NEW APPROACH TO THE CONTINUUM THEORY OF BIREFRINGENCE OF ORIENTED POLYMERS

The internal field in a transparent anisotropic dielectric is described with the aid of the classical electromagnetic theory by the introduction of the internal field or Lorentz-factor tensor. On the basis of the internal field equation generalized Lorentz-Lorenz relations are derived. A virtual refractive index in lieu of the mean refractive index is defined by the trace of the inverse susceptibility tensor. By the same token the harmonic mean replaces the arithmetic mean specific refractivity. The relation between birefringence, polarizability and structural anisotropy of the medium is formulated. In order to account for the influence of molecular orientation on the birefringence of polymers, at least quasi-crystalline order is assumed to exist in spherical microregions surrounding each monomeric unit. The dependence of uniaxial birefringence on the average molecular orientation is expressed by a function of the harmonic mean values of the dielectric constants of the microregions. It is shown that the point-dipole lattice theory cannot be applied to arrays of molecules which depart considerably from cubical symmetry as in polymer crystals. Since a general theory is not available for such cases it is assumed that the Lorentz factors can be approximated by using, instead of these, the values of the depolarization factors agreeing with the dimensions of the optical chain segment. In this way, for given values of the specific refractivity, birefringence, density, and the segment dimensions of a uniaxial, perfectly oriented polymer, the polarizability of the optical chain segment may be calculated. Assuming cylinder symmetry of the chain segments, the author gives numerical examples of six man-made polymer fibres, viz. polypropylene, polyethylene, regenerated cellulose, nylon 6, polyethylene terephthalate, and polyparaphenylene terephthalamide. The results are compared with those obtained by the application of the principle of additivity of bond polarizabilities. © 1979 Dr. Dietrich Steinkopff Verlag.