Physics-Based Circuit Modeling of the Impedance Characteristics of a Smart Hydrogel-Actuated Bending Sensor

Smart hydrogels are stimuli-responsive polymers which exhibit a volume-phase transition in response to external influences. This makes them promising candidates for sensing elements, especially in a biomedical context due to their easily achievable biocompatibility. The main challenge in harnessing the smart polymer's potential for sensor applications lies in a reliable transduction of the swelling change into an electrical signal. A novel platform approach is based on a bending sensor where the smart hydrogel acts as an actuator on a thin film with embedded metal traces. Mechanical deformation due to the hydrogel volume change alters the traces' electric impedance. However, besides deformation, the medium surrounding the sensor structure will also affect the impedance. For sensor design it is therefore crucial to understand the complex interdependencies between electric sensor properties, influences of the surrounding medium and mechanical deformation. Here, an electric circuit model is presented which considers all these contributions through a minimum number of lumped elements and is strictly based on physical considerations. By employing measured impedance spectra from an experimental sensor implementation subjected to different surrounding media and mechanical deformation, the validity of the simplified model is demonstrated. A detailed analysis and discussion give insights into the determination of the different model parameters and how external influences can clearly be attributed to specific circuit elements. This work provides a general approach for deducing minimalistic but strictly physics-based circuit models which can still adequately replicate the actual behavior of such types of impedance-based bending sensors.