Use of measurement models is suggested as an intermediate step in the analysis of impedance data. In a manner analogous to the routine use of measurement models in the deconvolution of optical spectra, the measurement model could be used to guide development of physicoelectrochemical models by determining whether a data set is consistent with the Kramers‐Kronig relations, by suggesting a form for the error structure of the data, and by providing an indication of the number and type of physical processes that can be resolved from the data. In this paper, a general measurement model is shown to apply for a wide variety of typical electrochemical impedance spectra. The application of the measurement models as a data filter will be addressed in subsequent papers.

The Kramers-Kronig equations and the current methods used to apply them to electrochemical impedance spectra are reviewed. Measurement models are introduced as 'a tool for identification of the frequency-dependent error structure of impedance data and for evaluating the consistency of the data with the Kramers-Kronig relations. Through the use of a measurement model, experimental data can be checked for consistency with the Kramers-Kronig relations without explicit integration of the Kramers-Kronig relations; therefore, inaccuracies associated with extrapolation of an incomplete frequency spectrum are resolved. The measurement model can be used to determine whether the residual errors in the regression are due to an inadequate model, to failure of data to conform to the Kramers-Kronig assumptions, or to noise.

Development of appropriate models for the interpretation of impedance spectra in terms of physical properties requires, in addition to insight into the chemistry and physics of the system, an understanding of the measurement error structure. The time-varying character of electrochemical systems has prevented experimental determination of the stochastic contribution to the error structure. A method is presented by which the stochastic contribution to the error structure can be determined, even for systems for which successive measurements are not replicate. Although impedance measurements are known to be heteroskedastic in frequency (i.e., have standard deviations that are functions of frequency) * Electrochemical Society Student Member.

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Max-Planck-Institut für Metallforschung assisted in meeting the publication costs of this article.

This paper presents a flexible and reliable chemiresistor-type NO 2 gas sensor based on single-walled carbon nanotubes (SWNTs) on polytetrafluoroethylene (PTFE) membrane filter substrates. The sensor is realized by using a cost-effective spray coating in the preparation of SWNTs thin film, followed by the fabrication of metal contacts using a shadow mask and polyethyleneimine (PEI) noncovalent functionalization of the SWNTs. This showed a high sensitivity to NO 2 gas at room temperature in dry air; 21.58% to 167.7% for concentrations of 0.75 ppm to 5 ppm, and was almost nonsensitive to ammonia. Gas sensing characterization results, obtained for various substrate bending/wrapping over different cylinders with diameters of 75 mm, 12.5 mm, and 6 mm showed that bending does not significantly affect sensitivity for NO 2 concentrations of 0.75 ppm to 2 ppm, while in the case of 3 ppm to 5 ppm NO 2 , the bent samples indicate enhanced sensitivity. This is probably because of the porous nature of PTFE substrates; these sensors were 1.5 to 2.7 times more sensitive than those fabricated over silicon substrate for 1 ppm and 5 ppm, respectively. Moreover, the relative humidity of 10% and 30% significantly reduced the sensitivity of the sensors. The presented results could be useful for the future development of flexible electronics/sensors for monitoring outdoor air quality and for the detection of volatile organic compounds.

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