Colloidal Surfaces with Boundaries, Apex Boojums, and Nested Elastic Self-Assembly of Nematic Colloids

Abstract

Self-assembly of colloidal particles is poised to become a powerful composite material fabrication technique, but remains challenged by a limited control over the ensuing structures. We develop a new breed of nematic colloids that are physical analogs of a mathematical surface with boundary, interacting with the molecular alignment field without inducing defects when flat. However, made from a thin nanofoil, they can be shaped to prompt formation of self-compensating defects that drive pre-programmed elastic interactions mediated by the nematic host. To show this, we wrap the nanofoil on all triangular side faces of a pyramid, except its square base. The ensuing pyramidal cones induce point defects with fractional hedgehog charges of opposite signs, spontaneously align with respect to the far-field director to form elastic dipoles and nested assemblies with tunable spacing. Nanofoils shaped into octahedrons interact as elastic quadrupoles. Our findings may drive realization of low-symmetry colloidal phases.Surface point defects, dubbed "boojums", arise in many condensed matter systems and often define their physical behavior [1][2][3][4][5][6][7]. For example, in nematic liquid crystal (LC) colloids and in confined LCs, topological characteristics of the particle-induced boojums are determined by the surface topology of colloidal inclusions [7,8]. Elastic interactions of particles in LCs, in turn, depend on these defects and their locations, ultimately leading to different forms of assembly [3][4][5][6][7][8][9]. By changing genus of colloidal particles, one can pre-determine the patterns, winding numbers, and hedgehog charges of induced surface defects [7,8]. However, surface genus is not the only means of controlling defects and self-assembly as even spherical particles can

Liquid Crystal Colloids

“…Yet, by morphing shapes of such foil-based particles, one can pattern the defects to achieve various elastic multipoles and drive LC-mediated self-assembly similar to that exhibited by nematic colloidal particles with surfaces without boundaries (96). They behave differently from both the microparticles (larger than  e ) with strong BCs (Figs.…”

“…They behave differently from both the microparticles (larger than  e ) with strong BCs (Figs. 1d,e, 2 and 3) and nanoparticles (smaller than  e ) with effectively weak surface anchoring (Figures 4 and 5), being capable of inducing no defects or various self-compensating defect structures, depending on their geometric shape and orientation relative to n 0 (96). Non-orientable colloidal particles with boundary have also been recently theoretically considered (97), though their experimental realization still presents a challenge.…”

“…Nematic colloidal particles in the form of thin foil with two lateral dimensions >> e but one dimension (thickness) << e behave as analogs of orientable surfaces with boundaries, to which the constrains on induced defects discussed above cannot apply and, generally, no defects need to be induced (91,96). Yet, by morphing shapes of such foil-based particles, one can pattern the defects to achieve various elastic multipoles and drive LC-mediated self-assembly similar to that exhibited by nematic colloidal particles with surfaces without boundaries (96).…”

N−SmA−SmCphase transitions probed by a pair of elastically bound colloids

“…The deformation increases the elastic energy of the liquid crystals. When the distortion regions of two physically separated particles tend to overlap they exhibit long-range elastic interaction [3,4,12,13]. The interaction energy is anisotropic and typically of the order of a few thousand k B T , where k B is the Boltzmann constant and T is the absolute temperature [2,14].…”

“…The interaction energy is anisotropic and typically of the order of a few thousand k B T , where k B is the Boltzmann constant and T is the absolute temperature [2,14]. The system minimizes the total elastic energy by sharing the topological defects associated with the particles, and based on this principle various interesting two-and three-dimensional colloidal assemblies have been reported [8,13,[15][16][17][18][19].…”