Warburg coefficient

Figure 20. Time dependence of EIS parameters for zinc-coated steel with polyurethane topcoat after exposure to artificial and natural seawater (a)yj, (b) and (c) Warburg coefficient. 

For given values of double layer capacitance solution resistance Rjj and Warburg coefficient a, plots of -Z versus Z have been made for selected values of charge transfer resistance. Ret (26). It is observed that at smaller values of R t ("10 S2 cm ) relaxation due to Rct dl Warburg diffusion behavior are both clearly seen. 

In systems where diffusion phenomena are of significance, the mechanistic study is facilitated by using the general expression for Impedance Z (26). This equation shows for instance how the Warburg coefficient can be evaluated by conducting impedance studies at very low frequencies. These coefficients in turn enable the evaluation of diffusion coefficients for the diffusing species. 

Figure 4.156 shows the simulated Nyquist plot of the modified Randles cell with a combination of kinetic and diffusion processes plus infinite thickness. As in the example, the Warburg coefficient is assumed to be er = 5 Qs 12. Other... 

Here, o represents the Warburg coefficient, which can be estimated from the slope of the log Zjeai vs. log / representation in the region of intermediate frequencies, where ... 

The Warburg coefficient can be experimentally determined from the average value for the slope ofthe Z versus co plot, and for the slope of the -Z" versus co plot. In many reports, the diffusion coefficients of lithium ions have been determined for various transition metal oxides [13, 97, 113, 114] and graphite [59] electrodes by using EIS. 

Z(a>) - Ra Rct + (1 - jymo-w and produce an electrochemical "spectrum as charge transfer-potential, double layer capacity-potential, ohmic resistance-potential, and Warburg coefficient-potential plots. Together with the current-potential curve, these present a useful representation of the steady-state electrochemical behaviour. 

The electrochemical behaviour of stainless steel has not been worked out completely, although the measured data are available. However, one aspect of the behaviour, based on the measured double layer capacity data, seems to be susceptible to interpretation. The capacity-potential curves are determined by the state of the metal surface and by the ionic environment. In this work, it has been assumed that the ionic environment is a constant. This means that the double layer capacity-potential curves should reflect the nature of the metal surface just as, say, an electron energy spectrum in surface science. Stainless steel has a complicated electrochemical behaviour. In previous work [22] an attempt has been made to compare the double layer capacity curves measured during dissolution and passivation of the stainless steel with that of the pure components. It seems that all the data in the high frequency regime can be fitted to eqn. (70) with the Warburg coefficient set equal to zero. 

Cadmium atomic layer electrodeposition above reversible Cd2+/Cd potential (underpotential deposition, upd) on bulk tellurium and Te atomic layer predeposited on gold has been characterised with potentiodynamic electrochemical impedance spectroscopy (PDEIS) by variations, with the electrode potential E, of double layer pseudocapacitance Q,u, charge transfer resistance Rrt and Warburg coefficient Aw of diffusion impedance. 

Figure 2. Variation of double layer pseudocapacitance (Qdi), inverses of the Warburg coefficient (An/ 2), and charge transfer resistance (/<-, ) in (a, c) Cd upd on bulk Te and (b, d) Cd upd on Te monolayer in cyclic potential scans. Concentrations of CdCb are shown in labels.

X 10 crxr/s. The charge-transfer resistance and Warburg coefficient were set to 18 Q and 1 O/s ", respectively. Decrease in the particle size or increase in the diffusion coefficient shifts the onset of the transition region to a higher frequency. 

Warburg coefficient, cm s characteristic time, relaxation time, s potential, V... 

It is evident that the shape of the impedance spectra varies with the potential since the values of the charge transfer resistance (Ret), the low frequency (redox) capacitance (Cl) and the Warburg coefficient change with the potential more exactly, they depend on the redox state of the polymer. In many cases D is also potential-dependent. The double-layer capacitance (Cdi) usually shows only slight changes with potential. The ohmic resistance (Rq) is the sum of the solution resistance and the film resistance, and the latter may also be a function of potential due to the potential-dependent electron conductivity, the sorption of ions, and the swelling of the film. In Fig. 3.9 three spectra are displayed, which were constructed using the data obtained for a PTCNQ electrode at three different potentials near its equilibrium potential [23]. 

The Warburg coefficient depends on the diffusion coefficient (D), the concentration (c) of redox sites and the temperature (T) ... 

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