Diffusion coefficient chronocoulometry

When the characteristic time for charge diffusion is lower than the experiment timescale, not all the redox sites in the film can be oxidized/reduced. From experiments performed under these conditions, an apparent diffusion coefficient for charge propagation, 13app> can be obtained. In early work choroamperometry and chronocoulometry were used to measure D pp for both electrostatically [131,225] and covalently bound ]132,133] redox couples. Laviron showed that similar information can be obtained from cyclic voltammetry experiments by recording the peak potential and current as a function of the potential scan rate [134, 135]. Electrochemical impedance spectroscopy (EIS) has also been employed to probe charge transport in polymer and polyelectrolyte-modified electrodes [71, 73,131,136-138]. The methods... 

Diffusion coefficients were taken from the literature or measured using chronocoulometry (5). The area of the electrode. A, was measured using FefCN) " in a solution of 0.004 m K3Fe(CN)5 in 0.1 m KCl, for which the diffusion coefficient is given as 762 + 0.01 x 10" cm sec" (S). It was found from six measurements to be 0.242 cm + 0.005 this value was then used to determine diffusion coefficients for species of interest (from the integrated Cottrell equation. Equation 5.9.1 in Reference 5). 

Note that the slope of the absorbancetime plot allows the determination of the (usually) unknown extinction coefficient r for the electrogenerated species, providing that c and Dq are known. No knowledge of the electrogenerated species diffusion coefficient Dr is necessary. Usually the concentration is known and it is a simple matter to determine Dq from a chronoamperometry, chronocoulometry, or ultramicroelectrode experiment. If both c and Do are unknown, then they can be obtained from a potential step experiment at an ultramicroelectrode [47, 48]. 

Chronoamperometry [1,2] is used to determine the charge transport diffusion coefficient, and also to study phase formation, phase transitions, and relaxation. Chronocoulometry is applied to determine the total charge consumed as well as to determine Q vs. E functions. 

Catalano and coworkers reported the synthesis and brief electrochemical characterization of [PtMe2Br(bpy-Fc2)CH2-]nR (R = substituted phenyl groups) [79]. In TBAH/AN solution, these dendrimers exhibited a single redox wave centered at -F0.50 V versus Ag/AgCl corresponding to the Fc/Fc+ redox reaction. Diffusion coefficients were also determined by a combination of chronocoulometry and cyclic voltammetry using a microelectrode and were found to be 1.1 to 1.7 x 10 cm s in DMF/TBAP solution. 

Therefore, the diffusion coefficient (D) and solubility of oxygen (C) can be calculated from the DC and C obtained from Eqs. 18.21 and 18.22. Hydrodynamic chronocoulometry (HCC) can be used to simultaneously determine the diffusion coefficient (D) and solubility of oxygen (C) [11]. The relationship between the charge (Q) and time (t) is given in the following equations ... 

The various terms in the equation are as follows i is the current, n is the number of electrons transferred, F is the Faraday, A is the electrode area, C is the concentration, D is the diffusion coefficient, and t is the time. Thus the technique may be used to estimate, among other things, the charge transport parameter. The reader interested in the solution of the Fick s law equation using the Laplace transformation should consult Ref. 6. A closely related technique is chronocoulometry, in which the excitation function is still the potential pulse, but instead of monitoring the current, the integrated charge is monitored as a function of time. This entails less error as a cumulative measurement is made. The equation for chronocoulometry is... 

The characteristic current ip is directly related to the electronhopping diffusion coefficient Dp- This quantity can be obtained either by using dual-electrode steady-state techniques or transient techniques of chronoamperometry or chronocoulometry. These procedures are discussed in detail in Chapter 1. 

Chronocoulometry (CC) is much less frequently used in CP work. It can also be used to calculate, among other parameters, apparent diffusion coefficients. The relevant equation, again under the "Cottrell conditions" described above, is... 

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