A Chemo-Mechanical Constitutive Model for Conducting Polymers

Conducting polymers undergo volumetric expansion through redox-mediated ion exchange with its electrolytic environment. The ion transport processes resulting from an applied electrical field controls the conformational relaxation in conducting polymer and regulates the generated stress and strain. In the last two decades, significant contributions from various groups have resulted in methods to fabricate, model and characterize the mechanical response of conducting polymer actuators in bending mode. An alternating electrical field applied to the polymer electrolyte interface produces the mechanical response in the polymer. The electrical energy applied to the polymer is used by the electrochemical reaction in the polymer backbone, for ion transport at the electrolyte-polymer interface and for conformational changes to the polymer. Due to the advances in polymer synthesis, there are multitudes of polymer-dopant combinations used to design an actuator. Over the last decade, polypyrrole (PPy) has evolved to be the most common conducting polymer actuator. Thin sheets of polymer are electrodeposited on to a substrate, doped with dodecylbezenesulfonate (DBS-) and microfabricated into a hermetic, air operated cantilever actuator. The electrical energy applied across the thickness of the polymer is expended by the electrochemical interactions at the polymer-electrolyte interface, ion transport and electrostatic interactions of the backbone. The widely adopted model for designing actuators is the electrochemically stimulated conformational relaxation (ESCR) model. Despite these advances, there have been very few investigations into the development of a constitutive model for conducting polymers that represent the input-output relation for chemoelectromechanical energy conversion. On one hand, dynamic models of conducting polymers use multiphysics-based non-linear models that are computationally intensive and not scalable for complicated geometries. On the other, empirical models that represent the chemomechanical coupling in conducting polymers present an over-simplified approach and lack the scientific rigor in predicting the mechanical response. In order to address these limitations and to develop a constitutive model for conducting polymers, its coupled chemomechanical response and material degradation with time, we have developed a constitutive model for polypyrrole-based conducting polymer actuator. The constitutive model is applied to a micron-scale conducting polymer actuator and coupling coefficients are expressed using a mechanistic representation of coupling in polypyrrole (dodecylbenzenesulfonate) [PPy(DBS)].