Nematic liquid crystal boojums with handles on colloidal handlebodies

Abstract

Topological defects that form on surfaces of ordered media, dubbed boojums, are ubiquitous in superfluids, liquid crystals (LCs), Langmuir monolayers, and Bose-Einstein condensates. They determine supercurrents in superfluids, impinge on electrooptical switching in polymerdispersed LCs, and mediate chemical response at nematic-isotropic fluid interfaces, but the role of surface topology in the appearance, stability, and core structure of these defects remains poorly understood. Here, we demonstrate robust generation of boojums by controlling surface topology of colloidal particles that impose tangential boundary conditions for the alignment of LC molecules. To do this, we design handlebody-shaped polymer particles with different genus g. When introduced into a nematic LC, these particles distort the nematic molecular alignment field while obeying topological constraints and induce at least 2g − 2 boojums that allow for topological charge conservation. We characterize 3D textures of boojums using polarized nonlinear optical imaging of molecular alignment and explain our findings by invoking symmetry considerations and numerical modeling of experiment-matching director fields, order parameter variations, and nontrivial handle-shaped core structure of defects. Finally, we discuss how this interplay between the topologies of colloidal surfaces and boojums may lead to controlled self-assembly of colloidal particles in nematic and paranematic hosts, which, in turn, may enable reconfigurable topological composites.eing inspired by Lewis Carroll's poem The Hunting of the Snark, Mermin (1, 2) introduced a term "boojum" to name elusive at the time surface defects in superfluids. This term and the concept of boojums quickly penetrated different fields of physics and materials science, ranging from liquid crystals (LCs) to Langmuir monolayers, and to Bose-Einstein condensates (3-6). However, unlike in the case of their bulk topological counterparts (7-10), called "hedgehog" point defects, the appearance of boojums is rarely controlled at will. In LCs, boojums can spontaneously appear at their interfaces with isotropic media, such as water. They are commonly associated with the geometries of thin LC films on surfaces of isotropic fluids (11), LC droplets (3, 4, 12), and colloidal inclusions (13,14). For example, spherical surfaces with tangential boundary conditions for rod-like LC molecules, and director n describing their local average orientation, are known to induce two boojums per LC droplet or per colloidal inclusion in the LC host (3,4,13,14). However, despite the recent progress in generating and controlling bulk LC defects using director realignment with focused laser beams, chirality, and surface topology of colloidal particles with perpendicular surface anchoring introduced into LCs (7-10), similar control of boojums has not been demonstrated.In this work, we fabricate polymer microparticles with the topology of a handlebody of genus g ranging from one to five that are capable of imposing tangentially degenerate s...

Magnetically responsive gourd-shaped colloidal particles in cholesteric liquid crystals

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] Two- [7][8][9][10][11] and three-dimensional 14 crystals were designed in nematics using different elastic dipoles and quadrupoles, and singular defects were tailored using spherical 16 and topologically non-trivial 17 colloidal particles. Recent studies also showed the importance of size [18][19][20][21][22][23][24] and shape [24][25][26][27][28][29][30][31] in elastic interactions and ensuing assemblies of colloidal particles in nematics. On the other hand, colloidal dispersions in twisted nematic and cholesteric LCs (CLCs) have received less attention [32][33][34][35][36][37][38][39][40][41][42][43]<...>…”

Liquid Crystal Colloids

“…The total winding number of boojums in the projection of n(r) to the particle surface, n s (r), is always  i s i =, also satisfying topological theorems (92). These simple relations describe defects induced both by the g=0 spherical surfaces (Figures 1 and 2) and by surfaces like handlebodies and torus knots with g0 (Figure 6), though additional self-compensating defects can appear to reduce the energetic cost of elastic distortions associated with matching BCs on colloidal surfaces to n 0 .…”

“…However, beyond the predictions of topological theorems, it was found that nematic colloids can also have mutually tangled physical knots of particles and line defects in n(r), as illustrated in Figure 6j-l (93). For all nematic colloidal particles, the interplay of topologies of surfaces, fields, and defects guides n(r) to comply with the particle shape, generating knotted, linked, and other 3D configurations (91)(92)(93)(94), providing experimental insights into the aspects of the mathematical knot theory (90,93,94).…”

Optically driven translational and rotational motions of microrod particles in a nematic liquid crystal

“…Among these materials, colloidal dispersions of microparticles and nanoparticles in LCs have been actively studied in research on soft-matter physics (2)(3)(4)(5)(6)(7). Tunable anisotropic interactions between microparticles dispersed in LCs give rise to self-assembled 1D and 2D colloidal structures (6,8,9). Such colloidal dispersions are interesting not only from a fundamental point of view but also from a technological one.…”