Thermodynamically consistent electro-chemo-mechanical model for polymer membranes

Nafion membranes, are polymeric thin films widely employed in micro-batteries and fuel cells. These devices are expected to play a key role in the next generation energy systems for use in vehicles as a replacement to combustion engines. In fact, a minimum environmental impact is guaranteed by reduced carbon dioxide emissions. It is usually complicated to investigate the behavior of thin membranes through experiments. Therefore, numerical simulations are carried out in order to enable a better understanding of the phenomena and of the multi-field couplings occurring in polymeric membranes. A continuum-based, three-dimensional and electro-chemo-mechanical (ECM) model for a hydrated polymer membrane is presented. Different effects are taken into account: (i) mechanics, (ii) water uptake, (iii) ion transport, and (iv) electrostatics. The dissipation inequality drives the choice of the suitable constitutive equations of the multi-physics theory. In the mechanical field, an additive decomposition of the deformation gradient in (i) a distortion part, related to the ion motion, and (ii) an elastic part, is assumed. The multi-field model is numerically solved within the finite element framework. Time-dependent simulations are performed by using the commercial tool COMSOL Multiphysics. Furthermore, two closed form solutions are obtained by using (i) a one-dimensional reduced model and (ii) an approach based on the bar theory with an electro-chemical distortion field.