Formation and ordering of topological defect arrays produced by dilatational strain and shear flow in smectic-A liquid crystals

A microscale shear cell is used to study the formation of parabolic focal conic defects in the thermotropic smectic-A liquid crystal 8CB (4-octyl-4'-cyanobiphenyl). Defects are produced by four distinct methods: by the application of dilatational strain alone, by shear flow alone, by dilatational strain and subsequent shear flow, and by the simultaneous application of dilatational strain and shear flow. We confirm that defects originate within the bulk, consistent with the previously suggested undulation instability mechanism. In the presence of a shear flow, we observe that defect formation requires micrometer-level dilatations, whose magnitude depends on the sample thickness. The size and ordering of both disordered and ordered defect arrays is quantified using a pair distribution function. Deviations from the predictions of linear stability theory are observed that have not been reported previously. For example, defects form a square array with greater ordering in the principal flow direction. Ordering due to shear flow does not change the average defect size. It has been shown previously that the principal defect sizes of ordered defects scale differently with sample thickness than the wavelength of the small amplitude undulations. We find that disordered defects show a similar deviation from this predicted wavelength.