Proper resistance, ionic conductivity

Ionic conductivity is defined as the reciprocal of proper resistance ( Rb). It is obtained by calculating... 

Equilibrium is assumed to prevail here at the boundaries of the membrane (e.g., the membrane is assumed to be thick or else it is a very thin film having a low ionic conductance so that the main resistance to the ionic fluxes is localized in the membrane proper and the equilibrium on the surfaces has enough time to be practically established) so that the boundary potential may be expressed by the Donnan ratios for the ions, and these ratios are determined from the fixed charge density in the membrane and the surrounding electrolyte concentrations. The diffusion potential, Eam, has a somewhat complicated expression. With the conditions of electroneutrality, zero electrical current, and a quasi-stationary state for each ion species, the expression for E m is... 

High-Frequency Resistance A more sophisticated approach to measurement of the ohmic losses is the HFR measurement, as discussed in the previous section. In this approach, an AC signal is superposed on the DC from the fuel cell. At very high fiequencies, the AC will render the various electrochemical double-layer capacitances to zero, and only the purely ohmic resistance will be measured. Typical frequencies high enough to successfully use this technique are > 1 kHz for PEFCs. This approach only measures the path of least resistance however, and care should be taken to properly understand results. For example, in the electrodes, the HFR will normally measure the electrical resistance only, since it is generally much less than the ionic loss in the mixed conductivity stracture. Therefore, HFR could not generally be used to determine electrode ionomer performance. 

---