Integrated absorption band

Net integrated absorption band intensities are usually characterized by one of the quantities A, 5, 5, F, or Gnet as defined in the table. The relation between these quantities is given by the (approximate) equations... 

This broadening of the bands partly compensates the obvious decrease of the molar absorption coefficient (6 ) at the band maxima. It is not true, however, that the compensation is complete, as was roughly estimated in an earlier paper (9). Perfect compensation would mean that the total absorption strength of a particular transition (n-+m), as measured by the oscillator strength (f) and related to the integrated absorption band (Equation 1), is the same in the polymer and in a suitable monomeric model. 

Je(v)dv is the integrated absorption band on the wave number, v, scale. If we assume the shape of the absorption band to be gaussian we obtain the following approximate relationship. 

The quantitative treatment of the intensities of 3+ lanthanide absorption bands relates an experimentally determined quantity, a normalized band envelope, to a theoretical model based on the mechanisms by which radiation can be absorbed. The integrated absorption bands observed in a solution of known concentration can be used to calculate the number of classical oscillators in one ion, which is more commonly referred to as the probability for absorption of radiant energy P (oscillator strength) by the expression (Hoogschagen, 1946) ... 

The relationship between tire theoretical quantity i-j and the experimental parameter e of absorption spectroscopy involves, not the value of e at any one wavelengdi, but its integral over the absorption band. The relationship is... 

If we further assume that the vibrational wavefunctions associated with normal mode i are the usual harmonic oscillator ones, and r = u + 1, then the integrated intensity of the infrared absorption band becomes... 

The value of the integral e has been determined empirically by use of the frequency of the strong absorption band of the triphenylcarbonium cation. Using this, other energy quantities can be evaluated from the absorption frequencies for other molecules. 

Fig. 21. Integrated intensity OH and OD bands versus time for adsorbed labeled propylene. CH3- CH=CD2 O, OH , OD. CD3—CH=CH2 A, OH A, OD. The integrated intensity for OD was multiplied by 1.35, the isotopic shift, in an attempt to correct for expected differences in the integrated absorption coefficient.

Chapter 3 is devoted to dipole dispersion laws for collective excitations on various planar lattices. For several orientationally inequivalent molecules in the unit cell of a two-dimensional lattice, a corresponding number of colective excitation bands arise and hence Davydov-split spectral lines are observed. Constructing the theory for these phenomena, we exemplify it by simple chain-like orientational structures on planar lattices and by the system CO2/NaCl(100). The latter is characterized by Davydov-split asymmetric stretching vibrations and two bending modes. An analytical theoretical analysis of vibrational frequencies and integrated absorptions for six spectral lines observed in the spectrum of this system provides an excellent agreement between calculated and measured data. 

As will be shown later, the surface coverages of CO vary with distance into the pellet during CO adsorption and desorption, as a result of intrapellet diffusion resistances. However, the infrared beam monitors the entire pellet, and thus the resulting absorption band reflects the average surface concentration of CO across the pellet s depth. Therefore, for the purpose of direct comparison between theory and experiment, the integral-averaged CO coverage in the pellet... 

Measurement of integrated absorption requires a knowledge of the absorption line profile. At 2000-3000 K, the overall line width is about 10-2 nm which is extremely narrow when compared to absorption bands observed for samples in solution. This is to be expected, since changes in molecular electronic energy are accompanied by rotational and vibrational changes, and in solution collisions with solvent molecules cause the individual bands to coalesce to form band-envelopes (p. 365). The overall width of an atomic absorption line is determined by ... 

Figure 8. Expanded section of Figure 5 showing examples of differences in the magnitude of integrated area for two absorption bands with the same changes in electrode potential.

Emeis, C.A. Determination of integrated molar extinction coefficients for infrared absorption bands of pyridine adsorbed on sohd acid catalysts. J. Catal. 1993,141, 347-354. 

The molar absorption coefficient, e(2), expresses the ability of a molecule to absorb light in a given solvent. In the classical theory, molecular absorption of light can be described by considering the molecule as an oscillating dipole, which allows us to introduce a quantity called the oscillator strength, which is directly related to the integral of the absorption band as follows ... 

We can integrate over the frequency range corresponding to the absorption band and so write... 

Figure 26. Dimerization of butadiene in the crystalline phase. Lower panel Logarithmic plots of the room-temperature evolution of the integrated absorption of characteristic vinylcyclohexene absorption bands at different pressures. The linear evolution unambiguously demonstrates the first-order kinetics of the reaction. Upper panel Evolution of the natural logarithm of the dimerization rate constant as a function of pressure (full squares, left axis the dotted line is intended as a guide for the eye) and evolution of the intensity ratio between selected polymer and dimer (vinylcyclohexene) bands (empty dots, right axis).

Figure 27. Evolution of the IR integrated absorption of the C—H stretching modes involving sp carbon atoms. The corresponding absorption band is indicated by the star in the IR spectra reported in the inset during a compression (full dots)-decompression (empty dots) cycle.

Strictly speaking, the values of e, Ac, A, and AA need to be obtained by integration over the spectral band however, since, for a fundamental transition, the VCD and its parent absorption band have the same shape, the anisotropy ratio can be obtained, in the absence of interfering bands due to other transitions, by taking the ratios of intensities at corresponding spectral positions, such as peak locations. The anisotropy ratio is also of interest for theoretical reasons since it is a dimensionless quantity that can be compared to the results of calculations vide infra). 

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