Sensitivity and correlation analysis of the physical parameters in absorption, four‐wave mixing, and Schlieren experiments

Abstract

Experimental data that are used to determine rate coefficients depend not only upon reaction rates but also the physical properties of the measured species. Sensitivity coefficients are presented for the physical parameters of three general experimental techniques: a signal linearly dependent on the concentration of a species, a signal quadratically dependent on concentration, and a schlieren signal, which depends upon a bulk property of the system. With these, both the physical and chemical parameters of a model may be treated on a comparable basis. The similarities and differences between these techniques are illustrated in a simple example of radical formation via first-order precursor decomposition followed by second-order recombination. The results are then applied to two important examples: HZ + 0 2 and CH3 + CH3. In almost all cases, the experimental data contains more information about the physical parameters, such as the optical cross section, than the kinetic rate coefficients. Furthermore, if a physical parameter is not properly treated; strong correlations between it and rate coefficients will introduce significant systematic biases in the rate coefficient. 0

Recombination of Methyl Radicals. 1. New Data between 1175 and 1750 K in the Falloff Region

“…The reduced sensitivity coefficient with respect to the cross section for optical absorption is given by [CH 3 ( t )]/[CH 3 ] max and varies between 0 and 1. The derivation of this result and a discussion of methyl−methyl recombination at 1300 K have been published . Here, we analyze our highest temperature measurement at 1742 K and discuss the influence of secondary reactions.…”

“…The derivation of this result and a discussion of methyl-methyl recombination at 1300 K have been published. 49 Here, we analyze our highest temperature measurement at 1742 K and discuss the influence of secondary reactions. Plots of the reduced sensitivity coefficients 50 as a function of time are shown in Figure 2.…”

Analysis of Kinetic Reaction Mechanisms

“…In reality, the comprehensive analysis of a model may require the combined application of several methods (Tebes-Stevens and Valocchi 2000; Ratto and Paladino 2000). Local sensitivity coefficients are widely used for the identification of parameters that can be estimated from a given set of experimental data (Hessler and Ogren 1992; Ogren and Hessler 1995;Turányi et al 2012). The features of various available methods are summarised in Table 5.2. Typically, local uncertainty analysis is based on the application of local sensitivity coefficients, i.e.…”

Recombination of Methyl Radicals. 2. Global Fits of the Rate Coefficient

“…Perhaps less apparent, but just as important, is the correlation in eq 1a. 16 Since most of the recombinational experiments have used the second approach, we must carefully consider the behavior of the cross section for optical absorption.…”

“…The correlation between the rate coefficient for radical recombination and the cross section is apparent in eq 1b. Perhaps less apparent, but just as important, is the correlation in eq 1a . Since most of the recombinational experiments have used the second approach, we must carefully consider the behavior of the cross section for optical absorption.…”