The effect of mass transfer on electrochemical impedance of a solid oxide fuel cell anode

This paper presents electrochemical impedance simulation of a solid oxide fuel cell (SOFC) anode in order to investigate the effect of mass transport processes on the impedance spectra. The current model takes in to account the gas-phase transport processes both in the gas channel and within the porous electrode and couples the gas transport processes with the electrochemical kinetics. The impedance simulation is carried out in time domain, and the correlation between the anode harmonic responses to the sinusoidal excitation and the impedance spectra is analyzed. In order to solve the system of non-linear equations, an in-house code based on the finite difference method is developed and utilized. Results show a depressed semicircle in the Nyquist plot, which originates from gas transport processes in the gas channel, in addition to a Warburg diffusion impedance originates from gas transport in the thick porous anode. The influence of parameters such as electrode thickness, inlet gas composition, and temperature is also investigated and the results are discussed. The simulation results are in good agreement with published data.     

玻碳电极界面的阻抗谱数学表达及定量分析

玻碳电极（GCE）是各类电化学传感器常用的基础电极,其界面特征直接影响检测性能。本文详细考察了电极体系的电化学过程,针对GCE传感界面,探讨了一个等效电路中电解质电阻、电荷输运电阻、扩散阻抗、电化学（氧化/还原）反应阻抗、表面吸附阻抗和双电层电容等电学元件的物理意义,并给出了对应的数学模型。通过改变模型中5个参数值,模拟了不同状态下的阻抗谱,分析了电极系统各参数对GCE阻抗谱的贡献规律。最后,采用该数学模型对裸GCE和修饰GCE在铁氰化钾溶液中的阻抗谱进行分析,拟合结果与实验数据吻合度高;基于拟合获得参数,定量对比分析了修饰前后电极表面的特征变化。     

Small-signal ac response theory for systems exhibiting diffusion and trapping of an electroactive species

A theoretical expression is derived for the interfacial admittance of an electrochemical system in which a product species diffuses into (or along internal surfaces of) an electrode subject to reversible trapping at one or more types of stationary sites in the electrode. The admittance obtained in a generalization of earlier results for diffusion without trapping and is exactly representable by an equivalent electrical circuit involving a lossy transmission line. Representative numerical data are given for the impedance of this distributed element. Trapping effects are found to be significant primarily when the number of trapped atoms is comparable to the number of mobile atoms. The results obtained may therefore be of greatest interest in the case of polycrystalline or amorphous electrodes.     

铜在低电导溶液中扩散机理的研究

双水内冷发电机空芯铜导线的腐蚀问题直接影响到火电厂发电机的安全经济运行．其腐蚀体系为纯铜和低电导水溶液（pH＝7．3，空气饱和，电导率＜10μS·cm－1）．我们已经用交流阻抗法对该体系进行了一些研究．由于该体系溶液电导率低，在交流阻抗谱的高频区出现高频半圆；低频区为一条文于实轴Z约45°的直线（不加缓蚀剂时）．如果在该体系中MABTA、MBT等缓蚀剂，低频区直线变为半圆．所以，低频区的阻抗代表了电极表面的特征，而高频区（如10k～100kHz范围）半圆是由于参比回路（包括参比电极、盐桥、鲁金毛细管等）中存在太大的电阻…     

Hydrogen transport through Pd-Ni alloy electrodeposited on Pd substrate

Hydrogen transport through a Pd-Ni alloy electrodeposited on a Pd substrate (Pd-Ni/Pd bilayer symmetric electrode) has been investigated using cyclic voltammetry and a.c. impedance spectroscopy combined with the electrochemical hydrogen permeation method. The permeation build-up current transients and the measured impedance spectra were analyzed using the time-lag method for the bilayer electrode and a complex non-linear least squares data-fitting method based upon the derived Faradaic admittance for the hydrogen absorption into and diffusion through the bilayer electrode under the permeable boundary condition, respectively. The value of the hydrogen diffusivity in the Pd-Ni layer was lower than that in the Pd layer. Furthermore, the values of the charge transfer resistance and equilibrium absorption constant for the Pd-Ni/Pd bilayer electrode were higher than those for the Pd single layer electrode. From the experimental results, the role of the thin Ni(OH)₂ film formed on the Pd-Ni layer surface in the hydrogen transport through the Pd-Ni/Pd bilayer electrode is discussed in terms of its passivating effect and extremely large hydrogen solubility. Received: 22 January 1997 / Accepted: 15 April 1997     

Convective-diffusion impedance for a partially blocked rotating-disc electrode

For a partially blocked electrode, the attenuation factor ρ of the diffusion admittance is defined. Its zero-frequency limit coincides with the corresponding steady-state factor for the diffusion limiting current. Calculation of ρ as a function of the frequency and the surface-coverage parameters were performed by the finite-element method using semi-analytical expressions derived from a transient mass-transport equation inspired by the Levich model of a RDE. Comparison between values of ρ so calculated and those drawn from impedance measurements on model electrodes is satisfactory; divergences observed at low and intermediate frequencies are explained by a contribution of the liquid velocity components parallel to the surface, which are neglected in this theory.     

Electrochemical behavior of europium perovskites (Ca<Subscript>0.6</Subscript>Eu<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript>) in alkaline aqueous media

In this paper, the electrochemical behavior of europium perovskites (Ca_0.6Eu_0.4MnO₃) prepared by a gel combustion method followed by a thermal treatment performed at 1073 and 1473 K is compared with the pristine oxide CaMnO₃ (T = 1073 K) obtained by the same method. The experiments were performed in alkaline aqueous media via open-circuit potential, cyclic voltammetry, chronopotentiometry, and impedance spectroscopy. The data show that the electrode roughness is inversely proportional to the oxide particle size. The chronopotentiometric curves show also that the presence of europium is advantageous due to the increase of the electrode roughness for the oxides formed at the same temperature (1073 K) or by increasing the charge per unit area for the oxide formed at 1473 K. The impedance spectra, which were obtained in the capacitive behavior domain, reflect the porous morphology of the electrode surfaces according to the theory developed by Levie. This feature is particularly evident for the electrodes with an average particle diameter of 90 and 60 nm, corresponding respectively to the oxides CaMnO₃ and Ca_0.6Eu_0.4MnO₃, both formed at 1073 K.     

Lithium ion phase-transfer reaction at the interface between the lithium manganese oxide electrode and the nonaqueous electrolyte

The lithium ion phase-transfer reaction between the spinel lithium manganese oxide electrode and a nonaqueous electrolyte was investigated by the ac impedance spectroscopic method. The dependence of the impedance spectra on the electrochemical potential of the lithium ion in the electrode, the lithium salt concentration in the electrolyte, the kind of solvent, and the measured temperature were examined. Nyquist plots, obtained from the impedance measurements, consist of two semicircles for high and medium frequency and warburg impedance for low frequency, indicating that the reaction process of two main steps for high and medium frequency obey the Butler-Volmer type equation and could be related to the charge-transfer reaction process accompanied with lithium ion phase-transfer at the interface. The dependency on the solvent suggests that both steps in the lithium ion phase-transfer at the electrode/electrolyte interface include the desolvation process and have high activation barriers.     

The effect of partial charge transfer on the electrochemical turbulent noise

Theoretical analysis of the effect of electrode potential on the spectral density of random alternating current emerged in electrochemical cell under the action of turbulent pulsations of the electrolyte solution velocity is carried out. An impedance model of metal electrode dissolution reaction, including two adsorption stages, is suggested, with allowance for the oxidized ion diffusion in electrolyte solution. It is known that in terms of the Ershler-Randles model, at low frequencies the experimentally measured slope of bilogarithmic frequency dependence of spectral density equals 3, which is characteristic of the diffusion control; at high frequencies the slope equals 4, which is characteristic of the kinetic control. It is shown that for the model of impedance of the two-stage adsorption oxidation process, in the middle segment of the spectrum the local slope must decrease down to 2, provided the first oxidation stage, which proceeds within the inner electrical double layer, is slow; the local slope must increase up to 6 (or 5, for diffusion control), provided the second oxidation stage (the partially oxidized ion desorption to solution) is slow. The “height” and “width” of the slope local changes appeared explicitly depending on the parameters of the partial charge transfer. This makes the turbulent noise method somewhat superior to the impedance method in the studying of the above-specified reaction type.     

Specific features of the behavior of an electrochemical system in the case of the Hopf instability for a spherical electrode

Model approximations are developed that allow establishing a quantitative relationship between the geometrical parameters of a spherical electrode, the faradaic impedance, and instabilities of the electrochemical system for an electrode reaction under potentiostatic conditions for the adsorption of species preceding their discharge. It is shown that the control parameter ω_H in the Hopf bifurcation point depends on the electrode size. The effect of the Nernst diffusion layer is observed at low frequencies in the range of negative faradaic impedance values.     

Pd/Mm(富铈稀土)薄膜电极在KOH溶液中的电化学行为

利用磁控溅射法制备了Pd/Mm(Mischmetal)混合稀土薄膜,采用X射线衍射、AFM及循环伏安和交流阻抗谱等电化学测试技术研究了Pd/Mm稀土薄膜的晶体结构、表面形貌及其在KOH溶液中的电化学行为.结果表明,Pd/Mm薄膜表面的Pd层由纳米级的孤岛状颗粒构成,颗粒大小为100～200 nm.循环伏安法研究表明,氢的电化学氧化和还原均通过表面Pd金属层进行.Pd/Mm稀土薄膜电极的交流阻抗图由两个容抗弧组成,低频区的容抗弧对应氢在电极中的固态扩散过程,而高频段的容抗弧对应氢在电极表面的电化学还原过程,其中氢在薄膜电极内部的扩散是速率控制步骤.     

钡添加剂对二次碱性锌电极性能的影响

采用直接化学合成法制备以钡作添加剂的二次碱性锌电极活性物质,样品的表面形貌及其晶态结构由SEM和XRD表征,并以循环伏安、充放电循环及电化学阻抗谱测定样品的电化学性能.实验表明,锌电极因Ba的添加而生成一种化学式为BaZn(OH)4·xH2O的锌酸钡,改善了电极的电化学性能.此外发现,Zn电极的电化学阻抗谱含有一个对应于电极表面放电产物覆盖率的时间常数.     

Fluoride electrode with LaF(3)-membrane and simple disjoining solid-state internal contact

Fluoride-selective electrode with LaF(3)-membrane and stainless steel internal contact has been prepared. The electrode has been tested in F(-) concentration range 10(-2)-10(-6) M and the results compared with those of commercial electrode and electrode with laboratory renewed internal electrolytic contact. The properties of simple disjoining solid-state contact have been investigated by means of electrochemical impedance spectroscopy (EIS). The impedance spectra show two time constants, which suggest that, at lower frequencies, proceed some Faradic reaction which probably stabilizes the potential between LaF(3)-membrane and stainless steel disk.     

多壁纳米碳管空气电极的交流阻抗研究

研究了多壁纳米碳管、活性炭和石墨等空气电极的交流阻抗特性.结果表明,纳米碳管空气电极的阻抗谱由两个半圆组成,高频区半圆对应欧姆极化阻抗,低频区半圆对应电化学极化阻抗.催化剂Pt以纳米颗粒的形式沉积在碳管的外表面,明显减小了电极的欧姆阻抗和电化学极化阻抗,提高了氧还原反应的电催化活性.活性炭电极除存在电化学阻抗外,还存在薄液膜扩散阻抗(Nernst扩散),石墨电极形成的薄液膜反应区域较小,电极反应呈Warburg扩散阻抗特征,相应的电催化活性较低.采用交流阻抗等效电路分析方法,对拟合的动力学数据进行了解释.     

Gas diffusion hindrances on Ni cermet anode in contact with Zr<Subscript>0.84</Subscript>Y<Subscript>0.16</Subscript>O<Subscript>1.92</Subscript> solid electrolyte

The electrochemical behavior of Ni cermet electrode with CeO_{2 ? x} additive in contact with YSZ electrode was studied by means of impedance spectroscopy in H₂, H₂O, CO₂, CO, He, and Ar gas media of various composition within the temperature range of 700 to 950°C. Near the equilibrium potential, the electrochemical impedance spectra of the studied electrodes indicate to three stages of electrode reaction. The polarization conductivity of the low-frequency stage of electrode reaction (σ_lf) is characterized with the following regularities: (a) temperature dependence of σ_lf has a positive slope in Arrhenius coordinates; (b) σ_lf increases upon replacement of gas mixture with lower mutual diffusion coefficient by mixture with higher mutual diffusion coefficient, while polarization conductivity values of other stages remain practically invariable; (c) concentration relationships of 1/σ_lfrecorded for constant activity of oxygen in the gas phase are linear in the 1/σ_lf vs. 1/P _{CO 2} (P _CO) coordinates; (d) no low-frequency stage of the electrode reaction is observed upon electrochemical inflow (outflow) of the gas reagents (reaction products) to (from) the test electrodes (current passing through closely pressed specimens and central specimen impedance measurement); and (e) no change in the gas flow rate affects σ_lf value. The observed regularities were explained by assuming the gas diffusion nature of the low-frequency stage of the electrode reaction. The gas diffusion layer thickness was estimated.     

定向多壁碳纳米管电化学储氢研究

利用恒流充放电、循环伏安曲线(CV)和电化学阻抗技术(EIS)等方法对定向多壁碳纳米管(AMWCNTs)储氢的电化学行为及其储氢机制进行了探讨.研究表明,定向AMWCNTs-Cu电极有较高的电化学储氢性能,其储氢容量在1500mA/g的电流密度下可以达到1162mA·h/g.定向AMWCNTs的电化学储氢能力强与其空间结构有关,而铜粉的加入有利于提高碳纳米管的电催化反应表面积和电极电化学反应活性,有利于氢在碳纳米管中扩散,从而提高了碳纳米管电极材料的储氢量.     

Couple axial gradients of potential and concentration in a cylindrical pore electrode: an impedance model

The impedance of a cylindrical pore electrode in the case where the potential gradient due to the electrolyte resistivity is coupled to the axial concentration gradient of reacting species has been calculated semi-analytically from the approximate solution reported previously for the steady-state concentration and current profiles in the pore. Complex plane impedance plots, computed by an iteration technique for the transmission line, indicate: (i) a quasi-semi-circular diffusion loop at low frequencies due to diffusion control; and (ii) a high frequency loop in which the frequency dispersion is strongly dependent on the electrode parameters (electrolyte resistivity, diffusion coefficient of the reacting species, pore depth, Tafel coefficient of the electrochemical reaction and overall current flowing through the pore).     

Impedance simulation of a solid oxide fuel cell anode in time domain

The purpose of the current study is to simulate the behavior of a solid oxide fuel cell (SOFC) anode under sinusoidal excitation. The obtained harmonic response is used as a base for electrochemical impedance spectra simulation. The electrochemical impedance spectroscopy (EIS) is a powerful non-destructive tool for SOFC researches. In order to evaluate the EIS experimental results, efforts are devoted to develop EIS numerical simulation tools. In this study, a planar SOFC is modeled, and the steady state behavior and frequency response, as well as the electrochemical spectra of the anode, are obtained. The developed model couples the electrochemical kinetics with mass transport. The Butler–Volmer equation is used for the anode electrochemistry, and the species equations are used for gas transport in the anode channel. In order to solve the system of the nonlinear equations, an in-house code based on finite difference method is developed and utilized. A parametric study is also carried out, and the results are discussed. The simulation results are in good agreement with published data. Results show a capacitive semicircle in the Nyquist plot, which is identical to the gas diffusion impedance as reported in literatures.     

Characterization of Electrode/Electrolyte Interface of ECIS Devices

Electric cell‐substrate impedance sensing requires low electrode/electrolyte interface impedance for effective biomedical and biophysical applications. Thus a complete understanding of physical processes involved in the formation of an electric double layer is required to design a low interface impedance device. This paper presents the numerical simulation of the impedance for the electrode/electrolyte interface of three‐electrode devices along with the practical realization for the effective workout of impedance sensing devices. The three‐electrode based impedance sensing devices along with phosphate buffered saline as electrolyte is simulated using COMSOL Multiphysics to evaluate the impedance of the electrode/electrolyte interface. Microfabrication technology is used to realize three‐electrode impedance sensing devices with diverse configuration which are used to measure the electrode/electrolyte interface impedance. The measured impedance data were then compared with the COMSOL simulated results and it is found that both the data sets fitted well with less than 5 % RSE. The results obtained from simulation and experiments indicate that the impedance due to double layer diffusion dominates in the low frequency region up to few kHz whereas electrolytic bulk resistance plays a major role in the higher frequency range. The experimental impedance data were further interpreted by electrochemical impedance spectroscopy analysis software to model the equivalent circuit of the electrochemical system.     

Impedance of metal hydride electrodes. Rate of phase transformation limited by nucleation and growth mechanisms

A mathematical model for the electrochemical impedance spectroscopy of a metal hydride electrode was developed. Ac impedance data of phase transformation were derived by considering a nucleation and growth mechanism based on the theory developed by Johnson–Mehl–Avramy. Different mechanisms such as grain edge and grain boundary preferential nucleation sites are discussed. Global Nyquist plots of the metal hydride electrode are obtained by adding a surface charge transfer reaction and a double-layer capacitance to the model.