Integrated molar absorptivity

Fig. 5. Data for frequency shift, Av monomer frequency minus H-bonded frequency), band width at half maximum iq, and integrated molar absorption coefficient per bonded OH minus integrated molar absorption coefficient for monomer, AB. Curves are those...

Attempts have been made by Rouxhet (1970) to determine absorption coefficients of OH stretching bands in micas. For the calculation of the molar OH absorption coefficient (s), the absorbance values (A) and the absolute H2O concentration values (c) have to be known. The basis of the quantitative IR spectroscopic water determination is the Lambert-Beer s law in the form s = a/c, where the absorption coefficient a = A/t (t is the thickness of the measured crystal plate Beran et al. 1993). From the data of Rouxhet (1970) for integrated absorption coefficients determined by polarized IR measurements and the water content determined by thermal extraction, the integrated molar absorption coefficients (sri for muscovites have been calculated to values ranging from 21000-23000... 

The stable fullerene clusters obtained from the fast method have higher molar absorptivities than the fullerene monomers, corresponding to larger transition probabilities [80]. As the acetonitrile composition in acetonitrile-toluene mixtures increases, the absorption of the fullerene clusters quickly predominates, resulting in a significant increase in integrated molar absorptivities (Fig. 24). 

Fluorescence and fluorescence excitation spectra, and fluorescence quantum yields of the fullerene clusters are different from those of the fullerene monomers. The excitation and absorption spectra of the fullerene clusters are in good agreement [80]. The observed fluorescence yields of fiillerenes decrease significantly upon the formation of clusters. This is opposite to the trend of increasing transition probabilities as measured by the integrated molar absorptivities. The lower fluorescence yields for the fullerene clusters are likely due to more efficient excited state nonradiative decays. One possible mechanism is the quenching of photoexcited fiillerenes by neighboring fullerene molecules in the clusters with excimer-like interactions [82]. However, no flillerene-fiillerene excimer emissions have been observed. 

Table 2.28 Decadic integral molar absorption coefficients e (0-H stretching modes) of some surface hydroxyls Sample v(OH), cm e, cm pmoD Note Ref. ...

Integrated molar absorption coefficient Filling fraction Geometric factor... 

Radiative decay is the inverse of absorption and requires coupling of the two states via either an incident photon, which results in stimulated emission, or the constantly fluctuating radiation field, which results in spontaneous emission. The radiative lifetime is also the inverse of the Einstein A coefficient. This can be calculated from the integrated molar absorption coefficient in the absorption spectrum using the Strickler-Berg relationship [55]. 

Consider the integrated molar absorptivity for an S S, absorption, Je(n)dn, obtained from the appropriate segment of the uv-visible absorption spectrum (using unpolarized light and isotropic samples) and plotted as the molar decadic extinction coefficient (absorptivity), e(n) in dm moT cm , as a function of n in wavenumbers. An approximate value of the radiative rate constant for the corresponding S Sq transition may be obtained directly from ... 

The integrated molar absorptivity can be seen as the sum of the e(v) values over the whole absorption band. Instead of the molar absorptivity, the dipole strength D or the oscillator strength P are reported. One has to be cautious of the fact that the sample can be an oriented crystal or a medium in which the molecules are randomly oriented (solution, glass, powder). Throughout the text, we will emphasize this orientational problem. We use the symbols D and P for oriented systems, and D and P for randomly-oriented systems. 

Equation (25) relates the oscillator strength P to the integrated molar absorptivity / e(v) dv. 

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 ... 

Quantitation of the number of acid sites present can be obtained from the integrated band areas for a particular vibrational band of the probe molecule and its molar absorption or molar extinction coefficient using the Lambert-Beer law as previous described in Section 4.5.2. In order to determine the molar extinction... 

More quantitative studies have shown that, although some hypochromism effects exist, they are small. For example, Monnerie I9) examined the integrated molar extinction coefficient of atactic PS in chloroform and found only a 2 % decrease for the polymer relative to ethyl benzene. In addition, Vala and Rice 15 reported a 10% decrease in absorption for the 260 nm band of isotactic PS relative to atactic PS, which was qualitatively confirmed by Longworth18>. Similarly, Cantow 8> observed a 4% hypochromism of the 261.5 nm band of isotactic PS in dioxane relative to atactic PS. Finally, Cantow 8) observed strong hypochromism (relative to atactic PS) ranging from 19% at 262 nm to 32% at 269 nm for an alternating styrene-methyl methacrylate copolymer and for random copolymers having a low styrene content. 

The strength or intensity of absorption is related to the dipole strength of transition D or square of the transition moment integral M m , and is pressed in terms of oscillator strength / or integrated molar extinction jfe Jv. A transition with /= 1, is known as totally allowed transition. But the transitions between all the electronic, vibrational or rotational states are not equally permitted. Some are forbidden which can become allowed under certain conditions and then appear as weak absorption bands. The rules which govern such transitions are known as selection rules. For atomic energy levels, these selection rules have been empirically obtained from a comparison between the number of lines theoretically... 

Although oscillator strength is proportional to the integrated intensity of absorption J rfv, there is often a fairly good correlation between / and emax, the molar absorption coefficient at the band maximum. This correlation is valid if we assume a Lorenzian shape for the absorption band and replace the integral by max A v, where Av is the half-band-width of the absorption band (Figure 3.5b). The half-band-width is defined as the width of the absorption band (in cm-1) where the value of Hence... 

The absorption coefficient can be expressed as the product of an absorber-specific, wavelength-dependent quantity, the molar absorption coefficient, and the concentration of this species. Integration gives the following ... 

Because the molar absorption coefficients of absorbing species in catalyst materials are usually not known, a calibration needs to be performed to relate intensity (at a certain wavelength or an integral over a range) to concentration. In a best-case scenario, the concentration is measured by a second independent method applied simultaneously. Published attempts include the use of EPR spectroscopy for the determination of the concentration of V4+ in VO /support materials in this case, the EPR tube was a "side-arm connected to the UV-vis cell, and samples could be transferred without exposure to air (Catana et al., 1998). EPR intensity and UV-vis intensity (KM function at a particular wavelength) were linearly correlated with each other. 

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