# Basic mechanisms of IPMC transduction¶

Ionic polymer-metal composite (IPMC) materials consist of a thin ionomeric membrane with typical thickness of upwards of 0.1~mm. Often Nafion is used as the polymer membrane. It is coated with a thin layer of a noble metal electrode, such as platinum. Sometimes, an additional layer of gold is added in order to improve the electric conductivity of the electrodes.

IPMCs can be used as electromechanical and mechanoelectrical transducers. In case of the electromechanical transduction, applied voltage (typically in the range of few volts) is converted into deformation, whereas in case of the mechanoelectrical transduction, applied deformation is converted into electrical energy (can be measured as voltage on the electrodes or extracted as current).

## Electromechanical transduction¶

Electromechanical transduction of IPMC is caused by voltage induced ionic current. In water solvent based IPMCs, positive cations drag along water molecules, thus causing both cation and solvent depletion and accumulation near anode and cathode electrodes, respectively.

The ionic current is described with the Nernst-Planck equation:

$\frac{\partial C}{\partial t} + \nabla \left( -D \nabla C - z\mu F C\nabla \phi \right) = 0,$

where $$C \$$ is cation concentration, D diffusion constant, $$\mu \$$ cation mobility $$F \$$ the Faraday number, and $$z \$$ charge number of cations. The potential gradient flux term is governed by the Poisson’s equation:

$-\nabla^2 \phi = \frac {\rho}{\varepsilon},$

where $$\rho=F\left(C - C_0 \right) \$$ and $$\varepsilon \$$ is absolute dielectric permittivity.

The charge near the electrodes can be related to deformation by using linear elasticity formulations where the charge density $$\rho \$$ is related to the body force:

$F=f\left(\rho, \rho^2\right).$

The bending with underlying ionic flux terms is illustrated: