Constant Phase Angle Element Research Articles

The Electrochemical Impedance Spectroscopy Features of the Lithium Nickel Manganese Cobalt Oxide Based Lithium Ion Batteries During Cycling

Electrochemical impedance spectroscopy (EIS) is a viable approach that can be used in lithium ion batteries (LIBs) to investigate the electrochemical behavior. In this paper, Lithium Nickel Manganese Cobalt Oxide (NMC) type lithium ion batteries were divided into four groups. They were charged and discharged under various currents. The results showed that the higher the charging or discharging currents were, the faster the NMC batteries capacities fading were. In order to investigate the electrochemical behavior of the NMC batteries during cycling, we established an equivalent circuit model including one capacitor element in parallel with resistor and one constant phase angle element in parallel with resistor elements to study the impedance characteristics of the NMC batteries. The simulated results indicate that when the capacities of the batteries are dropping, the sum ohmic resistance of them will go up, and the resistance of Li+ diffusion through the SEI layer keeps increasing during cycling. The charge transfer resistance of the NMC batteries decreased at first and then kept increasing after 100 cycles. Among the three parameters, the charge transfer resistance values are the most sensitive factors that are corresponding to the state of charge of the NMC batteries during one single discharging process. We think that the internal ohmic resistance values can be used to predict the state of health (SOH) of the batteries and the charge transfer resistance can be used to predict the state of charge of the NMC batteries.

State of Charge Effects on the Parameters of Electrochemical Impedance Spectroscopy Equivalent Circuit Model for Lithium Ion Batteries

It is essential to know the behavior of the battery at all relevant internal and external conditions when the battery cell is in the new and the aging state. Electrochemical impedance spectroscopy (EIS) is a viable approach that can be used in lithium ion batteries (LIBs) to investigate the electrochemical behavior. In this paper, in order to investigate the state of charge effects on the LIBs, three types of commercial LIB cells were used, and the EIS measurements were performed under 100%, 80%, 50%, 20% and 0% SOC, respectively. An equivalent circuit model (ECM) including two constant phase angle elements in parallel with resistor elements is established to study the impedance characteristics for LIBs. The influence of the state of charge on the parameters of the ECM was analyzed. Based on the results we think EIS combined with ECM simulation tool can be used to derive useful information for improving battery design and state of health prediction.

Structural, dielectric, ferroelectric and impedance spectroscopic studies on Ba1−xSrxTiO3(0.15 ≤ x ≤ 0.35)

Compositions with x = 0.15, 0.20, 0.25, 0.30 and 0.35 were synthesized in the system [Formula: see text] using conventional solid state reaction method and characterized by X-Ray Diffraction (XRD), Raman spectroscopy and Scanning Electron Microscopy (SEM). Tetragonal phase was confirmed in all the samples using Rietveld refinement of the XRD patterns and observation of their Raman spectra. Dielectric and impedance measurements were carried out in the temperature range 300–723 K in the frequency range 1 Hz to 1 MHz. The samples exhibit diffuse phase transition (DPT). Equivalent circuit model involving combination of Constant Phase angle Elements (CPE) and resistances (R) was developed which represents the data well. Expressions for the values of resistances (R) were established in terms of composition and temperature empirically. P-E loops indicated normal ferroelectric behavior for all the samples. Dielectric constant was also measured in the frequency range 8–12 GHz in the X band of microwaves.

Equivalent circuit models using CPE for impedance spectroscopy of electronic ceramics

ABSTRACTComplex immittance (Impedance Z, Modulus M, Admittance Y, Permittivity ϵ) spectra for some equivalent circuit models involving resistances, capacitances and constant phase angle elements (CPE) are calculated for different ratios of the parameters. A comparison of experimentally obtained complex immittance plots with these diagrams greatly facilitates the search for the most appropriate equivalent circuit representing the electrical properties of electronic ceramics. An equivalent circuit for Ba1-xSrxTiO3 (x = 0.35) ceramic system is developed by using these simulated plots.

Challenges in the Measurement of Passive Dissolution of Steel in Concrete

The corrosion rate of the steel reinforcement of concrete is measured and monitored in laboratory and civil structures by various techniques that include anodic or cathodic galvanostatic pulse, linear polarization resistance (using a given polarization rate), electrochemical impedance spectroscopy, etc. Considerable attention has been given to the suitability of those methods to measure the corrosion rate of steel in the active state, after passivity breakdown due to aggressive species contamination. However, fewer studies have evaluated the case of service in structures with required durability much in excess of one hundred years (as for example containment of radioactive waste) where the corrosion process is expected to remain in passive state, with anodic current densities typically lower than 10-8 A/cm2. The electrochemical measurement of such low corrosion rates is a challenging goal as it is difficult to separate polarization currents due to interfacial charge storage processes (which may be of actual or apparent non-Faradaic origin) to those related to the anodic, metal dissolution process itself. That separation often leads to the need for long duration of the measurements, which would make it impractical to monitor a large number of reinforcement locations in an actual structure. Understanding of the relevant measurement factors is needed to eventually develop more time efficient assessment methods for those systems.As part of developing that understanding, the objective of this work is the experimental and modeling analysis of steel in concrete in the passive state, in response to the application of cathodic cyclic polarization with polarization rates in the order of 0.001 mV/sec and polarization down to -300 mV with respect to the (passive) corrosion potential. This technique, implemented with higher polarization rates after appropriate adjustment as a refined form of Tafel extrapolation, is a possible candidate to monitor structures of interest. In order to interpret the passive corrosion process response to polarization excitation, a modified Randles interphase model analog was used. A novel feature of this study is the introduction of large amplitude time domain behavior of a constant phase angle element, which is then combined with the large amplitude response of the Faradaic current treated with a Butler-Volmer approach. The system steel/interface/concrete is described by a fractional order differential equation that is solved by the implementation of a finite differences aproach. Comparisons between the experimental results from multiple specimens at various scan rates and the response calculated by solution of the equations of the system were made, showing good agreement between both. Corrosion current densities obtained by numerically fitting the model to experimental results yielded values typically lower than 10-8 A/cm2 in agreement with other values reported in the literature for long term exposures of passive steel in concrete. Open issues on the applicability of these results for mechanistic interpretation of the processes at work on the rate of passive dissolution of steel in concrete are discussed.

Comparison of complex permittivities of isotonic colloids containing single‐wall carbon nanotubes of varying chirality

The application of bio-compatible, conductive nanoparticles in combination with radiofrequency (RF) irradiation to raise tissue temperatures between 40 and 60 °C for hyperthermia and ablation spurred interest in the complex permittivities of isotonic nanoparticle-based colloids. Nanoparticles with large aspect ratios and high permittivities increase the bulk permittivity of the colloid and RF losses at the macroscopic scale. The complex permittivities of isotonic colloids with and without single-wall carbon nanotubes (SWCNTs) containing either metallic, semiconducting, or mixed chiralities were measured from 20 MHz to 1 GHz at room temperature. The colloids were made with one of three different isotonic solvents: phosphate buffered saline (PBS), and Dulbecco's modified eagle medium (DMEM) with and without 0.5% weight/volume bovine serum albumin to simulate cytosol and blood, respectively. The concentration of elemental carbon from the SWCNTs in the colloids ranged from 16 to 17 mM. The permittivities were corrected for electrode polarization effects by fitting the data to the Cole-Cole relaxation model with a constant phase angle element. The presence of SWCNTs increased both the real and imaginary components of the permittivities of the colloids. For all three solvents, the direct current (DC) components of the real and imaginary permittivities were greatest for the colloids containing the mixed chirality SWCNTs, followed by the colloids with semiconducting SWCNTs, and then metallic SWCNTs.

Radiofrequency interaction with conductive colloids: Permittivity and electrical conductivity of single‐wall carbon nanotubes in saline

Conductive nanoparticles may enhance tissue heating during radiofrequency (RF) irradiation. Specific absorption rate (SAR) is known to rise with the electrical conductivity of tissue. However, no studies to date have measured the relationship between complex permittivity and nanoparticle concentration in tissue-like samples. The complex permittivities of colloids containing single-wall carbon nanotubes (SWCNTs) in normal (0.9%) saline were measured from 20 MHz to 1 GHz. Carbon concentrations ranged from 0 to 93 mM (0.06% volume), based on SWCNT weight per volume. Measurements were made with 0.02% Pluronic F108 surfactant added to the colloids to prevent SWCNT flocculation. The data were fit to the Cole-Cole relaxation model with an added constant phase angle element to correct for electrode polarization effects at low RF frequencies. Electrode polarization effects increased with carbon concentration. The real parts of the permittivities of the colloids increased with carbon concentration. The static conductivity rose linearly with carbon concentration, doubling from 0 to 93 mM. The SAR of the colloids is expected to increase with RF frequency, based on the properties of the imaginary part of the permittivity.

A Comparison of Two- and Four-Electrode Techniques to Characterize Blood Impedance for the Frequency Range of 100 Hz to 100 MHz

Measurement setups that characterize the impedance of suspensions of blood over the wide frequency range of 100 Hz to 100 MHz are presented in this paper. The performance of the two- and four-electrode techniques have been compared and evaluated. By applying a combination of the two measurement techniques the best result is achieved when taking into account the main nonidealities, such as electrode polarization impedance and parasitic capacitances. It has been found that the conventional three-element model for the impedance of blood can be used for frequencies up to 1 MHz. For frequencies exceeding 1 MHz, an extended model is introduced where a constant phase angle element is used for modeling the cell membrane and a capacitor C(liq) is added for modeling the electrical capacitance of water in blood.

Inhibitive effect of black pepper extract on the sulphuric acid corrosion of mild steel

The corrosion inhibitive effect of the extract of black pepper on mild steel (MS) in 1 M H 2SO 4 media was evaluated by conventional weight loss studies (303–323 K), electrochemical studies viz., Tafel polarization, ac impedance and scanning electron microscope (SEM) studies. Results of weight loss study reveal that black pepper extract acts as a good inhibitor even at high temperatures also. The inhibition is through adsorption which is found to follow Temkin adsorption isotherm. Tafel polarization method revealed the mixed mode inhibition of black pepper extract. Analysis of impedance data has been made with equivalent circuit with constant phase angle element for calculation of double layer capacitance value. SEM studies provide the confirmatory evidence for the protection of MS by the green inhibitor.

Influence of halide ions on the adsorption of diphenylamine on iron in 0.5 M H 2SO 4 solutions

Halide ions are found to enhance the inhibition performance of amines due to enhanced adsorption of amines by the adsorbed halide ions on the metal surface. In this work, the synergistic action of halide ions on the corrosion inhibition of iron in 0.5 M H 2SO 4 by diphenylamine has been found out by electrochemical impedance and polarization methods. Analysis of impedance data has been made with equivalent circuit with constant phase angle element for calculation of double layer capacitance values. Experiments have been carried out in the concentration range of 100–1000 ppm of diphenylamine in the presence of 0.5–1.0 × 10 −3 M of halide ions. Diphenylamine is found to be a cathodic inhibitor and the inhibition efficiency of about 65% is obtained at 1000 ppm. The anodic and cathodic Tafel slopes in the presence of diphenylamine alone and with halide ions are 65 ± 5 and 105 ± 5 mV, respectively. Diphenylamine inhibits corrosion by adsorption and the surface coverage values are increased considerably in the presence of halide ions. In the presence of iodide ions, the inhibition efficiency of diphenylamine at 100 ppm is increased to more than 90%. In the case of other halide ions, the inhibition efficiency of diphenylamine in increased to 80% at 1000 ppm. The order of synergism of halide ions is I − ≫ Br − > Cl −. The highest synergistic effect of iodide ions is due to chemisorption with metal surface due to its larger size and ease of polarizability.

Non-linear response of an electrode–electrolyte interface impedance with the frequency

In this paper we analyze the frequency response of a distributed parameters non-linear circuit. This circuit is a fractal model of an electrode–electrolyte interface. The results show that the series equivalent resistance R eq decreases as the number of fractal levels rises. Its frequency behavior is similar to the results described by other authors that used a constant phase angle element. At low frequency range, the series equivalent reactance X eq decreases with frequency and R eq shows a flat response in this range. The model also explains how interface geometry modifies the values of some electrochemical parameters. As roughness increases the Argand diagram shows smaller semicircles. The model behavior is like a single dispersion system with its central frequency increasing with the electrode roughness.

Wide-frequency-range dielectric response of polystyrene latex dispersions

In this work we analyze the dielectric properties of dilute colloidal suspensions of nonconducting spherical particles with a thin electrical double layer from experimental data obtained by performing impedance spectroscopy experiments over a broad frequency range, from 20 Hz to 1 GHz. The electrode polarization correction was made by fitting a circuit model in the complex impedance plane (impedance spectrum) using a constant phase angle (CPA) element to fit the electrode polarization in series with the sample impedance. This simple procedure is found to be effective in eliminating the electrode contribution. The dielectric response shows two different dispersions, the α relaxation (counterion relaxation) that occurs at low kilohertz frequencies, and the δ relaxation (Maxwell–Wagner effect) found in the MHz range. These are reasonably well fitted over a broad frequency range by the theoretical expressions given by a simplified standard model (not including anomalous conduction) and a generalized model (including anomalous conduction) for the low-frequency dispersion, plus Maxwell–Wagner–O'Konski theory for the δ relaxation in the mid-frequency range. An analysis was also made of the need to include, for these latices, the effects of ion mobility in the Stern layer in order for the values of the ζ-potential obtained from electrophoretic and dielectric data to be compatible with each other.

Electrochemical investigations of cholesterol enriched glassy carbon supported thin lipid films

The formation and study of stable cholesterol enriched thin lipid layers onto the surface of glassy carbon electrode is reported in this work. The method of formation relies on additional thinning of wetting films by electrostriction. Electrochemical techniques based on the concepts of impedance and voltammetry are used to explore the films’ features. The impedance data reveal a substantial change of relaxation characteristics of the modified films. In this respect, opportunities for the evaluation of the films’ stage based on the approximation with ‘constant phase angle element’ are discussed. The possible final structure of the films, as well as, their relevance for development of sensor elements are briefly viewed.

Reduction of the contribution of electrode polarization effects in the radiowave dielectric measurements of highly conductive biological cell suspensions

Electrode polarization effects in dielectric spectra of highly conductive biological cell suspensions cause a severe difficulty in the estimation of dielectric parameters of cells under physiological conditions. This problem becomes particularly serious with the increase of the electrical conductivity of the sample, preventing the use of low frequencies in the characterization of biological systems, especially aqueous biological systems. Although a variety of methods to correct the electrode polarization have been proposed in the past, no simple technique for its correction has been available so far. Since the magnitude of the polarization effect can be time-dependent owing to changes in the conductance of the suspending medium or to possible alteration in the electrode surface structure, it is clear that correction procedure should be based on a kind of “self-correction” method, avoiding the so-called “comparison methods” which, on the contrary, require time-independent effects. This note is aimed to address this problem considering an electrode polarization modelled by a constant phase angle (CPA) element in series with the sample admittance. A scaling-law frequency dependence has found to describe the a.c. response of the interface between the electrode and the bulk electrolyte solution. Although this approach has been extensively proposed in the past in the analysis of dielectric spectra of biological suspensions, we have somewhat modified the way it has been previously applied and have re-examined in detail its effectiveness in typical systems of biological interest. The results give support to the proposed analysis, allowing the complete low-frequency dielectric spectra characterization at frequencies of the order of 1 kHz for samples with a bulk ionic conductivity as large as that of the order of 1 mho/m. Typical examples with different dielectric behaviours are extensively discussed in order to show the applicability of the proposed method to biological samples.

Investigations of Reversible and Polarised Interfacial Surface Properties by Electrochemical Impedance Method

The article concerns measuring the impedance of blocking Pt, Au, Ni, Ti and reversible Ag and Ag 2 Te electrodes on the interface with superionic conductor. Infralow frequency dependences of impedance module are described by fractional-order frequency dependence, the phase angle being constant in a definite frequency range, thus constant phase angle element (CPE) peculiarities reveal. The impedance characteristics under the alternation of electrode potential, formation pressure and temperature have been obtained. Algorithms of constructing the electrical models of metalsuperionic conductor interface, whose impedance is described by CPE-element [1-5] have been considered. The possibility of presenting the interface equivalent electrical circuits as Foster's canonical RC-circuits and realizing the impedance and admittance frequency characteristics with necessary precision in the given frequency range under random fractional parameters α in 0-1 interval has been demonstrated.

The Electrode-Tissue Interface in Living Heart: Equivalent Circuit as a Function of Surface Area

Broadband impedance spectroscopy was performed in a three-electrode potentiostatic configuration to determine the equivalent circuit of the noble metal (smooth Pt) electrode–tissue interface in perfused living rat heart. The equivalent circuit was studied as a function of surface area (A = 0.049–13 mm2). Impedance plane plots (Nyquist plots) were determined. The large surface area impedance plane plot is characterized by two constant phase angle elements (CPE1 and CPE2), one of which is the finite (spatially-confined) Warburg impedance, CPE2 ≡ ZD, confirmed by its linearity with respect to ω−1/2. As the working electrode goes to smaller surface area the ZD circuit element becomes at first predominant. At 0.13–5.8 mm2 a discontinuous transition is seen to semicircular behavior in the impedance plane plot, indicating a circuit element composed of a parallel resistance and capacitance. Bulk resistance was in series with these circuit elements. The capacitance in the high frequency limit was linearly related to surface area C = kA, k = constant =δC/δS. The conductance at high frequency (at constant interelectrode distance) lim G=1/(Ral +RB) was an increasing function of surface area with intercept 0, where Ra1 denotes an access resistance and RB the bulk resistance. The unit equivalent circuit of the living electrode tissue interface was determined to be RBRa1 [(C)(Ra2 ΘZD)]. In this equation Ra2 is a second access resistance, and ZD is the finite (spatially confined) Warburg impedance. The surprising presence of ZD but not ZW∞ (the semi-infinite Warburg impedance) is diagnostic of thin film formation at the bioelectrode's surface, which was not predicted theoretically or reported experimentally. We present a model that accounts for this behavior based on the appropriate solution of the diffusion equation. This is the first observation of a Warburg impedance in such a living system outside the microelectrode or ultramicroelectrode size range.

An Improved Method for Estimating Polarization Resistance from Small-Amplitude Potentiodynamic Scans in Concrete

Abstract Many corroding interfaces exhibit electrochemical impedance response similar to that of a polarization resistance (Rp) associated with the corrosion process, in parallel with a constant phase angle element (CPE) having relatively large admittance. Such conditions are encountered often in the case of steel in concrete. While polarization measurements using a forward and reverse potential scan rate (dV/dt) can be helpful to subtract the contribution of an ideal interfacial capacitance (C) by using a C dV/dt correction, in concrete the pronounced frequency dispersion of the CPE complicates the time-domain response, and correction is not straightforward. A solution to this problem was presented and applied to evaluate the CPE parameters and estimate Rp of steel in concrete from cyclic-scan polarization measurements. The technique was demonstrated for experiments with plain steel and galvanized rebar in concrete.

Non-Debye and CPA Behaviors of Ionic Materials

ABSTRACTNon-Debye and constant-phase-angle (CPA) behaviors associated with the bulk and interfacial processes involving ionic materials are discussed in terms of complex impedance, admittance, and dielectric spectra. The yielding of a CPA and/or a broad non-Debye dielectric loss peak in a spectrum from fractal, pore, and ion-hopping models are compared and reviewed. The observed wide frequency ranges of the CPA behavior suggest that the fractal and pore models, which require a wide range of special structures down to very fine scales, may not be realistic. The ion-hopping model treats the bulk and interfacial processes as a chemical reaction having a thermally-activated Arrhenius form. Because of thermal fluctuations, the activation energies for ion hopping (e.g., in a potential double-well) have a double-exponential distribution which yields a non-Debye dielectric loss peak and a CPA spectrum over a wide frequency range above the loss peak. The distribution also has a special temperature dependence which may explain the invariance of dielectric spectral shapes with temperature, an observation by Joscher. The construction of CPA elements (in a generalized Warburg impedance form) using three distinct types of resistor-capacitor networks are presented and used to aid the discussion.

Evaluation of electrochemical impedance with constant phase angle component from the galvanostatic step response of steel in concrete

A current step excitation method for obtaining the parameters of a system characterized by a solution resistance R s in series with the parallel combination of a polarization resistance R P with a constant phase angle element ( cpe) is described. The cpe has a base admittance Y 0 and a frequency exponent n. A numerical procedure is developed to obtain the value of the system parameters ( R p , Y 0, n and R s ) by analysis of the potential response of the system to the current excitation step. Experiments with specimens of galvanized steel in concrete are reported in which the galvanostatic step technique is applied and the analysis procedure is performed. Good agreement with the results of independent electrochemical impedance spectroscopy (EIS) of the same specimens is demonstrated.

CuBr by impedance spectroscopy

The electrical properties of polycrystalline copper(I) bromide were investigated between 20 and 430 °C by impedance spectroscopy with copper electrodes. Extrinsic and intrinsic regions in γ-CuBr and a domain of fast ionic conduction in β-CuBr are separated. Enthalpies of migration of copper interstitials (25 kJ/mol) and copper vacancies (50 kJ/mol) and the enthalpy of formation of Frenkel defects (160 kJ/mol) are deduced. The phase boundary copper/copper(I) bromide can be represented by a parallel circuit of an interfacial resistance and a constant phase-angle (CPA) element. The interfacial resistance depends exponentially on temperature and is practically negligible above 350 °C. Contributions of charge transfer resistance and space charge resistance are discussed. Prefactors of CPA elements depend also exponentially on temperature; they are compared with interfacial capacitances.