Kinetic hard-modelling and spectral validation of rank-deficient spectroscopic data: A case study

Abstract

Hard-modelling Concentration matrix Rank deficiency and augmentation A priori information and experimental designIn this case study, we apply a recently developed method to systematically predict the linear dependencies in concentration profiles and identify minimum requirements to enable optimisation of rate constants and pure component spectra via direct multivariate kinetic hard-modelling of spectroscopic data. This systematic method was applied to the rank-deficient acid catalysed reaction of benzophenone with phenylhydrazine in THF. Various experimental conditions (different dosing and initial concentrations) and data treatments (defining uncoloured species, including known component spectra into the analysis) were considered. For all these conditions, the kinetic mechanism of this condensation reaction was successfully validated by the agreement between fitted and independently measured mid-IR and UV-vis pure component spectra and by the highly reproducible fitted rate constants. This case study particularly demonstrated the value of the direct spectral fitting as a tool for the validation of rank-deficient kinetic mechanisms, as inherent contributions within the fitted component spectra, due to the definition of uncoloured species, can be systematically addressed.

Combined in Situ Monitoring Method for Analysis and Optimization of the Lithiation-Fluoroacetylation of N-(4-Chlorophenyl)-Pivalamide

“…FT-IR spectroscopy used in conjunction with reaction calorimetry is a contemporary approach in process development. − In addition, online UV/vis spectroscopic applications are rather recent, − while the combination of UV/vis with calorimetry signals is a quite novel approach. Finally, in situ endoscopy has been proven to be a practical tool for monitoring color changes and physical transformations such as crystallization and dissolution …”

Comprehensive kinetic model for the dissolution, reaction, and crystallization processes involved in the synthesis of aspirin

“…Only the spectroscopically active species can be modeled directly from absorbance spectra using the method described in Equations (2)(3)(4). Attempting to directly model more than these species results in a rank-deficient matrix inverse problem during the model fitting process [29] (see Equation (2)). In this experiment, the rank of the concentration matrix C and of the pure component spectral matrix A (see Equation (1)) is three for the two following reasons: the mass balance for such a kinetic model only allows three spectroscopically active species to change in a linearly independent manner (rank condition on C); among these three possible spectroscopically active species, there are actually three absorbing species in this UV/Vis range (rank condition on A).…”

Towards Molecular Control of Spin States in Organic Solar Cell Electron Acceptor Materials

“…In hard modelling, the parameters for the given kinetic model or reaction mechanism are fitted to describe the dynamics of the system under study. 89,90 The expression of multivariate spectroscopic measurement D in terms of concentration (C i ), spectra (S T i ) and residuals is shown in Equation 3. 2.…”