Transport in doped conjugated polymers with polarons and bipolarons forming complexes with counter ions

In contrast to experimental evidence of bipolarons (BPs) in doped polymers, they have been ignored usually in both analyzing the electrochemical impedance spectra (EIS) and discussing the properties of organic devices. For EIS, the small-signal alternating current (ac) transport properties of polarons (P) and counter ions (C) are often modeled by transmission line equivalent circuits. Recently, this description has been extended to include steady-state effects and traps and, further, to account for the direct P–BP reaction. Here, the influence of traps and of the direct P–BP reaction are compared to each other. However, according to Kirova and Brazovskii [Synth. Metals 76 (1996) 229], the latter seems to be improbable, owing to the Coulomb repulsion except for the presence of a high counter ion concentration. They proposed a scenario with the formation of different complexes of Pʹs and BPs with counter ions, and they suggested that the kinetics of the formation processes will be responsible, e.g., for hysteresis effects observed in organic devices. Here, the description is complemented by the first step, the formation of complexes from a polaron and a counter ion. The resulting small-signal ac equations are presented and conditions are analyzed, under which such complex formation processes can be important in EIS and in organic devices.