A multilayer bending model for conducting polymer actuators

Electroactive conducting polymers (CPs) have been frequently used for fabricating bending actuators. To model this type of actuation, the traditional double-layer beam bending theory was implemented by neglecting the thickness of the thin intermediate metal layers for the sake of simplification. However, this common assumption has not been carefully validated and the associated errors have not been well acknowledged. In this work, a generic multilayer bending model was introduced to account for the actuators consisting of an arbitrary number of layers. Our model found the bending curvature, strain, stress, and in particular work density of the multilayer actuator as explicit functions of the thickness and modulus of each individual layer. The thickness of metals and conducting polymers were controlled in thermal evaporation and electrochemical synthesis, respectively. The modulus of polypyrrole (PPy), the conducting polymer used in this work, was determined within our model by the bending curvature measured using the charge-coupled device (CCD). This gave a modulus of our electrochemically synthesized PPy of 80 MPa, corresponding to an actuation strain of 2% in our model. It was concluded that neglecting the intermediate metal layers would lead to substantial errors. For instance, using a PPy/Au/Kapton trilayer actuator, a 5% error or below in strain can only be found if the Au layer is one thousand times thinner than Kapton. To enhance the actuation, a PPy/Pt/PVDF/Pt/PPy five-layer actuator has been often used. In this case, even if the Pt layer was reduced to 10 nm, our predicted error of neglecting the two metal layers would be 12.59%. Our results showed that the work density, chosen to measure the overall performance of the actuator, was highly sensitive to the modulus of the substrate polymer layer so that it was generally desirable of using a soft polymer substrate. With the multilayer bending model, we intend to provide an accurate and reliable tool for systematically analyzing the bending behavior and performance of the CP-based actuators.