Two-stage assembly of patchy ellipses: From bent-core particles to liquid crystal analogs

We investigate the two-dimensional behavior of colloidal patchy ellipsoids specifically designed to follow a two-step assembly process from the monomer state to mesoscopic liquid-crystal phases via the formation of the so-called bent-core units at the intermediate stage. Our model comprises a binary mixture of ellipses interacting via the Gay-Berne potential and decorated by surface patches, with the binary components being mirror-image variants of each other-referred to as left-handed and right-handed ellipses according to the position of their patches. The surface patches are designed so as in the first stage of the assembly the monomers form bent-cores units, i.e., V-shaped dimers with a specific bent angle. The Gay-Berne interactions, which act between the ellipses, drive the dimers to subsequently form the characteristic phase observed in bent-core liquid crystals. We numerically investigate-by means of both Molecular Dynamics and Monte Carlo simulations-the described two-step process: we first optimize a target bent-core unit and then fully characterize its state diagram in temperature and density, defining the regions where the different liquid crystalline phases dominate.

Directed assembly of small binary clusters of magnetizable ellipsoids

We report the effect of shape anisotropy and material properties on the directed assembly of binary suspensions composed of magnetizable ellipsoids. In a Monte Carlo simulation, we implement the ellipsoid-dipole model to calculate the pairwise dipolar interaction energy as a function of position and orientation. The analysis explores dilute suspensions of paramagnetic and diamagnetic ellipsoids with different aspect ratios in a superparamagnetic medium. We analyze the local order of binary structures as a function of particle aspect ratio, medium permeability, and dipolar interaction strength. Our results show that local order and symmetry are tunable under the influence of a uniform magnetic field when one component of the structure is dilute with respect to the other. The simulation results match previously reported experiments on the directed assembly of binary suspension of spheres. Additionally, we report the conditions on particle aspect ratios and medium properties for various structures with rotational symmetries, as well as open and enclosed structures under the influence of a uniform magnetic field.

Liquid crystals from curved colloidal rods: waves, twists and more

The curvature of elongated microscopic building blocks plays a crucial role on their self-assembly into orientationally ordered phases. While rod-like molecules form a handful of liquid crystal (LC) phases, curved or banana-shaped molecules show more than fifty phases, with fascinating physical properties, such as chirality or polarity. Despite the fundamental and technological importance of these so-called 'banana-shaped liquid crystals', little is known about their microscopic details at the single-molecule level. Curved colloidal liquid crystals-liquid crystals formed by curved colloidal rods-are excellent model systems to optically resolve the structure and dynamics of curved building blocks within these condensed phases. Recent advances in the synthesis of curved rod-like particles have unlocked the potential for studying-at the single-particle level-the intimate relationship between shape and phase symmetry, and even confirmed the stability of elusive LC phases. Further developments in this nascent field promise exciting findings, such as the first observation of the colloidal twist-bend nematic phase or the fabrication of functional materials with curvature-dependent properties. In this Report on Progress, we will highlight recent advances in the synthesis and assembly of curved colloidal liquid crystals and discuss the upcoming challenges and opportunities of this field.

Achiral hard bananas assemble double-twist skyrmions and blue phases

Skyrmions are topologically protected, vortex-like structures found in various condensed-matter systems including helical ferromagnets and liquid crystals, typically arising from chiral interactions. Using extensive particle-based simulations, we demonstrate that non-chiral hard banana-shaped particles, governed solely by excluded-volume interactions, spontaneously stabilize skyrmion structures through the bend-flexoelectric effect. Under thin confinement, we observe the formation of quasi-2D layers of isolated skyrmions or dense skyrmion lattices. These structures, comprising a racemic mixture of left- and right-handed skyrmions, show resilience against thermal fluctuations while remaining responsive to external fields, offering intriguing possibilities for manipulation. We also find that the size of these skyrmions can be adjusted by the dimensions and curvature of the banana-shaped particles. In the absence of geometric frustration due to confinement, a blue phase III may emerge, characterized by a 3D network of chiral skyrmion filaments of the nematic director field within an isotropic background. Our findings provide valuable insights into stabilizing skyrmion lattices and blue phases, showcasing non-Gaussian fluid-like dynamics in systems of achiral hard particles. Furthermore, they highlight the remarkable capacity of these complex fluids in designing advanced functional materials with diverse applications in photonics and memory devices.

Self-limiting stacks of curvature-frustrated colloidal plates: Roles of intraparticle versus interparticle deformations

In geometrically frustrated assemblies local intersubunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here we use theory and coarse-grained simulation to study a recently developed class of "curvamer" particles, flexible shell-like particles that exhibit self-limiting assembly due to the build up of curvature deformation in cohesive stacks. To address a generic, yet poorly understood aspect of frustrated assembly, we introduce a model of curvamer assembly that incorporates both intraparticle shape deformation as well as compliance of interparticle cohesive gaps, an effect we can attribute to a finite range of attraction between particles. We show that the ratio of intraparticle (bending elasticity) to interparticle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation through curvamer stacks. We find a transition from uniformly bound, curvature-focusing stacks at small size to gap opened, uniformly curved stacks at large size is controlled by a dimensionless measure of inter- versus intracurvamer stiffness. The finite range of interparticle attraction determines the range of cohesion in stacks that are self-limiting, a prediction which is in strong agreement with numerical studies of our coarse-grained colloidal model. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multiparticle scales.

Hydrogel-Reactive-Microenvironment Powering Reconfiguration of Polymer Architectures

Reconfiguration of architected structures has great significance for achieving new topologies and functions of engineering materials. Existing reconfigurable strategies have been reported, including approaches based on heat, mechanical instability, swelling, origami/kirigami designs, and electromagnetic actuation. However, these approaches mainly involve physical interactions between the host materials and the relevant stimuli. Herein, a novel, easy-manipulated, and controllable reconfiguration strategy for polymer architectures is proposed by using a chemical reaction of host material within a hydrogel reactive microenvironment. 3D printed polycaprolactone (PCL) lattices transformed in an aqueous polyacrylamide (PAAm) hydrogel precursor solution, in which ultraviolet (UV) light triggered heterogeneous grafting polymerization between PCL and AAm. In situ microscopy shows that PCL beams go through volumetric expansion and cooperative buckling, resulting in transformation of PCL lattices into sinusoidal patterns. The transformation process can be tuned easily and patterned through the adjustment of the PCL beam diameter, unit cell width, and UV light on-off state. Controlling domain formation is achieved by using UV masks. This framework enables the design, fabrication, and programming of architected materials and inspires the development of novel 4D printing approaches.

Role of Shape in Particle-Lipid Membrane Interactions: From Surfing to Full Engulfment

Understanding and manipulating the interactions between foreign bodies and cell membranes during endo- and phagocytosis is of paramount importance, not only for the fate of living cells but also for numerous biomedical applications. This study aims to elucidate the role of variables such as anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength in this essential process using a minimal experimental biomimetic system comprising giant unilamellar vesicles and rod-like particles with different curvatures and aspect ratios. We find that the particle wrapping process is dictated by the balance between the elastic free energy penalty and adhesion free energy gain, leading to two distinct engulfment pathways, tip-first and side-first, emphasizing the significance of the particle orientation in determining the pathway. Moreover, our experimental results are consistent with theoretical predictions in a state diagram, showcasing how to control the wrapping pathway from surfing to partial to complete wrapping by the interplay between membrane tension and adhesive strength. At moderate particle concentrations, we observed the formation of rod clusters, which exhibited cooperative and sequential wrapping. Our study contributes to a comprehensive understanding of the mechanistic intricacies of endocytosis by highlighting how the interplay between the anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength can influence the engulfment pathway.

Structural parameters of twist-bend nematics and splay-bend nematics in Dozov's theory

This paper presents the results of numerical calculations revealing how the structural parameters (i.e., the pitch p_{TB}, the spatial period p_{SB}, and the tilt angle θ_{TB} or θ_{SB}) of twist-bend nematics (N_{TB}) and splay-bend nematics (N_{SB}) depend on the values of elastic constants in Dozov's theory [I. Dozov, Europhys. Lett. 56, 247 (2001)10.1209/epl/i2001-00513-x]. Alternative formulas for p_{TB}, θ_{TB}, p_{SB}, and θ_{SB} have been derived and it has been proved that they give more accurate results than the expressions proposed by Dozov. Although the determination of the fourth-order elastic constants C_{1}, C_{2}, and C_{3} is not feasible in a simple way, the order of magnitude of the sum C_{1}+C_{2} has been easily estimated and is equal to 10^{-31}Jm. Moreover, the numerical calculations have shown that twist-bend nematics can exist even when K_{11} is smaller than 2K_{22} and thus Dozov's criterion K_{11}>2K_{22} for the stability of the N_{TB} phase is not strictly satisfied.

Properties of packings and dispersions of superellipse sector particles

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We compare three computational processes: pair-wise Monte Carlo simulations that explore particle-particle geometric constraints, Monte Carlo simulations that reveal how these geometric constraints play out over dispersions of many particles, and Molecular Dynamics simulations that form random loose and close packings. We investigate the dependence of critical random loose and close packing fractions on particle parameters, finding that both values increase with opening aperture and decrease with increasing corner sharpness. The identified packing fractions are compared with the mean-field prediction of the random contact model; we find deviations from the model's prediction due to correlations between particle orientations. The complex interaction of spatial proximity and orientational alignment is also explored with a generalized spatioorientational distribution area (SODA) plot, which shows how higher density packings are achieved through particles assuming a small number of preferred configurations that depend sensitively on particle shape and system preparation.

Thermal stability and secondary aggregation of self-limiting, geometrically frustrated assemblies: Chain assembly of incommensurate polybricks

In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multisubunit size which results from the competition between the elastic costs of frustration within an assembly and the surface energy at its boundaries. Physical realizations-from ill-fitting particle assemblies to self-twisting protein superstructures-are capable of multiple mechanisms of escaping the cumulative costs of frustration, resulting in unlimited equilibrium assembly, including elastic modes of "shape flattening" and the formation of weak, defective bonds that screen intra-assembly stresses. Here we study a model of one-dimensional chain assembly of incommensurate "polybricks" and determine its equilibrium assembly as a function of temperature, concentration, degree of shape frustration, elasticity, and interparticle binding, notably focusing on how weakly cohesive, defective bonds give rise to strongly temperature-dependent assembly. Complex assembly behavior derives from the competition between multiple distinct local minima in the free-energy landscape, including self-limiting chains, weakly bound aggregates of self-limiting chains, and strongly bound, elastically defrustrated assemblies. We show that this scenario, in general, gives rise to anomalous multiple aggregation behavior, in which disperse subunits (stable at low concentration and high temperature) first exhibit a primary aggregation transition to self-limiting chains (at intermediate concentration and temperature) which are ultimately unstable to condensation into unlimited assembly of finite-chains through weak binding beyond a secondary aggregation transition (at low temperature and high concentration). We show that window of stable self-limitation is determined both by the elastic costs of frustration in the assembly as well as energetic and entropic features of intersubunit binding.

Crystallization Regulation by Self-Assembling Liquid Crystal Template Enables Efficient and Stable Perovskite Solar Cells

It is found that the disordered growth of bottom perovskite film deteriorates the buried interface of perovskite solar cells (PSCs), so developing a new material to modify the buried interface for regulating the crystal growth and defect passivation is an effective approach for improving the photovoltaic performance of PSCs. Here, we developed a new ionic liquid crystal (ILC, 1-Dodecyl-3-methylimidazolium tetrafluoroborate) as both crystal regulator and defect passivator to modify the buried interface of PSCs. The high lattice matching between this ILC and perovskite promotes preferential growth of perovskite film along [001] direction, while the oriented ILC with mesomorphic phase has a strong chemical interaction with perovskite to passivate the interface defect, as a result, the modified buried interface exhibits suppressed defects, improved band alignment, reduced nonradiative recombination losses, and enhanced charge extraction. The ILC-modified PSC delivers a power conversion efficiency of 24.92 % and maintains 94 % of the original value after storage in ambient for 3000 h.

Uniform Colloidal Polymer Rods by Stabilizer-Assisted Liquid-Crystallization-Driven Self-Assembly

The synthesis of anisotropic colloidal building blocks is essential for their self-assembly into hierarchical materials. Here, a highly efficient stabilizer-assisted liquid-crystallization-driven self-assembly (SA-LCDSA) strategy was developed to achieve monodisperse colloidal polymer rods. This strategy does not require the use of block copolymers, but only homopolymers or random copolymers. The resulting rods have tunable size and aspect ratios, as well as well-defined columnar liquid crystal structures. The integrated triphenylene units enable the rods to exhibit unusual photo-induced fluorescence enhancement and accompanying irradiation memory effect, which, as demonstrated, are attractive for information encryption/decryption of paper documents. In particular, unwanted document decryption during delivery can be examined by fluorescence kinetics. This SA-LCDSA-based approach can be extended to synthesize other functional particles with desired π-molecular units.

Splay and polar order in a system of hard pear-like molecules: confrontation of Monte Carlo numerical simulations with density functional theory calculations

Recent experimental discoveries of novel nematic types with polar order, including ferroelectric nematic and splay nematic, have brought the resurgence of the interest in polar and modulated phases. One of the most important factors that is widely believed to be crucial for the formation of new phases is the pear-like shape of mesogenic molecules. Such molecules were treated using second-virial density functional theory in [De Gregorio, P et al., Soft Matter, 2016, 12(23), 5188-5198], where the authors showed that the K11 splay elastic constant can become negative due to solely entropic reasons leading to long-range splay and polar correlations. To verify whether the predictions are correct, we performed Monte Carlo simulations of the same hard-core molecules used in the DFT study. As our results suggest, no polar or modulated liquid crystalline phases emerge; polar and splay correlations are either at most short-range or completely absent. On the other hand, a polar ferroelectric splay crystal was observed.

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

Computational approach for structure generation of anisotropic particles (CASGAP) with targeted distributions of particle design and orientational order

The macroscopic properties of materials are governed by their microscopic structure which depends on the materials' composition (i.e., building blocks) and processing conditions. In many classes of synthetic, bioinspired, or natural soft and/or nanomaterials, one can find structural anisotropy in the microscopic structure due to anisotropic building blocks and/or anisotropic domains formed through the processing conditions. Experimental characterization and complementary physics-based or data-driven modeling of materials' structural anisotropy are critical for understanding structure-property relationships and enabling targeted design of materials with desired macroscopic properties. In this pursuit, to interpret experimentally obtained characterization results (e.g., scattering profiles) of soft materials with structural anisotropy using data-driven computational approaches, there is a need for creating real space three-dimensional structures of the designer soft materials with realistic physical features (e.g., dispersity in building block sizes) and anisotropy (i.e., aspect ratios of the building blocks, their orientational and positional order). These real space structures can then be used to compute and complement experimentally obtained characterization results or be used as initial configurations for physics-based simulations/calculations that can then provide training data for machine learning models. To address this need, we present a new computational approach called CASGAP - Computational Approach for Structure Generation of Anisotropic Particles - for generating any desired three dimensional real-space structure of anisotropic building blocks (modeled as particles) adhering to target distributions of particle shape, size, and positional and orientational order.

Shock compression of semiflexible polymers

We employ molecular dynamics simulations to investigate the shock compression of linear semiflexible polymers. While the propagation velocity of a shock primarily depends on density, both chain rigidity and chain orientation significantly influence the shock width and the final temperature of the system. In general, the shock wave triggers molecular buckling in chains oriented perpendicular to the compression front. Following the passage of the front, the semiflexible chains buckle with a wavelength that decreases with the compression speed as λm ∼ up-0.2, and subsequent relaxation leads to a banana-like liquid crystal phase. In ordered systems with molecules oriented perpendicular to the compression front, the shock width increases by a factor of up to 10 compared to a similar isotropic system, resulting in enhanced shock energy absorption. These findings indicate that chain stiffness plays a critical role in the impact absorption properties of polymeric materials.

Theoretical models of modulated nematic phases

Novel modulated nematic phases, such as twist-bend nematics, splay-bend nematics and splay nematics, are an important subject of research in the field of liquid crystals. In this article fundamental information about the discovery, structure and properties of these phases is presented. Various theoretical models of elastic properties are compared, especially the proposed formulae for the free energy density of modulated nematic phases and the conditions for their stability. The emphasis is put on the variety of material parameters and variables in the mathematical description of the structures. The elastic models are classified according to a few criteria. Flexopolarisation is indicated as a main phenomenon responsible for the formation of modulated nematic phases. The elastic models are used for analysing the deformations of the twist-bend nematic structure in external fields. Dielectric, flexoelectric, ferroelectric and magnetic effects are considered. Two types of distortions are distinguished: microscopic (connected with the deformation of the director distribution) and macroscopic (related to the change of the optic axis direction). This review can be a starting point for further studies, for example computer simulations of modulated phases and design of liquid crystalline devices.

Effect of curvature on the diffusion of colloidal bananas

Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods-also known as colloidal bananas-as a function of their opening angle α. We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from 0^{∘} (straight rods) to nearly 360^{∘}(closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when α>180^{∘}. We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.

Fluid Flow Templating of Polymeric Soft Matter with Diverse Morphologies

It is challenging to find a conventional nanofabrication technique that can consistently produce soft polymeric matter of high surface area and nanoscale morphology in a way that is scalable, versatile, and easily tunable. Here, the capabilities of a universal method for fabricating diverse nano- and micro-scale morphologies based on polymer precipitation templated by the fluid streamlines in multiphasic flow are explored. It is shown that while the procedure is operationally simple, various combinations of its intertwined mechanisms can controllably and reproducibly lead to the formation of an extraordinary wide range of colloidal morphologies. By systematically investigating the process conditions, 12 distinct classes of polymer micro- and nano-structures including particles, rods, ribbons, nanosheets, and soft dendritic colloids (dendricolloids) are identified. The outcomes are interpreted by delineating the physical processes into three stages: hydrodynamic shear, capillary and mechanical breakup, and polymer precipitation rate. The insights into the underlying fundamental mechanisms provide guidance toward developing a versatile and scalable nanofabrication platform. It is verified that the liquid shear-based technique is versatile and works well with many chemically diverse polymers and biopolymers, showing potential as a universal tool for simple and scalable nanofabrication of many morphologically distinct soft matter classes.

Self-Assembled Tetratic Crystals by Orthogonal Colloidal Force

Bonding simple building blocks to create crystalline materials with design has been sophisticated in the molecular world, but this is still very challenging for anisotropic nanoparticles or colloids, because the particle arrangements, including position and orientation, cannot be manipulated as expected. Here biconcave polystyrene (PS) discs to present a shape self-recognition route are used, which can control both the position and orientation of particles during self-assembly by directional colloidal forces. An unusual but very challenging two-dimensional (2D) open superstructure-tetratic crystal (TC)-is achieved. The optical properties of the 2D TCs are studied by the finite difference time domain method, showing that the PS/Ag binary TC can be used to modulate the polarization state of the incident light, for example, converting the linearly polarized light into left-handed or right-handed circularly polarized light. This work paves an important way for self-assembling many unprecedented crystalline materials.

Conformational degrees of freedom and stability of splay-bend ordering in the limit of a very strong planar anchoring

We study the self-organization in a monolayer (a two-dimensional system) of flexible planar trimer particles. The molecules are made up of two mesogenic units linked by a spacer, all of which are modeled as hard needles of the same length. Each molecule can dynamically adopt two conformational states: an achiral bent-shaped (cis-) and a chiral zigzag (trans-) one. Using constant pressure Monte Carlo simulations and Onsager-type density functional theory (DFT), we show that the system consisting of these molecules exhibits a rich spectrum of liquid crystalline phases. The most interesting observation is the identification of stable smectic splay-bend (S_{SB}) and chiral smectic-A (S_{A}^{*}) phases. The S_{SB} phase is also stable in the limit, where only cis- conformers are allowed. The second phase that occupies a considerable portion of the phase diagram is S_{A}^{*} with chiral layers, where the chirality of the neighboring layers is of opposite sign. The study of the average fractions of the trans- and cis- conformers in various phases shows that while in the isotropic phase all fractions are equally populated, the S_{A}^{*} phase is dominated by chiral conformers (zigzag), but the achiral conformers win in the smectic splay-bend phase. To clarify the possibility of stabilization of the nematic splay-bend (N_{SB}) phase for trimers, the free energy of the N_{SB} and S_{SB} phases is calculated within DFT for the cis- conformers, for densities where simulations show stable S_{SB}. It turns out that the N_{SB} phase is unstable away from the phase transition to the nematic phase, and its free energy is always higher than that of S_{SB}, down to the transition to the nematic phase, although the difference in free energies becomes extremely small when approaching the transition.

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.

The thermodynamic origins of chiral twist in monolayer assemblies of rod-like colloids

The propagation of chirality across scales is a common but poorly understood phenomenon in soft matter. Here, using computer simulations, we study twisted monolayer assemblies formed by both chiral and achiral rod-like particles in the presence of non-adsorbing polymer and characterise the thermodynamic driving forces responsible for the twisting. We observe assemblies with both like and inverted chirality relative to the rods and show that the preferred twist is already determined during the initial stage of the self-assembly. Depending on the geometry of the constituent rods, the chiral twist is regulated by either the entropy gain of the polymer, or of the rods, or both. This can include important contributions from changes in both the surface area and volume of the monolayer and from rod fluctuations perpendicular to the monolayer. These findings can deepen our understanding of why chirality propagates and of how to control it.

Self-assembled liquid crystal architectures for soft matter photonics

Self-assembled architectures of soft matter have fascinated scientists for centuries due to their unique physical properties originated from controllable orientational and/or positional orders, and diverse optic and photonic applications. If one could know how to design, fabricate, and manipulate these optical microstructures in soft matter systems, such as liquid crystals (LCs), that would open new opportunities in both scientific research and practical applications, such as the interaction between light and soft matter, the intrinsic assembly of the topological patterns, and the multidimensional control of the light (polarization, phase, spatial distribution, propagation direction). Here, we summarize recent progresses in self-assembled optical architectures in typical thermotropic LCs and bio-based lyotropic LCs. After briefly introducing the basic definitions and properties of the materials, we present the manipulation schemes of various LC microstructures, especially the topological and topographic configurations. This work further illustrates external-stimuli-enabled dynamic controllability of self-assembled optical structures of these soft materials, and demonstrates several emerging applications. Lastly, we discuss the challenges and opportunities of these materials towards soft matter photonics, and envision future perspectives in this field.

Active microrheology of colloidal suspensions of hard cuboids

By performing dynamic Monte Carlo simulations, we investigate the microrheology of isotropic suspensions of hard-core colloidal cuboids. In particular, we infer the local viscoelastic behavior of these fluids by studying the dynamics of a probe spherical particle that is incorporated in the host phase and is dragged by an external force. This technique, known as active microrheology, allows one to characterize the microscopic response of soft materials upon application of a constant force, whose intensity spans here three orders of magnitude. By tuning the geometry of cuboids from oblate to prolate as well as the system density, we observe different responses that are quantified by measuring the effective friction perceived by the probe particle. The resulting friction coefficient exhibits a linear regime at forces that are much weaker and larger than the thermal forces, whereas a nonlinear, force-thinning regime is observed at intermediate force intensities.

Molecular Simulation Approaches to the Study of Thermotropic and Lyotropic Liquid Crystals

Over the last decade, the availability of computer time, together with new algorithms capable of exploiting parallel computer architectures, has opened up many possibilities in molecularly modelling liquid crystalline systems. This perspective article points to recent progress in modelling both thermotropic and lyotropic systems. For thermotropic nematics, the advent of improved molecular force fields can provide predictions for nematic clearing temperatures within a 10 K range. Such studies also provide valuable insights into the structure of more complex phases, where molecular organisation may be challenging to probe experimentally. Developments in coarse-grained models for thermotropics are discussed in the context of understanding the complex interplay of molecular packing, microphase separation and local interactions, and in developing methods for the calculation of material properties for thermotropics. We discuss progress towards the calculation of elastic constants, rotational viscosity coefficients, flexoelectric coefficients and helical twisting powers. The article also covers developments in modelling micelles, conventional lyotropic phases, lyotropic phase diagrams, and chromonic liquid crystals. For the latter, atomistic simulations have been particularly productive in clarifying the nature of the self-assembled aggregates in dilute solution. The development of effective coarse-grained models for chromonics is discussed in detail, including models that have demonstrated the formation of the chromonic N and M phases.

Computer simulations of self-assembly of anisotropic colloids

Computer simulations have played a significant role in understanding the physics of colloidal self-assembly, interpreting experimental observations, and predicting novel mesoscopic and crystalline structures. Recent advances in computer simulations of colloidal self-assembly driven by anisotropic or orientation-dependent inter-particle interactions are highlighted in this review. These interactions are broadly classified into two classes: entropic and enthalpic interactions. They mainly arise due to shape anisotropy, surface heterogeneity, compositional heterogeneity, external field, interfaces, and confinements. Key challenges and opportunities in the field are discussed.

Coupling between splay deformations and density modulations in splay-bend phases of bent colloidal rods

Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped) rods, we investigate how spatial deformations in the nematic director field affect the local density of twist-bend and splay-bend nematic phases. The grand-canonical character of the theory naturally relates the local density to the local nematic order parameter S. In the splay-bend phase, we find S and hence the local density to modulate periodically along one spatial direction. As a consequence the splay-bend phase has the key symmetries of a smectic rather than a nematic phase. By contrast we find that S and hence the local density do not vary in space in the twist-bend phase, which is therefore a proper nematic phase. The theoretically predicted one-dimensional density modulations in splay-bend phases are in agreement with recent simulations.

Phase behavior of hard circular arcs

By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally thin circular arcs, from an aperture angle θ→0 to an aperture angle θ→2π, in the two-dimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally thin circular arcs autoassemble to form clusters. These clusters are either filamentous, for smaller values of θ, or roundish, for larger values of θ. Provided the density is sufficiently high, the filaments lengthen, merge, and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phase.

Hierarchical, Highly Open Microtubes and Columnar Liquid Crystals Self-Assembled from Symmetrical and Asymmetrical Colloidal Rings

The use of simple building blocks to produce hierarchical and porous structured materials is highly desired. Rings are simple colloidal particles but unique for their internal cavities. Here we report the self-assembly (SA) of colloidal rings with tunable asymmetry mediated by a depletion force and demonstrate that a variety of porous colloidal superstructures from microtubes, flexible chains, (plastic) crystals to highly open liquid crystals (LCs) can be formed along the predesigned SA paths. In particular, the SA is staged in binary or ternary systems. Large rings first form complex ring-in-ring and ring-in-ring-in-ring assemblies by capturing smaller rings, which, as new building blocks, can further form multi-walled microtubes and open columnar LCs. Moreover, a plastic columnar LC with alternating intracolumnar stacking is found from asymmetrical rings. The SA with colloidal rings opens a new avenue to construct hierarchical and porous ordered metamaterials.

Excluded area of superellipse sector particles

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We investigate the space of allowable (nonoverlapping) configurations of two SeSPs, which depends on both the center-of-mass separation and relative orientation. Radial correlation plots of the allowed configurations reveal circular regions centered at each of the particle's two end points that indicate configurations of mutually entangled particle interactions. Simultaneous entanglement with both end points is geometrically impossible; the overlap of these two regions therefore represents an excluded area in which no particles can be placed regardless of orientation. The regions' distinct boundaries indicate a translational frustration with implications for the dynamics of particle rearrangements (e.g., under shear). Representing translational and rotational degrees of freedom as a hypervolume, we find a topological change that suggests geometric frustration arises from a phase transition in this space. The excluded area is a straightforward integration over excluded states; for arbitrary relative orientation this decreases sigmoidally with increasing opening aperture, with sharper SeSP corners resulting in a sharper decrease. Together, this work offers a path towards a unified theory for particle shape control of bulk material properties.

Hierarchical self-assembly of polydisperse colloidal bananas into a two-dimensional vortex phase

Hierarchically self-assembled materials—structures with order at multiple length scales—can be found everywhere. Examples range from collagen structures in human bones to engineered photonic materials. These structures usually assemble from monodisperse microscopic building blocks that interact via complex directional interactions. In this work, we show that hierarchical materials can, in fact, also be assembled from polydisperse building blocks and by entropic interactions alone. Our simple yet powerful assembly mechanism opens up avenues toward rationally exploiting the often undesired polydispersity of colloidal building blocks for programming entropy-driven self-assembly of hierarchical materials.

Self-assembly of microscopic building blocks into highly ordered and functional structures is ubiquitous in nature and found at all length scales. Hierarchical structures formed by colloidal building blocks are typically assembled from monodisperse particles interacting via engineered directional interactions. Here, we show that polydisperse colloidal bananas self-assemble into a complex and hierarchical quasi–two-dimensional structure, called the vortex phase, only due to excluded volume interactions and polydispersity in the particle curvature. Using confocal microscopy, we uncover the remarkable formation mechanism of the vortex phase and characterize its exotic structure and dynamics at the single-particle level. These results demonstrate that hierarchical self-assembly of complex materials can be solely driven by entropy and shape polydispersity of the constituting particles.

Self-Assembly of Isostatic Self-Dual Colloidal Crystals

Self-dual structures whose dual counterparts are themselves possess unique hidden symmetry, beyond the description of classical spatial symmetry groups. Here we propose a strategy based on a nematic monolayer of attractive half-cylindrical colloids to self-assemble these exotic structures. This system can be seen as a 2D system of semidisks. By using Monte Carlo simulations, we discover two isostatic self-dual crystals, i.e., an unreported crystal with pmg space-group symmetry and the twisted kagome crystal. For the pmg crystal approaching the critical point, we find the double degeneracy of the full phononic spectrum at the self-dual point and the merging of two tilted Weyl nodes into one critically tilted Dirac node. The latter is "accidentally" located on the high-symmetry line. The formation of this unconventional Dirac node is due to the emergence of the critical flatbands at the self-dual point, which are linear combinations of "finite-frequency" floppy modes. These modes can be understood as mechanically coupled self-dual rhombus chains vibrating in some unique uncoupled ways. Our work paves the way for designing and fabricating self-dual materials with exotic mechanical or phononic properties.

From shaping to functionalization of micro-droplets and particles

The structure of microdroplet and microparticle is a critical factor in their functionality, which determines the distribution and sequence of physicochemical reactions. Therefore, the technology of precisely tailoring their shape is requisite for implementing the user demand functions in various applications. This review highlights various methodologies for droplet shaping, classified into passive and active approaches based on whether additional body forces are applied to droplets to manipulate their functions and fabricate them into microparticles. The passive approaches cover batch emulsification, solvent evaporation and diffusion, micromolding, and microfluidic methods. In active approaches, the external forces, such as electrical and magnetic fields or optical lithography, are applied to microdroplets. Special attention is also given to latest technologies using microdroplets and microparticles, especially in the fields of biological, optical, robotic, and environmental applications. Finally, this review aims to address the advantages and disadvantages of the introduced approaches and suggests the direction for further development in this field.

The Beauty of Twist-Bend Nematic Phase: Fast Switching Domains, First Order Fréedericksz Transition and a Hierarchy of Structures

The twist-bend nematic phase (NTB) exhibits a complicated hierarchy of structures responsible for several intriguing properties presented here. These are: the observation of a fast electrooptic response, the exhibition of a large electroclinic effect, and the observation of an unusual pattern of the temperature dependence of birefringence of bent-shaped bimesogens in parallel-rubbed planar-aligned cells. These unusual effects inspired the use of highly sophisticated techniques that led to the discovery of the twist-bend nematic phase. Results of the optical retardation of a parallel-rubbed planar-aligned cell show that the ‘heliconical angle’ (the angle the local director makes with the optical axis) starts increasing in the high temperature N phase, it exhibits a jump at the N–NTB transition temperature and continues to increase in magnitude with a further reduction in temperature. The liquid crystalline parallel-rubbed planar-aligned and twist-aligned cells in this phase exhibit fascinating phenomena such as a demonstration of the beautiful stripes and dependence of their periodicity on temperature. The Fréedericksz transition in the NTB phase is found to be of the first order both in rubbed planar and homeotropic-aligned cells, in contrast to the second order transition exhibited by a conventional nematic phase. This transition shows a significant hysteresis as well as an abrupt change in the orientation of the director as a function of the applied electric field. Hierarchical structures are revealed using the technique of polymer templating the structure of the liquid crystalline phase of interest, and imaging of the resulting structure by scanning electron microscopy.

Capillary forces drive buckling, plastic deformation, and break-up of 3D printed beams

Capillary forces acting at the interfaces of soft materials lead to deformations over the scale of the elastocapillary length. When surface stresses exceed a material's yield stress, a plastocapillary effect is expected to arise, resulting in yielding and plastic deformation. Here, we explore the interfacial instabilities of 3D-printed fluid and elastic beams embedded within viscoelastic fluids and elastic solid support materials. Interfacial instabilities are driven by the immiscibility between the paired phases or their solvents. We find that the stability of an embedded structure is predicted from the balance between the yield stress of the elastic solid, τ_y, the apparent interfacial tension between the materials, γ', and the radius of the beam, r, such that τ_y > γ'/r. When the capillary forces are sufficiently large, we observe yielding and failure of the 3D printed beams. Furthermore, we observe new coiling and buckling instabilities emerging when elastic beams are embedded within viscous fluid support materials. The coiling behavior appear analogous to elastic rope coiling whereas the buckling instability follows the scaling behavior predicted from Euler-Bernoulli beam theory.

Synthesis of Rough Colloidal SU-8 Rods and Bananas via Nanoprecipitation

Surface roughness plays an important role in determining the mechanical properties, wettability, and self-assembly in colloidal systems. In this work, we develop a simple and fast method to produce rough colloidal SU-8 rods, bananas, and spheres, via the nanoprecipitation of SU-8 in water. During this process, SU-8 nanospheres are absorbed onto the surface of the colloidal SU-8 particles and then cross-linked using UV-light. The size of the spherical asperities and the asperity density are controlled by the concentration of SU-8 used during the nanoprecipitation reaction. Fluorescent labeling of the rough SU-8 colloidal particles allows for their confocal imaging, which demonstrates their stability at high packing fractions. With these newly developed rough particles, we provide a colloidal model system that allows for studies addressing the impact of surface roughness on materials composed of anisotropic particles.

Interplay of Particle Morphology and Director Distortions in Nematic Fluids

The existing microscopic theories for elasticity of nematics are challenged by recent findings on systems, whether bent molecules or semiflexible polymers, which do not comply with the model of rigid rodlike particles. Here, we propose an extension of Onsager-Straley second-virial theory, based on a model for the orientational distribution function that, through explicit account of the director profile along a particle, changes in the presence of deformations. The elastic constants reveal specific effects of particle morphology, which are not captured by the existing theories. This paves the way to microscopic modeling of the elastic properties of semiflexible liquid crystal polymers, which is a longstanding issue.