Lenzi E K, Evangelista L R, Barbero G
J Phys Chem B. 2009 Aug 20;113(33):11371-4. doi: 10.1021/jp904741m.
The influence of the ions on the electrochemical impedance of a cell is calculated in the framework of a complete model in which the fractional drift-diffusion problem is analytically solved. The resulting distribution of the electric field inside the sample is determined by solving Poisson's equation. The theoretical model to determine the electrical impedance we are proposing here is based on the fractional derivative of distributed order on the diffusion equation. We argue that this is the more convenient and physically significant approach to account for the enormous variety of the diffusive regimes in a real cell. The frequency dependence of the real and imaginary parts of the impedance are shown to be very similar to the ones experimentally obtained in a large variety of electrolytic samples.
在一个完整模型的框架内计算离子对电池电化学阻抗的影响，在该模型中，分数阶漂移 - 扩散问题得到了解析求解。通过求解泊松方程确定样品内部电场的最终分布。我们在此提出的用于确定电阻抗的理论模型基于扩散方程的分布阶分数导数。我们认为，这是一种更方便且在物理上更有意义的方法，用于解释真实电池中各种扩散机制。阻抗实部和虚部的频率依赖性与在大量电解样品中实验获得的结果非常相似。
