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Basic Concepts
Published in P. Arpaia, U. Cesaro, N. Moccaldi, I. Sannino, Non-Invasive Monitoring of Transdermal Drug Delivery, 2022
P. Arpaia, U. Cesaro, N. Moccaldi, I. Sannino
The impedance of a biological tissue can be measured starting from an interaction between an electric current with the tissue at cellular and molecular level. The electrical properties of skin have been studied for over a century. An equivalent circuit, with a resistor (Re) in series with the parallel of a resistor (Rskin) and a particualr capacitor (CPE), has been used successfully to describe the skin's electrical properties (Fig. 1.6). In this model, CPE is a pseudo-capacitance, represented by a special element, called Constant Phase Element (CPE), as described by Cole-Cole [42]. It represents the properties of the stratum corneum, the skin's most superficial layer. Conversely, Re represents the resistance associated with the deeper tissues. From this circuit, more complex linear and nonlinear circuits have been proposed in order to model skin's electrical properties more closely. Additional resistors and capacitors, as well as inductors, voltage sources, and diodes, have ben involved. Nevertheless, the abovementioned circuit has proved to be an optimal linear model, where additional resistors and capacitors do not provide statistically significant improvement.
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Published in Stefan Ritter, Anders Molander, Corrosion monitoring in nuclear systems: research and applications, 2017
Jan Macák, Petr Sajdl, Pavel Kučera, Jan Voŝta, Radek Novotný
The impedance spectra for a system without chloride are shown in Fig. 7.3. From the Nyquist plot (Fig. 7.3a), it is evident that the general shape of the spectra includes the impedance response of a corrosion process at higher frequencies and a mass transfer process at lower frequencies. Such a shape of impedance dispersion can be characterised by a –Re[(RpZw)CPEdl]-equivalent circuit (Fig. 7.4a), where Re is the solution resistance, the serial combination RpZw corresponds to the faradaic electrode process and includes the polarisation resistance Rp and the Warburg impedance Zw associated with semi-infinite diffusion. CPEdl is connected in parallel to RpZw and represents a part of non-faradaic electrode phenomena – namely the response of a non-ideal (dispersive) double layer capacitance. CPE is a common abbreviation for the constant phase element, the impedance of which is expressed as ZCPE=Q–1(jω)–n where Q is the CPE coefficient, n the CPE exponent, j the imaginary unit and ω the angular frequency. The CPE exponent n is a measure of the capacitance dispersion having values between 1 (ideal capacitance) and 0.5 (highly dispersed capacitance, e.g. at porous electrodes).
Functionally Graded Materials for Bone Tissue Engineering Applications
Published in Ashutosh Kumar Dubey, Amartya Mukhopadhyay, Bikramjit Basu, Interdisciplinary Engineering Sciences, 2020
Ashutosh Kumar Dubey, Amartya Mukhopadhyay, Bikramjit Basu
A more comprehensive understanding of the electrical transport properties of piezoelectric materials demands the use of impedance spectroscopy. First, let us explain the principle. The general appearance of the impedance spectrum is semicircular arcs and the shape of the arc changes with an increase in temperature. The length of the vector from the origin to any point on the semicircular arc gives the magnitude of impedance at a particular frequency. The right side of the spectrum is the low-frequency region, while the left side (origin) is of high frequency. The conventional materials, generally utilized, are polycrystalline in nature, that is, having grains and grain boundaries. Therefore, their electrical characteristics are distinct and this can be clearly depicted in the impedance spectrum. The complete semicircular arc in the impedance plot can be represented by the parallel RC circuit. Such a type of impedance response is known as the ideal Debye-type behavior. However, the ideal Debye-type behavior is highly impractical for real materials. To compensate the deviation from the ideal Debye-type behavior, the constant phase element (CPE) has been introduced in place of capacitor in the RC circuit.85 CPE considers the inhomogeneous response in bulk and grain boundary regions.86 In addition, CPE explains the frequency dependence of impedance in the high-frequency region, which follow the Jonscher's power law. The CPE value can be calculated by the expression C = (R1−nCQ)1/n, where the parameters CQ and n are capacitance and a constant, respectively (n > 0, for non-ideal case).87
Comparison of corrosion behaviour and passive film properties of 316L austenitic stainless steel in CO2 and N2 environments
Published in Corrosion Engineering, Science and Technology, 2019
Yousuf Abdulwahhab, Thunyaluk Pojtanabuntoeng, Brian Kinsella, Jean-Pierre Veder, Ahmed Barifcani
Hence, different equivalent electrical circuits depicted in Figure 6(a,b) were used. First, the Randle equivalent circuit (Figure 6(a)) represents solution resistance (Rs) in series with the parallel combination of capacitance constant phase element (CPE) and charge transfer resistance (Rct). This equivalent circuit represents a system where no porous layer appears on the sample surface and was used to fit EIS data exhibiting one time constant. Owing to the non-ideal behaviour of capacitors in a corroding environment, a CPE is often used to replace the capacitor to improve the fitting [49]. For this particular equivalent circuit, CPE represents capacitance double layer (Cdl). Thought the physical meaning of CPE is unclear, and it can be converted into pure capacitance (C) using Equation (1) [50–52].where RCt is the charge transfer resistance (Ω cm2), is the CPE constant, (Ω−1 cm−2 sα), and α is the CPE exponent which represents a resistance if α = 0 and an ideal capacitance if α = 1.
Investigation on synthesis of SnO2 nano-particles using sol–gel process for energy storage application
Published in Australian Journal of Electrical and Electronics Engineering, 2020
Sudha Periathai R., Pon Vengatesh R., Jeyakumaran N., Prithivikumaran N.
In the equivalent circuit model, the ohmic resistance (RΩ) represents the resistance of an electrolyte, separator and electrical contacts. Rct denotes the charge-transfer resistance. The diffusion of lithium ions into the bulk of the electrode material is denoted by Warburg impedance (W) and the interfacial capacitance is related with a Constant Phase Element (CPE). The ohmic resistance (RΩ) and the charge-transfer resistance (Rct) as determined from the Z′-Z″ plot are found to be 2.28 Ω and 52 Ω, respectively. These low resistance values could promote easy flow of charges thus enhancing the electrochemical performance.
Passivation effects on corrosion and cavitation erosion resistance of UNS S32205 duplex alloy in 3.5% NaCl
Published in Canadian Metallurgical Quarterly, 2023
F. Alkhaleel, S. R. Allahkaram
Therefore, CPEs should be used in the proposed equivalent circuit, which is shown in Figure 5. RS is the solution resistance from the top of the reference electrode to the electrical double layer. RP is the polarisation resistance (charge transfer resistance) related to the electrical double layer. CPEdl coupled with RP expresses the capacitive behaviour of the electrical double layer. RPf is the passive film resistance and CPEPf represents its capacitive behaviour. A constant phase element CPE is used to clarify the shift of phase between the ac voltage signal and its current response independently of frequency.