrusive. Activity coefficients of the electroactive species are also less variable (and, therefore, quantities like formal potentials and rate constants), since... 

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