Investigation of molecular orientation distributions by polarized raman scattering and polarized fluorescence

It is assumed that the intensity of the vibrational Raman scattering from each of the structural units (molecular segments or crystallites) in an oriented polymer solid is determined by a symmetric second-rank tensor. The distribution of orientations of the principle axes of the tensors is expanded in a series of generalized spherical harmonics, Z_lmn(θ)e^?imψe^?in?, and it is shown that relations among the coefficients in this expansion can be obtained from suitable intensity measurements using polarized radiation. If the orientation of the tensor axes within the structural unit is known (in the general case, for several Raman lines), then the coefficients M_lmn of a similar expansion for axes fixed in the units can be obtained for l, m, and n even and l ≤ 4. The limitation to even m follows from the assumption that the solid has at least orthotropic statistical symmetry but the limitations on n and l arise from the nature of the Raman effect. Some simple special cases are considered and some orientation-independent intensity sums are derived. It is shown that, with the simplifying assumption usually made, the theory of the polarized fluorescence method for determining molecular orientations is a special case of the theory for the Raman method.