Refractive index and dielectric constant

One important macroscopic quantity related to the optical properties of non-metallic solids is their refractive index, which is closely related to their dielectric constant. Maxwell s equations for electromagnetic waves propagating in absorbing materials (see for instance [43]) lead to wave equations for the electric and magnetic fields in the material, and a solution for the amplitude of one component of these fields is  

In this expression, exp[—wkz/c] represents the attenuation (or absorption) of the electromagnetic wave component. As the energy flow is proportional to the product of amplitudes of the components of the electric and magnetic vectors, and since both contain the term exp [—wkz/c], the energy absorption is proportional to exp [—2Wz/c]. In absorption spectroscopy, one generally uses the absorption coefficient K defined by  

With this definition, the energy absorption is proportional to exp [—Kz. The reflectivity R of an electromagnetic wave or radiation propagating in vacuum and normally incident on the plane boundary of a material with complex refractive index h is (h — 1 )2 / (n + l)2. Its real part is the standard reflectivity  

For pure elemental semiconductors like silicon, the strong electronic absorption at energies above Eg produces a small non-linear dispersion of the refractive index below Eg in silicon, n = 3.57 near Eg at room temperature (RT) and it steadily decreases to 3.42 for wavelengths near 12 pm and stays close to this value down to radio frequency energies (see also [20]). For these elemental crystals, the dielectric constant at energies below Eg is real and equal to n2. The refractive index is isotropic for cubic crystals, but for crystals with one anisotropic axis, like those of the wurtzite type, the refractive index for the electric field component of the radiation parallel to this axis (n//) is slightly different from that for the component perpendicular to this axis (njJ. 

To introduce changes in the dielectric constant related to phonon modes in compound crystals, it is relevant to consider the classical interaction between an atomic system with resonant frequency uyi and an electromagnetic field E = Eoexp [iu t]. The 1-D equation of motion for such a system, also known as a Lorentz oscillator, is  

---

Ihrig and Smith extended their study by running a regression analysis including reaction field terms, dispersion terms and various combinations of the solvent refractive index and dielectric constant. The best least squares fit between VF F and solvent parameters was found with a linear function of the reaction field term and the dispersion term. The reaction field term was found to be approximately three times as important as the dispersion term and the coefficients of the terms were opposite in sign. 

Recently, the same series of six polyimides was studied by positron annihilation spectroscopy to determine die fractional free volume directly. In all three H/F analogue pairs, the increased free volume of the fluorinated polymer accounted for around 50% of the observed decrease in refractive index and dielectric constant. This result confims an astonishingly large free volume contribution predicted by our earlier estimates.Future work will investigate the generality of this result to other polymer systems. 

Figure 4.9 Effect of refractive index and dielectric constant of solvent on O—O transitions of a polar molecule.

A4.3 Basic physical properties oflnN TABLE 5 Refractive index and dielectric constants of indium nitride. 

A Simple Relationship between the Refractive Index and Dielectric Constant of Regular Crystals and the Coefficient of Repulsion in Born and Lande s Potential Equation. 

Photochromism is also accompanied by changes in refractive index and dielectric constant. When the photochromic moities are incorporated in polymers, the photoinduced molecular structural change is mirrored at the macroscopic level and leads to interesting properties, such as change in phase transition, viscosity, solubility, wettability, elasticity, and so on [5]. 

In particles possessing no permanent dipole moment, equation (5), by application of the Maxwell relation between refractive index and dielectric constant, becomes the Lorentz-Lorenz equation ... 

Figure 10 The relationship between refractive index and dielectric constant for porons MSSQ produced using a poly(alkylene oxide) porogen...

Uchino, K., Nomura, S., Vedam, K., etal. (1984) Pressure dependence of the refractive index and dielectric constant in a fluoroperovskite, KMgF3, Phys Rev., B29, 6921-5. 

As the spectral shifts in hydrocarbons represent a susbstantial part as compared with the other solvents (excepting water and alcohols) we consider that the dispersion forces of the London [25] type have an important contribution to the solvation energies, and then to the red shiftj because the polarizability of solute molecule in the excited state increases [26], and an instantaneous redistribution of the electric charge will take place. From the McRae s [27] theory results a formula giving the spectral shift under the solvent influence (in terms of solute polarizability and dipole moment of the solute molecule and in terms of the refractive index and dielectric constant of the solvent), which, for nonpolar solvents, reduces to ... 

Perhaps the first investigation into the chemical composition of the anodic oxide of HgCdTe was reported by Nemirovsky and Finkman in 1979 (50). Anodic oxide films were grown on n-type slush grown (Hg,Cd)Te (Ej = 0.1 eV) in 0.1 N KOH in methanol and various concentrations (< 0.1 N) of KOH in 90% ethylene glycol /10% HjO. The material surface was mechanically polished and etched in 20% Br in methanol prior to anodization. The refractive index and dielectric constant of the oxide were determined to be closer to TeOj than CdO or HgO, so the authors concluded that the... 

There are actually a variety of polymer properties that change at the glass transition (modulus, specific volume, enthalpy, entropy, specific heat, refractive index, and dielectric constants), a variety of physical methods to measure the glass transition and, indeed, a variety of ways to define glass transition (5,21). 

---