Fresnel reflection spectra

Diffuse reflection (DR) spectra result from the radiation incident on a powdered sample that is absorbed as it refracts through each particle and is scattered by the combined process of reflection, refraction, and diffraction. That fraction of the incident radiation that reemerges from the upper surface of the sample is said to be diffusely reflected. Because DR spectra result from an absorption process, they have the appearance of transmission spectra (i.e., bands appear in absorption), unlike the case for Fresnel reflection spectra of bulk samples (see Chapter 13). When DR spectra are acquired on Fourier transform spectrometers, the singlebeam spectra of the sample and a nonabsorbing reference are measured separately and ratioed to produce the reflectance spectrum, Rfy). 

Measurement of the Fresnel reflectance spectrum is a very useful way of obtaining the spectrum of solids with flat surfaces when sample preparation is not possible. For example, to measure the spectrum of an oriented polymer, the sample cannot be melted, dissolved, or finely ground. A microscopic sample of a hard polymer may be available that is too thick for transmission spectrometry. If the sample is so hard, rough, and/or thick that a good transmission or attenuated total reflection (see Chapter 15) spectrum cannot be measured, Fresnel reflection spectrometry presents a very useful means of obtaining the spectrum. 

For most materials the reflected energy is only 5-10%, but in regions of strong absorptions the reflected intensity is greater. The data obtained appear different from normal tra(nsmission spectra, as derivative-iike bands result from the superposition of the normal extinction coefficient spectrum with the refractive index dispersion (based upon the Fresnel relationships from physics). However, the reflectance spectrum can be corrected by using the Kramers-Kronig (K-K) transformation. The corrected spectrum appears similar to the familiar transmission spectrum. 

In order to interpret the reflectance spectrum, modeling of the interface is the key issue. For example, in the simulation above, we tacitly made some assumptions. One is that the change of the optical properties of the substrate and refractive index of the solution immediately adjacent to the film surface are independent of potential and the presence of the film. The use of the Fresnel model with optical constants is based on the assumption that the phases in the three-strata model are two-dimen-sionally homogeneous continua. However, if the adsorbed molecule is a globular polymer which possesses a chromophore at its core, a better model of the adsorption layer would be a homogeneously distributed point dipole incorporated in a colorless medium. To gain closer access to the interpretation of the spectrum, a more precise and detailed model would be necessary. But this may increase the number of adjustable parameters and may demand a too complex optical treatment to calculate mathematically. Moreover, one has to pile up approximations, the validity of which cannot easily be confirmed experimentally. 

Fig. 9.12 (a) Total reflection from the empty cell (b) reflection from the filled cell (c) reflectivity spectrum of the setup (dashed line) experimental values (solid line) calculated using Fresnel formulae for Bap2/D20/Au interface and the angle of incidence of 60°. Thin-cavity thickness was determined to be 2.4 pm. 

External reflection. This is not as well developed a technique as internal reflection the physics of reflection of light from surfaces is less accommodating to the infrared spectroscopist. Smooth or shiny surfaces are particular problems. Specular reflection from the surface itself is governed by Fresnel s equations—the reflectance depends on a complicated combination of refractive index, sample absorbance and polarisation. Consequently, samples where the reflectance is mainly from the surface give rise to spectra which bear little relation to conventional transmission spectra. A transformation known as the Kramers-Kronig transformation does exist which attempts to convert a specular reflectance spectrum into a conventional-looking one. It is not 100% successful, and also very computer-intensive. For these reasons, specular reflectance is not commonly used by the analyst. 

One note of caution should be sounded. If radiation is scattered from the interior of the sample, as might be the case because of the presence of a filler in the bulk of the sample, diffuse reflection (see Chapter 16) will take place along with the Fresnel reflection. In this case, the Kramers-Kronig transform will not yield an accurate estimate of the n and k spectra. One indication that diffuse reflection is contributing to the spectrum is that the bands in the fe spectrum calculated from a given reflection spectrum are asymmetric. 

Fresnel reflection from the front surface of the film is usually measured along with the radiation that is transmitted through the film. The distortion of the spectrum that is caused by the Fresnel reflection will lead to deviations from Beer s law,... 

Fresnel reflection measurements are convenient for certain types of microsamples because essentially no sample preparation is required. Ideally, only radiation reflected from the front surface of the sample is measured at the detector in this type of measurement, so that the absorption spectrum may be calculated by the Kramers-Kronig transform, as described in Chapter 13. However, for scattering samples, diffusely reflected radiation (see Chapter 16) also contributes to the signal measured by the detector. When both mechanisms contribute significantly to the measured spectrum, no amount of data manipulation will allow an undistorted absorption spectrum to be calculated. 

All the components mentioned interact with the powder and, therefore, contain information about its absorption coefficient. However, only the specular transmission and volume KM components give the absorptionlike spectra of the powder directly. The Fresnel components produce specular reflection (first derivative or inverted) specha [which can be converted into the spectra of the absorption coefficient using the KK transformation (1.1.13°)]. Therefore, to obtain the absorption spectrum of a powder, the Fresnel components must be eliminated from the final spectrum. In practice, this can be achieved by immersion of the sample in a hansparent matrix with a refractive index close to that of the powder, selection of appropriate powder size, or special construction of reflection accessories (Section 4.2). 

A theoretical analysis of the system consisting of either the ZnSe or Ge IRE, an Fe or hematite substrate layer, an adsorbate layer, and a solution of methylene chloride has been performed by Loring and Land [88], The system consisting of the ZnSe IRE, AI2O3 intermediate layer, the sputtered Si substrate layer, and water has been analyzed within the framework of the Fresnel formalism by Sper-line et al. [89], Calculations also reveal that within a narrow wavelength range and at a certain ratio of the optical refractive indices, enhancement of intensities is observed in the spectrum of a given layer in an arbitrary two-layer structure located on an IRE. The ATR spectra of such structures were considered in detail in Ref. [66], This enhancement is attributed to interference of the radiation, as is the enhancement of the reflectivity in BML-IRRAS (Section 2.3.3). 

Figure 3.72. Dependence of reflectivity in IRRAS spectrum of film on metal on film thickness, calculated with (1) linear approximation and (2) exact Fresnel formulas = 75°, 02 = 0.5 - 0.12/, / 3 = 15 - 60/, V = 1000 cm" . Reprinted, by permission, from V. P. Tolstoy, Methods of UV-Vis and IR Spectroscx)py of Nanolayors, St. Petersburg University Press, St. Petersburg, 1998, p. 189, Fig. 5.20. Copyright St. Petersburg University Press.

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