Figure 2. Nematic topological states stabilized by fractal Koch-star colloidal particles.

(a, I–f, I) Koch-star particles in the isotropic phase of the CCN mixture at 70 °C in unpolarized light. (a, II–f, II) The same particles as in panels I, now observed between crossed polarizers and at room temperature. The rubbing direction, indicating the far-field planar orientation of the nematic is shown by double-headed arrows in (a, II–IV). Defects are recognized as point regions in the optical image, surrounded by rapidly varying colour and intensity of the transmitted light, indicating strong director distortion. (a, III–f, III) The same particles as in a, II–f, II, now viewed between crossed polarizers and red plate added at 45°. Different colours are due to different in-plane orientations of the nematic molecules. (a, IV–f, IV) Landau-de Gennes (LdG) numerical modelling illustrating contour plots of the scalar order parameter in the mid-plane of the particles with l_b/ξ=100 where ξ is the correlation length of the liquid crystal molecules in the x–y coordinate plane containing the coordinate center. The calculated director field in the x–y plane of the contour plots is also superposed.