Generalized Susceptibility Theory. III. Spectral Properties of Extended Molecular Systems: Optical Rotation of Helical Polymers

Abstract

The spectral properties of an extended molecular system, such as a linear polymer, are considered in terms of the linear response tensor (LRT) which determines the part of the average current density that is proportional to the transverse electric field. In order to formulate such phenomena as optical rotatory dispersion (ORD) and circular dichroism (CD) use is made of Maxwell's equation for the transverse field components. Periodic boundary conditions are used for both the molecular system and the radiation field. The symmetry properties of the LRT with respect to time translation, time reversal, and reversal of propagation direction of the photon are given. Discussion is given of the relation between the components of the LRT and various optical properties such as ORD, CD, and linear birefringence. For an extended molecular system, having discrete symmetry operations (e.g., translations or screw axis), it is shown that a multicenter expansion is useful for formulating the LRT in terms of unit-cell spaces. This approach is applied to a helical polymer, and it is found that (in addition to Umklapp processes) components of the field having wave vector q are coupled to those having wave vector q ± 2s, where s corresponds to a wavelength equal to the pitch of the helix. These interactions produce second-order corrections to the refractive indices of right and left circularly polarized light. For the purpose of clarifying recent theoretical work by several groups and in order to present a unified development of the theory, a precise formulation is made of all terms (to first order in q) contributing to the ORD–CD of a helical polymer. It is found, in agreement with the work of others, that the leading term is an electric dipole strength term which is not included in the conventional Rosenfeld formula whenever periodic boundary conditions are used. The physical nature of the various terms are considered in detail and approximation methods for evaluating polymer properties in terms of a monomer basis are briefly reviewed.