Tetravalent Colloids by Nematic Wetting

– In an elegant paper, D. Nelson suggested a method to produce tetravalent colloids based on a tetrahedral configuration created on the surface of a spherical particle. It emerges from a two-dimensional nematic liquid crystal placed on a sphere due to the presence of four 1/2 disclinations, i.e., topological defects in the orientational order [1]. In this paper we show that such a tetrahedral configuration also occurs in the wetting layers which form around spheres dispersed in a liquid crystal above the nematic-isotropic phase transition. Nematic wetting therefore offers an alternative route towards tetravalent colloids. Recently, D. Nelson proposed a method by which tetravalent colloids could be produced [1]. These micron-sized particles would have four chemical linkers or DNA strands symmetrically attached to their surfaces. Similar to, e.g., carbon, silicon and germanium atoms with their sp hybridized chemical bonds, the tetravalent colloids could then arrange into, e.g., a colloidal crystal with a diamond lattice structure which is known to possess a large photonic band gap [2]. To create the attachment sites for the chemical linkers, Nelson considered the two-dimensional nematic liquid crystal phase on the particle surface realized by a monolayer of elongated constituents such as gemini lipids [3], ABA triblock copolymers [4] or nanorods [5]. One could first think that the rodlike particles on a sphere create Mermin’s boojums [6], i.e., point defects with topological charge 1 situated at the north and south pole of a sphere as illustrated in Fig. 1a). The lines indicate the director field. A vector order parameter would indeed create such a configuration. The nematic order, however, is described by an axis in space which allows the boojums to split up into a pair of disclinations with charge 1/2. Lubensky and Prost showed that the ground state of a 2D nematic texture on a sphere consists of four 1/2 disclinations situated at the vertices of a tetrahedron [7]. Fig. 1b) tries to illustrate such a configuration with tetrahedral symmetry in the angular space of spherical coordinates, i.e., polar angle θ versus azimuthal angle φ. For the moment, let the rectangles symbolize the nematic director. To visualize the boojum configuration in this representation, all the local directors would point along the vertical (lines of longitude). Squares situated on the θ = 0, π line (north and (∗) E-mail: [email protected]