ON THE NUMBER OF OBSERVABLE SPECIES, OBSERVABLE REACTIONS AND OBSERVABLE FLUXES IN CHEMOMETRIC STUDIES AND THE ROLE OF MULTICHANNEL INTEGRATION

It is assumed that preliminary experiments are performed to measure th e absorbance of a liquid in a chemically reactive system. Further, giv en the exploratory nature of the study it is assumed that no further i nformation is available concerning the species present nor the reactio ns occurring. The principle chemometric goals of such an exploratory e xperimental study can be stated as follows; (I) determine the number o f statistically significant factors associated with the observable spe cies in solution and (II) determine the number of statistically signif icant factors associated with the observable reactions, consistent wit h the set of spectroscopic measurements. In the case of infrared (IR) spectroscopy, numerous difficulties are encountered due to the sensiti vity of band positions and band shapes to changes in the liquid phase composition during reaction. Although the above mathematical problem a nd its subsequent goals are typically formulated in terms of the Lambe rt-Beer-Bouguer Law (LBBL) followed by factor analysis, the merits of utilizing the integral absorption law (IAL) for infrared spectroscopy in order to achieve goals I and II are examined in detail. First, the possibility of transport involving species into and out of the Liquid phase is considered, and the associated fluxes are defined. Second, te rms representing the model errors for goals I and II arising from the use of both the LBBL and the IAL are specified. Third, well-posed regi ons R-xTP for each model are defined in which the contribution of mod el error is less than the experimental error associated with the measu rements. Fourth, the existence of well-posed solutions for goals I and II for both the LBBL and the IAL representations are presented in ter ms of the singular value decomposition (SVD). Based on literature data for the sensitivity of LBBL and IAL absorptivities, it appears that g oals I and IT are considerably more difficult to achieve in the case o f a LBBL formulation compared to a IAL formulation, i.e. R-xTP(LBBL) subset of R-xTP(IAL). Furthermore, and perhaps most important, it see ms that only the IAL representation is suitable for systems where chan ges in band positions and shapes occur. As a generalization, multichan nel integration for goals I and II involving other absorption spectros copies are also considered. The consequences of both nondestructive an d destructive absorption spectroscopies on goals I and II are addresse d. (C) 1997 Elsevier Science B.V.