A practical method for estimating specific refractive index increments for flexible non-electrolyte polymers and copolymers in pure and mixed solvents using the Gladstone-Dale and Lorentz-Lorenz equations in conjunction with molar refraction structural constants, and solvent physical property databases

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Abstract

Equations for calculating the specific refractive index increment, ∂n/∂c, for polymer/solvent systems have been developed starting with either the Gladstone-Dale equation or the Lorentz-Lorenz equation for the refractive index of a dielectric medium. The resulting equations can be used to estimate ∂n/∂c as a function of polymer concentration, temperature, solvent composition, and, for copolymers, monomer composition. Simplifying assumptions have been made to generalize these equations and make them more usable: 1) molar refractions are treated as constants, 2) the density of the polymer solution, in the limit of low polymer concentration, can be approximated via the additivity of volumes approach; the densities of polymer-free solvents and solvent mixtures are not necessarily subject to this approximation, 3) the mass density of solvents and solvent mixtures can be estimated by any one of several models developed specifically for this purpose; we will consider the Rackett equation, the COSTALD equation, and the standard assumption of mass and volume additivity, and 4) the mass density of a copolymer can be obtained from a weight fraction average of the mass densities of the homopolymers from which it is comprised. Comparisons to experimental data show that (∂n/∂c)GD and (∂n/∂c)LL both yield average absolute deviations of approximately 0.009 ml/gm.

Keywords

Refractive index increment
Molar refraction
Lorentz-Lorenz equation
Gladstone-Dale equation

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