Alignment and rheo-oscillator criteria for sheared nematic polymer
films in the monolayer limit (Joohee Lee, UNC)
Abstract:
Monolayer films of liquid crystalline polymers (LCPs) are modelled
with a mesoscopic two-dimensional(2D)
analogue of the Doi-Hess (1981, 1976) rigid rod model. One aim is to
estabilish a more complete solution to the classical problem of
how orientational degeneracy of quiescent nematic equilibria breaks in
weak shear. We exploit the simplicity of 2D liquids to
extend results of Kuzuu and Doi (1983,1984), Marrucci and Maffetone
(1989-1991), See, Doi and Larson (1990), Forest et
al. (2003-2004). We recall the distinction between two versus three
dimensional quiescent phase diagrams and the
isotropic-nematic phase transition, where the transition is
2nd-order in 2D and 1st-order with hysteresis and
bistability in 3D. We then analyze the deformation of these respective
bifurcation diagrams in shear flow. We give a simple
proof that limit cycles, known as tumbling orbits, must arise beyond
the parameter boundary for the steady-unsteady transition.
Finally, we show the shear-perturbed 2D phase diagram is robust to
closure approximations, in spark contrast to 3D.
This is an abstract of a poster to be presented at the
2004 SEAMS Workshop in Charleston, SC. For more information, visit
the workshop's homepage at math.cofc.edu/SEAMS.