INDEX Absorption

Allen et al. (2007) produced puffed snack foods with com starch and pregelatinized waxy starch, WPC and instantized WPC, and protein concentrations of 16%, 32%, and 40% and showed that the air cell size, extru-date expansion ratio, and water solubility index decreased proportionally as protein and com starch levels increased. Protein concentration significantly affected total soluble protein, water absorption index, and water-soluble carbohydrate. A covalent complex between amylase and protein formed in the presence of cornstarch, but protein-protein interactions appeared with the presence of low levels of pregelatinized waxy starch. 

The parameters K1/ K2/ and K3 are defined by the refractive indices of the crystal and sample and by the incidence angle [32]. If the sample has uniaxial symmetry, only two polarized spectra are necessary to characterize the orientation. If the optical axis is along the plane of the sample, such as for stretched polymer films, only the two s-polarized spectra are needed to determine kz and kx. These are then used to calculate a dichroic ratio or a P2) value with Equation (25) (replacing absorbance with absorption index). In contrast, a uniaxial sample with its optical axis perpendicular to the crystal surface requires the acquisition of spectra with both p- and s-polarizations, but the Z- and X-axes are now equivalent. This approach was used, through dichroic ratio measurements, to monitor the orientation of polymer chains at various depths during the drying of latex [33]. This type of symmetry is often encountered in non-polymeric samples, for instance, in ultrathin films of lipids or self-assembled monolayers. 

In contrast with other methods, spectra recorded by specular reflection show dispersion-like shaped bands because both the refractive index (n) and the absorption index (k) contribute to reflection. These can nevertheless be separated... 

An alternative method for assessing cell layer integrity is through the use of hydrophilic paracellular transport markers (e.g., radiolabeled D-mannitol or fluorescein-Na+), which passively traverse cells by the paracellular route. Small amounts of compound required for in vitro conjunctival cell culture transport experiments make this approach well suited for screening purposes. Relative absorption index of a series of pharmacologically active molecules can be ranked against known markers for the identification of candidates with potential absorption problems, which is a reliable tool to select drug candidates with optimal characteristics. 

In Mie s theory, the scattering diameter Qs and the absorption diameter QA are related to the particle size D, the wavelength A, and the optical constants of the material (refractive index n and absorption index k). 

Mie s Theory. Mie applied the Maxwell equations to a model in which a plane wave front meets an optically isotropic sphere with refractive index n and absorption index k [1.26]. Integration gives the values of the absorption cross section QA and the scattering cross section Qs these dimensionless numbers relate the proportion of absorption and scattering to the geometric diameter of the particle. The theory has provided useful insights into the effect of particle size on the color properties of pigments. 

The consequences of Mie s theory for absorption (i.e., for tinting strength) are now considered. Calculations from Mie s theory, using the relative refractive index n and the absorption index k, are given in Figure 8 [1.30]. The parameter a on the abscissa can once more be taken as a relative measure of the particle size. The following conclusions may be drawn ... 

With increasing absorption index k, the absorption of very small particles increases. 

The top curve in Figure 8 applies to pigments with a high absorption index k and low refractive index rt (e.g., carbon black) and shows that the optimal particle size lies below a given limit. 

The lowest curve applies to pigments with a small absorption index k and high relative refractive index n, as is usually the case with inorganic pigments (e.g., red iron oxide). Here, there is a distinct maximum [1.11], [1.16]. 

The absorption index, k, introduces an exponential decay in E (and E ) with increasing z (see eq. [3]). Recalling that the intensity, I, is related to the electric field amplitude E, according to I lE 2 it follows from eqs. [3] and [4] that... 

Fourier transform infrared microscopes are equipped with a reflection capability that can be used under these circumstances. External reflection spectroscopy (ERS) requires a flat, reflective surface, and the results are sensitive to the polarization of the incident beam as well as the angle of incidence. Additionally, the orientations of the electric dipoles in the films are important to the selection rules and the intensities of the reflected beam. In reflectance measurements, the spectra are a function of the dispersion in the refractive index and the spectra obtained are completely different from that obtained through a transmission measurement that is strongly influenced by the absorption index, k. However, a complex refractive index, n + ik can be determined through a well-known mathematical route, namely, the Kramers-Kronig analysis. 

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. 

Fig. 55.—Effect of extrusion temperature on expansion (solid points), water absorption index (open points), water solubility index (stars), and viscosity at 50°C (triangles) of tapioca starch. (Initial moisture content was 22% on dry starch basis.) (Reprinted with permission of C. Mercier, R. Charbonniere, J. Grebaut, and J. F. de la Gueriviere, Cereal Chem., 57 (1980) 4-9.)...

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 considerations before refer to the non-absorbing case when and n are real quantities. In order to characterize the optical properties completely absorption must be included. This can be achieved by taking the optica] and dielectric functions to be complex quantities comprising two real figures each. The (real) refractive index n is complemented by the real absorption index k to constitute the complex refractive index... 

Figure 6.4-5 Simulated spectra of a strong oscillator (strength/ = 200 10 cm with resonance at t> real and imaginary part of the dielectric function = s + k", refractive index n and absorption index k, ellipsometric parameters A and ip, as well as reflectance R for the angles of incidence and the polarization states stated.

For the strong oscillator the n and k spectra are asymmetric. The shift of the k maximum away from the resonance frequency is particularly obvious. In such a case a reliable representation of the vibrational structure cannot be derived from transmittance spectra and thus, from the absorption index k alone. Another peculiarity of the strong oscillator is the spectral range where the (real) refractive index is below unity. This renders... 

V indicates the principal value) are applied to a function F = F + F" (Bode, 1950 Smith, 1985 Hopfe et al., 1981). Such so-called dispersion relations exist between the (real) refractive index and the absorption index. Dedicated software programs are available, also specially for (infrared) spectroscopic purposes (Hopfe, 1989), a generalization for oblique incidence on layered systems was given by Grosse and Offermann (1991). 

The ellipsometric parameters xl> and A experimentally determined with a homogeneous thick sample, are algebraically related with the components of the dielectric function, which in turn define the refractive index and the absorption index (Bom and Wolf, 1980). The parameters for the strong oscillator used to simulate the spectra shown in Fig. 6.4-5 were chosen to resemble the strong infrared resonance of quartz glass. Radiation reflected from such a sample was measured ellipsometrically the evaluation led to the results presented In Fig. 6.4-14. For weaker absorbers such as many molecular compounds. 

Figure 6.4-14 Spectra of the refractive index n, the absorption index k, and the degree of (phase) polarization Ppi, of quartz glass as derived from ellipsometric measurements.

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