Compact and diffuse double layer interaction in unsupported system small-signal response

Previous exact results for the small-signal impedance of an unsupported electrode/material/electrode system which include effects of the finite size of charge carriers are simplified and discussed. The material contains non-recombining charges of opposite sign with the positive one immobile and uniformly distributed. General boundary conditions which encompass the range from no electrode reaction to ohmic electrode behavior are employed. In the presence of an electrode reaction, the interaction of the compact and diffuse double layers leads to considerably more complexity in the equivalent circuit than might appear in simple treatments of the supported case, in which the diffuse double layer capacitance is neglected or the compact double layer and diffuse double layer capacitances are placed in series. Two different approximate equivalent circuits made up of frequency-independent elements are found which yield remarkable agreement with the exact results over the entire frequency range of interest. The first involves the ordinary approximate circuit (OAC) previously found in the absence of compact layer effects plus a series compact layer contribution involving a parallel resonant circuit with quality factor at resonance which may approach unity. Pseudo-inductance effects are found to be extremely significant in this representation. The second approximate equivalent circuit, simpler and almost as accurate as the first, has the same form as the original OAC but with its reaction element values altered by the presence of the compact layer. For non-Butler-Volmer electrode kinetics an upper limit is found for the experimentally determinable apparent reaction rate constant, a feature of practical importance for thin films or membranes. The response of thin films and membranes, including compact layer effects, can very readily be erroneously confused with pure bulk response, yielding entirely incorrect values for the geometrical capacitance and bulk resistance of the material.     

Deviations of capacitive and inductive loops in the electrochemical impedance of a dissolving iron electrode.

The electrochemical impedance of an iron electrode often shows the capacitive and inductive loops on the complex plane. The capacitive loop originates from the time constant of the charge transfer resistance and the electric double layer capacitance. The inductive loop is explained by Faradaic processes involving the reaction intermediate. In some cases, these loops deviate from a true semicircle. In this paper, the origins and curve-fitting methods for the deviated loops of electrochemical impedance are discussed. The constant phase element (CPE) was used to present the deviation of the capacitive loop instead of electric double layer capacitance. The reaction rate constants, which are a function of the frequency, are proposed for the Faradaic impedance to present the deviated inductive loop.     

Microelectrode Combinations of Gold and Polypyrrole Enable Highly Stable Two-electrode Electrochemical Impedance Spectroscopy Measurements under Turbulent Flow Conditions

An electrochemical impedance spectroscopy (EIS) sensor design is proposed based on a standard interdigitated electrode layout in which the smaller working electrode consists of gold (Au) whereas the larger combined counter and reference electrode is coated with a porous layer of polypyrrole (PPy) doped with polystyrene sulfonate (PSS) (PPy : PSS). Each electrode material was first characterized by EIS in a standard 3-electrode setup with subsequent spectra fitting by a modified Randles equivalent circuit. The differences in the spectra obtained by the PPy : PSS coated electrodes can be explained by an increased electroactive surface area due to the porous polymer film. The changes in morphology of the film are discussed with respect to the evolution of the elements of the electric equivalent circuit. When applying the Au/PPy : PSS electrode combination to a standard 2-electrode arrangement, the enlarged highly electroactive surface area of the PPy : PSS coating lowers the interfacial impedance in a way that mainly the gold working electrode contributes to the overall system impedance. Therefore, obtaining reproducible EIS signals depends only on the electrode's open-circuit potential (OCP) and on additional adsorption events at the gold electrode/electrolyte interface. We present a protocol for microelectrode coating with PPy : PSS, which enables highly stable 2-electrode EIS experiments without the need of a reference electrode. This combination is believed to be very useful if an integration of sensing electrodes inside Micro Total Analysis Systems is aspired.     

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。     

Electrochemical impedance of passive iron in sulfuric acid water-organic solutions

The passive state of iron in sulfuric acid solutions in dimethylformamide and dimethyl sulfoxide containing different amounts of water is studied by the impedance method in a wide range of ac frequencies and also by the methods of polarization curves and open-circuit potential transients. In the studied systems, the metal passivation potential is shown to shift in the positive direction with a decrease in the water content in the solvent. The open-circuit potential of the destruction of the passive layer (Flade potential) is independent both of the nature of the solvents and the water amount in them. The impedance characteristics of passive iron can adequately be modeled by an equivalent circuit consisting of two parallelR-C circuits, i.e. similarly to a circuit used earlier for modeling the impedance of a passive Fe electrode in neutral aqueous solutions. The physical meaning of the equivalent-circuit elements calculated from the impedance measurements is analyzed. The effects the electrode potential, the organic-solvent type, the water content in the latter, etc. have on the elements are discussed. The obtained results suggest that the potential difference applied to the interface between passive iron and studied solutions is located mainly in the Helmholtz layer. Dedicated to the ninetieth anniversary of Ya.M. Kolotyrkin’s birth.     

Electrochemical impedance spectroscopy analysis of chalcopyrite CuFeS2 electrodes

A chalcopyrite CuFeS₂ electrode obtained from the “El Teniente” mine has been studied by Electrochemical Impedance Spectroscopy (EIS) in an alkaline solution for different oxidation potentials. The experimental results can be interpreted from a Randles equivalent circuit, V_dc<0.4 V vs. saturated calomel electrode (SCE), and a surface layer model for V_dc>0.4 V vs. SCE. From these results, the variation with the d.c. applied potentials of charge transfer electrical resistance of the redox reaction, the double layer capacitance and other characteristic parameters are considered.     

Impedance of Indium(III) Hexacyanoferrate Films: Effect of the Supporting-Electrolyte Cation

Films of indium(III) hexacyanoferrate are studied in nitrate solutions of lithium, sodium, potassium, and ammonium using cyclic voltammetry and faradaic impedance. Effect of the supporting-electrolyte cation on parameters of the equivalent circuit corresponding to the impedance spectra is analyzed. The charge transport at the electrode/film interface is shown to be slow. The cation bonding in a film is discussed.     

A Gerischer phase element in the impedance diagram of the polymer electrolyte membrane fuel cell anode

We study the isothermal hydrogen adsorption and reaction at the E-TEK electrode of a polymer electrolyte fuel cell with a Nafion 117 membrane by impedance spectroscopy at 30 degrees C. We find that the impedance diagram must include a Gerischer phase element. Constant phase elements are not sufficient to describe the experimental data. This means that an adsorption reaction takes place in combination with surface diffusion of hydrogen in the carbon layer located before the platinum surface, separate from the charge transfer step at the platinum particle surface. We are not able to distinguish between molecular or atomic hydrogen diffusion on carbon. We predict and find that the relaxation time of the adsorption step is independent of the applied potential. Water may also enter rate-limiting steps in the electrode reaction, but its role needs further clarification.     

Influence of nanoporous carbon electrode thickness on the electrochemical characteristics of a nanoporous carbon|tetraethylammonium tetrafluoroborate in acetonitrile solution interface

Electrochemical characteristics for the nanoporous carbon|Et₄NBF₄+acetonitrile interface have been studied by cyclic voltammetry and impedance spectroscopy methods. The influence of the electrolyte concentration and thickness of the nanoporous electrode material on the shape of the cyclic voltammetry and impedance curves has been established and the reasons for these phenomena are discussed. A value of zero charge potential, depending slightly on the structure and concentration of the electrolyte, the region of ideal polarizability and other characteristics have been established. The nanoporous nature of the carbon electrodes introduces a distribution of resistive and capacitive elements, giving rise to complicated electrochemical behaviour. Analysis of the complex plane plots shows that the nanoporous carbon|Et₄NBF₄+acetonitrile electrolyte interface can be simulated by an equivalent circuit, in which two parallel conduction paths in the solid and liquid phases are interconnected by the double-layer capacitance in parallel with the complex admittance of the hindered reaction of the charge transfer or of the partial charge transfer (i.e. adsorption stage limited) process. The values of the characteristic frequency depend on the electrolyte concentration and electrode potential, i.e. on the nature of the ions adsorbed at the surface of the nanoporous carbon electrode. The value of the solid state phase resistance established is independent of the thickness of the electrode material.     

普鲁士蓝膜修饰电极的电化学阻抗谱

测量了应用电化学方法制备的不同厚度的普鲁士蓝膜修饰电极的循环伏安行为与电化学阻抗谱.由所得到的循环伏安图讨论了普鲁士蓝修饰膜的氧化还原过程,并对相关的Nyquist图进行了解析,提出了相应的等效电路.在此基础上计算出较薄膜中普鲁士蓝/普鲁士白电化学反应的表观速率常数和表观扩散系数,讨论了膜厚度对电荷扩散的影响.当膜相对较薄时,电极过程主要由动力学过程控制;当膜达到一定厚度时,电荷在膜中的扩散速率受到限制,电极过程由动力学过程和电荷扩散过程共同控制,证实了文献报导的普鲁士蓝膜修饰电极为多层空间分布电荷传递模型.     

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.     

Electrochemical properties of nanoporous carbon electrodes in various nonaqueous electrolytes

Electrical double layer and electrochemical characteristics at the nanoporous carbon|acetonitrile interface with additions of Et₄NBF₄, Et₃MeNBF₄, EtMe₃NBF₄, LiClO₄, and LiBF₄ have been studied by cyclic voltammetry and impedance spectroscopy methods. A value of zero charge potential, dependent on the structure of the cations as well as on the composition of the anions, the region of ideal polarizability, and other characteristics has been established. Analysis of the complex plane plots shows that the nanoporous carbon|acetonitrile+0.1 M electrolyte (Et₄NBF₄, Et₃MeNBF₄, or EtMe₃NBF₄) interface can be simulated by the equivalent circuit, in which the two parallel conduction parts in the solid and liquid phases are interconnected by the double layer capacitance in parallel with the complex admittance of the hindered reaction of the charge transfer process or of the partial charge transfer (i.e. adsorption stage limited) process. The values of the characteristic frequency depend on the electrolyte composition and on the electrode potential, i.e. on the nature of the ions adsorbed at the surface of the nanoporous carbon electrode. In the region of moderate a.c. frequencies, the modified Randles-like equivalent circuit has been used for simulation of the complex plane plots. In the region of negative surface charge densities, the intercalation process of Li⁺ ions from LiClO₄ and LiBF₄ solutions into the surface film is possible and these data can be simulated using the modified Ho et al. model or Meyer et al. model. Electronic Publication     

Impedance studies of porous lanthanum-phosphate-bonded nickel electrodes in concentrated sodium hydroxide solution

The hydrogen evolution reaction (HER) was investigated on a lanthanum-phosphate-bonded nickel (LPBN) powder electrode in 30 wt.% NaOH at 70°C using ac impedance and steady-state polarization techniques. Circuits containing one or two constant-phase elements (CPEs) in parallel with a resistance and corresponding to fractal and porous electrode models were tested in order to interpret the ac impedance data. The experimental impedance spectra were well described by the porous electrode model and the circuit containing two CPEs. The results obtained from the ac impedance and steady-state measurements allowed the mechanism and kinetics of the HER to be evaluated. Comparison of these parameters with those obtained on the polycrystalline nickel electrode in 1 M alkaline solution at 25°C indicates that an increase in activity is principally due to an increase in the real surface area.     

Effect of Temperature on the Impedance of a Lithium/Nonaqueous Solution Interface

Impedance of a lithium electrode in a lithium perchlorate solution in a propylene carbonate + dimethoxyethane mixed solvent is measured at 0.1–200 kHz and 0–55°C. The impedance is determined by electrical processes occurring in the passive solid-electrolyte film on the lithium surface. The temperature dependences of parameters of the equivalent circuit related to the passive film are described by Arrhenius-type exponential functions. The activation energies for the conduction and diffusion and the energy of formation of mobile charge carriers in the solid-electrolyte layer are determined.     

热处理碳纸电极上VO2+/VO+2氧化还原动力学

在不同温度下热氧化处理碳纸, 用循环伏安、极化曲线和交流阻抗方法研究碳纸电极上VO2+/VO+2氧化还原动力学. 循环伏安和极化曲线结果表明, 随着热处理温度的升高, VO2+/VO+2氧化还原反应的速率常数及交换电流增大. 建立了VO2+/VO+2氧化还原反应的交流阻抗等效电路模型. 拟合结果表明, 热处理增大了碳纸电极表面的双电层电容, 减小了VO2+/VO+2氧化还原反应的电荷转移电阻. 用循环伏安和交流阻抗两种方法求得的VO2+和VO+2的扩散系数基本相同, 表明所构建的交流阻抗等效电路模型与电极反应过程相符合.     

Electrochemical Impedance Spectroscopy in the Characterisation and Application of Modified Electrodes for Electrochemical Sensors and Biosensors

Electrochemical impedance spectroscopy is finding increasing use in electrochemical sensors and biosensors, both in their characterisation, including during successive phases of sensor construction, and in application as a quantitative determination technique. Much of the published work continues to make little use of all the information that can be furnished by full physical modelling and analysis of the impedance spectra, and thus does not throw more than a superficial light on the processes occurring. Analysis is often restricted to estimating values of charge transfer resistances without interpretation and ignoring other electrical equivalent circuit components. In this article, the important basics of electrochemical impedance for electrochemical sensors and biosensors are presented, focussing on the necessary electrical circuit elements. This is followed by examples of its use in characterisation and in electroanalytical applications, at the same time demonstrating how fuller use can be made of the information obtained from complete modelling and analysis of the data in the spectra, the values of the circuit components and their physical meaning. The future outlook for electrochemical impedance in the sensing field is discussed.     

La0.8Sr0.2MnO3／YSZ高温电极交流阻抗研究

用交流阻抗方法研究了Ｌａ０．８Ｓｒ０．２ＭｎＯ３电极上进行的氧化电化学还原反应。实验表明反应速度控制步骤随反应温度，氧分压及过电位发生显著变化，近平衡下反应的ｒｄｓ为氧的解离吸附过程。强阳极极化下，电解质表面产生大量电子空穴；强阴极极化下，ＬＳＭ电极表面形成大量氧空位，二者的结果均使界面电导增加，电化学反应区扩展。     

Protective Properties of Zinc-Rich Coatings: An Impedance Method Estimate

The impedance of zinc-rich polymer coatings on steel in a 3-% NaCl solution is studied. The electrochemical behavior of the electrode is satisfactorily described by an equivalent circuit that contains a constant-phase element, which reflects fractal properties of the zinc surface in the binder. From the results of calculations of the circuit elements for metal-rich electrodes with different zinc contents computed are fractions of the active area of the surface of the coating and its fractal dimensionality.     

对表面有膜层的金属电极阻抗半圆旋转的物理意义的探讨

提出了交流阻抗半圆旋转的介质损耗物理模型, 推导出由阻抗旋转半圆计算等效电路参数值的方法, 并推广到一般情况。     

硬脂酸二茂铁酯L-B膜修饰SnO2电极的阻抗研究

测定了二茂铁衍生物——硬脂酸二茂铁酯L-B膜修饰SnO₂电极在Fe(CN)₆^3-/4-溶液中的阻抗性能,用单纯形法求出了等效电路中的元件参数值,计算了电极反应速度常数K_s。从分析SnO₂电极修饰不同层的硬脂酸二茂铁酯L-B膜的界面阻抗和电极反应的动力学性能,表明与在固相中研究的硬脂酸二茂铁酯L-B膜的阻抗性能明显不同,在Fe(CN)₆^3-/4-溶液中表现了电活性分子修饰电极的界面阻抗行为,进一步证实了修饰在SnO₂电极上的硬脂酸二茂铁酯L-B膜在Fe(CN)₆^3-/4-的氧化还原电极反应过程中,起电荷传递的中介作用。