Molecular expression for birefringence

Intrinsic birefringence. The intrinsic birefringence of polymeric materials was first calculated by Kuhn. He considered a polymer segment whose end-to-end vector is fixed at r, and calculated its average polarizability assuming that 

so that the underlined terms can be neglected. Thus the anisotropic part of the polarizability tensor 

An important result of this model is diat in the Gaussian region A is independent of r and proportional to 1/n,. Actually this conclusion holds for more general models. In Appendix 4.IV, it is shown that the polarizability tensor is written in the form of eqn (4.212) with a constant A (proportional to nj ) provided the following conditions are satisfied. 

eqn (4.212) can be used for each Rouse segment boimded by two beads, say n and n - 1, then r and (r )eq can be replaced by R - l i = dRJdn and b, respectively. The polarizability of this Rouse segment is then written as 

To relate the polarizability of individual segments to macroscopic birefringence, Kuhn used the Qausius—Mossotti equation, according to which the (isotropic) refractive index n is related to the (isotropic) polarizabihty of individual molecules as  

---