Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as `unphysical' singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the `micro-physics' to obtain thermodynamically consistent, well-set models, that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.
The theory of nematic-smectic phase transition in the system of uniform semi-flexible chains with hard-core repulsion is presented. Both the general density-functional formalism the tube-model calculation show that the flexibility of the chains results in a strong first-order transition, in contrast to the common weak-cristallization scenario of the nematic-smectic transition in rigid rods. The calculated spinodal volume fraction of the uniform nematic phase and the period of the modulation instability are consistent with recent experimental results.
We propose a Landau-de Gennes phenomenological model to describe the pressure induced smectic A-nematic phase transition. The pressure induced smectic A phase transitions are discussed for varying coupling between orientational and translational order parameter. Increasing the pressure, the first order nematic-smectic A transition becomes second order at a tricritical point which agrees fairly with available experimental results.
Optical birefringence measurements on a rod-like liquid crystal (8OCB), imbibed in silica channels (7 nm diameter), are presented and compared to the thermotropic bulk behavior. The orientational and positional order of the confined liquid evolves continuously at the paranematic-to-nematic and sizeably broadened at the nematic-to-smectic order transition, resp., in contrast to the discontinuous and well-defined second-order character of the bulk transitions. A Landau-de-Gennes analysis reveals identical strengths of the nematic and smectic ordering fields (imposed by the walls) and indicates t…
We have studied the effects of quenched random disorder created by dispersed aerosil nanoparticle gels on the nematic to smectic-A (N-SmA) and smectic-A to reentrant nematic (SmA- RN) phase transitions of thermotropic liquid crystal mixtures of 6OCB (hexyloxycyanobiphenyl) and 8OCB (octyloxycyanobiphenyl). These effects are probed using high-resolution synchrotron x-ray diffraction techniques. We find that the reentrant characteristics of the system are largely unchanged by the presence of the aerosil gel network. By comparing measurements of the smectic static structure amplitude for this 8OC…
Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a smooth behavior of the solutions at "infinity" a boundary energy functional was derived by linearizing the Landau energy around its equilibrium solutions. We find that the intrinsic wave number of the smectic structure, which plays the role of a coupling between nematic and smectic order, strongly influences the director reorientation. Whereas the smectic order …
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$180 A) is mesosc…
Many bent-core nematic liquid crystals exhibit unusual physical properties due to the presence of smectic clusters, known as "cybotactic" clusters in the nematic phase. Effect of these clusters on complex shear modulus ($G^*(ω)$) of such liquid crystals hitherto unexplored. Here, we study flow viscosities and complex shear modulus of two asymmetric bent-core liquid crystals using microrheology technique. The results are corroborated with the measurements of curvature elastic constants. Compound with shorter hydrocarbon chain (8OCH$_\text{3}$) exhibit only nematic (N) phase whereas the compound…
Phase behaviours of liquid crystals under external fields, conjugate to the nematic order and smectic order, are studied within the framework of mean field approximation developed by McMillan. It is found that phase diagrams, of temperature vs interaction parameter of smectic A order, show several topologically different types caused by the external fields. The influences of the field conjugate to the smectic A phase, which is fictitious field, are precisely discussed.
We study transformations of self-organized defect arrays at the nematic-smectic A liquid crystal phase transition, and show that these defect configurations are correlated, or "remembered", across the phase transition. A thin film of thermotropic liquid crystal is subjected to hybrid anchoring by an air interface and a water substrate, and viewed under polarized optical microscopy. Upon heating from smectic-A to nematic, a packing of focal conic domains melts into a dense array of boojums---nematic surface defects---which then coarsens by pair-annihilation. With the aid of Landau-de Gennes num…
A high-resolution calorimetric study has been carried out on nano-colloidal dispersions of aerosils in the liquid crystal 4-\textit{n}-pentylphenylthiol-4'-\textit{n}-octyloxybenzoate ($\bar{8}$S5) as a function of aerosil concentration and temperature spanning the smectic-\textit{C} to nematic phases. Over this temperature range, this liquid crystal possesses two continuous XY phase transitions: a fluctuation dominated nematic to smectic-\textit{A} transition with $α\approx α_{XY} = -0.013$ and a mean-field smectic-\textit{A} to smectic-\textit{C} transition. The effective critical character …
McMillan liquid crystal model sandwiched between strong homeotropic anchoring walls is studied. Phase transitions between isotropic, nematic, and smectic A phases are investigated for wide ranges of an interaction parameter and of the system thickness. It is confirmed that the anchoring walls induce an increase in transition temperatures, dissappearance of phase transitions, and an appearance of non-spontaneous nematic phase. The similarity between influence of anchoring walls and that of external fields is discussed.
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…
Modeling and simulation studies using a high-order Landau-de Gennes type model for the direct isotropic/smectic-A liquid crystal transition are presented showing the existence of meta-stable nematic pre-ordering under certain conditions, in agreement with experimental observations (Tokita, M. et al. Macromolecules 2006, 39, 2021-2023)
Thermotropic biaxial nematic phases seem to be rare, but biaxial smectic A phases less so. Here we use molecular field theory to study a simple two-parameter model, with one parameter promoting a biaxial phase and the second promoting smecticity. The theory combines the biaxial Maier-Saupe and McMillan models. We use alternatively the Sonnet-Virga-Durand (SVD) and geometric mean approximations (GMA) to characterize molecular biaxiality by a single parameter. For non-zero smecticity and biaxiality, the model always predicts a ground state biaxial smectic A phase. For a low degree of smectic ord…
The effects of dispersed aerosil nanoparticles on two of the phase transitions of the thermotropic liquid crystal material 4-n-pentylphenylthiol-4'-n-octyloxybenzoate 8barS5 have been studied using high-resolution x-ray diffraction techniques. The aerosils hydrogen bond together to form a gel which imposes a weak quenched disorder on the liquid crystal. The smectic-A fluctuations are well characterized by a two-component line shape representing thermal and random-field contributions. An elaboration on this line shape is required to describe the fluctuations in the smectic-C phase; specifically…
Recent experiments on mixed liquid crystals have highlighted the hugely significant role of ferromagnetic nanoparticle impurities in defining the nematic-smectic-A phase transition point. Structured around a Flory-Huggins free energy of isotropic mixing and Landau-de Gennes free energy, this article presents a phenomenological mean-field model that quantifies the role of such impurities in analyzing thermodynamic phases, in a mixture of thermotropic smectic liquid crystal and ferromagnetic nanoparticles. First we discuss the impact of ferromagnetic nanoparticles on the isotropic-ferronematic a…
We study a model for the Nematic--Smectic-A (NA) transition in aerogel, and find that even arbitrarily weak quenched disorder (i.e., low aerogel density) destroys translational (smectic) order. Ignoring elastic anharmonicities, but keeping anharmonic couplings to disorder, leads to the prediction that there is no ``Bragg glass'' phase in this system: it is riddled with dislocation loops induced by the quenched disorder. Orientational (nematic) order is destroyed as well, as is the thermodynamically sharp NA transition, in agreement with recent experimental results.
Since a rigorous microscopic treatment of a nematic fluid system based on a pairwise interaction potential is immensely complex we had introduced a simple mean field potential which was a modification of the Maier-Saupe potential in a previous paper. Building up on that here we have modified that potential to take into account the various aspects of a smectic A-nematic phase transition. In particular we have studied the dependence of the phase transition on the coupling coefficient between the nematic and smectic order parameters which in turn depends on the length of alkyl chain, existence of…
We have conducted two quantitative tests of predictions based on the Halperin-Lubensky-Ma (HLM) theory of fluctuation-induced first-order phase transitions. First, we explore the effect of an external magnetic field on the nematic-smectic-A (NA) transition in a liquid crystal. Second, we examine the dependence of the first-order discontinuity as a function of mixture concentration in pure 8CB and three 8CB-10CB mixtures. We find the first quantitative evidence for deviations from the HLM theory.
Recent experiments on vesicles formed from block copolymers with liquid-crystalline side-chains reveal a rich variety of vesicle morphologies. The additional internal order ("structure") developed by these self-assembled block copolymer vesicles can lead to significantly deformed vesicles as a result of the delicate interplay between two-dimensional ordering and vesicle shape. The inevitable topological defects in structured vesicles of spherical topology also play an essential role in controlling the final vesicle morphology. Here we develop a minimal theoretical model for the morphology of t…
We study theoretically the effect of an external field on the nematic-smectic-A (NA) transition close to the tricritical point, where fluctuation effects govern the qualitative behavior of the transition. An external field suppresses nematic director fluctuations, by making them massive. For a fluctuation-driven first-order transition, we show that an external field can drive the transition second-order. In an appropriate liquid crystal system, we predict the required magnetic field to be of order 10 T. The equivalent electric field is of order $1 V/μm$.
We study anomalous elasticity in the tubule phases of nematic and smectic elastomer membranes, which are flat in one direction and crumpled in another. These phases share the same macroscopic symmetry properties including spontaneously-broken in-plane isotropy and hence belong to the same universality class. Below an upper critical value $D_c =3$ of the membranes' intrinsic dimension D, thermal fluctuations renormalize the elasticity with respect to elastic displacements along the tubule axis so that elastic moduli for compression along the tubule axis and for bending the tubule axis become le…
We discuss theoretically, using density-functional theory, the phase stability of nematic and smectic ordering in a suspension of platelets of the same thickness but with a high polydispersity in diameter, and study the influence of polydispersity on this stability. The platelets are assumed to interact like hard objects, but additional soft attractive and repulsive interactions, meant to represent the effect of depletion interactions are also considered. The aspect (diameter to thickness) ratio is taken to be very high, in order to model solutions of mineral platelets recently explored experi…
Particle tracking passive microrheology in 8CB liquid crystals is used to redefine the precessional motion of the orientation of nematic director in liquid crystals. Physical origin of tumbling director in presence of presmectic clusters under zero shear conditions is discussed. Different structural properties (pure nematic phase, presmectic(smectic C and smectic A clusters)) were differentiated with characteristic dependence of $G'$ on $ω$ in the nematic phase of 8CB liquid crystals. Also, dynamic viscosity is observed with a cross over between parallel and perpendicular components as the sme…
The surface phase behavior of binary mixtures of colloidal hard rods in contact with a solid substrate (hard wall) is studied, with special emphasis on the region of the phase diagram that includes the smectic A phase. The colloidal rods are modelled as hard cylinders of the same diameter and different lengths, in the approximation of perfect alignment. A fundamental--measure density functional is used to obtain equilibrium density profiles and thermodynamic properties such as surface tensions and adsorption coefficients. The bulk phase diagram exhibits nematic-smectic and smectic-smectic demi…
The effect of cylindrical confinement on the phase behaviour of a system of parallel hard rods is studied using Onsager's second virial theory. The hard rods are represented as hard cylinders of diameter $D$ and length $L$, while the cylindrical pore is infinite with diameter $W$. The interaction between the wall and the rods is hard repulsive, and it is assumed that molecules are parallel to the surface of the pore (planar anchoring). In very narrow pores ($D<W<2 D$), the structure is homogeneous and the system behaves as a one-dimensional Tonks gas. For wider pores, inhomogeneous fluid struc…
The McMillan liquid crystalline models under the influence of homeotropic anchoring walls and of external fields are investigated. For thin systems, the existence of the critical thickness, below which the system does not undergo a discrete phase transition, is confirmed. Apparent differences between the influence of the anchoring walls and of external fields are elucidated by investigating the order parameters and a temperature vs external field phase diagram for the bulk systems.
We study the stability of inhomogeneous liquid crystalline states in systems of monodisperse, stiff, charged rods. By means of a bifurcation analysis applied to the Onsager free energy for charged rods in strongly nematic states, we investigate nematic-smectic and nematic-columnar instabilities as a function of the Debye screening length. While the nematic-smectic transition clearly pre-emts the nematic-columnar one in the regime of strong screening a marked stability of hexagonal columnar order is observed at larger screening lengths. The theoretical results are substantiated by Brownian dyna…
A Landau-de Gennes model that integrates the nematic quadrupolar tensor order parameter and complex smectic-A order parameters is used to simulate the two-dimensional growth of an initially homogeneous smectic-A spherulite in an isotropic matrix. These simulations are performed in the shape-dynamic (nano-scale) regime of growth under two material conditions: isotropic nematic elasticity and equal splay-bend nematic elasticity. A comparison of the growth kinetics, spherulite morphology, interfacial/bulk energy landscapes between both cases is made showing that equal nematic splay-bend elasticit…
We elucidate the roles of the isotropic-nematic (I-N) and nematic-smectic A (N-SmA) transitions in magnetic field directed self-assembly of a liquid crystalline block copolymer (BCP), using \textit{in situ} x-ray scattering. Cooling into the nematic from the disordered melt yields poorly ordered and weakly aligned BCP microdomains. Continued cooling into the SmA however results in an abrupt increase in BCP orientational order with microdomain alignment tightly coupled to the translational order parameter of the smectic layers. These results underscore the significance of the N-SmA transition i…
We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 μm-thick samples, and in the planar configuration (director parallel to the plane of the sample). The nematic - smectic B interface presents a facet in one direction -- the direction parallel to the smectic layers -- and is otherwise rough, and devoid of forbidden directions. We measure the Mullins-Sekerka instability threshold and establish the morphology diagram of the system as a function of the solidification rate V a…
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 report a computer simulation study of an electroneutral mixture of oppositely charged oblate ellipsoids of revolution with aspect ratio A = 1/3. In contrast to hard or soft repulsive ellipsoids, which are purely nematic, this system exhibits a smectic-A phase in which charges of equal sign are counterintuitively packed in layers perpendicular to the nematic director.
We report a high-resolution x-ray scattering study of the smectic liquid crystal octylcyanobiphenyl (8CB) confined to aligned colloidal aerosil gels. The aligned gels introduce orientational fields that promote long-range nematic order while imposing positional random fields that couple to the smectic density wave and disrupt the formation of an ordered smectic phase. At low densities of aerosil, the low-temperature scattering intensity is consistent with the presence of a topologically ordered XY Bragg glass phase that is predicted to form in response to such anisotropic quenched disorder. Th…
We study experimentally the nonequilibrium phase behaviour of a horizontal monolayer of macroscopic rods. The motion of the rods in two dimensions is driven by vibrations in the vertical direction. Aside from the control variables of packing fraction and aspect ratio that are typically explored in molecular liquid crystalline systems, due to the macroscopic size of the particles we are also able to investigate the effect of the precise shape of the particle on the steady states of this driven system. We find that the shape plays an important role in determining the nature of the orientational …
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.
Understanding the relaxation dynamics of colloidal suspensions is crucial to identify the elements that influence the mobility of their constituents, assess their macroscopic response across the relevant time and length scales, and thus disclose the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft-repulsive rod-like particles, which are able to self-organise into nematic and smectic liquid-crystalline phases. By performing Dynamic Monte Carlo simulat…
We report the smectic $A_F$, a new liquid crystal phase of the ferroelectric nematic realm. The smectic $A_F$ is a phase of small polar, rod-shaped molecules which form two-dimensional fluid layers spaced by approximately the mean molecular length. The phase is uniaxial, with the molecular director, the local average long-axis orientation, normal to the layer planes, and ferroelectric, with a spontaneous electric polarization parallel to the director. Polarization measurements indicate almost complete polar ordering of the $\sim 10$ Debye longitudinal molecular dipoles, and hysteretic polariza…
We have calculated the phase diagrams of one--component fluids made of five types of biaxial particles differing in their cross sections. The orientation of the principal particle axis is fixed in space, while the second axis is allowed to freely rotate. We have constructed a free-energy density functional based on fundamental--measure theory to study the relative stability of nematic and smectic phases with uniaxial, biaxial and tetratic symmetries. Minimization of the density functional allows us to study the phase behavior of the biaxial particles as a function of the cross-section geometry…
The continuous nematic to smectic-A (N-SmA) phase transition has been studied by high-resolution ac-calorimetry in binary mixtures of the liquid crystal octylcyanobiphenyl(8CB) and a non-mesogenic, low-molecular weight, solvent n-hexane(hex) as a function of temperature and solvent concentration. Heating and cooling scans about the N-SmA transition temperature were repeatedly performed on pure and six 8CB+hex samples having hexane molar concentration ranging from x_{hex}= 0.02 to 0.12. All 8CB+hex samples in this range of x_{hex} remain macroscopically miscible and exhibit an N-SmA heat capaci…
We investigated the nematic to smectic transition undergone by parallel hard spherocylinders in the framework provided by the residual multi-particle entropy (RMPE) formalism. The RMPE is defined as the sum of all contributions to the configurational entropy of the fluid which arise from density correlations involving more than two particles. The vanishing of the RMPE signals the structural changes which take place in the system for increasing pressures. Monte Carlo simulations carried out for parallel hard spherocylinders show that such a one-phase ordering criterion accurately predicts also …
We report the nematic and smectic ordering in a new aqueous suspension of monolayer $α$-Zirconium phosphate platelets possessing a high polydispersity in diameter but uniform thickness. We observe an isotropic--nematic transition as the platelet volume fraction increases, followed by the formation of a smectic, an elusive phase that has been rarely seen in discotic liquid crystals. The smectic phase is characterized by X-ray diffraction, high-resolution transmission electron microscopy, and optical microscopy. The phase equilibria in this highly polydisperse suspension is rationalized in terms…
Chiral rodlike colloids exposed to strong depletion attraction may self-assemble into chiral membranes whose twisted director field differs from that of a 3D bulk chiral nematic. We formulate a simple microscopic variational theory to determine the elastic moduli of rods assembled into a bi-dimensional smectic membrane. The approach is based on a simple Onsager-Straley theory for a non-uniform director field that we apply to describe rod twist within the membrane. A microscopic approach enables a detailed estimate of the individual Frank elastic moduli (splay, twist and bend) as well as the tw…
We study the layer-to-layer diffusion in smectic-A liquid crystals of colloidal hard rods with different length-to-diameter ratios using computer simulations. The layered arrangement of the smectic phase yields a hopping-type diffusion due to the presence of permanent barriers and transient cages. Remarkably, we detect stringlike clusters composed of inter-layer rods moving cooperatively along the nematic director. Furthermore, we find that the structural relaxation in equilibrium smectic phases shows interesting similarities with that of out-of-equilibrium supercooled liquids, although there …
We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter $3.0\leq x_0\leq 4.0$ in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows s…
Liquid crystals (LCs) composed of mesogens play important roles in various scientific and engineering problems. How a system with many mesogens can enter a LC state is an interesting and important problem. Using stiff and free-joint Lennard-Jones chain molecules as mesogens, we study the conditions under which the mesogens can enter various LC phases. The guideline is to eliminate the unwanted translational orders under a controlled fine-tuning procedure across a sequence of systems. Instead of monitoring the growth of order out of the disorder, we prepare a configuration of high orientation o…
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 non-convex 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 …
We have numerically studied a liquid composed of achiral, bent-shaped molecules built of tangent spheres. The system is known to spontaneously break mirror symmetry, as it forms a macroscopically chiral, twist-bend nematic phase [Phys. Rev. Lett. 115, 147801 (2015)]. Here, we have examined the full phase diagram of such liquid and observed several phases characterized by orientational and/or translational ordering of molecules. Apart from conventional nematic, smectic A, and the above-mentioned twist-bend nematic phase, we have identified antiferroelectric smectic A phase. For large densities …
An extension to a high-order model for the direct isotropic/smectic-A liquid crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase-ordering. Multi-scale multi-transport simulations of the non-isothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth, under shallow quench/undercooling conditions. Non-isothermal simulations, where meta-stable nematic pre-ordering preced…
We present an experimental study of the surface effects (interactions with the container walls) during the nucleation and growth of smectic B crystals from the nematic in free growth and directional solidification of a mesogenic molecule ($C_4H_9-(C_6H_{10})_2CN$) called CCH4 in thin (of thickness in the 10 $μ$m range) samples. We follow the dynamics of the system in real time with a polarizing microscope. The inner surfaces of the glass-plate samples are coated with polymeric films, either rubbed polyimid (PI) films or monooriented poly(tetrafluoroethylene) (PTFE) films deposited by friction …
