Convective Diffusion Impedance at Small Electrodes

While assumption that the time constant is distributed can be better than assuming that the time constant has a single value, the physical system may not follow the specific distribution implied in equation (13.7). The examples presented in the subsequent sections illustrate systems for which a time-constant dispersion results that resembles that of a CPE, but with different distributions of time constants. 

A satisfactory fit of a CPE to experimental data may not necessarily be correlated to the physical processes that govern the system. As shown in Section 4.4, models for impedance are not unique thus, an excellent fit to the data does not in itself guarantee that the model describes correctly the physics of a given system. 

The graphical methods described in Chapter 17 can be used to determine whether a system follows CPE behavior in a given frequency range. 

Small electrodes are currently used to study fast electrochemical kinetics or as flow measurement devices in chemical engineering systems. In the latter case, the first experimental and theoretical studies appeared in the early fifties. The goal of these studies was to achieve probes sensitive to the local wall velocity gradient 

The well-known property of those probes is that the limiting diffusion current is proportional to rmder steady-state conditions. For use in electrochemical engineering, an increasing interest is now focused on the nonsteady behavior of those small electrodes under conditions of fluctuating velocity gradient y(f). 

---