Refractive index, polarizability from

Polarizability Attraction. AU. matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaket constant for interaction energy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where is the frequency of the principal electronic absorption... 

The general or universal effects in intermolecular interactions are determined by the electronic polarizability of solvent (refraction index n0) and the molecular polarity (which results from the reorientation of solvent dipoles in solution) described by dielectric constant z. These parameters describe collective effects in solvate s shell. In contrast, specific interactions are produced by one or few neighboring molecules, and are determined by the specific chemical properties of both the solute and the solvent. Specific effects can be due to hydrogen bonding, preferential solvation, acid-base chemistry, or charge transfer interactions. 

Here, A and v 2 are fitting parameters amenable to physical interpretation using Equation 12.11. The point of present concern is that the isotope effect on polarizability can now be expressed in terms of isotopic differences in refractive index. It follows from Equation 12.14 that a plot of AR/R = [6n2/((n2—l)(n2 + 2))][An/n] vs. v2 gives an approximately straight line,... 

Mean molecular polarizability can be calculated through the Lorenz-Lorentz- Equation from refractive index, n, molecular weight, MW, and density, d, of a compound, demonstrating that the parameters can be derived from these elementary molecular properties (Figure 3). 

For each crystal, the upper figure gives the observed refractive index for the sodium D line (Winchell, 1954), the lower figure that calculated from the bond polarizabilities of Table IX.)... 

As has been pointed out (63), this is a rather artificial model and, moreover, its application is quite unnecessary. In fact, (a> can be calculated from the refractive index increment (dnjdc), as has extensively been done in the field of light scattering. This procedure is applicable also to the form birefringence effect of coil molecules, as the mean excess polarizability of a coil molecule as a whole is not influenced by the form effect. It is still built up additively of the mean excess polarizabilities of the random links. This reasoning is justified by the low density of links within a coil. In fact, if the coil is replaced by an equivalent ellipsoid consisting of an isotropic material of a refractive index not very much different from that of the solvent, its mean excess polarizability is equal to that of a sphere of equal volume [cf. also Bullough (145)]. 

Ellipsometry27,60 62) is based on the principle that light undergoes a change in polarizability when it is reflected at a surface. The refractive index of the surface and the reflection coefficient of a system can be calculated from the change in the phase retardation A and the change in the amplitude ratio tan ip. Adsorption of a polymer on a surface gives rise... 

Although only a1 and e are used as additional descriptors so far, some others might be useful in the future. One of the most apparent is the local electronic polarizability of the molecule in the vicinity of a surface segment i, which we may represent by a local refractive index n,. Such local polarizability or local refractive index would allow for a refinement of the electrostatic misfit term, which presently only takes into account an average electronic polarizability of organic molecules. It is also likely that the local electronic polarizability is of importance to the strength of hydrogen bonds, which so far in COSMO-RS are only a function of polarity. Finally, from a physical perspective, the vdW interactions should be a function of the local polarizability as well. 

In this subsection, the connection is made between the molecular polarizability, a, and the macroscopic dielectric constant, e, or refractive index, n. This relationship, referred to as the Lorentz-Lorenz equation, is derived by considering the immersion of a dielectric material within an electric field, and calculating the resulting polarization from both a macroscopic and molecular point of view. Figure 7.1 shows the two equivalent problems that are analyzed. 

The dependence of radiative lifetime on the index of refraction, n, arises from the change in the density of states for photons in the medium of reduced light velocity and the modification of the polarizability of the surrounding medium. Since the nanoparticles occupy only a small fraction of the total volume, in order to compare the experimental results with eq. (3) it is necessary to introduce an effective index of refraction for the medium, eff, which consists of... 

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