The effect of shear flow on the Isotropic-Nematic transition in liquid crystals
Olmsted, Peter David
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https://hdl.handle.net/2142/18892
Description
Title
The effect of shear flow on the Isotropic-Nematic transition in liquid crystals
Author(s)
Olmsted, Peter David
Issue Date
1991
Doctoral Committee Chair(s)
Goldbart, Paul M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
shear flow
isotropic-nematic transition
liquid crytals
Language
en
Abstract
In this thesis I will discuss the effects of shear flow on the Isotropic-Nematic phase
transition in liquid crystals. Shear flow has dramatic orienting effects on the rod-like
constituents of nematic liquid crystals, with the general effects of (1) inducing order
in the high-temperature isotropic phase, and (2) dictating a direction of alignment
for the low-temperature nematic phase. Shear flow also imposes a biaxial symmetry
on both the high and low temperature phases, thereby changing the nature of the
symmetry-breaking at the transition.
We develop coupled deterministic dynamical equations for the 5-component nematic
order parameter and the fluid velocity, which may be considered generalizations
of the Leslie-Ericksen and Navier-Stokes equations, respectively. We examine
the stable stationary solutions to these equations to determine the nature of the nonequilibrium
phases, and discuss the analogies and differences between this system
and equilibrium systems. From homogeneous solutions we obtain a state diagram
analogous to that of a Van der Waals fluid, including a two-state region and a discontinuous
transition which terminates at a critical point. To resolve the question
of the analog of the Maxwell construction to distinguish locally stable states, we
construct stable inhomogeneous interfacial states. From an analysis of these states
we determine a coexistence line and find exponents characterizing the shape of the
coexistence curve and the interface thickness as the critical point is approached. We
find mean-field critical behavior, and comment on the possibility of the analogs of
spinodal decomposition and nucleation.
Finally, we develop a formalism for describing light scattering from biaxial steady
state, and investigate the Gaussian level fluctuations about these states. In the
vicinity of the critical point we find singular behavior analogous to critical opalescence
of a simple fluid at its critical point. We also find anisotropic correlations at the
critical point which reflect the manner in which shear flow suppresses fluctuations, as
was found by Onuki and Kawasaki in their studies of a binary fluid under shear flow.
We finish by commenting on the application of these ideas to lyotropic systems, and
combining flow and magnetic field effects in the same system.
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