Order reconstruction and solution landscapes for liquid crystalline systems

Liquid crystals are the surprisingly less well known fourth phase of matter, sitting between the familiar solid and liquid phases. These materials combine fluidity with orientational and/or positional order, yielding surprising and desirable properties relevant for use in tailor-made applications. In this thesis, we place an emphasis on the study of order reconstruction (OR) solutions. These OR solutions describe polydomain structures i.e., multiple sub-domains separated by domain walls. We study OR solutions within the Landau de Gennes continuum theory for liquid crystals in a reduced, one-dimensional setting relevant for microfluidic problems. OR solutions in nematic liquid crystals are well known, but we demonstrate the existence of OR solutions in the physical settings of ferronematics, and both passive and active nematodynamics, demonstrating the universality of such solutions. This work involves studying coupled systems of non-linear ordinary differential equations, and utilising techniques from the calculus of variations, partial differential equation theory, and asymptotic analysis, to gain insight. We also place significant emphasis on studying solution landscapes i.e., how all critical points (stable and unstable) of an energy functional connect to one another, and this is implemented through advanced numerical methods. In our final chapter, this sheds light on a competition between uniaxiality and biaxiality in cholesteric liquid crystals, and a way to potentially observe biaxiality experimentally.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral-pg

Grantor dc:publisher.institution

University of Strathclyde

Year dc:date.issued

2023

Author dc:creator

• Dalby, James

Advisor dc:contributor.advisor

• Majumdar, Apala

DOI

10.48730/w1jx-zz49

Identifier

T16636

Author Identifier

201982189

OAI identifier oai:identifier

oai:strathclyde:n296wz71s