Date of Award

Fall 2017

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Linda Jane Cummings

Second Advisor

Lou Kondic

Third Advisor

Michael R. Booty

Fourth Advisor

Ian Griffiths

Fifth Advisor

Richard O. Moore


This dissertation considers a mathematical model that consists of a nematic liquid crystal layer sandwiched between two parallel bounding plates, across which an external field may be applied. Particular attention is paid to the effect of an applied field on the layer as well as the interaction between the liquid crystal molecules and the molecules of the substrate. The system studied may be considered as a simple model of a Liquid Crystal Display (LCD) device, and the results obtained are discussed and interpreted within this context.

The first part of this dissertation considers a study that investigates how the number and type of solutions for the director orientation within the layer change as the field strength, anchoring conditions and material properties of the nematic liquid crystal layer vary. During this investigation, particular attention is paid to how the inclusion of flexoelectric effects alters the Freedericksz and saturation thresholds.

In the second part of the dissertation, the interaction between nematic liquid crystal (NLC) and polymer coated substrates with and without an external applied field is considered. Under certain conditions, such polymeric substrates can interact with the NLC molecules, exhibiting a phenomenon known as director gliding or easy axis gliding. Mathematical models for gliding, inspired by the physics and chemistry of the interaction between the NLC and polymer substrate are presented. These models, though simple, lead to non-trivial results, including loss of bistability under gliding. Perhaps surprisingly, it is observed that externally imposed switching between the steady states of a bistable system may reverse the effect of gliding, preventing loss of bistability if switching is sufficiently frequent. These findings may be of relevance to a variety of technological applications involving liquid crystal devices, and particularly to a new generation of flexible Liquid Crystal Displays (LCDs) that implement polymeric substrates.

Finally, this dissertation considers how well the proposed models fit published experimental data. The results of two experimental papers are discussed, and a quantitative fit of the mathematical model to the data is made.

Included in

Mathematics Commons