Physically-Based Models for the Analysis of Raman Spectra

In recent years, spectroscopy has developed into an increasingly valuable tool to determine the composition of mixtures; for scientific questions as well as for the industry. The increasing use of spectroscopy raises the question how to best use the obtained data. For the analysis of spectral data, the method of Indirect Hard Modeling (IHM) has been established besides statistical methods like PLS. IHM is a nonlinear method that can therefore efficiently treat nonlinear effects such as peak-shifts. In the present work, the IHM method is expanded to increase its applicability. IHM treats nonlinear effects in the spectral evaluation. Therefore, the direct proportionality between the concentration and the Raman signal of a component can be used for calibration. The resulting linear calibration model allows for reliable extrapolation. Thus, IHM can be used to study reactive systems, even if only binary subsystems can be used for calibration. However, thermodynamic systems with intermediates can so far only be calibrated by using thermodynamic models. In this work, a method is established that calibrates a reactive system with intermediates only based on the reaction mechanism as well as stoichiometry and electroneutrality. Spectral backgrounds, e.g., fluorescence, can be treated by a spectral pretreatment or via background models. However, spectral backgrounds are still a common source of error in IHM. Derivatives have long been used very effectively in statistical methods. Therefore, IHM is adapted so that it becomes possible to evaluate the first derivative of spectra. The calibration of IHM is mostly limited to the relative spectral intensities of the involved components. In the present work, a method is presented that uses the information in the calibration spectra more thoroughly. For this purpose, nonlinear effects are parametrized as a function of concentration. The commonly used peak profiles do not reflect the physical reality at a detector very well. As a result, narrow modelled peaks may change their apparent intensity if they are shifted. To correct these shortcomings, a new peak model is proposed in this work that is more closely aligned to the physical reality of a detector.