A thermodynamic chemomechanical constitutive model for conducting polymers

Conducting polymers undergo volumetric expansion through redox-mediated ion exchange with an electrolyte under an applied electrical field. The resulting ion transport processes control the conformational relaxation of the polymer backbone and regulate the generated stress and strain. In this paper, a constitutive model has been developed from first principles to examine coupled chemomechanical response for a polypyrrole-based conducting polymer actuator. The mechanics of charge ingress and egress is used to compute chemomechanical coupling coefficient of a polypyrrole doped with dodecylbenzene sulfonate (PPy(DBS)) cantilever actuator and the resulting values are compared with experimental data over a range of sodium chloride (NaCl) electrolyte concentrations from 1 mM to 1 M. The model predicts concentration dependent strain and chemomechanical coupling coefficient for the actuator and it is observed that the strain generated by the actuator saturates above a certain value of cation concentration in the electrolyte. The maximum strain developed by the conducting polymer is found to be dependent on the volume of the PPy(DBS) layer and it is estimated that the chemomechanical coupling coefficient varies between 0.016 and 0.023 dm3/mole as a function of electrolyte concentration (0.001 to 1 M). A mechanistic approach to interpret the results from the model and experiments is proposed and correlations between structure (number of redox sites in the polymer, packing density), input (electrolyte concentration, electrical potential), output (strain) and constitutive relation (chemomechanical coupling coefficient) are derived.