Double layer capacitance Linearity

Active electrochemical techniques are not confined to pulse and linear sweep waveforms, which are considered large ampHtude methods. A-C voltammetry, considered a small ampHtude method because an alternating voltage <10 mV is appHed to actively couple through the double-layer capacitance, can also be used (15). An excellent source of additional information concerning active electroanalytical techniques can be found in References 16—18. Reference 18, although directed toward clinical chemistry and medicine, also contains an excellent review of electroanalytical techniques (see also... 

Col The double layer capacitance in a linearized model c The ionic strength of the electrolyte ... 

At high frequencies, the plot is linear and the slope is similar to that for a bare Pt electrode. The double-layer capacitance is 28 pF cm-2 for the PPY-PSS film and 23 pF cm-2 for the bare Pt electrode. The plot of real resistance minus the solution resistance versus log(tw) over the frequency range shown in Figure 4.43 is also linear and fits Equation 4.121 well. This indicates that a Randles circuit is at the electrode/polymer interface. 

These considerations can be put into quantitative form by analyzing the information content of the measurement. To understand this concept, let us first consider the choice of the optimum time scale for making a measurement. We already know that by using a very fast transient we can minimize the effects of diffusion, so we would first be inclined to use the fastest transients allowed by instrumentation. But if the measurement is conducted on a time scale that is short compared to X, all we can observe is a linear variation of potential with time, which depends on the double-layer capacitance (dtl/dt = We cannot calculate i... 

From Eq. (8.64) it is evident that unless the double-layer capacitance Cg is zero, Rs will not be a linear function of except at low frequencies. Many authors have assumed such linearity in the whole frequency range and obtained Re values from the linear extrapolation of Rs. to = 0 (i.e. to infinite frequency). 

Second-harmonic ac voltammetry gains its freedom from nonfaradaic interference from the relative linearity of the double-layer capacitance as a circuit element. There is consequently only a very small second-harmonic capacitive current, although it too can become important at low analyte concentrations. 

For the data in Fig. 6, the ohmic and polarization resistances can be determined to be about 0.3 and just under 100 cm, respectively. The value of Rp is slightly higher than that determined by linear polarization (Fig. 4) in a measurement that just preceded the EIS experiment on the same electrode. The double layer capacitance is seen to be 1/3000 SI cm = 333 pF cm . The polarization resistance determined by EIS can be used to determine the corrosion rate with the Stern-Geary equation, just as was described above for polarization resistance determined by linear polarization. EIS data provide no estimation of the Tafel slopes, which are required in the Stem-Geary equation. 

As it was shown in Ref [81] within the linearized Poisson-Boltzmann approximation the diffuse double-layer capacitance takes the form. 

Capacitance measurements have become an important method in electrochemistry. Combinations of resistance and capacitance elements, the so-called equivalent circuits, describe the electrochemical properties of the double layer. In the case of an ideally polarizable electrode, the equivalent circuit is a linear combination of a double layer capacitance and an Ohmic electrolyte resistance (Figure 4.9a). The equivalent circuit of an... 

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