Kinetic hard-modelling is often the method of choice in order to determine kinetic parameters of reactions by non-linear optimisation and fitting of measured data. In spectroscopy, kinetic hard-modelling allows decomposing time and wavelength resolved data into concentrations, obtained by integration of the postulated mechanism (rate law), and absorptivity spectra, which are linearly deduced by a calibration-free approach [1]. The validity of the kinetic model can then be assessed by comparing the estimated absorptivity spectra with independently measured ones.

The calibration-free approach inherently leads to a mathematical ambiguity referred to as rank deficiency if concentrations are linearly dependent, since absorptivity spectra cannot be uniquely estimated. Strategies have been developed to circumvent this rank deficiency, but, until recently, the validation of the kinetic model was frequently hampered, as estimated absorptivity spectra could be unknown linear combinations of the real spectra.

We have recently introduced a systematic method for the experimental and data analytical design of spectroscopic kinetic data that allows identifying the suitable strategy to circumvent rank deficiency [2]. Also, linear combinations observed in the estimated absorptivity spectra can be elucidated, allowing spectral validation of any postulated kinetic model, even with rank deficient concentrations [3]. In this contribution, we will present the impact of our systematic method on various simulated and experimental kinetic models commonly encountered in mid-IR and UV-vis spectroscopy.

[1] Maeder, Zuberbühler, Anal. Chem., 1990, 62, 2220.
[2] Billeter et al., Chemom. Intell. Lab. Syst., 2009, 95, 170.
[3] Billeter et al., Chemom. Intell. Lab. Syst., 2009, 98, 213.