Entropy-Driven Chiral Order in a System of Achiral Bent Particles

Why should achiral particles organize into a helical structure? Here, using theory and molecular dynamics simulations we show that at high concentration crescent-shaped particles interacting through a purely repulsive potential form the twist-bend nematic phase, which features helical order of the twofold symmetry axes of particles, with doubly degenerate handedness. Spontaneous breaking of the chiral symmetry is driven by the entropic gain that derives from the decrease in excluded volume in the helical arrangement. Crucial to this purpose is the concave shape of particles. This study is based on a general formulation of the Onsager theory, which includes biaxiality and polarity of phase and particles, in addition to the space modulation of order. Molecular dynamics simulations corroborate the theoretical predictions and provide further insights into the structure of the helical phase

Left or right cholesterics? A matter of helix handedness and curliness

We have investigated the relationship between the morphology of helical particles and the features of the cholesteric (N$^\ast$) phase that they form. Using an Onsager-like theory, applied to systems of hard helices, we show that the cholesteric handedness and pitch depend on both the pitch and the curliness of the particles. The theory leads to the definition of pseudoscalars that correlate the helical features of the phase to the chirality of the excluded volume of the constituent particles

From rods to helices: evidence of a screw-like nematic phase

Evidence of a special chiral nematic phase is provided using numerical simulation and Onsager theory for systems of hard helical particles. This phase appears at the high density end of the nematic phase, when helices are well aligned, and is characterized by the C$_2$ symmetry axes of the helices spiraling around the nematic director with periodicity equal to the particle pitch. This coupling between translational and rotational degrees of freedom allows a more efficient packing and hence an increase of translational entropy. Suitable order parameters and correlation functions are introduced to identify this screw-like phase, whose main features are then studied as a function of radius and pitch of the helical particles. Our study highlights the physical mechanism underlying a similar ordering observed in colloidal helical flagella [E. Barry et al. \textit{Phys. Rev. Lett.} \textbf{96}, 018305 (2006)] and raises the question of whether it could be observed in other helical particle systems, such as DNA, at sufficiently high densities.Comment: List of authors correcte

Cholesteric and screw-like nematic phases in systems of helical particles

Recent numerical simulations of hard helical particle systems unveiled the existence of a novel chiral nematic phase, termed screw-like, characterised by the helical organization of the particle C2 symmetry axes round the nematic director with periodicity equal to the particle pitch. This phase forms at high density and can follow a less dense uniform nematic phase, with relative occurrence of the two phases depending on the helix morphology. Since these numerical simulations were conducted under three-dimensional periodic boundary conditions, two questions could remain open. First, the real nature of the lower density nematic phase, expected to be cholesteric. Second, the influence that the latter, once allowed to form, may have on the existence and stability of the screw-like nematic phase. To address these questions, we have performed Monte Carlo and molecular dynamics numerical simulations of helical particle systems confined between two parallel repulsive walls. We have found that the removal of the periodicity constraint along one direction allows a relatively-long-pitch cholesteric phase to form, in lieu of the uniform nematic phase, with helical axis perpendicular to the walls while the existence and stability of the screw-like nematic phase are not appreciably affected by this change of boundary conditions

Understanding the twist-bend nematic phase: the characterisation of 1-(4-cyanobiphenyl-4'-yloxy)-6-(4-cyanobiphenyl-4'-yl) hexane (CB6OCB) and comparison with CB7CB

Acknowledgements The FFTEM data were obtained at the (Cryo) TEM facility at the Liquid Crystal Institute, Kent State University, supported by the Ohio Research Scholars Program Research Cluster on Surfaces in Advanced Materials. ODL acknowledges the support of NSF DMR-1410378 grant. The authors are grateful for financial support from MINECO/FEDER MAT2015-66208-C3-2-P and from the Gobierno Vasco (GI/IT-449-10) OA via RSC Gold4GoldPeer reviewedPublisher PD

The theory of elastic constants

The elastic theory of liquid crystals can be traced back to the early 1930s, but the origin of the molecular theory of elastic constants must be postponed to more than 30 years later, when Alfred Saupe wrote his famous papers on this subject. At approximately the same time, the seminal works by Priest and Straley also appeared. Since then, several theories have been developed to connect intermolecular interactions to curvature deformations, on a quite different length-scale, in liquid crystals. This field was particularly alive between the end of the 1970s and the beginning of the 1980s, in parallel with experimental investigations. In more recent times, a renewed interest was aroused by the controversy about the second-order splay-bend contribution, which appears in the Nehring-Saupe expression for the deformation energy density. In the first part of the present contribution the molecular theory of elastic constants is briefly reviewed. This paper focuses on the effects of molecular structure on the elastic constants of thermotropic nematics and the ability of different models to account for them. A few classical examples are discussed to illustrate these issues. The second part of this paper is dedicated to our recent 'Surface Interaction' model, a molecular field approach based on the Maier-Saupe theory, implemented into a framework allowing for atomistic molecular modelling. The theoretical background is outlined, then some new results are reported and the insights derived from a realistic molecular representation are discussed. We conclude that, after about 40 years of theoretical investigations, there is a general consensus on the importance of the molecular shape in determining the elastic constants of nematics: for fairly rigid compounds these can be simply related to the length-to-width ratio, but for the general case of non-rigid mesogens the molecular flexibility and shape curvature have to be taken into account

Dielectric permittivity of nematics with a molecular based continuum model

A theoretical model for the dielectric permittivity of nematics has been recently proposed [1], based on the atomistic representation of a probe molecule interacting with a medium which is characterised by its macroscopic properties. Electrostatic interactions are described through the classical model of a charge distribution contained in a molecular- shaped cavity embedded in an anisotropic dielectric continuum. Short-range intermolecular interactions are parameterized in terms of the anisometry of the molecular surface, which is defined according to the "rolling sphere" representation. The results obtained for the isotropic and nematic phases of 4,4'-pentyl-cyanobiphenyl and 4,4'-pentyl-cyanobicyclohexyl are reported; a good agreement with experiment appears, with a significant improvement with respect to the Maier-Meier theory

Shape model for the molecular interpretation of the flexoelectric effect

A mean-field model for the flexoelectric polarization in nematics is presented, based on a continuous description of director deformations coupled to the molecular degrees of freedom via surface interactions. In such a framework, a consistent picture of the flexoelectric effect is obtained, including both dipolar and quadrupolar contributions, with a realistic account of the molecular characteristics of shape and charge distribution. The method is aimed at establishing a quantitative link between chemical structure and flexoelectric response. It provides numerical estimates of the effect and its temperature dependence and allows the recognition of the relevant molecular features for its emergence. Application to some representative systems, comprising mesogenic molecules and photoisomerizable dopants, is considered; it is shown that simple interpretative schemes can be misleading and a comparison with experimental data is reported