Impedance spectroscopy noise

ENA was recently used for remote on-line corrosion monitoring of carbon steel electrodes in a test loop of a surge water tank at a gas storage field. An experimental design and system for remote ENA and collection of electrochemical impedance spectroscopy (EIS) data (Fig. 13) have been presented elsewhere. In the gas storage field, noise measurements were compared with electrode weight loss measurements. Noise resistance (R ) was defined as... 

The traditional way is to measure the impedance curve, Z(co), point-after-point, i.e., by measuring the response to each individual sinusoidal perturbation with a frequency, to. Recently, nonconventional approaches to measure the impedance function, Z(a>), have been developed based on the simultaneous imposition of a set of various sinusoidal harmonics, or noise, or a small-amplitude potential step etc, with subsequent Fourier- and Laplace transform data analysis. The self-consistency of the measured spectra is tested with the use of the Kramers-Kronig transformations [iii, iv] whose violation testifies in favor of a non-steady state character of the studied system (e.g., in corrosion). An alternative development is in the area of impedance spectroscopy for nonstationary systems in which the properties of the system change with time. 

More detailed information can be obtained from noise data analyzed in the frequency domain. Both -> Fourier transformation (FFT) and the Maximum Entropy Method (MEM) have been used to obtain the power spectral density (PSD) of the current and potential noise data [iv]. An advantage of the MEM is that it gives smooth curves, rather than the noisy spectra obtained with the Fourier transform. Taking the square root of the ratio of the PSD of the potential noise to that of the current noise generates the noise impedance spectrum, ZN(f), equivalent to the impedance spectrum obtained by conventional - electrochemical impedance spectroscopy (EIS) for the same frequency bandwidth. The noise impedance can be interpreted using methods common to EIS. A critical comparison of the FFT and MEM methods has been published [iv]. 

Regression problems in impedance spectroscopy may become ill-conditioned due to improper selection of measurement frequencies, excessive stochastic errors (noise) in the measured values, excessive bias errors in the measured values, and incomplete frequency ranges. The influences of stochastic errors and foequency range on regression are demonstrated by examples in this section. The issue of bias errors in impedance measurement is discussed in Chapter 22. The origin of stochastic errors in impedance measurements is presented in Chapter 21. 

In principle, the Kramers-Kronig relations can be used to determine whether the impedance spectrum of a given system has been influenced by bias errors caused, for example, by instrumental artifacts or time-dependent phenomena. Although this information is critical to the analysis of impedance data, the Kramers-Kronig relations have not found widespread use in the analysis and interpretation of electrochemical impedance spectroscopy data due to difficulties with their application. The integral relations require data for frequencies ranging from zero to infinity, but the experimental frequency range is necessarily constrained by instrumental limitations or by noise attributable to the instability of the electrode. 

This part introduces methods used to measure impedance and other transfer functions. The chapters in this section are intended to provide an understanding of frequency-domain techniques and the approaches used by impedance instrumentation. This understanding provides a basis for evaluating and improving experimental design. The material covered in this section is integrated with the discussion of experimental errors and noise. The extension of impedance spectroscopy to other transfer-function techniques is developed in Part III. 

F. Mansfeld, C. H. Hsu, D. Omek etal.. Corrosion control using regenerative biofilms (CCURB) on almninum 2024 and brass in different media, Proc. Symp. "Neiv Trends in Electrochemical Impedance Spectroscopy (EIS) and Electrochemical Noise Analysis (ENA)", PV 2000-2024, The Electrochemical Society, Pennington, N, 2001, pp. 99-118. 

Many different electrochemical and non-electrochemical techniques exist for the study of corrosion and many factors should be considered when selecting a technique. Corrosion rate can be determined by Tafel extrapolation from a potentiodynamic polarization curve. Corrosion rate can also be determined using the Stem-Geary equation from the polarization resistance derived from a linear polarization or an electrochemical impedance spectroscopy (EIS) experiment. Techniques have recently been developed to use electrochemical noise for the determination ofcorrosion rate. Suscephbility to localized corrosion is often assessed by the determination of a breakdown potenhal. Other techniques exist for the determinahon of localized corrosion propagahon rates. The various electrochemical techniques will be addressed in the next section, followed by a discussion of some nonelectrochemical techniques. 

NOTE AE, activation energy ER, electrical resistance EIS, electrochemical impedance spectroscopy EN, electrochemical noise LPR, linear polarization resistance. 

Mansfeld, F., Huet, F., and Mattos, O., New Trends in Electrochemical Impedance Spectroscopy and Electrochemical Noise Analysis," The Electrochemical Society, Inc., Pennington, NJ, 2000. 

The veirious types of measurement technologies for assessment of corrosion may be summarized as shown in Tables 2 to 5. These techniques cover both laboratory Jind field use. However, many of the direct methods, particularly the electrochemical methods of potentiodynamic polarization and electrochemical impedance spectroscopy (EIS) are generally more suited to laboratoiy evaluation. In the laboratory, test conditions are clean and more controlled. Consequently, more sophisticated measurement electrode systems can be used that take advantage of their more sophisticated measurements technologies. In the field, practicalities of changing process conditions, high flow rates, debris, electrical noise, and electrical safety limit their use. 

The other techniques of potentiodynamic scanning, EIS, harmonic impedance spectroscopy (HIS), and pure electrochemical current and potential noise are primarily laboratory methods that are used only in a limited way in field investigations. This is because of their relative expense, requirement for a low noise measurement environment, and clean and stable process conditions. However, simple qualitative electrochemical noise or pitting indications are used in a simple way in field applications to look at uniform versus nonuniform corrosion. Greater fluctuations and instability in the noise measurements are generally indicative of conditions leading to nonuniform or pitting corrosion. 

The corrosion test methods may be any method that can provide corrosion data in the low water environments. This is generally coupon testing, but may include electrochemical tests that are applicable to the high resistivity crude oil continuous environments at low water levels, e.g., electrochemical impedance spectroscopy and electrochemical noise. 

Many other techniques and methodologies have been used to monitor effectiveness in inhibitor testing and the evaluation of inhibitors. Some of these are EIS (electrochemical impedance spectroscopy), EN (electrochemical noise measurements), galvanic testing, and many variations of these methods. The theoretical bases for these techniques have been discussed by Scully in Chapter 7 of this book, and specific applications are extensively referenced there. 

Mansfeld, F., Hsu, C. H., Oemek, D., Wood, T. K-, and Syrett, B. C., "Corrosion Control Using Regenerative Biofilms on Aluminum 2024 and Brass in Different Media, Proceedings of New Trends in Electrochemical Impedance Spectroscopy and Electrochemical Noise Analysis, F. Mansfeld, F. Huet, and O. Mattos, Eds., 2001, The Electrochemical Society, Proceedings, Vol. 2000-24, pp. 99-118. 

The choice of electrochemical techniques that can be implemented in a tribocorrosion test and the development of relevant models for the interpretation of the tribocorrosion mechanism are determined by the mechanical contact conditions being continuous or reciprocating. Electrochemical measurements can be performed with both types of tribometers. However, to be implemented under conditions that allow the interpretation of results, some methods require stationary electrochemical conditions, at least prior to starting up the measurements. In the case of continuous sliding, a quasi-stationaiy electrochemical surface state can often be reached, and all the electrochemical techniques available for corrosion studies (polarization curves, impedance spectroscopy, electrochemical noise,...), can be used. On the contrary, when reciprocating contact conditions prevail, the interpretations of experimental results are more complex due to the non-stationary electrochemical conditions. Measuring techniques suitable for the recording of current or potential transients will be used preferentially (Mischler et al., 1997 Rosset, 1999). 

The full investigation of the tribocorrosion tests requires generally the use of in situ tools like open circuit measurements, polarization measurements, current transients, impedance spectroscopy, and noise measurements, and ex situ tools like elemental surface analysis techniques, optical or electron microscopy, micro-topography, micro and nanohardness measurements texture and internal stress analyses. 

As electrochemical measurements are of particular importance for corrosion studies, this chapter will only concentrate on them. However, since many textbooks and monographs discuss the earlier-mentioned simple analysis of current-voltage plots, this discussion will not be covered here. In recent years, more sophisticated techniques have been developed, and these partly overcome the restrictions of conventional electrochemical measurements as they either provide only a small potential perturbation on the corroding system (impedance spectroscopy), use no perturbation at all (electrochemical noise analysis), are able to measure current and potential fluctuations on inhomogeneous corroding surfaces (vibrating electrochemical electrode techniques), or... 

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