Under a polarising microscope, liquid crystals exhibit beautiful optical patterns such as the Schlieren texture of a nematic, the fingerprint texture of a cholesteric and the focal conic structure of smectics. These textures are due to an assembly of topological defects and are determined by the molecular ordering of the particular mesophase. Such defect textures are useful in identifying liquid crystal phases but are generally an unwanted effect causing a reduction in contrast of a liquid crystal display. Whether needed for identification or unwanted in displays, a clear understanding of defects will be extremely useful.
The above picture shows a typical Schlieren texture of a nematic sample when it is placed between crossed polarisers (two polarisers with polarising directions perpendicular to each other) and light is shone through the cell. The presence of crossed polarisers means that, at any point in the sample where the average molecular direction (the director) is aligned with either one of the polarisers, the transmission of light through the cell is blocked resulting in a dark area. When the director is not aligned with a polariser a lighter region is visible. The lightest regions occur when the director is at 45 degrees to both polarisers. We can see that there are points in the cell where the director orientation changes as we trace a path around that point. In fact each such point is a line perpendicular to the plane called a disclination or defect line. For example, if we pick any point in the above picture where four dark regions merge then trace a path around that point, in going from one dark region to another the director has changed alignment from one polariser direction to the other polariser direction, in other words by 90 degrees. In a full circuit the director must have rotated by 360 degrees. A full rotation by 360 degrees indicates a disclination line of strength S=+1 or S=-1 (depending on whether the director rotated clockwise or anti-clockwise as we went round the disclination). When two dark regions merge at a point a defect of strength S=+1/2 or S=-1/2 occurs.
This project considers the director structure around disclination lines of strength S=+1/2 and S=-1/2. Analysis has shown that only defects of half-integral strength are singular because defects with integral strength can escape into the third dimension. The director distortion that occurs around 1/2 defects can be characterised by bend and splay distortion. Each type of distortion is dominant in different regions around the defect.
References:
G. Kelly, N. J. Mottram, A. Ramage, The effect of elastic anisotropy on nematic disclination lines, BLCS Newsletter (2003). [pdf]