Relaxation spectra of the electrode impedance

A new analytical form is proposed enabling one to calculate the impedance of systems that contain no inductances. The method is based on breaking the overall impedance into a sum of isolated contours corresponding to a set of intrinsic frequencies of the system. Intrinsic frequencies, which exist in any real system, can be uniquely determined from the frequency characteristics. In this, they advantageously differ from speculative elements of equivalent circuits. For inductionless circuits, sets of intrinsic frequencies are replaced by intrinsic sets of reciprocal relaxation times. This allows one to construct a relaxation spectrum for the system, which describes quantitative contributions made by each relaxation contour to the overall impedance. As a result, one can estimate quantitatively conditions under which the system’s individual parameters may be observed, evaluate the resolving power of the experimental setup, and determine the full information capacity of an experiment (the maximum number of system’s parameters that can be determined).     

Electrical impedance spectroscopy study of piezoelectric PVDF membranes

Piezoelectric poly (vinylidene fluoride) (PVDF) membranes were prepared from pre-fabricated membranes by electrically poling in an intense electric field. The electrical impedance of PVDF membranes measured over a frequency range of 10^?2–10⁵ Hz before and after poling is presented. The effect of pressure on the impedance characteristics of un-poled and poled PVDF membranes was also studied. A four element model circuit, including a constant phase element (CPE) was fitted to the impedance spectra. The elements of the circuit fitted to the poled sample were more conductive compared with those of the un-poled sample. Stronger CPE elements in the circuit were detected in the poled samples under pressure suggesting that the piezoelectric activity of PVDF is the major contributor to the constant phase angle seen at low frequencies.     

Electric and dielectric behavior of copper-chromium layered double hydroxide intercalated with dodecyl sulfate anions using impedance spectroscopy

The Cu₂Cr-DS-LDH hybrid was successfully prepared by the anion exchange method at room temperature. The structure, the chemical composition and the physico-chemical properties of the sample were determined using powder X-ray diffraction (PXRD), Fourier transform infrared spectroscopy (FT-IR), thermogravimetric analysis (TGA) and inductively coupled plasma (ICP). In this work, the electrical and dielectric properties investigated are determined using impedance spectroscopy (IS) in a frequency range of 1 Hz to 1 MHz. Indeed, the Nyquist diagram modelized by an electrical equivalent circuit showed three contributions attributed respectively to the polarization of grains, grains boundaries and interface electrode-sample. This modelization allowed us to determine the intrinsic electrical parameters of the hybrid (resistance, pseudo-capacitance and relaxation time). The presence of the non-Debye relaxation phenomena was confirmed by the frequency analysis of impedance. Moreover, the evolution of the alternating current conductivity (σ_ac) studied obeys the double power law of Jonscher. The ionic conduction of this material was generated through a jump movement by translation of the charge carriers. As for the dielectric behavior of the material, the evolution of dielectric constant as a function of frequency shows relatively high values in a frequency range between 10 Hz and 1 KHz. The low values of the loss tangent obtained in this frequency zone can valorize this LDH hybrid.     

Dielectric Dispersion and Electric Relaxation Processes Induced by Ionic Conduction in Formamide, 2-Aminoethanol and Their Binary Mixtures

The complex dielectric permittivity, ionic conductivity, electric modulus and impedance spectra of the dipolar molecules formamide (FA), 2-aminoethanol (AE) and their binary mixtures were investigated in the frequency range from 20 Hz to 1 MHz at 303.15 K. Debye-type distributions of the frequency dependent electric modulus and complex impedance were found, corresponding to an ionic conduction relaxation process in the upper frequency regime of the spectra, whereas a spike in the impedance spectra at low frequencies confirms the contribution of an electrode polarization (EP) relaxation process induced by ionic conduction. Due to the high static permittivity of FA, its ionic conductivity was found more than one order of magnitude higher than that of the AE, which is also shown by the comparative values of their EP and ionic conductivity relaxation times. The dependences of dc ionic conductivity values of the binary mixtures on their relaxation times and static permittivity were explored. The concentration dependent static permittivity and the relaxation times led us to infer the formation of a 1:1 H-bonded stable complex between FA and AE molecules with reduction in the number of effective parallel-aligned dipoles.     

Electrochemical impedance spectroscopy studies of the Ag(111)/<Emphasis Type="Italic">n</Emphasis>-decanethiol monolayer/NaNO<Subscript>3</Subscript> interface

Surface properties of a modified single-crystal silver (111) face are studied in aqueous 1 M NaNO₃ solutions with different acidity in the presence of a monolayer n-decanethiol (DT) film by the methods of electrochemical impedance spectroscopy (EIS) and cyclic voltammetry that employs the meniscus contact technique. It is shown experimentally that in the potential range from 0 to −0.5 V, a DT-modified silver electrode in NaNO₃ solutions with pH 6 behaves as an ideal capacitance in a wide frequency range (from 0.01 Hz to 100 kHz). It is found that with the increase in the solution acidity up to pH 4 and 2, the region of stable capacitance characteristics narrows down. The concomitant changes in the adsorbed monolayer structure lead to deviations of impedance characteristics measured using a low-frequency ac signal from those of the ideal capacitance. A potential shift to values more negative than −0.5 V leads to the destruction of the monolayer. Based on the analysis of experimental EIS characteristics, system’s deviation from the ideal behavior that may indicate violation of the layer continuity is assessed and the relaxation frequencies of the DT/Ag(111) interface in solutions of different acidity are calculated. Estimates of capacitance, resistance, and thickness of the adsorbed monolayer are obtained as a function of the solution pH.     

Software and Instrumentational Methods of Enhancing the Resolution in Electrochemical Noise Measurements

Several methods of enhancing the signal-to-noise ratio for instrumentation designed to measure electrochemical noise are practically tested. The experiments are carried out using model RC-circuits and lielectrolyte electrochemical cells. Strong limitations in the tested objects’ impedance values are found due to the input current noise of the instrumentation, especially during the parallel connection of several channels. The advantages of a two-channel scheme for automatically compensating the instrument’s self noise are demonstrated. Different methods of lowering the dispersion of the frequency dependences of the spectral power density of electrochemical noise are compared. It is shown that averaging over segments with an overlap is the most effective method but averaging over frequencies can lead to large distortions when investigating electrochemical systems.

     

用CR传输线模型研究涂层/金属体系阻抗谱

根据CR传输线模型和QR电路之间的关系,建立了拟合其初值的计算方法,借助Z-View软件,可求得各元件精确值.根据电容（Ci）和电阻（Ri）随特征频率（f*）的分布,推导了元件相对增量与恒相位角元件（Q）指数参数n的关系. 结果表明, 当n小于0.5时,Ci比Ri增加得更快,从新的角度说明了n的物理意义及其和界面脱层之间的关系.作为应用实例,拟合了不同特征的电化学阻抗谱,分析了有机涂层/金属腐蚀体系阻抗变化的具体过程,区分了点蚀和脱层因素对阻抗谱的影响,从高阻抗体系同时得到了与不同空隙率有关的涂层电容和电阻值,并根据涂层体系的不均匀特征探讨了模型结构的物理意义.     

Non-equilibrium shear relaxation in liquids

A theory for non-equilibrium shear relaxation in liquids at low frequencies is presented. It is based on molecular considerations used in theories of low frequency depolarized light scattering.The results for the complex shear impedance contain terms in addition to those obtained by the phenomenological relaxation theory.     

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.     

Adsorption from a Layer of Finite Thickness on a Planar Electrode

Within the Nernst diffusion model, the effect the convection has on the adsorption at a planar electrode is studied for the case of a diffusion-controlled stage of adsorption and the behavior of the Frumkin–Melik–Gaikazyan finite adsorption impedance is analyzed. Allowing for the convection leads to new functional frequency dependences of constituents of this impedance at low frequencies, where the active constituent depends on the diffusion layer thickness more heavily than the capacitive one. During adsorption of neutral molecules from a layer of finite thickness, an additional relaxation time emerges in an electrochemical system, which results from a finite rate of motion of species in the near-electrode layer. Ignoring the convection may lead to erroneous interpretation of the adsorption mechanism.     

High speed multi-frequency impedance analysis of single particles in a microfluidic cytometer using maximum length sequences

A novel impedance spectroscopy technique has been developed for high speed single biological particle analysis. A microfluidic cytometer is used to measure the impedance of single micrometre sized latex particles at high speed across a range of frequencies. The setup uses a technique based on maximum length sequence (MLS) analysis, where the time-dependent response of the system is measured in the time domain and transformed into the impulse response using fast M-sequence transform (FMT). Finally fast Fourier transform (FFT) is applied to the impulse response to give the transfer-function of the system in the frequency domain. It is demonstrated that the MLS technique can give multi-frequency (broad-band) measurement in a short time period (ms). The impedance spectra of polystyrene micro-beads are measured at 512 evenly distributed frequencies over a range from 976.5625 Hz to 500 kHz. The spectral information for each bead is obtained in approximately 1 ms. Good agreement is shown between the MLS data and both circuit simulations and conventional AC single frequency measurements.     

Dielectric spectroscopy of some heteronuclear amino alcohol complexes

The temperature dependent dielectric spectroscopic properties of two heteronuclear complexes of monoethanolamine (MEA) at a wide temperature range (303-413 K) were investigated by impedance spectroscopy, in the frequency range from 100 Hz to 100 kHz. The frequency dependence of the impedance spectra plotted in the complex plane shows semi-circles. The Cole-Cole diagrams have been used to determine the molecular relaxation time, tau. The temperature dependence of tau is expressed by thermally activated process. Relaxation frequencies corresponding to the rotation of the molecules about their long axes are expected to lie above 10 MHz and exhibit Arrhenius behavior, where a single slope is observed with activation energy values equal to 0.67 and 0.78 eV. The ac conductivity sigma(ac) (omega) is found to vary as omega(s) with the index s相似文献   

外在因素对TiO2膜电极/溶液界面CPE行为的影响

电极反应过程本质上是一个界面过程,电极／溶液界面的特性对界面电子转移有决定性的影响,对于同 个电极反应,电极表面性质的不同,界面电子传递的机理就有可能不同,因此,对电极／溶液界面特性进行充分的研究,有助于揭示界面电荷转移的机理,从而有可能有效地按照我们的主观愿望去影响电机反应进行的方向和速度,研究电极／溶液界面最简单的情形是研究所谓的理想极化电极,长期以来,很多学者研究了固体电极／溶液界面的理想极化情况,并将电极／溶液界面的阻抗特性与电极表面的孔隙度、粗糙度、电极表面原子排列不均一性以及溶液的电导等相关联,其中,对电极／溶液界面的恒相位元(CPE,constant phase element）行为－－这个困惑人们多年的问题更是进行了持久、深入、细致的研究。     

Dielectric properties and frequency response of self-assembled monolayers of alkanethiols

This paper presents dielectric properties of alkanethiol self-assembled monolayers (SAMs) under an ac electric field. Using a Hg-SAM/SAM-Hg junction, we measured the ac impedance of alkanethiol SAMs using a sinusoidal perturbation of 30 mV (peak-to-peak) with frequency ranging from 1 Hz to 1 MHz at zero bias. Semicircles at higher frequencies and at middle frequencies along with Warburg lines at lower frequencies were observed in complex plane impedance plots, that is, Nyquist plots. The frequency response of SAMs was analyzed by modeling the junction using an equivalent circuit and fitting the Nyquist plots. The semicircles at higher frequencies are attributed to the effect of the SAM/SAM interfaces, and the ones at middle frequencies are attributed to the effect of alkanethiol SAMs. The comparison in the plots of the imaginary part of the impedance Z against frequency for the bare Hg electrodes (in pure ethanal) and the SAM-covered Hg electrodes (in alkanethiol solution) supports the analysis. The Warburg lines are attributed to a certain ionic impurity. The dielectric loss spectra are further analyzed. Chain-length-dependent peaks, which correspond to different relaxation mechanisms, at higher frequencies and middle frequencies were observed in the spectra of the dissipation factor (tan delta vs frequency). The peaks move to small frequency with the increase of chain length of alkanethiols. Using a correlation of peak position with the chain length, we then derived active energies of 39-99 meV for alkanethiol SAMs of C7-C18 under an ac electric field.     

Miscibility behavior of di(ethyl-2 hexyl) phthalate in binary and ternary chlorinated polymer blends

The miscibility behavior of ternary blends made by the addition of di(ethyl-2 hexyl) phthalate (DOP) to a mixture of chlorinated polymers was investigated by differential scanning calorimetry. Two chlorinated polymer mixtures were selected: polyvinyl chloride (PVC) with a chlorinated polyethylene containing 48 wt% Cl (CPE48), and PVC with a chlorinated PVC containing 67 wt% Cl (CPVC67). Each binary DOP/chlorinated polymer pair is miscible whereas PVC/CPE48 and PVC/CPVC67 blends are immiscible. DOP/CPE48/PVC and DOP/PVC/CPVC67 ternary blends containing, respectively, more than 55 and 20% DOP exhibit a single glass transition temperature (T_g). The spinodal between the one-T_g zone and the two-T_g zone is symmetrical in the two cases. At high DOP concentrations, a quantitative analysis of the results leads to the conclusion of the presence of a true ternary phase. At low DOP concentrations where two T_gs are observed, the DOP is distributed equally between the two chlorinated polymers forming, in the DOP/CPE48/PVC case for instance, two binary DOP/CPE48 and DOP/PVC phases. The broad immiscibility zone observed in the DOP/CPE48/PVC ternary blend as compared to the DOP/PVC/CPVC67 blend appears to be mainly caused by the high molecular weight of CPE48, as compared with PVC and CPVC67. © 1994 John Wiley & Sons. Inc.     

Viscoelastic behavior of an amorphous polymer under oscillations of large amplitude

The influence of periodic shear deformation and steady flow on a typical amorphous polymer is discussed. Forced sinusoidal vibrations were applied and the complex viscosity was determined. The action of a vibration of finite amplitude is equivalent to steady flow with a definite finite shear rate. Both processes cause truncation of the long-time part of the relaxation specturm. It may be accepted to a first approximation that the long-time boundary of the remaining part of the relaxation spectrum conforms to the long-time part of the initial spectrum, even if the plateau region of the spectrum is truncated. The concept of limiting truncation of the short-time part of the spectrum is introduced, this corresponding to the minimum absolute value of the complex viscosity versus reduced frequency and the lowest values of the dynamic and apparent viscosities. With an approximate representation of the relaxation spectrum, calculations were made of the maximum values of the viscosity and the coefficient relating the first difference of normal stresses to the square of the shear rate, and also of the apparent viscosity and normal stresses as functions of the shear rate. The calculated values are compared with experimental measurements, and it is shown that the correlation of the apparent viscosity and the absolute value of the complex viscosity is distributed at high frequencies, being superseded by a correlation between the apparent and dynamic viscosities.     

The interfacial dilational properties of hydrophobically modified associating polyacrylamide studied by the interfacial tension relaxation method at an oil-water interface

The interfacial dilational viscoelastic properties of hydrophobically associating block copolymer composed of acrylamide (AM) and a low amount of 2-phenoxylethyl acrylate (POEA) (<1.0 mol%) at the octane-water interfaces were studied by means of the interfacial tension relaxation method. The dependencies of interfacial dilational elasticity and viscous component on the dilational frequency were investigated. The interaction of hydrophobically associating block copolymer [P(AM/POEA)] with sodium dodecyl sulfate (SDS) has been explored. The results show that at lower frequency, the dilational elasticity for different concentration copolymer is close to zero; at higher frequency, the dilational elasticity shows no change with increased frequency; At moderate frequency (10(-3)-1 Hz), the dilational elasticity decreased with a decrease in the dilational frequency. The results show that the hydrophobic groups of [P(AM/POEA)] chains can be associated by inter- or intrachain liaisons in water solution. The dilational viscous component for P(AM/POEA) comes forth a different maximum value at different frequencies when the polymer concentration is different. It is generally believed that the dilational viscous component reflects the summation of the various microscopic relaxation processes at and near the interface and different relaxation processes have different characteristic frequencies. The spectrum of dilational viscous component may appear more than once maximum values at different frequencies. The influence of SDS on the limiting dilational elasticity and viscous component for polymer solution was elucidated. For 5000 ppm polymer solution, the limiting dilational elasticity decreased with an increase in SDS concentration. The dilational viscous component passed through a maximum value with a rise in the dilational frequency, which appeared at different frequency when SDS concentration is different; and the higher is the concentration, the lower is the dilational frequency. It can be explained that macromolecules may be substituted by SDS molecules in the interface and the interaction of molecules decrease, which makes the limiting dilational elasticity decrease. For 200 ppm polymer solution, the limiting dilational elasticity increased firstly and then decreased with SDS concentration increasing. This may be explained that the interfacial polymer concentration is so low that SDS molecules absorbed in the interface dominate dilational properties of the interfacial film even at very low SDS concentration. However, SDS molecules can gradually substitute the polymer molecules in the interface with a rise in SDS concentration, which results in the decrease in the limiting dilational elasticity.     

Electrochemical impedance spectroscopy of tethered bilayer membranes

The electrochemical impedance spectra (EIS) of tethered bilayer membranes (tBLMs) were analyzed, and the analytical solution for the spectral response of membranes containing natural or artificially introduced defects was derived. The analysis carried out in this work shows that the EIS features of an individual membrane defect cannot be modeled by conventional electrical elements. The primary reason for this is the complex nature of impedance of the submembrane ionic reservoir separating the phospholipid layer and the solid support. We demonstrate that its EIS response, in the case of radially symmetric defects, is described by the Hankel functions of a complex variable. Therefore, neither the impedance of the submembrane reservoir nor the total impedance of tBLMs can be modeled using the conventional elements of the equivalent electrical circuits of interfaces. There are, however, some limiting cases in which the complexity of the EIS response of the submembrane space reduces. In the high frequency limit, the EIS response of a submembrane space that surrounds the defect transforms into a response of a constant phase element (CPE) with the exponent (α) value of 0.5. The onset of this transformation is, beside other parameters, dependent on the defect size. Large-sized defects push the frequency limit lower, therefore, the EIS spectra exhibiting CPE behavior with α ≈ 0.5, can serve as a diagnostic criterion for the presence of such defects. In the low frequency limit, the response is dependent on the density of the defects, and it transforms into the capacitive impedance if the area occupied by a defect is finite. The higher the defect density, the higher the frequency edge at which the onset of the capacitive behavior is observed. Consequently, the presented analysis provides practical tools to evaluate the defect density in tBLMs, which could be utilized in tBLM-based biosensor applications. Alternatively, if the parameters of the defects, e.g., ion channels, such as the diameter and the conductance are known, the EIS data analysis provides a possibility to estimate other physical parameters of the system, such as thickness of the submembrane reservoir and its conductance. Finally, current analysis demonstrates a possibility to discriminate between the situations, in which the membrane defects are evenly distributed or clustered on the surface of tBLMs. Such sensitivity of EIS could be used for elucidation of the mechanisms of interaction between the proteins and the membranes.     

Dielectric properties and high-frequency conductivity of the sodium chloride-water system

An analysis has been performed of the dielectric characteristics and high-frequency (hf) electrical conductivity (EC) of aqueous solutions of NaCl. A method of the estimation of the static dielectric constant and of the time of dipole relaxation of concentrated aqueous solutions of NaCl in a wide range of concentrations and temperatures has been suggested. It has been shown that the limiting hf EC of the solutions and the hf EC at the frequency of 2455 MHz decrease with increasing salt concentration and differently change with increasing temperature: the limiting hf EC increases, whereas the hf EC at the frequency of 2455 MHz decreases. The decrease in the hf EC leads to a reduction of the rate of the hf heating of the NaCl solution with increasing salt concentration.