Near-normal specular reflectance

Fig. 5.3 Optical transmittance (a) and near-normal specular reflectance (b) of CD PbS films of different thicknesses. The thickness increases from A to F over an estimated range of ca. 50 nm to <200 nm. (Adapted from Ref. 46 with permission from lOP Publishing Ltd.).

Specular reflection IR spectroscopy has been used by Cole and coworkers to study the orientation and structure in PET films [36,37]. It has allowed characterizing directly very highly absorbing bands in thick samples, in particular the carbonyl band that can show saturation in transmission spectra for thickness as low as 2 pm. The orientation of different conformers could be determined independently. Specular reflection is normally limited to uniaxial samples because the near-normal incident light does not allow measuring Ay. However, it was shown that the orientation parameter along the ND can be indirectly determined for PET by using the ratio of specifically selected bands [38]. This approach was applied to the study of biaxially oriented PET bottles [39]. 

These results are interesting because they show the effects of specular reflection. Portions of the mannequin s surface which are nearly normal to the scanned imaging aperture remain visible in the images, and portions that are curved away tend to reflect the illumination away from the aperture and are dark in the imagery. This effect may decrease at even higher frequencies, because smaller features will reflect more significantly as the frequency is increased (wavelength is decreased). 

Light (or near-ir and uv radiation) that is incident on opaque minerals is partly absorbed and partly reflected by them. There are two kinds of reflection processes that occurring when light is reflected from a flat polished surface of the mineral (specular reflectance) and that occurring when the light is reflected from the mineral after it has been finely powdered (diffuse reflectance). The latter arises from radiation that has penetrated the crystals (as in an electronic absorption spectrum) and reappeared at the surface after multiple scatterings in this case there will also be a specular component to the reflectance from light that is reflected from the surfaces of the particles. The specular reflectance of a flat polished surface of an opaque mineral measured at normal incidence can be related to the n and k terms of the complex refractive index (N) in which ... 

The accommodation coefficient or represents the fraction of the gas molecules that leave the surface in equilibrium with the surface. The fraction I — cr is specularly reflected such that the velocity normal to the surface is reversed. As in the case of Stokes law, the drag is proportional to the velocity of the spheres. However, for the free molecule range, the friction coefficient is proportional to dj whereas in the continuum regime dp ip), it is proportional to dp. The coefficient a must, in general, be evaluated experimentally but is usually near 0.9 for momentum transfer (values differ for heat and mass transfer). The friction coefficient calculated from (2.19) is only 1% of that from Stokes law for a 20-A particle. 

Of the many X-ray based techniques available, a very powerful approach for probing interfacial structures is based on the measurement of X-ray reflectivity. The X-ray reflectivity is simply defined as the ratio of the reflected and incident X-ray fluxes. In the simple case of the mirror-like reflection of X-rays from a surface or interface, i.e., specular reflectivity, the structure is measured along the surface normal direction. Lateral structures are probed by non-specular reflectivity. The measurement and interpretation of X-ray reflectivity data (i.e., the angular distribution of X-rays scattered elastically from a surface or interface) (Als-Nielsen 1987 Feidenhans l 1989 Robinson 1991 Robinson and Tweet 1992) are derived from the same theoretical foundation as X-ray crystallography, a technique used widely to study the structure of bulk (three-dimensional or 3D) materials (Warren 1990 Als-Nielsen and McMorrow 2001). The immense power of the crystallographic techniques developed over the past century can therefore be applied to determine nearly all aspects of interfacial structure. An important characteristic of X-ray reflectivity data is that they are not only sensitive to, but also specifically derived from interfacial structures. 

Figure 24. (A) Specular reflectivity of the muscovite-water interface, and (B) the same data normalized by the generic CTR shape, Rctr = 1 l[Q sin(0c/2)]2, where c is the lattice spacing of the mica lattice. (C) The derived near-surface water structure, plotted as the electron density profile of the adsorbed and fluid water above the muscovite surface. (D) A schematic representation of the adsorbed and primary hydration-layer water molecules, corresponding to the electron density profile in (C). [Figure 24 (A-C) used by permission of the editor of Physical Review Letters, from Cheng et al. (2001), Fig. 2, p. 156103-2, and Fig. 3, p. 156103-3.]...

The most common type of device for measurement of specular reflectance is a near-normal incidence, near-normal collection accessory for a spectropho-... 

Specular surfaces can also be measured by using at integrating sphere at 8° incidence or collection geometry. The measurement technique is identical to the near-normal technique described previously. A reference mirror is used to establish the instrument baseline, and then the sample mirror replaces the reference and a scan is obtained. The reflectance of the sample is the product of the measured value for sample times the actual reflectance for the reference. This technique is quite convenient to use and is as accurate as the multiple mirror method. Care must be taken, however, to ensure that the incidence or collection angle is not 0°, because a specular-excluded measurement of a mirror will certainly give the incorrect answer for reflectance ... 

The specular reflectivity R is ordinarily expressed in units of the Fresnel reflectivity Rp, given by Eq. (38), and for nearly normal incidence it can be written, in the Born approximation, as ... 

What technique should be employed for measuring infrared spectra from thick samples for which a transmission measurement does not work Examples of target samples in this category are crystals and polymers (including rubber) having flat surfaces. To analyze such samples, reflection measurements should be considered. To record infrared reflection spectra from such samples, two representative techniques are available, namely, specular reflection (reflection at normal or near-normal incidence) and attenuated total reflection (ATR). This chapter deals with external reflection at normal incidence, which has been used for a long time for measuring mid-infrared spectra from optically thick materials with flat surfaces. ATR will be discussed in Chapter 13. 

Figure 3 (A) Specular reflectance (SR) spectrum of a black acrylonitrile-butadiene-styrene polymer film measured at near normal incidence, (B) Absorbance spectrum after data treatment of SR spectrum by a Kramers-Kronig transformation. Reproduced in part with permission of Elsevier Science from Zachman G (1995) Journal of Molecular Structure 348 453-456.

RAS at near normal incidence This is one of the most common and straightforward external reflection techniques. The IR beam is directed to the sample in the angular range 10-50 . The sample film must be on a reflective support. Under these conditions the RA spectrum is dominated by absorption since specular reflectance from the outer sample surface results in only 4-10% as shown by Figure 4. For this reason RA spectra resemble transmission spectra very closely. Accordingly, typical sample thicknesses are between 0.5 and 20 Xm. 

When the sample is deposited on the surface of a smooth mirror-like substrate, it is possible to use the specular reflection technique, or external reflection spectroscopy (ERS), which is carried out with the beam at near normal incidence [28]. The specular reflectance is completely governed by Fresnel s formalism and is predominately a function of refractive index. The impinging light reflects from the sample surface and does not penetrate the sample. If the surface is smooth, the reflection and the incidence angles are equal and the reflected beam retains the polarization characteristics of the impinging beam. This type of reflection is called regular Fresnel reflection [29]. 

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