Identification of the electroelastic coupling from full multi-physical fields measured at the micrometre scale

Abstract

Metal coated microcantilevers are used as transducers of their electrochemical environment. Using the metallic layer of these cantilevers as a working electrode allows one to modify the electrochemical state of the cantilever surface. Since the mechanical behaviour of micrometre scale objects is significantly surface-driven, this environment modification induces bending of the cantilever. Using a full-field interferometric measurement set-up to monitor the objects then provides an optical phase map, which is found to originate from both electrochemical and mechanical effects. The scaling of the electrochemically-induced phase with respect to the surface charge density is modelled according to Gouy–Chapman–Stern theory, whereas the relationship between the mechanical effect and the surface charge density is analysed. An identification technique is described to determine a modelling of the electroelastic coupling and to identify the spatial charge density distribution from full-field phase measurements. Minimizing the least-squares gap between the measured phase and a statically admissible phase field, the mechanical effect is found to be charge-driven. The charge density field is also found to be singular on the cantilever edge, and the shear stress versus charge density is found to be non-linear.