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-Alternating 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.