Coupled chemo-electro-mechanical simulation of polyelectrolyte gels as actuators and sensors

Polyelectrolyte gets are ductile elastic electroactive materials. They consist of a polymer network with charged groups and a liquid phase with mobile ions. Changing the chemical or electric conditions in the gel-surrounding solution leads to a change of the chemo-electro-mechanical state in the gel phase: diffusion and migration of ions and solvent between the gel and solution phases trigger the swelling or shrinkage of the polymer gel. In case of chemical stimulation (change of pH or salt concentration), a swelling ratio of up to 100% may be obtained. Due to this large swelling ratio the gels exhibit excellent actuatoric capabilities. In this paper, a polyelectrolyte gel placed in a solution bath is investigated. The actuatoric and sensoric capabilities are described by a chemo-electro-mechanical model. The chemical field is represented by a convection-migration-diffusion equation while the electric field is described by a quasi-static Laplace equation. For the mechanical field a partial differential equation of first order in time is applied. Inertia effects are neglected due to the relatively slow swelling/shrinkage process. On the one hand, the coupling between the chemo-electrical and the mechanical field is realised by the differential osmotic pressure stemming from the concentration differences between gel and solution. On the other hand, the mechanical deformation influences the concentration of the bound charged groups in the gel. The three fields are solved simultaneously by applying the Newton Raphson method using finite elements in space and finite differences in time. The developed model is applicable for both, hydrogel actuators and sensors. Numerical results of swelling and bending are given for chemically and electrically stimulated polymer gels. In this paper we show the differences between the chemo-electric and the fully coupled chemo-electro-mechanical formulation for polymer gels in different solution baths. The inverse (sensor-) effect is demonstrated by the influence of the mechanical deformation on the gel, which results in a change of the chemical and electrical unknowns in the gel. The validity of the employed numerical model is shown by a comparison of the obtained results with experimental measurements.