Cholesteric order in systems of helical Yukawa rods

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.

Chiral Structure Formation during Casting of Cellulose Nanocrystalline Films

A Landau-de Gennes formulation coupled with a mass-transfer equation was used to track the evaporation front and the development of chiral microstructures during the casting of sulfuric acid-hydrolyzed cellulose nanocrystal (CNC) films. These simulations are compared to thin-film casting experiments that used analogous processing parameters and environments. The results show that the initial concentration, chiral strength, surface anchoring, speed of drying, and the influence of initial shear alignment all affect the uniformity of the microstructure and the orientation of the chiral director. In this report, we aim to show that under optimal casting conditions, the lateral size of planar microstructural domains that exhibit uniform selective reflection can be achieved on the order of millimeters.

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.

Orientation Relaxation Dynamics in Cellulose Nanocrystal Dispersions in the Chiral Liquid Crystalline Phase

A Landau-de Gennes formulation was implemented in dynamic finite element simulations to compare with postshear relaxation experiments that were conducted on cholesteric cellulose nanocrystal (CNC) dispersions. Our study focused on the microstructural reassembly of CNCs in lyotropic dispersions as parameters such as chiral strength and gap confinement were varied. Our simulation results show that homeotropic and/or more complicated three-dimensional helical configurations are possible, depending on the choice of these parameters. We also observed how dynamic banding patterns develop into the hierarchical microstructures that are characterized by an equilibrium pitch length in both the experiments and simulations. This work has immediate relevance for cellulose nanocrystal dispersion processing and provides new insight into fluid phase ordering for tailorable optical properties.

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.

Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal

The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.

Enhancing Self-Assembly in Cellulose Nanocrystal Suspensions Using High-Permittivity Solvents

Helical liquid crystal self-assembly in suspensions of cellulose nanocrystals (CNCs), bioderived nanorods exhibiting excellent mechanical and optical properties, opens attractive routes to sustainable production of advanced functional materials. For convenience, in most studies until now, the CNCs were suspended in water, leaving a knowledge gap concerning the influence of the solvent. Using a novel approach for aggregation-free solvent exchange in CNC suspensions, here we show that protic solvents with a high dielectric permittivity εr significantly speed up self-assembly (from days to hours) at high CNC mass fraction and reduce the concentration dependence of the helix period (variation reducing from more than 30 μm to less than 1 μm). Moreover, our computer simulations indicate that the degree of order at constant CNC content increases with increasing εr, leading to a shorter pitch and a reduced threshold for liquid crystallinity. In low-εr solvents, the onset of long-range orientational order is coupled to kinetic arrest, preventing the formation of a helical superstructure. Our results show that the choice of solvent is a powerful parameter for tuning the behavior of CNC suspensions, enhancing our ability to control the self-assembly and thereby harvesting valuable novel cellulose-based materials.

Hierarchical Propagation of Chirality through Reversible Polymerization: The Cholesteric Phase of DNA Oligomers

Unveiling the subtle rules that control the buildup of macroscopic chirality starting from chiral molecular elements is a challenge for theory and computations. In this context, a remarkable phenomenon is the formation of helically twisted nematic (cholesteric) phases, with pitch in the micrometer range, driven by self-assembly of relatively small chiral species into supramolecular semiflexible polymers. We have developed a theoretical framework to connect the cholesteric organization to the shape and chirality of the constituents, described with molecular detail, in this kind of system. The theory has been tested against new accurate measurements for solutions of short DNA duplexes. We show that the cholesteric organization is determined by steric repulsion between duplexes, and we identify distinctive features of linear self-assembly in the temperature and concentration dependence of the pitch.

Generalized Onsager theory for strongly anisometric patchy colloids

The implications of soft "patchy" interactions on the orientational disorder-order transition of strongly elongated colloidal rods and flat disks is studied within a simple Onsager-van der Waals density functional theory. The theory provides a generic framework for studying the liquid crystal phase behaviour of highly anisometric cylindrical colloids which carry a distinct geometrical pattern of repulsive or attractive soft interactions localized on the particle surface. In this paper, we apply our theory to the case of charged rods and disks for which the local electrostatic interactions can be described by a screened-Coulomb potential. We consider infinitely thin rod like cylinders with a uniform line charge and infinitely thin discotic cylinders with several distinctly different surface charge patterns. Irrespective of the backbone shape the isotropic-nematic phase diagrams of charged colloids feature a generic destabilization of nematic order at low ionic strength, a dramatic narrowing of the biphasic density region, and a reentrant phenomenon upon reducing the electrostatic screening. The low screening regime is characterized by a complete suppression of nematic order in favor of positionally ordered liquid crystal phases.

Density functional theory for chiral nematic liquid crystals

Even though chiral nematic phases were the first liquid crystals experimentally observed more than a century ago, the origin of the thermodynamic stability of cholesteric states is still unclear. In this Rapid Communication we address the problem by means of a density functional theory for the equilibrium pitch of chiral particles. When applied to right-handed hard helices, our theory predicts an entropy-driven cholesteric phase, which can be either right or left handed, depending not only on the particle shape but also on the thermodynamic state. We explain the origin of the chiral ordering as an interplay between local nematic alignment and excluded-volume differences between left- and right-handed particle pairs.

Liquid crystal phase behaviour of attractive disc-like particles

We employ a generalized van der Waals-Onsager perturbation theory to construct a free energy functional capable of describing the thermodynamic properties and orientational order of the isotropic and nematic phases of attractive disc particles. The model mesogen is a hard (purely repulsive) cylindrical disc particle decorated with an anisotropic square-well attractive potential placed at the centre of mass. Even for isotropic attractive interactions, the resulting overall inter-particle potential is anisotropic, due to the orientation-dependent excluded volume of the underlying hard core. An algebraic equation of state for attractive disc particles is developed by adopting the Onsager trial function to characterize the orientational order in the nematic phase. The theory is then used to represent the fluid-phase behaviour (vapour-liquid, isotropic-nematic, and nematic-nematic) of the oblate attractive particles for varying values of the molecular aspect ratio and parameters of the attractive potential. When compared to the phase diagram of their athermal analogues, it is seen that the addition of an attractive interaction facilitates the formation of orientationally-ordered phases. Most interestingly, for certain aspect ratios, a coexistence between two anisotropic nematic phases is exhibited by the attractive disc-like fluids.