Extensions of a previously presented Landau-de Gennes type liquid crystalline phase transition model for the direct isotropic/smectic-A (lamellar) a phase transition to the direct isotropic/smectic-C (tilted lamellar) transition are studied. Two different proposed extensions to the model are studied both in the context of ideal ordering (point volume) and full three-dimensional uniaxial scalar/vector decomposition. Recommendations based upon the inclusion of essential physics and computational feasibility are made, distinguishing each of the two proposed extensions based upon these criteria. Additionally, it is found that the approach used for the isotropic/smectic-A model to deterministically compute phase diagram data is not possible for either of the two proposed isotropic/smectic-C models.
Freezing of ice has been largely reported from many aspects, especially its complex pattern formation. Ice grown from liquid phase is usually characteristic of lamellar morphology which plays a significant role in various domains. However, tilted growth of ice via transition from coplanar to non-coplanar growth in directional solidification has been paid little attention in previous studies and there is misleading explanation of the formation of tilted lamellar ice. Here, we in-situ investigated the variations of tilting behavior of lamellar ice tip under different conditions within a single i…
Motivated by numerous X-ray scattering studies of lamellar phases with membrane proteins, amphiphilic peptides, polymers, or other inclusions, we have determined the modifications of the classical Caille law for a smectic phase as a function of the nature and concentration of inclusions added to it. Besides a fundamental interest on the behavior of fluctuating systems with inclusions, a precise characterization of the action of a given protein on a lipid membrane (anchoring, swelling, stiffening ...) is of direct biological interest and could be probed by way of X-ray measurements. As a first …
Smectic materials represent a unique state between fluids and solids, characterized by orientational and partial positional order, making them notoriously difficult to model, particularly in confining geometries. We propose a complex order parameter tensor to describe the local degree of lamellar ordering, layer displacement and orientation. The theory accounts for both dislocations and disclinations, as well as arrested configurations and colloid-induced local ordering. It considerably simplifies numerics, facilitating studies on the dynamics of topologically complex lamellar systems.
We present detailed systematic studies of structural transformations in thin liquid crystal films with the smectic-C to hexatic phase transition. For the first time all possible structures reported in the literature are observed for one material (5 O.6) at the variation of temperature and thickness. In unusual modulated structures the equilibrium period of stripes is twice with respect to the domain size. We interpret these patterns in the frame work of phenomenological Landau type theory, as equilibrium phenomena produced by a natural geometric frustration in a system having spontaneous splay…
We demonstrate that the sequence of distorted commensurate phases observed in tilted chiral smectics is explained by the gain in electrostatic energy due to the lock-in of the unit cell to a number of layers which is the integer closest to the ratio pitch over thickness of the subjacent Sm-C$^*_α$ phase. We also explain the sign change of the helicity in the middle of the sequence by a balance between two twist sources one intrinsic and another due to the distortion of the Sm-C$^*_α$.
We investigate the dynamic behavior of long guest rod-like particles immersed in liquid crystalline phases formed by shorter host rods, tracking both guest and host particles by fluorescence microscopy. Counter-intuitively, we evidence that long rods diffuse faster than short rods forming the one-dimensional ordered smectic-A phase. This results from the larger and non-commensurate size of the guest particles as compared to the wavelength of the energy landscape set by the lamellar stack of liquid slabs. The long guest particles are also shown to be still mobile in the crystalline smectic-B ph…
We investigate the effect of chemically patterned surfaces on the morphology of diblock copolymers below the order-disorder transition. Profiles for lamellar phases in contact with one surface, or confined between two surfaces are obtained in the weak segregation limit using a Ginzburg-Landau expansion of the free energy, and treating it with mean-field theory. The periodically patterned surface induces a tilt of the lamellae in order to match the surface periodicity. The lamellae relax from the constrained periodicity close to the surface to the bulk periodicity far from it. The phases we inv…
We report the direct visualization at the scale of single particles of mass transport between smectic layers, also called permeation, in a suspension of rod-like viruses. Self-diffusion takes place preferentially in the direction normal to the smectic layers, and occurs by quasi-quantized steps of one rod length. The diffusion rate corresponds with the rate calculated from the diffusion in the nematic state with a lamellar periodic ordering potential that is obtained experimentally.
Modulated Anti-Ferroelectric Smectic Phases with Orthogonal and Tilted Structures
School of Physics & Astronomy, University of Leeds（利兹大学物理与天文学院）；School of Chemistry, University of Leeds（利兹大学化学学院）；Complex Matter Department, Jožef Stefan Institute（约瑟夫·斯蒂芬研究所复杂物质部）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）
Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted with respect to the smectic layer normal. As in the previous papers of the series (Phys. Rev. A {\bf 45}, 974 (1992), E {\bf 49}, 501, (1994)) the expressions for the elastic constants are written in terms of order and structural parameters. The structural parameters involve the generalised spherical harmonic coefficients of the direct pair correlation functi…
We present important new results from light-microscopy and rheometry on a moderately concentrated lyotropic smectic, with and without particulate additives. Shear-treatment aligns the phase rapidly, except for a striking network of oily-streak defects, which anneals out much more slowly. If spherical particles several microns in diameter are dispersed in the lamellar medium, part of the defect network persists under shear-treatment, its nodes anchored on the particles. The sample as prepared has substantial storage and loss moduli, both of which decrease steadily under shear-treatment. Adding …
Riemann's minimal surfaces are a complete, embeddable, one-parameter family of minimal surfaces with translational symmetry along one direction. It's infinite number of planar ends are joined together by an array of necks, closely matching the morphology of a bicontinuous, lamellar system with pores connecting alternating layers. We demonstrate explicitly that Riemann's minimal surfaces are composed of a nonlinear sum of two oppositely-handed helicoids. This description is particularly appropriate for describing smectic liquid crystals containing two screw dislocations.
The phase behavior of a melt of monodisperse rod-coil diblocks is studied. We derive a Landau free energy functional for both a compositional and a nematic order parameter. The excluded volume interaction between the rod blocks is modeled by an attractive Maier-Saupe interaction. The incompatibility between rod- and coil blocks is modeled by the usual Flory-Huggins interaction. For a large volume fraction of the rods, a transition from isotropic to nematic to smectic C is observed upon decreasing the temperature, whereas for small rod volume fraction, spherical, hexagonal, and lamellar structu…
We analyse the effect of thermal fluctuations on the elastic constants of the decoupled lamellar phase of tethered, crystalline membranes. Using a momentum-shell renormalization group technique, we show that the smectic-A -like compressional elastic constant, the in-plane Lamé coefficients, and the cross-coupling elastic constant vanish as (\ln q)^{- a} whereas the bend elastic constant diverges as (\ln q)^{b}, with a, b > 0, as the wavenumber q tends to zero. The exponents a and b satisfy the relation a + 3b = 2.
The phase behavior of the system of parallel rigid triblock copolymers is examined using the second-virial density functional theory. The triblock particle consists of two identical infinitely thin hard rods of finite lengths on the opposite ends of one central hard cylinder with nonzero length and diameter. Stability analyses and free energy calculations show that the system of parallel particles can form not only uniform nematic and smectic A phases, but a smectic-C phase too. The stability and structure of the tilted structure is controlled by only the diameter and the length of the central…
We investigate thermal fluctuations in a smectic A phase of an amphiphile-solvent mixture with molecular dynamics simulations. We use an idealized model system, where solvent particles are represented by simple beads, and amphiphiles by bead-and-spring tetramers. At a solvent bead fraction of 20 % and sufficiently low temperature, the amphiphiles self-assemble into a highly oriented lamellar phase. Our study aims at comparing the structure of this phase with the predictions of the elastic theory of thermally fluctuating fluid membrane stacks [Lei et al., J. Phys. II 5, 1155 (1995)]. We suggest…
Using simulations, we study the diffusion of rod-like guest particles in a smectic environment of rod-like host particles. We find that the dynamics of guest rods across smectic layers changes from a fast nematic-like diffusion to a slow hopping-type dynamics via an intermediate switching regime by varying the length of the guest rods with respect to the smectic layer spacing. We determine the optimal rod length that yields the fastest and the slowest diffusion in a lamellar environment. We show that this behavior can be rationalized by a complex 1D effective periodic potential exhibiting two …
Experimental and modeling/simulation studies of phase equilibrium and growth morphologies of novel polymer-dispersed liquid crystal (PDLC) mixtures of PS (polystyrene) and liquid crystals that exhibit a direct isotropic/smectic-A (lamellar) mesophase transition were performed for PS/10CB (decyl- cyanobiphenyl) and PS/12CB (dodecyl-cyanobiphenyl). Partial phase diagrams were determined using polarized optical microscopy (POM) and differential scanning calorimetry (DSC) for different compositions of both materials, determining both phase separation (liquid/liquid demixing) and phase ordering (is…
When thermal energies are weak, two dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We present broad design principles to engineer the geometry of the underlying substrate so that a desired lamellar pattern can be obtained by self-assembly. Two distinct physical effects are identified as key factors that contribute to the interaction between the shape of the underlying surface and the resulting lamellar morphology. The first is a local ordering fi…
We have structurally characterized the liquid crystal phase that appears as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-year-old void in the taxonomy of smectics and which we term the "smectic $Z_A$", is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer. The period of this polarization wave ($\sim$180 A) is mesosc…
We investigate the self-organization of a binary mixture of similar sized rods and dipolar soft spheres by means of Monte-Carlo simulations. We model the interparticle interactions by employing anisotropic Gay-Berne, dipolar and soft-sphere interactions. In the limit of vanishing magnetic moments we obtain a variety of fully miscible liquid crystalline phases including nematic, smectic and lamellar phases. For the magnetic mixture, we find that the liquid crystalline matrix supports the formation of orientationally ordered ferromagnetic chains. Depending on the relative size of the species the…
The effects of dipolar interactions and molecular flexibility on the structure and phase behavior of bent-core molecular fluids are studied using Monte Carlo computer simulations. Some calculations of flexoelectric coefficients are also reported. The rigid cores of the model molecules consist of either five or seven soft spheres arranged in a `V' shape with external bend angle $γ$. With purely repulsive sphere-sphere interactions and $γ=0^\circ$ (linear molecules) the seven-sphere model exhibits isotropic, uniaxial nematic, smectic-A, and tilted phases. With $γ\geq 20^\circ$ the smectic-A phas…
We study the relaxation modes of an interface between a lyotropic lamellar phase and a gas or a simple liquid. The response is found to be qualitatively different from those of both simple liquids and single-component smectic-A liquid crystals. At low rates it is governed by a non-inertial, diffusive mode whose decay rate increases quadratically with wavenumber, $|ω|=Aq^2$. The coefficient $A$ depends on the restoring forces of surface tension, compressibility and bending, while the dissipation is dominated by the so-called slip mechanism, i.e, relative motion of the two components of the phas…
Within the framework of a discrete Gaussian model, we present analytical results for the interaction induced by a lamellar phase between small embedded colloids. We consider the two limits of particles strongly adherent to the adjacent membranes and of particles impenetrable to the membranes. Our approach takes into account the finite size of the colloids, the discrete nature of the layers, and includes the Casimir-like effect of fluctuations, which is very important for dilute phases. Monte Carlo simulations of the statistical behavior of the membrane-interacting colloids account semi-quantit…
A series of asymmetric dimers with an odd number of atoms in the spacer were found to form different types of twisted structures despite being achiral. The formation of a variety of helical structures is accompanied by a gradual freezing of molecular rotation. The tight pitch heliconical nematic (NTB) phase and heliconical tilted smectic C (SmCTB) phase are formed. In the lowest temperature smectic phase, HexI, the twist is expressed through the formation of hierarchical structure: nano-scale helices and mesoscopic helical filaments. The short pitch helical structure in smectic phases is confi…
The structure of nematic liquid crystals formed by bent-core mesogens (BCMs) is studied in the context of Monte Carlo simulations of a simple molecular model that captures the symmetry, shape and flexibility of achiral BCMs. The results indicate the formation of (i) clusters exhibiting local smectic order, orthogonal or tilted, with strong in-layer polar correlations and anti-ferroelectric juxtaposition of successive layers and (ii) large homochiral domains through the helical arrangement of the tilted smectic clusters, whilst the orthogonal clusters produce achiral (untwisted) nematic states.
In twist-bend nematic (N\textsubscript{TB}) liquid crystals (LCs), the mean molecular orientation exhibits heliconical structure with nanoscale periodicity. On the mesoscopic scale, N\textsubscript{TB} resembles layered systems (like smectics), where the helical pitch is equivalent to "pseudo-layers" without a true mass density wave. We study rheological properties of a N\textsubscript{TB} phase and compare the results with those of an usual SmA phase. Analysing the shear response and adapting a simplified physical model for rheology of defect mediated lamellar systems we measure the pseudo-la…
We explore theoretically the modifications to the interactions between charged surfaces across an ionic solution caused by the presence of dielectric polymers. Although the chains are neutral, the polymer physics and the electrostatics are coupled; the intra-surface electric fields polarise any low permittivity species (e.g., polymer) dissolved in a high permittivity solvent (e.g., water). This coupling enhances the polymer depletion from the surfaces and increases the screening of electrostatic interactions with respect to a model which treats polymeric and electrostatic effects as independen…
We consider the relative stability of parallel and perpendicular lamellar layers on corrugated surfaces. The model can be applied to smectic phases of liquid crystals, to lamellar phases of short-chain amphiphiles and to lamellar phases of long-chain block copolymers. The corrugated surface is modelled by having a single $q$-mode lateral corrugation of a certain height. The lamellae deform close to the surface as a result of chemical interaction with it. The competition between the energetic cost of elastic deformations and the gain in surface energy determines whether parallel or perpendicula…
We present large scale computer simulations of the nonlinear bulk rheology of lamellar phases (smectic liquid crystals) at moderate to large values of the shear rate (Peclet numbers 10-100), in both two and three dimensions. In two dimensions we find that modest shear rates align the system and stabilise an almost regular lamellar phase, but high shear rates induce the nucleation and proliferation of defects, which in steady state is balanced by the annihilation of defects of opposite sign. The critical shear rate at onset of this second regime is controlled by thermodynamic and kinetic parame…
We report on the first direct nanoscale imaging of elementary edge dislocations in a thermotropic chiral smectic C liquid crystal with the Burgers vector equal to one smectic layer spacing d. We find two different types of dislocation profiles. In the dislocation of type A, the layers deformations lack mirror symmetry with respect to the plane perpendicular to the Burgers vector; the dislocation core size is on the order of d. In the dislocation of type S, the core is strongly anisotropic, extending along the Burgers vector over distances much larger (by a factor of 4) than d. The difference i…
Recent experiments indicate that doping low concentrations of bent-core molecules into calamitic smectic solvents can induce anticlinic and biaxial smectic phases. We have carried out Monte Carlo (MC) simulations of mixtures of rodlike molecules (hard spherocylinders with length/breadth ratio $L_{\rm rod}/D = 5$) and bow- or banana-shaped molecules (hard spherocylinder dimers with length/breadth ratio $L_{ban}/D = 5$ or 2.5 and opening angle $ψ$) to probe the molecular-scale organization and phase behavior of rod/banana mixtures. We find that a low concentration (3%) of $L_{ban}/D = 5$ dimers …
We have carried out Monte Carlo simulations of zig-zag shaped molecules where the the molecules is composed of three rigidly linked hard spherocylinder arranged in a zigzag fashion. By varying zigzag angle we have mapped out the whole phase diagram as a function of pressure, molecular density and zigzag angle $Ψ$. For $Ψ$ between $35^0$ and $80^0$ our model simulation exhibits SmC phase. This is the first conclusive evidence where steric interaction arising out of molecular shape alone induce the occurrence of SmC phase for a wide range of zigzag angle. For smaller $Ψ$, a transition from tilte…
Weakly attractive interactions between the tips of rod-like colloidal particles affect their liquid-crystal phase behaviour due to a subtle interplay between enthalpy and entropy. Here, we employ molecular dynamics simulations on semi-flexible, repulsive bead-spring chains of which one of the two end beads attract each other. We calculate the phase diagram as a function of both the volume fraction of the chains and the strength of the attractive potential. We identify a large number of phases that include isotropic, nematic, smectic A, smectic B and crystalline states. For tip attraction energ…
Under appropriate conditions, mixtures of cationic and neutral lipids and DNA in water condense into complexes in which DNA strands form local 2D smectic lattices intercalated between lipid bilayer membranes in a lamellar stack. These lamellar DNA-cationic-lipid complexes can in principle exhibit a variety of equilibrium phases, including a columnar phase in which parallel DNA strands from a 2D lattice, a nematic lamellar phase in which DNA strands align along a common direction but exhibit no long-range positional order, and a possible new intermediate phase, the sliding columnar (SC) phase, …
The chiral, heliconical (twist-bend) nematic ground state is reported in an achiral, rigid, bent-core mesogen (UD68). Similar to the nematic twist-bend (NTB) phase observed in bent molecular dimers, the NTB phase of UD68 forms macroscopic, smectic-like focal-conic textures and exhibits nanoscale, periodic modulation with no associated modulation of the electron density, i.e., without a detectable lamellar x-ray reflection peak. The NTB helical pitch is pTB ~ 14 nm. When an electric field is applied normal to the helix axis, a weak electroclinic effect is observed, revealing 50 um-scale left- a…
Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）；Institute of Chemistry, Military University of Technology（军事科技大学化学研究所）；Faculty of Chemistry, Jagiellonian University（雅盖隆大学化学学院）；Research Center for Thermal and Entropic Science, Graduate School of Science, Osaka University（大阪大学理学研究科热力学与熵科学研究中心）
Using the classical density functional theory of freezing and Monte Carlo computer simulations, we explore the liquid-crystalline phase behavior of hard rectangles on flat and cylindrical manifolds. Moreover, we study the effect of a static external field which couples to the rectangles' orientations, aligning them towards a preferred direction. In the flat and field-free case, the bulk phase diagram involves stable isotropic, nematic, tetratic, and smectic phases depending on the aspect ratio and number density of the particles. The external field shifts the transition lines significantly and…
Competing crystallization pathways and cold crystallization kinetics in 10OS5 liquid crystal
Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）；Faculty of Science, University of Siedlce（谢德尔采大学理学院）；Research Center for Thermal and Entropic Science, Graduate School of Science, Osaka University（大阪大学理学研究科热与熵科学研究中心）
We report Monte-Carlo simulation studies of some systems consisting of polar rod-like molecules interacting via a pair potential that exhibit liquid crystal phases, attributed with tilt angles of large magnitude. For theoretical understanding of the microscopic origin of the tilted phases, different systems consisting of prolate ellipsoidal molecules of three different lengths, embedded with two symmetrically placed anti-parallel terminal dipoles are considered. We find that the presence of a stable tilted phase crucially depends on the molecular elongation which effectively makes dipolar sepa…
In search for novel nematic materials, a laterally linked H-shaped liquid crystal dimer have been synthesized and characterized. The distinct feature of the material is a very broad temperature range (about 50 oC) of the nematic phase, which is in contrast with other reported H-dimers that show predominantly smectic phases. The material exhibits interesting textural features at the scale of nanometers (presence of smectic clusters) and at the macroscopic scales. Namely, at a certain temperature, the flat samples of the material show occurrence of domain walls. These domain walls are caused by …
The nanostructure of two novel sulfur containing dimer materials has been investigated experimentally by hard and by resonant tender X-ray scattering techniques. On cooling the dimers through the nematic to twist-bend nematic (N-NTB) phase transition, the correlation length associated with short-range positional order drops, while the heliconical orientational order becomes more correlated. The heliconical pitch shows a stronger temperature dependence near the N-NTB transition than observed in previously studied dimers, such as the CBnCB series of compounds. We explain both this strong variati…
An axial next-nearest-neighbor XY model is studied as a model of chiral liquid crystals which exhibit many ferro-, ferri- and antiferroelectric tilted smectic phases. Depending on the values of interaction parameters, this model exhibits Ising symmetric (i.e., the tilt directions of directors are parallel or anti parallel) phases or XY symmetric phases. Phases with each type-of-symmetry show the character of devil's staircase, which has been observed in experiments.
Total Internal Reflection (TIR) is used to probe the molecular organization at the surface of a tilted chiral smectic liquid crystal at temperatures in the vicinity of the bulk antiferroelectric-ferroelectric phase transition. Data are interpreted using an exact analytical solution of a real model for ferroelectric order at the surface. In the mixture T3, ferroelectric surface order is expelled with the bulk ferroelectric-antiferroelectric transition. The conditions for ferroelectric order at the surface of an antiferroelectric bulk are presented.
Since the discovery of graphene oxide (GO), the most accessible of the precursors of graphene, this material has been widely studied for applications in science and technology. In this work, we describe a procedure to obtain GO dispersions in water at high concentrations, these highly dehydrated dispersions being in addition fully redispersible by dilution. With the availability of such concentrated samples, it was possible to investigate the structure of hydrated GO sheets in a previously unexplored range of concentrations, and to evidence a structural phase transition. Tentatively applying m…
