Anisotropic nanoparticles immersed in a nematic liquid crystal: defect structures and potentials of mean force

Elastocapillary interaction for particles trapped at the isotropic-nematic liquid crystal interface

We present numerical simulations on pairwise interactions between particles trapped at an isotropic-nematic liquid crystal (Iso-N) interface. The particles are subject to elastocapillary interactions arising from interfacial deformations and elastic distortions of the nematic phase. We use a recent model based on a phase-field approach [see Qiu et al., Phys. Rev. E 103, 022706 (2021)2470-004510.1103/PhysRevE.103.022706] to take into account the coupling between elastic and capillary phenomena. The pair potential is computed in a two-dimensional geometry for a range of particle separations and two anchoring configurations. The first configuration leads to the presence of an anchoring conflict at the three-phase contact line, whereas such a conflict does not exist for the second one. In the first case, the results show that significant interfacial deformations and downward particle displacements occur, resulting in sizable attractive capillary interactions able to overcome repulsive elastic forces at intermediate separations. The pair potential exhibits an equilibrium distance since elastic repulsions prevail at short range and prevent the clustering of particles. However, in the absence of any anchoring conflict, the interfacial deformations are very small and the capillary forces have a negligible contribution to the pair potential, which is fully repulsive and overwhelmed by elastic forces. These results suggest that the self-assembly properties of particles floating at Iso-N interfaces might be controlled by tuning anchoring conflicts.

Electrophoretic propulsion of matchstick-shaped magnetodielectric particles in the presence of external magnetic fields in a nematic liquid crystal

Synthesis of micro- and nanoparticles of pre-designed shape and surface properties is an integral part of soft and synthetic active matter. We report synthesis of matchstick-shaped (MS) magnetodielectric particles and demonstrate their potential as active agents with field-controllable trajectories in a nematic liquid crystal (NLC). The MS particles with homeotropic anchoring in NLCs align either parallel or perpendicular to the director depending on the dipolar or quadrupolar director distortions. When subjected to transverse electric and magnetic fields, the particles experience electric and magnetic torques trying to align them in the respective field directions. At equilibrium, the long axis is tilted at an angle with respect to the director. The change in orientation alters the surrounding elastic distortion, which results in unbalanced electroosmotic flows. These flows provide the necessary impetus for propelling the particles in various directions with different velocities depending on their orientations.

Spontaneous electric-polarization topology in confined ferroelectric nematics

Topological textures have fascinated people in different areas of physics and technologies. However, the observations are limited in magnetic and solid-state ferroelectric systems. Ferroelectric nematic is the first liquid-state ferroelectric that would carry many possibilities of spatially-distributed polarization fields. Contrary to traditional magnetic or crystalline systems, anisotropic liquid crystal interactions can compete with the polarization counterparts, thereby setting a challenge in understating their interplays and the resultant topologies. Here, we discover chiral polarization meron-like structures, which appear during the emergence and growth of quasi-2D ferroelectric nematic domains. The chirality can emerge spontaneously in polar textures and can be additionally biased by introducing chiral dopants. Such micrometre-scale polarization textures are the modified electric variants of the magnetic merons. Both experimental and an extended mean-field modelling reveal that the polarization strength plays a dedicated role in determining polarization topology, providing a guide for exploring diverse polar textures in strongly-polarized liquid crystals.

Particle trapped at the isotropic-nematic liquid crystal interface: Elastocapillary phenomena and drag forces

We present numerical simulations of a particle trapped at the isotropic-nematic liquid crystal (Iso-N) interface. We use our recent model, based on a phase-field approach [see Qiu et al., Phys. Rev. E 103, 022706 (2021)10.1103/PhysRevE.103.022706], to couple the capillary forces acting on the interface with the elastic stresses in the nematic phase along with topological defects. A range of floating configurations are first investigated as a function of the contact angle and various anchoring conditions at the fluid interface. The results show that the response of the system is driven by the existence of an anchoring conflict at the contact line. Substantial particle displacements and/or interfacial deformations may occur in this case even for moderate anchoring strengths. These findings highlight the coupling between elastic and capillary forces. In a second part, we compute drag forces exerted on a particle that moves along the Iso-N interface for several contact angles and a moderate Ericksen number. Because of the coupling between the velocity and order parameter fields, topological defects are swept downstream of the particle by the flow and sometimes escape from the particle or merge with the interface. We also find linear force-velocity laws, with drag forces at the Iso-N interface being slightly greater than their isotropic counterparts due to director distortions. We discuss these results in light of past studies on the behavior of particles being dragged in the bulk of a liquid crystal matrix.

Nontrivial topological defects of micro-rods immersed in nematics and their phototuning

Combinations of different geometries and surface anchoring conditions give rise to the diversity of topological structures in nematic colloid systems. Tuning these parameters in a single system offers possibilities for observing the evolution of the topological transformation and for manipulating colloids through topological forces. Here we investigate the nontrivial topological properties of micro-rods dispersed in nematic liquid crystals through experimental observation and computer simulation. The topological variation is driven by photodynamically changing the surface anchoring using azobenzene-based surface-commander molecules, the majority of which are localized on both the substrates and the surface of micro-rods. By comparing experimental and simulation results, we show previously unidentified topological properties of the two-body LC-rod-colloid system. Moreover, unlike the traditional photoresponsive liquid crystal systems, the localization of azobenzene molecules on the surfaces makes it possible to change only the direction of the surface orientation, not disordering of the bulk structures. The results assist in the development of photo-driven micro-robotics in fluids.

Nonequilibrium Dynamics of a Magnetic Nanocapsule in a Nematic Liquid Crystal

Colloidal particles in nematic liquid crystals show a beautiful variety of complex phenomena with promising applications. Their dynamical behaviour is determined by topology and interactions with the liquid crystal and external fields. Here, a nematic magnetic nanocapsule reoriented periodically by time-varying magnetic fields is studied using numerical simulations. The approach combines Molecular Dynamics to resolve solute–solvent interactions and Nematic Multiparticle Collision Dynamics to incorporate nematohydrodynamic fields and fluctuations. A Saturn ring defect resulting from homeotropic anchoring conditions surrounds the capsule and rotates together with it. Magnetically induced rotations of the capsule can produce transformations of this topological defect, which changes from a disclination curve to a defect structure extending over the surface of the capsule. Transformations occur for large magnetic fields. At moderate fields, elastic torques prevent changes of the topological defect by tilting the capsule out from the rotation plane of the magnetic field.

Phase-field model for elastocapillary flows of liquid crystals

We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients: A tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.

Dynamics of defects around anisotropic particles in nematic liquid crystals under shear

Nematic multiparticle collision dynamics is used to simulate disclination ring defects around spherocylinders suspended in a liquid crystal. A solvent-solute interaction potential is integrated over a short-time scale by an auxiliary molecular dynamics procedure that updates the translational and angular coordinates of the spherocylinders. For suspended particles with length in the range ∼(60,160)nm and a fixed aspect ratio, this method is able to simulate static defects reported previously in the literature. It also simulates orientation fluctuations of the elongated colloids that exhibit a broad distribution and a slow relaxation rate. Finally, a nematic host driven from equilibrium by shear flow is simulated, and the consequent dynamic behavior of the colloid-defect pair is studied. Defects under shear present significant structural transformations from chairlike disclination rings to extended defects that cover most of the cylindrical surface of the colloid. This effect results from the hydrodynamic torque on the nematic field caused by the distorted flow around the spherocylinder, and it is present for small Reynolds and Ericksen numbers of order unity.

Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

Nematic Liquid-Crystal Colloids

This article provides a concise review of a new state of colloidal matter called nematic liquid-crystal colloids. These colloids are obtained by dispersing microparticles of different shapes in a nematic liquid crystal that acts as a solvent for the dispersed particles. The microparticles induce a local deformation of the liquid crystal, which then generates topological defects and long-range forces between the neighboring particles. The colloidal forces in nematic colloids are much stronger than the forces in ordinary colloids in isotropic solvents, exceeding thousands of kBT per micrometer-sized particle. Of special interest are the topological defects in nematic colloids, which appear in many fascinating forms, such as singular points, closed loops, multitudes of interlinked and knotted loops or soliton-like structures. The richness of the topological phenomena and the possibility to design and control topological defects with laser tweezers make colloids in nematic liquid crystals an excellent playground for testing the basic theorems of topology.

Colloidal transport within nematic liquid crystals with arrays of obstacles

We have investigated the gravity-driven transport of spherical colloids suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) within microfluidic arrays of cylindrical obstacles arranged in a square lattice. Homeotropic anchoring at the surfaces of the obstacles created periodic director-field patterns that strongly influenced the motion of the colloids, whose surfaces had planar anchoring. When the gravitational force was oriented parallel to a principal axis of the lattice, the particles moved along channels between columns of obstacles and displayed pronounced modulations in their velocity. Quantitative analysis indicates that this modulation resulted from a combination of a spatially varying effective drag viscosity and elastic interactions engendered by the periodic director field. The interactions differed qualitatively from a sum of pair-wise interactions between the colloids and isolated obstacles, reflecting the distinct nematic environment created by confinement within the array. As the angle α between the gravitational force and principal axis of the lattice was varied, the velocity did not follow the force but instead locked into a discrete set of directions commensurate with the lattice. The transitions between these directions occurred at values of α that were different from those observed when the spheres were in an isotropic liquid, indicating the ability of the liquid crystal forces to tune the lateral displacement behavior in such devices.

Directed Self-Assembly of Colloidal Particles onto Nematic Liquid Crystalline Defects Engineered by Chemically Patterned Surfaces

In exploiting topological defects of liquid crystals as the targeting sites for trapping colloidal objects, previous work has relied on topographic features with uniform anchoring to create defects, achieving limited density and spacing of particles. We report a generalizable strategy to create topological defects on chemically patterned surfaces to assemble particles in precisely defined locations with a tunable interparticle distance at nanoscale dimensions. Informed by experimental observations and numerical simulations that indicate that liquid crystals, confined between a homeotropic-anchoring surface and a surface with lithographically defined planar-anchoring stripes in a homeotropic-anchoring background, display splay-bend deformation, we successfully create pairs of defects and subsequently trap particles with controlled spacing by designing patterns of intersecting stripes aligned at 45° with homeotropic-anchoring gaps at the intersections. Application of electric fields allows for dynamic control of trapped particles. The tunability, responsiveness, and adaptability of this platform provide the opportunities for assembly of colloidal structures toward functional materials.

Segregation of liquid crystal mixtures in topological defects

The structure and physical properties of liquid crystal (LC) mixtures are a function of composition, and small changes can have pronounced effects on observables, such as phase-transition temperatures. Traditionally, LC mixtures have been assumed to be compositionally homogenous. The results of chemically detailed simulations presented here show that this is not the case; pronounced deviations of the local order from that observed in the bulk at defects and interfaces lead to significant compositional segregation effects. More specifically, two disclination lines are stabilized in this work by introducing into a nematic liquid crystal mixture a cylindrical body that exhibits perpendicular anchoring. It is found that the local composition deviates considerably from that of the bulk at the interface with the cylinder and in the defects, thereby suggesting new assembly and synthetic strategies that may capitalize on the unusual molecular environment provided by liquid crystal mixtures.

Liquid crystal mixtures are used in commercial applications and their composition affects their properties. Here Rahimi et al. use atomistic simulations to show that defects influence the molecular arrangement of the mixture components leading to a deviation of the local order from that of the bulk.

Controlled deformation of vesicles by flexible structured media

Liquid crystalline (LC) materials, such as actin or tubulin networks, are known to be capable of deforming the shape of cells. Here, elements of that behavior are reproduced in a synthetic system, namely, a giant vesicle suspended in a LC, which we view as a first step toward the preparation of active, anisotropic hybrid systems that mimic some of the functionality encountered in biological systems. To that end, we rely on a coupled particle-continuum representation of deformable networks in a nematic LC represented at the level of a Landau-de Gennes free energy functional. Our results indicate that, depending on its elastic properties, the LC is indeed able to deform the vesicle until it reaches an equilibrium, anisotropic shape. The magnitude of the deformation is determined by a balance of elastic and surface forces. For perpendicular anchoring at the vesicle, a Saturn ring defect forms along the equatorial plane, and the vesicle adopts a pancake-like, oblate shape. For degenerate planar anchoring at the vesicle, two boojum defects are formed at the poles of the vesicle, which adopts an elongated, spheroidal shape. During the deformation, the volume of the topological defects in the LC shrinks considerably as the curvature of the vesicle increases. These predictions are confirmed by our experimental observations of spindle-like shapes in experiments with giant unilamellar vesicles with planar anchoring. We find that the tension of the vesicle suppresses vesicle deformation, whereas anchoring strength and large elastic constants promote shape anisotropy.

Relevance of saddle-splay elasticity in complex nematic geometries

We demonstrate the relevance of saddle-splay elasticity in nematic liquid crystalline fluids in the context of complex surface anchoring conditions and the complex geometrical confinement. Specifically, nematic cells with patterns of surface anchoring and colloidal knots are shown as examples where saddle-splay free energy contribution can have a notable role which originates from nonhomogeneous surface anchoring and the varying surface curvature. Patterned nematic cells are shown to exhibit various (meta)stable configurations of nematic field, with relative (meta)stability depending on the saddle-splay. We show that for high enough values of saddle-splay elastic constant K24 a previously unstable conformation can be stabilised, more generally indicating that the saddle-splay can reverse or change the (meta)stability of various nematic structures affecting their phase diagrams. Furthermore, we investigate saddle-splay elasticity in the geometry of highly curved boundaries - the colloidal particle knots in nematic - where the local curvature of the particles induces complex spatial variations of the saddle-splay contributions. Finally, a nematic order parameter tensor based saddle-splay invariant is shown, which allows for the direct calculation of saddle-splay free energy from the Q-tensor, a possibility very relevant for multiple mesoscopic modelling approaches, such as Landau-de Gennes free energy modelling.

Homeotropic nano-particle assembly on degenerate planar nematic interfaces: films and droplets

A continuum theory is used to study the effects of homeotropic nano-particles on degenerate planar liquid crystal interfaces. Particle self-assembly mechanisms are obtained from careful examination of particle configurations on a planar film and on a spherical droplet. The free energy functional that describes the system is minimized according to Ginzburg-Landau and stochastic relaxations. The interplay between elastic and surface distortions and the desire to minimize defect volumes (boojums and half-Saturn rings) is shown to be responsible for the formation of intriguing ordered structures. As a general trend, the particles prefer to localize at defects to minimize the overall free energy. However, multiple metastable configurations corresponding to local minima can be easily observed due to the high energy barriers that separate distinct particle arrangements. We also show that by controlling anchoring strength and temperature one can direct liquid-crystal mediated nanoparticle self-assembly along well defined pathways.

Metal nanoparticle dispersion, alignment, and assembly in nematic liquid crystals for applications in switchable plasmonic color filters and E-polarizers

Viewing angle characteristics of displays and performance of electro-optic devices are often compromised by the quality of dichroic thin-film polarizers, while dichroic optical filters usually lack tunability and cannot work beyond the visible part of optical spectrum. We demonstrate that molecular-colloidal organic-inorganic composites formed by liquid crystals and relatively dilute dispersions of orientationally ordered anisotropic gold nanoparticles, such as rods and platelets, can be used in engineering of switchable plasmonic polarizers and color filters. The use of metal nanoparticles instead of dichroic dyes allows for obtaining desired polarizing or scattering and absorption properties not only within the visible but also in the infrared parts of an optical spectrum. We explore spontaneous surface-anchoring-mediated alignment of surface-functionalized anisotropic gold nanoparticles and its control by low-voltage electric fields, elastic colloidal interactions and self-assembly, as well as the uses of these effects in defining tunable properties of the ensuing organic-inorganic nanostructured composites. Electrically tunable interaction of the composites may allow for engineering of practical electro-optic devices, such as a new breed of color filters and plasmonic polarizers.

Equilibrium state of a cylindrical particle with flat ends in nematic liquid crystals

A continuum theory is employed to numerically study the equilibrium orientation and defect structures of a circular cylindrical particle with flat ends under a homeotropic anchoring condition in a uniform nematic medium. Different aspect ratios of this colloidal geometry from thin discotic to long rodlike shapes and several colloidal length scales ranging from mesoscale to nanoscale are investigated. We show that the equilibrium state of this colloidal geometry is sensitive to the two geometrical parameters: aspect ratio and length scale of the particle. For a large enough mesoscopic particle, there is a specific asymptotic equilibrium angle associated to each aspect ratio. Upon reducing the particle size to nanoscale, the equilibrium angle follows a descending or ascending trend in such a way that the equilibrium angle of a particle with the aspect ratio bigger than 1:1 (a discotic particle) goes to a parallel alignment with respect to the far-field nematic, whereas the equilibrium angle for a particle with the aspect ratio 1:1 and smaller (a rodlike particle) tends toward a perpendicular alignment to the uniform nematic direction. The discrepancy between the equilibrium angles of the mesoscopic and nanoscopic particles originates from the significant differences between their defect structures. The possible defect structures related to mesoscopic and nanoscopic colloidal particles of this geometry are also introduced.

Liquid-crystal mediated nanoparticle interactions and gel formation

Colloidal particles embedded within nematic liquid crystals exhibit strong anisotropic interactions arising from preferential orientation of nematogens near the particle surface. Such interactions are conducive to forming branched, gel-like aggregates. Anchoring effects also induce interactions between colloids dispersed in the isotropic liquid phase, through the interactions of the pre-nematic wetting layers. Here we utilize computer simulation using coarse-grained mesogens to perform a molecular-level calculation of the potential of mean force between two embedded nanoparticles as a function of anchoring for a set of solvent conditions straddling the isotropic-nematic transition. We observe that strong, nontrivial interactions can be induced between particles dispersed in mesogenic solvent, and explore how such interactions might be utilized to induce a gel state in the isotropic and nematic phases.

Elastic and hydrodynamic torques on a colloidal disk within a nematic liquid crystal

The orientationally dependent elastic energy and hydrodynamic behavior of colloidal disks with homeotropic surface anchoring suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) have been investigated. In the absence of external torques, the disks align with the normal of the disk face â parallel to the nematic director n[over ^]. When a magnetic field is applied, the disks rotate â by an angle θ so that the magnetic torque and the elastic torque caused by distortion of the nematic director field are balanced. Over a broad range of angles, the elastic torque increases linearly with θ in quantitative agreement with a theoretical prediction based on an electrostatic analogy. When the disks are rotated to angles θ>π/2, the resulting large elastic distortion makes the disk orientation unstable, and the director undergoes a topological transition in which θ→π-θ. In the transition, a defect loop is shed from the disk surface, and the disks spin so that â sweeps through π radians as the loop collapses back onto the disk. Additional measurements of the angular relaxation of disks to θ=0 following removal of the external torque show a quasi-exponential time dependence from which an effective drag viscosity for the nematic can be extracted. The scaling of the angular time dependence with disk radius and observations of disks rotating about â indicate that the disk motion affects the director field at surprisingly modest Ericksen numbers.

Liquid crystal mediated interactions between nanoparticles in a nematic phase

A continuum theory is used to study the interactions between nanoparticles suspended in nematic liquid crystals. The free energy functional that describes the system is minimized using an Euler-Lagrange approach and an unsymmetric radial basis function method. It is shown that nanoparticle liquid-crystal mediated interactions can be controlled over a large range of magnitudes through changes of the anchoring energy and the particle diameter. The results presented in this work serve to reconcile past discrepancies between theoretical predictions and experimental observations, and suggest intriguing possibilities for directed nanoparticle self-assembly in liquid crystalline media.

Towards total photonic control of complex-shaped colloids by vortex beams

We demonstrate optical trapping and orientational control over colloidal particles having complex shapes in an anisotropic host fluid using a dynamic holographic optical tweezers system. Interactions between a colloidal particle and the toroidal intensity distributions of focused Laguerre-Gaussian beams allow for stable optical tweezing and provide a tunable tilt of the particle out of the focal plane. Use of an aligned nematic liquid crystal as the host fluid suppresses rotations about the optical axis arising from angular momentum transfer from the beam and effectively defines a rotational axis for the colloid within the trap.

Finite-size effects on order reconstruction around nematic defects

By use of the Landau-de Gennes phenomenological theory, we study the texture of a nematic liquid crystal confined within a hybrid cell. Precisely, we consider cylindrically symmetric solutions containing topological defects dictated by appropriate boundary conditions. We focus our attention on cells whose dimensions are comparable with the biaxial correlation length xi(b) . For such severe confinements the order reconstruction (OR) configuration could be stable. Its structural details reflect the balance among boundary-enforced frustration, elastic penalties, and finite-size effects. In particular, we analyze the interplay between finite-size effects and topological defects. We show that defects are always pinned to the negatively (planar) uniaxial sheet of the OR structure. The presence of a ring defect can dramatically increase the critical threshold below which the OR structure is stable.

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.

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.

Manipulation and organization of ferromagnetic nanowires by patterned nematic liquid crystals

We introduce a method to manipulate and organize ferromagnetic nanowires using the elastic forces imposed on nanowires suspended in nematic liquid crystals via patterned variations in the nematic director. As a test case for the technique, we investigate nematic environments consisting of stripes of alternating director orientations formed by lithographically patterned substrates. Nanowires oriented by small external magnetic fields are driven by the liquid crystal to specific locations of the pattern. The observed forces on the nanowires agree with calculations based on nematic elasticity.

Using localized surface plasmon resonances to probe the nanoscopic origins of adsorbate-driven ordering transitions of liquid crystals in contact with chemically functionalized gold nanodots

We report that localized surface plasmon resonances (LSPRs) of gold nanodots immersed under liquid crystals (LCs) can be used to characterize adsorbate-induced ordering transitions of the LCs on the surfaces of the nanodots. The nanoscopic changes in ordering of the LCs, as measured by LSPR, were shown to give rise to macroscopic ordering transitions of the LCs that were observed by polarized light microscopy. The results reported herein suggest that (i) LCs may be useful for enhancing the sensitivity of LSPR-based detection of binding events and (ii) that LSPR measurements of gold nanodots provide a means to characterize the nanoscopic origins of macroscopic, adsorbate-induced LC ordering transitions.

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.