Alternating Current Methods for Battery Evaluation
The alternating current (AC) method is a powerful electrochemical measurement tool to evaluate the performance of batteries because the time constants in electrochemical signals can be discriminated without damage to the electrodes. An electrochemical imp
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Alternating Current Methods for Battery Evaluation M. Itagaki
11.1 Introduction to Alternating Current Methods Alternating current (AC) methods are powerful electrochemical measurement tools to evaluate the performance of batteries because the time constants in electrochemical signals can be discriminated without damage to the electrodes. An electrochemical impedance is determined by measuring the alternating current response to the alternating voltage imposed on the electrode/electrolyte interface. The electrode/ electrolyte interface can be characterized by the interpretation of the electrochemical impedance spectrum. The AC method was recently called electrochemical impedance spectroscopy (EIS) because the impedance spectrum measured in a wide frequency range provides information concerning the detailed structure of the electrode/electrolyte interface. The typical interpretation of an impedance spectrum is explained using a simple equivalent circuit (Fig. 11.1). Figure 11.1a shows a conceptual scheme of an electrode contacted with an electrolyte. The anodic or cathodic reaction rate at the electrode/electrolyte interface has to do with the charge-transfer resistance Rct. In addition, an electric double layer is formed at the interface, and the double-layer capacitance is represented by Cdl. Figure 11.1b describes an equivalent circuit involving Rct in parallel with Cdl, which is in series with the electrolyte resistance Rele.
M. Itagaki (*) Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo, Japan e-mail: [email protected] T. Osaka and Z. Ogumi (eds.), Nanoscale Technology for Advanced Lithium Batteries, Nanostructure Science and Technology 182, DOI 10.1007/978-1-4614-8675-6_11, © Springer Science+Business Media New York 2014
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M. Itagaki
124 Fig. 11.1 Simple equivalent circuit for electrode/ electrolyte interface. Rct: charge-transfer resistance, Cdl: electric double-layer capacitance, Rele: electrolyte resistance
11.2 Principle of AC Methods 11.2.1 Impedance Presented by Complex Number The impedance Z is presented by the following complex number with real part Z′ and imaginary part Z′′:
Z = Z ′ − jZ ″
(11.1)
The relation of Z′ and Z′′ on the complex plane is depicted in Fig. 11.2. The imaginary axis of the complex plane is usually represented by a minus value of the imaginary component because almost electrochemical impedance shows the capacitive behavior, and thus Z′′ means a minus value of the imaginary part. The complex- plane plot of Z is called a Nyquist plot. The magnitude and phase shift of Z are represented as follows:
Z =
(Z ) + (Z ) ′ 2
″ 2
Z″ −j = arctan ′ Z q=
90 j p
(11.2) (11.3)
(11.4)
11 Alternating Current Methods for Battery Evaluation
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Fig. 11.2 Complex plane to represent impedance Z as a complex number
The angle of vector Z against the real axis corresponds to −φ (radian) or −θ (degrees) on the complex plane in Fig. 11.2. The magnitude and phase shift of Z are often displayed on a Bode plot, namely, plots of log|Z
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