Lorentz-Lorenz relationship

The velocity of light passing through a polymer is affected by the polarity of the bonds in the molecule. Polarizability P is related to the molecular weight per unit volume, M, and density p as follows (the Lorenz-Lorentz relationship) ... 

The above equation is known as Rayleigh s Law. In order to replace polarizabilities with refractive indexes, one uses the Lorenz - Lorentz relationship, namely... 

The refractive index n of a material depends according to Lorenz-Lorentz relationship, on the polarizability P of all the molecules residing in a uniform field ... 

Hz, a material s ability to respond to light, as indicated by a property like the refractive indices, nDh is related to the material s polarizability. This relationship is known as the Lorenz-Lorentz equation (Israelachvili, 1992) ... 

If the craze layer extends with complete lateral constraint, the strain in the craze is related to the change in its density. From a relationship between density and refractive index, an equation between strain in the craze and its refractive index can be derived. Although it is usual to start with the Lorenz-Lorentz equation, this may not be the correct relationship for a material having the structure of the craze (9). For the present purposes a linear relationship is assumed. The error introduced is at most 10% and only a few percent for the stretched craze with a high void content. 

To calculate micelle size and diffusion coefficient, the viscosity and refractive index of the continuous phase must be known (equations 2 to 4). It was assumed that the fluid viscosity and refractive index were equal to those of the pure fluid (xenon or alkane) at the same temperature and pressure. We believe this approximation is valid since most of the dissolved AOT is associated with the micelles, thus the monomeric AOT concentration in the continuous phase is very small. The density of supercritical ethane at various pressures was obtained from interpolated values (2B.). Refractive indices were calculated from density values for ethane, propane and pentane using a semi-empirical Lorentz-Lorenz type relationship (25.) Viscosities of propane and ethane were calculated from the fluid density via an empirical relationship (30). Supercritical xenon densities were interpolated from tabulated values (21.) The Lorentz-Lorenz function (22) was used to calculate the xenon refractive indices. Viscosities of supercritical xenon (22)r liquid pentane, heptane, decane (21) r hexane and octane (22.) were obtained from previously determined values. 

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 relationship between the molar refraction RLL/ the refractive index n and the polarisability a is known as the molar Lorentz-Lorenz relation (1880), which reads... 

The refractive index of the ethane/propane mixture, needed for calculation of the scattering vector, was determined from experimental density measurements and an empirical Lorentz-Lorenz relationship (12). Incorporating the errors from the viscosity and refractive index calculations into the Stokes-Einstein relation results in a maximum error in the hydrodynamic radius of approximately 5%. 

This relationship as such is not well obeyed for most compounds if the static or low-frequency relative permittivity is used, as can be judged from Table 11.1. The relationship can be correctly interpreted by using the relative permittivity due to electronic polarisation in the equation. With this in mind, substitution of the relationship given in Equation (11.10) into the Clausius-Mossotti equation yields the Lorentz-Lorenz equation ... 

The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. 

Values for the intrinsic birefringence (Anc, An ) may be obtained experimentally [306] or analytically [307]. The analytical approaches are based on the relationships between the principal polarizability of the molecule (P) and the refractive indices as represented by the Lorentz-Lorenz equation ... 

The relationship between a and the concentration of scattering centers is derived next (Tanford, 1961). The Lorentz-Lorenz formula (another aspect of electromagnetic theory) is... 

The numerical value of the glass-transition temperature depends on the rate of measurement (see Section 10.1.2). The techniques are therefore subdivided into static and dynamic measurements. The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. Static and dynamic glass transition temperatures can be interconverted. The probability p of segmental mobility increases as the free volume fraction / Lp increases (see also Section 5.5.1). For /wlf = of necessity, p = 0. For / Lp oo, it follows that p = 1. The functionality is consequently... 

The refractive index of binary ionic liquid mixtures can be interpreted in terms of electron polarizability if the density is a linear function of the mixtures composition, the refractive index is also linearly related to the molar refraction by the Lorentz-Lorenz equation. Our data show that the refractive index increases linearly for all ionic liquids with the mole fraction of [C2mim][OAc] (Fig. 9). Linear relationships were also found for [C4mpy][(CN)2N]/[C4mpy][BF4],... 

One of the first attempts about ILs density predictions was performed by Deetlefs et al. [78] They described two different methods a) one is based on the equation proposed by Macleod[79] that correlate the density and the surface tension (Equation 3) b) the other is based in the value of refractive index Ri, molar refractivity Rm and molar mass of the compound M through the relationship of Lorentz-Lorenz (Equation 4) ... 

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