Koklu Anil, Ajaev Vladimir, Beskok Ali
Department of Mechanical Engineering , Southern Methodist University , Dallas , Texas 75205 , United States.
Department of Mathematics , Southern Methodist University , Dallas , Texas 75275 , United States.
Anal Chem. 2019 Sep 3;91(17):11231-11239. doi: 10.1021/acs.analchem.9b02162. Epub 2019 Aug 19.
Classical electrochemistry problem of polarization of an electrode immersed in a symmetric binary electrolyte and subjected to a small external ac voltage is revisited. The Nernst-Planck equations are simplified to the Debye-Falkenhagen equation, which is solved together with the Poisson equation, leading to analytical formulas for the space charge density and impedance of the system for two parallel plate electrodes. We then define a limit of thin electrical double layer and illustrate the emergence of the characteristic time scale, τ = λ/, a function of the Debye length, λ, the electrode separation distance, , and the ionic diffusion coefficient . Normalizing the impedance magnitude with the solution resistance and making the frequency dimensionless with the τ, we show that all analytical, numerical, and experimental data for different solution conductivities and electrode separation distances collapse onto a single curve. To account for the Stern layer effects, we conducted numerical simulations based on the modified Poisson-Nernst-Planck model and showed that the results agree with our analytical solution for a range of concentrations, with small discrepancies observed only above 0.1 M. Based on the proposed model, experimental impedance spectroscopy results at ac potentials can be used to obtain detailed knowledge of the corresponding surface (and space) charge densities on the electrodes.
重新审视了将浸入对称二元电解质中并施加小外部交流电压的电极极化的经典电化学问题。能斯特 - 普朗克方程被简化为德拜 - 法尔肯哈根方程，该方程与泊松方程一起求解，得到了两个平行板电极系统的空间电荷密度和阻抗的解析公式。然后，我们定义了薄双电层的极限，并说明了特征时间尺度(\tau = \lambda / v)的出现，它是德拜长度(\lambda)、电极间距(v)和离子扩散系数(v)的函数。用溶液电阻对阻抗幅值进行归一化，并使频率与(\tau)无量纲化，我们表明，对于不同的溶液电导率和电极间距，所有的解析、数值和实验数据都汇聚到一条单一曲线上。为了考虑斯特恩层效应，我们基于修正的泊松 - 能斯特 - 普朗克模型进行了数值模拟，结果表明，在一定浓度范围内，结果与我们的解析解一致，仅在浓度高于(0.1 M)时观察到小的差异。基于所提出的模型，交流电位下的实验阻抗谱结果可用于获取电极上相应表面（和空间）电荷密度的详细信息。
