Exploiting imperfections in the bulk to direct assembly of surface colloids

Abstract

We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals (LCs) to assemble colloidal particles trapped at the LC interface into reconfigurable structures with complex symmetries and packings. Spherical colloids with homeotropic anchoring trapped at the interface between air and the nematic LC 4-cyano-4'-pentylbiphenyl create quadrupolar distortions in the director field causing particles to repel and consequently form close-packed assemblies with a triangular habit. Here, we report on complex open structures organized via interactions with defects in the bulk. Specifically, by confining the nematic LC in an array of microposts with homeotropic anchoring conditions, we cause defect rings to form at well-defined locations in the bulk of the sample. These defects source elastic deformations that direct the assembly of the interfacially trapped colloids into ring-like assemblies, which recapitulate the defect geometry even when the microposts are completely immersed in the nematic. When the surface density of the colloids is high, they form a ring near the defect and a hexagonal lattice far from it. Because topographically complex substrates are easily fabricated and LC defects are readily reconfigured, this work lays the foundation for a versatile, robust mechanism to direct assembly dynamically over large areas by controlling surface anchoring and associated bulk defect structure.

Keywords: 2D superstructures; directed assembly; elastic interaction; nematic interface; topology.

Fig. 1.

Micropost-induced bulk defect rings. (A) Polarized optical microscopy image of a micropost array where all surfaces have homeotropic anchoring resulting in defect rings that circumscribe each micropost. (Inset) Bright-field image of a single micropost where the bright line indicates the approximate lateral position of the defect loop. (B) FCPM image indicates the location of defects in an otherwise uniform director field. (Upper) Top view of the micropost. (Lower) Z-stack of FCPM images in which the maximum intensity represents the location of the defect core that occurs at approximately midheight of the post. (C) Disclination lines are dictated by the shape of the micropost as shown around triangular, square, and pentagonal microposts. (Scale bars: 50 μm.)

Fig. 2.

Numerical and topological evaluation of the director field. (A) System has two corners, X and Y, where the director field can choose between two winding senses. (B–D) Director fields correspond to the relative minima of the LdG free energy for a cylindrical micropost and planar interfaces, found numerically. Isosurfaces of are shown in red, where S is the leading eigenvalue of Q. Blue ellipsoids indicate the director field. The nematic is locally melted at the sharp corners. (B) Opposite winding at the two corners precludes the possibility of a disclination in the bulk. (C) Bulk disclination with (i.e., anticlockwise) winding number requires positive winding at both corners. (D) Bulk disclination with (i.e., clockwise) winding number requires negative winding at both corners. Because the numerics show that the (meta)stable states have azimuthal symmetry and that the director has no azimuthal component, we may think of these winding numbers as pseudocharges.

Fig. 3.

Effect of surface curvature. (A) Where the 5CB–air interface curves upward to meet the micropost, LdG numerical modeling predicts that negative winding is favored. (B) Likewise, curvature at the bottom of the micropost favors positive winding; the surface defect in this case can be viewed as virtual, inside the micropost. SEM image of microposts with a curved base (C) and a corresponding FCPM image (D) detects the presence of a disclination loop when the micropost array is filled with LCs. Typically, this defect will sit toward the upper half of the micropost. (E–G) Curved microposts tapered along their entire lengths (SEM image shown in E) do not induce the formation of a bulk disclination ring (verified with FCPM), as is evident when viewed between crossed polarizers. The relaxation of the director to the vertical direction with increasing distance from the micropost is much more gradual in F than in Fig. 1A. (G) Axial symmetry is lost at smaller micropost spacing. (Scale bars: 50 μm.)

Fig. 4.

Elastic migration of colloidal particles induced by bulk topological defects. (A) Time-lapsed images of the migration of spherical colloids toward a micropost . (B) Ring of colloids forms above a submerged micropost. (C) At moderate surface coverage, ordered rings assemble around the micropost due to attraction by the bulk defect and repel one another via long-range interparticle repulsion. As particle density continues to increase, radial assemblies evolve into hexagonal ordering (D) until highly ordered structures form at a very high surface coverage (E). (Scale bars: 50 μm.)

Fig. 5.

Elastic potential. (A) Migration of colloids implies bulk–colloid interaction energies on the order of and follows (solid curves), where is the inferred elastic potential and r is the radial distance in the horizontal plane from the center of the micropost. As the height of a micropost is increased (different curves), attractions become weaker due to an increased separation between particles and the bulk defect. (Inset) Migration rates are faster for microposts with base curvature compared with those of comparable height that have a sharp corner at the base (corner Y in Fig. 2A). This is due to the tendency of the bulk disclination to position itself closer to the free interface for microposts with curved bases. Closed symbols indicate microposts with a curved base. (B) Numerically modeled energy of a colloidal sphere approaching a micropost capturing the dependence of the quadrupolar colloid interacting with a disclination ring. The red dashed line represents the asymptotic value for at large distances, and is the radius of the micropost’s disclination ring. (Inset) Representative image of the numerical modeling.