Recovery and analysis of director profiles in liquid crystal cells
Cornford, Stephen Leslie
Date: 1 October 2008
Thesis or dissertation
Publisher
University of Exeter
Degree Title
PhD in Physics
Abstract
This thesis is concerned with the determination of the director profile within a nematic
liquid crystal cell from optical experiments. The larger part of the work details the de-
velopment of computational methods which can be used to find the director profile, and
the application of these tools to the fully leaky guided mode experiment. ...
This thesis is concerned with the determination of the director profile within a nematic
liquid crystal cell from optical experiments. The larger part of the work details the de-
velopment of computational methods which can be used to find the director profile, and
the application of these tools to the fully leaky guided mode experiment. In a second
part, a simple conoscopic device is built, and then used to undertake a novel viscodynamic
experiment.
In essence, the fully leaky guided mode experiments and its relatives measure the de-
pendence of the transmission and reflection coefficients of a liquid crystal cell upon incident
angle. It is simple enough to calculate these coefficients if the director profile is known,
but experimentalists actually need to achieve the opposite. That is, having measured the
transmission and reflection coefficients, they must determine the director profile. However,
this turns out to be an ill-posed problem, and so some additional information about the
director profile is required.
There is indeed an appropriate source of additional information - the continuum theory
of nematic liquid crystals - and it is exploited here to develop two computational tools.
In the first, it is used to adapt a mathematical technique, Tikhonov regularization, to
both steady-state and time-dependent situations, so that director profiles can be recov-
ered having made only weak assumptions about their behaviour. A second tool makes
stronger assumptions and can be deployed after the first to estimate some of the unknown
parameters which appear in the continuum theory.
These tools are use in the first instance to analyze data drawn from two fully leaky
guided mode experiments. In the first experiment, a hybrid aligned cell was measured
during AC switching, and from its data director profiles and several phenomenological
parameters including four viscosities are determined. Following that, the DC switching of
the same cell is studied, which turns out to be critically affected by the motion of tiny
concentrations of charged impurities. Then, having noted that only limited information
about the director profile can be recovered from even the most elaborate optical experi-
ment, a conoscopy experiment is designed to recover it quickly. Following this approach,
a previously unknown flow-induced transition between topologically distinct states in a
homoetropically aligned cell is observed.
Doctoral Theses
Doctoral College
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