Nonlinear capacitance and electrochemical response of ionic liquid-ionic polymers

In this paper we present a physics-based model for the electrochemical response of ionic liquid-ionic polymer transducers (IPTs) and show how the mobile ionic liquid ions influence the charging characteristics and actuation performance of a device. It is assumed that a certain fraction of the ionic liquid ions exist as "free," making for a total of 3 mobile ions. This leads to predictions of distinctly different charging characteristics for ionic liquid versus water-based IPTs, since for the latter there is only a single mobile ion. The large ionic liquid ions are modeled by including steric effects in a set of modified Nernst-Planck/Poisson equations, and the resulting system of equations is solved using the method of matched asymptotic expansions (MAE). The inclusion of steric effects allows for a realistic description of boundary layer composition near actuator operating voltages (similar to 1 V). Analytical expressions for the charge transferred and differential capacitance are derived as a function of the fraction of free ionic liquid ions, influence of steric effects in formation of the electric double layer, and applied voltage. It is shown that the presence of free ionic liquid ions tends to increase the overall amount of charge transferred, and also leads to a nonmonotonic capacitance-voltage curve. We suggest that these results could be used to experimentally identify the extent of free ionic liquid ion movement and to test the validity of the assumptions made in the underlying theory. A comparison with numerical results shows that while the MAE solution procedure gives valid results for capacitance and charge transferred, it cannot predict the dynamic response due to the presence of multiple time scales in the current decay. This is in contrast to previous results in analyzing water-based IPTs, where the MAE solution is in good agreement with numerical results at all times and applied voltages due to the presence of only a single mobile ion. By examining the structure of the electric double layer in the ionic liquid IPT, it is shown that although the additional mobile ions lead to more charge transferred, they likely do not increase the bending moment generated by a cantilevered IPT because of the increase in symmetry in boundary layer charge density profiles. These results are in good qualitative agreement with recent experiments. VC 2011 American Institute of Physics. [doi: 10.1063/1.3569709]