Nonlinear Two-Dimensional Transmission Line Models for Electrochemically Driven Conducting Polymer Actuators

The electronic and ionic conductivities of conducting polymers can change as a function of oxidation state, and yet, these properties are not generally considered in modeling the electrochemistry and electrochemically driven actuation of these materials. These effects can be significant particularly over large ranges of oxidation state and in long films where electrical contact is made from one end. In this study, a transmission line model is implemented, in which conductivities vary as a function of local oxidation state, with this variation being based on measured values. Our time-domain model is based on a 2-D RC transmission line model implemented using a state-space representation. Voltage drop along the length of the film away from the attachment point and the variation in electronic conductivity with state of charge along this length necessitated the use of a 2-D nonlinear model to obtain effective predictions of response for the film dimension used. The general approach demonstrated may be applied to any situation where properties vary with position and oxidation state, such as in batteries and supercapacitors. The last step showed the successful application of the model to predict actuation of a polypyrrole linear actuator.