Long-range Orientational Order Research Articles

Nano and micro-structural complexity of nematic liquid crystal configurations

Of our interest are frustration-driven pattern generating mechanisms in systems which in bulk equilibrium display spatially homogeneous long-range orientational order in absence of perturbations. As testbed material, we select thermotropic nematic liquid crystals. In bulk, they exhibit weakly discontinuous order–disorder phase transformation on varying temperature where the ordered nematic phase features spatially uniform axial order along an arbitrary symmetry breaking direction. However, due to continuous symmetry breaking (CSB) the established order is extremely susceptible to various perturbations which are in real systems in general always present. We theoretically illustrate how diverse complex patterns could be excited. Particularly intriguing configurations could appear if topological defects are present that could be generated via CSB. Our analysis is based on a relatively simple Lebwohl-Lasher-type model in which we could get analytical insight into phenomena of our interest. Using it we illustrate history dependent early stage isotropic-nematic phase evolution and final patterns in presence of “impurities” (e.g., nanoparticles). We show how characteristic effective interaction characteristics predict qualitatively different emerging patterns. Our analysis is based on CSB which is ubiquitous in nature. Consequently, demonstrated mechanisms are expected to manifest also in other condensed matter systems whose ordered phase is formed via CSB. We illustrate how kinetics and impurities could impact key structural properties of the systems of our interest.

Fine-Tuning the Microstructure and Photophysical Characteristics of Fluorescent Conjugated Copolymers Using Photoalignment and Liquid-Crystal Ordering.

Replicating the microstructural basis and the near 100% excitation energy transfer efficiency in naturally occurring light-harvesting complexes (LHCs) remains challenging in synthetic energy-harvesting devices. Biological photosynthesis regulates active ensembles of light-absorbing and funneling chlorophylls in proteins in response to fluctuating sunlight. Here, use of long-range liquid crystal (LC) ordering to tailor chain orientation and packing structure in liquid crystalline conjugated polymer (LCCP) layers for bio-mimicry of certain structural basis and light-harvesting properties of LHCs is reported. It is found that long-range orientational ordering in an LC phase of poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT) copolymer stabilizes a small fraction of randomly-oriented F8BT nanocrystals dispersed in an amorphous matrix of F8BT chains, resembling a self-doped host-guest system whereby excitation energy funneling and photoluminescence quantum efficiencies are enhanced significantly by triggering 3D donor-to-acceptor Förster resonance energy transfer (FRET) and dominant intrachain emission in the nano-crystal acceptor. Further, photoalignment of nematic F8BT layers is combined with LC orientational ordering to fabricate large-area-extended monodomains exhibiting >60% crystallinity and ≈20nm-long interchain packing order. Remarkably, these monodomains demonstrate strong linearly polarized emission, whilst also promoting a new band-edge absorption species and an extra emissive interchain excited state as compared to the non-aligned films.

Symmetry and stability of orientationally ordered collective motions of self-propelled, semiflexible filaments

Ordered, collective motions commonly arise spontaneously in systems of many interacting, active units, ranging from cellular tissues and bacterial colonies to self-propelled colloids and animal flocks. Active phases are especially rich when the active units are sufficiently anisotropic to produce liquid crystalline order and thus active nematic phenomena, with important biophysical examples provided by cytoskeletal filaments including microtubules and actin. Gliding assay experiments have provided a test bed to study the collective motions of these cytoskeletal filaments and unlocked diverse collective active phases, including states with long-range orientational order. However, it is not well understood how such long-range order emerges from the interplay of passive and active aligning mechanisms. We use Brownian dynamics simulations to study the collective motions of semiflexible filaments that self-propel in quasi-two-dimensions, in order to gain insights into the aligning mechanisms at work in these gliding assay systems. We find that, without aligning torques in the microscopic model, long-range orientational order can only be achieved when the filaments are able to overlap. The symmetry (nematic or polar) of the long-range order that first emerges is shown to depend on the energy cost of filament overlap and on filament flexibility. However, our model also predicts that a long-range-ordered active nematic state is merely transient, whereas long-range polar order is the only active dynamical steady state in systems with finite filament rigidity. Published by the American Physical Society 2024

Photoresponsive Biomimetic Functions by Light-Driven Molecular Motors in Three Dimensionally Printed Liquid Crystal Elastomers.

Despite the fascinating developments in design and synthesis of artificial molecular machines operating at the nanoscales, translating molecular motion along multiple length scales and inducing mechanical motion of a three-dimensional macroscopic entity remains an important challenge. The key to addressing this amplification of motion relies on the effective organization of molecular machines in a well-defined environment. By taking advantage of long-range orientational order and hierarchical structures of liquid crystals and unidirectional rotation of light-driven molecular motors, we report here photoresponsive biomimetic functions of liquid crystal elastomers (LCEs) by the repetitive unidirectional rotation of molecular motors using 3D printing. Molecular motors were built in the main chain of liquid crystals oligomers to serve as photoactuators. The oligomers were then used as the ink, and liquid crystal elastomers with different morphologies were printed. The obtained LCEs are able to conduct multiple types of motions including bending, helical coiling, closing of petals, and flipping of wings of a butterfly upon UV illumination, which paves the way for future design of responsive materials with enhanced complex actuating functions.

Molecular dynamics simulation as a promising approach for computational study of liquid crystal-based aptasensors

As a potent computational methodology, molecular dynamics (MD) simulation provides advantageous knowledge about biological compounds from the molecular viewpoint. In particular, MD simulation gives exact information about aptamer strands, such as the short synthetic oligomers, their orientation, binding sites, folding-unfolding state, and conformational re-arrangement. Also, the effect of the different chemicals and biochemicals as the components of aptamer-based sensors (aptasensors) on the aptamer-target interaction can be investigated by MD simulation. Liquid crystals (LCs) as soft substances with characteristics of both solid anisotropy and liquid fluidity are new candidates for designing label-free aptasensors. To now, diverse aptasensors have been developed experimentally based on the optical anisotropy, fluidity, and long-range orientational order of LCs. Here, we represent a computational model of an LC-based aptasensor through a detailed MD simulation study. The different parameters are defined and studied to achieve a comprehensive understanding of the computational design of the LC-based aptasensor, including the density of LCs, their orientation angle, and lognormal distribution in the absence and presence of aptamer strands, both aptamer and target molecules with various concentrations, and interfering substance. As a case study, the tobramycin antibiotic is considered the target molecule for the computational model of the LC-based aptasensor. Communicated by Ramaswamy H. Sarma

Mesostructured Materials with Controllable Long-Range Orientational Ordering and Anisotropic Properties.

Inorganic-organic mesophase materials provide a wide range of tunable properties, which are often highly dependent on their nano-, micro-, or meso-scale compositions and structures. Among these are macroscopic orientational order and corresponding anisotropic material properties, the adjustability of which are difficult to achieve. This is due to the complicated transient and coupled transport, chemical reaction, and surface processes that occur during material syntheses. By understanding such processes, general criteria are established and used to prepare diverse mesostructured materials with highly aligned channels with uniform nanometer dimensions and controllable directionalities over macroscopic dimensions and thicknesses. This is achieved by using a micropatterned semipermeable poly(dimethylsiloxane) stamp to manage the rates, directions, and surfaces at which self-assembling phases nucleate and the directions that they grow. This enables mesostructured surfactant-directed silica and titania composites, including with functional guest species, and mesoporous carbons to be prepared with high degrees of hexagonal order, as well as controllable orthogonal macroscopic orientational order. The resulting materials exhibit novel anisotropic properties, as demonstrated by the example of direction-dependent photocurrent generation, and are promising for enhancing the functionality of inorganic-organic nanocomposite materials in separations, catalysis, and energy conversion applications.

Splay-induced order in systems of hard tapers.

The main objective of this work is to clarify the role that taper-shaped elongated molecules, i.e., molecules with one end wider than the other, can play in stabilizing orientational order. The focus is exclusively on entropy-driven self-organization induced by purely excluded volume interactions. Drawing an analogy to RM734 (4-[(4-nitrophenoxy)carbonyl]phenyl-2,4-dimethoxybenzoate), which is known to stabilize ferroelectric nematic (N_{F}) and nematic splay (N_{S}) phases, and assuming that molecular biaxiality is of secondary importance, we consider monodisperse systems composed of hard molecules. Each molecule is modeled using six collinear tangent spheres with linearly decreasing diameters. Through hard-particle, constant-pressure Monte Carlo simulations, we study the emergent phases as functions of the ratio between the smallest and largest diameters of the spheres (denoted as d) and the packing fraction (η). To analyze global and local molecular orderings, we examine molecular configurations in terms of nematic, smectic, and hexatic order parameters. Additionally, we investigate the radial pair distribution function, polarization correlation function, and the histogram of angles between molecular axes. The last characteristic is utilized to quantify local splay. The findings reveal that splay-induced deformations drive unusual long-range orientational order at relatively high packing fractions (η>0.5), corresponding to crystalline phases. When η<0.5, only short-range order is affected, and in addition to the isotropic liquid, only the standard nematic and smectic-A liquid crystalline phases are stabilized. However, for η>0.5, apart from the ordinary nonpolar hexagonal crystal, three additional frustrated crystalline polar blue phases with long-range splay modulation are observed: antiferroelectric splay crystal (Cr_{S}P_{A}), antiferroelectric double-splay crystal (Cr_{DS}P_{A}), and ferroelectric double-splay crystal (Cr_{DS}P_{F}). Finally, we employ Onsager-Parsons-Lee local density functional theory to investigate whether any sterically induced (anti)ferroelectric nematic or smectic-A type of ordering is possible for our system, at least in a metastable regime.

Charge-driven liquid-crystalline behavior of ligand-functionalized nanorods in apolar solvent.

Concentrated colloidal suspensions of nanorods often exhibit liquid-crystalline (LC) behavior. The transition to a nematic LC phase, with long-range orientational order of the particles, is usually well-captured by Onsager's theory for hard rods, at least qualitatively. The theory shows how the volume fraction at the transition decreases with increasing aspect ratio of the rods. It also explains that the long-range electrostatic repulsive interaction occurring between rods stabilized by their surface charge can significantly increase their effective diameter, resulting in a decrease in the volume fraction at the transition, as compared to sterically stabilized rods. Here, we report on a system of ligand-stabilized LaPO4 nanorods, of aspect ratio ≈11, dispersed in apolar medium exhibiting the counter-intuitive observation that the onset of nematic self-assembly occurs at an extremely low volume fraction of ≈0.25%, which is lower than observed (≈3%) with the same particles when charged-stabilized in polar solvent. Furthermore, the nanorod volume fraction at the transition increases with increasing concentration of ligands, in a similar way as in polar media where increasing the ionic strength leads to surface charge screening. This peculiar system was investigated by dynamic light scattering, Fourier-transform infrared spectroscopy, zetametry, electron microscopy, polarized light microscopy, photoluminescence measurements, and X-ray scattering. Based on these experimental data, we formulate several tentative scenarios that might explain this unexpected phase behavior. However, at this stage, its full understanding remains a pending theoretical challenge. Nevertheless, this study shows that dispersing anisotropic nanoparticles in an apolar solvent may sometimes lead to spontaneous ordering events that defy our intuitive ideas about colloidal systems.

Insight into the Viscoelasticity of Self-Assembling Smectic Liquid Crystals of Colloidal Rods from Active Microrheology Simulations.

The rheology of colloidal suspensions is of utmost importance in a wide variety of interdisciplinary applications in formulation technology, determining equally interesting questions in fundamental science. This is especially intriguing when colloids exhibit a degree of long-range positional or orientational ordering, as in liquid crystals (LCs) of elongated particles. Along with standard methods, microrheology (MR) has emerged in recent years as a tool to assess the mechanical properties of materials at the microscopic level. In particular, by active MR one can infer the viscoelastic response of a soft material from the dynamics of a tracer particle being dragged through it by external forces. Although considerable efforts have been made to study the diffusion of guest particles in LCs, little is known about the combined effect of tracer size and directionality of the dragging force on the system's viscoelastic response. By dynamic Monte Carlo simulations, we apply active MR to investigate the viscoelasticity of self-assembling smectic (Sm) LCs consisting of rodlike particles. In particular, we track the motion of a spherical tracer whose size is varied within a range of values matching the system's characteristic length scales and being dragged by constant forces that are parallel, perpendicular, or at 45° to the nematic director. Our results reveal a uniform value of the effective friction coefficient as probed by the tracer at small and large forces, whereas a nonlinear, force-thinning regime is observed at intermediate forces. However, at relatively weak forces the effective friction is strongly determined by correlations between the tracer size and the structure of the host fluid. Moreover, we also show that external forces forming an angle with the nematic director provide additional details that cannot be simply inferred from the mere analysis of parallel and perpendicular forces. Our results highlight the fundamental interplay between tracer size and force direction in assessing the MR of Sm LC fluids.

Liquid Crystal Assembly for Ultra-dissymmetric Circularly Polarized Luminescence and Beyond.

Circularly polarized luminescence (CPL) is attracting much interest because it can carry extensive optical information. CPL shows left- or right-handedness and can be regarded as part of high-level visual perception to supply an extra dimension of information with regard to regular light. A key to meeting the needs for practical applications is to develop the emerging field of ultra-dissymmetric CPL. Chiral liquid crystal (LC) assemblies─otherwise referred to as cholesteric liquid crystals (CLCs)─are essentially organized helical superstructures with a highly ordered one-dimensional orientation, and distinctly superior to regular helical supramolecules. CLCs can achieve a perfect equilibrium of molecular short-range interaction and long-range orientational order, enabling molecule-scale chirality on a helical pitch and observable scale. LC assembly could be an ideal strategy for amplifying chirality, making it accessible to ultra-dissymmetric CPL. Herein, we focused on some basic but important issues regarding CPL: (i) How can CPL be created from chiral dyes? (ii) Is the chirality of luminescent dyes an essential factor for the generation of CPL? That is, can all chiral dyes emit CPL and vice versa? (iii) How can CPL be transferred within intermolecular systems, and what principles of CPL transmission should be followed? Given these queries and our work, in this Perspective we discuss the generation, transmission, and modulation of CPL with chiral LC assembly, aiming to design and build up novel chiroptical materials. Recent applications of CPL-active LC microstructures in three-dimensional displays, circularly polarized lasers, and asymmetric catalysis are also discussed.

Disordered hyperuniform solid state materials

Disordered hyperuniform (DHU) states are recently discovered exotic states of condensed matter. DHU systems are similar to liquids or glasses in that they are statistically isotropic and lack conventional long-range translational and orientational order. On the other hand, they completely suppress normalized infinite-wavelength density fluctuations like crystals and, in this sense, possess a hidden long-range correlation. Very recently, there have been several exciting discoveries of disordered hyperuniformity in solid-state materials, including amorphous carbon nanotubes, amorphous 2D silica, amorphous graphene, defected transition metal dichalcogenides, defected pentagonal 2D materials, and medium/high-entropy alloys. It has been found that the DHU states of these materials often possess a significantly lower energy than other disorder models and can lead to unique electronic and thermal transport properties, which results from mechanisms distinct from those identified for their crystalline counterparts. For example, DHU states can enhance electronic transport in 2D amorphous silica; DHU medium/high-entropy alloys realize the Vegard's law and possess enhanced electronic bandgaps and thermal transport at low temperatures. These unique properties open up many promising potential device applications in optoelectronics and thermoelectrics. Here, we provide a focused review on these important new developments of hyperuniformity in solid-state materials, taking an applied and “materials” perspective, which complements the existing reviews on hyperuniformity in physical systems and photonic materials. Future directions and outlook are also provided, with a focus on the design and discovery of DHU quantum materials for quantum information science and engineering.

Rotational Dynamics of Discoid Colloidal Particles in Attractive Quasi-Two-Dimensional Plastic Crystals.

Plastic crystals formed from anisotropic molecules or particles are an important state of matter characterized by the presence of long-range positional order and the lack of long-range orientational order. The rotational motion of molecules or particles in plastic crystals is the most attractive characteristic of the system. Here the rotational dynamics of the discoid particles in quasi-two-dimensional colloidal plastic crystals stabilized via depletion interactions are quantitatively studied using time-resolved confocal microscopy. The measured probability distribution of particle orientation reveals the existence of a strong coupling between the lattice symmetry and particle rotation, resulting in anisotropic rotational dynamics modes resembling the underlying hexagonal crystalline symmetry. Furthermore, the orientational distribution function provides information about the potential surface of rotational dynamics. The observed slow rotational diffusion can be attributed to the presence of orientational minima and potential barriers on the potential surface. Our findings with a real experimental system provide important insights into the role of attraction in the phase behaviors of plastic crystals.

Ferroelectric nematic liquids with conics

Spontaneous electric polarization of solid ferroelectrics follows aligning directions of crystallographic axes. Domains of differently oriented polarization are separated by domain walls (DWs), which are predominantly flat and run along directions dictated by the bulk translational order and the sample surfaces. Here we explore DWs in a ferroelectric nematic (NF) liquid crystal, which is a fluid with polar long-range orientational order but no crystallographic axes nor facets. We demonstrate that DWs in the absence of bulk and surface aligning axes are shaped as conic sections. The conics bisect the angle between two neighboring polarization fields to avoid electric charges. The remarkable bisecting properties of conic sections, known for millennia, play a central role as intrinsic features of liquid ferroelectrics. The findings could be helpful in designing patterns of electric polarization and space charge.

Magnetocontrollable droplet mobility on liquid crystal-infused porous surfaces.

Supplementary material (further details of the stability of LCIPS against water-induced dewetting, the interfacial tension and contact angle measurement using a goniometer, the estimation of the thickness of LC wrapping layer at air-water interface on droplets, SEM measurements, the average sliding velocity of a water droplet on 5CB, E7, silicone oil, and mineral oil films with and without a magnetic field, representative force diagram (Fd versus time) of a 3-µL water droplet moving at a speed of 0.1 mm/s on a nematic 8CB film, Fdynamic acting on 3 µL water droplets moving at speeds of 0.1-1 mm/s on an isotropic 8CB film, the calculated magnetic coherence length as a function of the magnitude of the magnetic field applied to the nematic LCIPS, and the apparent advancing and receding contact angles of a moving water droplet on nematic LCIPS as a function of time, and polarized light micrographs (top view) of a nematic 8CB film between two DMOAP-functionalized glass slides before and after applying a horizontal magnetic field) is available in the online version of this article at 10.1007/s12274-022-5318-y.

Single-orientation colloidal crystals from capillary-action-induced shear.

We study the crystallization of colloidal dispersions under capillary-action-induced shear as the dispersion is drawn into flat walled capillaries. Using confocal microscopy and small angle x-ray scattering, we find that the shear near the capillary walls influences the crystallization to result in large random hexagonal close-packed (RHCP) crystals with long-range orientational order over tens of thousands of colloidal particles. We investigate the crystallization mechanism and find partial crystallization under shear, initiating with hexagonal planes at the capillary walls, where shear is highest, followed by epitaxial crystal growth from these hexagonal layers after the shear is stopped. We then characterize the three-dimensional crystal structure finding that the shear-induced crystallization leads to larger particle separations parallel to the shear and vorticity directions as compared to the equilibrium RHCP structure. Confocal microscopy reveals that competing shear directions, where the capillary walls meet at a corner, create differently oriented hexagonal planes of particles. The single-orientation RHCP colloidal crystals remain stable after formation and are produced without the need of complex shear cell arrangements.

Splay-bend nematic phases of bent colloidal silica rods induced by polydispersity

Liquid crystal (LC) phases are in between solids and liquids with properties of both. Nematic LCs composed of rod-like molecules or particles exhibit long-range orientational order, yielding characteristic birefringence, but they lack positional order, allowing them to flow like a liquid. This combination of properties as well as their sensitivity to external fields make nematic LCs fundamental for optical applications e.g. liquid crystal displays (LCDs). When rod-like particles become bent, spontaneous bend deformations arise in the LC, leading to geometric frustration which can be resolved by complementary twist or splay deformations forming intriguing twist-bend (NTB) and splay-bend (NSB) nematic phases. Here, we show experimentally that the elusive NSB phases can be stabilized in systems of polydisperse micron-sized bent silica rods. Our results open avenues for the realization of NTB and NSB phases of colloidal and molecular LCs.

Disentangling the Orientations of Spectrally Overlapping Transition Dipoles in Dense Dye Layers

The transition dipole orientations of dye assemblies in heterostructures have a crucial impact on the efficiency of novel optoelectronic devices such as organic thin-film transistors and light-emitting diodes. These devices are frequently based on heterojunctions and tandem structures featuring multiple optical transitions. Precise knowledge of preferred orientations, spatial order, and spatial variations is highly relevant. We present a fast and universal large-area screening method to determine the transition dipole orientations in dye assemblies with diffraction-limited spatial resolution. Moreover, our hyperspectral imaging approach disentangles the orientations of different chromophores. As a demonstration, we apply our technique to dye monolayers with two optical transitions sandwiched between two ultrathin silicate nanosheets. A comprehensive model for dipole orientation distributions in monolayers reveals a long-range orientational order and a strong correlation between the two transitions.

Rough or crumpled: Phases in kinetic growth with surface relaxation.

We show that generic kinetic growth processes with surface relaxations can exhibit a hitherto unexplored crumpled phase with short-range orientational order at dimensions d<4. A sufficiently strong spatially nonlocal part of the chemical potential associated with the particle current above a threshold in the system can trigger this crumpling. The system can also be in a perturbatively accessible rough phase with long-range orientational order but short-range positional order at d<4 with known scaling exponents. Intriguingly, in d>4 we argue that there is no crumpling transition; instead, there is a roughening transition from a smooth to a rough phase for large enough nonlocal particle chemical potential. Experimental and theoretical implications of these results are discussed.

Hydrodynamic theory of p-atic liquid crystals.

We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic p-fold rotational symmetry, also known as p-atics, of which nematics (p=2) and hexatics (p=6) are the two best known examples. Previous hydrodynamic theories of p-atics are characterized by continuous O(2) rotational symmetry, which is higher than the discrete rotational symmetry of p-atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for p>2. Furthermore, we show that any finite imposed shear will induce long-ranged orientational order in any p-atic liquid crystal, in contrast to the quasi-long-ranged order that occurs in the absence of shear. The induced order parameter scales like a nonuniversal power of the applied shear rate at small shear rates.

Long-Ranged Order and Flow Alignment in Sheared p-atic Liquid Crystals.

We formulate a hydrodynamic theory of p-atic liquid crystals, namely, two-dimensional anisotropic fluids endowed with generic p-fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of p-atic phases, allows us to unveil several unknown aspects of flowing p-atics, that previous theories, characterized by O(2) rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.