Topological defect transformation and structural transition of two-dimensional colloidal crystals across the nematic to smectic-A phase transition

Topological Defect Guided Order Evolution across the Nematic-Smectic Phase Transition

Topological defects usually emerge and vary during the phase transition of ordered systems. Their roles in thermodynamic order evolution keep being the frontier of modern condensed matter physics. Here, we study the generations of topological defects and their guidance on the order evolution during the phase transition of liquid crystals (LCs). With a given preset photopatterned alignment, two different types of topological defects are achieved depending on the thermodynamic process. Because of the memory effect of LC director field across the Nematic-Smectic (N-S) phase transition, a stable array of toric focal conic domains (TFCDs) and a frustrated one are generated in S phase, respectively. The frustrated one transfers to a metastable TFCD array with a smaller lattice constant, and further changes to a crossed-walls type N state due to the inheritance of orientational order. A free energy on temperature diagram and corresponding textures vividly describe the phase transition process and the roles of topological defects in the order evolution across the N-S phase transition. This Letter reveals the behaviors and mechanisms of topological defects on order evolution during phase transitions. It paves a way for investigating topological defect guided order evolution which is ubiquitous in soft matter and other ordered systems.

The fate of liquid crystal topological defects on chemically patterned surfaces during phase transitions

Controlling topological defects in liquid crystals (LCs) is an essential element in the development of areas such as directed self-assembly and micropatterning materials. However, during the phase transition on confined patterned surfaces, how the morphologies in one liquid crystalline phase change from deformations or defects into another phase is much less known. Here, we examine the fate of defects in a LC confined on a patterned surface during smectic-A-nematic and nematic-isotropic phase transitions, using experiments and simulation analyses. Upon heating from smectic-A to nematic, a Toric focal conical domain (TFCD) melts into a +1 converging boojum defect, which then transitioned into a concentric configuration as temperature increases, attributed to a steeper decrease of the bend and twist modulus compared to splay modulus. During cooling, TFCDs are developed from two distinct pathways depending on the cooling rates. Our continuum simulation recapitulates these transformations and provides elastic constant-based explanations for the two pathways. Although the phase transition pathways of defects are independent of the geometry of the confined patterns, the arrangement of FCDs is highly dependent on the size and shape of the patterns. Taken together, this simple approach offers promising opportunities for tuning the micro- or nano-patterning of topological defects in liquid crystals.

Interactions of charged microrods in chiral nematic liquid crystals

We study the pair interaction of charged silica microrods in chiral nematic liquid crystals and show that the microrods with homeotropic surface anchoring form a bound state due to the competing effect of electrostatic (Coulomb) and elastic interactions. The robustness of the bound state is demonstrated by applying external electrical and mechanical forces that perturbs their equilibrium position as well as orientation. In the bound state we have measured the correlated thermal fluctuations of the position, using two-particle cross-correlation spectroscopy that uncovers their hydrodynamic interaction. These findings reveal unexplored aspects of liquid-crystal dispersions which are important for understanding the assembly and dynamics of nano- and microparticles in chiral nematic liquid crystals.

Molecular theory of a ferromagnetic nematic liquid crystal

We employ a version of classical density functional theory to study the phase behavior of a simple model liquid crystal in an external field. The uniaxially symmetric molecules have a spherically symmetric core with superimposed orientation-dependent attractions. The interaction between the cores consists of a hard-sphere repulsion plus an isotropic square-well attraction. The anisotropic part of the interaction potential allows for the formation of a uniaxially symmetric nematic phase. The orientation of the molecules couples to an external polar field. The external field is capable of rotating the nematic director n[over ̂] in the x-z plane. The field is also capable of changing the topology of the phase diagram in that it suppresses the phase coexistence between an isotropic liquid and a nematic phase observed in the absence of the field. We study the transition from an unpolar to a polar nematic phase in terms of the orientation-distribution function (odf), nematic and polar order parameters, and components of n[over ̂]. If represented suitably the odf allows us to study orientational changes during the switching process between nonpolar and polar nematic phases. We also give a simple argument that explains why nematic order is lost whereas polar order persists up to the gas-liquid critical point along the coexistence curve. We also discuss the relevance of our theory for future experimental studies.

Colloidal analogues of polymer chains, ribbons and 2D crystals employing orientations and interactions of nano-rods dispersed in a nematic liquid crystal

Robust control over the position, orientation and self-assembly of nonspherical colloids facilitate the creation of new materials with complex architecture that are important from technological and fundamental perspectives. We study orientation, elastic interaction and co-assembly of surface functionalized silica nano-rods in thin films of nematic liquid crystal. With homeotropic boundary condition, the nano-rods are predominantly oriented perpendicular to the nematic director which is different than the mostly parallel orientation of the micro-rods. The percentage of perpendicular nano-rods are significantly larger than the parallel nano-rods. The perpendicular nano-rods create very weak elastic deformation and exhibit unusual, out-of-plane, attractive interaction. On the other hand, the nano-rods oriented parallel to the director create strong elastic deformation and shows anisotropic, in-plane, dipolar interaction. In both orientations, the induced defects reside in the nano-rods. With the help of a dynamic laser tweezers and using nano-rods as building blocks we demonstrate colloidal analogues of linear polymer chains, ribbons and two-dimensional binary crystals.

Orientation, elastic interaction and magnetic response of asymmetric colloids in a nematic liquid crystal

Colloidal particles in nematic liquid crystals create elastic distortion and experience long-range forces. The symmetry of elastic distortion and consequently the complexity of interaction strongly depends largely on the liquid crystal anchoring, topology and shape of the particles. Here, we introduce a new nematic colloidal system made of peanut-shaped hematite particles. We report experimental studies on spontaneous orientation, mutual interaction, laser assisted self-assembly and the effect of external magnetic fields on the colloids. Majority of the colloids spontaneously orient either parallel or perpendicular to the nematic director. The colloids that are oriented perpendicularly exhibit two types of textures due to the out of plane tilting, which is corroborated by the Landau-de Gennes Q-tensor modelling. The transverse magnetic moment of the peanut-shaped colloids is estimated by using a simple analysis based on the competing effects of magnetic and elastic torques.

N-SmA-SmC phase transitions probed by a pair of elastically bound colloids

The competing effect of surface anchoring of dispersed microparticles and elasticity of nematic and cholesteric liquid crystals has been shown to stabilize a variety of topological defects. Here we study a pair of colloidal microparticles with homeotropic and planar surface anchoring across N-SmA-SmC phase transitions. We show that below the SmA-SmC phase transition the temperature dependence of interparticle separation (D) of colloids with homeotropic anchoring shows a power-law behavior; D∼(1-T/T_{AC})^{α}, with an exponent α≈0.5. For colloids with planar surface anchoring the angle between the joining line of the centers of the two colloids and the far field director shows characteristic variation elucidating the phase transitions.

Morphogenesis of liquid crystal topological defects during the nematic-smectic A phase transition

The liquid crystalline phases of matter each possess distinct types of defects that have drawn great interest in areas such as topology, self-assembly and material micropatterning. However, relatively little is known about how defects in one liquid crystalline phase arise from defects or deformations in another phase upon crossing a phase transition. Here, we directly examine defects in the in situ thermal phase transition from nematic to smectic A in hybrid-aligned liquid crystal droplets on water substrates, using experimental, theoretical and numerical analyses. The hybrid-aligned nematic droplet spontaneously generates boojum defects. During cooling, toric focal conic domains arise through a sequence of morphological transformations involving nematic stripes and locally aligned focal conic domains. This simple experiment reveals a surprisingly complex pathway by which very different types of defects may be related across the nematic–smectic A phase transition, and presents new possibilities for controlled deformation and patterning of liquid crystals.

Defects in liquid crystals play a central role in determining their structural and dynamic properties, whilst it is challenging to characterize the defects at a molecule level. Here, Gim et al. trace the evolution pathway of defects during a phase transition from a nematic to a smectic state.

The Impact of Colloidal Surface-Anchoring on the Smectic A Phase

Liquid-crystalline phases are known for their unique properties, i.e., the combination of fluidity and long-range orientational and/or positional order. The presence of a colloidal particle gives rise to perturbations of this order locally. These perturbations are the origin of intercolloidal forces driving the colloidal self-assembly in a directed manner. Hence, the understanding of these perturbations is the first step in understanding and controlling the self-assembly process. Here, we perform Monte Carlo simulations to investigate the perturbations of orientational and positional order in a smectic A phase caused by a spherical colloid. We model the host phase via an interaction potential that reproduces characteristic features of phase behavior, structure, dynamics, and elasticity [S. Püschel-Schlotthauer et al. J. Chem. Phys. 2016, 145, 164903]. For strong homeotropic anchoring conditions, we find a Saturn ring defect and an onion structure in the smectic A phase; the latter has never been reported for colloids so far. For strong planar anchoring conditions, we find Boojum defects that become elongated at low temperature, similar to what is observed in experiments. However, for weak planar anchoring conditions, a double surface ring defect is exhibited in the smectic A phase.

Magnetic-field tuning of whispering gallery mode lasing from ferromagnetic nematic liquid crystal microdroplets

We report magnetic field tuning of the structure and Whispering Gallery Mode lasing from ferromagnetic nematic liquid crystal micro-droplets. Microlasers were prepared by dispersing a nematic liquid crystal, containing magnetic nanoparticles and fluorescent dye, in a glycerol-lecithin matrix. The droplets exhibit radial director structure, which shows elastic distortion at a very low external magnetic field. The fluorescent dye doped ferromagnetic nematic droplets show Whispering Gallery Mode lasing, which is tunable by the external magnetic field. The tuning of the WGM lasing modes is linear in magnetic field with a wavelength-shift of the order of 1 nm/100 mT. Depending on the lasing geometry, the WGMs are red- or blue-shifted.

A novel model for smectic liquid crystals: Elastic anisotropy and response to a steady-state flow

By means of a combination of equilibrium Monte Carlo and molecular dynamics simulations and nonequilibrium molecular dynamics we investigate the ordered, uniaxial phases (i.e., nematic and smectic A) of a model liquid crystal. We characterize equilibrium behavior through their diffusive behavior and elastic properties. As one approaches the equilibrium isotropic-nematic phase transition, diffusion becomes anisotropic in that self-diffusion D_⊥ in the direction orthogonal to a molecule's long axis is more hindered than self-diffusion D_∥ in the direction parallel to that axis. Close to nematic-smectic A phase transition the opposite is true, D_∥ < D_⊥. The Frank elastic constants K₁, K₂, and K₃ for the respective splay, twist, and bend deformations of the director field n̂ are no longer equal and exhibit a temperature dependence observed experimentally for cyanobiphenyls. Under nonequilibrium conditions, a pressure gradient applied to the smectic A phase generates Poiseuille-like or plug flow depending on whether the convective velocity is parallel or orthogonal to the plane of smectic layers. We find that in Poiseuille-like flow the viscosity of the smectic A phase is higher than in plug flow. This can be rationalized via the velocity-field component in the direction of the flow. In a sufficiently strong flow these smectic layers are not destroyed but significantly bent.

Effect of temperature and electric field on 2D nematic colloidal crystals stabilised by vortex-like topological defects

We report experimental studies on 2D colloidal crystals of dimers stabilized by vortex-like defects in planar nematic and π/2 twisted nematic cells. The dimers are prepared and self-assembled using a laser tweezer. We study the effect of temperature and electric field on the lattice parameters of the colloidal crystals. The lattice parameters vary with the temperature in the nematic phase and a discontinuous structural change is observed at the nematic to smectic-A phase transition. In the nematic phase, we observed a large change in the lattice parameters (≃30%) by applying an external electric field perpendicular to the plane of the 2D crystals. The idea and the active control of the lattice parameters could be useful for designing tunable colloidal crystals.

Spherical microparticles with Saturn ring defects and their self-assembly across the nematic to smectic-A phase transition

We report experimental studies on the Saturn ring defect associated with a spherical microparticle across the nematic (N) to smectic-A (SmA) phase transition. We observe that the director distortion around the microparticle changes rapidly with temperature. The equilibrium interparticle separation and the angle between two quadrupolar particles in the N phase are larger than those of the SmA phase. They are almost independent of the temperature in both phases, except for a discontinuous jump at the transition. We assembled a few particles using a laser tweezer to form a two-dimensional colloidal crystal in the N phase. The lattice structure of the crystal dissolves irreversibly across the N-SmA phase transition. The results on the pretransitional behavior of the defect are supported by the Landau-de Gennes Q-tensor modeling.

Orientation, interaction and laser assisted self-assembly of organic single-crystal micro-sheets in a nematic liquid crystal

Colloidal self-assembly has been one of the major driving themes in material science to obtain functional and advanced optical materials with complex architecture. Most of the nematic colloids reported so far are based on the optically isotropic spherical microparticles. We study organic single crystal micro-sheets and investigate their orientation, interaction and directed assembly in a nematic liquid crystal. The micro-sheets induce planar surface anchoring of the liquid crystal. The elasticity mediated pair interaction of micro-sheets shows quadrupolar characteristics. The average orientation angle of the micro-sheets in a planar cell and the angle between two micro-sheets in a homeotropic cell are supported by the Landau-de Gennes Q-tensor modeling. The self-assembly of the micro-sheets is assisted by a laser tweezer to form larger two-dimensional structures which have the potential for application of colloids in photonics.