We show that the optimal packing of hard spheres in an infinitely long cylinder yields structures characterised by a screw symmetry. Each packing can be assembled by stacking a basic unit cell ad infinitum along the length of the cylinder with each subsequent unit cell rotated by the same twist angle with respect to the previous one. In this paper we quantitatively describe the nature of this screw operation for all such packings in the range 1 <= D/d <= 2.715 and also briefly discuss their helicity.
The interaction of two screw dislocations in smectic-A liquid crystals is treated using an anharmonic correction to the elastic energy density. In the present contribution the elastic energy and the force between two screw dislocations is evaluated and discussed. For screw dislocations with both parallel and opposite Burgers vectors there is an attraction of dislocations for their small separations while for greater separations there is a repulsion. It can be explained by dominating terms in interaction energy which do not depend on signs of dislocations. In this way, the interaction energy of…
A hexagonal columnar crystal undergoes a shear-melting transition above a critical shear rate or stress. We combine the analysis of the shear-thinning regime below the melting with that of synchrotron X-ray scattering data under shear and propose the melting to be due to a proliferation of dislocations, whose density is determined by both techniques to vary as a power law of the shear rate with a 2/3 exponent, as expected for a creep model of crystalline solids. Moreover, our data suggest the existence under shear of a line hexatic phase, between the columnar crystal and the liquid phase.
The mistakes of the classical solution of screw dislocations in smectic-A liquid crystals are pointed out. This reveals a serious problem of the well-known theory, which may be named de Gennes-Kleman-Pershan paradox, for many decades in the scientific community of liquid crystal study. The correct solution is given in this letter in terms of simplest, elementary and straightforward solution method. Furthermore, the stress filed and energy of dislocation are discussed in detail. The present article gives a corrected stress field and dislocation energy as well.
We introduce a model to describe columnar phases of chiral discotic liquid phases in which the normals to disc-like molecules are constrained to lie parallel to columnar axes. The model includes separate chiral interactions favoring, respectively, relative twist of chiral molecules along the axes of the columns and twist of the two-dimensional columnar lattice. It also includes a coupling between the lattice and the orientation of the discotic molecules. We discuss the instability of the aligned hexagonal lattice phase to the formation of a soliton lattice in which molecules twist within their…
Nuclei of ordered materials emerging from the isotropic state usually show a shape topologically equivalent to a sphere; the well-known examples are crystals and nematic liquid crystal droplets. In this work, we explore experimentally and theoretically the nuclei of columnar lyotropic chromonic liquid crystal coexisting with the isotropic phase that are toroidal in shape. The geometry of toroids depends strongly on the molecular concentrations and presence of a crowding agent, polyethylene glycol. High concentrations result in thick toroids with small central holes, while low concentrations yi…
In order to understand the possible sequence of transitions from the disordered columnar phase to the helical phase in hexa(hexylthio)triphenylene (HHTT), we study a three-dimensional planar model with octupolar interactions inscribed on a triangular lattice of columns. We obtain thermal phase diagrams using a mean-field approximation and Monte Carlo simulations. These two approaches give similar results, namely, in the quasi one-dimensional regime, as the temperature is lowered, the columns order with a linear polarization, whereas helical phases develop at lower temperatures. The helicity pa…
In the wake of previous studies on the rattling-and-jumping diffusion in smectic liquid crystal phases of colloidal rods, we analyze here for the first time the heterogeneous dynamics in columnar phases. More specifically, we perform computer simulations to investigate the relaxation dynamics of a binary mixture of perfectly aligned hard spherocylinders. We detect that the columnar arrangement of the system produces free-energy barriers the particles should overcome to jump from one column to another, thus determining a hopping-type diffusion. This phenomenon accounts for the non-Gaussian inte…
We report a molecular dynamics simulation demonstrating that a columnar liquid crystal, commonly formed by disc-shaped molecules, can be formed by identical particles interacting via a spherically symmetric potential. Upon isochoric cooling from a low-density isotropic liquid state the simulated system performed a weak first order phase transition which produced a liquid crystal phase composed of parallel particle columns arranged in a hexagonal pattern in the plane perpendicular to the column axis. The particles within columns formed a liquid structure and demonstrated a significant intracolu…
An accurate description of a columnar liquid crystal of hard disks at high packing fractions is presented using an improved free-volume theory. It is shown that the orientational entropy of the disks in the one-dimensional fluid direction leads to a different high-density scaling pressure compared to the prediction from traditional cell theory. Excellent quantitative agreement is found with recent Monte-Carlo simulation results for various thermodynamic and structural properties of the columnar state.
We study how dispersions of colloidal particles in a cholesteric liquid crystal behave under a time-dependent electric field. By controlling the amplitude and shape of the applied field wave, we show that the system can be reproducibly driven out of equilibrium through different kinetic pathways and navigated through a glassy-like free energy landscape encompassing many competing metastable equilibria. Such states range from simple Saturn rings to complex structures featuring amorphous defect networks, or stacks of disclination loops. A non-equilibrium electric field can also trigger the align…
We show that discotics, lying deep in the columnar phase, can exhibit an x-ray scattering pattern which mimics that of a somewhat unusual smectic liquid crystal. This exotic, new glassy phase of columnar liquid crystals, which we call a ``hybrid columnar Bragg glass'', can be achieved by confining a columnar liquid crystal in an anisotropic random environment of e.g., strained aerogel. Long-ranged orientational order in this phase makes {\em single domain} x-ray scattering possible, from which a wealth of information could be extracted. We give detailed quantitative predictions for the scatter…
Columnar crystals contain defects in the form of vacancy/interstitial loops or strings of vacancies and interstitials bounded by column ``heads'' and ``tails''. These defect strings are oriented by the columnar lattice and can change size and shape by movement of the ends and forming kinks along the length. Hence an analysis in terms of directed living polymers is appropriate to study their size and shape distribution, volume fraction, etc. If the entropy of transverse fluctuations overcomes the string line tension in the crystalline phase, a string proliferation transition occurs, leading to …
After a short review on the physics of pulled threads and their mechanical properties, the paper reports and discusses on the strand elongation of disordered columnar phases, hexagonal or lamello-columnar, of small molecules or polymers. The mechanical properties appear to be relevant to the length of the columns of molecules compared to the thread length, instead of the usual correlation length. When short, the column entanglement being taken into account, the strand exhibits rather fluid properties that may even look like nematic at a macroscopic scale. Then, the Plateau-Rayleigh instability…
Using Deposition Rate and Substrate Temperature to Manipulate Liquid Crystal-like Order in a Vapor-deposited Hexagonal Columnar Glass
University of Wisconsin – Madison（威斯康星大学麦迪逊分校）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Centre de Recherche Paul Pascal, CNRS & Université de Bordeaux（保罗·帕斯卡研究中心，法国国家科学研究中心与波尔多大学）
We use the Dynamic Density-Functional Formalism and the Fundamental Measure Theory as applied to a fluid of parallel hard squares to study the dynamics of heterogeneous growth of non-uniform phases with columnar and crystalline symmetries. The hard squares are (i) confined between soft repulsive walls with square symmetry, or (ii) exposed to external potentials that mimic the presence of obstacles with circular, square, rectangular or triangular symmetries. For the first case the final equilibrium profile of a well commensurated cavity consists of a crystal phase with highly localized particle…
We explore micropatterned director structures of aqueous lyotropic chromonic liquid crystal (LCLC) films created on square lattice cylindrical-micropost substrates. The structures are manipulated by modulating the LCLC mesophases and their elastic properties via concentration through drying. Nematic LCLC films exhibit preferred bistable alignment along the diagonals of the micropost lattice. Columnar LCLC films, dried from nematics, form two distinct director and defect configurations: a diagonally aligned director pattern with local squares of defects, and an off-diagonal configuration with z…
Hexakis(n-alkyloxy)triphenylene) (HATn) consisting of an aromatic triphenylene core and alkyl side chains are model discotic liquid crystal (DLC) systems forming a columnar mesophase. In the mesophase, the molecules of HATn self-assemble in columns, which has one-dimensional high charge carrier mobility along the columns. Here, a homologous series of HATn with different length of the alkyl chain (n=5,6,8,10,12) is investigated using differential scanning calorimetry (DSC), broadband dielectric spectroscopy (BDS) and advanced calorimetric techniques including fast scanning calorimetry (FSC) and…
We test the performance of a recently proposed fundamental measure density functional of aligned hard cylinders by calculating the phase diagram of a monodisperse fluid of these particles. We consider all possible liquid crystalline symmetries, namely nematic, smectic and columnar, as well as the crystalline phase. For this purpose we introduce a Gaussian parameterization of the density profile and use it to minimize numerically the functional. We also determine, from the analytic expression for the structure factor of the uniform fluid, the bifurcation points from the nematic to the smectic a…
We apply a recently proposed density functional for mixtures of parallel hard cylinders, based on Rosenfeld's fundamental measure theory, to study the effect of length-polydispersity on the relative stability between the smectic and columnar liquid crystal phases.To this purpose we derive from this functional an expression for the direct correlation function and use it to perform a bifurcation analysis. We compare the results with those obtained with a second and a third virial approximation of this function. All three approximations lead to the same conclusion: there is a terminal polydispers…
Using density-functional theory, we have analyzed the phase behavior of binary mixtures of hard rods of different lengths and diameters. Previous studies have shown a strong tendency of smectic phases of these mixtures to segregate and, in some circumstances, to form microsegregated phases. Our focus in the present work is on the formation of columnar phases which some studies, under some approximations, have shown to become thermodynamically stable prior to crystallization. Specifically we focus on the relative stability between smectic and columnar phases, a question not fully addressed in p…
Disklike molecules with aromatic cores spontaneously stack up in linear columns with high, one-dimensional charge carrier mobilities along the columnar axes making them prominent model systems for functional, self-organized matter. We show by high-resolution optical birefringence and synchrotron-based X-ray diffraction that confining a thermotropic discotic liquid crystal in cylindrical nanopores induces a quantized formation of annular layers consisting of concentric circular bent columns, unknown in the bulk state. Starting from the walls this ring self-assembly propagates layer by layer tow…
We demonstrate that an arbitrary system of screw dislocations in a smectic-A liquid crystal may be consistently treated within harmonic elasticity theory, provided that the angles between dislocations are sufficiently small. Using this theory, we calculate the ground state configuration of the TGB-A phase. We obtain an estimate of the twist-grain-boundary spacing and screw dislocation spacing in a boundary in terms of the macroscopic parameters, in reasonable agreement with experimental results.
In this article we consider systems of parallel hard {\it superellipsoids}, which can be viewed as a possible interpolation between ellipsoids of revolution and cylinders. Superellipsoids are characterized by an aspect ratio and an exponent $α$ (shape parameter) which takes care of the geometry, with $α=1$ corresponding to ellipsoids of revolution, while $α=\infty$ is the limit of cylinders. It is well known that, while hard parallel cylinders exhibit nematic, smectic, and solid phases, hard parallel ellipsoids do not stabilize the smectic phase, the nematic phase transforming directly into a …
We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsager's second virial theory with the Parsons-Lee decoupling approximation to account for higher-body interactions in the isotropic and nematic fluid phases. The stability of the solid (columnar) state at high packing fraction is included by invoking a simple equation of state based on a Lennard-Jones-Devonshire (LJD) cell model which has proven to be quantitatively reliable over a large range of packing fractions. By employing an asymptotic analysis based on the Gaussian appro…
Optical polarimetry measurements of the orientational order of a discotic liquid crystal based on a pyrene derivative and confined in parallel-aligned nanochannels of monolithic mesoporous alumina, silica, and silicon as a function of temperature, channel radius (3 - 22 nm) and surface chemistry reveal a competition of radial and axial columnar order. The evolution of the orientational order parameter of the confined systems is continuous, in contrast to the discontinuous transition in the bulk. For channel radii larger than 10 nm we suggest several, alternative defect structures, which are co…
