Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic-to-nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau-de Gennes model for rod-like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic-isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic-nematic interface and the substrate-nematic-isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

A thermodynamic approach to the anchoring phenomenon in the nematic liquid crystal-substrate system

The phenomenon of anchoring in the nematic liquid crystal-amorphous substrate system is considered and model independent definitions of the surface nematic director, the surface tension and the anchoring energy coefficient are proposed. Then the Landau-de Gennes model of the system is studied for a specific choice of the surface parameters, which leads to a continuous homeotropic-conical anchoring transition. The free energy as a function of the director at a distance l from the surface is found. It is shown that its form is different in two regions of the temperature-distance plane separated by the line of a Freedericksz transition. The asymptotic behaviour of the free energy for large l and for infinitesimal deviations of the director from the anchoring direction is studied. It is found that the asymptotic formula holds also in the vicinity of the anchoring transition. Finally, the results of numerical studies of the Landau-de Gennes model are compared with the predictions of a simple phenomenological model.     

Influence of non-mesogenic impurities on a nematic to isotropic phase transition

Non-mesomorphic solutes depress the normal nematic-isotropic transition temperature in liquid crystals. When non-mesomorphic solutes are added to a nematic liquid crystal, the nematic-isotropic transition temperature is depressed and a two phase region is formed due to the presence of impurities of the solutes. The present paper explains the formation of this two phase region by the Landau-de Gennes phenomenological theory, which agrees fairly well with the experimental observations. We also note that this two phase region indicates the tricritical behaviour of the nematic-isotropic phase transition and the phase diagram near the tricritical point is also obtained.     

Quasi-mesoscopic model for ferroelectric switching in the chevron geometry

We present a theory of ferroelectric liquid crystal switching which combines elements of standard macroscopic continuum theories with mesoscopic Landau-de Gennes chevron theories. The macroscopic elements of the theory apply in the chevron arms, and are subject to a boundary condition at the chevron interface. This boundary condition can be derived from an anchoring energy associated with the director discontinuity at the chevron tip. The anchoring energy, which corresponds to the degree to which the cone mismatch condition is not satisfied, is calculated using the mesoscopic Landau-de Gennes theory. In the combined theory the frequently used cone-matching condition emerges as a thick cell limit. We are able to calculate a free energy associated with the imposition of a field on particular configurations. There follows a switching phase diagram determining the conditions for thresholdless and bistable switching. We further show that the time dependence of the switching process is determined by the slower bulk relaxation dynamics rather than by the fast chevron surface dynamics.     

Anchoring of a nematic liquid crystal on an anisotropic substrate

A nematic liquid crystal in contact with a flat solid substrate is studied by means of a mesoscopic Landau-de Gennes theory. It is assumed that the substrate is anisotropic, i.e. the directions x and y in the surface of the substrate are not equivalent, and the only symmetry is the mirror symmetry y ? - y. Assuming the simplest form of the bare surface free energy, where only the linear terms in the nematic order parameter are taken into account, we study anchoring directions induced by the interaction of the liquid crystal with the substrate. A phase diagram in terms of the surface fields and the temperature is obtained. Depending on the values of the surface fields we find four types of anchoring: the symmetric planar anchoring, with the director along x, the symmetric tilted anchoring, with the director in the xz plane, the antisymmetric planar anchoring, with the director along y, and the asymmetric tilted anchoring, with the director tilted with respect to all three axes.     

Charge transfer interaction between the nematogen 5CB and non-liquid crystal

In general, when a non-nematic solute is added to a nematic, the nematic-isotropic phase transition temperature (T _NI) decreases with increase in non-nematic concentration. But when there are hydrogen bonded complexes or π-complexes of suitable strength formed between the nematic and the solute molecules, the T _NI can rise. Mixing of p-terphenyl or anthracene with 5CB (4-cyano-4'-pentylbiphenyl) results in a T _NI rise. On the other hand, in a binary system consisting of a substance with strong acceptor properties (e.g. tetracyanoethylene; TCNE) and nematic 5CB, T _NI fell remarkably. We have now studied the effect of intermolecular interactions on the T _NI of 5CB by using various acceptor molecules and donor molecules as solutes. We have found that for binary systems in which 5CB and a solute molecule form distinct one-to-one complexes, T _NI falls rather rapidly. When the solute molecules have a strong acceptor power, the rate of T _NI fall with solute concentration is found to be correlated well with the electonegativity of the solute molecules.     

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.     

Nematic-isotropic phase transition in lyotropic liquid crystals

We propose a Landau-de Gennes phenomenological model to describe the nematic-isotropic phase transition in lyotropic liquid crystals. The possibility of a first or second order transition is explored by means of the variation of the concentration of surfactant. We show that a Landau point on the nematic-isotropic phase transition line can be achieved under certain conditions. The theoretical predictions are found to be in good qualitative agreement with available experimental results.     

Nematic-isotropic phase transition in lyotropic liquid crystals

We propose a Landau-de Gennes phenomenological model to describe the nematic-isotropic phase transition in lyotropic liquid crystals. The possibility of a first or second order transition is explored by means of the variation of the concentration of surfactant. We show that a Landau point on the nematic-isotropic phase transition line can be achieved under certain conditions. The theoretical predictions are found to be in good qualitative agreement with available experimental results.     

Effects of wetting and anchoring on capillary phenomena in a confined liquid crystal

A fluid of hard spherocylinders of length-to-breadth ratio L/D=5 confined between two identical planar, parallel walls--forming a pore of slit geometry--has been studied using a version of the Onsager density-functional theory. The walls impose an exclusion boundary condition over the particle's centers of mass, while at the same time favoring a particular anchoring at the walls, either parallel or perpendicular to the substrate. We observe the occurrence of a capillary transition, i.e., a phase transition associated with the formation of a nematic film inside the pore at a chemical potential different from micro(b)-the chemical potential at the bulk isotropic-nematic transition. This transition terminates at an Ising-type surface critical point. In line with previous studies based on the macroscopic Kelvin equation and the mesoscopic Landau-de Gennes approach, our microscopic model indicates that the capillary transition is greatly affected by the wetting and anchoring properties of the semi-infinite system, i.e., when the fluid is in contact with a single wall or, equivalently, the walls are at a very large distance. Specifically, in a situation where the walls are preferentially wetted by the nematic phase in the semi-infinite system, one has the standard scenario with the capillary transition taking place at chemical potentials less than micro(b) (capillary nematization transition or capillary ordering transition). By contrast, if the walls tend to orientationally disorder the fluid, the capillary transition may occur at chemical potentials larger than micro(b), in what may be called a capillary isotropization transition or capillary disordering transition. Moreover, the anchoring transition that occurs in the semi-infinite system may affect very decisively the confinement properties of the liquid crystal and the capillary transitions may become considerably more complicated.     

On the temperature dependence of the order parameter of liquid crystals over a wide nematic range

Abstract

Based on the ideas of Landau-de Gennes theory applied to nematic liquid crystals, several forms for the variation of the order parameter as a function of temperature are investigated over a wide nematic range. These functional forms are used to fit the experimental order parameters, determined through the use of C-13 NMR, for 4-methoxybenzylidene-4′-butylaniline (MBBA) and 4-n-pentyl-4′-cyanobiphenyl (5CB), and the physical significance of the parameters is discussed. A comparison of the results shows that the functional form which fits the experimental data best is similar to the Haller equation, a useful relation which is usually regarded as empirical. In this case, the coefficients resulting from a semi-empirical approach based on the Landau-de Gennes treatment may be thought of as quantifying the importance of the structure and rigidity of the liquid crystal in determining the temperature dependence of the order parameter for that liquid crystal. In the process, we have also examined the pretransitional behaviour in the C-13 NMR chemical shifts of liquid crystals observed within a few tenths of a degree above the nematic to isotropic transition temperature.     

Elastic,dielectric and optical constants of 4'-pentyl-4-cyanobiphenyl

4'-n-Pentyl-4-cyanobiphenyl (5CB) is a room temperature nematic liquid crystal with a high positive dielectric anisotropy and a high chemical stability. Many experimental results concerning the elastic and dielectric constants of 5CB are available in the literature, although there is often no satisfactory agreement between the experimental data obtained by different groups, especially as far as the dielectric constants are concerned. Furthermore, no detailed investigation of the temperature dependence of the elastic and dielectric constants close to the nematic-isotropic transition temperature T _NI has yet been reported. In this paper, we report the measurement of the elastic and dielectric constants of 5CB, and the temperature behaviour close to T _NI has been investigated in detail. The experiment consists in the measurement of the director deformation induced by an electric field using simultaneously both a dielectric and an optical method. The simultaneous use of these two methods provides an indirect check on the reliability of the measurements. Special attention has been devoted to control possible sources of uncertainty. In particular, the effects of finite anchoring energy and of finite pretilt angle have been considered. The temperature dependence of the anisotropy of the refractive indices is also obtained in the experiment.     

Fluctuating Interfaces in Liquid Crystals

Summary: We review and compare recent work on the properties of fluctuating interfaces between isotropic and nematic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.     

Surface tension and capillary waves at the nematic-isotropic interface in ternary mixtures of liquid crystal, colloids, and impurities

In mixtures of thermotropic liquid crystals with spherical poly(methyl methacrylate) particles, self-supporting networklike structures are formed during slow cooling past the isotropic-to-nematic phase transition. Experimental results support the hypothesis that a third component, alkane remnants slowly liberated from the particles, plays a crucial role. A theoretical model, based on the phenomenological Landau-de Gennes, Carnahan-Starling, and hard-sphere crystal theories, is developed to describe the continuous phase separation in a ternary nematic-impurity-colloid mixture. The interfacial tension and the dispersion relation of the surface modes of the nematic-isotropic interface are determined. The colloids decrease the interfacial tension and the damping rate of surface waves, whereas impurities act in an opposite way. This should strongly influence the formation of abovementioned networklike structures and could help explain some of their rheological properties.     

Alignment of carbon nanotubes in nematic liquid crystals

The self-organizing properties of nematic liquid crystals can be used to align carbon nanotubes dispersed in them. Because the nanotubes are so much thinner than the elastic penetration length, the alignment is caused by the coupling of the unperturbed director field to the anisotropic interfacial tension of the nanotubes in the nematic host fluid. In order to relate the degree of alignment of the nanotubes to the properties of the nematic liquid crystal, we treat the two components on the same footing and combine Landau-de Gennes free energies for the thermotropic ordering of the liquid crystal and for the lyotropic nematic ordering of carbon nanotubes caused by their mutually excluded volumes. The phase ordering of the binary mixture is analyzed as a function of the volume fraction of the carbon nanotubes, the strength of the coupling and the temperature. We find that the degree of ordering of the nanorods is enslaved by the properties of the host liquid and that it can be tuned by raising or lowering the temperature or by increasing or decreasing their concentration. By comparing the theory to recent experiments, we find the anchoring energy of multiwalled carbon nanotubes to be in the range from 10(-10) to 10(-7) N m(-1).     

The Twist Elastic Constant and Anchoring Energy of the Nematic Liquid Crystal 4-N-Octyl-4-Cyanobiphenyl

Abstract

The twist elastic constant of the nematic liquid crystal 4-n-octyl-4′-cyano-biphenyl (8CB) and the azimuthal anchoring energy at the SiO-nematic interface have been measured by using the torsion pendulum technique. The twist elastic constant of 8CB is found to be systematically larger than that measured by the Freedericksz transition technique. The azimuthal anchoring energy is found to decrease rapidly as the nematic-isotropic transition temperature is approached. This behaviour is analogous to that already reported by us for the nematogen 5CB and can be interpreted by extending the Berreman model of the anchoring energy at a grooved interface.     

Ringlike cores of cylindrically confined nematic point defects

Nematic liquid crystals confined in a cylindrical capillary and subjected to strong homeotropic anchoring conditions is a long-studied fundamental problem that uniquely incorporates nonlinearity, topological stability, defects, and texture physics. The observed and predicted textures that continue to be investigated include escape radial, radial with a line defect, planar polar with two line defects, and periodic array of point defects. This paper presents theory and multiscale simulations of global and fine scale textures of nematic point defects, based on the Landau-de Gennes tensor order parameter equations. The aim of this paper is to further investigate the ringlike nature of point defect cores and its importance on texture transformation mechanisms and stability. The paper shows that the ringlike cores can be oriented either along the cylinder axis or along the radial direction. Axial rings can partially expand but are constrained by the capillary sidewalls. Radial rings can deform into elliptical structures whose major axis is along the capillary axis. The transformation between several families of textures under capillary confinement as well as their stability is discussed in terms of defect ring distortions. A unified view of nematic textures found in the cylindrical cavities is provided.