Abstract
In this work a finite element model is proposed to describe the swelling of poly(acrylic acid) hydrogels under the influence of an external electric field. The specific application of this model is for optical applications, but the design could be used equally well for other applications such as sensors and actuators.The model is proposed as five individual modules, which work in conjunction with each other but which can also function independently. This independence allows the model to provide intermediate results to the user, and also permits each module to be improved or adjusted individually without affecting the operation of the overall model. The first module is the Electrical module, which calculates the external electric field present in the hydrogel by solving Laplace's equation. The second module is the Chemical module, which uses the electric field to calculate the diffusion and migration of ions through the hydrogel/solvent regions. The third module is the Force module, which uses the change in ion concentrations to calculate the resulting change in osmotic pressure (force). This force is then used in the Mechanical module to calculate the deformation of the hydrogel, based on the assumption of linear elasticity. Finally, the fifth module is the Optical module, which uses the deformation to calculate the theoretical change in focal length.To verify the operation of the model, numerous experiments were conducted with the deformation of a poly(acrylic acid) hydrogel being measured under various external voltages with different electrode configurations. Overall, the model agrees quite well with the experimental results, but also highlights some interesting discrepancies that will need to be considered in future work. There is also some scope for improvement in the experimental method used, but again this is left for future work.
