Lorentz and Lorenz equation

The specific refraction r is given by the Lorentz and Lorenz equation. 

Example 1-Propynyl acetate has nn = 1.4187 and density = 0.9982 at 20°C the molecular weight is 98.102. From the Lorentz and Lorenz equation,... 

The refractive index is usually estimated in terms the molar refraction R, which quantifies the intrinsic refractive power of the structural units of the material. Several definitions have been proposed for R. Two of these definitions incorporate both of the key physical factors determining the refractive index, and are thus especially useful. Equation 8.5 expresses n in terms of the molar refraction RT T according to Lorentz and Lorenz [1,2], and Equation 8.6 expresses n in terms of the molar refraction Rgd according to Gladstone and Dale [3]. 

The small temperature dependence of the dielectric constant of a nonpolar insulator can generally be approximated in terms of the molar polarization according to Lorentz and Lorenz (Pll, in units of cc/mole), by Equation 9.2. Comparison of equations 9.1, 9.2 and 8.1 shows that Equation 9.3 holds for nonpolar materials. 

Step 15. Calculate the key optical properties. The refractive index n at room temperature (298K) is calculated by using equations 8.14 and 8.15. The predicted n(289K) for polystyrene is 1.6037. The predicted values of V(298K)=97.0 cc/mole and n(298K) l. 6037 are inserted into Equation 8.7 to predict the molar refraction according to Lorentz and Lorenz to be R ( -33.35 1. To estimate n(T) at temperatures other than 298K, V(T) and RLL are substituted... 

Lorentz-Lorenz equation, 19 380 Lorivox, molecular formula and structure, 5 92t... 

The refractive index is an important quantity for characterizing the structure of polymers. This is because it depends sensitively on the chemical composition, on the tacticity, and - for oligomeric samples - also on the molecular weight of a macromolecular substance. The refractive indices (determined using the sodium D line) of many polymers are collected in the literature. In order to characterize a molecule s constitution one requires knowledge of the mole refraction, Rg. For isotropic samples, it can be calculated in good approximation by the Lorentz-Lorenz equation ... 

Clausius-Mossotti equation). In this expression, V designates the mole volume and Ae, Be, Cf,... are the first, second, third,... virial dielectric coefficients. A similar expansion exists for the refractive index, n, which is related to the (frequency dependent) dielectric constant as n2 = e (Lorentz-Lorenz equation, [87]). The second virial dielectric coefficient Be may be considered the sum of an orientational and a polarization term, Be = B0r + Bpo, arising from binary interactions, while the second virial refractive coefficient is given by just the polarization term, B = Bpo at high enough frequencies, the orientational component falls off to small values and the difference Be — B may be considered a measurement of the interaction-induced dipole moments [73],... 

Lorentz-Lorenz equation). The A , B ,. .. differ from the Ae, BE,. .. by the absence of the permanent dipole terms. At sufficiently high frequencies, the molecules have not sufficient time to reorient themselves in response to the high-frequency electric field and the contributions of the... 

For white pigments, the hiding power can be expressed through the Lorentz-Lorenz equation (4) as a function of pigment, and medium, nm,... 

The Lorentz-Lorenz equation [2] defines the molar refraction, RD, as a function of the refractive index, density, and molar mass ... 

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 Lorentz-Lorenz equation can be used to express the components of the refractive index tensor in terms of the polarizability tensor. Recognizing that the birefringence normalized by the mean refractive index is normally very small, ( A/i / 1), it is assumed that Aa /a 1, where the mean polarizability is a = (al + 2oc2)/3 and the polarizability anisotropy is Aa = a1-a2. It is expected that the macroscopic refractive... 

For semi-polar substances or mixtures of semi-polar substances and non-polar substances the Lorentz-Lorenz equation applies... 

One of the most widely used steric parameters is molar refraction (MR), which has been aptly described as a "chameleon" parameter by Tute (160). Although it is generally considered to be a crude measure of overall bulk, it does incorporate a polarizability component that may describe cohesion and is related to London dispersion forces as follows MR = 4TrNa/By where N is Avogadro s number and a is the polarizability of the molecule. It contains no information on shape. MR is also defined by the Lorentz-Lorenz equation ... 

The calculated moment thus considerably exceeds the experimental value and furthermore represents the dipole as acting in the opposite direction the chlorine is represented as positive and the hydrogen negative. This result is clearly incorrect and Debye has shown that the error is due to the fact that the Lorentz-Lorenz equation is not valid at the small distances considered owing to the non-uniform character of the field. If the internuclear distances were of the order of 5 A, this type of calculation would be permissible. Attempts have been made to calculate the polarizability in a non-uniform electric field by the methods of wave mechanics , but have not yet been successful in producing a theory of the intermediate type of bond. 

Figure 47 shows taken from Equation 20 versus Vj. It shows that S. is quite sensitive to Vp and is therefore a good means to evaluate v, with the numerical values of Fig. 47. It can be estimated that the tensile modulus E of the bulk PMMA is not affected by the very low pressure toluene gas environment during the short duration of the experiment. The optical craze index in PMMA in air without load is known as n = 1.32, which corresponds to v = 0.6. From the optical interferometry, it is known that the craze just before breakage is twice as thick as unloaded, (v, = 0.3) and hence using Lorentz-Lorenz equation its optical index is n = 1.15. From Figs. 46 and 47 it can be concluded that the bulk modulus around the propagating crack is about 4400 MPa, which is a somewhat high value, in view of the strain rates at a propagating crack tip (10 to s" ). Using the scatter displayed in Fig. 46, it can be concluded from Fig. 47 that the fibril volume fraction is constant, v = 0.3, within a scatter band of 0.08, and is therefore not sensitive to the toluene gas.

Refractive Index Experimental Data for Gas and Liquid. From a measured refractive index it is always possible to extract formally an average linear dipole polarizability, a, from the Lorentz-Lorenz equation,... 

Liquid Phase Calculations of the Linear Response. The data in Table 5 for the isotropic polarizability, derived formally via the Lorentz-Lorenz equation (1) from the measured refractive index, shows that the assumption that individual molecular properties are largely retained at high frequency in the liquid is very reasonable. While the specific susceptibilities for the gas and liquid phases differ, once the correction for the polarization of the surface of a spherical cavity, which is the essential feature of the Lorentz-Lorenz equation, has been applied, it is clear that the average molecular polarizabilities in the gas and liquid have values which always agree within 5 or 10%. 

The application of the Lorentz-Lorenz equation gives a convincing demonstration of the general similarity of the linear response in gas and liquid but its application in the liquid introduces an approximation which has not yet been quantified. A more precise objective for the theory would be to calculate the frequency dependent susceptibility or refractive index directly. For a continuum model this may lead to a polarizability rigorously defined through the Lorentz-Lorenz equation as shown in treatments of the Ewald-Oseen theorem (see, for example Born and Wolf, plOO),59 but the polarizability defined in this way need not refer to one molecule and would not be precisely related to the gas parameters. 

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