Diffusion limiting equivalent capacitance

Differential capacitance measurements by Niki et for cytochrome C3 from D. vulgaris, strain Miyazaki, were consistent with irreversible, diffusion-limited adsorption for 4-s drop times above a concentration of 10 fiM. The surface excess of cytochrome C3 was calculated to be 0.92 x 10 " mole/cm. Niki etal also investigated the a.c. polarographic behavior of cytochrome C3 at the reversible half-wave potential. The capacitive peak height was frequency independent while the resistive peak height decreased with increasing frequency to a value of zero above 2000 Hz. These results were fit to a Laitinen-Randles equivalent circuit yielding an n value of... 

In the presence of a redox reaction without diffusion limitations, the system impedance is described by the electrical equivalent circuit / s(Cdi ct) displayed in Fig. 2.34. Replacing the double-layer capacitance with the CPE produces complex plane and Bode plots (Fig. 8.4) corresponding to the equation for the impedance of such a system ... 

Fig. 8.17 Complex plane plots of complex capacitance, C, defined using Eq. (8.28) for limiting cases of slow continuous line), fast (diffusion limited, dotted line), and intermediate (dashed line) adsorption. Insert equivalent electrical model for this process (From Ref. [367], copyright (2002), with permission from Elsevier)...

Figure 4.5.1 compares the impedance spectrum of reflective finite-length diffusion with the spectrum of its limiting equivalent circuit, a limiting resistance in series with a limiting capacitance. It can be seen that these responses approach each other as the frequency deaeases. 

Fig. 12. The complex capacitance plot and a corresponding equivalent circuit for diffusion-limited adsorption of electro-inactive surfactant represented by an additional capacity C. ...

Figure 6.3 (a) Schematic representation of equivalent circuit for an ion conductor put between a pair of blocking electrode, and (b) the corresponding Nyquist plot. Ideally the sample-electrode interface is composed only of the double-layer capacitance. However, the practical Nyquist plot that corresponds to this frequency region is not vertical to the real axis. The rate-limiting process of this plot is that the ion diffuses to form a double layer. 

Diffusion-Related Elements. Although we usually employ ideal resistors, capacitors, and inductances in an equivalent circuit, actual real elements only approximate ideality over a limited frequency range. Thus an actual resistor always exhibits some capacitance and inductance as well and, in fact, acts somewhat like a transmission line, so that its response to an electrical stimulus (output) is always delayed compared to its input. All real elements are actually distributed because they extend over a finite region of space rather than being localized at a point. Nevertheless, for equivalent circuits which are not applied at very high frequencies (say over 10 or 10 Hz), it will usually be an adequate approximation to incorporate some ideal, lumped-constant resistors, capacitors, and possibly inductances. 

Coulometric titration techniques were used to measure chemical diffusion at between 700 and lOOOC. The transient current response to a potentiostatic step was transformed from the time domain to the frequency domain. The equivalent circuit which was used to fit the resultant impedance data contained an element which described the finite-length diffusion of O into the sample. Other elements which were included were the gas-phase capacitance, and the sum of the gas-phase diffusion resistance and that which was associated with the limited surface exchange kinetics of the sample. The chemical diffusion coefficient of the perovskite, Laq gSrq 2C0O3,... 

Figure 14,1 The equivalent circuit for partial mass-transport limitation by diffusion. The Warburg impedance, Zw, is in series with the Faradaic resistance, Rf, and in parallel with the double-layer capacitance.

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