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Seminar Abstracts

## Gregory Forest, Applied Mathematics, UNC-Chapel Hill

"Laminar Flows of Nematic Polymers: High-Performance Materials in the Making"

#### Abstract

Nematic polymers (NPs) are pervasive in biological as well as synthetic soft matter" materials, and contribute to remarkable material property enhancements ranging from strength, electrical and thermal conductivity, and barrier properties. These macromolecules are distinguished by highly anisotropic shapes, so that collectively, above a critical concentration, a spontaneous ordering transition occurs (the isotropic-nematic phase transition). The Tobacco Mosaic Virus and spider silk are rod-like NPs, whereas nano-clays and carbon pitch are platelets (discotic NPs). Bulk properties of NPs, and many nano-composite materials, are the result of features, dynamical and morphological, created during flow processing. These nonlinear phenomena are very poorly understood and far from controlled or optimized. The lecture aims to motivate a class of dynamics and structure problems, which by nature result from microscopic-macroscopic coupling. I will explain different pieces of this program that our research group is tackling. We combine theory, modeling, and simulation of nematic polymers in laminar flows. These projects target experimental and technological behavior, so that one must always know how to upscale or downscale to benchmark and predict.

I hope to convey why much of the mystery and subtlety in NP and nano-composite materials commands mathematical guidance to have any hope of controlling and optimizing the huge parameter space. Nature's conspiracy is this: concentrations of NPs sufficient to achieve remarkable property enhancements turn out to be close to the natural order-disorder bulk phase transition. To add extra intrigue, this phase transition is highly degenerate, already understood by Onsager in the 1940's. So laminar flow processing drives a degenerate phase transition, with truly remarkable and diverse consequences thta ultimately determine material properties!

Our group has focused on model NP systems and phenomena associated with molecule architecture, flow type and strength, confinement scales and anchoring conditions. The Doi kinetic theory for flowing, anisotropic macromolecules is the starting scale of description, yet one is compelled to upscale" to mesoscopic moment averages of the molecular distribution function to match experimental data, and ton continuum Leslie-Ericksen approximations to make contact with a generation of intuition and experimental benchmarks. Regarding behavior, we focus first on monodomain bulk attractors in linear flows, which are the precursors to structure formation. This is already a challenging problem to resolve which stationary orientational distributions are selected at the onset of flow from the degenerate phase diagram of Onsager. We then model onset and evolution of spatial morphology in the flow between shear plates.

Our research group includes Qi Wang, Florida State University, Ruhai Zhou, UNC-CH, and Hong Zhou, UC-Santa Cruz, together with graduate students Eric Choate, Joohee Lee, Lingxing Yao, and Xiaoyu Zheng at UNC-CH. Our group is supported by the AFOSR Physical Applied Mathematics Program a NASA-URETI on bio-inspired materials, and NSF DMS and Engineering Directorates.

THURSDAY, May 1, 2003
Time: 1:30 P.M.
Location: PPB 300