Integrated absorption intensities measurement

Section BT1.2 provides a brief summary of experimental methods and instmmentation, including definitions of some of the standard measured spectroscopic quantities. Section BT1.3 reviews some of the theory of spectroscopic transitions, especially the relationships between transition moments calculated from wavefiinctions and integrated absorption intensities or radiative rate constants. Because units can be so confusing, numerical factors with their units are included in some of the equations to make them easier to use. Vibrational effects, die Franck-Condon principle and selection mles are also discussed briefly. In the final section, BT1.4. a few applications are mentioned to particular aspects of electronic spectroscopy. 

Analysis of Defined Fractions. Quantitative infrared analysis was used for those fractional groups that have definitive bands average absorptivities were estimated using model compounds (12, 16, 17). Table I lists the infrared bands and the apparent integrated absorption intensities (B) used. Quantitative IR spectra were measured in methylene chloride with 0.05 cm sodium chloride cells, using a Perkin-Elmer 521 infrared spectrophotometer. Peak area was measured by planimetry. Molecular weights were determined by vapor-pressure osmometry in benzene. 

Because of the use of finite slit widths, the radiation is not monochromatic (and covers an appreciable part of the band envelope) and the measured quantity is an apparent integrated absorption intensity (B),... 

Since the two ratios of the right-hand side of Eq. (14) have been tabulated, it is easy to present K in the same form so that by measuring the apparent peak intensity and the apparent half-intensity band width of an absorption band and consulting the relevant tables, the true integrated absorption intensity can be calculated from Eq. (13). 

In order to make quantitative measurements. Miles (1958f)) has determined integrated infrared absorption intensities for some nucleosides, nucleotides, and polynucleotides in DjO solution (Fig. 12.8 and Table 12.2) by application of Ramsay s method I (Ramsay, 1952). When there is a well-resolved band, the application of Ramsay s method encounters no difficulty, but when overlapping bands occur, as in uridine and its derivatives, some uncertainty exists in determining the halfband width of a particular band. (The half-band width is a factor in Ramsay s equation and is defined as, Av, 2 = the width of the band in cm" at half-maximum intensity.) The equation as used by Miles to obtain A, the true integrated absorption intensity... 

To make accurate measurements of the integrated absorption associated with such narrow lines requires that the linewidth of the radiation source be appreciably smaller than that of the absorption line. In practice, this could be achieved with a continuum source only if expensive instrumentation of extremely high resolving power were used, and it is doubtful whether conventional photomultiplier detectors would be sufficiently sensitive at the resulting low radiation intensities. An alternative arrangement is to... 

UV-VIS-NIR diffuse reflectance (DR) spectra were measured using a Perkin-Elmer UV-VIS-NIR spectrometer Lambda 19 equipped with a diffuse reflectance attachment with an integrating sphere coated by BaS04. Spectra of sample in 5 mm thick silica cell were recorded in a differential mode with the parent zeolite treated at the same conditions as a reference. For details see Ref. [5], The absorption intensity was calculated from the Schuster-Kubelka-Munk equation F(R ,) = (l-R< )2/2Roo, where R is the diffuse reflectance from a semi-infinite layer and F(R00) is proportional to the absorption coefficient. 

The radiative lifetime may be calculated from the Einstein B coefficient as determined from the integrated absorption spectrum. The absolute intensity of electronic transitions is usually determined from the absorption spectrum since for emission it is difficult to determine the number of molecules in the excited state. The parameter measured experimentally is the absorption coefficient, kv, which is defined by the relation... 

Paul and Dalby have investigated the reactions of CN radicals produced in the flash photolysis of C2N2 and CNCl. The kinetics were inferred from the time-dependent absorption by CN radicals. The absorbed intensity was related to concentration by means of a numerically evaluated theoretical expression. This expression was calibrated using an experimental measurement of the integrated absorption coefficient. 

For absorptive transition it can be shown that the measurable integrated inherent intensity (the molar absorptivity, e) of an absorption band, expressed as absorbance A per unit concentration of absorber c and optical depth d of the sample, is given by... 

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