Chemical capacitance

Figure 24. Models illustrating the source of chemical capacitance for thin film mixed conducting electrodes, (a) Oxygen reduction/oxidation is limited by absorption/de-sorption at the gas-exposed surface, (b) Oxygen reduction/ oxidation is limited by ambipolar diffusion of 0 through the mixed conducting film. The characteristic time constant for these two physical situations is different (as shown) but involves the same chemical capacitance Cl, as explained in the text.

Some authors have expressed concerns that bulk accumulation of reactive intermediates (and thus chemical capacitance) violates electroneutrality. ° However, it should be recalled that reduction (or oxidation) of a material not only involves depletion (or accumulation) of oxygen ions in the bulk but neutral combinations of oxygen ions and compensating electrons/holes which together may accumulate without violating electroneutrality. Indeed, no other mechanisms have yet been proposed which satisfac-... 

One limit of behavior considered in the models cited above is an entirely bulk path consisting of steps a—c—e in Figure 4. This asymptote corresponds to a situation where bulk oxygen absorption and solid-state diffusion is so facile that the bulk path dominates the overall electrode performance even when the surface path (b—d—f) is available due to existence of a TPB. Most of these models focus on steady-state behavior at moderate to high driving forces however, one exception is a model by Adler et al. which examines the consequences of the bulk-path assumption for the impedance and chemical capacitance of mixed-conducting electrodes. Because capacitance is such a strong measure of bulk involvement (see above), the results of this model are of particular interest to the present discussion. 

Equation 9 shows that the chemical capacitance in this case is similar to that derived previously in eq 6 for a thin film (Ci) however, in the co-limited situation the important length parameter is not L but rather a characteristic utilization length given by... 

Chemical capacitance. When the mechanism involves significant involvement of the bulk, accumulation of reactive intermediates not only involves surface species but oxidation and reduction of the bulk. This can be detected as an anomalously high effective capacitance, often referred to as a chemical (or pseudo) capacitance. This capacitance can be as large as 0.1 — 1 F/cm and thus easily detected by current-interruption or impedance techniques. Thus, capacitance is a strong indicator (independent of resistance) as to what degree the interface, surface, and/or bulk are playing in the... 

What this calculation shows is that the rate of bulk transport observed in a thin film of LSM is at least 3 orders of magnitude too low to explain the performance of porous LSM at low overpotential, assuming an entirely bulk transport path. This calculation echoes prior estimates of Adler and co-workers, who showed that the zero-bias impedance of porous LSM cannot be explained in terms of a bulk path. In addition, estimates of the chemical capacitance based on loroi s impedance for porous LSM yield values of 10 —10 F/cm , which as mentioned previously in section 5.2 are more consistent with a surface process... 

Moreover, despite the many advances in electrochemical measurement and modeling, our understanding of SOFC cathode mechanisms remains largely circumstantial today. Our understanding often relies on having limited explanations for an observed phenomenon (e.g., chemical capacitance as evidence for bulk transport) rather than direct independent measures of the mechanism (e.g., spectroscopic evidence of oxidation/reduction of the electrode material). At various points in this review we saw that high-vacuum techniques commonly employed in electrocatalysis can be used in some limited cases for SOFC materials and conditions (PEEM, for example). New in-situ analytical techniques are needed, particularly which can be applied at ambient pressures, that can probe what is happening in an electrode as a function of temperature, P02, polarization, local position, and time. 

This additional capacitive element (Cl)315 represents a chemical capacitance in the sense of Part I,2 Section VI.7 (see Figure 37). 

As the oxygen partial pressure ratio, and hence A/u0, is known, the ambipolar conductivity is readily determined from the flux. This knowledge can be further used to calculate the partial conductivities, and by knowing Ef from the transient (i.e., by also evaluating the delay time231) to derive the thermodynamic factor (i.e., the chemical capacitance). 

In mixed conductors the chemical capacitance plays an important role. This will be extensively considered in Part II1 (see also Section VI, in particular VI.7.). 

The thermodynamic factor d//o/dc0 refers to the bulk and reflects its (inverse) chemical capacitance. This term reduces to RTwo/co for the chemical experiment and to RT/c0 for the tracer experiment. The prefactor Aod//o/dco evidently defines what is called effective rate... 

Now let us consider briefly electrode kinetics, i.e., k or—since we have not involved any chemical capacitance effects—the exchange rate... 

Since we only allow for small driving forces Apo, this implies large chemical capacitances dColdpo, a relevant example is the high temperature superconductor YBa Cu307.6. 

Figure 10.2 A universal equivalent circuit for the photoelectric effect. The photochemical event is represented by an RC network including (i) the photoemf ( p(0). (ii) the internal resistance (Rp) of the photocurrent source, (iii) the chemical capacitance (C,), and (iv) the transmembrane resistance Rp). With the exception of a strictly short-circuit measurement, the time course of the photocurrent so generated is further shaped via interaction with the RC network formed by (i) the membrane resistance (/ ,), (ii) the membrane capacitance (C ), and (iii) the access resistance Re). The access resistance (impedance) includes the input impedance of the amplifier, the electrode impedance, and the impedance of the intervening electrolyte solution. (Reproduced from [17].)...

Figure 2. Equivalent circuit of a bacteriorhodopsin membrane that includes the circuit parameters of the inert supporting structure and the access impedance of the measuring system. Re is the access impedance, which includes the input impedance of the measuring device, the electrode impedance, and the electrolyte impedance between the membrane and the electrodes. Rm and Cm are the resistance and the capacitance of the membrane, C p is the chemical capacitance, Rp is the internal resistance of the photoelectric voltage source, Ep(U, which is a function of the illuminating light power, and Rs is the transmembrane resistance encountered by the dc photocurrent. (Reproduced from reference 19.

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