Modeling of Temperature-Sensitive Polyelectrolyte Gels by the Use of the Coupled Chemo-Electro-Mechanical Formulation

Polyelectrolyte gels show adaptive viscoelastic characteristics. In water-based solutions they have enormous swelling capabilities under the influence of different possible stimulation types, such as chemical, electrical, or thermal stimulation. Possible applications for these intelligent materials can be either actuators, e.g., when used as artificial muscles or chemo-electric energy converters, or sensors, e.g., for measuring ion concentrations or pH-values of the solutions. In order to represent this active behavior, a coupled multi-field model is applied. The chemo-electro-mechanical multi-field formulation considers changes of concentrations, electric potential, or strains due to varying (initial) conditions. In the present work, a fully coupled 3-field formulation for polyelectrolyte gels using the Finite Element Method is applied. This formulation consists of a chemical, electrical, and mechanical field equation. The chemical field is described by a partial differential equation (PDE) first order in time and second order in space and includes diffusional, migrational, and convectional effects. The electrical field is represented by the Poisson equation, an elliptical PDE of second order in space. Finally, the mechanical field is described by a PDE of first order derived from the conservation of momentum. Due to the slow processes in time, inertia terms are neglected. The mechanical field is coupled to the chemo-electrical field by a prescribed strain stemming from an osmotic pressure term. A large dependency between the applied temperature and the actual swelling degree of the gel has been proven in experiments. In the present research, the thermal stimulation is investigated using two alternative approaches: The first is a straight forward modeling by modifying the actual temperature in the osmotic pressure term. As this approach does not lead to promising results, as a second alternative temperature-dependent material parameters obtained from experimental measurements are applied. The calibration of the derived simulation results is performed with experimental results from the literature. The Finite Elements introduced for the coupled multi-field formulation contain degrees of freedom for concentrations, electric potential, and mechanical displacements. They are adopted and applied in the commercial software package ABAQUS as a user defined element. For the numerical solution, the Newton-Raphson method in conjunction with the implicit backward Euler time integration scheme is applied.