A generalized Van der Waals approach is developed for anisotropic fluids in disordered porous media. As the reference system a hard spherocylinder fluid in a disordered porous medium is considered and described in the framework of the scaled particle theory with the Carnahan-Starling and Parsons-Lee corrections. The attractive part of interaction is treated in the framework of the mean field approximation in which due to orientational dependence of the excluded volume of two spherocylinders, a coupling between attractive and repulsive contributions is found. We focus on spherocylinder fluids with sufficiently long particle lengths for which the nematic-nematic transition was established. It is shown that these two nematic phases have different densities and are characterized by different orientational ordering. Strong influence of the type of interparticle attraction on the phase behaviour of anisotropic fluids in disordered porous media is established. Three simple models for this purpose are considered, namely a model with the Lennard-Jones anisotropic attraction, a model with modified Lennard-Jones attraction and a model with anisotropic square-well potential. For all considered models, the phase diagram shifts to the region of lower densities and lower temperatures as the porosity decreases.
We develop the scaled particle theory to describe the thermodynamic properties and orientation ordering of a binary mixture of hard spheres (HS) and hard spherocylinders (HSC) confined in a disordered porous medium. Using this theory the analytical expressions of the free energy, the pressure and the chemical potentials of HS and HSC have been derived. The improvement of obtained results is considered by introducing the Carnahan-Starling-like and Parsons-Lee-like corrections. Phase diagrams for the isotropic-nematic transition are calculated from the bifurcation analysis of the integral equati…
We study the effect of random porous matrices on the ordering in nematic liquid crystals. The randomness destroys orientational lang-range order and drives the liquid crystal into a glass state. We predict two glass phases one of which possesses quasi-long-range order. In this state the correlation length is infinite and the correlation function of the order parameter obeys a power dependence on the distance. The small-angle light-scattering amplitude diverges but slower than in the bulk nematic. In the uniaxially strained porous matrices two new phases emerge. One type of strain induces an an…
When a nematic liquid crystal is confined in a porous medium with strong anchoring conditions, topological defects, called disclinations, are stably formed with numerous possible configurations. Since the energy barriers between them are large enough, the system shows multistability. Our lattice Boltzmann simulations demonstrate dynamic couplings between the multistable defect pattern and the flow in a regular porous matrix. At sufficiently low flow speed, the topological defects are pinned at the quiescent positions. As the flow speed is increased, the defects show cyclic motions and nonlinea…
We theoretically analyze the waveguide regime of light propagation in a cylindrical pore of a polymer matrix filled with liquid crystals assuming that the effective radial optical anisotropy is biaxial. From numerical analysis of the dispersion relations, the waveguide modes are found to be sensitive to the field-induced changes of the anisotropy. The electro-optic properties of the polymer porous polyethylene terephthalate (PET) films filled with the nematic liquid crystal 5CB are studied experimentally and the experimental results are compared with the results of the theoretical investigatio…
We study the phase behaviour of hard rods with length polydispersity, treated within a simplified version of the Onsager model. We give a detailed description of the unusual phase behaviour of the system when the rod length distribution has a "fat" (e.g. log-normal) tail up to some finite cutoff. The relatively large number of long rods in the system strongly influences the phase behaviour: the isotropic cloud curve, which defines the where a nematic phase first occurs as density is increased, exhibits a kink; at this point the properties of the coexisting nematic shadow phase change discontin…
The generalized van der Waals equation of state for anisotropic liquids in porous media consists of two terms.One of them is based on the equation of state for hard spherocylinders in random porous media obtained from the scaled particle theory.The second term is expressed in terms of the mean value of attractive intermolecular interactions.The obtained equation is used for the investigation of the gas-liquid-nematic phase behavior of a molecular system depending on the anisotropy of molecule shapes, anisotropy of attractive intermolecular interactions, and porosity of a porous medium.It is sh…
The generalized van der Waals equation for anisotropic fluids in porous media, proposed by the authors in previous works, is used to describe the effect of porous media on the phase behavior of polypeptide solutions. By introducing the temperature dependence for the depth of the potential well and the geometric parameters of the spherocylinder, the main features of phase behavior of the polypeptide poly ($γ$-benzyl-$L$-glutamate) (PBLG) in a solution of dimethylformamide, including the existence of two nematic phases, is reproduced. It is shown that the presence of a porous medium shifts the p…
Polydispersity is believed to have important effects on the formation of liquid crystal phases in suspensions of rod-like particles. To understand such effects, we analyse the phase behaviour of thin hard rods with length polydispersity. Our treatment is based on a simplified Onsager theory, obtained by truncating the series expansion of the angular dependence of the excluded volume. We describe the model and give the full phase equilibrium equations; these are then solved numerically using the moment free energy method which reduces the problem from one with an infinite number of conserved de…
We analyse the effect of a continuous spread of particle lengths on the phase behavior of rodlike particles, using the Onsager theory of hard rods. Our aim is to establish whether ``unusual'' effects such as isotropic-nematic-nematic (I-N-N) phase separation can occur even for length distributions with a single peak. We focus on the onset of I-N coexistence. For a log-normal distribution we find that a finite upper cutoff on rod lengths is required to make this problem well-posed. The cloud curve, which tracks the density at the onset of I-N coexistence as a function of the width of the length…
We study the static equilibria of a simplified Leslie--Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient $\mathcal{G}$ and inverse anchoring strength, $\mathcal{B}$. We numerically find multiple static equilibria for admissible pairs $(\mathcal{G}, \mathcal{B})$ and classify them according to their winding numbers and stability. The case $\mathcal{G}=0$ is analytically tractable and we numerically study how the solution landscape is transformed as $\mathcal{G}$ increases. We study the one-dimensional dynamical …
The isotropic-nematic phase behavior of length polydisperse hard rods with arbitrary length distributions is calculated. Within a numerical treatment of the polydisperse Onsager model using the Gaussian trial function Ansatz we determine the onset of isotropic-nematic phase separation, coming from a dilute isotropic phase and a dense nematic phase. We focus on parent systems whose lengths can be described by either a Schulz or a `fat-tailed' log-normal distribution with appropriate lower and upper cutoff lengths. In both cases, very strong fractionation effects are observed for parent polydisp…
The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the case of two-dimensional nematic liquid crystals coating a toroidal particle. Our aim is to show how a different modeling of the effect of extrinsic curvature acts as a selection principle among equilibria of the classical energy, and how new configurations emerge. In particular, our analysis predicts the existence of new stable equilibria with complex windin…
We consider the effects of polydispersity on isotropic-nematic phase equilibria in thermotropic liquid crystals, using a Maier-Saupe theory with factorized interactions. A sufficient spread (approx. 50%) in the interaction strengths of the particles leads to phase separation into two or more nematic phases, which can in addition coexist with an isotropic phase. The isotropic-nematic coexistence region widens dramatically as polydispersity is increased, leading to re-entrant isotropic-nematic phase separation in some regions of the phase diagram. We show that similar phenomena will occur also f…
The scaled particle theory (SPT) approximation is applied for the study of the influence of a porous medium on the isotropic-nematic transition in a hard spherocylinder fluid. Two new approaches are developed in order to improve the description in the case of small lengths of spherocylinders. In one of them, the so-called SPT-CS-PL approach, the Carnahan-Starling (CS) correction is introduced to improve the description of thermodynamic properties of the fluid, while the Parsons-Lee (PL) correction is introduced to improve the orientational ordering. The second approach, the so-called SPT-PL ap…
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…
Motivated by recent experiments, the isotropic-nematic phase transition in chromonic liquid crystals is studied. As temperature decreases, nematic nuclei nucleate, grow, and coalesce, giving rise to tactoid microstructures in an isotropic liquid. These tactoids produce topological defects at domain junctions (disclinations in the bulk or point defects on the surface). We simulate such tactoid equilibria and their coarsening dynamics with a model using degree of order, a variable length director, and an interfacial normal as state descriptors. We adopt Ericksen's work and introduce an augmented…
Free volume theory (FVT) is a versatile and tractable framework to predict the phase behaviour of mixtures of platelets and non-adsorbing polymer chains in a common solvent. Within FVT, three principal reference phases for the hard platelets are considered: isotropic (I), nematic (N), and columnar (C). We derive analytical expressions that enable us to systematically trace the different types of phase coexistences revealed upon adding depletants and confirm the predictive power of FVT by testing the calculated diagrams against phase stability scenarios from computer simulation. A wide range of…
We study the phase behaviour of the Zwanzig model of suspensions of hard rods, allowing for polydispersity in the lengths of the rods. In spite of the simplified nature of the model (rods are restricted to lie along one of three orthogonal axes), the results agree qualitatively with experimental observations: the coexistence region broadens significantly as the polydispersity increases, and strong fractionation occurs, with long rods found preferentially in the nematic phase. These conclusions are obtained from an analysis of the exact phase equilibrium equations. In the second part of the pap…
We report combined optical birefringence and neutron scattering measurements on the liquid crystal 12CB nanoconfined in mesoporous silicon layers. This liquid crystal exhibits strong nematic-smectic coupling responsible for a discontinuous isotropic-to-smectic phase transition in the bulk state. Confined in porous silicon, 12CB is subjected to strong anisotropic quenched disorder: a short-ranged smectic state evolves out of a paranematic phase. This transformation appears continuous, losing its bulk first order character. This contrasts with previously reported observations on liquid crystals …
