Twisted Wall Research Articles

Collective variable model for the dynamics of liquid crystal skyrmions

Liquid crystal skyrmions are topologically protected spatially-localized distortions of the director field which exhibit particle-like properties including translational motion in oscillating electric fields. Here, we develop a collective variable model of the skyrmion dynamics, extending the approach of Long and Selinger proposed earlier for one dimensional systems. The model relates the skyrmion motion to a complex dynamics of the width of the twist wall around the skyrmion core. The width evolves in a non-reciprocal way, quantifying squirming deformations of the high twist region within on and off states of the field. We analyze in details the average skyrmion velocity as a function of the frequency and strength of the field as well as its duty cycle. The model predictions agrees qualitatively with experiments and results of numerical minimization of the Frank-Oseen model. Our results provide insights into the conditions necessary to observe velocity reversal as a function of the field parameters.

Homochiral Nanopropeller via Chiral Active Surface Growth.

Under the control of chiral ligand glutathione and in the presence of hexadecyltrimethylammonium bromide, Au deposition on Au seeds is known to give chiral nanostructures. We have previously shown that the protruding chiral patterns, as opposed to flat facets, are likely caused by active surface growth, where nonuniform ligand coverage could be responsible for the focused growth at a few active sites. By pushing the limit of such a growth mode, here, we use decahedral seeds to prepare homochiral nanopropellers with intricate patterns of deep valleys and protruding ridges. Control experiments show that the focused growth depends on the rates of Au deposition by changing either the seed concentration or the reductant concentration, consistent with the proposed mechanism. The dynamic growth competition between the ligand-deficient active sites and the ligand-rich surfaces gradually focuses the growth onto a few active sites, causing the expansion of grooves, squeezing of steep ridges, and a surprising 36° rotation of the pentagonal outline. The imbalanced deposition on the prochiral slopes is responsible for the tilted grooves, the twisted walls, and thus the well-separated and distorted blades, which become the origin of the chiroptical responses.

Topological solitons in chiral liquid crystals

ABSTRACT Topological solitons are quasi-particles of field deformations that are topologically nontrivial. Conceptualised by celebrated mathematicians and scientists including Carl Friedrich Gauss, Lord Kelvin, and Tony Skyrme, the ideas of knots, topology, and solitons have found a wealth of experimental embodiments in chiral liquid crystals in recent years. This is largely due to the exceptional capacity of the material for stabilising, characterising, and controlling topological solitons. In this review, I report the recent progress in realising and characterising topological solitons in chiral liquid crystals. Following the homotopy classification, I begin with the 1D twist walls and subsequently introduce 2D skyrmions and skyrmion bags, followed by 3D Hopf solitons including both hopfions and heliknotons. Physical properties of topological solitons are discussed, which include stability, soliton–soliton interaction, field-controlled transformation, field-activated dynamics, and crystalline self-assembly. Finally, the review ends by illustrating how liquid-crystal solitons can provide insights into topological solitons in other physical systems, and perspectives of future studies on the subject. The purpose of this review is to provide a fundamental overview of topological solitons in chiral liquid crystals.

Chiral fluid membranes with orientational order and multiple edges.

We carry out Monte Carlo simulations on fluid membranes with orientational order and multiple edges in the presence and absence of external forces. The membrane resists bending and has an edge tension, the orientational order couples with the membrane surface normal through a cost for tilting, and there is a chiral liquid crystalline interaction. In the absence of external forces, a membrane initialized as a vesicle will form a disk at low chirality, with the directors forming a smectic-A phase with alignment perpendicular to the membrane surface except near the edge. At large chirality a catenoid-like shape or a trinoid-like shape is formed, depending on the number of edges in the initial vesicle. This shape change is accompanied by cholesteric ordering of the directors and multiple π walls connecting the membrane edges and wrapping around the membrane neck. If the membrane is initialized instead in a cylindrical shape and stretched by an external force, it maintains a nearly cylindrical shape but additional liquid crystalline phases appear. For large tilt coupling and low chirality, a smectic-A phase forms where the directors are normal to the surface of the membrane. For lower values of the tilt coupling, a nematic phase appears at zero chirality with the average director oriented perpendicular to the long axis of the membrane, while for nonzero chirality a cholesteric phase appears. The π walls are tilt walls at low chirality and transition to twist walls as chirality is increased. We construct a continuum model of the director field to explain this behavior.

Intensified single-phase forced convective heat transfer with helical-twisted tube in coil heat exchangers

The twisting structure is proposed to enhance the thermal performance of a coil heat exchanger equipped with the helical tube. Actually, it intensifies the fluid mixing and breaks continuously increased thickness of thermal boundary layers. Firstly, experiments are conducted on a smooth helical tube, and the obtained results are validated using correlations proposed by other researchers. A reasonable agreement within ±7% is detected. Then, simulations are carried out to apprise the benefits of helical-twisted tube as compared to the original geometry, i.e. helical tube. It is found that the twisted walls prevent the development of thermal boundary layers through the flow direction and change continuously the location and strength of generated secondary flows and velocity contours, leading to more uniform temperature. At the studied range of Reynolds number (600 ≤ Re ≤ 1200), the Nusselt number enhancement of 14.2% and the friction factor augmentation of 7.7% are recorded for a model at middle levels of design parameters. Finally, a parametrization analysis is performed to find the effects of each specific design parameter (helical-diameter, helical-pitch, and twist-pitch). It is observed that the helical-diameter has the highest impacts on thermal–hydraulic characteristics of the helical-twisted tube, and the twist-pitch and helical-pitch come in the second and third, respectively. The overall hydrothermal performance improves as both the helical-diameter and the twist-pitch are decreased. The maximum performance index of 1.98 is obtained for the model with the helical-diameter of 50 mm at the Reynolds number of 900.

Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers, and their hybrids in chiral nematics.

Chiral condensed matter systems, such as liquid crystals and magnets, exhibit a host of spatially localized topological structures that emerge from the medium's tendency to twist and its competition with confinement and field coupling effects. We show that the strength of perpendicular surface boundary conditions can be used to control the structure and topology of solitonic and other localized field configurations. By combining numerical modeling and three-dimensional imaging of the director field, we reveal structural stability diagrams and intertransformation of twisted walls and fingers, torons, and skyrmions and their crystalline organizations upon changing boundary conditions. Our findings provide a recipe for controllably realizing skyrmions, torons, and hybrid solitonic structures possessing features of both of them, which will aid in fundamental explorations and technological uses of such topological solitons. Moreover, we discuss how other material parameters can be used to determine soliton stability and how similar principles can be systematically applied to other liquid crystal solitons and solitons in other material systems.

Electric field-induced structural transition of domain walls in nanoconfined nematic liquid crystal systems

ABSTRACTThe electric field-induced structural transition of domain walls in nanoconfined nematic liquid crystal systems was investigated on the basis of Landau–de Gennes theory. Two models of nanoconfined domain wall systems were established as splay–bend and twist wall systems under Fréedericksz transitions with two different rotation directions under the effect of electric field E/E0. Results showed that two structural transition processes occur in both models. Pincement transition occurs under a critical external field Ec1/E0. In pincement transition, walls change into two squeezed symmetric surface defects with opposite charges. Surface defects spread along the direction of the substrates and attain surface order reconstruction states as E/E0 is enhanced to Ec2/E0. The increment in cell gap d from the nanoscale to the microscale will not affect Ec2/E0 in both models.

P-148: 3D Modelling of Twist Wall at the Electrode Edge of Liquid Crystal Cells

Q-tensor simulation of the liquid crystal structure at the edge of electrodes has been carried out. The modeling shows a twist wall, which reverses direction to form a zig-zag structure. The results are compared with experiment. Also a defect loop is found in micro-lenses formed using a hole electrode structure.

Intensification of heat transfer in a liquid film evaporator

AbstractInfluence of the heat exchanger shape on the heat transfer efficiency investigated. Heat transfer efficiency of two vertical pipe-in-pipe heat exchangers, one with a straight wall and the other with a twisted wall were compared. Both heat exchangers worked on the principle of liquid falling film. Electric transformer oil was used as the heated liquid and water vapor at atmospheric pressure was used as the heating agent. Oil was just heated, not evaporated during the experiments. Oil inlet and outlet temperature were measured at six different oil mass flows. Heat flux and heat flux density in the straight- and twisted-wall heat exchangers were compared. Mathematical model was built to verify the possibility of the oil outlet temperature prediction.

Colloidal membranes of hard rods: unified theory of free edge structure and twist walls.

Monodisperse suspensions of rod like chiral fd viruses are condensed into a rod-length thick colloidal monolayers of aligned rods by depletion forces. Twist deformations of the molecules are expelled to the monolayer edge as in a chiral smectic A liquid crystal, and a cholesteric band forms at the edge. Coalescence of two such isolated membranes results in a twist wall sandwiched between two regions of aligned rods, dubbed π-walls. By modeling the membrane as a binary fluid of coexisting cholesteric and chiral smectic A liquid-crystalline regions, we develop a unified theory of the π-walls and the monolayer edge. The mean-field analysis of our model yields the molecular tilt profiles, the local thickness change, and the crossover from smectic to cholesteric behavior at the monolayer edge and across the π-wall. Furthermore, we calculate the line tension associated with the formation of these interfaces. Our model offers insights regarding the stability and the detailed structure of the π-wall and the monolayer edge.

Propulsion Efficiency of a Dynamic Self-Assembled Helical Ribbon

We study the dynamic self-assembly and propulsion of a ribbon formed from paramagnetic colloids in a dynamic magnetic field. The sedimented ribbon assembles due to time averaged dipolar interactions between the beads. The time dependence of the dipolar interactions together with hydrodynamic interactions cause a twisted ribbon conformation. Domain walls of high twist connect domains of nearly constant orientation and negligible twist and travel through the ribbon. The particular form of the domain walls can be controlled via the frequency and the eccentricity of the modulation. The flux of twist walls-a true ribbon property absent in slender bodies-provides the thrust onto the surrounding liquid that propels this biomimetic flagellum into the opposite direction. The propulsion efficiency increases with frequency and ceases abruptly at a critical frequency where the conformation changes discontinuously to a flat standing ribbon conformation.

SIMULATION OF NANOSCALE ETCHING FOR NANOTUBE AND GRAPHENE DEVICES

ABSTRACTIn order to find an efficient method to etch nano-carbon materials by hydrogenation in a controlled manner, we have studied hydrogen-atom adsorption on various deformed nanotubes using computer simulations based on the density-functional theory. The nanotube with an atomic lack is compared to a deformed tube with the Stone-Wales defect and a twisted tube wall. Similar to the known experimental etching condition for graphene, an atomic lack is effective to accumulate hydrogen atoms around the defect. Compared to the flat graphene, however, nanotube walls with curvature allow on-top adsorption of a hydrogen atom and selectivity in the hydrogenated site becomes worse. To achieve a controlled etching process, usage of a tungsten tip which realizes focused hydrogenation is proposed for natotubes and curved graphene.

Conformational collapse of surface-bound helical filaments

Chiral polymers are ubiquitous in nature and in the cellular context they are often found in association with membranes. Here we show that surface bound polymers with an intrinsic twist and anisotropic bending stiffness can exhibit a sharp continuous phase transition between states with very different effective persistence lengths as the binding affinity is increased. Above a critical value of the binding strength, determined solely by the torsional modulus and intrinsic twist rate, the filament can exist in a zero twist, surface bound state with a homogeneous stiffness. Below the critical binding strength, twist walls proliferate and function as weak or floppy joints that sharply reduce the effective persistence length that is measurable on long length scales. The existence of such dramatically different conformational states has implications for both biopolymer function in vivo and for experimental observations of such filaments in vitro.

Structure of toroidal DNA collapsed inside the phage capsid

The structure of DNA toroids made of individual DNA molecules of various lengths (3,000 to 55,000 bp) was studied, by using partially filled bacteriophage capsids in conjunction with cryoelectron microscopy. The tetravalent cation spermine was diffused through the capsid to condense the DNA under conditions that were chosen to produce a hexagonal packing. Our results demonstrate that the frustration arising between chirality and hexagonal packing leads to the formation of twist walls; the correlation between helices combined with their strong curvature impose variations of the DNA helical pitch.

Drift of a twisted domain wall (TDW) in perpendicularly magnetized films of uniaxial ferromagnetic materials

Drift motion of a twisted domain wall (TDW) in a strong magnetic field circularly polarized in the plane of a perpendicularly magnetized film is considered. The twisted structure reduces the threshold for the regime of stationary motion of a TDW (on both the velocity of motion and frequency of the rotating field) in comparison with a one-dimensional DW of the Bloch or Neel type. The dependence of the boundary of optimum (from the experimental viewpoint) observation of drift of a TDW in the regime of stationary motion on the ratio of the width of a Bloch line to the thickness of the film has been determined.

Effect of an in-plane magnetic field on the velocity of a domain wall in a two-layered uniaxial magnetic film

The motion of an isolated domain wall in a two-layered uniaxial magnetic film has been investigated by solving Slonczewski equations by the progonka method with allowance for the demagnetizing fields of the layers. Perpendicular to the plane of the domain wall, there was applied an in-plane external magnetic field, whose intensity was varied. Static configurations of a twisted domain wall have been calculated. In the dependence of the domain-wall velocity on the magnetic field applied along the normal to the film plane, additional maxima have been revealed in the range of middle fields. The dependences of the position of the domain wall and of the phase angle on the time and the coordinate along the normal to the film plane have been calculated.

Expression of chirality in columnar hexagonal phases or DNA and nucleosomes

Abstract It is surprising to see how eukaryotic chromosomes or sperm nuclei are highly condensed chromatin materials and how they can sometimes present spectacular helical morphologies. We may suspect that these helical shapes originate from the chiral properties of DNA and other components of chromatin. Dense solutions of DNA and nucleosomes can be prepared in vitro to reproduce some of the characteristics of chromatin. They form multiple ordered phases, either mesophases or 3D crystals, that can be useful to analyze precisely how chiral structures can emerge, or not, from interactions between these constitutive elements. We address the question of the competition between twist and hexagonal packing in dense states of DNA, nucleosomes, chromatin and chromosomes. From the microscopic analysis of many examples, we show how the twist arising from the chirality of the objects can be diluted in the phase and/or expelled along twist walls. These walls are either parallel or normal to the direction of the columns. In the first case, we determine that the twist axis lies parallel to one θ2 direction of the hexagonal network. Helical shapes of chromosomes and bundles of DNA and chromatin may also be consequences of this competition, as illustrated here.

Microscopic Observations and Simulations of Bloch Walls in Nematic Thin Films

We study Bloch wall defects formed by quenching nematic thin films from planar anchoring to homeotropic anchoring through a temperature-driven anchoring transition. The director profiles of the walls are directly visualized using fluorescence confocal polarizing microscopy, and shown to agree well with the simulation based on the Frank elasticity theory. A pure twist wall exists if the ratio of sample thickness to surface extrapolation length p is smaller than or close to 1; while a diffuse Bloch wall is obtained if p is much greater than 1.

Micromagnetic analyses of reversal process with twisted wall structure

The magnetization reversal process in a magnetic film is discussed with a focus on the effects of surface anisotropy. Assuming an adiabatic rotation of magnetization, the entire configuration is determined by applying the variational technique to the total energy of the system including the surface and bulk anisotropy energy, the exchange energy, and also Zeeman energy. The magnetization reversal can proceed through both coherent and/or incoherent rotations depending on the values of magnetization, anisotropy, exchange stiffness, and film thickness. In the case of incoherent rotation, the magnetization configuration exhibits the normal twisted wall structure. The expression for the bifurcating condition is given explicitly.

Critical velocities of a twisted domain wall in very thin magnetic films

An integro-differential variant of the Slonczewski equations has been formulated so as to take into account the effect of a nonlocal magnetostatic field on the structure of twisted domain walls (TDWs) in films of very small (below DW width) thicknesses. Apart from the features specific to magnetic multilayer films, the limiting TDW velocity in this range of film thicknesses is very low (despite the small DW twist) and the TDW dynamics has a predominantly precessional character. For film thicknesses above the DW width, a maximum peak velocity determined by numerical methods has proved to be 20% higher than the well-known Walker’s value.