Quantitative Studies of Apparent Rotational Temperatures of OH in Emission and Absorption (Spectral Lines with Doppler Contour)

Even if a Boltzmann distribution exists for the population of molecules in various energy levels, it is not possible to obtain a satisfactory interpretation of experimental data by the use of conventional procedures unless the product of maximum spectral absorption coefficient P_(max) and optical density χ is sufficiently small. Detailed calculations are presented which show that the experimental results, which suggest an anomalous rotational temperature for the ^2Σ state of OH in low pressure combustion flames, can be accounted for by using sufficiently large values for P_(max)χ (Sec. II). Whether or not experimental data should be interpreted in this manner must be determined by auxiliary studies. Representative absorption studies for the determination of rotational temperatures in isothermal systems have been analyzed for the P_1 branch, (0,0) band, ^2π-->^2Σ transitions of OH at 3000°K. The calculations show that erroneous interpretation of experimental results occurs if the product P_(max)χ is not small compared to unity. Sample calculations for a blackbody light source show that the customary procedure for treating experimental results will permit adequate correlation of the data by straight lines up to relatively large values for P_(max)χ. It is remarkable that the preceding statement remains true even under conditions in which emission data clearly indicate that P_(max)χ is no longer small compared to unity (Sec. III). Representative calculations to determine observable peak and total intensity ratios in emission for spectral lines with Doppler contour have been carried out for ^2Σ-->^2π transitions, (0,0) band, P_1 branch of OH at 3000°K. The calculations show that the ratios of peak and total intensities are functions of the products of maximum absorption coefficients (P_(max)) and optical density (χ) for the lines under study (Sec. IV). Quantitative calculations have been carried out of apparent rotational temperatures in systems containing nonequilibrium distributions of OH at 3000°K and at 6000°K. The calculations on the P_1 branch, ^2Σ-->^2π transitions, indicate that, in the absence of self-absorption, conventional plots showing discontinuities necessarily overestimate one and underestimate the other of the known temperatures of 3000°K and 6000°K (Sec. V). Quantitative calculations on the nature of distortions produced when an isothermal region at 3000°K is viewed through an isothermal region at 1500°K show that the presence of a non-isothermal field of view magnifies the distortion produced by self-absorption alone (Sec. VI). On the basis of the noncontroversial quantitative calculations described in Secs. II to VI for idealized systems, some speculations regarding the significance of reported flame temperature anomalies for OH are presented in Sec. VII