Enhancement of time resolution in transient kinetics

• Enhancement of temporal resolution in the transient response of a reactive system.
• Description of an algorithm for deconvolution of a distorted concentration signal.
• Basics of regularization theory for inverse problems in heterogeneous catalysis.
• Deviations from the Beer–Lambert law and the consequent error in transient kinetics.

A methodology for enhancement of time resolution in transient experiments has been formulated where the mathematical background of the deconvolution problem is outlined. The analysis leads to an algorithm based on the discrepancy principle for calculation of the regularization parameter, which exhibits satisfactory convergence and can successfully handle the noise that is present in the original measurements. Application of the algorithm for different synthetic datasets has shown that the extent of enhancement in time resolution depends on the broadening function and the sampling frequency of the detector. Consequently, shorter residence times and higher sampling frequencies are in general desirable.The impact of deviations from the Beer–Lambert law in Fourier-transform infra-red spectroscopy has also been evaluated using computational fluid dynamics simulations. The flow field and concentration distribution in a gas cell with ∼5 m optical pathlength have been simulated, and the absorbance–concentration correlations have been implemented in the analysis. Carbon monoxide and nitric oxide have been chosen as species with significant nonlinear infra-red absorption features, and their mixtures with different concentrations have been considered in separate simulations. Due to the nonlinear characteristics of the problem, various levels of error have been observed in the results, which are dependent on the concentration at the inlet of the gas cell and the gas phase species as well.The variance of concentration distribution normalized with mean squared concentration has been defined as a measure of intensity of segregation, which displays strong similarity for the same flow field pattern and relatively close molecular diffusivities.