Small signal response of an unsupported solid electrolyte to a dc external electric field

The electrical response of a solid electrolyte to an external electric field is investigated. The case of non-blocking electrodes is discussed by assuming two boundary cases: (i) the conduction current of ionic origin in the external circuit is proportional to the surface electric field (called Ohmic case); (ii) the conduction current is proportional to the variation of the bulk density of ions just in front to the electrode with respect to its thermodynamic value (Chang–Jaffe case). We show that the two descriptions for the conduction current are equivalent in terms of the resistance response to slight variations of an external applied field, and the correspondence between the phenomenological parameters of the two models is univocally determined. A possible generalization of the boundary conditions, having diffusive character, is also discussed, and its equivalence with the Ohmic model described.