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Decay of skeins of dislocations in cholesterics
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Resumo(s)
Knotted and linked skeins of vortices and disclinations generated, respectively, by symmetry-breaking normal → superfluid and isotropic → nematic phase transitions are known to untie, by rewiring of their crossings, into independent unknots that finally shrink and collapse until the defect-free ground state is reached. We demonstrate that the decay of skeins of dislocations, generated by the isotropic → cholesteric phase transition within a cylinder/cylinder gap, leads to stable necklace-like states made of numerous minimal loops, called bangles, tethered to kinks of much larger loops called cargo. We analyze the topological decay of skeins of dislocations in terms of the Conway-Kauffman theory of knots, showing that the necklace state results from rewiring of crossings triggered by collisions of tangles with their numerator closure. We point out that, in general, for symmetry reasons, kinks on edge dislocations are chiral. Their handedness, right or left, directly depends on the sign of kinks on which they are localized. In cholesterics with intrinsic chirality, the energy of kinks bearing bangles depends on their handedness. For this reason, within necklaces, all bangles are tethered to kinks of the same sign.
Descrição
Funding Information: P. P. thanks Yves Pomeau and Bernard Derrida for the invitation to participate to the memorial issue of Comptes Rendus de l’Académie des Sciences (France) in honor of Gérard Toulouse. The writing of our contribution stimulated greatly the recent experiments on objects with a double topological character, i.e., on the links and necklaces made of dislocation loops in cholesterics. We acknowledge financial support from European Cooperation in Science and Technology (COST) ActionPhoBioS, CA21159. The experimental setup tailored for production of the cholesteric dislocations in the cylinder/cylinder mica wedges was built by V. Klein, J. Sanchez, and S. Saranga. I. I. S. acknowledges the support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-SC0019293 with the University of Colorado at Boulder. J.-Y. L., I. I. S. and P. P. acknowledge the support of the International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), and the international institute of Japan's World Premier Initiative, which facilitated and supported their collaboration. We have greatly benefitted from discussions with Y. Pomeau, P. Ostwald, O. Lavrentovich, A. Leforestier and C. Goldmann, as well as from the help of S. Assimomitis, J. Saen, Y. Simon, M. Bottineau, B. Senyuk, J.-S. Wu and I. Nimaga.
Palavras-chave
General Chemistry Condensed Matter Physics