This chapter will analyse the molecular organisation of liquid crystalline polymers (LCPs) on a scale much larger than the molecular level, and in particular examine the director field and the nature of defects within it. In fact, many of the spatial variations in the director field which are considered here have been observed by optical microscopy and treated using continuum theories. However, the availability of other techniques, some of them, such as fractography of quenched samples, being unique to the polymeric state of liquid crystals, has provided additional valuable experimental data. Advances in the computational simulation of director fields have contributed further to the understanding of disclination structures and their interactions, especially in three dimensions.
The treatment of distortions and defects is largely in terms of the director field. The impact of different types of liquid crystalline phase, whether small molecule or polymeric, nematic or smectic, is largely accounted for in terms of the relative resistance of the material type to the different types of orientational distortion, that is in terms of the elastic constants. In general, continuum models form the basis for understanding distortions and defects, and they will provide the essential thread for this chapter.
Distortions and the order parameter
The order parameter, S, as defined in Chapter 2, describes the quality of alignment of the molecular reference axes with the director. For a small molecule liquid crystal in which the molecules have been aligned parallel to some external field, the order parameter will remain constant irrespective of the particular volume of material sampled, at least right down to molecular dimensions.