(Invited) Secondary Modulation in Electrochemical Impedance Spectroscopy Instrumentation
Authors: Zhang Xueyuan , Moosbauer Dominik 
Published: February 2020

Electrochemical Impedance Spectroscopy (EIS) is widely applied in Electrochemistry for studying the electrode/electrolyte interface, films, coating, and ion transport mechanisms amongst others. Most EIS measurements are based on primary modulation in frequency and amplitude of a sine wave which serves as perturbation signal – either potentiostatic or galvanostatic. Three requirements in an electrochemical system including stability, causality, and linearity are necessary for an accurate EIS measurement. This is described in detail by Macdonald, Orazem, and Tribollet et al [1-2].
Further modulation instrumentations relating to single-sine and multi-sine wave modulations with the purpose to increase the signal-to-noise ratio, measurement time [3], and obtaining additional information about the current system (e.g. corrosion rate) are discussed in this presentation.
An applied signal of two superimposed sine waves with two different frequencies can act as perturbation for measuring the general corrosion rate and pitting corrosion. This technique – also referred to as Electrochemical Frequency Modulation (EFM) – was well developed and described by Bosch and Bogaerts et al [4-5]. Impedance measurements with non-linear perturbation can provide further information relating to corrosion kinetics of the Tafel slope and corrosion rate based on Taylor expansion using the traditional Butler–Volmer equation. The overpotential (η) can be expressed as follows:

η = V [sin(ω
1t) + sin(ω
2t)]
After rearranging the equation and substituting various parameters, a useful relationship between potential and current can be derived.
Analysis of the corrosion rate using beverages cans and soda is presented in this study. EFM is compared to other techniques such as EIS, LPR (Linear Polarization Resistance), and EN (Electrochemical Noise). Instrumentation issues relating to frequency modulation and harmonics are discussed based on applications in the corrosion and fuel cell field.
The second signal modulation in EIS is the variable amplitude. Noise level or impedance increases at lower frequency. Impedance data can scatter with lower signal amplitudes. Wojcik and Orazem used variable-amplitude signals in galvanostatically modulated impedance spectroscopy to assess reactivity at the corrosion potential without distorting temporal evolution of the system relating to copper in seawater [6-7]. Variable-amplitude signals can increase the signal level for a higher quality of EIS data. However, the voltage amplitude cannot follow a linear relationship when the impedance increases at lower frequencies during galvanostatic EIS. A fixed voltage (less than 10 mV) with a variable current amplitude for the sine wave can be used to achieve this goal. Instrumentation of amplitude modulation relating to noise from instruments and electrochemical system is further discussed in this presentation. The application of variable amplitude modulation is discussed based on EIS measurements of coatings and lithium-ion batteries.
References:

E.Barsoukov and J. R.Macdonald, Impedance Spectroscopy: Theory, Experiment, and Applications 2nd Edition, p129, Wiley-Interscience, New Jersey(2005).

M.E.Orazem and B.Tribollet, Electrochemical Impedance Spectroscopy, 1 edition, p146, Wiley-Interscience, New Jersey(2008)

G.S. Popkirov and R.N. Schindler, Rev. Sci. Instrum. 64(11), 3111( 1993).

R.W. Bosch,W.F. Bogaerts, Corrosion 52, 2014 (1996).

R.W. Bosch,W.F. Bogaerts, Corrosion Science 52, 2773(2010)

P.T.Wojcik and M.E.Orazem, Corrosion 54, 289(1998).

P.T.Wojcik, P.Agarwal and M.E.Orazem, Electrochimica Acta 41, 977(1996).