Absorption band depth

In this expression, z is the distance from the surface into the sample, a(z) is the absorption coefficient, and S, the depth of penetration, is given by Eq. 2. A depth profile can be obtained for a given functional group by determining a(z), which is the inverse Laplace transform of A(S), for an absorption band characteristic of that functional group. 

From this equation it can be seen that the depth of penetration depends on the angle of incidence of the infrared radiation, the refractive indices of the ATR element and the sample, and the wavelength of the radiation. As a consequence of lower penetration at higher wavenumber (shorter wavelength), bands are relatively weaker compared to a transmission spectrum, but surface specificity is higher. It has to be kept in mind that the refractive index of a medium may change in the vicinity of an absorption band. This is especially the case for strong bands for which this variation (anomalous dispersion) can distort the band shape and shift the peak maxima, but mathematical models can be applied that correct for this effect, and these are made available as software commands by some instrument manufacturers. 

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... 

The reasons for the great width of the et absorption bands have not yet been made clear conclusively. One of them may be the scatter in the depth of the traps, i.e. in the energy of electron binding in them. For example, in alcohol matrices the absorption spectra of etr are known to shift temporarily... 

The depth of any reasonable potential well should of course be finite. Moreover, the recorded spectrum of such an important liquid as water comprises two absorption bands One, rather narrow, is placed near the frequency 200 cm, and another, wide and intense band, is situated around the frequency 500 or 700 cm-1, for heavy or ordinary water, respectively. In view of the rules (56) and (57), such an effect can arise due to dipoles reorientation of two types, each being characterized by its maximum angular deflection from the equilibrium orientation of a dipole moment.20 The simplest geometrically model potential satisfying this condition is the rectangular potential with finite well depth, entitled hat-flat (HF), since its form resembles a hat. We shall demonstrate in Section VII that the HF model could be used for a qualitative description of wideband spectra recorded in water21 and in a nonassociated liquid. 

The thickness of the membrane should exceed the penetration depth of the IR radiation in order to suppress the absorption bands of water. The optimum thickness is about 10 to 20 pm. The stability of such a membrane is satisfactory and the resulting time constant for the enrichment process is not too large. 

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... 

Micro-Fourier transform infrared (FT-IR) spectroscopy was employed to examine the chemical structures by observing absorption bands at 1716 cm 1 (carbonyl group), 964 cm"1 (trans- inylene) and 910 cm 1 (end-vinyl). After 2 months from the irradiation, samples were sliced into 100-150 pm films along the direction of ion-beam penetration and the FT-IR spectra were measured as a function of depth from the surface [6]. We obtained the net absorbance AAbs. for the three bands for carbonyl group, /raws-vinylene and end-vinyl at each depth by subtraction of the measured spectrum from that of the unirradiated sample. Sliced samples were stored in the dark at room temperature. They were repeatedly measured after 4, 6 and 12 months from the irradiation to observe the effect of long-term storage. 

To explain the difference between the 248- and 308-nm irradiation some properties of the polymer and laser at the two irradiation wavelengths must be discussed. At 248 nm the penetration depth of the laser is about 150 nm, whereas for 308 nm the penetration depth is only 60 nm. In addition, the photon energy at 248 nm is 5 eV as compared to the 4 eV at 308 nm. This is one of the reasons why the quantum yield (QY) of photolysis in solution for 248 nm is higher (1.5%) than for 308 nm (0.22%) [120]. A closer inspection of the UV spectra (Fig. 10) reveals that 248 nm is at a minimum of the absorption curve. Assuming a Lorentzian profile for the different absorption bands, it is obvious that an irradiation with 248 nm can lead to a direct excitation of the absorption bands below and above 248 nm. 

Similar behavior has been observed in CdSe clusters [60], Using laser excitation near the red edge of the absorption band, sharp luminescence with well-defined vibronic structures can be observed. The decay kinetics shows two components—a temperature-insensitive 100-ps component and a microsecond, temperature-sensitive component. The luminescence spectrum develops a 70-cm-1 red shift as the fast component decays. The three-level thermal equilibration model again has to be invoked to explain these kinetic data. Based on the polarization measurement, the authors suggest that it is the hole, instead of the electron, that is shallowly trapped. The trap depth is estimated to be 9 meV. The authors further propose that strong resonant mixing exists between the internal MOs and surface MOs. 

In the ultraviolet spectrum of polyethylene taken at 77 °K. after an irradiation to a dose of 40 Mrads there is also a broad absorption band in the region of 310 m/x to be seen. This is shown more clearly in Figure 3 in terms of a plot of the difference in the absorbance between Curve 1 of Figure 2 and curve 2. Actually the A A values of Figure 3 were not calculated from curves 1 and 2 of Figure 2, but from similar curves observed in another experiment. It is unlikely that the 310 m/x band can be attributed to trapped electrons because the energy of this band, 4.0 e.v., is much greater than the depth of electron traps in polyethylene,... 

Bacteriochlorophyll a (Figure 12) is a natural pigment with an absorption band around 780 nm. At this wavelength, the penetration depth of light is approximately three times greater than that reached at 630 nm, the wavelength generally used in clinical PDT with Photofrin [73,74]. 

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