Modelling and Simulation of the Chemo-Electro-Mechanical Behaviour

Abstract

Ionic polymer gels are attractive actuation materials with a great similarity to biological contractile tissues. They consist of a polymer network with bound charged groups and a liquid phase with mobile ions. Absorption and delivery of the solvent lead to a large change of volume. This swelling mechanism results from the equilibrium between different forces such as osmotic pressure forces, electrostatic forces and visco-elastic restoring forces and can be triggered by chemical (change of salt concentration or pH in the solution), thermal or electrical stimulation. In this chapter, an overview over different modelling alternatives for chemically and electrically stimulated electrolyte polymer gels in a solution bath are investigated. The modelling can be conducted on different scales in order to describe the various phenomena occurring in the gels. If only the global macroscopic behaviour is of interest, the statistical theory which can describe the global swelling ratio is sufficient. By refining the scale, the Theory of Porous Media (TPM) may be applied. This is a macroscopic continuum theory which is based on the theory of mixtures extended by the concept of volume fractions. By further refining, the mesoscopic coupled multi-field theory can be applied. Here, the chemical field is described by a convection-diffusion equation for the different mobile species. The electric field is obtained directly by solving the Poisson equation in the gel and solution domain. The mechanical field is formulated by the momentum equation. By investigating the structure on the micro scale, the Discrete Element (DE) method is predestined. In this model, the material is represented by distributed particles comprising a certain amount of mass; the particles interact mechanically with each other by a truss or beam network of massless elements. The mechanical behaviour, i.e. the dynamics of the system, is examined by solving the Newton's equations of motion while the chemical field, i.e. the ion movement inside the gel and from the gel to the solution, is described by diffusion equations for the different mobile particles. All four formulations can give chemical, possibly electrical and mechanical unknowns and all rely on the assumption of the concentration differences between the different regions of the gel and between gel and solution forming the osmotic pressure difference, which is a main cause for the mechanical deformation of the polyelectrolyte gel film.