Cha Youngsu, Porfiri Maurizio
Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University, Brooklyn, New York 11201, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):022403. doi: 10.1103/PhysRevE.87.022403. Epub 2013 Feb 6.
In this paper, we analyze the charge dynamics of ionic polymer-metal composites (IPMCs) in response to voltage inputs composed of a large dc bias and a small superimposed time-varying voltage. The IPMC chemoelectrical behavior is described through the modified Poisson-Nernst-Planck framework, in which steric effects are taken into consideration. The physics of charge build-up and mass transfer in the proximity of the high surface electrodes is modeled by schematizing the IPMC as the stacked sequence of five layers, in which the ionomeric membrane is separated from the metal electrodes by two composite layers. The method of matched asymptotic expansions is used to derive a semianalytical solution for the concentration of mobile counterions and the electric potential in the IPMC, which is, in turn, used to establish an equivalent circuit model for the IPMC electrical response. The circuit model consists of the series connection of a resistor and two complex elements, each constituted by the parallel connection of a capacitor and a Warburg impedance. The resistor is associated with ion transport in the ionomeric membrane and is independent of the dc bias. The capacitors and the Warburg impedance idealize charge build-up and mass transfer in the vicinity of the electrodes and their value is controlled by the dc bias. The proposed approach is validated against experimental results on in-house fabricated IPMCs and the accuracy of the equivalent circuit is assessed through comparison with finite element results.
在本文中，我们分析了离子聚合物-金属复合材料（IPMCs）在由大直流偏置和小叠加时变电压组成的电压输入响应下的电荷动力学。通过修正的泊松-能斯特-普朗克框架描述IPMC的化学电行为，其中考虑了空间位阻效应。通过将IPMC简化为五层的堆叠序列来模拟高表面电极附近的电荷积累和传质物理过程，其中离子交换膜通过两个复合层与金属电极隔开。采用匹配渐近展开法推导了IPMC中移动反离子浓度和电势的半解析解，进而用于建立IPMC电响应的等效电路模型。该电路模型由一个电阻器和两个复元件串联组成，每个复元件由一个电容器和一个沃伯格阻抗并联构成。电阻器与离子交换膜中的离子传输相关，且与直流偏置无关。电容器和沃伯格阻抗理想化了电极附近的电荷积累和传质，其值由直流偏置控制。所提出的方法针对内部制造的IPMC的实验结果进行了验证，并通过与有限元结果的比较评估了等效电路的准确性。
