External radiation reflection

This section has been devoted to the study of the surface excitons of the (001) face of the anthracene crystal, which behave as 2D perturbed excitons. They have been analyzed in reflectivity and transmission spectra, as well as in excitation spectra bf the first surface fluorescence. The theoretical study in Section III.A of a perfect isolated layer of dipoles explains one of the most important characteristics of the 2D surface excitons their abnormally strong radiative width of about 15 cm -1, corresponding to an emission power 10s to 106 times stronger than that of the isolated molecule. Also, the dominant excitonic coherence means that the intrinsic properties of the crystal can be used readily in the analysis of the spectroscopy of high-quality crystals any nonradiative phenomena of the crystal imperfections are residual or can be treated validly as perturbations. The main phenomena are accounted for by the excitons and phonons of the perfect crystal, their mutual interactions, and their coupling to the internal and external radiation induced by the crystal symmetry. No ad hoc parameters are necessary to account for the observed structures. 

The refracted component is further attenuated according to Beer s law when travelling through the second medium. In a slab of limited thickness d, radiation reflected at the back surface returns to the front surface where it is refracted out of the slab. This radiation might interfere with externally reflected radiation (see Fig. 6.4-8). Including further reflections results in a multibeam interference pattern which is described by the general Airy equation... 

In external reflectance the incident radiation is focused on to the sample, and two forms of reflectance can occur, namely specular and diffuse. External reflectance measures the radiation reflected from a surface. The material must therefore be reflective, or be attached to a reflective backing. A particularly useful application of this technique is the study of surfaces. 

Reflectance techniques may be used for samples that are difficult to analyze by the conventional transmittance method. In all, reflectance techniques can be divided into two categories internal reflection and external reflection. In internal reflection method, interaction of the electromagnetic radiation on the interface between the sample and a meditnn with a higher refraction index is studied, while external reflectance techniques arise from the radiation reflected from the sample surface. External reflection covers two different types of reflection specular (regular) reflection and diffuse reflection. The former usually associated with reflection from smooth, polished surfaces Hke mirror, and the latter associated with the reflection from rough surfaces. 

The incident radiation focused onto the sample may be directly reflected by the sample surface, giving rise to specular reflection, and it may also undergo multiple reflections at the sample, resulting in diffuse reflection. In external reflectance techniques, the radiation reflected from a surface is evaluated (Figure 8). 

The external boundary conditions of the fire should represent radiation, reflection and convection. The temperature is specified by the Regulations as an average of 800°C, so, in general, a uniform average temperature of SOO C should be used for the radiation source and for convective heat transfer. 

Generally, conduction and radiation can be modelled exphdtly and external convection provides few problems for general purpose computer codes but experimental evidence may be required to support modelling assumptions and basic data used to represent internal convection and radiation. Radiation reflection will be important in gas filled packages, and insufficient knowledge of thermal emissivities may restrict the final accuracy. A sensitivity study with different emissivities can be used to show that the assumptions are adequate or to provide conservative (i.e. maximum) limits on calculated temperatures. 

Some radiation reflected from the sample in the Bjln mode may be lost out of the entrance port when external optics are used or off of the focusing mirror or lens and its support structure when internal optics are used. This effect can result in an error in the measured reflectance. Similarly, for 2nl6 mode reflectometers, the optics used to collect reflected radiation from the sample reduces the radiant power striking the sample and may affect the measured reflectance. If the sample is a Lambertian reflector and the illumination (0/27i) or viewing (2ti/0) is near normal, then the fraction of radiation intercepting the sample optics is given by... 

IR reflection spectroscopy is normally used for samples which are difficult to analyze in transmission, such as bulk samples or thin layers on nontransparent substrates. In this case, the IR radiation is directed at a sample surface, usually at an angle larger than 0° off-normal, with the attenuated radiation, reflected back from that surface, being detected. Reflection techniques can be based on specular reflection (internal or external reflection), where the reflectivity R, at normal incidence, is given by... 

The external reflection of infrared radiation can be used to characterize the thickness and orientation of adsorbates on metal surfaces. Buontempo and Rice [153-155] have recently extended this technique to molecules at dielectric surfaces, including Langmuir monolayers at the air-water interface. Analysis of the dichroic ratio, the ratio of reflectivity parallel to the plane of incidence (p-polarization) to that perpendicular to it (.r-polarization) allows evaluation of the molecular orientation in terms of a tilt angle and rotation around the backbone [153]. An example of the p-polarized reflection spectrum for stearyl alcohol is shown in Fig. IV-13. Unfortunately, quantitative analysis of the experimental measurements of the antisymmetric CH2 stretch for heneicosanol [153,155] stearly alcohol [154] and tetracosanoic [156] monolayers is made difflcult by the scatter in the IR peak heights. 

In employing a thin-layer configuration the external reflectance approach reduces the problem of the strong solvent absorption in two ways. Firstly, this configuration yields a solution layer only a few microns thick. Secondly, exact calculations employing the Fresnel reflection equations show that the radiation absorbed by an aqueous layer c. 1 urn thick in contact with a reflective electrode is attenuated to a lesser extent than would be predicted by the Beer - Lambert law. 

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