Professor Iain Stewart

Reference No.: IWS1

Supervisor: Professor Iain Stewart

Date Advertised: 10th February 2010

Please contact Professor Iain Stewart for further information.

Liquid crystals are all around us. As well as being of importance in flat panel display technologies, such as those used for computer and television monitors, mobile telephones, cameras, etc…, they are also being developed for use in non-display technologies such as biosensors (for detecting disease and/or pollutants) because of their sensitivity to small disturbances. This research will involve aspects related to displays and sensors.

In their simplest description, liquid crystals can be thought of as consisting of elongated rod-like molecules which have a preferred local average direction denoted by a unit vector n which depends upon its location in space and time. Smectic liquid crystals form particular phases that have layers of molecules stacked upon each other. Smectic A can be modelled mathematically upon the links between the orientation of n and the orientation of the smectic layers. A general introduction to the mathematics of liquid crystals has been written by the proposed supervisor [1] where more details can be found.

The aim of this research project is to apply the nonlinear smectic A liquid crystal dynamic theory recently proposed by Stewart [2,3] to some unexpected and novel effects which have been observed by various researchers (eg, [4,5], who have reported the occurrence of transverse flow and transient two-dimensional instability patterns). It is known that smectic A liquid crystals behave in unusual ways in simple shear experiments and that these effects are highly nonlinear.

The mathematical model equations for shear problems can be derived from the aforementioned nonlinear theory. The solutions to these equations will provide qualitative results which will be central to the understanding of these phenomena and will form the first major part of the research. The results will have direct relevance to liquid crystal displays and sensors.

Other effects will then be investigated, especially those relating to defects and disclinations in smectic liquid crystals. Many of these effects have been examined experimentally and theoretically for nematic liquid crystals where it is known that pattern formation states can be induced.

Developments in the analogous theory of grid-like 2-dimensional instability patterns in smectics have been reported by the proposed supervisor [6], and others, and the research work will consider the influence of different boundary conditions and anchoring energies [1] upon the nature of the patterns and defects. Such patterns are precursors to "membrane rupture" [7] and are crucial to the understanding of smectic medical detection devices/sensors and drug delivery systems at an extremely small scale.

The proposed research will involve analysing and finding solutions to nonlinear model equations for smectic liquid crystals. These equations are coupled partial differential equations which are often reduced to systems of ordinary differential equations.

Some knowledge of continuum theory and/or fluid mechanics would be useful but is not absolutely necessary. Please feel free to contact Professor Stewart for further information.

• [1] Stewart IW 2004 The Static and Dynamic Continuum Theory of Liquid Crystals (London and New York: Taylor and Francis)
• [2] Stewart IW 2007 Continuum Mech. Thermodyn., 18, p343-360
• [3] Stewart IW 2007 J. Phys. A: Math. Theor., 40, p5297-5318
• [4] Auernhammer GK, Brand HR and Pleiner H 2002 Phys. Rev. E, 66, art.061707
• [5] Stewart IW and Stewart F 2009 J. Phys.: Condens. Matter, 21, art. 465101
• [6] Walker AJ and Stewart IW 2007 J. Phys. A: Math. Theor., 40, pp. 11849-11861
• [7] Gallez D,  Pinto NM, Bisch PM 1993 J. Colloid. Interface Sci., 160, 141-148