A multi-cation model for the actuation of ionic membranes with ionic liquids

Abstract

Soft actuators based on water-swollen ionic membranes are able to operate in water, a critical feature for applications in biomedical engineering and underwater robotics. On the contrary, extended use of these actuators in air is hindered by the evaporation of water from the membrane, which negatively affects the actuation performance. To address this limitation, water solvent can be substituted by ionic liquids (ILs). The introduction of ILs in ionic membranes substantially modifies their microscopic composition, requiring dedicated models to describe their electrochemistry and mechanics. However, current physically based models of IL-swollen ionic membranes only partially capture this complex microscopic composition. This manuscript proposes a multi-cation theory, based on first physical principles, that captures the electromigration of ions produced by the dissociation of the IL in the membrane and membrane counterions. The theory, grounded in a thermodynamically consistent formulation at the continuum level, explicitly accounts for the different sizes of these mobile ions, which play a critical role on actuation. Under a series of simplifying hypotheses, we specialize this theory to beam-like actuators. We put forward a numerical solution for the resulting one-dimensional reduced-order model, which we use to perform a series of parametric analyses. We investigate the physics of actuation at steady-state by systematically varying the concentrations of ions and their sizes, the applied voltage and the thickness of the Stern layer. Our results hint at a complex interaction between ions, modulated by their relative concentration and sizes. These parameters dramatically affect the bending moments associated with hydraulic pressure and Maxwell stress, and, in turn, the actuator curvature. Our theory paves the way to more accurate descriptions of the coupled electrochemistry and mechanics of ionic membranes swollen by ILs.