Complex Impedance Data Research Articles

Bayesian parameter estimation of porous materials.

This work proposes a new application of Bayesian analysis to determine the physical parameters of a rigid frame porous material from the measurement of the material’s acoustic impedance. Bayesian analysis allows for numerical estimation of physical parameters, their uncertainties, and inter-relationship of the parameters from the measured complex impedance. Complex impedance data are simulated based on measurements of a sample material to test the Bayesian formulation. Using synthesized data allows for investigations of different frequency resolutions and different levels of noise on the algorithm. Results obtained from testing the parameter estimation algorithm with synthesized data will be utilized in applying the algorithm to measured complex impedance data.

Impedance and Magnetic Permeability of Soft Ferromagnetic Metals

We report on impedance measurements in the Heusler compound Pd2MnSn, Gd metal and the re-entrant alloy Au0.82Fe0.18. Using a computational procedure, the real and imaginary components of the circumferential permeability could be determined from the complex impedance data. We show that the temperature dependence of the permeability is useful to study magnetic phase transitions, whereas valuable information on domain-wall motion and spin rotation processes may be obtained from appropriate analyses of the frequency and external magnetic field dependences of the complex permeability.

Li+ ion constriction in presence of Bi2O3 and ac conductivity in Li2O·P2O5·Bi2O3 glasses

Glasses having composition (25+ x )Li 2 O·(65− x) P 2 O 5 ·10Bi 2 O 3 (0⩽ x ⩽25 mol%) were investigated using impedance spectroscopy in the frequency range from 20 Hz to 1 MHz and in the temperature range from 150 to 300 °C. The ac and dc conductivities, activation energy of dc conductivity and conductivity relaxation are extracted from the impedance spectra. The complex impedance data have been analyzed using the conductivity and electric modulus formalisms to study the relaxation dynamics of charge carriers in these glasses. The observed conductivity spectra follow the power law with exponent “ n ”. The exponent “ n ” decreases with increase in Li 2 O:P 2 O 5 ratio and has been correlated with both the constriction of the Li + ions and the dimensionality of the available conduction pathways. The conductivity increases with increase in Li 2 O:P 2 O 5 ratio and is ionic in nature. Summerfield scaling model has been applied to obtain single “super curve” for all the ac conductivity spectra at various temperatures in the present glasses. However, a deviation from “super curve” for various isotherms of conductivity spectra was also observed in high frequency region and at low temperatures.

Impedance spectroscopy and dielectric relaxation in alkali tungsten borate glasses

Glasses with composition xWO 3·(30 − x)M 2O·70B 2O 3 (M = Li, Na, 0 ≤ x ≤ 15 mol%) have been prepared using normal melt-quench technique. Variation of density, molar volume and theoretical optical basicity with glass composition has been studied. The complex impedance of these glasses has been measured in the temperature range from 523 to 623 K and in frequency range from 100 Hz to 1 MHz. The complex impedance data have been analyzed using the conductivity and electric modulus formalism. The effects of composition and temperature on conductivity are discussed. The frequency dependence of the ac conductivity is found to obey Jonscher’s relation. The dc conductivity is dominated by alkali ions and increases with rise of temperature. The correlation between the conductivity and conductivity relaxation is analyzed. Scaling of the conductivity data has been carried out. The stretching exponent β is found to be temperature independent. The overlapping of the normalized peaks corresponding to impedance and electric modulus and the same thermal activation energy for conduction and relaxation suggest the single mechanism for the dynamic processes in the present glasses.

Structural and spectroscopic characterization of poly(styrene sulfonate) films doped with neodymium ions

Abstract This work reports the structural and spectroscopy characterization of poly(styrene sulfonate) (PSS) films doped with neodymium (Nd) ions. Nd–PSS films were processed using the acid of poly(styrene sulfonate) – H–PSS and neodymium nitrate – Nd(NO 3 ) 3 ; the maximum incorporation of Nd ions in the polymeric matrix was equal 19.3%. The absorption in the UV–Vis–NIR spectral region presents typical electronic transitions of Nd 3+ ions, with well resolved peaks. The infrared spectra present the transition bands of PSS with characteristic line shape broadening, and the presence of vibrational modes of N–O groups in the range of 1400–720 cm −1 , prove the permanence of Nd(NO 3 ) x , with x = 1, 2 and/or 3, in the H–PSS matrix. UV–Vis site selective photoluminescence data indicate that the incorporation of Nd 3+ introduces a blue shift in PSS emission (325–800 nm), decreasing the interaction between adjacent PSS lateral groups (aromatic rings). Nd 3+ reabsorption and energy transfer effects between the PSS matrix and Nd 3+ were also observed. The IR emission of Nd–PSS films at 1076 nm ( 4 F 3/2 → 4 I 11/2 ) present constant efficiency, independent on Nd 3+ concentration. The Judd–Ofelt theory was employed to analyze radiative properties. The excitation spectra prove the energy transfer between the polymeric matrix and Nd 3+ . Complex impedance data was used to probe relaxation processes during the charge transport within the polymeric matrix.

Electrochemical sensor array forin situmeasurements of hydrogen peroxide concentration in high temperature water

AbstractA common index of corrosive conditions in boiling water reactors (BWRs) is the electrochemical corrosion potential (ECP), which is determined by a combination of factors such as specimen surface conditions and oxidant concentrations (e.g. O2, H2O2 and other corrosive radiolytic species). ECP sensors can be applied to determine corrosive conditions directly at elevated temperature, but a disadvantages of this approach is the broad plateau observed in the range 10–100 ppb H2O2. To determine the concentration [H2O2] directly in high temperature water, an array consisting of an ECP sensor and a complex impedance sensor has been developed. From the results, it is concluded: (1) the radii of the low frequency semicircle of the frequency dependent complex impedance (FDCI) data (Cole–Cole plots) decreased with increasing [H2O2]. The radii for the specimen exposed to 100 ppb H2O2 were determined by the electric resistance of the oxide film, and had reached the saturation level caused by saturation of oxide...

Ionic transport studies on (PEO) 6:NaPO 3 polymer electrolyte plasticized with PEG 400

Conduction characteristics of the poly(ethylene oxide) based new polymer electrolyte (PEO) 6:NaPO 3, plasticized with poly(ethylene glycol) are investigated. Free standing flexible electrolyte films of composition (PEO) 6:NaPO 3 + x wt.% PEG 400 (30 ⩽ x ⩽ 70) are prepared by solution casting method. A combination of X-ray diffraction (XRD), optical microscopy and differential scanning calorimetry (DSC) studies have indicated enhancement in the amorphous phase of polymer due to the addition of plasticizer. Further, a reduction in the glass transition temperature observed from the DSC result has inferred increase in the flexibility of the polymer chains. The cationic transport number ( t Na + ) of 0.42 determined through combined ac–dc technique has confirmed ionic nature of conducting species. Ionic conductivity studies are carried out as a function of composition and temperature using complex impedance spectroscopy. The electrolyte with maximum PEG 400 content has exhibited an enhancement in the conductivity of about two orders of magnitude compared to the host polymer electrolyte. The complex impedance data is analyzed in conductivity, permittivity and electric modulus formalism in order to throw light on transport mechanism. A solid state electrochemical cell based on the above polymer electrolyte with a configuration Na|SPE|(I 2 + acetylene black + PEO) has exhibited an open circuit voltage of 2.94 V. The discharge characteristics are found to be satisfactory as a laboratory cell.

Temperature dependent impedance spectroscopy on polyaniline based devices

Polyaniline (PANI) sandwich structures with Al and/or Au electrodes have been investigated using temperature dependent I-V measurements and impedance spectroscopy in the 50 mHz -1 MHz frequency range. The I-V measurements on the Au/PANI/Au structure have shown a practically Ohmic behavior, while the Au/PANI/Al structure has presented a clear non-linear behavior in the voltage range studied. From the complex impedance data analysis we have observed that while in the Au/PANI/Au structure the conductive process is best described with a single distribution of relaxation times, associated only to the bulk region, in the Au/PANI/Al structure the active layer is divided in two regions with distinct resistances: one associated to the bulk region, and the other, much higher, associated to a thin region close to the PANI/Al interface. We have also analyzed the real capacitance data of the Au/PANI/Al structure using two models based on an abrupt cut-off frequency concept. The application of these models has enabled the determination of some important parameters, such as: Debye length (ap20 nm), energetic position (ap320 meV) and associated density of states (ap2times1018 eV-1.cm-3) of the bulk Fermi level, width of the space charge region (ap70 nm), built-in potential (ap780 meV), and the gap states distribution. Correlating the results obtained from the I-V measurements, impedance and capacitance spectra, we have concluded that a highly resistive layer is formed in the vicinity of the polymer/Al interface in the Au/PANI/Al structure, which is responsible for the presence of a high density of localized states. In the Au/PANI/Al structure, such localized density of gap states dominates the electronic transport, in contrast to the Au/PANI/Au structure, where this resistive layer can be neglected and the bulk effects dominate the electronic transport

Characterization of Magneto-Optic Imaging Data for Aircraft Inspection

The magneto-optic imager (MOI) is widely used in detecting surface and subsurface cracks and corrosion in aircraft skins. The instrument provides analog images of the anomalies based on eddy current induction techniques and a magneto-optic (MO) sensor using the Faraday rotation effect. The merits of the MOI that make it attractive include rapid and large-area inspection, insensitivity to liftoff variations, and easy interpretation in contrast to the complex impedance data of conventional eddy current inspections. The current MOI system lacks the capability of providing a quantitative measure of the defects. In addition, the presence of noise due to the underlying domain structures in the MO sensor can lead to inconsistent accept or reject decisions by the inspector. This paper presents an image processing and automated classification algorithm for MO image analysis and also provides a quantitative basis for characterizing these images

Design and fabrication of a 40-MHz annular array transducer

This paper investigates the feasibility of fabricating a five-ring, focused annular array transducer operating at 40 MHz. The active piezoelectric material of the transducer was a 9-microm thick polyvinylidene fluoride (PVDF) film. One side of the PVDF was metallized with gold and forms the ground plane of the transducer. The array pattern of the transducer and electrical traces to each annulus were formed on a copper-clad polyimide film. The PVDF and polyimide were bonded with a thin layer of epoxy, pressed into a spherically curved shape, then back filled with epoxy. A five-ring transducer with equal area elements and 100-microm kerfs between annuli was fabricated and tested. The transducer had a total aperture of 6 mm and a geometric focus of 12 mm. The pulse/echo response from a quartz plate located at the geometric focus, two-way insertion loss (IL), complex impedance, electrical crosstalk, and lateral beamwidth all were measured for each annulus. The complex impedance data from each element were used to perform electrical matching, and the measurements were repeated. After impedance matching; fc approximately equal to 36 MHz and -6-dB bandwidths ranged from 31 to 39%. The ILs for the matched annuli ranged from -28 to -38 dB.

Optimized Structure of Nanoporous Carbon-Based Double-Layer Capacitors

Electrochemical double-layer capacitors with micro-to-nanoporous electrodes based on activated carbon utilize the gross interface between carbon and the electrolyte, which fills the pores of two main classes, (i) micrometer voids between agglomerates of carbon grains and micro-to-nanometer pores inside agglomerates and grains. The bigger pores provide good transport of ions throughout the layer whereas the smaller pores generate a large interfacial area. This essentially bifunctional architecture prompted us to combine two complementary concepts in the pertinent theory of double-layer capacitors, viz. linear transmission line models and self-affine fractal models. The merit of this structure-based approach, involving also the effect of hindrance of ionic conductivity in nanopores, is that it relates basic structural characteristics to the dynamic performance. Practically, with no fitting parameters, it reproduces the main features of recently reported complex impedance data. This refers to the effect of electrode thickness, constant phase angle (CPA) and crossover between CPA and non-CPA behavior. Routes toward the optimization of the capacitor architecture for the largest possible static capacitances and rapid charging-discharging are explored. The comparison of calculated optimum capacitance values with recent experimental data reveals remarkable reserves for advanced structural design. © 2004 The Electrochemical Society. All rights reserved.

AC impedance spectroscopy: a new equivalent circuit for titania thick film humidity sensors

The variation of the electrical signal with humidity in ceramic sensors is originated by the chemical and physical sorptions of water molecules existing in the atmosphere. The aim of the work described in the present paper is to establish an equivalent electrical circuit for the case of two titania thick-film samples. It is shown, at least for the temperature of 23 °C, that the same type of circuit represents adequately these two samples for various relative humidities. Chemisorption and physisorption are responsible for the different charge transport mechanisms – ion hopping, ion diffusion and electrolytic conduction. Complex impedance data were obtained at the temperature of 23 °C and various relative humidities, in the frequency range 0.1 Hz–40 MHz. The best and simpler circuit representation we found, which gives the best fitting for the Cole–Cole and Bode plots, consists of two RC parallel circuits in series with two constant-phase elements (CPEs). The values of the electrical components are tabled and, as an example, the Cole–Cole and Bode plots fitting obtained for one of our samples, the sample B, for 87.5% RH, in the frequency range 0.1 Hz–40 MHz is shown.

Physical and ionic transport studies on poly(ethylene oxide)–NaNO 3 polymer electrolyte system

Solid polymer electrolyte thin films based on poly(ethylene oxide) (PEO) complexed with NaNO 3 salt with compositions between 2 and 10 ether oxygens per sodium have been prepared using the solution cast method as a possible sodium ion-conducting polymer electrolyte system. The complexation of the films has been investigated through X-ray diffraction (XRD), differential scanning calorimetry (DSC), and Fourier transform infrared spectroscopy (FTIR) measurements. Electrical properties have been measured as a function of composition and temperature using complex impedance spectroscopy. The maximum ionic conductivity has been found to be ∼3.5×10 −6 S/cm at room temperature for the composition O/Na=3:1. The transference numbers of different mobile species have been determined by means of DC polarization and combined AC/DC techniques. The complex impedance data have been analysed in conductivity and permittivity formalisms to cast light on possible ion transport mechanisms. The peaks found in the electric modulus plot have been characterized in terms of the stretched exponential parameter.

Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data

Signal processing in dielectric spectroscopy implies that it is necessary to find a ‘true’ fitting function (having a certain physical meaning), which describes well the complex permittivity and impedance data. In dielectric spectroscopy for description of complex permittivity/impedance data researches usually use the empirical Cole–Davidson (CD) and Havriliak–Negami (HN) equations that contains one relaxation time. But the parameters figuring in CD and HN equations do not have clear physical meaning as well as fitting parameters entering into linear combination of several CD or HN equations. For description of dielectric (especially asymmetric) spectra we suggest the complex permittivity functions containing two or more characteristic relaxation times. These complex susceptibility functions correspond in time domain to new type of kinetic equation containing non-integer (fractional) integrals and derivatives. We suppose that these kinetic equations describe a wide class of dielectric relaxation phenomena taking place in heterogeneous substances. To support and justify this statement the special recognition procedure has been developed that helps to identify this new kinetic equation from raw dielectric data. It incorporates the ratio presentation (or RP) format and separation procedure. Separation procedure was turned out to be helpful in detection of number of relaxation processes (each process is described by a characteristic relaxation time) taking place in the dielectric material under consideration. We suppose that this procedure can be applicable also for identification of fractal noises.

On the adequacy of identified Cole–Cole models

The Cole–Cole model has been widely used to interpret electrical geophysical data. Normally an iterative computer program is used to invert the frequency domain complex impedance data and simple error estimation is obtained from the squared difference of the measured (field) and calculated values over the full frequency range. Recently a new direct inversion algorithm was proposed for the ‘optimal’ estimation of the Cole–Cole parameters, which differs from existing inversion algorithms in that the estimated parameters are direct solutions of a set of equations without the need for an initial guess for initialisation. This paper first briefly investigates the advantages and disadvantages of the new algorithm compared to the standard Levenberg–Marquardt “ridge regression” algorithm. Then, and more importantly, we address the adequacy of the models resulting from both the “ridge regression” and the new algorithm, using two different statistical tests and we give objective statistical criteria for acceptance or rejection of the estimated models. The first is the standard χ 2 technique. The second is a parameter-accuracy based test that uses a joint multi-normal distribution. Numerical results that illustrate the performance of both testing methods are given. The main goals of this paper are (i) to provide the source code for the new ‘‘direct inversion’’ algorithm in Matlab and (ii) to introduce and demonstrate two methods to determine the reliability of a set of data before data processing, i.e., to consider the adequacy of the resulting Cole–Cole model.

Impedance analysis of the electron transfer process in redox polymer Langmuir–Blodgett films

Abstract The electron transfer process in redox polymer Langmuir–Blodgett films containing tris(bipyridine)ruthenium complex has been investigated as a function of the number of monolayers by an impedance spectroscopy. The complex impedance and capacitance data show that the equivalent circuit model consists of the parallel circuit with the membrane capacitance of the LB films as a fast charging process and the faradaic capacitance controlled by the charge transfer resistance as a slow charging process. The charge transfer resistance and the faradaic capacitance increases with the number of the monolayers whereas the membrane capacitance decreases with increasing number of the monolayers.

Effect of sorbed oil on the dielectric properties of sand and clay

The dielectric response of geologic materials is related to the amount of water‐wetted solid surface present. This dependence raises the possibility that dielectric measurements may be used to detect changes in the state of the solid‐fluid interface such as those caused by the sorption of a chemical species. In this study, complex impedance data are collected for systems of clean and oil‐bearing sand and kaolinite vacuum‐ saturated with a 0.001 M NaCl brine in the frequency range 100 kHz to 10 MHz. The effective dielectric constant k and electrical conductivity σ of the samples are calculated from these measurements assuming quasi‐static conditions. We define the components in our system as brine, air, and a “wetted” solid phase. In this way, the contribution of the solid‐fluid interface to the bulk dielectric response is included in the last component. We use an inclusion‐based effective medium theory to extract the dielectric response of the wetted solid from the experimental data. The presence of sorbed oil is found to have little effect on the dielectric response of the wetted sand matrix, presumably because of the very low surface area (0.2 m2/g) of the solid‐fluid interface. In contrast, the kaolinite (5–12 m2/g) data indicate a decrease of the order of 50% in the dielectric constant of the wetted matrix phase as the amount of water‐wetted surface in the sample decreases. The results from this experimental study show that the presence of sorbed oil leads to a detectable change in the dielectric properties of high surface area geologic materials.

Characterization of a 300-W linear actuator

The linear parameters of a moving magnet electrodynamic actuator were measured using several different procedures. The methods employed included blocked carriage tests, regression of free decay of voltage and acceleration for known mass addition, regression of complex impedance data resulting from peak-averaged voltage/current transfer functions in swept sine tests, and solution of nonlinear equations for impedance and velocity/voltage relationships for three or four data point sets. It was found that the mechanical system parameters are strong functions of the motional amplitude, and that electrical system parameters are functions of frequency and amplitude. A brief review of the literature and a comparison of the methods and results will be presented. Simulated data will be used to benchmark the methods, enabling clearer interpretation of the results.

Derivation of the Smith chart equations for use with MathCAD

A MathCAD document is described that provides the capability for plotting a set of normalized complex impedance data, which can be provided either from a data array or from an analytical expression. The generation of the Smith chart axis is done with analytical expressions, rather than with numerical techniques. An example of the use of this program is given, using a rectangular microstrip patch antenna model, generated by the HP Momentum electromagnetic simulator. The complete MathCAD document is provided as part of this paper.

Electrical conductivity, relaxation and the glass transition: A new look at a familiar phenomenon

Annealed samples from a single melt of a 10 mol% K2O-90SiO2 glass were reheated to temperatures ranging from 450 to 800 C, held isothermally for 20 min, and then quenched in either air or a silicon oil bath. The complex impedance of both the annealed and quenched samples was measured as a function of temperature from 120 to 250 C using ac impedance spectroscopy from 1 Hz to 1 MHz. The dc conductivity, sigma(sub dc), was measured from the low frequency intercept of depressed semicircle fits to the complex impedance data. When the sigma(sub dc) at 150 C was plotted against soak temperature, the results fell into three separate regions that are explained in terms of the glass structural relaxation time, tau(sub S). This sigma(sub dc) plot provides a new way to look the glass transition range, Delta T(sub r). In addition, sigma(sub dc) was measured for different soak times at 550 C, from which an average relaxation time of 7.3 min was calculated. It was found that the size and position of the Delta T(sub r) is controlled by both the soak time and cooling rate.