Lorentz—Lorenz 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... 

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). 

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 ... 

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. 

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) ... 

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. 

Polarizabilities measure the response of ions or atoms to an electric field. Electronic polarizabilities, a, arise from deformation of the electron cloud relative to the nucleus and are given by the Lorenz-Lorentz equation ... 

By combining the rheochor formula with the Lorenz-Lorentz equation for the molar refraction, where =refractive index,... 

Molecular descriptor of a liquid which contains both information about molecular volume and polarizability, usually defined by the Lorenz-Lorentz equation [Lorentz, 1880 Lorentz, 1880] ... 

The molar refractivity is the volume of the substance taken up by each mole of that substance. In SI units, MR is expressed as m /mol. MR is a molecular descriptor of a liquid, which contains both information about molecular volume and polarizability, usually defined by the Lorenz-Lorentz equation [Lorentz, 1880a, 1880b] (also known as the Clausius-Mosotti equation) ... 

By combining the rheochor formula with the Lorenz-Lorentz equation for the molar refraction, i L=[( 2— 1) /( 2+2)](M/o), where =refractive index, Chacravarti7 found ... 

Index of Refraction. The refraction of index of a fluid is usually a function of the thermodynamic state, often only the density. According to the Lorenz-Lorentz equation, the relation between the index of refraction and temperature is given by... 

Molar refraction (R) - A property of a dielectric defined by the equation f = V [(m -1)/(m +2)], where n is the index of refraction of the medium (at optical wavelengths) and the molar volume. It is related to the polarizability a of the molecules that make up the medium by the Lorenz-Lorentz equation, R =, where is Avogadro s constant and is the... 

In 1983 we were able to validate two exact formulae, based on the Lorenz-Lorentz equations, allowing the calculation of the mass of the adsorbed layer from the refractive index and thickness. This experimental validation was performed by measuring stacked multilayers of known mass of phosphatidylserine and by the adsorption of radiolabeled albumin and prothrombin on these multilayers (9 ). 

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