Usefulness of the Distribution of Relaxation Time Method in Electroanalytical Systems: The Case of Voltammetric Ion-Selective Electrodes

Despite the distribution of relaxation time (DRT) method providing clear insights about processes that go unnoticed by traditional electrochemical impedance spectroscopy (EIS) analysis, it has not yet been adopted to solve electroanalytical systems. As an illustration case, we apply the DRT method to deconvolve EIS data from solid-state voltammetric ion-selective electrodes (ISEs). The main aim is to shed light on the underlying working mechanism across the different materials and interfaces, specifically, the doping of a conducting polymer when covered with a very thin (ca. 230 nm) permselective membrane. Although frequency-dependent AC measurements in EIS allow the separation of processes that contribute to the electrical signal, interpretation of the data is challenging. DRT may overcome this inconvenience by revealing a series of peaks corresponding to the predominant electrochemical processes, without any preknowledge on those. To demonstrate our hypothesis, we examine the conducting polymer poly(3-octylthiophene) (POT) linked to a membrane with sodium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (Na⁺TFPB^-) as the cation exchanger, in which the lipophilic anionic part (TFPB^-) is responsible for the POT doping when it gets electrochemically oxidized (POT⁺). The investigation of EIS data obtained under different conditions with the DRT method showed the occurrence of several processes. We have attributed two of these to two different conformational changes in the POT film in connection with p-type charge-transfer doping. Indeed, the kinetics is found to follow a Butler-Volmer behavior, with average charge transfers of 0.5 and 0.3 mol of electrons for each peak. Overall, we demonstrate the utility of the EIS-DRT tandem to separately study charge-transfer events that interconnect along the same (interfacial segmented) system, which cannot be reached by using classical electrochemical approaches. These kinds of insights are necessary for a more efficient design and high-level exploitation of voltammetric ISEs but also other electrochemical systems such as catalysts, batteries, and photovoltaic cells.