Binary electrolyte small-signal frequency response

Abstract

The frequency response is considered of a two-electrode linearized system containing a single positively charged species and a single negatively charged species. These species may have arbitrary valences and mobilities and may individually react at the electrodes. The results follow from a detailed solution of the equations of charge motion given earlier. Normalized response is exhibited for this unsupported, intrinsic-conduction situation for a wide range of mobility ratios, valence number ratios, and reaction rate ratios. Results are given in the form of specific formulas, impedance-plane plots, and the dependences on normalized frequency of series and parallel resistive and capacitative components of the normalized total impedance of the system. Impedance-plane plots exhibit from one to three connected arcs, depending on the specific situation. Approximate Warburg frequency response appears for the “interface” impedance over a certain frequency region when normalized reaction rate parameters differ, but it only shows up strongly in the total impedance when the mobility ratio departs appreciably from unity as well. Under such conditions, a plateau region, where the total parallel capacitance remains essentially independent of frequency over a wide frequency range, may appear at frequencies just above the Warburg region. The plateau capacitance is close to but not identical to the conventional double-layer capacitance present when both species of charge are completely blocked. In incomplete blocking cases, however, this double-layer capacitance only makes a significant appearance in the approximate equivalent circuit under slow reaction conditions; it is thus not present when one of the reaction rate constants is infinite. In general, the system can show ω − m frequency response for the parallel capacitance over a wide frequency range with 0⩽ m⩽2, and with the experimentally common regions where m≌0, 0.5, 1.5, and 2 especially likely. Particular attention is given to deviations from ideal Warburg behavior which led to a combined charge-transfer and heterogeneous chemical reaction resistance. Results are compared to those from conventional supported treatments and show both important similarities and differences. Finally, several new equivalent circuits are presented which are pertinent in various frequency ranges for the unsupported situation.