Hybrid hard- and soft-modeling applied to difference spectra

Difference spectroscopy is used to monitor small changes or variations in a complex environment. Processes monitored by difference spectroscopy always have the spectrum of the initial stage subtracted and, as a consequence, a rank-deficient data set is obtained. This inherent rank-deficiency of the measurement can add to typical rank-deficiency problems in process spectroscopic monitoring, such as the presence of co-evolving reactions. In this work, we first demonstrate that a rank decrease occurs when working with difference spectra irrespective of the fact that we have full-rank or rank-deficient processes and we provide an interpretation of the chemical meaning of the process profiles and difference spectra that can be actually resolved. In a second point, the hybrid Hard-Soft-Modeling version of Multivariate Curve Resolution-Altemating Least Squares is used to resolve this kind of data sets. Special attention is paid to the strategy of application of specific hard-modeling constraints to circumvent rank-deficiency in difference spectroscopy. It is illustrated on simulated data and on two case studies chosen in the field of time-resolved FTIR spectroscopy and UV-Vis transient absorption spectroscopy. Differences in interpretation of the resolved profiles and in the application of constraints between direct and difference spectroscopy are exposed in detail. (c) 2007 Elsevier B.V. All rights reserved.