Cholesterics of colloidal helices: Predicting the macroscopic pitch from the particle shape and thermodynamic state

Elucidating chirality transfer in liquid crystals of viruses

Chirality is ubiquitous in nature across all length scales, with major implications spanning fields from biology, chemistry and physics to materials science. How chirality propagates from nanoscale building blocks to meso- and macroscopic helical structures remains an open issue. Here, working with a canonical system of filamentous viruses, we demonstrate that their self-assembly into chiral liquid crystal phases quantitatively results from the interplay between two main mechanisms of chirality transfer: electrostatic interactions from the helical charge patterns on the virus surface, and fluctuation-based helical deformations leading to viral backbone helicity. Our experimental and theoretical approach provides a comprehensive framework for deciphering how chirality is hierarchically and quantitatively propagated across spatial scales. Our work highlights the ways in which supramolecular helicity may arise from subtle chiral contributions of opposite handedness that act either cooperatively or competitively, thus accounting for the multiplicity of chiral behaviours observed for nearly identical molecular systems.

Structural Color from Cellulose Nanocrystals or Chitin Nanocrystals: Self-Assembly, Optics, and Applications

Widespread concerns over the impact of human activity on the environment have resulted in a desire to replace artificial functional materials with naturally derived alternatives. As such, polysaccharides are drawing increasing attention due to offering a renewable, biodegradable, and biocompatible feedstock for functional nanomaterials. In particular, nanocrystals of cellulose and chitin have emerged as versatile and sustainable building blocks for diverse applications, ranging from mechanical reinforcement to structural coloration. Much of this interest arises from the tendency of these colloidally stable nanoparticles to self-organize in water into a lyotropic cholesteric liquid crystal, which can be readily manipulated in terms of its periodicity, structure, and geometry. Importantly, this helicoidal ordering can be retained into the solid-state, offering an accessible route to complex nanostructured films, coatings, and particles. In this review, the process of forming iridescent, structurally colored films from suspensions of cellulose nanocrystals (CNCs) is summarized and the mechanisms underlying the chemical and physical phenomena at each stage in the process explored. Analogy is then drawn with chitin nanocrystals (ChNCs), allowing for key differences to be critically assessed and strategies toward structural coloration to be presented. Importantly, the progress toward translating this technology from academia to industry is summarized, with unresolved scientific and technical questions put forward as challenges to the community.

The effect of shape, polydispersity, charge, and fraction of crystallite bundles on the cholesteric pitch of cellulose nanocrystal suspensions

Using Onsager-Straley's second-virial theory, we investigate the cholesteric pitch of cellulose nanocrystal (CNC) suspensions. We model the CNCs as hard chiral bundles of microfibrils and examine the effect of the shape of these chiral bundles, characterized by aspect ratio and chirality, on the cholesteric pitch. Additionally, we explore the impact of length polydispersity and surface charge on the cholesteric phase of CNCs. Furthermore, we consider binary mixtures of twisted bundles and achiral primary crystallites to provide a more realistic representation of CNC suspensions. Our findings reveal that the degree of bundle twisting significantly affects the helical twisting of the cholesteric phase. We also observe that the average particle length and length polydispersity have substantial effects on strongly twisted bundles but minimal effects on weakly twisted ones. Finally, our study indicates that as the range of electrostatic interactions increases, the transfer of chirality from the microscopic to macroscopic length scales becomes masked, resulting in an increase in the cholesteric pitch. In the case of binary mixtures, the bundles act as chiral dopants, and an increasing fraction of bundles progressively enhances the helical twisting of the cholesteric phase.

Janus helices: From fully attractive to hard helices

The phase diagram of hard helices differs from its hard rods counterpart by the presence of chiral "screw" phases stemming from the characteristic helical shape, in addition to the conventional liquid crystal phases also found for rod-like particles. Using extensive Monte Carlo and Molecular Dynamics simulations, we study the effect of the addition of a short-range attractive tail representing solvent-induced interactions to a fraction of the sites forming the hard helices, ranging from a single-site attraction to fully attractive helices for a specific helical shape. Different temperature regimes exist for different fractions of the attractive sites, as assessed in terms of the relative Boyle temperatures, that are found to be rather insensitive to the specific shape of the helical particle. The temperature range probed by the present study is well above the corresponding Boyle temperatures, with the phase behaviour still mainly entropically dominated and with the existence and location of the various liquid crystal phases only marginally affected. The pressure in the equation of state is found to decrease upon increasing the fraction of attractive beads and/or on lowering the temperature at fixed volume fraction, as expected on physical grounds. All screw phases are found to be stable within the considered range of temperatures with the smectic phase becoming more stable on lowering the temperature. By contrast, the location of the transition lines do not display a simple dependence on the fraction of attractive beads in the considered range of temperatures.

Pre-Smectic Ordering and the Unwinding Helix in Monte Carlo Simulations of Cholesteric Liquid-Crystals

In this paper, molecular chirality is studied for liquid-crystal fluids represented by hard rods with the addition of an attractive chiral dispersion term. Chiral forces between molecular pairs are assumed to be long-ranged and are described in terms of the pseudotensor of Goossens [W. J. A. Goossens, Mol. Cryst. Liq. Cryst. 1971, 12, 237-244]. Following Varga and Jackson [S. Varga and G. Jackson, Chem. Phys. Lett. 2003, 377, 6-12], this is combined with a hard-spherocylinder core. We investigate the relationship between molecular chirality and the helical pitch of the system, which occurs in the absence of full three-dimensional periodic boundary conditions. The dependence of the wavenumber of this pitch on the thermodynamic variables, temperature, and density is measured. We also explore the use of a novel surface boundary interaction model. As a result of this approach, we are able to lower the temperature of the system without the occurrence of nematic droplets, which would interfere with the formation of a uniaxial pitch. Regarding the theoretical predictions of Wensink and Jackson [H. H. Wensink and G. Jackson, J. Chem. Phys. 2009, 130, 234911], on the one hand, we have qualitative agreement with the observed non-monotonic density dependence of the wavenumber. Initially increasing with density, the wavenumber reaches a maximum, before falling as the density moves toward the point of phase transition from cholesteric to smectic. However, further analysis for shorter rods, in the presence of novel boundary conditions, reveals some disagreement with the theory, at least in this case; the unwinding of the cholesteric helix in the cholesteric phase occurs simultaneously with subtle increases in smectic ordering. These pre-smectic fluctuations have not been accounted for so far in theories on cholesterics but turn out to play a key role in controlling the pitch of cholesteric phases of rod-shaped mesogens with a small to moderate aspect ratio.

Flow and assembly of cellulose nanocrystals (CNC): A bottom-up perspective - A review

Cellulosic sources, such as lignocellulose-rich biomass, can be mechanically or acid degraded to produce inclusions called cellulose nanocrystals (CNCs). They have several uses in the sectors of biomedicine, photonics, and material engineering because of their biodegradability, renewability, sustainability, and mechanical qualities. The processing and design of CNC-based products are inextricably linked to the rheological behaviour of CNC suspension or in combination with other chemicals, such as surfactants or polymers; in this context, rheology offers a significant link between microstructure and macro scale flow behaviour that is intricately linked to material response in applications. The flow behaviour of CNC items must be properly specified in order to produce goods with value-added characteristics. In this review article, we provide new research on the shear rheology of CNC dispersion and CNC-based hydrogels in the linear and nonlinear regime, with storage modulus values reported to range from ~10^-3 to 10³ Pa. Applications in technology and material science are also covered simultaneously. We carefully examined the effects of charge density, aspect ratio, concentration, persistence length, alignment, liquid crystal formation, the cause of chirality in CNCs, interfacial behaviour and interfacial rheology, linear and nonlinear viscoelasticity of CNC suspension in bulk and at the interface using the currently available literature.

Effects of shape and solute-solvent compatibility on the efficacy of chirality transfer: Nanoshapes in nematics

Chirality, as a concept, is well understood at most length scales. However, quantitative models predicting the efficacy of the transmission of chirality across length scales are lacking. We propose here a modus operandi for a chiral nanoshape solute in an achiral nematic liquid crystal host showing that that chirality transfer may be understood by unusually simple geometric considerations. This mechanism is based on the product of a pseudoscalar chirality indicator and of a geometric shape compatibility factor based on the two-dimensional isoperimetric quotients for each nanoshape solute. The model is tested on an experimental set of precisely engineered gold nanoshapes. These libraries of calculated and in-parallel acquired experimental data among related nanoshapes pave the way for predictive calculations of chirality transfer in nanoscale, macromolecular, and biological systems, from designing chiral discriminators and enantioselective catalysts to developing chiral metamaterials and understanding nature's innate ability to transfer homochirality across length scales.

Modeling the cholesteric pitch of apolar cellulose nanocrystal suspensions using a chiral hard-bundle model

Cellulose nanocrystals (CNCs) are naturally sourced elongated nanocolloids that form cholesteric phases in water and apolar solvents. It is well accepted that CNCs are made of bundles of crystalline microfibrils clustered side-by-side, and there is growing evidence that each individual microfibril is twisted. Yet, the origin of the chiral interactions between CNCs remains unclear. In this work, CNCs are described with a simple model of chiral hard splinters, enabling the prediction of the pitch using density functional theory and Monte Carlo simulations. The predicted pitch P compares well with experimental observations in cotton-based CNC dispersions in apolar solvents using surfactants but also with qualitative trends caused by fractionation or tip sonication in aqueous suspensions. These results suggest that the bundle shape induces an entropy-driven chiral interaction between CNCs, which is the missing link in explaining how chirality is transferred from the molecular scale of cellulose chains to the cholesteric order.

Concentric chiral nematic polymeric fibers from cellulose nanocrystals

Hierarchical biological materials, such as osteons and plant cell walls, are complex structures that are difficult to mimic. Here, we combine liquid crystal systems and polymerization techniques within confined systems to develop complex structures. A single-domain concentric chiral nematic polymeric fiber was obtained by confining cellulose nanocrystals (CNCs) and hydroxyethyl acrylate inside a capillary tube followed by UV-initiated polymerization. The concentric chiral nematic structure continues uniformly throughout the length of the fiber. The pitch of the chiral nematic structure could be controlled by changing the CNC concentration. We tracked the formation of the concentric structure over time and under different conditions with variation of the tube orientation, CNC concentration, CNC type, and capillary tube size. We show that the inner radius of the capillary tube is important and a single-domain structure was only obtained inside small-diameter tubes. At low CNC concentration, the concentric chiral nematic structure did not completely cover the cross-section of the fiber. The highly ordered structure was studied using imaging techniques and X-ray diffraction, and the mechanical properties and structure of the chiral nematic fiber were compared to a pseudo-nematic fiber. CNC polymeric fibers could become a platform for many applications from photonics to complex hierarchical materials.

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.

Cellulose nanocrystal research; A personal perspective

This contribution to the special issue of Carbohydrate Polymers commemorating the 100th Anniversary of the Cellulose and Renewable Materials Division of the American Chemical Society is a personal account, from a research chemist's point of view, of some aspects of the discovery, development and utilization of nanocellulosic materials. The main focus is on cellulose nanocrystals stabilized by sulfate half-ester surface charges.

Chiral shape fluctuations and the origin of chirality in cholesteric phases of DNA origamis

Lyotropic cholesteric liquid crystal phases are ubiquitously observed in biological and synthetic polymer solutions, characterized by a complex interplay between thermal fluctuations and entropic and enthalpic forces. The elucidation of the link between microscopic features and macroscopic chiral structure, and of the relative roles of these competing contributions on phase organization, remains a topical issue. Here, we provide theoretical evidence of a previously unidentified mechanism of chirality amplification in lyotropic liquid crystals, whereby phase chirality is governed by fluctuation-stabilized helical deformations in the conformations of their constituent molecules. Our results compare favorably to recent experimental studies of DNA origami assemblies and demonstrate the influence of intramolecular mechanics on chiral supramolecular order, with potential implications for a broad class of experimentally relevant colloidal systems.

Morphological analysis of chiral rod clusters from a coarse-grained single-site chiral potential

We present a coarse-grained single-site potential for simulating chiral interactions, with adjustable strength, handedness, and preferred twist angle. As an application, we perform basin-hopping global optimisation to predict the favoured geometries for clusters of chiral rods. The morphology phase diagram based upon these predictions has four distinct families, including previously reported structures for potentials that introduce chirality based on shape, such as membranes and helices. The transition between these two configurations reproduces some key features of experimental results for fd bacteriophage. The potential is computationally inexpensive, intuitive, and versatile; we expect it will be useful for large scale simulations of chiral molecules. For chiral particles confined in a cylindrical container we reproduce the behaviour observed for fusilli pasta in a jar. Hence this chiropole potential has the capability to provide insight into structures on both macroscopic and molecular length scales.

Manipulation of cholesteric liquid crystal phase behavior and molecular assembly by molecular chirality

Molecular simulation is used to study the effect of molecular chirality on liquid crystalline phase transition and molecular assembly behavior. Based on a flexible chain (FCh) model with helical arrangement of side beads, the phase behavior of FCh models with various molecular chiralities are studied as functions of pressure (or density). By modifying the molecular chirality of FCh, we can manipulate the relative stability of the nematic and cholesteric phases continuously; and we found that increasing molecular chirality may destabilize cholesteric order due to the effective reduction of chiral interactions. A semismectic phase is identified in the high-density region, in which the two-dimensional fluid layers overlap due to shift alignment formed by FCh particles. The global phase diagram of the FCh model is constructed and the potential energy surface is calculated to elucidate the formation of cholesteric phase in terms of two-body interactions.

Effect of Size Polydispersity on the Pitch of Nanorod Cholesterics

Many nanoparticle-based chiral liquid crystals are composed of polydisperse rod-shaped particles with considerable spread in size or shape, affecting the mesoscale chiral properties in, as yet, unknown ways. Using an algebraic interpretation of Onsager-Straley theory for twisted nematics, we investigate the role of length polydispersity on the pitch of nanorod-based cholesterics with a continuous length polydispersity, and find that polydispersity enhances the twist elastic modulus, K 2 , of the cholesteric material without affecting the effective helical amplitude, K t . In addition, for the infinitely large average aspect ratios considered here, the dependence of the pitch on the overall rod concentration is completely unaffected by polydispersity. For a given concentration, the increase in twist elastic modulus (and reduction of the helical twist) may be up to 50% for strong size polydispersity, irrespective of the shape of the unimodal length distribution. We also demonstrate that the twist reduction is reinforced in bimodal distributions, obtained by doping a polydisperse cholesteric with very long rods. Finally, we identify a subtle, non-monotonic change of the pitch across the isotropic-cholesteric biphasic region.

Temperature dependence of the pitch in chiral lyotropic chromonic liquid crystals

One of the most simple cases in which chirality at the microscopic level produces a chiral macroscopic structure is the chiral nematic liquid crystal phase. In such a phase, the preferred direction of molecular orientation rotates in helical fashion, with the pitch of the helix in different systems ranging from around 100 nm to as large as can be measured (∼10 mm). For almost all thermotropic and lyotropic liquid crystals, the ordered entities are formed from strong bonds, so the pitch varies in accordance with how the interactions between these largely immutable entities are affected by changing conditions. A unique exception are lyotropic chromonic liquid crystals (LCLCs) that spontaneously form weakly bound assemblies in solution, the size of which depends strongly on experimental parameters. While the temperature dependence of the pitch has been measured for chiral LCLCs formed by short strands of DNA (DNA-LCLCs), such is not the case for chiral LCLCs formed by small molecules. Polarized optical microscopy experiments on small molecule chiral LCLCs reveal the changing assembly size through a temperature dependence of the pitch not typical for many other systems, including the most recent measurements on DNA-LCLCs. In fact, the pitch measurements in small molecule chiral LCLCs strongly increase in value as the temperature is increased and the assemblies shrink in size. Theoretical considerations provide some help in understanding this phenomena, but leave much to be explained.

Self-Assembled Chiral Photonic Crystals from a Colloidal Helix Racemate

Chiral crystals consisting of microhelices have many optical properties, while presently available fabrication processes limit their large-scale applications in photonic devices. Here, by using a simplified simulation method, we investigate a bottom-up self-assembly route to build up helical crystals from the smectic monolayer of a colloidal helix racemate. With increasing the density, the system undergoes an entropy-driven cocrystallization by forming crystals of various symmetries with different helical shapes. In particular, we identify two crystals of helices arranged in binary honeycomb and square lattices, which are essentially composed of two sets of opposite-handed chiral crystals. Photonic calculations show that these chiral structures can have large complete photonic band gaps. In addition, in the self-assembled chiral square crystal, we also find dual polarization band gaps that selectively forbid the propagation of circularly polarized light of a specific handedness along the helical axis direction. The self-assembly process in our proposed system is robust, suggesting possibilities of using chiral colloids to assemble photonic metamaterials.

Hierarchical bounding structures for efficient virial computations: Towards a realistic molecular description of cholesterics

We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of neighbour lists through the combined use of recursive atom-decomposition techniques and binary overlap search schemes, is shown to scale sub-logarithmically with particle resolution in the case of molecular systems with high aspect ratios. Its implementation within an efficient numerical and theoretical framework based on classical density functional theory enables us to investigate the cholesteric self-assembly of a wide range of experimentally relevant particle models. We illustrate the method through the determination of the cholesteric behavior of hard, structurally resolved twisted cuboids, and report quantitative evidence of the long-predicted phase handedness inversion with increasing particle thread angles near the phenomenological threshold value of 45°. Our results further highlight the complex relationship between microscopic structure and helical twisting power in such model systems, which may be attributed to subtle geometric variations of their chiral excluded-volume manifold.

The Self-Assembly of Cellulose Nanocrystals: Hierarchical Design of Visual Appearance

By controlling the interaction of biological building blocks at the nanoscale, natural photonic nanostructures have been optimized to produce intense coloration. Inspired by such biological nanostructures, the possibility to design the visual appearance of a material by guiding the hierarchical self-assembly of its constituent components, ideally using natural materials, is an attractive route for rationally designed, sustainable manufacturing. Within the large variety of biological building blocks, cellulose nanocrystals are one of the most promising biosourced materials, primarily for their abundance, biocompatibility, and ability to readily organize into photonic structures. Here, the mechanisms underlying the formation of iridescent, vividly colored materials from colloidal liquid crystal suspensions of cellulose nanocrystals are reviewed and recent advances in structural control over the hierarchical assembly process are reported as a toolbox for the design of sophisticated optical materials.

Hard Competition: Stabilizing the Elusive Biaxial Nematic Phase in Suspensions of Colloidal Particles with Extreme Lengths

We use computer simulations to study the existence and stability of a biaxial nematic N_{b} phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long (L), medium (M), and short (S) particle axis. For all three shape families, we find stable N_{b} states provided the shape is not only close to the so-called dual shape with M=sqrt[LS] but also sufficiently anisotropic with L/S>9,11,14,23 for rhombi, (two types of) triangular prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-N_{b} transition does not occur in these systems due to a destabilization of N_{b} by a smectic (for cuboids and prisms) or a columnar (for platelets) phase at small L/S or by an intervening uniaxial nematic phase at large L/S. Our results are confirmed by a density functional theory provided the third virial coefficient is included and a continuous rather than a discrete (Zwanzig) set of particle orientations is taken into account.

Cholesteric ordering predicted using a coarse-grained polymeric model with helical interactions

The understanding of cholesteric liquid crystals at a molecular level is challenging. Limited insights are available to bridge between molecular structures and macroscopic chiral organization. In the present study, we introduce a novel coarse-grained (CG) molecular model, which is represented by flexible chain particles with helical interactions (FCh), to study the liquid crystalline phase behavior of cholesteric molecules such as double strand DNA and α-helix polypeptides using molecular dynamics (MD) simulations. The isotropic-cholesteric phase transitions of FCh molecules were simulated for varying chain flexibilities. A wall confinement was used to break the periodicity along the cholesteric helix director in order to predict the equilibrium cholesteric pitch. The left-handed cholesteric phase was shown for FCh molecules with right-handed chiral interactions, and a spatially inhomogeneous distribution of the nematic order parameter profile was observed in cholesteric phases. It was found that the chain flexibility plays an important role in determining the macroscopic cholesteric pitch and the structure of the cholesteric liquid crystal phase. The simulations provide insight into the relationship between microscopic molecular characteristics and the macroscopic phase behavior.

The Landau-de Gennes approach revisited: A minimal self-consistent microscopic theory for spatially inhomogeneous nematic liquid crystals

We design a novel microscopic mean-field theory of inhomogeneous nematic liquid crystals formulated entirely in terms of the tensor order parameter field. It combines the virtues of the Landau-de Gennes approach in allowing both the direction and magnitude of the local order to vary, with a self-consistent treatment of the local free-energy valid beyond the small order parameter limit. As a proof of principle, we apply this theory to the well-studied problem of a colloid dispersed in a nematic liquid crystal by including a tunable wall coupling term. For the two-dimensional case, we investigate the organization of the liquid crystal and the position of the point defects as a function of the strength of the coupling constant.

Filamentous phages as building blocks for reconfigurable and hierarchical self-assembly

Filamentous bacteriophages such as fd-like viruses are monodisperse rod-like colloids that have well defined properties of diameter, length, rigidity, charge and chirality. Engineering these viruses leads to a library of colloidal rods, which can be used as building blocks for reconfigurable and hierarchical self-assembly. Their condensation in an aqueous solution with additive polymers, which act as depletants to induce attraction between the rods, leads to a myriad of fluid-like micronic structures ranging from isotropic/nematic droplets, colloid membranes, achiral membrane seeds, twisted ribbons, π-wall, pores, colloidal skyrmions, Möbius anchors, scallop membranes to membrane rafts. These structures, and the way that they shape-shift, not only shed light on the role of entropy, chiral frustration and topology in soft matter, but also mimic many structures encountered in different fields of science. On the one hand, filamentous phages being an experimental realization of colloidal hard rods, their condensation mediated by depletion interactions constitutes a blueprint for the self-assembly of rod-like particles and provides a fundamental foundation for bio- or material-oriented applications. On the other hand, the chiral properties of the viruses restrict the generalities of some results but vastly broaden the self-assembly possibilities.

Twisting with a twist: supramolecular helix fluctuations in chiral nematics

Most theoretical descriptions of lyotropic cholesteric liquid crystals to date focus on homogeneous systems in which the rod concentration, as opposed to the rod orientation, is uniform. In this work, we build upon the Onsager-Straley theory for twisted nematics and study the effect of weak concentration gradients, generated by some external potential, on the cholesteric twist. We apply our theory to chiral nematics of nanohelices in which the supramolecular helix sense is known to spontaneously change sign upon variation of particle concentration, passing through a so-called compensation point at which the mesoscopic twist vanishes. We show that the imposed field offers exquisite control of the handedness and magnitude of the helicoidal director field, even at weak field strengths. Within the same framework we also quantify the director fluctuation spectrum and find evidence for a correlation length diverging at the compensation point.

Dynamically Controlled Iridescence of Cholesteric Cellulose Nanocrystal Suspensions Using Electric Fields

Cellulose nanocrystal suspensions in apolar solvent spontaneously form iridescent liquid-crystalline phases but the control of their macroscopic order is usually poor. The use of electric fields can provide control on the cholesteric orientation and its periodicity, allowing macroscopic sample homogeneity and dynamical tuning of their iridescent hues, and is demonstrated here.

Chiral self-assembly of helical particles

The shape of the building blocks plays a crucial role in directing self-assembly towards desired architectures. Out of the many different shapes, the helix has a unique position. Helical structures are ubiquitous in nature and a helical shape is exhibited by the most important biopolymers like polynucleotides, polypeptides and polysaccharides as well as by cellular organelles like flagella. Helical particles can self-assemble into chiral superstructures, which may have a variety of applications, e.g. as photonic (meta)materials. However, a clear and definite understanding of these structures has not been entirely achieved yet. We have recently undertaken an extensive investigation on the phase behaviour of hard helical particles, using numerical simulations and classical density functional theory. Here we present a detailed study of the phase diagram of hard helices as a function of their morphology. This includes a variety of liquid-crystal phases, with different degrees of orientational and positional ordering. We show how, by tuning the helix parameters, it is possible to control the organization of the system. Starting from slender helices, whose phase behaviour is similar to that of rodlike particles, an increase in curliness leads to the onset of azimuthal correlations between the particles and the formation of phases specific to helices. These phases feature a new kind of screw order, of which there is experimental evidence in colloidal suspensions of helical flagella.

Domed Silica Microcylinders Coated with Oleophilic Polypeptides and Their Behavior in Lyotropic Cholesteric Liquid Crystals of the Same Polypeptide

Liquid crystals can organize dispersed particles into useful and exotic structures. In the case of lyotropic cholesteric polypeptide liquid crystals, polypeptide-coated particles are appealing because the surface chemistry matches that of the polymeric mesogen, which permits a tighter focus on factors such as extended particle shape. The colloidal particles developed here consist of a magnetic and fluorescent cylindrically symmetric silica core with one rounded, almost hemispherical end. Functionalized with helical poly(γ-stearyl-l-glutamate) (PSLG), the particles were dispersed at different concentrations in cholesteric liquid crystals (ChLC) of the same polymer in tetrahydrofuran (THF). Defects introduced by the particles to the director field of the bulk PSLG/THF host led to a variety of phases. In fresh mixtures, the cholesteric mesophase of the PSLG matrix was distorted, as reflected in the absence of the characteristic fingerprint pattern. Over time, the fingerprint pattern returned, more quickly when the concentration of the PSLG-coated particles was low. At low particle concentration the particles were "guided" by the PSLG liquid crystal to organize into patterns similar to that of the re-formed bulk chiral nematic phase. When their concentration increased, the well-dispersed PSLG-coated particles seemed to map onto the distortions in the bulk host's local director field. The particles located near the glass vial-ChLC interfaces were stacked lengthwise into architectures with apparent two-dimensional hexagonal symmetry. The size of these "crystalline" structures increased with particle concentration. They displayed remarkable stability toward an external magnetic field; hydrophobic interactions between the PSLG polymers in the shell and those in the bulk LC matrix may be responsible. The results show that bio-inspired LCs can assemble suitable colloidal particles into soft crystalline structures.

Empty smectic liquid crystals of hard nanorings: Insights from a second-virial theory

Inspired by recent simulations on highly open liquid crystalline structures formed by rigid planar nanorings, we present a simple theoretical framework explaining the prevalence of smectic over nematic ordering in systems of ring-shaped objects. The key part of our study is a calculation of the excluded volume of such nonconvex particles in the limit of vanishing thickness to diameter ratio. Using a simple stability analysis we then show that dilute systems of ring-shaped particles have a strong propensity to order into smectic structures with an unusual antinematic order while solid disks of the same dimensions exhibit nematic order. Since our model rings have zero internal volume, these smectic structures are essentially empty, resembling the strongly porous structures found in simulation. We argue that the antinematic intralamellar order of the rings plays an essential role in stabilizing these smectic structures.

Simulating the pitch sensitivity of twisted nematics of patchy rods

Stiff, elongated biomolecules such as filamentous viruses, DNA or cellulose nanocrystals are known to form liquid crystals often exhibiting a helical supramolecular organization. Little is known about the microscopic origin, size and handedness of the helical pitch in these, so-called cholesteric phases. Experimental observations in chiral lyotropics suggest that long-ranged chiral forces of electrostatic origin acting between the mesogens are responsible for such organization. Using large-scale computer simulation we study the sensitivity of the pitch imparted by soft microscopic helices and confirm that the helical sense is sensitive to a change of packing fraction, magnitude of the molecular pitch and amplitude of the chiral interactions. In particular, we find evidence that the cholesteric helix sense may change spontaneously upon variation of particle density, at fixed molecular chirality. These pitch inversions have been reported in recent theoretical studies but simulation evidence remains elusive. We rationalize these sudden changes in the supramolecular helical symmetry on the basis of detailed measurements of the mean-torque generated by the twisting of the helices. The simulation methodology employed does not require confining the twisted nematic in a slab geometry and allows for a simultaneous measurement of the pitch and the twist elastic constant. We find that the twist elastic constant increases almost linearly with density suggesting that twisted nematic shows no signs of anomalous stiffening due to pre-smectic fluctuations at higher packing fraction.

Entropy-driven formation of chiral nematic phases by computer simulations

Predicting the macroscopic chiral behaviour of liquid crystals from the microscopic chirality of the particles is highly non-trivial, even when the chiral interactions are purely entropic in nature. Here we introduce a novel chiral hard-particle model, namely particles with a twisted polyhedral shape and obtain a stable fully entropy-driven cholesteric phase by computer simulations. By slightly modifying the triangular base of the particle, we are able to switch from a left-handed prolate (calamitic) to a right-handed oblate (discotic) cholesteric phase using the same right-handed twisted particle model. Furthermore, we show that not only prolate and oblate chiral nematic phases, but also other novel entropy-driven phases, namely chiral blue phases, chiral nematic phases featuring both twist and splay deformations, chiral biaxial nematic phases with one of the axes twisted, can be obtained by varying particle biaxiality and chirality. Our results allow to identify general guidelines for the stabilization of these phases.

Into the polymer brush regime through the "grafting-to" method: densely polymer-grafted rodlike viruses with an unusual nematic liquid crystal behavior

The current work reports an intriguing discovery of how the force exerted on protein complexes like filamentous viruses by the strong interchain repulsion of polymer brushes can induce subtle changes of the constituent subunits at the molecular scale. Such changes transform into the macroscopic rearrangement of the chiral ordering of the rodlike virus in three dimensions. For this, a straightforward "grafting-to" PEGylation method has been developed to densely graft a filamentous virus with poly(ethylene glycol) (PEG). The grafting density is so high that PEG is in the polymer brush regime, resulting in straight and thick rodlike particles with a thin viral backbone. Scission of the densely PEGylated viruses into fragments was observed due to the steric repulsion of the PEG brush, as facilitated by adsorption onto a mica surface. The high grafting density of PEG endows the virus with an isotropic-nematic (I-N) liquid crystal (LC) phase transition that is independent of the ionic strength and the densely PEGylated viruses enter into the nematic LC phase at much lower virus concentrations. Most importantly, while the intact virus and the one grafted with PEG of low grafting density can form a chiral nematic LC phase, the densely PEGylated viruses only form a pure nematic LC phase. This can be traced back to the secondary to tertiary structural change of the major coat protein of the virus, driven by the steric repulsion of the PEG brush. Quantitative parameters characterising the conformation of the grafted PEG derived from the grafting density or the I-N LC transition are elegantly consistent with the theoretical prediction.

A novel chiral phase of achiral hard triangles and an entropy-driven demixing of enantiomers

We investigate the phase behavior of a system of hard equilateral and right-angled triangles in two dimensions using Monte Carlo simulations. Hard equilateral triangles undergo a continuous isotropic-triatic liquid crystal phase transition at packing fraction ϕ = 0.7. Similarly, hard right-angled isosceles triangles exhibit a first-order phase transition from an isotropic fluid phase to a rhombic liquid crystal phase with a coexistence region ϕ ∈ [0.733, 0.782]. Both these liquid crystals undergo a continuous phase transition to their respective close-packed crystal structures at high pressures. Although the particles and their close-packed crystals are both achiral, the solid phases of equilateral and right-angled triangles exhibit spontaneous chiral symmetry breaking at sufficiently high packing fractions. The colloidal triangles rotate either in the clockwise or anti-clockwise direction with respect to one of the lattice vectors for packing fractions higher than ϕχ. As a consequence, these triangles spontaneously form a regular lattice of left- or right-handed chiral holes which are surrounded by six triangles in the case of equilateral triangles and four or eight triangles for right-angled triangles. Moreover, our simulations show a spontaneous entropy-driven demixing transition of the right- and left-handed "enantiomers".

Controlling Chirality of Entropic Crystals

Colloidal crystal structures with complexity and diversity rivaling atomic and molecular crystals have been predicted and obtained for hard particles by entropy maximization. However, thus far homochiral colloidal crystals, which are candidates for photonic metamaterials, are absent. Using Monte Carlo simulations we show that chiral polyhedra exhibiting weak directional entropic forces self-assemble either an achiral crystal or a chiral crystal with limited control over the crystal handedness. Building blocks with stronger faceting exhibit higher selectivity and assemble a chiral crystal with handedness uniquely determined by the particle chirality. Tuning the strength of directional entropic forces by means of particle rounding or the use of depletants allows for reconfiguration between achiral and homochiral crystals. We rationalize our findings by quantifying the chirality strength of each particle, both from particle geometry and potential of mean force and torque diagrams.