Nano-composite material properties: homogenization over flow-induced
orientational distributions (Xiaoyu Zheng, UNC-CH)
Abstract:
The purpose of this talk is to connect two critical aspects of
nano-composite materials engineering: the orientational distribution
of quiescent or flowing macromolecules, and homogenization theory of
composites with spheroidal inclusions at low volume fractions. The
nano-elements considered here derive from the class of high aspect
ratio, nematic polymers, either rod-like or platelet spheroids.
Putting the two features together, we derive the effective electrical
conductivity tensor in closed form. Scaling properties
of enhanced conductivity versus volume fraction and weak shear rate
become explicit. The most dramatic effect is that the effective
conductivity tensor inherits hysteresis, bi-stability and
discontinuous jumps from the isotropic-nematic first order phase
transition. These formulas reveal finer estimates depending on a
competition between two inherently extreme parameters in nematic
polymer nano-composites: the molecular aspect ratio and the
conductivity ratio of the inclusions and matrix.
This is an abstract of a talk to be presented at the
2004 SEAMS Workshop in Charleston, SC. For more information, visit
the workshop's homepage at math.cofc.edu/SEAMS.