Lorentz equations

The molecular refractivity can be computed from the Lorenz and Lorentz equation ... 

The molar refraction, / m, is a measure of the size of a molecule. It is calculated with Eq. (8.5), the Lorenz-Lorentz equation, where , d, and M are the refractive index, the density, and the molecular weight, respectively. 

At optical frequencies in non-magnetic materials we may replace fr by to give the Lorenz-Lorentz equation... 

Matko, Karba and Zupancic (1992) quote the Lorentz equations in the form... 

In 1991 Groh and Zimmerman16 estimated the theoretical lower limit of the refractive index of amorphous organic polymers by using the Lorentz-Lorentz equation and reported the lower limit to be very close to 1.29, while in 1979 Dislich17 proposed a limit of about 1.33 from a screening of published polymer data. 

Mean molecular polarizability can be calculated through the Lorenz-Lorentz- Equation from refractive index, n, molecular weight, MW, and density, d, of a compound, demonstrating that the parameters can be derived from these elementary molecular properties (Figure 3). 

In general, all metals, magnetic or otherwise, display some degree of magnetoresistivity, as noted by Kelvin almost 150 years ago. This property may be seen as a direct result of the Lorentz equation,... 

Su Chang stated that their equation falls into the general form of the Lorentz Equation of State (qv). It may also be regarded as a simplified, generalized form of Beattie-Bridgeman Equation of State (qv)... 

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) ... 

Substituting this result into the Lorenz-Lorentz equation, and then using that result in Eq. 3-4, we find ... 

The force exerted on an ion carrying a charge q with a velocity v and subjected to a magnetic field of intensity B is given by the Lorentz equation ... 

This equation, called the Lorenz-Lorentz equation, was derived in 1880 by combining the Clausius-Mossotti expression for the local field with the idea of molecular polarizability. 

Molecular refractivity. Molecular refractivity is an additive quantity which is often used to assist in determining molecular structures via the Lorentz-Lorentz equation. This generally gives good agreement between values derived from experimental measurements of density and refractive index and values... 

The first ellipsometric measurement of the thickness of the adsorbed layer and the adsorbance of a polyelectrolyte and a negative adsorbance of salt onto a solid surface was reported by Takahashi et al.U4) They measured the adsorption of sodium poly(acrylate) (M = 950 x 103) onto a platinum plate as a function of the concentration of added sodium bromide. In an aqueous polyelectrolyte solution with an added simple salt, the bulk phase is a three-component system which consists of a polyelectrolyte, a simple salt, and water. The adsorbed layer on the solid surface is a three-component phase as well. The adsorbance of polyelectrolytes thus cannot easily be determined from measurements of the refractive index nf of the adsorbed phase. Hence, it was assumed that the adsorbed layer is a homogeneous layer of thickness t and further that nf is represented by the Lorenz-Lorentz equation as follows ... 

The molar refractions of the amino acids were determined by measurements on their aqueous solutions and the expanded Lorenz-Lorentz equation. The refractive indices of a number of proteins were calculated from their amino acid compositions and the values for the refraction of the amino acid residues. These calculated results are in good agreement with those experimentally determined, demonstrating that refractive index is a unique characteristic of a protein. A comparison of the refractive index of heat denatured /3-lactoglobulin with the native protein demonstrated that changes in structure produced a small change in refractive index, not associated with a change in volume. 

Calculations. Refractive Indices and Molar Refractions of Solutions of Amino Acids and Proteins. The mean refractive indices of the amino acids and proteins were calculated by means of the following expanded Lorenz-Lorentz equation as given by Doty and Geiduschek (11) ... 

Amino Acids. The values for the refractive indices and molar refractions of the amino acids calculated from the refractive indices by Lorenz-Lorentz Equations 1 and 2 are recorded in Table I. Values for molar refractions of the aliphatic amino acids are in good agreement with values calculated from atomic refraction factors. However, the molar refractions of tryptophan, tyrosine, phenylalanine, and histidine are larger than those calculated from atomic refraction factors and larger than might be expected from their comparative specific volumes. 

In appraising the average accuracy one must bear in mind that experimentally the mean polarizabilities are usually obtained from the refractive index n (at 5893 A, the sodium D-line) and the Lorenz-Lorentz equation (with M molecular weight, p macroscopic density, Vav Avogadro s number) ... 

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