Coupled chemo-electro-mechanical formulation for ionic polymer gels––numerical and experimental investigations

doi:10.1016/S0167-6636(03)00068-1

Mechanics of Materials

Volume 36, Issues 5–6, May–June 2004, Pages 411-420

https://doi.org/10.1016/S0167-6636(03)00068-1 Get rights and content

Abstract

Polyelectrolyte gels consist of a network of crosslinked polymers with attached electric charges and a liquid phase. Variations of the chemical milieu surrounding the gel or application of an external electric field lead to a change in the swelling ratio of the gels. This phenomenon may be used for contraction and relaxation of chemo-electro-mechanical actuators and in particular of artificial muscles. In this paper electrically stimulated polymer gels, placed in a solution bath, are investigated. For these gels, we present a volume- and surface-coupled chemo-electro-mechanical multi-field formulation. This formulation consists of a convection–diffusion equation describing the chemical field, a Poisson equation for the electric field and a mechanical field equation. The model is capable to describe the local swelling and deswelling of ionic polymer gels as well as the ion concentrations and the electric potential in the gel and in the solution. A chemo-electric simulation is performed for a gel fiber at a given electric field; the anionic and cationic ion concentrations as well as the electric potential inside and outside the gel are computed for a given number of bound anionic groups. The resulting increase in the concentration differences on the anode side of the anionic gel can be considered as an indicator for a higher swelling ratio of the gel fiber. Mechanical and electrical measurements on anionic polyelectrolyte gels are in good agreement with the numerical results. This demonstrates the validity of the employed numerical model.

Introduction

Certain polyelectrolyte gels are distinguished by enormous swelling capabilities under the influence of external physical and chemical stimuli. No other kind of material attains comparable volume expansiveness. These unique properties make them most attractive candidates for a new promising generation of “pseudomuscular” actuators. The typical architecture of a polyelectrolyte gel consists of a network of crosslinked polymers to which electric charges are attached. Suitable polyelectrolyte gels can be synthesized by crosslinked copolymerisation of weakly ionisable comonomers often bonded chemically in a polymer network (see Fig. 1).

Variations in the surrounding chemical milieu or exposition to an external electric field may induce changes in the degree of ionisation of the polyelectrolyte gel and in the distribution of ions within the gel entailing a change in the swelling capacity of the gel. The characteristic deformations of polyelectrolyte gels under the influence of external fields lead to reversible bending. In the present study we want to model the mechanisms behind the effect of external electric fields on ionic polyelectrolyte gels leading to spatially different swelling and deswelling and thus to bending motions. In contrast to various studies in this field assuming a constant Donnan potential throughout the polyelectrolyte gels we investigate a coupled chemo-electro-mechanical formulation which is capable to describe the local swelling of a gel on the basis of concentration differences at the complete gel–solution interface.

Section snippets

Chemo-electro-mechanical multi-field formulation

The dynamic behavior of ionic polymer gels in electric fields has been investigated quasi-statically by Doi et al. (1992), Shiga and Kurauchi (1990), Shahinpoor (1995). Brock et al. (1994) have given a coupled formulation for the ion-dynamics and a theory for large displacements. Nemat-Nasser and Li (2000) have presented an electro-mechanical model for ionic polymer metal composites, while, Neubrand (1999), Grimshaw et al. (1990), de Gennes et al. (2000), Wallmersperger et al. (2001) have

Numerical simulation of electrical stimulation

In this section, electrical stimulation of an electrolyte polymer gel fiber is investigated.

The testcase is conducted for a fixed gel fiber (4 × 10 mm²) with a concentration of bound anionic groups c_A⁻=5 mM, placed between two electrodes in a solution bath (50 × 50 mm²) having a concentration of c_Na⁺^(s)=c_Cl⁻^(s)=1 mM (see Fig. 4). The boundary conditions for Na⁺ and Cl⁻ in the solution near the electrodes are set to c_Na⁺=c_Cl⁻=1 mM. Since the concentrations of H⁺ and OH⁻ ions are very small, they can

Conclusion

In the present study, a coupled chemo-electro-mechanical multi-field formulation for polyelectrolyte gels has been presented. This formulation consists of convection–diffusion equations describing the chemical field, a Poisson equation for the electric field and a mechanical field equation. The model is capable to describe the local swelling and deswelling of ionic polymer gels as well as the ion concentrations and the electric potential in the gel and in the solution.

Numerical simulations of

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Polyelectrolyte gels in electric fields: A theoretical and experimental approach

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Coupled chemo-electro-mechanical formulation for ionic polymer gels––numerical and experimental investigations

Abstract

Introduction

Section snippets

Chemo-electro-mechanical multi-field formulation

Numerical simulation of electrical stimulation

Conclusion

A dynamic model of a linear actuator based on polymer hydrogel

J. Intell. Mater. Syst. Struct.

Mechanoelectric effects in ionic gels

Europhys. Lett.

Deformation of ionic polymer gels by electric fields

Macromolecules

Kinetics of electrically and chemically induced swelling in polyelectrolyte gels

J. Chem. Phys.

Polyelectrolyte gels in electric fields: A theoretical and experimental approach