Multiscale modeling of polyelectrolyte gels

Electrolyte polymer gels are a very attractive class of actuation materials with remarkable electronic and mechanical properties having a great similarity to biological contractile tissues. They consist of a polymer network with ionizable groups and a liquid phase with mobile ions. Absorption and delivery of solvent lead to a considerably large change of volume. Due to this capability, they can be used as actuators for technical applications, where large swelling and shrinkage is desired. In the present work chemically and electrically stimulated polymer gels in a solution bath are investigated. To describe the different complicated phenomena occurring in these gels adequately, the modeling can be conducted on different scales. Therefore, models based on the statistical theory and porous media theory, as well as a multi-field model and a discrete element formulation are derived. A refinement of the different theories from global macroscopic to microscopic are presented in this paper: The statistical theory is a macroscopic theory capable to describe the global swelling or bending e.g. of a gel film, while the general theory of porous media (TPM) is a macroscopic continuum theory which is based on the theory of mixtures extended by the concept of volume fractions. The TPM is a homogenized model, i.e. all geometrical and physical quantities can be seen as statistical averages of the real quantities. The presented chemo-electromechanical multi-field formulation is a mesoscopic theory. It is capable of giving the concentrations and the electric potential in the whole domain. Finally the (micromechanical) discrete element (DE) theory is employed. In this case, the continuum is represented by distributed particles with local interaction relations combined with balance equations for the chemical field. This method is predestined for problems involving large displacements, strains and discontinuities. The presented formulations are compared and conclusions on their applicability in engineering practice are finally drawn.