Actuation and ion transportation of polyelectrolyte gels

Consisting of charged network swollen with ionic solution, polyelectrolyte gels are known for their salient characters including ion exchange and stimuli responsiveness. The active properties of polyelectrolyte gels are mostly due to the migration of solvent molecules and solute ions, and their interactions with the fixed charges on the network. In this paper, we extend the recently developed nonlinear field theory of polyelectrolyte gels by assuming that the kinetic process is limited by the rate of the transportation of mobile species. To study the coupled mechanical deformation, ion migration, and electric field, we further specialize the model to the case of a laterally constrained gel sheet. By solving the field equations in two limiting cases: the equilibrium state and the steady state, we calculate the mechanical responses of the gel to the applied electric field, and study the dependency on various parameters. The results recover the behavior observed in experiments in which polyelectrolyte gels are used as actuators, such as the ionic polymer metal composite. In addition, the model reveals the mechanism of the selectivity in ion transportation. Although by assuming specific material laws, the reduced system resembles those in most existing models in the literature, the theory can be easily generalized by using more realistic free-energy functions and kinetic laws. The adaptability of the theory makes it suitable for studying many similar material systems and phenomena.