Time-scales for Spectroscopic Measurements

The quality of the system identification results is strongly dependent on the manner in which the spectroscopic measurements are made. In this regard, the time-scale of the individual spectral measurements Tgpect is crucial. Many good resolution FTIR, Raman, UV-VIS, fluorescence and H, F, P NMR spectra can be obtained in 100 s or less. Also, many VCD, ECD, and 2D NMR spectra can be obtained in 1000 s or less. 

The time-dependence of the concentrations of the observable species Si...Ss L,obs provide estimates for the half-lives ti...tJ. Although these half-lives are not known during the data acquisition period, they can be obtained during data analysis. Let min Ti...Ts denote the smallest value. It is important to check that Eq. (6) is valid. If Eq. (6) does not hold, then one or more of the pure component spectra possess some temporal induced distortion and are therefore inaccurate. 

We note in passing that many more spectra will be accumulated compared to the observable species present. This represents an over-determined problem, one of many qualities present in real physical ill-posed problems. 

Spin relaxation times are a very important issue in flow-through NMR, and may preclude some types of measurements. 

One can and should enquire about the time-scale of the spectroscopic measurements and the reaction time-scales. In general, there will be a few observable species i. e. organometallics, associated with the induction kinetics, and the deactivation kinetics. Therefore, the kinetic time-scales are similar to the half-lives of these species. If is short compared to the half-lives of these species, both the induction and deactivation kinetics can be modeled accurately. 

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