Complex impedance spectroscopy

The complex impedance spectroscopy (CIS) technique has been extensively used in recent years to examine electrochemical characteristics of surface-deposited electroactive polymer films. A useful summary of the fundamental principles is found in the monograph by McDonald. Applying impedance methods to electroactive polymers has recently been reviewed by Musiani.  

The fundamental principles of impedance spectroscopy are outlined in a number of basic textbooks/ and review articles/ and so only a very brief summary of the fundamental ideas are presented here. In essence we examine the sinusoidal voltage response of an electrochemical system to a small-amplitude sinusoidal current perturbation. Let the perturbation have the form A/ = / sin ot, where / denotes the amplitude of the perturbation. Then the response has the form 

The relationship between AV and A/ is completely determined by the ratio of the amplitudes K /4i and the phase shift f between current and voltage. Therefore we can define the impedance Z as a vector with a modulus Z given by Z = V Hm and argument l (see Fig. 1.66). It is well-known that a vector can in general be resolved into orthogonal components, so from Fig. 1.66 we note that the components of Z, labeled Z and Z , can be written as Z = Z cos 0, Z = Z sin 0. From the latter relationships we obtain an expression for the phase angle 

This procedure is repeated over a very large frequency range, typically from 100 k Hz-0.1 m Hz. The result is an impedance profile or spectrum Z( i ) as a function of frequency to. 

FIGURE 1.66. Schematic representation of Argand diagram illustrating modulus Z and phase angle of a complex number Z. Note that Z and Z represent the real and imaginary components of Z, respectively, since Z = Z — jZ . Note also that Z = Z cos t and Z = Z sin . and Z = (Z + Z .  

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The measuring head connects the sample plate via high frequency capable relay matrices (multiplexers, model KRE-2450-TFCU, MTS-Systemtechnik, 3) to the measuring instruments (1, 2). The setup is usable for complex impedance spectroscopy... 

A number of results, more specifically those concerning beta-alumina, zirconia and tin dioxide when they are associated with gold electrodes, will help us illustrate the importance of complex impedance spectroscopy. 

The complex impedance spectroscopy results in Figure 6.49 show that this material has some characteristics related to electrode polarization, at least in the temperature range we are working on, that is to say between 200 and 600°C, and under air. 

The results obtained through complex impedance spectroscopy for various samples are presented in Figure 6.52 in two representation modes, that is to say the variations of the resistance Y and the capacitance X as a function of frequency, and the variations of Y according to X at various frequency values (Nyquist diagram). 

Complex impedance spectroscopy, Mosi-elastic neutron scattering and nuclear magnetic resonance spectroscopies may also contribute considerably to a good knowledge of proton dynamics. 

Prabakar, K. and Mallikarjun Rao, S.P. (2007) Complex impedance spectroscopy studies on fatigued soft and hard PZT ceramics./. AUoys Compd., 437, 302-310. 

The composites are analyzed by means of complex impedance spectroscopy as the total Impedance is a function of temperature and frequency. Impedance measurements are often made with a Wheatstone bridge type of apparatus in which the resistance, R , and capacitance, C of the sample are balanced against variable resistors and capacitors. The central problem with this measurement arises over the interpretation of the data. This is because the sample and the electrode arrangement is electrically a black box whose equivalent circuit (i.e. its representation by some... 

WUhams JC, Hippertsteel JA, DUgen J, Shain W, Kipke DR (2007) Complex impedance spectroscopy for morritoring hssue respratses to irtserted neural implants. J Nemal Eng 4 410-423... 

FIGURE 1.10. (a) Variation of with redox site concentration according to the He-Chen model [see Eqn. 38(a)]. (b) Comparison between the He-Chen prediction and experimental data for electron-hopping diffusion coefficients for Os(bpy)f loaded in Nafion films obtained via complex impedance spectroscopy by Sharp and coworkers (Ref. 40). 

FIGURE 1.68. A flowchart outlining the mode of examining electroactive polymer materials using complex impedance spectroscopy. 

New York WUey Interscience, 2002, pp. 356-362 JQein L.C., Ho S.F., Szu S.-P, Greenblatt M. Applications of AC complex impedance spectroscopy to understanding transport properties in lithium silicate gels. In Applications of Anal34ical Techniques to the Characterization ofMaterials, Perry D.L., ed. New York Plenum Press, 1991, pp. 101-118... 

Williams JC, Hippensteel JA, Dilgen J (2007) Complex impedance spectroscopy for monitoring tissue responses to inserted neural implants. Journal of Neural Engineering, 4 410 23. 

The electrical properties of liquid crystalline phthalocyanines have been determined for example by complex impedance spectroscopy measurements [10a,72]. Thus it was possible to observe that liquid crystalline phthalocyanines show a slight increase in conductivity when going from the solid to the mesophase. The conductivities of these compounds are low ca.5 x 10 ° S/cm) [75]. Higher conductivities are obtained if crown ether phthalocyanines (CEPcM) are aggregated by adding metal pricate salts (M = K +, Rb +, Cs+ (Trt 10 ° to lO " S/cm)... 

Mattos et also reported an NMR and complex impedance spectroscopy study of a gelatin-based SPE plasticized with glycerol and containing lithium perchlorate. Gelatin also constitutes a polymer host for electrolyte as it can dissolve ionic salts. Ionic conductivities of about 10 S/cm were obtained at room temperature for samples prepared with 8-10 wt% of lithium salt. The temperature dependence of the Li spin-lattice relaxation suggested that there are two dynamic processes associated with lithium diffusion in the plasticized gelatin-based electrolytes. 

Julien C, Massot M (1990) Complex impedance spectroscopy. In Balkanski M (ed) Microionics solid state integrable batteries. North-Holland, Amsterdam, pp 173-195... 

Impedance spectroscopy (IS) is a powerful tool used to study the electrical characteristics in oxide dielectrics [94-97], and is progressively utilized to analyze the resistive switching [70,93,98]. Complex impedance spectroscopy can be employed to identify the response of grain bulk from those of grain boimdary and electrode interface by representing the samples... 

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