Charge dynamics in ionic polymer metal composites

In this paper, we study the charge dynamics in ionic polymer metal composites (IPMCs) in response to a voltage difference applied across their electrodes. We use the Poisson-Nernst-Planck equations to model the time evolution of the electric potential and the concentration of mobile counterions. We present an analytical solution of the nonlinear initial-boundary value problem by using matched asymptotic expansions. We determine the charge and electric potential distributions as functions of time in the whole IPMC region. We show that in the bulk polymer region the IPMC is approximately electroneutral; in contrast, charge distribution boundary layers arise at the polymer-electrode interfaces. Prominent charge depletion and enrichment at the polymer-electrode interface are present even at moderately low input-voltage levels. We use the proposed analytical solution to derive a physics-based circuit model of IPMCs. The equivalent circuit comprises a linear resistor in series connection with a nonlinear capacitor. We derive closed-form expressions for the resistance and the capacitance by conducting a qualitative phase-plane analysis of the inner approximation of the asymptotic expansion. The circuit conductivity is independent of the IPMC dielectric constant and is proportional to the ion diffusivity; whereas, the capacitance is proportional to the square root of the dielectric constant and is independent of the diffusivity. The conductivity depends on the polymer thickness, while the capacitance is independent of it. The capacitance nonlinearity is extremely pronounced, and dramatic capacitance reduction is observed for moderately low voltage levels. We validate the proposed analytical solution along with the derived circuit model through extensive comparisons with finite element results available in the technical literature.