# Conservation laws of an electro-active polymer

## TL;DR

This paper derives conservation laws for ionic electro-active polymers using a two-phase continuum model, revealing energy conversion mechanisms and dissipative effects during deformation under electric fields.

## Contribution

It introduces a comprehensive continuum model for E.A.P. that accounts for microscale physics and derives macroscale conservation laws, including interface exchanges and energy dissipation.

## Key findings

- Identification of energy conversion phenomena in E.A.P.
- Derivation of macroscale conservation laws from microscale physics.
- Analysis of dissipative effects like viscous friction and Joule heating.

## Abstract

Ionic electro-active polymers (E.A.P.) is an active material consisting in a polyelectrolyte (for example Nafion). Such material is usually used as thin film sandwiched between two platinum electrodes. The polymer undergoes large bending motions when an electric field is applied across the thickness. Conversely, a voltage can be detected between both electrodes when the polymer is suddenly bent. The solvent-saturated polymer is fully dissociated, releasing cations of small size. We used a continuous medium approach. The material is modelled by the coexistence of two phases; it can be considered as a porous medium where the deformable solid phase is the polymer backbone with fixed anions; the electrolyte phase is made of a solvent (usually water) with free cations. The microscale conservation laws of mass, linear momentum and energy and the Maxwell's equations are first written for each phase. The physical quantities linked to the interfaces are deduced. The use of an average technique applied to the two-phase medium finally leads to an Eulerian formulation of the conservation laws of the complete material. Macroscale equations relative to each phase provides exchanges through the interfaces. An analysis of the balance equations of kinetic, potential and internal energy highlights the 2 Mireille Tixier, Jo{\"e}l Pouget phenomena responsible of the conversion of one kind of energy into another, especially the dissipative ones : viscous frictions and Joule effect.