Experimental methods for isothermal infrared reaction data

2 Experimental methods for isothermal infrared reaction data 

The basis of all determinations under this heading is the Beer-Lambert law [ 14—16]. All reaction spectra obtained by any spectroscopic sensors can be used as long as the Beer-Lambert law is obeyed. For spectra of a reaction containing several components and absorbances measured a number of times at several wavelengths, the matrix form of Equation 8.19 can be used  

A is the reaction s measured IR spectral absorbance, Nt is the number of measurements at different times, N0 is the number of wavelengths, C is the concentration matrix with the concentration-time profiles of each absorbing component in the columns, Nc is the number of chemical components and E is the pure spectra matrix with the spectral absorption at each wave number of each pure absorbing component in the rows. If a chemical component does not absorb, the corresponding spectrum of the pure chemical will be a vector of zeros. 

It should be noted that, by measuring reaction spectra for the purpose of estimating reaction-model parameters (such as rate constants or activation energies), a new set of unknown parameters is introduced, i.e. the spectral absorbances of the pure chemical components involved in the reaction (matrix ). 

The aim of the multivariate evaluation methods is to fit a reaction model to the measured reaction spectrum on the basis of the Beer-Lambert law and thus identify the kinetic parameters of the model. The general task can be described by the non-linear least-squares optimisation described in Equation 8.20  

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