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,... 

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 ... 

Sparrow, C, The Lorenz Equations Bifurcation, Chaos, and Strange Attractions (Appl. Math. Sci. 41). Springer-Verlag, New York, 1982. 

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... 

Beattie and Bridgeman made these substitutions in the Lorenz equation, Equation 4-6, producing... 

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 ... 

The Lorenz equations have a simple structure and contain two nonlinear terms only. Let us briefly consider the main bifurcations in the system (42) (a more detailed analysis can be found in Ref. 181). We fix the parameters ct = 10, b = and vary the parameter r in this case two global bifurcations take place (see the bifurcation diagram in Fig. 20). For r = 1, a supercritical... 

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 directly to model the birefringence of a solution of rigid rod molecules subject to an orienting, external field. Figure 7.2 shows a representative molecule, which is modeled as having a uniaxial polarizability of the form... 

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... 

If I is oriented along the principal-axis system of the optical indicatrix, then for each of the three components of the refractive index (nlr n2, n3) the anisotropic Lorentz-Lorenz equation is... 

This is a simplification of the Lorentz-Lorenz equation. Looyenga showed that the expression (n2— 1 )/(n2 + 2) can, with high accuracy be approximated by the more simple expressions (n213 — 1) for the polymer refraction indices mentioned in Table 10.5, the differences vary from 2.9% (n = 1.35) to 8.8% (n = 1.654). 

Fig. 4 C02 refractive index as a function of pressure at four different temperatures (calculated for X = 546 nm, based on the Lorentz-Lorenz equation [2])...

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