Absorption-index spectra

Figure 9 Specular reflection FT-IR and application of Kramers-Kronig algorithm (A) schematic showing external (front-surface, specular) mid-infrared reflection measurement from an optically thick sample (B) specular reflectance spectrum recorded from a 0.6-mm thick polymer molding (C and D) refractive index and absorption index spectra derived by applying Kramers-Kronig algorithm to the recorded specular reflection spectrum (B), respectively.

Figure 1.4. (a) Refractive index and (b) absorption index spectra of poly(methyl methacrylate). 

Figure 13.3. Refractive index and absorption index spectra calculated from the spectra shown in Figure 13.2.

Figure 16.17 Absorption-index spectra of a polycarbonate resin, (a) Resin before light-resistance test and (b) resin after light-resistance test. (See text for details spectra have been offset for clarity.)...

Figure 3.10a, b shows ATR-FUV spectra in the 140-260 nm region for formamide (FA), N-methylformamlde (NMF), N-methylacetamide (NMA), NJ l-dimethylformamide (NdMF), and N,N-dimethylacetamide (NdMA) in the liquid phase and their absorption index spectra obtained by the Kramers-Kronig transformation, respectively [9]. All FUV spectra show a peak due to amide group in the 180-200 nm region. The peak maximum varies in the order of FA (6.88 eV), NMA (6.81 eV), NMF (6.67 eV), NdMA (6.44 eV), and NdMF (6.44 eV) with the intensity being lowered as the number of methyl groups on the N atom increases. 

Occasionally, transmission spectra of small inhomogeneous samples show the presence of artifacts. For example, the effect of scattering may cause symmetrical bands to lose their symmetry. Instead of having the symmetric shape of the absorption index spectrum, the stronger bands begin to take on the appearance of the... 

These results are then used for an extended and profound band assignment in the measured IR spectra. Thereby, the absorption index spectrum, as purely a property of the material, is preferred to reflectance or transmittance spectra, which are affected by the measuring conditions. As a result, procedures are developed that describe which IR bands can be used for peak analysis in order to monitor the curing reaction and the resulting network structure of the adhesive. 

Table 3.9. Maximum in-piane absorption indices kx, of absorption index spectrum in Fig. 3.84...

Specular reflection is the term used to describe mirror-like reflection, from the surface of a sample (angle of reflection equals angle of incidence). Specular reflected radiation ostensibly carries no information about the IR absorption of a sample and is a source of interference in diffuse reflection experiments when the sample is not completely matte, i.e., has an element of shininess about it. However, if the reflected intensity from a sample is due principally to reflection from the front surface of the sample, then an absorption index spectrum of the sample can be generated from the reflected intensity over the whole spectrum using the Kramers-Kronig transformation. (This complex transformation is an... 

Specular reflectance Pure specular reflection spectra may be recorded directly from the surfaces of flat, nonscattering, optically thick (opaque) samples from which the absorption index spectrum may be extracted by application of the Kramers-Kronig algorithm. This is sometimes a useful approach for generically fingerprinting intractable or heavily filled polymer samples. An example is shown in Figure 9. 

The absorption index k is a characteristic function of the wave-length and obviously increases as the wave-length of an absorption peak is approached. Most polymers show no specific absorption in the visible region of the spectrum and are therefore colourless in principle. 

ATR or diffuse reflection techniques are widely used for materials which are difficult to analyze by absorption methods, such as thin layers on nontransparent substrates, substances with very high absorption which are difficult to prepare in thin layers, or substances with a special consistency. Some basic considerations concerning quantitative ATR spectroscopy have been described by Muller et al. (1981). This publication emphasizes the fact that the functional behavior of the ATR spectrum of an absorbing sample must be evaluated with regard to the refractive index as well as to the absorption index of the sample. It is shown that, as a consequence, reflection measurements can be used to determine concentrations of nonabsorbing samples. Further information on reflection spectroscopy is presented in Sec. 6.4. 

The above relationships (Figure 1.10) show that the optical pigment properties depend on the particle size D and the complex refractive index n = n (1 - i/c), which incorporates the real refractive index n and the absorption index k. As a result, the reflectance spectrum, and hence the color properties, of a pigment can be calculated if its complex refractive index, concentration, and particle size distribution are known [1.40]. Unfortunately, reliable values for the necessary optical constants (refractive index n and absorption index k) are often lacking. These two parameters generally... 

The last point which will be examined in this subsection is that of extracting the true transmission values from a DAC experiment, in order to calculate the absorption-coefficient spectrum. In the case of a plane-parallel slab of sample with a thickness d, a refractive index n, and an absorption coefficient a which is immersed in a transparent medium with an index n and negligible absorption, the theoretical transmission in the absence of interference fringes is... 

Figure 3.29. Dependence of band shape in p-polarized IRRAS spectrum of hypothetical organic layer 1 nm thick on absorption index of substrate with ns = 3.4. Absorption indices are indicated. Dielectric function of film was specified by S = 0.001, y = lOcm vo =2800cm and Boo = 1-7 = 80°.

Derived from absorption index (k) spectrum of bulk dioctadecyl disulfide. 

Even at normal incidence, the transmission spectra may be relatively sensitive. To demonstrate this. Fig. 7.13 shows the vOH band of water adsorbed on NaCl(lOO) at -27°C, which is lower than the freezing point of a saturated NaCl solution, and a pressure of 0.2 mbar (35% RH) [358]. The spectrum was recorded by the multiple-transmission technique. For this purpose, 11 crystals cleaved along the (100) faces of NaCl were collected in a pile with spacers of 0.1-mm Ta wire, so that the NaCl faces did not touch each other. To reduce reflection from the external air-NaCl boundary, wedged silicon windows were attached to both ends of the pile. Comparison of the band position of adsorbed water with that of water in various phases (the top of Fig. 7.13) suggests that at this temperature the adlayer is mostly in the liquid state. On this basis, the surface coverage can be evaluated by introducing the absorption index of bulk water in the modified BLB relationship ... 

Fig. 10. Spectra of photochromic p>roperties of Indolyfulgimide /PMMA film (a) Absorption spectra of two forms (b) Absorption difference spectrum and the corresponding refractive index changing spectrum...

From Fig.lOa and Fig.lla, the photo-induced absorption changing spectrum AA(/1) = A (A)-Aq(A) and the photo-induced dichroism spectrum AAd(X.) = Ai(X.)-A//(X.)= lg(T//(X)/T (X)) were obtained, which are shown as solid lines in Fig.lOb and Fig.llb respectively. Assuming that AA and AAd are zero outside of the band 300 800nm, the photo-induced refractive index changing spectrum An(A) = n (A)-iiQ X) and the photo-induced birefringence spectrum Ans(X.) =n X)-n// X) can be calculated according to the Kramers-Kronig relation PI, where jie, tic, ni i and are the refractive indexes of E-form, C-form and of the film... 

Thus the birefringence of the liquid crystal is much more critical in the fluorescence polarization studies. Measurements of the order parameter of excited molecules are possible if the rotational relaxation time of the solute is small compared with the lifetime of the emitting state. The birefringence of the liquid crystal is also of critical importance if one wishes to determine the solvent order from the absorption polarization spectrum of the solvent in its nematic phase. The complications arise from the strong refractive index dispersion in the wavelength regions of the solvent absorption bands. Saupe and Maier [104] have treated this case. The same difficulties arise of course if the solute and the solvent absorption overlap. 

The absorbance spectrum, of a sample with an effective optical path length through the sample, /, and the absorption index, a, are related by... 

For any material, n( is determined by Snell s law. A few materials have no significant absorption in the mid- and near infrared. Those materials with low refractive index (1.45 high refractive index (2.4 internal reflection elements (see Chapter 15). For organic and inorganic molecules whose spectra exhibit typical absorption bands, the refractive index changes across the absorption band. A typical refractive index spectrum has the appearance shown in Figure. Aa. This... 

On the other hand, the maximum absorption index of bands in the spectra of most organic molecules (including polymers) rarely exceeds 0.3 above 1000cm In these cases, ( 2 — 1) > and the reflection spectrum looks more like the n spectrum (see Figure Ab) than the k spectrum. The specular reflection spectrum of a polycarbonate polymer is shown in Figure 13.2. Few experienced spectroscopists would immediately recognize this spectrum as a polycarbonate. To convert this spectrum to the optical constant (n and k) spectra, the Kramers-Kronig... 

The imaginary part of the complex refractive index k, which is called the absorption index, is a quantity directly related with absorbance (see Section 1.2.4). In Equations (8.4a) and (8.4b), k and 8 as well as are functions of wavenumber v, and k v) is essentially the same as an absorbance spectrum from a transmission measurement. 

The reflection spectrum of PrSe and data derived therefrom are discussed on p. 26 for a figure, see the paper. Dispersion curves of the refractive index n and absorption index k for PrSe powder are shown in Fig. 43. They were obtained by Kramers-Kronig analysis of the reflection spectrum in the range 400 to 50000 cm" Ivanchenko et al. [31]. 

It should be noted that low-loss spectra are basically connected to optical properties of materials. This is because for small scattering angles the energy-differential cross-section dfj/dF, in other words the intensity of the EEL spectrum measured, is directly proportional to Im -l/ (E,q) [2.171]. Here e = ei + iez is the complex dielectric function, E the energy loss, and q the momentum vector. Owing to the comparison to optics (jqj = 0) the above quoted proportionality is fulfilled if the spectrum has been recorded with a reasonably small collection aperture. When Im -l/ is gathered its real part can be determined, by the Kramers-Kronig transformation, and subsequently such optical quantities as refraction index, absorption coefficient, and reflectivity. 

Solvent — The transition energy responsible for the main absorption band is dependent on the refractive index of the solvent, the transition energy being lower as the refractive index of the solvent increases. In other words, the values are similar in petroleum ether, hexane, and diethyl ether and much higher in benzene, toluene, and chlorinated solvents. Therefore, for comparison of the UV-Vis spectrum features, the same solvent should be used to obtain all carotenoid data. In addition, because of this solvent effect, special care should be taken when information about a chromophore is taken from a UV-Vis spectrum measured online by a PDA detector during HPLC analysis. 

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