Single spectroscopic measurements with

This procedure may seem rather formidable but it readily will be illustrated by a simple example which forms the basis of much of the studies in this area. Consider an aggregate of units with fibre symmetry (i.e. defined by the orientation of a single axis), the aggregate also possessing fibre symmetry. The spectroscopic measurements will then yield values for (cos2 P>, (cos4 P>, etc. The distribution function will be a function of 0 only, and can be expanded in terms of P2(cos 0), P4(cos 0), etc. 

For their characterization, electrochromic compounds are initially tested at a single working electrode under potentiostatic control using a three-electrode arrangement. Traditional characterization techniques such as cyclic voltammetry, coulometry, chronoamperometry, all with in situ spectroscopic measurements, are applied to monitor important properties [27]. From these results, promising candidates are selected and then incorporated into the respective device. 

Extracting analyte concentrations from spectra of complex systems containing multiple analyte contributions with overlapping spectral features requires more information than is obtainable in a single wavelength measurement. Multivariate techniques take the full-range spectrum into account and exploit the multichannel (data at many wavelengths) nature of spectroscopic data to extract concentration information from analytes.19 20... 

In the resolution of any multicomponent system, the main goal is to transform the raw experimental measurements into useful information. By doing so, we aim to obtain a clear description of the contribution of each of the components present in the mixture or the process from the overall measured variation in our chemical data. Despite the diverse nature of multicomponent systems, the variation in then-related experimental measurements can, in many cases, be expressed as a simple composition-weighted linear additive model of pure responses, with a single term per component contribution. Although such a model is often known to be followed because of the nature of the instrumental responses measured (e.g., in the case of spectroscopic measurements), the information related to the individual contributions involved cannot be derived in a straightforward way from the raw measurements. The common purpose of all multivariate resolution methods is to fill in this gap and provide a linear model of individual component contributions using solely the raw experimental measurements. Resolution methods are powerful approaches that do not require a lot of prior information because neither the number nor the nature of the pure components in a system need to be known beforehand. Any information available about the system may be used, but it is not required. Actually, the only mandatory prerequisite is the inner linear structure of the data set. The mild requirements needed have promoted the use of resolution methods to tackle many chemical problems that could not be solved otherwise. 

The diffusion coefficient may be measured via several experimental techniques. The most prominent ones at present are the direct observation of a diffusion boundary in either a field electron microscope [159, 160] or a photoelectron emission microscope [158] or via laser desorption experiments [161, 162], In the latter case a short laser pulse is used to heat the surface to momentarily desorb the adsorbate from a well defined region of the crystal. Subsequent laser pulses with well defined time delays with respect to the first one, and measurement of the number of particles leaving the surface, allow one to determine the rate of diffusion into the depicted zone. Other methods to determine surface diffusion are spectroscopic measurements which cover the proper time window, for example magnetic resonance-based methods [163, 164]. In favorable cases these methods may even be applied to single crystal surfaces [165],... 

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