Nematic Order Research Articles

Hydroxypropyl Cellulose-Based Meter-Long Structurally Colored Fibers for Advanced Fabrics.

Structurally colored fibers are attractive alternatives to chemically colored fibers due to their rich optical properties, color stability, and environmental friendliness. However, the fabrication of structurally colored fibers using cost-effective raw materials with the possibility to scale up remains challenging. Here, a simple and scalable approach is developed to fabricate continuous meter-long structurally colored fibers exhibiting brilliant structural colors across the visible spectrum and helix orientation-dependent polarization states. The fibers are fabricated by extrusion of concentrated aqueous solutions of chemically crosslinked hydroxypropyl cellulose (HPC). The wavelengths and polarization states can be tuned by solution concentration, relaxation time, and collector's surface energy. The HPC-based structurally colored fibers display excellent optical stability to mechanical straining, repeated drying/water impregnation, and prolonged heating at 150°C. It is demonstrated that the HPC-based structurally colored fibers can be woven into structurally colored fabrics with wavelength- and polarization-coded optical patterns. The current work presents a strategy to tune the chiral nematic order, which constitutes an important step toward mass production of structurally colored fibers with stable and rich optical properties using easily available raw materials.

Strain rate controls alignment in growing bacterial monolayers.

Growing monolayers of rod-shaped bacteria exhibit local alignment similarly to extensile active nematics. When confined in a channel or growing inward from a ring, the local nematic order of these monolayers changes to a global ordering with cells throughout the monolayer orienting in the same direction. The mechanism behind this phenomenon is so far unclear, as previously proposed mechanisms fail to predict the correct alignment direction in one or more confinement geometries. We present a strain-based model relating net deformation of the growing monolayer to the cell-level deformation resulting from single-cell growth and rotation, producing predictions of cell orientation behavior based on the velocity field in the monolayer. This model correctly predicts the direction of preferential alignment in channel-confined, inward growing, and unconfined colonies. The model also quantitatively predicts orientational order when the velocity field has no net negative strain rate in any direction. We further test our model in simulations of expanding colonies confined to spherical surfaces. Our model and simulations agree that cells away from the origin cell orient radially relative to the colony's center. Additionally, our model's quantitative prediction of the orientational order agrees with the simulation results in the top half of the sphere but fails in the lower half where there is a net negative strain rate. The success of our model bridges the gap between previous works on cell alignment in disparate confinement geometries and provides insight into the underlying physical effects responsible for large-scale alignment.

Chiral, Topological, and Knotted Colloids in Liquid Crystals

The geometric shape, symmetry, and topology of colloidal particles often allow for controlling colloidal phase behavior and physical properties of these soft matter systems. In liquid crystalline dispersions, colloidal particles with low symmetry and nontrivial topology of surface confinement are of particular interest, including surfaces shaped as handlebodies, spirals, knots, multi-component links, and so on. These types of colloidal surfaces induce topologically nontrivial three-dimensional director field configurations and topological defects. Director switching by electric fields, laser tweezing of defects, and local photo-thermal melting of the liquid crystal host medium promote transformations among many stable and metastable particle-induced director configurations that can be revealed by means of direct label-free three-dimensional nonlinear optical imaging. The interplay between topologies of colloidal surfaces, director fields, and defects is found to show a number of unexpected features, such as knotting and linking of line defects, often uniquely arising from the nonpolar nature of the nematic director field. This review article highlights fascinating examples of new physical behavior arising from the interplay of nematic molecular order and both chiral symmetry and topology of colloidal inclusions within the nematic host. Furthermore, the article concludes with a brief discussion of how these findings may lay the groundwork for new types of topology-dictated self-assembly in soft condensed matter leading to novel mesostructured composite materials, as well as for experimental insights into the pure-math aspects of low-dimensional topology.

Generation of nematic order in itraconazole by cryo-milling

Mechanical milling is a well-known method of solid-state amorphization of crystalline materials. Here, it is revealed that cryo-milling of itraconazole, a model thermotropic liquid-crystalline active pharmaceutical ingredient, leads to a preferred nematic order of molecules in solid particles instead of isotropic disorder − usually observed for most molecules that do not form liquid-crystalline mesophases. While standard quenching of itraconazole isotropic liquid down to room temperature results in the formation of glass with some degree of smectic order, cryo-milling easily destroys not only crystalline order but also smectic organization of molecules into layers, omitting the melting. The cryo-milled itraconazole samples exhibit faster α-relaxation and slightly slower δ-mode above the glass transition temperature. They are also more physically stable, with the stability dependent on the grinding time, below this temperature, with respect to the ordinary glass. The explanation for this behavior is believed to be increased short-range intermolecular disorder. Moreover, the cryo-milled particles with nematic order are better soluble than ordinary glass. Therefore, this work can guide the formulation of stable pharmaceuticals with nematic order/disorder and enhanced solubility.

Intercellular friction and motility drive orientational order in cell monolayers

Spatiotemporal patterns in multicellular systems are important to understanding tissue dynamics, for instance, during embryonic development and disease. Here, we use a multiphase field model to study numerically the behavior of a near-confluent monolayer of deformable cells with intercellular friction. Varying friction and cell motility drives a solid-liquid transition, and near the transition boundary, we find the emergence of local nematic order of cell deformation driven by shear-aligning cellular flows. Intercellular friction contributes to the monolayer's viscosity, which significantly increases the spatial correlation in the flow and, concomitantly, the extent of nematic order. We also show that local hexatic and nematic order are tightly coupled and propose a mechanical-geometric model for the colocalization of [Formula: see text] nematic defects and 5-7 disclination pairs, which are the structural defects in the hexatic phase. Such topological defects coincide with regions of high cell-cell overlap, suggesting that they may mediate cellular extrusion from the monolayer, as found experimentally. Our results delineate a mechanical basis for the recent observation of nematic and hexatic order in multicellular collectives in experiments and simulations and pinpoint a generic pathway to couple topological and physical effects in these systems.

Symmetry and Value of the Order Parameter in 2d Nematic Superconductors

We derive equations for the superconducting nematic order parameter and chemical potential for the hexagonal lattice by accounting for nearest- and next-nearest-neighbor hoppings of electrons. By analyzing the energy of the superconducting ground state, we have found that the symmetry of the order parameter and some other superconducting properties of the system strongly depend on the sign and the magnitude of the next-nearest neighbor hopping. As we will demonstrate, both extended s- and d-pairings significantly contribute to the pairing in the system, that be tuned by changing the hopping parameters. We discuss a possible connection of the obtained results to the properties of several doped monolayer superconductors – graphene and transition metal dichalcogenides.

Environment-Stored Memory in Active Nematics and Extra-Cellular Matrix Remodeling.

Many active systems display nematic order, while interacting with their environment. In this Letter, we show theoretically how environment-stored memory acts an effective external field that aligns active nematics. The coupling to the environment leads to substantial modifications of the known phase diagram and dynamics of active nematics, including nematic order at arbitrarily low densities and arrested domain coarsening. We are motivated mainly by cells that remodel fibers in their extra-cellular matrix (ECM), while being directed by the fibers during migration. Our predictions indicate that remodeling promotes cellular and ECM alignment, and possibly limits the range of ordered ECM domains, in accordance with recent experiments.

The effect of dynamic cross-links and mesogenic groups on the swelling and collapse of polymer gels

The polymer gels containing dynamic cross-links and mesogenic groups are among the key candidates for the development of soft actuators and detectors, displays, sensors and other programmable and self-healing materials. In this article, firstly, the collapse of polymer networks with irreversible cross-links in the presence of a dynamic cross-linker is investigated by means of Flory-type theory. It is shown that, at not a very poor solvent quality (near the theta-conditions), the swelling ratio for a gel containing irreversible and dynamic cross-links is less than for a gel with irreversible cross-links only, whereas at poor or good solvent qualities sizes of these gels are close to each other. The number of dynamic cross-links monotonically increases with worsening the solvent quality. The gel contraction can be also achieved by increasing the dynamic cross-linker concentration, which allows one to change the transition point in a wide range of solvent conditions. Secondly, polymer networks containing irreversible and dynamic cross-links and incorporating mesogenic side groups is studied using the Maier–Saupe theory. With decreasing in the temperature, the continuous transition from a swollen to collapsed state occurs. With further increase in the temperature, the swelling ratio discontinuously decreases and the nematic order parameter sharply increases from zero to a value ​​close to one. By increasing the dynamic cross-linker concentration, the swelling-to-collapse transition and, then, the isotropic-nematic transition are observed. A phase diagram of the gel is constructed and, depending on the dynamic cross-linker concentration and temperature, the swollen gel with the zero nematic order parameter, the collapsed gel with the zero nematic order parameter, and the collapsed gel with the nematic ordering can be formed. A growth of the length of the mesogenic side group leads to an increase in the area of ​​existence of the collapsed gel with the nematic ordering in the phase diagram. The obtained theoretical results are in agreement with corresponding experimental data from the literature.

Magnetisation control of the nematicity direction and nodal points in a superconducting doped topological insulator

We study the effects of magnetisation on the properties of the doped topological insulator of the $\text{Bi}_2\text{Se}_3$ family with nematic superconductivity. We found that the direction of the in-plane magnetisation fixes the direction of the nematicity in the system. The chiral state is more favourable than the nematic state for large values of out-of-plane magnetisation. Overall, the critical temperature of the nematic superconductivity is robust against magnetisation. We explore in detail the spectrum of the system with the pinned direction of the nematic order parameter $\Delta_{y}$. Without magnetisation, there is a full gap in the spectrum because of finite hexagonal warping. At an out-of-plane $m_z$ or orthogonal in-plane $m_x$ magnetisation that is strong enough, the spectrum is closed at the nodal points that are split by the magnetisation. Flat Majorana surface states connect such split bulk nodal points. Parallel magnetisation $m_y$ lifts the nodal points and opens a full gap in the spectrum. We discuss relevant experiments and propose experimental verifications of our theory.

Self-organization of mortal filaments and its role in bacterial division ring formation

Filaments in the cell commonly treadmill. Driven by energy consumption, they grow on one end while shrinking on the other, causing filaments to appear motile even though individual proteins remain static. This process is characteristic of cytoskeletal filaments and leads to collective filament self-organization. Here we show that treadmilling drives filament nematic ordering by dissolving misaligned filaments. Taking the bacterial FtsZ protein involved in cell division as an example, we show that this mechanism aligns FtsZ filaments in vitro and drives the organization of the division ring in living Bacillus subtilis cells. We find that ordering via local dissolution also allows the system to quickly respond to chemical and geometrical biases in the cell, enabling us to quantitatively explain the ring formation dynamics in vivo. Beyond FtsZ and other cytoskeletal filaments, our study identifies a mechanism for self-organization via constant birth and death of energy-consuming filaments.

Density-Nematic Coupling in Isotropic Solution of DNA: Multiscale Model.

Monte Carlo simulations of isotropic solutions of double-stranded DNA (deoxyribonucleic acid) are performed using the well-established oxDNA model. By comparing the fluctuation amplitudes with theoretical predictions, the parameters of a generic macroscopic model of an isotropic linear polymer solution/melt are determined. A multiscale continuum field model is thus obtained, corresponding to the full specificity of the isotropic phase of double-stranded DNA in the usual B-form as perceived at the macroscopic level. Present research is particularly focused on the coupling between spatial concentration/density variations of the polymer and the emerging nematic orientation order of the chains. This rather unfamiliar, only recently described phenomenon, inherent to linear polymers, is outlined and interpreted. Quantitative predictions are provided for the degree of nematic order induced by concentration gradients in isotropic solutions of double-strandedDNA.

Evident structural anisotropies arising from near-zero particle asphericity in granular spherocylinder packings.

With magnetic resonance imaging experiments, we study packings of granular spherocylinders with merely 2% asphericity. Evident structural anisotropies across all length scales are identified. Most interestingly, the global nematic order decreases with increasing packing fraction, while the local contact anisotropy shows an opposing trend. We attribute this counterintuitive phenomenon to a competition between gravity-driven ordering aided by frictional contacts and a geometric frustration effect at the marginally jammed state. It is also surprising to notice that such slight particle asphericity can trigger non-negligible correlations between contact-level and mesoscale structures, manifested in drastically different nonaffine structural rearrangements upon compaction from that of granular spheres. These observations can help improve statistical mechanical models for the orientational order transformation of nonspherical granular particle packings, which involves complex interplays between particle shape, frictional contacts, and external force field.

Random close packing of semi-flexible polymers in two dimensions: Emergence of local and global order.

Through extensive Monte Carlo simulations, we systematically study the effect of chain stiffness on the packing ability of linear polymers composed of hard spheres in extremely confined monolayers, corresponding effectively to 2D films. First, we explore the limit of random close packing as a function of the equilibrium bending angle and then quantify the local and global order by the degree of crystallinity and the nematic or tetratic orientational order parameter, respectively. A multi-scale wealth of structural behavior is observed, which is inherently absent in the case of athermal individual monomers and is surprisingly richer than its 3D counterpart under bulk conditions. As a general trend, an isotropic to nematic transition is observed at sufficiently high surface coverages, which is followed by the establishment of the tetratic state, which in turn marks the onset of the random close packing. For chains with right-angle bonds, the incompatibility of the imposed bending angle with the neighbor geometry of the triangular crystal leads to a singular intra- and inter-polymer tiling pattern made of squares and triangles with optimal local filling at high surface concentrations. The present study could serve as a first step toward the design of hard colloidal polymers with a tunable structural behavior for 2D applications.

Emergence of cellular nematic order is a conserved feature of gastrulation in animal embryos.

Cells undergo dramatic changes in morphology during embryogenesis, yet how these changes affect the formation of ordered tissues remains elusive. Here we find that the emergence of a nematic liquid crystal phase occurs in cells during gastrulation in the development of embryos of fish, frogs, and fruit flies. Moreover, the spatial correlations in all three organisms are long-ranged and follow a similar power-law decay with less than unity for the nematic order parameter, suggesting a common underlying physical mechanism unifies events in these distantly related species. All three species exhibit similar propagation of the nematic phase, reminiscent of nucleation and growth phenomena. Finally, we use a theoretical model along with disruptions of cell adhesion and cell specification to characterize the minimal features required for formation of the nematic phase. Our results provide a framework for understanding a potentially universal features of metazoan embryogenesis and shed light on the advent of ordered structures during animal development.

Van Hove annihilation and nematic instability on a kagome lattice.

A nematic phase breaks the point-group symmetry of the crystal lattice and is known to emerge in correlated materials. Here we report the observation of an intra-unit-cell nematic order and associated Fermi surface deformation in the kagome metal ScV6Sn6. Using scanning tunnelling microscopy and scanning tunnelling spectroscopy, we reveal a stripe-like nematic order breaking the crystal rotational symmetry within the kagome lattice itself. Moreover, we identify a set of Van Hove singularities adhering to the kagome-layer electrons, which appear along one direction of the Brillouin zone and are annihilated along other high-symmetry directions, revealing rotational symmetry breaking. Via detailed spectroscopic maps, we further observe an elliptical deformation of the Fermi surface, which provides direct evidence for an electronically mediated nematic order. Our work not only bridges the gap between electronic nematicity and kagome physics but also sheds light on the potential mechanism for realizing symmetry-broken phases in correlated electron systems.

Nematodynamics with odd and rotational viscosities

We explore a novel mechanism of interactions between nematic order and flow including odd and rotational viscosities, and investigate activity-induced instabilities in the framework of this model. We show how these modes of viscous dissipation can be incorporated in the Ericksen–Leslie formalism, but it does not eliminate deficiencies of the approach based on Onsager’s reciprocal relations that lead to spurious instabilities. The suggested way of deriving nematodynamic equations, based on a specific mechanism applicable to rigid rods, is not universal, but it avoids referring to Onsager’s relations and avoids spurious instabilities in the absence of an active inputs. The model is further applied to the analysis of instabilities in active media

Effect of external fields and currents on electronic nematic ordering with quadrupole moments

We theoretically investigate the effect of external fields and currents on electronic nematic orderings based on the concept of augmented multipoles consisting of electric, magnetic, magnetic toroidal, and electric toroidal multipoles. We show the relation between rank-2 electric quadrupoles and the other multipoles, the former of which corresponds to the microscopic order parameter for the nematic phases. The electric (magnetic) field induces the rank-1 and rank-3 electric (magnetic) multipoles and rank-2 electric toroidal (magnetic toroidal) quadrupoles, while the electric current induces the rank-1 and rank-3 magnetic toroidal multipoles and rank-2 magnetic quadrupoles. We classify the active multipoles under magnetic point groups, which will be a reference to explore cross-correlation and transport phenomena in nematic phases. As a demonstration, we show that unconventional symmetric and antisymmetric spin splittings are brought about by field-induced toroidal multipoles.

Active nematic-isotropic interfaces on flat surfaces: Effects of anchoring, ordering field and activity

A surface in contact with the isotropic phase of a passive liquid crystal can induce nematic order over distances that range from microscopic to macroscopic when the nematic-isotropic interface undergoes an orientational-wetting transition. If the nematic is active, what happens to the interface? Does it propagate and, if it does, is its structure different from the passive one? In this paper, we address these questions. We investigate how the active nematic-isotropic interface is affected by the anchoring strength of the surface, the bulk ordering field and the activity. We find that while passive interfaces are one-dimensional the active ones exhibit two dynamical regimes: a passive-like regime and a propagating regime where the interfaces propagate until the entire domain is active nematic. Active interfaces break the translational symmetry within the interfacial plane above a threshold activity, where the active nematic fluctuations, which are ultimately responsible for the emergence of an active turbulent nematic phase, drive non-steady dynamical interfacial regimes.

Fluctuation-induced spin nematic order in magnetic charge ice

A pyrochlore charge ice consisting of two magnetic cation types gives rise to a Heisenberg magnet with an interesting type of long-range correlated bond disorder. If the antiferromagnetic exchange among cations of the same type dominates over the interspecies exchange, closed antiferromagnetic chains following the fully packed loops of like cations emerge as nonlocal effective low-temperature degrees of freedom. Monte Carlo simulations reveal a fluctuation driven first-order phase transition from an algebraically correlated spin liquid to a long-range ordered spin nematic, which mean-field theory captures with very high accuracy. The global O(3) Heisenberg symmetry is suddenly reduced to a Z2 Ising symmetry as the Néel vectors of the strongly antiferromagnetically correlated loops align with each other to optimize the entropy of their thermal fluctuations. Interestingly, the nematic transition is found to be sensitive to the size statistics of the cation loops and thus provides a direct thermodynamic probe of otherwise elusive structural properties. In turn this sensitivity offers a structural route to engineering the nematic phase stability. Published by the American Physical Society 2024

Adsorption characteristics of Janus tadpole polymers

The shape of Janus particles is directly connected to their adsorption behavior. Janus tadpole polymers offer a unique topological architecture that includes competition between entropic, enthalpic, and topological terms in the adsorption free energy; accordingly, non-trivial adsorption behavior patterns are expected. We study the surface adsorption of Janus tadpole polymers by means of Monte Carlo simulations, finding that, depending on which part of the tadpole polymers is preferentially adsorbing on the surface, very different types of behavior for both the adsorbed polymeric phase and of the brush arise. The adsorbed phase and the brush mutually influence each other, leading to a variety of phenomena such as nematic ordering of the adsorbed stiff tadpole tails and intriguing changes in the territoriality of adsorbed ring polymers on the surface. We analyze in detail our findings, revealing the mechanisms behind the organization and ordering, and opening up new possibilities to tune and control the structure of such systems.