On the Modeling of Polyelectrolyte Gels

Authors

  • Thomas Wallmersperger,

    Corresponding author
    1. Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, Universität Stuttgart, Pfaffenwaldring 27, D-70569 Stuttgart, Germany
    • Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, Universität Stuttgart, Pfaffenwaldring 27, D-70569 Stuttgart, Germany. Fax: +49 711-685-63706
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  • Dirk Ballhause,

    1. Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, Universität Stuttgart, Pfaffenwaldring 27, D-70569 Stuttgart, Germany
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  • Bernd Kröplin

    1. Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, Universität Stuttgart, Pfaffenwaldring 27, D-70569 Stuttgart, Germany
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Abstract

Summary: Ionic polymer gels are very 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 solvent lead to a considerably large change of volume. This swelling mechanism results from the equilibrium of different forces such as osmotic pressure forces, electrostatic forces and viscoelastic restoring forces and can be triggered by chemical (change of salt concentration or pH in the solution), thermal or electrical stimulation. In the present work, chemically and electrically stimulated electrolyte polymer gels in a solution bath are investigated. To describe the different phenomena occurring in these gels adequately, the modeling can be conducted on different scales. If only the global macroscopic behavior is of interest, the statistical theory which is capable to describe the global swelling ratio, is sufficient. By refining the scale, 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 directly obtained by solving the Poisson equation in the gel and solution domain. The mechanical field is formulated by the momentum equation. By further refining the scale, the whole structure can be investigated on the microscale by the discrete element (DE) method. In this model, the material is represented by distributed particles comprising a certain amount of mass; the particles interact with each other mechanically by a truss or beam network of massless elements. The mechanical behavior, i.e. the dynamics of the system, is followed 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 three formulations can give chemical, (electrical) and mechanical unknowns and all rely on the assumption that the concentration differences between the different regions of the gel and between gel and solution form the osmotic pressure difference, which is a main cause for the mechanical deformation of the polyelectrolyte gel film.

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