2007-05-02
10:15 at HCI J 574

Rigid-rod macromolecular dispersions: 30 years after the Hess 1976 classic

Greg Forest

Department of Mathematics, Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina at Chapel Hill, USA

In 1976, Professor Siegfried Hess derived the Smoluchowski equation governing orientational distributions of a dispersion of rigid-rod macromolecules in a prescribed flow field. The Hess kinetic equation generalizes several classical works: of Jeffery on a single rod in Stokes flow; of Onsager on the isotropic-nematic phase transition of hard-rod ensembles; and, of Leslie & Ericksen on the director theory of small-molecule liquid crystals. This is not your garden variety kinetic equation; it is an infinite-dimensional nonlinear diffusion equation on the sphere in which a Brownian rod senses its local environment of rods while accepting a deterministic flow torque. The second-moment of the distribution function can be modeled by a finite-mode spherical harmonic projection of the Hess model with an ad hoc closure, which recovers the Landau-deGennes class of models. Around 1981, Doi rederived the Hess equation. Since 1976, a remarkable history has unfolded, punctuated by several major physical predictions, rigorous and formal mathematical analyses, and computational phenomena. This lecture will reflect one person’s historical view of the past 30 years downstream of this landmark paper, ending with remaining open questions and challenges regarding nano-rod and nano-clay composites, for which the Hess-Doi model remains the foundation!