Manipulation of m = 1 topological disclination line core structure

There is considerable interest in the dynamics of topological defects formed during a symmetry breaking phase transition in fields as diverse as condensed matter physics, particle physics and cosmology. Liquid crystals, with their many symmetry breaking phase transitions are ideal materials for such studies. Here we report on light transmission studies of the coarsening of three-dimensional defect tangles in uniaxial nematic liquid crystals subjected to a sudden pressure jump from the isotropic phase to the nematic phase. We have verified that the type 1/2 disclination line density, as a function of time, scales as t−v with v = 1.0 ± 0.1 over four decades in time. The transmitted light intensity exhibits two distinct scaling regimes depending on whether propagation without scattering or diffusive propagation with multiple scattering dominates the light reaching the detector.

We report two viable strategies to assemble and manipulate arrays of nano- and micro-particles by means of topological defects (TDs) in anisotropic fluids. Exploiting different boundary conditions, single TD, 1D arrays of TDs are tailored in liquid crystal twist cells. In a first approach, light-guided control of particles captured in disclination lines is demonstrated involving the use of a photosensitive chiral dopant within a nematic host. In the second one, an applied voltage enables a continuous displacement and deformation of the particles arrays. The reported results open up new possibilities for managing nano- and micro-metric objects over large distances.

Topological defects (TDs) in liquid crystals may have their locations experimentally altered by locally distorting the liquid crystalline (LC) order, e.g., by the melting induced by optical tweezers. In this research, we investigated the nematic ordering profiles and accompanying topological defect configurations in thin nematic liquid crystalline shells that are subject to externally forced local LC order distortions. We show that inside curved LC films these manipulations are greatly influenced by local Gaussian curvature if it displays strong spatial variability. We use a mesoscopic model in which the curvature of the surface and the nematic order parameter tensor serve to explain the shell geometry and LC orientational order. We demonstrate that TDs are rather tightly "glued" to a local Gaussian curvature on increasing the prolateness of shells. Keywords: Topological defects; Liquid crystals; Distortions; Gaussian curvature; Prolate shells

Liquid crystals are starting to attract attention for applications beyond the display technology. Their high birefringence, softness, and possibility to form complex topological defect structures allow for easy light manipulation in systems ranging from cholesteric lasers to droplet resonators and wave guides. Recent interest in light-induced topological defects and light propagation along the defects stimulated us to develop a customized version of the Finite-Difference Time-Domain (FDTD) method for solving Maxwell's equations on a discrete time and space lattice. Here, we present an overview of our recent simulations, modeling the time-evolution of electromagnetic fields along birefringent structures in nematic liquid crystals, specifically light propagation along nematic defect lines. In the regime of high light intensity beams the modelling approach includes also a light induced modification of local nematic ordering obtained via a qtensor free energy minimization procedure. We show how topological invariants of the nematic and polarization fields combine and also affect the beam intensity profile. Finally, off-axis propagation of beams with respect to the defect lines is considered.

This review discusses static properties of topological defects, such as line defectsdisclinations and dislocations, point defects — hedgehogs (monopoles) and boojums; focal conic domains and tilt grain boundaries in basic types of liquid crystals: uniaxial and biaxial nematics, cholesterics and smectics. We present the most popular experimental techniques to study defects in soft matter, namely, polarizing microscopy and fluorescence confocal polarizing microscopy. The role of bounding surfaces and the so-called surface anchoring that lifts the degeneracy of the order parameter in stability of defects is discussed. Because of the surface anchoring, the equilibrium state of a bounded liquid crystal might contain topological defects. For example, nematic bubbles nucleating during the first-order phase transition from the isotropic melt, might contain point defects (hedgehogs and boojums) and disclination loops when their size is larger than the anchoring extrapolation length defined by the ratio of the Frank elastic constant of the director curvature and the (polar) anchoring coefficient. Depending on the strength of surface anchoring, an edge dislocation might be expelled from the system with ID positional order or be stabilized in the bulk. Furthermore, focal conic domains play the role of “surface anchoring facets” by providing the necessary orientation of the liquid crystal director at the smectic boundary.

Smectic liquid crystals exhibit a remarkable ability to self-organize into a variety of textures, patterns, and arrays extending over large surface areas with microscale periodicity. These structures provide a useful platform for the bottom-up fabrication of microdevices and functional materials, such as microlens arrays and nanoparticle templates. Periodic structures appear in response to a conflict of director alignment created within the smectic film by external fields such as hybrid (planar-homeotropic) anchoring conditions at the film interfaces or an electric field applied normal to the surface anchoring direction. In this article, we review the formation, structure, and applications of one-dimensional (1d) patterns obtained in response to a director bend, typically induced by unidirectional hybrid anchoring conditions in thin films or under applied electric fields. Compared to lattices of focal conics, 1d patterns harbor an unusual array of topological defects, including disclination and dislocation lines, grain boundaries, and curvature walls, running along periodically spaced and bend-free cylindrical stacks of smectic layers. These defects, most of which have been described by Maurice Kleman, appear to drive the structural evolution of 1d patterns as a function of the film thickness. Under unidirectional hybrid anchoring, the defects are oriented perpendicular to the planar anchoring direction and provide highly anisotropic templates for building ordered networks of close-packed nanoparticles. Moreover, the array formation at the transition from the nematic to the smectic phase is intimately connected to the smectic phase frustration by bend distortions, producing an ‘intermediate’ smectic phase with partial penetration of the bend distortion through undercooled nematic domains.

We explore the structure of nuclei and topological defects in the first-order phase transition between the nematic (N) and isotropic (I) phases in lyotropic chromonic liquid crystals (LCLCs). The LCLCs are formed by self-assembled molecular aggregates of various lengths and show a broad biphasic region. The defects emerge as a result of two mechanisms: (1) surface-anisotropy that endows each N nucleus (‘tactoid’) with topological defects thanks to preferential (tangential) orientation of the director at the closed I–N interface, and (2) Kibble mechanism with defects forming when differently oriented N tactoids merge with each other. Different scenarios of phase transition involve positive (N-in-I) and negative (I-in-N) tactoids with nontrivial topology of the director field and also multiply connected tactoid-in-tactoid configurations. The closed I–N interface limiting a tactoid shows a certain number of cusps; the lips of the interface on the opposite sides of the cusp make an angle different from π. The N side of each cusp contains a point defect-boojum. The number of cusps shows how many times the director becomes perpendicular to the I–N interface when one circumnavigates the closed boundary of the tactoid. We derive conservation laws that connect the number of cusps c to the topological strength m of defects in the N part of the simply connected and multiply connected tactoids. We demonstrate how the elastic anisotropy of the N phase results in non-circular shape of the disclination cores. A generalized Wulff construction is used to derive the shape of I and N tactoids as a function of I–N interfacial tension anisotropy in the approximation of frozen director field of various topological charges m. The complex shapes and structures of tactoids and topological defects demonstrate an important role of surface anisotropy in morphogenesis of phase transitions in liquid crystals.

Topological defects are a universal concept across many disciplines, such as crystallography, liquid-crystalline physics, low-temperature physics, cosmology, and even biology.In nematic liquid crystals, topological defects called disclinations have been widely studied.For their three-dimensional (3D) dynamics, however, only recently have theoretical approaches dealing with fully 3D configurations been reported.Further, recent experiments have observed 3D disclination line reconnections, a phenomenon characteristic of defect line dynamics, but detailed discussions were limited to the case of approximately parallel defects.In this paper, we focus on the case of two disclination lines that approach at finite angles and lie in separate planes, a more fundamentally 3D reconnection configuration.Observing and analyzing such reconnection events, we find the square-root law of the distance between disclinations and the decrease of the interdisclination angle over time.We compare the experimental results with theory and find qualitative agreement on the scaling of distance and angle with time, but quantitative disagreement on distance and angle relative mobilities.To probe this disagreement, we derive the equations of motion for systems with reduced twist constant and also carry out simulations for this case.These, together with the experimental results, suggest that deformations of disclinations may be responsible for the disagreement.

Active colloids and liquid crystals are capable of locally converting the macroscopically supplied energy into directional motion and promise a host of new applications, ranging from drug delivery to cargo transport at the mesoscale. Here we uncover how topological solitons in liquid crystals can locally transform electric energy to translational motion and allow for the transport of cargo along directions dependent on frequency of the applied electric field. By combining polarized optical video microscopy and numerical modeling that reproduces both the equilibrium structures of solitons and their temporal evolution in applied fields, we uncover the physical underpinnings behind this reconfigurable motion and study how it depends on the structure and topology of solitons. We show that, unexpectedly, the directional motion of solitons with and without the cargo arises mainly from the asymmetry in rotational dynamics of molecular ordering in liquid crystal rather than from the asymmetry of fluid flows, as in conventional active soft matter systems.

It is with great pleasure that we present this special issue focused on topological structures in ferroic materials. It is composed of invited contributions from the International Workshop on Topological Structures in Ferroic Materials held at the University of South Wales, Sydney, Australia from 19-21 st May 2015. The aim of the workshop was to capture current research interests regarding interfaces, domains, domain walls, vortices and skyrmions in ferroics as an emerging and highly active fi eld in solid state physics and materials science. Signifi cant emphasis was placed on understanding the fundamental commonalities that bridge topological defects across various types of ferroic materials, and therefore lessons learned on how new and groundbreaking functionalities afforded by the aforementioned concepts could be translated into emerging technologies.

Our understanding of the mechanism by which topological defects are formed in symmetry breaking phase transitions has recently changed. We examine the non-equilibrium dynamics of defect formation for weakly-coupled global O(N) theories possessing vortices (strings) and monopoles. It is seen that, as domains form and grow, defects are swept along on their boundaries at a density of about one defect per coherence area (strings) or per coherence volume (monopoles).

Undergraduate labs teaching solid state physics usually do not encompass experiments that lie in the domain of `soft materials '- materials that have large response functions and dramatic visco-elastic responses. One of the most exciting topics in soft condensed matter is liquid crystals. From calculators to computer screens, liquid crystal (LC) based displays are ubiquitous today. Liquid crystals can flow like a liquid but their molecules show some degree of orientational order like a crystalline solid. They possess special properties like birefringence, and under an applied electric field, liquid crystal molecules develop induced dipole moments and therefore tend to align with the applied field (Fréedericksz transition). Because of these special characteristics, liquid crystals have found use in a wide variety of applications. In this work, we outline a simple undergraduate lab project that brings the exciting world of liquid crystals to the level of physics and chemistry undergraduates. We discuss in detail the fabrication of a liquid crystal-based temperature sensor and a one-pixel liquid crystal display that can be easily made in an undergraduate teaching lab. While the one-pixel display can succinctly illustrate the principles of an LCD screen to an undergraduate student, the LC based temperature sensor can be utilized to develop smart clothing, biomedical devices and flexible sensors. In designing the experiments, special care has been taken to keep the cost within the reach of undergraduate teaching labs in developing countries.

Swelling behaviour of poly(butadiene) gels in liquid crystal solvents

Domain walls are topological defects which occur at symmetry-breaking phase transitions. While domain walls have been intensively studied in ferromagnetic materials, where they nucleate at the boundary of neighbouring regions of oppositely aligned magnetic dipoles, their equivalent in optics have not been fully explored so far. Here, we experimentally demonstrate the existence of a universal class of polarization domain walls in the form of localized polarization knots in conventional optical fibres. We exploit their binding properties for optical data transmission beyond the Kerr limits of normally dispersive fibres. In particular, we demonstrate how trapping energy in well-defined train of polarization domain walls allows undistorted propagation of polarization knots at a rate of 28 GHz along a 10 km length of normally dispersive optical fibre. These results constitute the first experimental observation of kink-antikink solitary wave propagation in nonlinear fibre optics.

Cosmic strings are generic cosmological predictions of many extensions of the standard model of particle physics, such as a $U(1{)}^{\ensuremath{'}}$ symmetry-breaking phase transition in the early Universe or remnants of superstring theory. Unlike other topological defects, cosmic strings can reach a scaling regime that maintains a small fixed fraction of the total energy density of the Universe from a very early epoch until today. If present, they will oscillate and generate gravitational waves with a frequency spectrum that imprints the dominant sources of total cosmic energy density throughout the history of the Universe. We demonstrate that current and future gravitational wave detectors, such as LIGO and LISA, could be capable of measuring the frequency spectrum of gravitational waves from cosmic strings and discerning the energy composition of the Universe at times well before primordial nucleosynthesis and the cosmic microwave background where standard cosmology has yet to be tested. This work establishes a benchmark case that gravitational waves may provide an unprecedented, powerful tool for probing the evolutionary history of the very early Universe.