Theoretical studies of smectic liquid crystals in the presence of flow, oscillatory perturbations, and edge dislocations

• Main Author: Snow, Ben C
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-2016

A range of theoretical studies regarding the static and dynamic behaviour of smectic liquid crystals will be presented. The thesis is mainly concerned with the smectic A phase as modelled by the continuum theory of Stewart, though a working knowledge of the smectic C phase, modelled using the Leslie-Stewart-Nakagawa continuum theory, proves necessary. In Chapter 3, reductions of Stewart's theory by appeal to certain physically motivated assumptions upon the smectic and the flow pattern to which it is subjected are outlined. The linear stability of each of the resultant systems is then analysed. Chapter 4 presents the derivation of a "lubrication-type" theory based on one of these resultant systems of equations, which is then analysed in general terms before being applied to the problem of flow past a finite obstacle. Chapter 5 presents an investigation of a shear wave incident at a planar boundary between an isotropic elastic solid and a smectic A liquid crystal. The behaviour of the wave upon reflection and refraction at the interface is established, as is the response of the smectic; a comparison with the smectic C case as considered by Gill and Leslie concludes the chapter. Finally, Chapter 6 discusses the static configuration of a smectic A liquid crystalin the presence of an isolated edge dislocation. After constructing the energy density to fourth order, we first recover the results of previous investigations by assuming the director and layer normal always coincide, in addition to examining a perturbation to a known solution. We then relax the constraint director-layer normal equivalence, obtaining exact solutions for the smectic's configuration for a quadratic energy density and deriving equilibrium equations for special cases for the fourth order formulation.