Revolutionary developments in the fabrication of nanosized particles have created enormous expectations in the last few years for the use of such materials in areas such as medical diagnostics and drug-delivery, and in high-tech devices. By its very nature, nanotechnology is of immense academic and industrial interest as it involves the creation and exploitation of materials with structural features in between those of atoms and bulk materials, with at least one dimension limited to between 1 and 100 nm. Most importantly, the properties of materials with nanometric dimensions are, in most instances, significantly different from those of atoms or bulk materials. Research efforts geared towards new synthetic procedures for shape and size-uniform nanoscale building blocks as well as efficient self-assembly protocols for manipulation of these building blocks into functional materials has created enormous excitement in the field of liquid crystal research. Liquid crystals (LCs) by their very nature are suitable candidates for matrix-guided synthesis and self-assembly of nanoscale materials, since the liquid crystalline state combines order and mobility at the molecular (nanoscale) level. Based on selected relevant examples, this review attempts to give a short overview of current research efforts in LC-nanoscience. The areas addressed in this review include the synthesis of nanomaterials using LCs as templates, the design of LC nanomaterials, self-assembly of nanomaterials using LC phases, defect formation in LC-nanoparticle suspensions, and potential applications. Despite the seeming diversity of these research topics, this review will make an effort to establish logical links between these different research areas.

Nanoparticles in Liquid Crystals: Synthesis, Self-Assembly, Defect Formation and Potential Applications

The production of strings (disclination lines and loops) has been observed by means of the Kibble mechanism of domain (bubble) formation in the isotropic-nematic phase transition of the uniaxial nematic liquid crystal 4-cyano-4'-n-pentylbiphenyl. The number of strings formed per bubble is about 0.6. This value is in reasonable agreement with a numerical simulation of the experiment in which the Kibble mechanism is used for the order parameter space of a uniaxial nematic liquid crystal.

The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals

Point defects in nematics, also called hedgehogs, are topological entities that have no equivalent in ordered atomic solids, despite the homonymy. They have been the subject of intense experimental and, above all, theoretical (analytical and computational) investigations in the last thirty years. They are present in bulk specimens and at the specimen boundaries. This review article stresses the importance of the core structure of the defect, the possibility of it splitting into a disclination loop, and boundary conditions, as well as taking stock of the recent advances on point defects in nematic colloidal suspensions. An important topic is the formation of strings between opposite hedgehogs (radial and hyperbolic), and their role in the dynamic properties of nematics.

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Topological point defects in nematic liquid crystals

Mixtures of nematic liquid crystals (LCs) were produced by doping small quantities of gold nanoparticles coated with non-chiral hexane- (Au1), dodecane- (Au2) or chiral Naproxen-functionalized dodecane thiolates (Au3, Au4). Circular dichroism (CD) spectroscopy confirmed the optical activity for both Naproxen-functionalized gold nanoclusters. The small CD measured for Au1 and Au2 as well as the weak CD above 400 nm measured for Au3 and Au4 is attributed to scattering artifacts of dense particles aggregating in solution. For all mixtures, characterization of the nanoparticle doped nematic phase by polarized optical microscopy revealed the formation of uniform stripe textures or patterns separated by areas of homeotropic alignment due to a spatial separation of particle-rich and particle-poor domains. Similar characteristic textures were also observed for mixtures of the chiral nematic phase produced by doping either only the Naproxen-functionalized thiol 3b or Naproxen and additionally dodecane thiolate-protected gold nanoparticles Au2. On the basis of these findings, observed for the first time for alkane thiolate-capped gold nanoclusters doped into nematic LCs, two different scenarios are suggested. In the first scenario, the optically active gold nanoparticles Au3 and Au4 transfer chirality to the non-chiral nematic LC host. In the second scenario, all functionalized gold nanoclusters Au1–Au4 form topological defects resulting in chain-like particle aggregates, separated by areas of homeotropic alignment due to particles residing at the LC–glass interface.

Formation of periodic stripe patterns in nematic liquid crystals doped with functionalized gold nanoparticles

The extraordinary responsiveness and large diversity of self-assembled structures of liquid crystals are well documented and they have been extensively used in devices like displays. For long, this application route strongly influenced academic research, which frequently focused on the performance of liquid crystals in display-like geometries, typically between flat, rigid substrates of glass or similar solids. Today a new trend is clearly visible, where liquid crystals confined within curved, often soft and flexible, interfaces are in focus. Innovation in microfluidic technology has opened for high-throughput production of liquid crystal droplets or shells with exquisite monodispersity, and modern characterization methods allow detailed analysis of complex director arrangements. The introduction of electrospinning in liquid crystal research has enabled encapsulation in optically transparent polymeric cylinders with very small radius, allowing studies of confinement effects that were not easily accessible before. It also opened the prospect of functionalizing textile fibers with liquid crystals in the core, triggering activities that target wearable devices with true textile form factor for seamless integration in clothing. Together, these developments have brought issues center stage that might previously have been considered esoteric, like the interaction of topological defects on spherical surfaces, saddle-splay curvature-induced spontaneous chiral symmetry breaking, or the non-trivial shape changes of curved liquid crystal elastomers with non-uniform director fields that undergo a phase transition to an isotropic state. The new research thrusts are motivated equally by the intriguing soft matter physics showcased by liquid crystals in these unconventional geometries, and by the many novel application opportunities that arise when we can reproducibly manufacture these systems on a commercial scale. This review attempts to summarize the current understanding of liquid crystals in spherical and cylindrical geometry, the state of the art of producing such samples, as well as the perspectives for innovative applications that have been put forward.

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Liquid crystals in micron-scale droplets, shells and fibers

Molecular dynamics is used to simulate nematic liquid crystal structures confined to a submicron cylindrical cavity. Molecules, fixed at the lattice points, are set to interact via a modified induced-dipole--induced-dipole type coupling. Stability regions of characteristic nematic structures are determined as functions of the cylinder radius, homeotropic anchoring strength, and degree of the interaction anisotropy. A connection linking elastic and microscopic approaches is established. Results confirm most of the predictions of the elastic free energy deep in the submicron regime.

Molecular dynamics study of nematic structures confined to a cylindrical cavity

The annihilation of the nematic hedgehog and anti-hedgehog within an infinite cylinder of radius R is studied. The semi-microscopic lattice-type model and Brownian molecular dynamics are used. We distinguish among the i) early pre-collision, ii) late pre-collision, iii) early post-collision, and iv) late post-collision stages. In the pre-collision stage our results agree qualitatively with the existing experimental observations and also continuum-type simulations. The core of each defect exhibits a ring-like structure, where the ring axis is set perpendicular to the cylinder symmetry axis. For ξ(0)d/(2R) > 1 the interaction between defects is negligible, where ξ(0)d describes the initial separation of defects. Consequently, the defects annihilate within the simulation time window for ξ(0)d/(2R) < 1. For close enough defects their separation scales as ξd $ \varpropto$
 (tc - t)0.4±0.1, where tc stands for the collision time. In elastically anisotropic medium the hedgehog is faster than the anti-hedgehog. In the early pre-collision stage the defects can be treated as point-like particles, possessing inherent core structure, that interact via the nematic director field. In the late pre-collision stage the cores reflect the interaction between defects. After the collision a charge-less ring structure is first formed. In the early post-collision stage the ring adopts an essentially untwisted circular structure of the radius ξr. In the late post-collision stage we observe two qualitatively different scenarios. For μ = ξr/R μc the chargeless ring triggers the nucleation growth into the planar polar structure with line defects.

Annihilation of nematic point defects: Pre-collision and post-collision evolution

Effects of cylindrical and spherical confinement on the kinetics of the isotropic-nematic quench is studied numerically. The nematic liquid crystal structure was modeled by a modified induced-dipole\char21{}induced-dipole interaction. Molecules were allowed to wander around points of a hexagonal lattice. Brownian molecular dynamics was used in order to access macroscopic time scales. In the bulk we distinguish between the early, domain, and late stage regime. The early regime is characterized by the exponential growth of the nematic uniaxial order parameter. In the domain regime domains are clearly visible and the average nematic domain size ${\ensuremath{\xi}}_{d}$ obeys the dynamical scaling law ${\ensuremath{\xi}}_{d}\ensuremath{\sim}{t}^{\ensuremath{\gamma}}.$ The late stage evolution is dominated by dynamics of individual defects. In a confined system the qualitative change of the scaling behavior appears when ${\ensuremath{\xi}}_{d}$ becomes comparable to a typical linear dimension R of the confinement. In the confining regime $({\ensuremath{\xi}}_{d}g~R)$ the scaling coefficient \ensuremath{\gamma} depends on the details of the confinement and also the final equilibrium nematic structure. The domain growth is well described with the Kibble-Zurek mechanism.

Molecular dynamics study of the isotropic-nematic quench.

We study numerically the early stage domain coarsening dynamics of the temperature driven isotropic-nematic (I-N) liquid crystal phase transition. System of rod like objects which interact via the modified Lebwohl-Lasher pairwise interaction is considered in 3D. The coarsening dynamics is followed using Brownian molecular dynamics. The box-restricted lattice point fluctuations are allowed in order to get rid of lattice geometry enforced phenomena. We analyze order parameter growth and domain coarsening in the early regime of the I-N phase transition as a function of the quench rate. We show that soon after the transition bimodal distribution of domains appears, where the shorter branch gradually vanishes. The behavior of the system is in accordance with predictions of the Kibble-Zurek mechanism which was originally introduced to model conditions in the early universe.

Early stage domain coarsening of the isotropic-nematic phase transition.

We study the influence of nanoparticles (NPs) on liquid crystal (LC) ordering. As regards the structural ordering we consider NPs as a source of a quenched random field. Roughly such a situation is encountered in mixtures of LCs and aerosil NPs (aerosil NPs are spherular ones). Using the semi-microscopic lattice model and Brownian molecular simulation we show that after a quench from the isotropic phase a quasi-stable domain pattern forms. The characteristic size of an average domain is inversely proportional to the concentration of NPs, and domain patterns exhibit memory effects. In the study of the phase behaviour we limit consideration to NPs resembling LC molecules. A Landau-type free energy expression is derived for the mixture, originating from the Maier‐Saupe molecular approach. We show that the resulting phase behaviour exhibits the slave–master behaviour as the temperature or pressure is varied.

Z. Bradač

Papers

Molecular dynamics study of nematic structures confined to a cylindrical cavity

Annihilation of nematic point defects: Pre-collision and post-collision evolution

Molecular dynamics study of the isotropic-nematic quench.

Early stage domain coarsening of the isotropic-nematic phase transition.

The influence of nanoparticles on the phase and structural ordering for nematic liquid crystals