The effects of topology have been investigated in systems as diverse as molecules and the cosmos, but rarely at the micrometre scale. In this issue, Senyuk et al. explore how topology affects the alignment of micro-scale particles suspended in a 'nematic' host matrix — a liquid crystal in which the molecules are aligned but do not form well-defined planes (B. Senyuk et al. Nature 493, 200–205; 2013).
The particles in naturally occurring colloids — systems of tiny particles of one material suspended in a different material — are often spheres or faceted crystals. Such particles are said to have a topology of genus (g) zero. To explore the effects of different topologies on colloid particles, Senyuk et al. synthesized particles constructed from rings 5–10 μm in diameter. These ranged from simple hoops (g = 1) to 'Olympic rings' (g = 5; pictured).
The authors found that when the particles were dispersed in a nematic liquid crystal, they typically aligned with their ring planes perpendicular to the direction of alignment of the liquid crystal (the 'director'). Each particle of genus g generated at least g – 1 defects in the liquid-crystal matrix, in agreement with topological theorems. These were either point defects in the rings' holes, or loop defects that could run around the inside or outside of the rings. What's more, the orientation of the liquid-crystal molecules around each particle was dictated by the particle's topology.
Senyuk and co-workers went on to show that the particles could be aligned parallel to the director by melting and rapidly cooling the surrounding liquid crystals. In this case, defects appeared in the liquid crystal both within and next to the particles. And by applying an electric field at different rates, the authors could switch either the orientation of the colloidal particles or the configuration of the liquid-crystal molecules around the particles; the resulting states were stable when the electric field was removed.
Finally, the researchers found that the particles diffused more easily along the nematic director than in other directions, and that the rate of diffusion decreased with increasing genus number. Taken together, these findings open up fresh opportunities for colloidal organization and self-assembly, as well as potential applications — in electro-optic or photonic devices, for example.
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Physical Review E (2019)