Cholesteric dislocations in mica wedges
Résumé
A large part of the scientific legacy of Maurice Kleman concerns topological defects in liquid crystals. Here, we focus on the very first article of Kleman on liquid crystals coauthored with Jacques Friedel and devoted to linear defects in cholesterics discovered in 1921 by François Grandjean who observed them in wedges made from partially cleaved mica sheets. Kleman and Friedel interpreted the thin (single) and thick (double) Grandjean lines as dislocations with Burgers vectors equal respectively to p/2 (half pitch) or p (whole pitch) and have shown that they are composed of pairs of disclinations that they called τ and λ. We report on a recent work accomplished specifically in memoriam of Maurice Kleman, with the aim to show the beauty of nets of Grandjean lines in wedges made of mica sheets. We stress that such nets carry also information on the crystal structure and cleavage properties of the muscovite mica. Beside classical wedges made with partially cleaved mica sheets, we used also wedges made with crossed cylindrical mica sheets. This alternative setup allowed us to nucleate in a controlled manner dislocation loops of the two kinds. We show that due their metastability both types of dislocation loops can persist indefinitely independently of the local thickness and angle of the wedge. We show also that in thin wedges, surprisingly, the double dislocation loops are not smooth but contain one or two cusps corresponding to kinks predicted by Kleman and Friedel. Their presence is a fingerprint of the helicoidal symmetry of cholesterics.
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