Correction of effective refractive index

There is another question with respect to the lifetime behavior of lanthanides in nanocrystals. Will the lifetime of all excited states be lengthened The answer is obviously no since the observed lifetime depends on both the radiative and nonradiative relaxation rates. Although the correction of effective refractive index (eq. (9)) may be applicable to all excited states, it affects only the radiative lifetime. 

Therefore, within limits, we may interpret N in (3.41) as the effective refractive index of the slab of particles. This leads naturally to the question To what extent is N similar to the refractive index of a homogeneous medium For example, under what conditions, if any, will substitution of N into the expression for the reflection coefficient of a homogeneous slab yield physically correct results We can answer the latter and more specific of these two questions by calculating the field Er at the point P (Fig. 3.8), which is the sum... 

This result shows that electroosmotic flow and backflow in the capillary cancel when the factor (2r1/R — 1) equals zero. This condition corresponds to r/Rc = 0.707. Thus at 70.7% of the radial distance from the center of the capillary lies a circular surface of zero liquid flow. Any particle tracked at this position in the capillary will display its mobility uncomplicated by the effects of electroosmosis. This location may also be described as lying 14.6% of the cell diameter inside the surface of the capillary. Experimentally, then, one establishes the inside diameter of the capillary and focuses the microscope 14.6% of this distance inside the walls of the capillary. Corrections for the effect of the refractive index must also be included. Additional details of this correction can be found in the book by Shaw (1969). 

Extensive applications experience has shown that most particulate materials can be analyzed without any consideration of the refractive index. This is generally true because most practical materials have a high index, or are somewhat absorbing. In the exceptional case in which refractive index corrections must be applied, the values of the real and complex indices must be determined carefully. Arbitrary use of index corrections to arbitrarily alter instrument calibration may produce highly erroneous results. Table I serves as a guide to the effects of the refractive index on small particle measurements. 

The crudest approximation to the density matrix for the system is obtained by assuming that there are no statistical correlations between the elementary excitations (perfect fluid), so that can be written as a simple product of molecular density matrices A. A better approximation is obtained if one does a quantum field theory calculation of the local field effects in the system which in a certain approximation gives the Lorentz-Lorenz correction L(TT) in terms of the refractive index n53). One then writes,... 

The internal reflectance technique is usually called attenuated total reflection (ATR) spectroscopy. It is especially useful for studying strongly absorbing media, for example, aqueous solutions. When the infrared radiation is absorbed in the test medium, one obtains a spectrum similar to that from a transmission experiment. However, there are distortions in the ATR spectrum, especially in the region of intense bands. One reason for distortion is the fact that the depth of penetration varies with wavelength. The other effect is due to the change of the refractive index of the solution in the region of the intense band. ATR spectra should be corrected for these effects so that they may be compared to normal transmission spectra. 

For higher concentrations, a number of corrective factors have to be introduced, as for example the refraction index variation related to the concentration of the analyte. One way to correct this effect is to substitute the value of ex of the Beer-Lambert equation by e n/(n2 +2)2, where n is the value of the refraction index. Usually, this correction is not very high for concentrations lower than 0.01 M. Another effect that can distort the Beer-Lambert law linearity may be the use of a polychromatic radiation. This problem, encountered with instruments using filters (photometers), obliges the use of instruments allowing the selection of narrower wavelength ranges by means of monochromators (spectrophotometers), and are, therefore, more expensive. 

HB interactions, is claimed to lie in different responses to solvent polarizability effects. Likewise, in the relationship between the Ji scale and the reaction field functions of the refractive index (whose square is called the optical dielectric constant e ) and the dielectric constant, the aromatic and the halogenated solvents were found to constitute special cases." This feature is also reflected by die polarizability correction term in eq. [13.1.2] below. For the select solvents, the various polarity scales are more or less equivalent. A recent account of the various scales has been given by Marcus, and in particular of by Laurence et al., and of Ey by Reichardt. ... 

Such a technique has been shown [26] to work well, for example, for the computation of the refractive index of CH3CN in the microwave and far-infrared. Crawford and co-workers [22-24] have also advocated using a correlation function based on the complex part of the local susceptibility, (introduced to correct for dielectric effects on the optical constants). In that case. 

In many commercially available FT-IR spectrometer systems, software (called the ATR correction) for correcting the band intensities of an observed ATR spectrum for the wavelength-dependent depth of penetration expressed in Equation (13.4) is installed, in order to make the observed ATR spectrum more closely resemble a transmission spectrum. In ATR spectra, peak positions, particularly those of intense bands, tend to have wavenumbers lower than those in corresponding transmission spectra. As described earlier, this is related to the anomalous dispersion of the refractive index in the vicinity of the absorption band. The effect has been discussed and software for correcting ATR spectra to take account of this effect is available [9]. The software for this purpose is also installed in some commercially available FT-IR spectrometers. Input data necessary for this software are the refractive index of the sample and the IRE, the angle of incidence, and the number of internal reflections. 

Using the correct refractive index values is very important in retrieving an accurate particle size distribution when Mie theory is used in the matrix inversion. It is especially important when the relative refractive index approaches unity in which case even a minor error in the choice of a relative refractive index may lead to a significant variation in the result [54]. Figure 3.37 shows an example of the effect of refractive index in resolving particle size using laser diffraction. Correct results can only be obtained when correct values of the refractive index are used in the matrix inversion. Otherwise, an either... 

The refractive power is a value which attempts to correct the effects of temperature, pressure, and concentration of the substance, all of which cause the refractive index, n, to vary with the slightest alteration of the conditions. The most accurate expression for the refmctive power is that of Lorenz and Lorentz, which is... 

From this equation it can be seen that the depth of penetration depends on the angle of incidence of the infrared radiation, the refractive indices of the ATR element and the sample, and the wavelength of the radiation. As a consequence of lower penetration at higher wavenumber (shorter wavelength), bands are relatively weaker compared to a transmission spectrum, but surface specificity is higher. It has to be kept in mind that the refractive index of a medium may change in the vicinity of an absorption band. This is especially the case for strong bands for which this variation (anomalous dispersion) can distort the band shape and shift the peak maxima, but mathematical models can be applied that correct for this effect, and these are made available as software commands by some instrument manufacturers. 

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