We investigate by means of continuum percolation theory and Monte Carlo simulations how spontaneous uniaxial symmetry breaking affects geometric percolation in dispersions of hard rod-like particles. If the particle aspect ratio exceeds about twenty, percolation in the nematic phase can be lost upon adding particles to the dispersion. This contrasts with percolation in the isotropic phase, where a minimum particle loading is always required to obtain system-spanning clusters. For sufficiently short rods, percolation in the uniaxial nematic mimics that of the isotropic phase, where the addition of particles always aids percolation. For aspect ratios between twenty and infinity, but not including infinity, we find re-entrance behavior: percolation in the low-density nematic may be lost upon increasing the amount of nanofillers but can be re-gained by the addition of even more particles to the suspension. Our simulation results for aspect ratios of 5, 10, 20, 50 and 100 strongly support our theoretical predictions, with almost quantitative agreement. We show that a new closure of the connectedness Ornstein-Zernike equation, inspired by Scaled Particle Theory, is more accurate than the Lee-Parsons closure that effectively describes the impact of many-body direct contacts.
We report the elaboration of a hybrid mesophase combining the lamellar order of a lyotropic system of nonionic surfactant and the nematic order of a concentrated solution of inorganic nanorods confined between the surfactant layers. Highly aligned samples of this mesophase can be obtained by thermal annealing, and the orientation of the nanorods is readily controlled with a magnetic field. High-resolution synchrotron X-ray scattering and polarized optical microscopy show that, compared to their isolated counterparts, both the nematic and lamellar orders are altered, demonstrating their interpl…
We study DC and AC electrophoresis of silica micro and nanorods in a thin film of a nematic liquid crystal. These particles induce virtual topological defects and also demonstrate nontrivial electrophoresis in a nematic liquid crystal. We measure several nonlinear electrophoretic mobility coefficients and compare with those calculated theoretically. We demonstrate a competing effect of the elastic and electrostatic torques that arises due to tilting of the rods with respect to the liquid crystal director. A basic theory describing this effect allows us to measure the effective polarizability o…
We study the role of the control parameter triggering nematic order (temperature or concentration) on the dynamical behavior of a system of nanorods under shear. Our study is based on a set of mesoscopic equations of motion for the components of the tensorial orientational order parameter. We investigating these equations via a systematic bifurcation analysis based on a numerical continuation technique, focusing on spatially homogeneous states. Exploring a wide range of parameters we find, unexpectedly, that states with oscillatory motion can exist even under conditions where the equilibrium s…
We report a hybrid mesophase consisting of magnetic nanorods confined between the non-ionic surfactant bilayers of a lamellar phase. The magnetic field-induced ordering of the nanorods was measured experimentally and modeled by a two-dimensional Onsager theory including the third virial coefficient. The nanorods are strongly confined in layers, with no orientational coupling from one layer to the next. At high volume concentration they exhibit spontaneous in-plane orientational ordering and form a stack of independent two-dimensional nematic systems. This isotropic-nematic transition is first-…
We explore the nematic order of model goethite nanorods in an external magnetic field within Onsager-Parsons density functional theory. The goethite rods are represented by monodisperse, charged spherocylinders with a permanent magnetic moment along the rod main axis, forcing the particles to align parallel to the magnetic field at low field strength. The intrinsic diamagnetic susceptibility anisometry of the rods is negative which leads to a preferred perpendicular orientation at higher field strength. It is shown that these counteracting effects may give rise to intricate phase behavior, inc…
Using Landau theory, it is shown that eight phenomenological parameters are needed to describe and distinguish the twelve viscosity coefficients of a biaxial nematic phase, or the five viscosity coefficients of a uniaxial nematic phase. The dependence of the coefficients on the macroscopic uniaxial and biaxial order parameters is established. Since these order parameters are determined by the anisotropies of the dielectric constant, we show that it should be possible to determine values for all eight of the phenomenological parameters of the theory from measurements of the temperature dependen…
In nematic liquid crystals (NLCs), topological defects of a chiral origin play a role in phase transitions and lead to phase configurations of nontrivial topology, like those in neutron stars and helium in the A-phase. In the biaxial-uniaxial phase transition, the deformation of the orbit, as the order parameter degeneracy of the NLC, connects together an evolution of topological defects, the surface anchoring energy and elastic Frank modui. In this work we estimate the chiral gauge field presentation of the constrained Ladnau-de Gennes theory of the biaxial nematics, which have to explain the…
Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame, that can be extracted from the tensorial description of the nematic order, vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. New defects and degrees of freedom are unveiled and th…
We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of …
Field-induced reorientation of colloidal particles is especially relevant to manipulate the optical properties of a nanomaterial for target applications. We have recently shown that surprisingly feeble external stimuli are able to transform uniaxial nematic liquid crystals (LCs) of cuboidal particles into biaxial nematic LCs. In the light of these results, here we apply an external field that forces the reorientation of colloidal cuboids in nematic LCs and sparks a uniaxial-to-biaxial texture switching. By Dynamic Monte Carlo simulation, we investigate the unsteady-state reorientation dynamics…
Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation for the single-particle non-homogeneous distribution function of particle orientations and the evolution equations for the second and fourth order orientational tensor parameters. Afterwards, two dynamic closure approximations are discussed, one of them considering the relaxation of the fourth order orientational parameter and leading to a novel expression f…
Lyotropic liquid crystalline quaternary mixtures of potassium laurate (KL), potassium sulphate (K2SO4)/alcohol (n-OH)/water, with the alcohols having different number of carbon atoms in the alkyl chain (n), from 1 octanol to 1-hexadecanol, were investigated by optical techniques (optical microscopy and laser conoscopy). The biaxial nematic phase domain is present in a window of values of n = nKL \pm 2, where nKL = 11 is the number of carbon atoms in the alkyl chain of KL. The biaxial phase domain got smaller and the uniaxial-to-biaxial phase transition temperatures shifted to the relatively hi…
Based on Monte Carlo (MC) computer simulations we study the structure formation of a system of magnetic nanorods. Our model particles consist of fused spheres with permanent magnetic dipole moments, as inspired by recent experiments. The resulting system behaves significantly different from a system of hard (non-magnetic) rods or magnetic rods with a single longitudinal dipole. In particular, we observe for the magnetic nanorods a significant decrease of the percolation threshold (as compared to non-magnetic rods) at low densities, and a stabilization of the high-density nematic phase. Moreove…
Influence of an external magnetic field on the nematic-isotropic ($N-I$) phase transition in a dispersion model of nematic liquid crystals, where the molecules are either perfectly uniaxial or biaxial (board-like), has been studied by Monte Carlo simulation. Using multiple histogram reweighting technique and finite size scaling analysis the order of the phase transition, the transition temperature at the thermodynamic limit and the stability limit of the isotropic phase below the transition temperature for different magnetic field strengths have been determined. The magnetic field dependence o…
Monodisperse rod-like colloidal particles are known for spontaneously forming both nematic and smectic liquid crystal phases, but their self-assembly was typically exploited from the fundamental soft condensed matter physics perspective. Here we demonstrate that depletion interactions, driven by non-adsorbing polymers like dextran and surfactants, can be used to enrich self-organization of photon-upconversion nanorods into orientationally ordered nematic and smectic-like membrane colloidal superstructures. We study thermodynamic phase diagrams and demonstrate polarization-dependent photon upco…
The article presents a straightforward experiment that directly and illustratively demonstrates double refraction. For this purpose, two liquid crystalline cells were designed, which enable qualitative and quantitative measurements of the extraordinary refractive index direction dependency in a uniaxial nematic liquid crystal.
Different liquid crystalline phases with long-range orientational but not positional order, so-called nematic phases, are scarce. It rarely occurs that a new nematic phase is discovered and such event is inevitably accompanied by a great interest. Here, we describe a transition from uniaxial to novel nematic phase characterized by a periodic splay modulation of the director. In this new nematic phase, defect structures not present in the uniaxial nematic are observed, which indicates that the new phase has lower symmetry than the ordinary nematic phase. The phase transition is weakly first ord…
Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. For an arbitrary form of the bulk energy density, we show that energy minimizers among uniaxially symmetric configurations are usually not equilibrium configurations. It was known before that uniaxiality can sometimes be broken by energy minimizers. We prove here that this is always the case in one or two dimensions. Even more we prove that equilibrium configurations (not only minimizers) cannot be uniaxial in one or two dimensions (unless they are constant). Nam…
We present a numerical study on geometric percolation in liquid dispersions of hard slender colloidal particles subjected to an external orienting field. In the formulation and liquid-state processing of nanocomposite materials, the alignment of particles by external fields such as electric, magnetic or flow fields is practically inevitable, and often works against the emergence of large nanoparticle networks. Using continuum percolation theory in conjunction with Onsager theory, we investigate how the interplay between externally induced alignment and the spontaneous symmetry breaking of the …
Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. We show that the uniaxial symmetry constraint is very restrictive and can in general not be satisfied, except in very symmetric situations. For one- and two-dimensional configurations, we characterize completely the uniaxial equilibria: they must have constant director. In the three dimensional case we focus on the model problem of a spherical droplet with radial anchoring, and show that any uniaxial equilibrium must be spherically symmetric. It was known before …
We theoretically study the phase behaviour of monolayers of hard rod-plate mixtures using a fundamental-measure density functional in the restricted-orientation (Zwanzig) approximation. We consider both species to be subject to an attractive potential proportional to the particle contact area on the surface and with adsorption strengths that depend on the species type. Particles have board-like shape, with sizes chosen using a symmetry criterion: same volume and same aspect ratio $κ$. Phase diagrams were calculated for $κ=10$, 20 and 40 and different values of adsorption strengths. For small a…
Using x-ray photon correlation spectroscopy, we studied the dynamics in the nematic phase of a nanorodsuspension. The collective diffusion coefficient in the plane perpendicular to the director varies sharply with the wave vector. Combining the structure factor and the diffusion coefficient, we find that the hydrodynamic function of the phase decreases by more than a factor of 10 when going from length scales comparable to the interparticle distance toward larger values. Thus, the collective dynamics of the nematic phase experiences strong and scale-dependent slowing down, in contrast with iso…
We study in detail the influence of molecular interactions on the Frank elastic constants of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. A brief summary of the status of theoretical development for the elastic constants of nematics is presented. Considering a pair potential having both repulsive and attractive parts numerical calculations are reported for three systems MBBA, PAA and 8OCB. For these systems the length-to-width ratio ${x_0}$ is estimated from the experimentally proposed structure of the molecules. The repulsive interaction is represented by a …
How change in molecular structure can affect relative stability and structural properties of the twist-bend nematic phase (N$_\text{TB}$)? Here we extend the mean-field model [C. Greco et al., Soft Matter, 2014, 10, 9318] for bent-shaped achiral molecules, to study the influence of arm molecular biaxiality and the value of molecule's bend angle on relative stability of N$_\text{TB}$. In particular we show that by controlling biaxiality of molecule's arms up to four ordered phases can become stable. They involve locally uniaxial and biaxial variants of N$_\text{TB}$, together with the uniaxial …
A promising approach of designing mesostructured materials with novel physical behavior is to combine unique optical and electronic properties of solid nanoparticles with long-range ordering and facile response of soft matter to weak external stimuli. Here we design, practically realize, and characterize orientationally ordered nematic liquid crystalline dispersions of rod-like upconversion nanoparticles. Boundary conditions on particle surfaces, defined through surface functionalization, promote spontaneous unidirectional self-alignment of the dispersed rod-like nanoparticles, mechanically co…
The phase ordering kinetics of the two-dimensional uniaxial nematic has been studied using a Cell Dynamic Scheme. The system after quench from T=infinity was found to scale dynamically with an asymptotic growth law similar to that of two-dimensional O(2) model (quenched from above the Kosterlitz - Thouless transition temperature), i.e. L(t) ~ t/ln(t/t0 ^{1/2} (with nonuniversal time scale t0). We obtained the true asymptotic limit of the growth law by performing our simulation for sufficiently long time. The presence of topologically stable 1/2-disclination points is reflected in the observed …
We study the effect of fluctuations in opening angle of bent-core molecules on stability of the nematic phases. The molecules are built out of two Gay-Berne centers of $κ= 4$, $κ' = 5$, $μ= 1$ and $ν= 2$, each corresponding to one of the molecular arms. Constant-pressure Monte Carlo (MC NPT) simulations are carried out for two versions of the model, with fixed- and fluctuating opening angle, where fluctuations are taken harmonic about the angle of 140o. The systems studied are first cooled down from the isotropic liquid to a highly ordered crystalline smectic phase and then heated up all the w…
We perform optical, surface anchoring, and textural studies of an organo-siloxane tetrapode material in the broad temperature range of the nematic phase. The optical, structural, and topological features are compatible with the uniaxial nematic order rather than with the biaxial nematic order, in the entire nematic temperature range -25C < T < 46C studied. For homeotropic alignment, the material experiences surface anchoring transition, but the director can be realigned into an optically uniaxial texture by applying a sufficiently strong electric field. The topological features of textures in …
The improved expansion in width is applied to curved domain walls in uniaxial nematic liquid crystals in external magnetic field. In the present paper we concentrate on the case of equal elastic constants. We obtain approximate form of the director field up to second order in magnetic coherence length.
Wrinkles commonly develop in a thin film deposited on a soft elastomer substrate when the film is subject to compression. Motivated by recent experiments [Agrawal et al., Soft Matter 8, 7138 (2012)] that show how wrinkle morphology can be controlled by using a nematic elastomer substrate, we develop the theory of small-amplitude wrinkles of an isotropic film atop a nematic elastomer. The directors of the nematic elastomer are assumed to lie in a plane parallel to the plane of the undeformed film. For uniaxial compression of the film along the direction perpendicular to the elastomer directors,…
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…
Nematic states are characterized by rotational symmetry breaking without translational ordering. Recently, nematic superconductivity, in which the superconducting gap spontaneously lifts the rotational symmetry of the lattice, has been discovered. However the pairing mechanism and the mechanism determining the nematic orientation remain unresolved. A first step is to demonstrate control of the nematicity, through application of an external symmetry-breaking field, to determine the sign and strength of coupling to the lattice. Here, we report for the first time control of the nematic orientatio…
An intermediate nematic phase is proposed for the interpretation of recent experimental results on phase biaxiality in bent-core nematics. The phase is macroscopically uniaxial but consists of microscopic biaxial, and possibly polar, domains. On applying an electric field the phase exhibits substantial macroscopic biaxial ordering resulting from the collective alignment of the domains. A phenomenological theory is developed for the molecular order in this phase and for its transitions to purely uniaxial and to spontaneously biaxial nematic phases.
We construct phase diagrams for charged rodlike colloids within the second-virial approximation as a function of rod concentration, salt concentration, and colloidal charge. Besides the expected isotropic-nematic transition, we also find parameter regimes with a coexistence between a nematic and a second, more highly aligned nematic phase including an isotropic-nematic-nematic triple point and a nematic-nematic critical point, which can all be explained in terms of the twisting effect. We compute the Frank elastic constants to see if the twist elastic constant can become negative, which would …
A new theory of hydrodynamics of uniaxial nematic liquid crystal films in the presence of defects is developed. A gauge field incorporating screening is introduced, resulting in the static elastic free energy having the form of a two-dimensional Abelian-Higgs model. Hydrodynamic equations are derived via the standard methods of de~Groot and Mazur. By working in the vicinity of the Bogomol'nyi equations consequences for defect centre motion are outlined.
Inspired by the observations of a remarkably stable biaxial nematic phase [E.v.d. Pol et al., Phys. Rev. Lett. 103, 258301 (2009)], we investigate the effect of size polydispersity on the phase behavior of a suspension of boardlike particles. By means of Onsager theory within the restricted orientation (Zwanzig) model we show that polydispersity induces a novel topology in the phase diagram, with two Landau tetracritical points in between which oblate uniaxial nematic order is favored over the expected prolate order. Additionally, this phenomenon causes the opening of a huge stable biaxiality …
The effect of confinement on the phase behaviour and structure of fluids made of biaxial hard particles (cuboids) is examined theoretically by means of Onsager second-order virial theory in the limit where the long particle axes are frozen in a mutually parallel configuration. Confinement is induced by two parallel planar hard walls (slit-pore geometry), with particle long axes perpendicular to the walls (perfect homeotropic anchoring). In bulk, a continuous nematic-to-smectic transition takes place, while shape anisotropy in the (rectangular) particle cross section induces biaxial ordering. A…
The dipole flexoelectric (FE) polarization in liquid crystals is derived in the thermodynamic limit at small distortions and small density. General microscopic expressions for the FE coefficients are obtained in the case of the uniaxial and biaxial nematic phases composed of C_2v molecules. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. In the case of the biaxial nematic phase, six basic deformations produce FE polarization but there are only five independent FE coefficients.
The paper analyses kinematics and dynamics of internal rotations with spin and their effects on the constitutive relations for uniaxial (nematic) liquids and for weakly elastic nematic solids. It is shown that neglecting the internal rotational inertia terms and effects of director gradient made the stress symmetric. This not only highly simplifies the theories but also allows calculating all the kinematic variables of internal rotations without any additional constants, other than those presented in the simplified theory with symmetric stress.
For many important applications, the performance of polymer-anisotropic particle nanocomposite materials strongly depends on the orientation of the nanoparticles. Using the very peculiar magnetic properties of goethite (α-FeOOH) nanorods, we produced goethite-poly(hydroxyethyl methacrylate) nanocomposites in which the alignment direction and the level of orientation of the nanorods could easily be tuned by simply adjusting the intensity of a magnetic field applied during polymerization. Because the particle volume fraction was kept low (1-5.5 vol \%), we used the orientational order induced by…
We report temperature dependencies of material properties such as dielectric anisotropy, birefringence, splay (K11), twist (K22), and bend (K33) elastic constants of the uniaxial nematic (N) phase formed by flexible dimers of DTC5C9 and compare their behavior to that of a corresponding monomer MCT5. DTC5C9 forms a twist-bend nematic (Ntb) at temperatures below the N phase. Anisotropic properties of MCT5 are typical of the rod-like mesogens. In particular, birefringence increases as the temperature is reduced, following the classic behavior, described by Haller. The elastic constants also follo…
The dielectric dispersion in the uniaxial nematic liquid crystals affects the switching dynamics of the director, as the dielectric torque is determined by not only the present values of the electric field and director but also by their past values. We demonstrate that this dielectric memory leads to an unusual contribution to the dielectric torque that is linear in the present field and thus polarity-sensitive. This torque can be used to accelerate the switch-off phase of director dynamics.
We examine the ordering behavior of hard plate-like particle in a very narrow slit-like pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first order layering transition occurs between uniaxial nematic structures having n and n+1 layers at intermediate densities and even a phase transition between a monolayer with parallel (edge-on) orientational order and n layers with perpendicular one can be detected at high densities. I…
Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces. In this paper we show that any spatially-varying director pattern may be a source of biaxiality. We prove that biaxiality arises naturally whenever the symmetric tensor $\Sb=(\grad \nn)(\grad \nn)^T$ possesses two distinct nonzero eigenvalues. The eigenvalue difference may be used as a meas…
We show by means of continuum theory and simulations that geometric percolation in uniaxial nematics of hard slender particles is fundamentally different from that in isotropic dispersions. In the nematic, percolation depends only very weakly on the density and is, in essence, determined by a distance criterion that defines connectivity. This unexpected finding has its roots in the non-trivial coupling between the density and the degree of orientational order that dictate the mean number of particle contacts. Clusters in the nematic are much longer than wide, suggesting the use of nematics for…
The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries $O(3)$ of isotropic space to a discrete subgroup, i.e. a three-dimensional point group. The subgroups form a rich hierarchy and allow for many different phases of matter with orientational order. Such spontaneous symmetry breaking occurs in nematic liquid crystals and a highlight of such anisotropic liquids are the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point group symmetry, referred to as \emph{generalized n…
We study the quantum-mechanical effects arising in a single semiconductor core/shell quantum dot controllably sandwiched between two plasmonic nanorods. Control over the position and the sandwich confinement structure is achieved by the use of a linear-trap, liquid-crystal line defect and laser tweezers that push the sandwich together. This arrangement allows for the study of exciton plasmon interactions in a single structure, unaltered by ensemble effects or the complexity of dielectric interfaces. We demonstrate the effect of plasmonic confinement on the photon-antibunching behavior of the q…
We present numerical and analytic results for uniaxial and biaxial order at the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory. We study the case where an oblique anchoring condition is imposed asymptotically on the nematic side of the interface, reproducing results of previous work when this condition reduces to planar or homoeotropic anchoring. We construct physically motivated and computationally flexible variational profiles for uniaxial and biaxial order, comparing our variational results to numerical results obtained from a minimization of the Ginzburg-Landau-de Genn…
The understanding of self-organization in the twist-bend nematic $(N_\text{TB})$ phase, identified in 2011 in liquid crystal dimers, is at the forefront of soft matter research worldwide. This new nematic phase develops structural chirality in the isotropic $(I)$ and the uniaxial nematic $(N_\text{U})$ phases, despite the fact that the molecules forming the structure are chemically achiral. Molecular, shape-induced flexopolarization provides a viable mechanism for a qualitative understanding of $N_\text{TB}$ and the related phase transitions. The key question that remains is whether with this …
Nematic twist--bend is the fifth nematic phase recognized in nature. This phase exhibits spiral orientational order, thus it is a chiral structure and it can be stabilized in systems composed of achiral molecules. The microscopic origin of this spontaneous chiral symmetry breaking is to a large extent unknown but phenomenologically it appears stabilized by assuming coupling between steric polar and orientational orderings. Understanding of how external fields affect the stability of this phase is of great intellectual interest and of relevance to potential applications. Within mesoscopic Landa…
We study a class of models for \sbentcore molecules using low density version of Local Density Functional Theory. Arms of the molecules are modeled using two- and three Gay-Berne (GB) interacting units of uniaxial and biaxial symmetry. Dipole-dipole interactions are taken into account by placing a dipole moment along the ${\mathcal{C}}_2$symmetry axis of the molecule. The main aim of the study is to identify molecular factors that can help stabilizing the biaxial nematic phase. The phase diagrams involving isotropic ($I$), uniaxial ($N_U$) and biaxial ($N_B$) nematic phases are determined at g…
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 …
Orientational and positional ordering properties of liquid crystal monolayers are examined by means of Fundamental-Measure Density Functional Theory. Particles forming the monolayer are modeled as hard parallelepipeds of square section of size $σ$ and length $L$. The particle centers of mass are restricted to a flat surface and three possible and mutually perpendicular orientations (in-plane and along the layer normal) of their uniaxial axes are allowed. We find that the structure of the monolayer depends strongly on particle shape and density. In the case of rod-like shapes, particles align a…
Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic coexistence. We discuss a computational study of inhomogeneous configurations that is based on a field theory extension of the Maier-Saupe molecular model of a uniaxial, nematic liquid crystal. A tensor order parameter is defined as the second moment of an orientational probability distribution, leading to a free energy that is not convex within the isotropic-nematic …
We introduce shape fluctuations in a liquid-crystalline system by considering an elementary Maier--Saupe lattice model for a mixture of uniaxial and biaxial molecules. Shape variables are treated in the annealed (thermalized) limit. We analyze the thermodynamic properties of this system in terms of temperature $T$, concentration $c$ of intrinsically biaxial molecules, and a parameter $Δ$ associated with the degree of biaxiality of the molecules. At the mean-field level, we use standard techniques of statistical mechanics to draw global phase diagrams, which are shown to display a rich structur…
We propose a simple surface potential favoring the planar degenerate anchoring of nematic liquid crystals, i.e., the tendency of the molecules to align parallel to one another along any direction parallel to the surface. We show that, at lowest order in the tensorial Landau-de Gennes order-parameter, fourth-order terms must be included. We analyze the anchoring and wetting properties of this surface potential. In the nematic phase, we find the desired degenerate planar anchoring, with positive scalar order-parameter and some surface biaxiality. In the isotropic phase, we find, in agreement wit…
