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Chapter 1. Introduction 14 equivalent circuit using complex nonlinear least-squares (CNLS) regression. Other transformations of impedance data are also useful to try to more clearly understand the data [1]. Techniques such as analysis of differences in impedance spectra (ADIS) [7] and transformation to the distribution function of relaxation times (DRT) [8-10] increase the frequency domain resolution, enabling clearer visual identification of peaks of specific processes at their characteristics frequencies. The DRT method is used in Chapter 4. Ideally, the distribution function of relaxation times could be obtained directly from an impedance spectrum using the convolution equation (1.6) [1, 8-10]. (1.6) where is the impedance data, is the ohmic part of the impedance, is the polarization part of the impedance, and is the polarization resistance of the impedance. However, in practical measurements, only part of the entire impedance spectrum is sampled at a limited number of discrete points over a finite frequency range. The deconvolution must therefore be solved numerically, however erroneous results are obtained due to large amplification of experimental error. Algorithms have been developed to minimize these errors, by extrapolating the data at high and low frequency to artificially enlarge the frequency range of the data and by filtering data in Fourier space (performing a Fourier transform on the data, applying a filter, and then performing the inverse Fourier transform) to reduce noise [1, 8-10]. In all cases it is useful to compare measurements taken with small changes in experimental conditions and keeping as many of the other parameters fixed as possible. Parameter changes can then be correlated with changes in the impedance response, which can help to reveal the number of and nature of the impedance processes and possible reaction mechanisms. With modern automated control and data acquisition systems, variation of test conditions can be performed in a systematic and thorough manner over the course of hours to months without the experimenter sitting at the test set-up. This is used extensively in Chapters 4 and 5. For further information about impedance spectroscopy, good textbooks have been recently published [5, 11]. Besides electrochemical properties, other properties of the electrode materials are studied in Chapters 4, 5, and 6. The techniques used are generally more straightforward and well-known than impedance spectroscopy. Before and/or after the electrochemistry tests, surfaces and interfaces were most often examined with a scanning electron microscope (SEM) (and occasionally an atomic force microscope, AFM) to characterize the microstructure, and sometimes the energy-dispersive X-ray spectrometer (EDX) equipped in the SEM was used toPDF Image | Electrolysis of CO2 and H2O
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