In spite of a rapid growth of data processing software, that has allowed for a huge advancement in many fields of chemistry, some research issues still remain problematic. A standard example of a troublesome challenge is the analysis of multi-component mixtures. The classical approach to such a problem consists of separating each component from a sample and performing individual measurements. The advent of computers, however, gave rise to a relatively new domain of data processing – chemometry – focused on decomposing signal recorded for the sample rather than the sample itself. Regrettably, still a very few chemometric methods are practically used in everyday laboratory routines. The Authors believe that a brief ‘user-friendly’ guide-like article on several ‘flagship’ algorithms of chemometrics may, at least partly, stimulate an increased interest in the use of these techniques among researchers specializing in many fields of chemistry. In the paper, five different techniques of factor analysis are used for the analysis of a three-component system of fluorophores. These algorithms, applied on the excitation-emission spectra, recorded for the ‘unknown’ mixture, allowed to unambiguously determine its composition without the need for physical separation of the components. An example of using chemometric methods for physical chemistry research is also provided. For each presented technique of the data analysis, a short description of its theoretical background followed by an example of its practical performance is given. In addition, the Reader is supplemented with a basic information on matrix algebra, detailed experimental ‘recipes’, reference specialist literature and ready-to-use MATLAB codes. Graphical abstract
‘White’ and ‘grey’ methods of data modeling have been employed to resolve the heterogeneous fluorescence from a fluorophore mixture of 9-cyanoanthracene (CNA), 10-chloro-9-cyanoanthracene (ClCNA) and 9,10-dicyanoanthracene (DCNA) into component individual fluorescence spectra. The three-component spectra of fluorescence quenching in methanol were recorded for increasing amounts of lithium bromide used as a quencher. The associated intensity decay profiles of differentially quenched fluorescence of single components were modeled on the basis of a linear Stern-Volmer plot. These profiles are necessary to initiate the fitting procedure in both ‘white’ and ‘grey’ modeling of the original data matrices. ‘White’ methods of data modeling, called also ‘hard’ methods, are based on chemical/physical laws expressed in terms of some well-known or generally accepted mathematical equations. The parameters of these models are not known and they are estimated by least squares curve fitting. ‘Grey’ approaches to data modeling, also known as hard-soft modeling techniques, make use of both hard-model and soft-model parts. In practice, the difference between ‘white’ and ‘grey’ methods lies in the way in which the ‘crude’ fluorescence intensity decays of the mixture components are estimated. In the former case they are given in a functional form while in the latter as digitized curves which, in general, can only be obtained by using dedicated techniques of factor analysis. In the paper, the initial values of the Stern-Volmer constants of pure components were evaluated by both ‘point-by-point’ and ‘matrix’ versions of the method making use of the concept of wavelength dependent intensity fractions as well as by the rank annihilation factor analysis applied to the data matrices of the difference fluorescence spectra constructed in two ways: from the spectra recorded for a few excitation lines at the same concentration of a fluorescence quencher or classically from a series of the spectra measured for one selected excitation line but for increasing concentration of the quencher. The results of multiple curve resolution obtained by all types of the applied methods have been scrutinized and compared. In addition, the effect of inadequacy of sample preparation and increasing instrumental noise on the shape of the resolved spectral profiles has been studied on several datasets mimicking the measured data matrices. Graphical Abstractᅟ
An elegant, well-established effective data filter concept, proposed originally by Abraham Savitzky and Marcel J.E. Golay, is undoubtedly a very effective tool, however not free from limitations and drawbacks. Despite the latter, over the years it has become a "monopolist” in many fields of spectra processing, claiming a "commercial" superiority over alternative approaches, which would potentially allow to obtain equivalent or in some cases even more reliable results. In order to show that basic operations performed on spectral datasets, like smoothing or differentiation, do not have to be equated to the application of the one particular single algorithm, several of such alternatives are briefly presented within this paper and discussed with regard to their practical realization. A special emphasis is put on the fast Fourier methodology (FFT), being widespread in the general domain of signal processing. Finally, a user-friendly Matlab routine, in which the outlined algorithms are implemented, is shared, so that one can select and apply the technique of spectral data processing more adequate for their individual requirements without the need to code it prior to use.
The undertaken research allows to explain and characterize the occurrence and anomalous increase of an additional absorption band observed in the spectrum of fumaronitrile dissolved in toluene. The formation of...
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