Biaxial, Twist-bend, and Splay-bend Nematic Phases of Banana-shaped Particles Revealed by Lifting the "Smectic Blanket"

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.

The effect of particle geometry and initial configuration on the phase behavior of twisted convex n-prisms

We study the phase behavior of twisted convex n-prisms with n = 3 and 4, via Monte Carlo simulations. Biaxial phases, in untwisted prisms, can be induced by choosing specific geometries of the prisms. However, due to the convexity of the twisted particles, a strong twisting disables the formation of biaxial phases and stabilizes uniaxial nematic and smectic phases. Using the increased volume of the twisted convex particles, we define an effective aspect ratio of the twisted prisms and find a homogeneous phase behavior across the geometry of the prisms' cross-section and even across different shapes of the cross-section. In this representation biaxial phases are found for large aspect ratios, while the low aspect ratio behavior can be compared to the hard cylinder phase diagram. For 3-prisms with a small base angle, we show the influence of the initial configuration; a polar initial configuration results in a (polar) splay nematic phase, whereas a non-polar initial configuration results in a biaxial phase.

Machine learning methods for liquid crystal research: phases, textures, defects and physical properties

Liquid crystal materials, with their unique properties and diverse applications, have long captured the attention of researchers and industries alike. From liquid crystal displays and electro-optical devices to advanced sensors and emerging technologies, the study and application of liquid crystals continue to be of paramount importance in the fields of materials science, chemistry and physics. With the ever-increasing complexity and diversity of liquid crystal materials, researchers face new challenges in understanding their behaviors, properties, and potential applications. On the other hand, machine learning, a rapidly evolving interdisciplinary field at the intersection of computer science and data analysis, has already become a powerful tool for unraveling implicit correlations and predicting new properties of a wide variety of physical and chemical systems and structures. Here we aim to consider how machine learning methods are suitable for solving fundamental problems in the field of liquid crystals and what are the advantages of this artificial intelligence based approach.

What promotes smectic order: Applying mean-field theory to the ends

Not every particle that forms a nematic liquid crystal makes a smectic. The particle tip is critical for this behavior. Ellipsoids do not make a smectic, but spherocylinders do. Similarly, only those N-CB alkylcyanobiphenyls with sufficiently long (N≥8 carbons) alkane tails form smectics. We understand the role of the particle tip in the smectic transition by means of a simple two-dimensional model. We model spherocylinders by "boubas" with rounded tips, and ellipsoids by "kikis" with pointed tips. The N-CB molecules are modeled by a small body with a polymer tail. We find that rounded tips and longer polymer tails lead to a smectic at lower densities by making the space between layers less accessible, destabilizing the nematic.

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.

Reduced-variance orientational distribution functions from torque sampling

We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium. Instead of the traditional counting of events, we reconstruct the orientational distribution function via an orientational integral of the torque acting on the particles. We test the torque sampling method in two- and three-dimensions, using both Langevin dynamics and overdamped Brownian dynamics, and with two interparticle interaction potentials. In all cases the torque sampling method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. The accuracy of the torque sampling method is independent of the bin size, and hence it is possible to resolve the orientational distribution function with arbitrarily small angular resolutions.

Ground State Configurations and Metastable Phases of Charged Linear Rods

This computational study investigates the energy minimum, that is, ground state, of suspensions of monodisperse (single-component) charged linear rods at various densities and screening lengths. We find that closed-packed unidirectional configurations have the lowest energies for all studied cases. We further specify the lattice parameters for these crystalline structures. In addition, we identify a few metastable phases, including heliconical structures. These metastable heliconical phases are composed of hexagonal smectic C layers with particle orientations forming a conical helicoid with a short pitch of three layers. We evidence this by zero-temperature Monte Carlo simulations starting from an energy-minimized hexagonal cholesteric configuration, which rapidly transforms to a heliconical phase. Furthermore, this heliconical phase is remarkably stable even at finite temperatures and melts to a disordered phase at high temperatures. Finally, we conduct simulations at room temperature and conditions typical for cellulose nanocrystal suspensions to study the onset of nematic order and compare our results to available experimental data. Our findings suggest that electrostatics play an important role in the isotropic/anisotropic transition for dense suspensions of charged rods.

Spontaneous Twisting of Achiral Hard Rod Nematics

Since Onsager's seminal work, hard rods have been taken as a prototype of nematic liquid crystals, characterized by uniaxial order and a uniform director field as a ground state. Here, using Onsager theory to calculate the free energy in the presence of arbitrary deformations, we find that hard rod nematics have an intrinsic tendency to twist around their ordering axis (double twist), driven by a mechanism in which the orientational fluctuations of particles play a key role. The anisotropic hard core potential used here is arguably the simplest form of interaction able to originate spontaneous breaking of mirror symmetry in a 3D fluid. Our results are discussed in relation to the recent discovery of a double twisted ground state in cylindrically confined lyotropic chromonic liquid crystals.

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.

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.

All-atom simulations of bent liquid crystal dimers: the twist-bend nematic phase and insights into conformational chirality

The liquid crystal dimer 1,7-bis-4-(4'-cyanobiphenyl)heptane (CB7CB) is known to exhibit a nematic-nematic phase transition, with the lower temperature phase identified as the twist-bend nematic (N_TB) phase. Despite the achiral nature of the mesogen, the N_TB phase demonstrates emergent chirality through the spontaneous formation of a helical structure. We present extensive molecular dynamics simulations of CB7CB using an all-atom force field. The N_TB phase is observed in this model and, upon heating, shows phase transitions into the nematic (N) and isotropic phases. The simulated N_TB phase returns a pitch of 8.35 nm and a conical tilt angle of 29°. Analysis of the bend angle between the mesogenic units reveals an average angle of 127°, which is invariant to the simulated phase. We have calculated distributions of the chirality order parameter, χ, for the ensemble of conformers in the N_TB and N phases. These distributions elucidate that CB7CB is statistically achiral but can adopt chiral conformers with no preference for a specific handedness. Furthermore, there is no change in the extent of conformational chirality between the N_TB and N phases. Using single-molecule stochastic dynamics simulations in the gas phase, we study the dimer series CBnCB (where n = 6, 7, 8 or 9) and CBX(CH₂)₅YCB (where X/Y = CH₂, O or S) in terms of the bend angle and conformational chirality. We confirm that the bent molecular shape determines the ability of a dimer to exhibit the N_TB phase rather than its potential to assume chiral conformers; as |χ|_max increases with the spacer length, but the even-membered dimers have a linear shape in contrast to the bent nature of dimers with spacers of odd parity. For CBX(CH₂)₅YCB, it is found that |χ|_max increases as the bend angle of the dimer decreases, while the flexibility of the dimers remains unchanged through the series.

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.

Microscopic modelling of nematic elastic constants beyond Straley theory

Recent findings on various classes of nematics, whose microscopic structure differs from the prototypical rod-like shape, evidence unusual elastic properties, which challenge existing theories. Here we develop a theoretical and numerical methodology for the calculation of Frank elastic constants, accounting for the coupling between the molecular shape and each specific deformation mode. This is done in the framework of Onsager-Straley's second-virial theory, using a non-local form of the orientational distribution function. The comparison between two benchmark systems, a straight and a bent rod, allows us to illustrate the distinct features of this approach, which include additional order parameters induced by the deformation and, related to this, an ideal contribution to the deformation free energy. Then, using a simple system that can be seen as a minimalist model of liquid crystal trimers, we discuss the impact of different molecular conformations on elastic constants.

All Structures Great and Small: Nanoscale Modulations in Nematic Liquid Crystals

The nature of the nanoscale structural organization in modulated nematic phases formed by molecules having a nonlinear molecular architecture is a central issue in contemporary liquid crystal research. Nevertheless, the elucidation of the molecular organization is incomplete and poorly understood. One attempt to explain nanoscale phenomena merely “shrinks down” established macroscopic continuum elasticity modeling. That explanation initially (and mistakenly) identified the low temperature nematic phase (N_X), first observed in symmetric mesogenic dimers of the CB-n-CB series with an odd number of methylene spacers (n), as a twist–bend nematic (N_TB). We show that the N_X is unrelated to any of the elastic deformations (bend, splay, twist) stipulated by the continuum elasticity theory of nematics. Results from molecular theory and computer simulations are used to illuminate the local symmetry and physical origins of the nanoscale modulations in the N_X phase, a spontaneously chiral and locally polar nematic. We emphasize and contrast the differences between the N_X and theoretically conceivable nematics exhibiting spontaneous modulations of the elastic modes by presenting a coherent formulation of one-dimensionally modulated nematics based on the Frank–Oseen elasticity theory. The conditions for the appearance of nematic phases presenting true elastic modulations of the twist–bend, splay–bend, etc., combinations are discussed and shown to clearly exclude identifications with the nanoscale-modulated nematics observed experimentally, e.g., the N_X phase. The latter modulation derives from packing constraints associated with nonlinear molecules—a chiral, locally-polar structural organization indicative of a new type of nematic phase.

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.

Topology of Orientational Defects in Confined Smectic Liquid Crystals

We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in pointlike units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.

A generalized density-modulated twist-splay-bend phase of banana-shaped particles

In 1976, Meyer predicted that bend distortions of the nematic director field are complemented by deformations of either twist or splay, yielding twist-bend and splay-bend nematic phases, respectively. Four decades later, the existence of the splay-bend nematic phase remains dubious, and the origin of these spontaneous distortions uncertain. Here, we conjecture that bend deformations of the nematic director can be complemented by simultaneous distortions of both twist and splay, yielding a twist-splay-bend nematic phase. Using theory and simulations, we show that the coupling between polar order and bend deformations drives the formation of modulated phases in systems of curved rods. We find that twist-bend phases transition to splay-bend phases via intermediate twist-splay-bend phases, and that splay distortions are always accompanied by periodic density modulations due to the coupling of the particle curvature with the non-uniform curvature of the splayed director field, implying that the twist-splay-bend and splay-bend phases of banana-shaped particles are actually smectic phases.

The so-called twist-bend and splay-bend nematic liquid crystal phases are important concepts for studying bent-core mesogens. Chiappini et al. use a theory/simulation approach to suggest that the transition proceed via a twist-splay-bend phase which may be obscured by density modulations.

Stability of the uniform ferroelectric nematic phase

The recent discovery of the ferroelectric nematic phase N_{F} resurrects a question about the stability of the uniform N_{F} state with respect to the formation of either a standard for the solid ferroelectric domain structure or for the often occurring liquid crystal space modulation of the polarization vector P (and naturally coupled to P nematic director n). In this work, within Landau mean-field theory, we investigate the linear stability of the minimal model admitting the conventional paraelectric nematic N and N_{F} phases. Our minimal model (in addition to the standard terms of the expansion over the P and director gradients) includes the standard for liquid crystals, the director flexoelectric coupling term (f), and, often overlooked in the literature (although similar by its symmetry to the director flexoelectric coupling), the flexodipolar coupling (β). We find that in the easy-plane anisotropy case (when the configuration with P orthogonal to n is energetically favorable), the uniform N_{F} state loses its stability with respect to one-dimensional (1D) or two-dimensional (2D) modulation. If f≠0, the 2D modulation threshold (β_{c2} value) is always higher than its 1D counterpart value β_{c1}. There is no instability at all if one neglects the flexodipolar coupling (β=0). In the easy-axis case (when n prefers to align along P), both instability (1D and 2D) thresholds are the same, and the instability can occur even at β=0. We speculate that the phases with 1D or 2D modulations can be identified as discussed in the literature [see M. P. Rosseto and J. V. Selinger, Phys. Rev. E 101, 052707 (2020)2470-004510.1103/PhysRevE.101.052707] for single-splay or double-splay nematics.

Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement

Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic colloidal layers dictated by the interplay between entropy and an imposed external topology. Considering an annular confinement as a basic example, a plethora of competing states is found with nontrivial defect structures ranging from laminar states to multiple smectic domains and arrays of edge dislocations, which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of thermal colloidal rods and fundamental-measure-based density functional theory of hard anisotropic bodies, agree on a quantitative level.

Orientational ordering in a fluid of hard kites: A density-functional-theory study

Using density-functional theory we theoretically study the orientational properties of uniform phases of hard kites-two isosceles triangles joined by their common base. Two approximations are used: scaled particle theory and a new approach that better approximates third virial coefficients of two-dimensional hard particles. By varying some of their geometrical parameters, kites can be transformed into squares, rhombuses, triangles, and also very elongated particles, even reaching the hard-needle limit. Thus, a fluid of hard kites, depending on the particle shape, can stabilize isotropic, nematic, tetratic, and triatic phases. Different phase diagrams are calculated, including those of rhombuses, and kites with two of their equal interior angles fixed to 90^{∘}, 60^{∘}, and 75^{∘}. Kites with one of their unequal angles fixed to 72^{∘}, which have been recently studied via Monte Carlo simulations, are also considered. We find that rhombuses and kites with two equal right angles and not too large anisometry stabilize the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to 60^{∘} stabilize the triatic phase to some extent, although it is very sensitive to changes in particle geometry. Kites with the two equal interior angles fixed to 75^{∘} have a phase diagram with both tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stable at different densities. Finally, the success of the new theory in the description of orientational order in kites is shown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to 72^{∘}. These particles also present a phase diagram with stable tetratic and triatic phases.

Molecular Order of Topologically Variant Flexible Mesogens by 13C Nuclear Magnetic Resonance

¹³C nuclear magnetic resonance investigations in the nematic phase of mesogens comprising a rod-like core with three phenyl rings connected to a fourth phenyl ring via a flexible spacer are reported. The molecules are abbreviated as monomer, dimer, and trimer as they comprised one, two, and three pairs of core and spacer combinations linked to ring IV, respectively. Hot-stage optical polarizing microscopy and differential scanning calorimetry studies confirmed that all of them exhibit an enantiotropic nematic phase with additional monotropic or enantiotropic smectic mesophases. Large values of ¹³C-¹H dipolar couplings of the order of 11 kHz are observed for all the cases for the terminal carbon C1 of the core unit. These high values indicated that the corresponding CH vector is collinear with the long axis of the molecule, which itself is aligned parallel to the magnetic field. In contrast, the terminal carbon of the ring IV (C19/C17) exhibits a relatively smaller value in the range of 2.0-2.5 kHz, reflecting the divergent local dynamics at different sections of the mesogens. The orientational order parameters of the phenyl rings computed from the ¹³C-¹H dipolar couplings have been used to obtain the conformation of the mesogens in the nematic phase. It is concluded that the dimer and trimer exhibit C₂ and C₃ symmetry with the ring IV connected by spacers tilted away from the symmetry axis by 35.9 and 90^° for the two cases, respectively. This leads to the interesting tripod-like molecular shape for the trimer in the nematic phase rather than the planar representation of the λ shape.

Helicoidal dynamics of biaxial curved rods in twist-bend nematic phases unveiled by unsupervised machine learning techniques

Uniaxial rods in a nematic phase diffuse preferentially in the direction parallel to the nematic director n[over ̂]. The nematic director field n[over ̂](r) of a chiral twist-bend nematic (N_{TB}) phase of achiral banana-shaped particles, recently discovered experimentally, displays a heliconical twist of given handedness and periodicity. Using simulations, we investigate the long-time macroscopic diffusion in N_{TB} phases, and find that the predilection of curved rods to diffuse in the direction of the twisting n[over ̂](r) yields a fascinating chiral dynamics along helices, even though achiral curved rods display Brownian motion with a nontrivial rototranslational coupling. We devise a machine learning protocol to characterize the helicoidal particle trajectories, finding that their pitch and radius are determined by the pitch and conical angle of the N_{TB} phase thereby connecting its structural and dynamical properties.

Shaping colloidal bananas to reveal biaxial, splay-bend nematic, and smectic phases

Understanding the impact of curvature on the self-assembly of elongated microscopic building blocks, such as molecules and proteins, is key to engineering functional materials with predesigned structure. We develop model “banana-shaped” colloidal particles with tunable dimensions and curvature, whose structure and dynamics are accessible at the particle level. By heating initially straight rods made of SU-8 photoresist, we induce a controllable shape deformation that causes the rods to buckle into banana-shaped particles. We elucidate the phase behavior of differently curved colloidal bananas using confocal microscopy. Although highly curved bananas only form isotropic phases, less curved bananas exhibit very rich phase behavior, including biaxial nematic phases, polar and antipolar smectic-like phases, and even the long-predicted, elusive splay-bend nematic phase.

Self-assembly of freely-rotating polydisperse cuboids: unveiling the boundaries of the biaxial nematic phase

Colloidal cuboids have the potential to self-assemble into biaxial liquid crystal phases, which exhibit two independent optical axes. Over the last few decades, several theoretical works have predicted the existence of a wide region of the phase diagram where the biaxial nematic phase would be stable, but imposed rather strong constraints on the particle rotational degrees of freedom. In this work, we use molecular simulation to investigate the impact of size dispersity on the phase behaviour of freely-rotating hard cuboids, here modelled as self-dual-shaped nanoboards. This peculiar anisotropy, exactly in between the oblate and prolate geometry, has been proposed as the most appropriate to promote phase biaxiality. We observe that size dispersity radically changes the phase behaviour of monodisperse systems and leads to the formation of an elusive biaxial nematic phase, being found in a large region of the packing fraction vs. polydispersity phase diagram. Although our results confirm the tendencies reported in past experimental observations on colloidal dispersions of slightly prolate goethite particles, they cannot reproduce the direct isotropic-to-biaxial nematic phase transition observed in these experiments.

A Landau-de Gennes theory for twist-bend and splay-bend nematic phases of colloidal suspensions of bent rods

We develop a phenomenological Landau-de Gennes (LdG) theory for lyotropic colloidal suspensions of bent rods using a Q-tensor expansion of the chemical-potential dependent grand potential. In addition, we introduce a bend flexoelectric term, coupling the polarization and the divergence of the Q-tensor, to study the stability of uniaxial (N), twist-bend (N_TB), and splay-bend (N_SB) nematic phases of colloidal bent rods. We first show that a mapping can be found between the LdG theory and the Oseen-Frank theory. By breaking the degeneracy between the splay and bend elastic constants, we find that the LdG theory predicts either an N-N_TB-N_SB or an N-N_SB-N_TB phase sequence upon increasing the particle concentration. Finally, we employ our theory to study the first-order N-N_TB phase transition, for which we find that K₃₃ as well as its renormalized version K₃₃ ^eff remain positive at the transition, whereas K₃₃ ^eff vanishes at the nematic spinodal. We connect these findings to recent simulation results.

Dynamics of hard colloidal cuboids in nematic liquid crystals

We perform dynamic Monte Carlo simulations to investigate the equilibrium dynamics of hard board-like colloidal particles in oblate and prolate nematic liquid crystals. In particular, we characterize the particles' diffusion along the nematic director and perpendicularly to it, and observe a structural relaxation decay that strongly depends on the particle anisotropy. To assess the Gaussianity of their dynamics and eventual occurrence of collective motion, we calculate two- and four-point correlation functions that incorporate the instantaneous values of the diffusion coefficients parallel and perpendicular to the nematic director. Our simulation results highlight the occurrence of Fickian and Gaussian dynamics at short and long times, locate the minimum diffusivity at the self-dual shape, the particle geometry that would preferentially stabilise biaxial nematics, and exclude the existence of dynamically correlated particles.

Chemically induced splay nematic phase with micron scale periodicity

Nematic liquid crystals lack positional order of their constituent molecules, which share an average orientational order only. Modulated nematic liquid crystal phases also lack positional order, but possess a periodic variation in this direction of average orientation. In the recently discovered splay nematic (NS) phase the average orientational order is augmented with a periodic splay deformation of orientation perpendicular to the director. In this communication we report the first example of a splay nematic phase which is chemically induced by mixing two materials, neither of which exhibit the NS phase. The splay-nematic phase is identified based on its optical textures, X-ray scattering patterns, and small enthalpy of the associated phase transition. We measure the splay periodicity optically, finding it to be ∼9 μm. This unexpected generation of the splay-nematic phase through binary mixtures offers a new route to materials which exhibit this phase which complements ongoing studies into structure-property relationships and could accelerate the development of technologies utilising this remarkable polar nematic variant.

Molecular Flexibility and Bend in Semi-Rigid Liquid Crystals: Implications for the Heliconical Nematic Ground State

The NTB phase phases possess a local helical structure with a pitch length of a few nanometers and is typically exhibited by materials consisting of two rigid mesogenic units linked by a flexible oligomethylene spacer of odd parity, giving a bent shape. We report the synthesis and characterisation of two novel dimeric liquid crystals, and perform a computational study on 10 cyanobiphenyl dimers with varying linking groups, generating a large library of conformers for each compound; this allows us to present molecular bend angles as probability weighted averages of many conformers, rather than use a single conformer. We validate conformer libraries by comparison of interproton distances with those obtained from solution-based 1D 1 H NOESY NMR, finding good agreement between experiment and computational work. Conversely, we find that using any single conformer fails to reproduce experimental interproton distances. We find the use of a single conformer significantly overestimates the molecular bend angle while also ignoring flexibility; in addition, we show that the average bend angle and flexibility are both linked to the relative stability of the NTB phase.