Instabilities in liquid crystals

This thesis contains theoretical work dealing with the effects of magnetic and electric fields on samples of nematic, smectic A and smectic C liquid crystals. Some background material along with the continuum theory is introduced in Chapter 2. In Chapter 3 we consider the effect on the director within an infinite sample of nematic liquid crystal which is subjected to crossed electric and magnetic fields. In particular we examine the stability of the travelling waves which describe the director motion by considering the behaviour of the stable perturbations as time increases. The work of Chapter 4 examines a bounded sample of smectic A liquid crystal in two dimensions which is subjected to a magnetic field. It can be shown that layer undulations may occur after a critical threshold is reached. The effects of various forms of pressure are also studied and in the case when pressure is included it is shown that layer undulations will always occur regardless of the field strength. Chapter 5 extends the work of Chapter 4 to three dimensions. We consider the effect of adding a dynamical term and study the stability of these solutions. Also we examine how the layers undulate when the sample of smectic A liquid crystal is confined to various cylindrical geometries and subjected to a magnetic field and a uniform pressure. In Chapter 6 we consider a sample of smectic C liquid crystal which is subjected to an oscillatory electric field. The motion of the c-director is complicated and we examine the differences which occur for differing dielectric anisotropies. Finally, in Chapter 7 we study how a sample of smectic C liquid crystal behaves when it is subjected to a uniform shear flow within the smectic plane. We find travelling wave solutions for the behaviour of the c-director and adapt these solutions to incorporate the effects of an applied field. (author)