A Method for Calculating Orientational Distribution Functions in Flows of Nematic Polymers.

A numerical solution technique is presented for solving Doi's equation for the evolution of the orientation distribution of rod-like polymers in the isotropic and liquid crystalline states. The technique involves expansions in terms of spherical harmonic functions of the terms describing rotary diffusivity, flow, and excluded-volume interactions. Although Doi and Edwards used this approach earlier to describe systems without excluded volume interactions, we extend the approach by developing an expansion of the Onsager excluded volume potential, and of the contribution of that potential to the stress tensor. The resulting algorithm allows computation of the time evolution of the three-dimensional orientation distribution and of the stress and birefringence tensors during flows of isotropic and liquid crystalline solutions of rigid-rod polymers.