Colloidal aggregation in a nematic liquid crystal: topological arrest of particles by a single-stroke disclination line

Dynamic coupling between a multistable defect pattern and flow in nematic liquid crystals confined in a porous medium

When a nematic liquid crystal is confined in a porous medium with strong anchoring conditions, topological defects, called disclinations, are stably formed with numerous possible configurations. Since the energy barriers between them are large enough, the system shows multistability. Our lattice Boltzmann simulations demonstrate dynamic couplings between the multistable defect pattern and the flow in a regular porous matrix. At sufficiently low flow speed, the topological defects are pinned at the quiescent positions. As the flow speed is increased, the defects show cyclic motions and nonlinear rheological properties, which depend on whether or not they are topologically constrained in the porous networks. In addition, we discover that the defect pattern can be controlled by controlling the flow. Thus, the flow path is recorded in the porous channels owing to the multistability of the defect patterns.

Nematic director-induced switching of assemblies of hexagonally packed gold nanorods

Self-assembled disc-shaped clusters of hexagonally packed, thiol-functionalized gold nanorods are prepared and dispersed in thermotropic nematic liquid crystals. The resultant hybrid complex fluids exhibit colloidal anisotropy with very high orientational order and are characterized by SAXS as shown in the figure. Precise, reconfigurable control of the cluster orientation at very low electric field strengths (0.18 V μm(-1) ) is achieved.

Self-assembly and nonlinear dynamics of dimeric colloidal rotors in cholesterics

We study by simulation the physics of two colloidal particles in a cholesteric liquid crystal with tangential order parameter alignment at the particle surface. The effective force between the pair is attractive at short range and favors assembly of colloid dimers at specific orientations relative to the local director field. When pulled through the fluid by a constant force along the helical axis, we find that such a dimer rotates, either continuously or stepwise with phase-slip events. These cases are separated by a sharp dynamical transition and lead, respectively, to a constant or an ever-increasing phase lag between the dimer orientation and the local nematic director.

Colloidal entanglement in highly twisted chiral nematic colloids: twisted loops, Hopf links, and trefoil knots

The topology and geometry of closed defect loops is studied in chiral nematic colloids with variable chirality. The colloidal particles with perpendicular surface anchoring of liquid crystalline molecules are inserted in a twisted nematic cell with the thickness that is only slightly larger than the diameter of the colloidal particle. The total twist of the chiral nematic structure in cells with parallel boundary conditions is set to 0, π, 2π, and 3π, respectively. We use the laser tweezers to discern the number and the topology of the -1/2 defect loops entangling colloidal particles. For a single colloidal particle, we observe that a single defect loop is winding around the particle, with the winding pattern being more complex in cells with higher total twist. We observe that colloidal dimers and colloidal clusters are always entangled by one or several -1/2 defect loops. For colloidal pairs in π-twisted cells, we identify at least 17 different entangled structures, some of them exhibiting linked defect loops-Hopf link. Colloidal entanglement is even richer with a higher number of colloidal particles, where we observe not only linked, but also colloidal clusters knotted into the trefoil knot. The experiments are in good agreement with numerical modeling using Landau-de Gennes theory coupled with geometrical and topological considerations using the method of tetrahedral rotation.

Direct and inverted nematic dispersions for soft matter photonics

General properties and recent developments in the field of nematic colloids and emulsions are discussed. The origin and nature of pair colloidal interactions in the nematic colloids are explained and an overview of the stable colloidal 2D crystalline structures and superstructures discovered so far is given. The nature and role of topological defects in the nematic colloids is discussed, with an emphasis on recently discovered entangled colloidal structures. Applications of inverted nematic emulsions and binding force mechanisms in nematic colloids for soft matter photonic devices are discussed.

Nematic braids: topological invariants and rewiring of disclinations

The conventional topological description given by the fundamental group of nematic order parameter does not adequately explain the entangled defect line structures that have been observed in nematic colloids. We introduce a new topological invariant, the self-linking number, that enables a complete classification of entangled defect line structures in general nematics, even without particles, and demonstrate our formalism using colloidal dimers, for which entangled structures have been previously observed. We also unveil a simple rewiring scheme for the orthogonal crossing of two -1/2 disclinations, based on a tetrahedral rotation of two relevant disclination segments, that allows us to predict possible nematic braids and calculate their self-linking numbers.

Memory and topological frustration in nematic liquid crystals confined in porous materials

Orientational ordering is key to functional materials with switching capability, such as nematic liquid crystals and ferromagnetic and ferroelectric materials. We explored the confinement of nematic liquid crystals in bicontinuous porous structures with smooth surfaces that locally impose normal orientational order on the liquid crystal. We find that frustration leads to a high density of topological defect lines permeating the porous structures, and that most defect lines are made stable by looping around solid portions of the confining material. Because many defect trajectories are possible, these systems are highly metastable and efficient in memorizing the alignment forced by external fields. Such memory effects have their origin in the topology of the confining surface and are maximized in a simple periodic bicontinuous cubic structure. We also show that nematic liquid crystals in random porous networks exhibit a disorder-induced slowing-down typical of glasses that originates from activated collisions and rearrangements of defect lines. Our findings offer the possibility to functionalize orientationally ordered materials through topological confinement.

Shape-induced dispersion of colloids in anisotropic fluids

We experimentally study the behavior of micrometer-sized prolate ellipsoidal particles dispersed in a nematic liquid crystal. The latter is an aqueous solution of rodlike micelles. When embedded into such a solvent, ellipsoids with small enough aspect ratios aggregate to form anisotropic structures oriented at an angle with respect to the local background director (as already observed for spheres). This is, however, no longer the case when the aspect ratio reaches a well-defined value: above that value, the ellipsoids remain well dispersed and apparently do no interact with each other, even over very long periods of time (several months). Therefore, there exists a transition from an aggregated to a nonaggregated state as a function of aspect ratio and for a given particle concentration. This behavior has not been predicted so far and we put forward simple calculations to rationalize our observations.

The influence of disorder on thermotropic nematic liquid crystals phase behavior

We review the theoretical research on the influence of disorder on structure and phase behavior of condensed matter system exhibiting continuous symmetry breaking focusing on liquid crystal phase transitions. We discuss the main properties of liquid crystals as adequate systems in which several open questions with respect to the impact of disorder on universal phase and structural behavior could be explored. Main advantages of liquid crystalline materials and different experimental realizations of random field-type disorder imposed on liquid crystal phases are described.

Defect structures in nematic liquid crystals around charged particles

We numerically study the orientation deformations in nematic liquid crystals around charged particles. We set up a Ginzburg-Landau theory with inhomogeneous electric field. If the dielectric anisotropy epsilon 1 is positive, Saturn-ring defects are formed around the particles. For epsilon 1< 0 , novel "ansa" defects appear, which are disclination lines with their ends on the particle surface. We find unique defect structures around two charged particles. To lower the free energy, oppositely charged particle pairs tend to be aligned in the parallel direction for epsilon 1> 0 and in the perpendicular plane for epsilon 1< 0 with respect to the background director. For identically charged pairs the preferred directions for epsilon 1> 0 and epsilon 1< 0 are exchanged. We also examine competition between the charge-induced anchoring and the short-range anchoring. If the short-range anchoring is sufficiently strong, it can be effective in the vicinity of the surface, while the director orientation is governed by the long-range electrostatic interaction far from the surface.

Quadrupolar particles in a nematic liquid crystal: effects of particle size and shape

We investigate the effects of particle size and shape on the quadrupolar (Saturn-ring-like) defect structures formed by a nematic liquid crystal around nm-sized and mum -sized particles with spherical and spherocylindrical shapes. We also report results for the potentials of mean force in our systems, calculated using a mesoscale theory for the tensor order parameter Q of the nematic. Our results indicate that for pairs of nm-sized particles in close proximity, the nematic forms "entangled hyperbolic" defect structures regardless of the shape of the nanoparticles. In our calculations with nanoparticles we did not observe any other entangled or unentangled defect structures, in contrast to what was reported for pairs of mum -sized spherical particles. Such a finding suggests that the "entangled hyperbolic" defect structures are the most stable for pairs of nanoparticles in close proximity. For pairs of mum -sized particles, our results indicate that the nematic forms entangled "figure-of-eight" defect structures around pairs of spheres and spherocylinders. Our results suggest that the transition between "entangled hyperbolic" and figure-of-eight defect structures takes place when the diameter of the particle is between D=100 nm and 1 microm . We have also calculated the torques that develop when pairs of spherocylindrical nanoparticles in a nematic approach each other. Our calculations suggest that the nematic-mediated interactions between the nm-sized particles are fairly strong, up to 5700 k{B}T for the case of pairs of spherocylindrical nanoparticles arranged with their long axis parallel to each other. Furthermore, these interactions can make the particles to bind together at specific locations, and thus could be used to assemble the particles into ordered structures with different morphologies.

Hierarchical self-assembly of nematic colloidal superstructures

We show that colloidal superstructures could be assembled in mixtures of large and small colloidal particles dispersed in a nematic liquid crystal. Using elastic interaction of small colloidal particles with the disclination lines we succeed to demonstrate how one can decorate with small particles a topological matrix of defect rings and loops formed by an array of large colloidal particles. Our simulations show that this concept of colloidal self-assembly in nematics could be extended down to the nanoscale particles.

Self-assembly of polymer droplets in a nematic liquid crystal at phase separation

We have studied the phase separation of a binary mixture of a polymer and a nematic liquid crystal at a dilute polymer concentration. Various types of regular self-assemblies of polymer droplets such as branched chains and zigzag chains have been observed in addition to the previously reported straight chains. The kinetic process of the self-assembly is dominated by the transformations of a topological defect accompanied by a droplet in addition to the simple growth of the droplet. The spontaneous transformation from a ring defect (Saturn-ring defect) to a point defect (dipole) is an essential process in forming a straight chain composed of droplets with the same size. We also find that the transformations are induced by a nearby droplet with a point defect. This leads to a wide size distribution of droplets in a chain cluster and results in a branched chain. The difference in the chaining mechanisms is discussed using an electrostatic analogy. We also clarify that the symmetry breaking in the assembly is governed by the direction in which the cell containing the binary mixture is rubbed.

Entangled nematic colloidal dimers and wires

It has been predicted, but never confirmed, that colloidal particles in a nematic liquid crystal could be self-assembled by delocalized topological defects and entangled disclinations. We show experimentally and theoretically that colloidal dimers and 1D structures bound by entangled topological defect loops can indeed be created by locally thermally quenching a thin layer of the nematic liquid crystal around selected colloidal particles. The topological entanglement provides a strong stringlike binding, which is ten thousand times stronger compared to water-based colloids. This unique binding mechanism could be used to assemble resonator optical waveguides and robust chiral and achiral structures of topologically entangled colloids that we call colloidal wires.

Nanoparticles in nematic liquid crystals: Interactions with nanochannels

A mesoscale theory for the tensor order parameter Q is used to investigate the structures that arise when spherical nanoparticles are suspended in confined nematic liquid crystals (NLCs). The NLC is "sandwiched" between a wall and a small channel. The potential of mean force is determined between particles and the bottom of the channels or between several particles. Our results suggest that strong NLC-mediated interactions between the particles and the sidewalls of the channels, on the order of hundreds of k(B)T, arise when the colloids are inside the channels. The magnitude of the channel-particle interactions is dictated by a combination of two factors, namely, the type of defect structures that develop when a nanoparticle is inside a channel, and the degree of ordering of the nematic in the region between the colloid and the nanochannel. The channel-particle interactions become stronger as the nanoparticle diameter becomes commensurate with the nanochannel width. Nanochannel geometry also affects the channel-particle interactions. Among the different geometries considered, a cylindrical channel seems to provide the strongest interactions. Our calculations suggest that small variations in geometry, such as removing the sharp edges of the channels, can lead to important reductions in channel-particle interactions. Our calculations for systems of several nanoparticles indicate that linear arrays of colloids with Saturn ring defects, which for some physical conditions are not stable in a bulk system, can be stabilized inside the nanochannels. These results suggest that nanochannels and NLCs could be used to direct the assembly of nanoparticles into ordered arrays with unusual morphologies.