Absorption coefficient, optical principles

The book starts with a short introduction to the fundamentals of optical spectroscopy, (Chapter 1) describing the basic standard equipment needed to measure optical spectra and the main optical magnitudes (the absorption coefficient, transmittance, reflectance, and luminescence efficiency) that can be measured with this equipment. The next two chapters (Chapters 2 and 3) are devoted to the main characteristics and the basic working principles of the general instrumentation used in optical spectroscopy. These include the light sources (lamp and lasers) used to excite the crystals, as well as the instrumentation used to detect and analyze the reflected, transmitted, scattered, or emitted light. 

Equation (4.41) contains all selection rules for optical transitions and it contains all transitions between pairs of states involving the same photon energy fko. It thereby models a system with broad bands as being made up of a multitude of 2-level systems. The absorption coefficient can in principle be calculated from theoretical models. Here we will use it as an experimentally determined quantity. 

The optical properties of materials are determined by the so-called dielectric function. This dielectric function for para-phenyl-type molecules was determined by first-principles band-structure calculations on PPP.14 In Fig. 8.3, we depict one of the main results, namely the dependence of the imaginary part of the dielectric function (which is proportional to the optical absorption coefficient) on the orientation parallel (ec) and perpendicular (ea, ch) to the chain axis. From a comparison to the experiment, one can see that the optical absorption in the visible and ultraviolet ranges is mainly determined by the dielectric function parallel to the polymer chain. This is shown in Fig. 8.4, where the calculated absorption coefficient of para-hexaphenyl perpendicular to the chains is compared to the experimentally determined absorption perpendicular and parallel to the chains. 

Pure MCD with no rotation occurs if the sample is optically thick and completely absorbing in one circular polarisation, but not in the other. Pure MOR will occur when both circular polarisations are equally absorbed, i.e. the absorption coefficients ot+ v) and ot-(v) are equal, but the refractive indices n+(v) and n-(v) are not equal. The latter condition is satisfied at the centre of symmetry of the rotation pattern, viz. the field-free resonance frequency vq.6 In principle, the situation seems simpler when either pure MOR or pure MCD occurs, which is why most of the effort has traditionally been expended in separating one from the other, leading to MOR and MCD spectroscopies. 

Due to its principle and instrumental realisation, atomic absorption spectrometry is a technique for quantitative analysis and is practically unsuitable for qualitative analysis. Quantitative response is governed by the law of Lambert and Beer, i. e. the absorption A is proportional to the optical pathlength I, the absorption coefficient k at the observed wavelength, and the concentration c of the species. 

According to the above-mentioned effect of polarization, in principle each molecule exhibits absorption at different wavelengths and intensity distributions. Bouguer, Lambert, and Beer realized many years ago a correlation between the number of particles, their properties, and the optical pathlength through a cell. It is described by a linear dependency between the attenuation and the concentration, whereby the molar decadic absorption coefficient e is derived as the proportionality constant speciflc to the molecular properties of the molecules analyzed [2,12,13]. This so-called Lambert-Beer law allows quantitative analysis of gaseous, liquid, or solid samples by absorption spectrometry. 

A prerequisite of the derivation of this law is that the optical pathway is defined. Radiation has to penetrate perpendicularly the interface of the sample, otherwise the pathway is longer than the physical thickness of the sample. In addition, part of the radiation is reflected at the interface. This principle is demonstrated in Fig. 4, which shows a cuvette for liquid analyte [12]. Since the proportional constant ex is a function of the wavelength, the law is only valid if the correct constant is taken at the chosen wavelength X. Furthermore, radiation has to be monochromatic and the analyte has to consist of just one single component. Otherwise, this law has to be written as a sum over the produets of concentrations c,- times absorption coefficients of all the different components i ... 

In case the internal absorbance is divided by the optical absorption pathlength, the decadic linear absorption coefficient is given in units of cm". It is usually used at the examination of thin films because in such cases it is difficult to determine molar concentrations. In Table 2 all these terms and symbols are defined according to the lUPAC recommendations [14] and given with their units. Further terms and symbols for physical quantities, related to fundamental processes occurring in light sources, and general principles of nomenclature standardization are stated in other lUPAC recommendations of the Analytical Division [21]. 

Besides the fluorescence coefficient, the optical absorption and scattering coefficients of the sample are the most important parameters in quantative fluorescence spectroscopy of turbid media. In principle two or, if the anisotropy parameter has to be determined, three independent measurements are sufficient to separate the coefficients that appear in all equations as sums or proportions. However, for better accuracy, one of the geometrical parameters (sample thickness, angle of incidence, distance from the irradiated spot) as well as the wavelength of irradiation should be varied over a wide range, and then the data should be fitted with the help of the corresponding model equation. 

Assuming an exact knowledge of the nature of the electronic transition or vibration associated with each absorption band, and assuming that the effect of the electrostatic field of a surface on these transitions can be calculated reliably, it should be possible, in principle at least, to deduce the orientation of the molecule on the surface from observation of the change in extinction coefficient with coverage. Unfortunately, our knowledge and understanding of optical transition and of the effects of an electrostatic field on these transitions is not sufficiently developed to permit such detailed conclusions. 

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