Received: 25 June 2018 Accepted: 26 August 2018 DOI: 10.1002/pamm.201800472 Behaviour of Anionic and Cationic Hydrogels Karsten Keller 1, * , Thomas Wallmersperger 2 , and Tim Ricken 1 1 Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, Universität Stuttgart 2 Institut für Festkörpermechanik, TU Dresden Ionic polyelectrolytic gels in an aqueous solution, i.e. hydrogels – also known as smart materials – react to different kinds of environmental changes, e.g. chemical, electrical, mechanical, and thermal stimulation. As a reaction, they show enormous swelling capabilities resulting from the delivery or uptake of ions and solvent. These properties make them attractive for chemo-electro-mechanical energy converters and for the application as actuators or sensors. The applied multi-field formulation consists of the chemical, electrical, and mechanical field and is capable of giving local concentrations, electric potential distributions and displacements. In this excerpt the reaction of a modelled hydrogel finger gripper under electrical stimulation is shown. The swelling ratio is assumed to be in the regime of small volume changes and corresponding displacements. c  2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction Ionic polyelectrolyte gels immersed in an aqueous solution bath respond to changing environmental conditions, such as chem- ical, electrical or other stimuli. This sensitive reaction capability stems from the polymer structure and the mobile anions and cations in both phases – the gel itself and the surrounding solution – as well as the bound anions or cations in the crosslinked polymer network. Due to non-equilibrium driving forces – e.g. chemical, electrial, and mechanical – diffusive and migrative processes develop. An ionic flux sets in to form an equilibrium state. Quite similar to natural structures, the hydrogels tend to balance these gradients in the physical fields. The resulting flux of ions surrounded by hydrate shells leads to swelling or shrinking of the gel. These deformations can be measured or triggered and a variety of applications is derived - as sensors for pressure (cf. Gerlach et al. [5]) or concentrations (pH, medicine), or actuators and artificial muscles (cf. Brock and Carpi et al. [3, 4]), just to name a few. An electrically stimulated finger gripper will be shown in this paper. 2 Modeling To describe the coupled chemo-electro-mechanical behaviour of hydrogels within a continuum model three main governing relations are proposed. Firstly, the chemical field is given by ˙ c α =[D α c α,i + z α c α μ α ψ ,i ] ,i (1) with diffusive (first term) and migrative (second term) contributions via neglecting source terms and convective influences. The variables in (1) are for the species α the diffusion coefficient D, the mobile ion concentration c, the valence z, the ion mobility μ, and the electric potential ψ. The operator () ,i denotes the derivative in x i -direction . Secondly, the electrical field is described by a Poisson type PDE formulated as ψ ,ii = - F  r  0  Nα+N b  α=1 (z α c α )+ z g c g  (2) with the Faraday constant F , the permittivity  r  0 , and the sum over mobile N α and bound species N b . And thirdly for the equation of the mechanical field which is derived from the balance of momentum neglecting inertia terms and body forces σ ij,i =(C ijkl ( kl -  π kl )) ,i =0 (3) with the stress tensor σ, the elasiticity tensor C and the total  and swelling strain  π . The osmotic pressure difference Δπ ∝ Σ α (c α - c ref α ) is the driving force in the mechanical field, specified over the local concentration values c α and a non-local approach for the reference concentrations c ref α . The coupling between the chemical and electrical field is ensured directly via a two-way coupling (i.e. within a monolithic approach), while the coupling to the mechanical field is realized by a one-way coupling. Only infinitesimal deformations are assumed in this research, with negligible differences between current and reference configuration. For a more detailed derivation of the governing PDEs and the discretization please refer to Attaran and Wallmersperger et al. [1,2,9]. * Corresponding author: e-mail karsten.keller@isd.uni-stuttgart.de, phone +00 49 711 685 69543, fax +00 49 711 685 63706 PAMM · Proc. Appl. Math. Mech. 2018;18:e201800472. www.gamm-proceedings.com c  2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 1 of 2 https://doi.org/10.1002/pamm.201800472