Model-based signal tracking in the quantitative analysis of time series of NMR spectra.

Hard modeling of NMR spectra by Gauss-Lorentz peak models is an effective way for dimensionality reduction. In this manner high-dimensional measured data are reduced to low-dimensional information as peak centers, amplitudes or peak widths. For time series of spectra these parameters can be assumed to be smooth functions in time. We suggest to model these time-dependent parameter functions by cubic spline functions, which makes a stable quantitative analysis of NMR series possible even for crossing, highly overlapping peaks. Applications are presented for the batch distillation of methanol and diethylamine, and the reaction of acetic anhydride with 2-propanol.

Reaction rate ambiguities for perturbed spectroscopic data: Theory and implementation.

The analysis of reaction systems and their kinetic modeling is important for both exploratory research and process design. Multivariate curve resolution (MCR) methods are state-of-the-art tools for the analysis of spectral series, but are also affected by an unavoidable solution ambiguity that impacts the obtained concentration profiles, spectra and model parameters. These uncertainties depend on the underlying model and the magnitude of the measurement perturbations. We present a general theoretical approach together with a computational method for the analysis of the solution ambiguity underlying arbitrary kinetic models. The main idea is to determine all those model parameters for which the corresponding pure component factorizations satisfy all given constraints within small error tolerances. This makes it possible to determine bands of concentration profiles and spectra that reflect the underlying ambiguity and circumscribes the potential reliability of MCR solutions. False conclusions on the uniqueness of a solution can be prevented. The procedure can be applied as a post-processing step to MCR methods as MCR-ALS, ReactLab or others. The Matlab program code is freely accessible and includes not only the proposed ambiguity analysis but also an MCR hard-modeling approach. Application studies are presented for two experimental data sets, namely for UV/Vis spectra on the relaxation of a photoexcited state of benzophenone and for Raman spectra on an aldehyde formation process.

Application of a new method for simultaneous phase and baseline correction of NMR signals (SINC).

Recently, we presented a new approach for simultaneous phase and baseline correction of nuclear magnetic resonance (NMR) signals (SINC) that is based on multiobjective optimization. The algorithm can automatically correct large sets of NMR spectra, which are commonly acquired when reactions and processes are monitored with NMR spectroscopy. The aim of the algorithm is to provide spectra that can be evaluated quantitatively, for example, to calculate the composition of a mixture or the extent of reaction. In this work, the SINC algorithm is tested in three different studies. In an in-house comparison study, spectra of different mixtures were corrected both with the SINC method and manually by different experienced users. The study shows that the results of the different users vary significantly and that their average uncertainty of the composition measurement is larger than the uncertainty obtained when the spectra are corrected with the SINC method. By means of a dilution study, we demonstrate that the SINC method is also applicable for the correction of spectra with low signal-to-noise ratio. Furthermore, a large set of NMR spectra that was acquired to follow a reaction was corrected with the SINC method. Even in this system, where the areas of the peaks and their chemical shifts changed during the course of reaction, the SINC method corrected the spectra robustly. The results show that this method is especially suited to correct large sets of NMR spectra and it is thus an important contribution for the automation of the evaluation of NMR spectra.