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Chirality-dictated alignment of single helices in a nematic liquid crystal a–f, Optical micrographs of left-handed microhelices obtained using bright-field (a,d) and polarizing microscopy without (b,e) and with (c,f) a phase retardation plate. g,h, Self-diffusion of particles oriented with roughly orthogonal (g) and parallel (h) to n0. The insets show optical bright-field micrographs at the corresponding orientations with respect to n0 (D∥ ≈ D⊥ ≈ 2.2 × 10⁻³ μm² s⁻¹ in g and D∥ ≈ 2.7 × 10⁻³ μm² s⁻¹, D⊥ ≈ 0.68 × 10⁻³ μm² s⁻¹ in h). i, Orientation-dependent free energy cost of elastic distortions induced by particles versus the angle between and n0 for different orientations of the tilt direction of , for left- (squares) and right-handed (circles) helices. Open (solid) symbols correspond to anticlockwise rotation of about (), as shown in Fig. 2b–e. The insets depict free energy variations near the stable and metastable orientation states. j–m, Director structures around right-handed helices at θ = 8° (j) (blue solid circles in i) and at θ = 82° (l) (blue solid circles in i) and left-handed helices at θ = 0° (k) (red open squares in i) and at θ = 90° (m) (red open squares in i), which are stable (j,k) and metastable (l,m) particle orientations. The director field is shown with the help of rods and colour-coded azimuthal orientations of n(r) on particle surfaces relative to n0 according to the colour scheme shown in the inset of k. Scale bars are 5 μm.
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Colloidal particles disturb the alignment of rod-like molecules of liquid crystals, giving rise to long-range interactions that minimize the free energy of distorted regions. Particle shape and topology are known to guide this self-assembly process. However, how chirality of colloidal inclusions affects these long-range interactions is unclear. Her...
Citations
... Interestingly, topological particlelike localized LC structures bear some resemblance to colloidal particles dispersed in a LC host (see reviews [6,36,37] for details on liquid crystal colloids). Colloidal interactions are mediated by elastic distortions induced by the interacting particles [38][39][40][41][42][43][44][45][46]. ...
We study pairwise interactions between localized topological structures in chiral magnetic and cholesteric liquid crystal (CLC) systems confined in the planar geometry. Our calculations for magnetics are based on the lattice model that takes into account the bulk and surface anisotropies along with the exchange and the Dzyaloshinskii-Moriya interactions. In CLC cells, these anisotropies describe the energy of interaction with an external magnetic or electric field and the anchoring energy assuming that the magnetic or electric anisotropy is negative and the boundary conditions are homeotropic. We have selected the region of the phase diagram, where various localized solitonlike structures, including skyrmion tubes, torons, and leeches, embedded in the ground state of the z-cone (conical phase) coexist, and carried out numerical analysis of the distance dependencies of the effective intersoliton interaction potentials. For skyrmions and torons, the potentials are found to be attractive in the large separation region. It turned out that for these potentials, the effects of axial asymmetry are negligible. By contrast, it turned out that for the intermediate structures between the skyrmions and torons known as the leeches, the leech-leech potentials generally depend on the orientation of the intersoliton separation vector and their large distance parts may become repulsive at certain directions of the vector. All the potentials have the short distance repulsive parts and the local minima located at the equilibrium separations. It is found that the skyrmion-skyrmion potential has an additional metastable configuration shifted towards the short-distance region.
... Such insights emerge from novel design concepts for mechanochromic, thermochromic, and colorimetric sensors responding to external stimuli [126,214]. Concerning in situ alignment of chiral nematic LCs colloids [215] via vdW forces, nano-entities are aligned prior to being dispersed within the LCs structure [121,[123][124][125][126]. This can be facilitated using either surface with specific textures [123] or pa erns as templates [121] to assist in achieving the desired orientation [121,127]. ...
... Such insights emerge from novel design concepts for mechanochromic, thermochromic, and colorimetric sensors responding to external stimuli [126,214]. Concerning in situ alignment of chiral nematic LCs colloids [215] via vdW forces, nano-entities are aligned prior to being dispersed within the LCs structure [121,[123][124][125][126]. This can be facilitated using either surface with specific textures [123] or patterns as templates [121] to assist in achieving the desired orientation [121,127]. ...
In the pursuit of advanced functional materials, the role of low-dimensional van der Waals (vdW) heterointerfaces has recently ignited noteworthy scientific interest, particularly in assemblies that incorporate quasi-2D graphene and quasi-1D nanocellulose derivatives. The growing interest predominantly stems from the potential to fabricate distinct genres of quasi-2D/1D nanoarchitecture governed by vdW forces. Despite the possibilities, the inherent properties of these nanoscale entities are limited by in-plane covalent bonding and the existence of dangling π-bonds, constraints that inhibit emergent behavior at heterointerfaces. An innovative response to these limitations proposes a mechanism that binds multilayered quasi-2D nanosheets with quasi-1D nanochains, capitalizing on out-of-plane non-covalent interactions. The approach facilitates the generation of dangling bond-free iso-surfaces and promotes the functionalization of multilayered materials with exceptional properties. However, a gap still persists in understanding transition and alignment mechanisms in disordered multilayered structures, despite the extensive exploration of monolayer and asymmetric bilayer arrangements. In this perspective, we comprehensively review the sophisticated aspects of multidimensional vdW heterointerfaces composed of quasi-2D/1D graphene and nanocellulose derivatives. Further, we discuss the profound impacts of anisotropy nature and geometric configurations, including in-plane and out-of-plane dynamics on multiscale vdW heterointerfaces. Ultimately, we shed light on the emerging prospects and challenges linked to constructing advanced functional materials in the burgeoning domain of quasi-3D nanoarchitecture.
... studies of systems with complicated particle shapes. [43][44][45][46][47][48][49][50][51] Even though we introduce this method as a tool for the investigation of relatively complex chiral particles, we also suspect that it will be insightful to apply it to hard-rod fluids, since the network analysis can be readily applied to visualize the half-layers in conventional smectics. We expect it to provide also insight, applied in the analysis of gyroid phases in systems of particles without chirality. ...
Self-assembly of chiral particles with an L-shape is explored by Monte-Carlo computer simulations in two spatial dimensions. For sufficiently high packing densities in confinement, a carpet-like texture emerges due to the interlocking of L-shaped particles, resembling a distorted smectic liquid crystalline layer pattern. From the positions of either of the two axes of the particles, two different types of layers can be extracted, which form distinct but complementary entangled networks. These coarse-grained network structures are then analyzed from a topological point of view. We propose a global charge conservation law by using an analogy to uniaxial smectics and show that the individual network topology can be steered by both confinement and particle geometry. Our topological analysis provides a general classification framework for applications to other intertwined dual networks.
... Computer simulations are carried out to study the interplay between molecular LC order near the colloidal surface and the colloidal orientation. The simulations are based on minimizing the mean-field Landau-de Gennes free energy for the molecular LC host [5,17,[42][43][44]. We consider a thermotropic bulk free energy density describing the isotropic-nematic transition of LCs complemented with elastic contributions associated with LC director distortions occurring in the bulk volume of the LC: ...
Chiral nematic or cholesteric liquid crystals (LCs) are mesophases with long-ranged orientational order featuring a quasi-layered periodicity imparted by a helical configuration but lacking positional order. Doping molecular cholesteric LCs with thin colloidal rods with a large length-to-width ratio or disks with a large diameter-to-thickness ratio adds another level of complexity to the system because of the interplay between weak surface boundary conditions and bulk-based elastic distortions around the particle-LC interface. By using colloidal disks and rods with different geometric shapes and boundary conditions, we demonstrate that these anisotropic colloidal inclusions exhibit biaxial orientational probability distributions, where they tend to orient with the long rod axes and disk normals perpendicular to the helix axis, thus imparting strong local biaxiality on the hybrid cholesteric LC structure. Unlike the situation in achiral hybrid molecular-colloidal LCs, where biaxial order emerges only at modest to high volume fractions of the anisotropic colloidal particles, the orientational probability distribution of colloidal inclusions immersed in chiral nematic hosts are unavoidably biaxial even at vanishingly low particle volume fractions. In addition, the colloidal inclusions induce local biaxiality in the molecular orientational order of the LC host medium, which enhances the weak biaxiality of the LC in a chiral nematic phase coming from the symmetry breaking caused by the presence of the helical axis. With analytical modeling and computer simulations based on minimizing the Landau de Gennes free energy of the host LC around the colloidals, we explain our experimental findings and conclude that the biaxial order of chiral molecular-colloidal LCs is strongly enhanced as compared to both achiral molecular-colloidal LCs and molecular cholesteric LCs and is rather unavoidable.
... The nematic order parameter simultaneously describes the extent of phase ordering and local direction of broken symmetry in an arbitrary reference frame. Thus, both the bulk and deformation free energy densities can written in terms of Q r, t ð Þ. Practically, the introduction of Q has enabled numerical simulations of confined nematics 52,53 , colloidal liquid crystals [54][55][56] and active fluids 57-59 , by treating defects as locally disordered cores, rather than singularities. Explicitly, the tensor Q regularizes these singularities in n and remains continuous at the center of defects. ...
Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials — they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.
... Using novel techniques to produce complex colloidal particles with different topological genus numbers in the NLC has extended defect studies from a theoretical perspective [12][13][14][15][16][17][18]. Compared to spherical particles, the elastic deformations around the geometries with low symmetry depend critically on their shape and spatial arrangement in the nematic host. ...
... The elastic distortions of chiral superstructure colloids with strong surface boundary conditions can lead to local chiral configurations in the nematic field. The effects of the distortions give rise to anisotropic and long-range interactions between like-and opposite-handed particles with different geometric parameters [13]. The iteration of Koch fractals provides the conditions to study induced topological singularities in the nematic orientation. ...
The present study investigates the arrangement of hollow pyramidal cone shells and their interactions with degenerate planar anchoring on the inner and outer surfaces of particles within the nematic host. The shell thickness is in order of the nematic coherence length. The numerical behavior of colloids is determined by minimizing the Landau-de Gennes free energy in the presence of the Fournier surface energy and using the finite element method. Colloidal pyramidal cones can orient parallel and perpendicular with the far director orientation. In the parallel alignment, we found the splay director distortion into the pyramid with two boojum defects at the inner and outer tips. The director shows bending distortion without defect patterns when the pyramid is aligned perpendicularly. They induce long-range dipolar interaction and can form nested structures in close contact.
... Chiral spring-like colloidal particles of different handedness and with tangential boundary conditions (Figure 9j−q) were fabricated using two-photon polymerization to study the effects of chirality on the director structures and LCmediated elastic interactions between chiral particles. 98 To study coupling between the fractal order and the uniaxial nematic vector-type ordering, polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations were produced by two-photo polymerization, 99 and their surfaces were treated with DMOAP silane to create a homeotropic surface alignment of LC molecules (Figure 9r). ...
Colloidal systems are abundant in technology, in biomedical settings, and in our daily life. The so-called "colloidal atoms" paradigm exploits interparticle interactions to self-assemble colloidal analogs of atomic and molecular crystals, liquid crystal glasses, and other types of condensed matter from nanometer- or micrometer-sized colloidal building blocks. Nematic colloids, which comprise colloidal particles dispersed within an anisotropic nematic fluid host medium, provide a particularly rich variety of physical behaviors at the mesoscale, not only matching but even exceeding the diversity of structural and phase behavior in conventional atomic and molecular systems. This feature article, using primarily examples of works from our own group, highlights recent developments in the design, fabrication, and self-assembly of nematic colloidal particles, including the capabilities of preprogramming their behavior by controlling the particle's surface boundary conditions for liquid crystal molecules at the colloidal surfaces as well as by defining the shape and topology of the colloidal particles. Recent progress in defining particle-induced defects, elastic multipoles, self-assembly, and dynamics is discussed along with open issues and challenges within this research field.
... [1][2][3] In synthetic systems, prior studies have reported composites formed from fibers dispersed in isotropic matrices, but the mechanical coupling of soft nanofibers with anisotropic matrices such as liquid crystals (LCs) has not been widely explored. [1,2,4,5] Motivated by the observation that soft biological assemblies (e.g., vesicles, red blood cells, and bacterial cells), when dispersed in LCs, can be stretched or folded by the elasticity of LCs, [6][7][8][9][10] in this paper, we synthesize appearance characterized by four extinction bands (dark area in Figure 1d). The extinction bands of the PCH film correspond to regions of the film where the azimuthal orientation of the LC director is parallel to one of the crossed polarizers. ...
Fibers embedded in soft matrices are widely encountered in biological systems, with the fibers providing mechanical reinforcement or encoding of instructions for shape changes. Here, the mechanical coupling of end‐attached polymeric nanofiber forests and liquid crystals (LCs) is explored, where the nanofibers are templated into prescribed shapes by the chemical vapor polymerization of paracyclophane‐based monomers in supported films of the LCs. It is shown that the elastic energies of the nanofibers and LCs are comparable in magnitude, leading to reversible straining of nanofibers via the application of an electric field to the LC. This coupling is shown to encode complex electrooptical responses in the LC (e.g., optical vortices), thus illustrating how LC‐templated nanofiber forests offer the basis of fresh approaches for programming configurational changes in soft materials.
... Recently, to explore the more complex interactions in LC colloids, the interests in understanding and controlling the topology of LC colloids have started to shift from using spherical colloids to embedding other geometric particles like rod-shaped, disk-shaped and chiral colloids into NLCs. [1][2][3][13][14][15][16][17][18][19][20] Such modifications allow us to access more diverse multipole topological structures and the resultant assemblies. In particular, the rotational invariant symmetry is broken in rod-shaped nanoand micro-particles. ...
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.
... 14,15,20 One of the latest innovations in MXene processing is the discovery of its liquid crystal (LC) phases, 15,16 -dened as thermodynamically stable mesophases simultaneously exhibiting liquid-like uidity and crystal-like order. [21][22][23] The hydrophilic transition metal oxide and hydroxide bonds present on MXene's basal plane promotes preferential sheet ordering and alignment while being dispersed, which can be tuned or induced by changing parameters such as concentration and temperature, or by applying shear force. 15,16,21 In particular, the ease of manipulating the sheet alignment can be extended to LC MXene formation, which allows the production of highly aligned macro-architectures, such as lms and bers with enhanced sheet orientation for improved ion transport, conductivity and physical properties compared to those made from typical non-LC dispersions. ...
... [21][22][23] The hydrophilic transition metal oxide and hydroxide bonds present on MXene's basal plane promotes preferential sheet ordering and alignment while being dispersed, which can be tuned or induced by changing parameters such as concentration and temperature, or by applying shear force. 15,16,21 In particular, the ease of manipulating the sheet alignment can be extended to LC MXene formation, which allows the production of highly aligned macro-architectures, such as lms and bers with enhanced sheet orientation for improved ion transport, conductivity and physical properties compared to those made from typical non-LC dispersions. [24][25][26] For example, lms composed of vertically aligned sheets can be formed through mechanically shearing LC mixed MXene-CNT-cetyltrimethylammonium bromide (CTAB) dispersions. ...
The liquid crystal (LC) phases of two-dimensional (2D) transition metal carbides/nitrides (MXenes) have enabled the production of their unique macro-architectures with an ordered microstructure and enhanced properties. However, LC phases in additive-free MXene dispersions are known to occur above relatively high sheet size and concentration thresholds, which can be difficult to obtain and process. Easily prepared non-LC MXene dispersions composed of small sheets at low concentrations on the other hand, do not possess adequate rheological properties to form desired macro-architectures. Here, we report that LC phases in dilute MXene dispersions can be induced by adding cellulose nanocrystals (CNCs), even at concentrations significantly below its own LC threshold. The favorable mutual interaction lowers the concentration and size threshold for MXene solution processing into robust superior macro-architectures, and improves the properties of LC-MXene fibers produced at conventional concentrations (∼30 mg mL−1). As an example, fibers wet-spun from 10 mg mL−1 LC CNC–MXene containing 75% MXene (M75), exhibit high tensile strength (∼60 MPa), conductivity (∼3000 S cm−1), and volumetric capacitance (∼950 F cm−3), in contrast to 10 mg mL−1 pure MXene (M100), which was unspinnable. The synergistic improvements brought by CNCs on LC formation may be extended to mixed dispersions of other nanomaterials and is anticipated to further broaden the array of solution processing of MXenes into functional architectures and devices.
