Influence of electrode surface roughness and steric effects on the nonlinear electromechanical behavior of ionic polymer metal composites

In this paper, we analyze the influence of electrode surface roughness and steric effects on the nonlinear electromechanical behavior of ionic polymer metal composites (IPMCs). We use the modified Poisson-Nernst-Planck equations to describe the electric potential and mobile counterion distributions within the IPMC for a steady voltage applied across the IPMC rough electrodes. We present an analytical solution of the nonlinear three-dimensional boundary value problem based on the method of matched asymptotic expansions. The distribution of mobile counterions within the polymer region is characterized by thin boundary layers in the proximity to the polymer-electrode interfaces, where enrichment and depletion of mobile charges take place. The presence of rough landscapes drastically increases the polymer-electrode surfaces and thereby significantly improves the overall charge storage. We determine closed-form expressions for the average bending moment produced by the IPMC and for its average stored charge and capacitance. We show that the bending moment produced by an IPMC is linearly proportional to the stored charge, which in turn increases nonlinearly as the voltage applied across the electrodes increases. The average charge stored in the IPMC increases as the electrode surface roughness increases and decreases as steric effects become prominent.

Figure 1

Sketch of an IPMC illustrating (a) the problem geometry and coordinate system and (b) cation enrichment in the proximity of the cathode and cations depletion in the vicinity of the anode region.

Figure 2

(Color online) Level curves of Eq. (44) for two different values of the parameter $\nu$.

Figure 3

(Color online) $\vartheta$ as a function of the bulk polymer potential $A$ for different values of the packing parameter $\nu$: (a) large parameter variation in logarithmic scale and (b) detailed plot in the neighborhood of the origin.

Figure 4

(Color online) Relative bulk potential as a function of the applied potential for equal surface area electrodes.

Figure 5

(Color online) Relative bulk potential for unequal surface electrodes and (a) $\alpha =1$ and (b) $\alpha =10$.

Figure 6

(Color online) Concentration and relative electric potential in the proximity to the electrodes at $\alpha =1$.

Figure 7

(Color online) Concentration and relative electric potential in the proximity to the electrodes at $\alpha =10$.

Figure 8

(Color online) Extent of concentration boundary layers in the proximity to (a) the anode and (b) cathode and numerical values of the concentration values at (c) the anode and (d) cathode.

Figure 9

(Color online) Nondimensional functions defining the overall IPMC response as the applied voltage increases, according to Eqs. (51, 52, 53).

Figure 10

(Color online) Dependence of the stored charge and bending moment on the applied voltage for (a) larger anode surface and (b) larger cathode surface.

Figure 11

(Color online) Comparison between the proposed analytical solution (solid line) and experimental results of [20] (dots): (a) stored charge per unit surface and (b) bending strain.