INDEX permittivity properties

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

Water absorption can also cause significant changes in the permittivity and must be considered when describing dielectric behavior. Water, with a dielectric constant of 78 at 25°C, can easily impact the dielectric properties at relatively low absorptions owing to the dipolar polarizability contribution. However, the electronic polarizability is actually lower than solid state polymers. The index of refraction at 25°C for pure water is 1.33, which, applying Maxwell s relationship, yields a dielectric constant of 1.76. Therefore, water absorption may actually act to decrease the dielectric constant at optical frequencies. This is an area that will be explored with future experiments involving water absorption and index measurements. 

Dependence of certain physical properties, like the electric permittivity, refractive index and magnetic susceptibility on direction. It is created by long-range orientational order in a mesophase, provided the corresponding molecular property is anisotropic. 

Thus, we see the initial connection between optical properties and the electrical and magnetic properties from the two previous sections. Substimtion of Eqs. (6.78) and (6.79) into (6.77) shows that the refractive index can be expressed in terms of the relative electric permittivity (dielectric constant), (cf. Table 6.5), and relative magnetic permeability of the medium, (1 - - x) [cf. Eq. (6.63)], where x is the magnetic susceptibility ... 

Physical properties of the solvent are used to describe polarity scales. These include both bulk properties, such as dielectric constant (relative permittivity), refractive index, latent heat of fusion, and vaporization, and molecular properties, such as dipole moment. A second set of polarity assessments has used measures of the chemical interactions between solvents and convenient reference solutes (see table 3.2). Polarity is a subjective phenomenon. (To a synthetic organic chemist, dichloromethane may be a polar solvent, whereas to an inorganic chemist, who is used to water, liquid ammonia, and concentrated sulfuric acid, dichloromethane has low polarity.)... 

There are two sets of quantities that are often used to describe optical properties the real and imaginary parts of the complex refractive index N = n + ik and the real and imaginary parts of the complex dielectric function (or relative permittivity) e = c + ie". These two sets of quantities are not independent either may be thought of as describing the intrinsic optical properties of matter. The relations between the two are, from (2.47) and (2.48),... 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

IR spectra measurements as well as variation of the film thickness, shrinkage, and refractive index demonstrated substantial differences in the mechanisms of thermal decomposition of films prepared from the exclusively metal alkoxide precursor and from the metal alkoxides modified by 2-ethylhexanoic acid. These differences affect the evolution of film microstructure and thus determine the different dielectric properties of the obtained films. The dielectric permittivity of the films prepared from metal alkoxide solutions was relatively low (about 100) and showed weak dependence ofthe bias field. This fact may be explained by the early formation of metal-oxide network (mostly in the... 

Most of the physical properties of the polymer (heat capacity, expansion coefficient, storage modulus, gas permeability, refractive index, etc.) undergo a discontinuous variation at the glass transition. The most frequently used methods to determine Tg are differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical thermal analysis (DMTA). But several other techniques may be also employed, such as the measurement of the complex dielectric permittivity as a function of temperature. The shape of variation of corresponding properties is shown in Fig. 4.1. 

The two polarity parameters, t and tz, are related also in a general manner to certain physical properties of the solvents beyond the dipole moment mentioned above, namely functions of their refractive index and relative permittivity (Bekarek 1981) (cf. Chapter 3) ... 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

Solvent permittivity — is an index of the ability of a solvent to attenuate the transmission of an electrostatic force. This quantity is also called the -> dielectric constant. -> permittivity decreases with field frequency. Static (related to infinite frequency) and optical op (related to optical frequencies) permittivities are used in numerous models evaluating the solvation of ions in polar solvents under both static and dynamic conditions. Usually the refractive index n is used instead of op (n2 = eop), as these quantities are available for the majority of solvents. The theory of permittivity was first proposed by Debye [i]. Systematic description of further development can be found in the monograph of Frohlich [ii]. Various aspects of application to reactions in polar media and solution properties, as well as tabulated values can be found in Fawcetts textbook [iii]. 

Here, Co = 2.99792458 x 10 ms is the speed of light in vacuum and Ao the vacuum wavelength. For non-absorbing (transparent) media, far from resonances, is a real quantity. It is then related by (13) to a property better known in chemistry, the refractive index of the material. A high refractive index, n , is therefore an expression of a high linear susceptibility. For optical frequencies as provided by light in the UV-visible range, is also related to the relative permittivity (dielectric constant), because Maxwell s relation, holds. 

The following physical constants can be used to characterize the properties of a solvent melting and boiling point, vapour pressure, heat of vapourization, index of refraction, density, viscosity, surface tension, dipole moment, relative permittivity, polarizability, specific conductivity, etc. A compilation of data of usual organic solvents is given in... 

Because of the complicated interactions between solvents and solutes, the prediction of solvent effects on reaction rates, and the correlation of these effects with intrinsic solvent properties, is very difficult. Nevertheless, many authors have tried to establish -empirieally or theoretically - correlations between rate constants or Gibbs energies of aetivation and characteristic solvent parameters such as relative permittivity, r, dipole moment, fi, refractive index, n, solubility parameter, 5, empirical solvent polarity parameters, etc., as schematically shown by Eq. (5-9). 

It has been stated that, when specific hydrogen-bonding effects are excluded, and differential polarizability effects are similar or minimized, the solvent polarity scales derived from UV/Vis absorption spectra Z,S,Ei 2Qi),n, Xk E- ), fluorescence speetra Py), infrared spectra (G), ESR spectra [a( " N)], NMR spectra (P), and NMR spectra AN) are linear with each other for a set of select solvents, i.e. non-HBD aliphatic solvents with a single dominant group dipole [263]. This result can be taken as confirmation that all these solvent scales do in fact describe intrinsic solvent properties and that they are to a great extent independent of the experimental methods and indicators used in their measurement [263], That these empirical solvent parameters correlate linearly with solvent dipole moments and functions of the relative permittivities (either alone or in combination with refractive index functions) indicates that they are a measure of the solvent dipolarity and polarizability, provided that specific solute/ solvent interactions are excluded. 

Freezing of a dipolar liquid is accompanied by a rapid decrease in its electric permittivity [8-10]. Following solidification, dipole rotation ceases and the electric permittivity is almost equal to n, where n is refractive index, as it arises from deformation polarisation only. Investigation of the dynamics of a confined liquid is possible from the frequency dependences of dielectric properties, which allows both the determination of the phase transition temperature of the adsorbed substance and characteristic relaxation frequencies related to molecular motion in particular phases. 

An Outline of Non-linear Effects in Dielectrics. Constitutive Relations in Linear Media. We shall be considering homogeneous and isotropic dielectrics, the electric, magnetic, and optical properties of which, in the absence of external fields, are described by the following three scalar quantities, characteristic of the material of which the medium consists e = electric permittivity /X = magnetic permeability n = refractive index. 

BekSrek and coworkers40 related the effect of the medium on the spectrum of 2-nitroaniline to the relative permittivity and refractive index of the solvents. In subsequent work, BekSrek and coworkers52 53 employed several probes, including 5, 8, 9, 10 and 15 as well as some that have not been mentioned previously 3-nitro-AAAAdimethylaniline (46), 4-nitroso-A ,A -dimethy I aniline (47) and Af-(2-nitrophenyl)piperidine (48), as probes to explore the polarity/polarizability and HBA/EPD properties of a large number of polar and non-polar aprotic aliphatic solvents. The wavenumbers could be fitted to expressions similar to equations 10 and 11, but with a cross-term of the permittivity and refractive index included (equation 12) ... 

The dielectric properties of the solvents considered here are summarized in table 4.2. These properties are important in evaluating the solvation of ions in polar solvents under both static and dynamic conditions. The relative permittivity of a solvent at high frequencies, Sop, can be calculated from the refractive index, nop, the relationship being... 

The ratio c/u is always greater than 1, and is called the index of refraction of the material (through which the wave travels at the speed u). Note that though c is popularly called the velocity of light, it is the same for any electromagnetic wave. It can be shown that c = l/ y/( Xo o)> where x0 is the permeability of free space (vacuum or air) and e0 is the permittivity of free space. x0 and e0 are fundamental constants, since they represent the properties of our universe. 

The Hamaker constant can be evaluated accmately using the continuum theory, developed by Lifshitz and coworkers [40]. A key property in this theory is the frequency dependence of the dielectric permittivity, e( ). If this spectrum were the same for particles and solvent, then A=0. Since the refractive index n is also related to t ( ), the van der Waals forces tend to be very weak when the particles and solvent have similar refractive indices. A few examples of values for for interactions across vacuum and across water, obtained using the continuum theory, are given in table C2.6.3. 

This anisotropy, illustrated by refractive index, extends to other properties, and common properties of interest would be the anisotropy in linear polarizability (Aa), dielectric permittivity (Ae), and diamagnetism (Ax). In the nematic phase, these properties are quite strongly temperature dependent the order parameter, S, increases as samples cool away from the N-I transition. This is illustrated in Figure 19 where it is also seen that the parallel component has the stronger temperature dependence as it is the orientational correlations that increase on cooling. 

---