Landau-de Gennes Model Research Articles

Kerr effect of low melting nematic liquid crystals with negative dielectric anisotropy

The two low melting nematic liquid crystals, 2‐chloro‐4‐heptylphenyl 4‐pentylbicyclo[2,2,2]octane‐1‐carboxylate (7CP5BOC) and 2‐chloro‐4‐heptylphenyl 4‐heptylbicyclo[2,2,2]octane‐1‐carboxylate (7CP7BOC) have been investigated to determine their electro‐optical behaviour and third order non‐linearity by the static Kerr effect method. Both liquid crystals are laterally substituted by a single chlorine atom located close to the ester linking group. The temperature dependence of the electric Kerr constant in the isotropic phase and the pretransitional behaviour have been investigated for these low birefringence nematic liquid crystals in the isotropic phase. Both the compounds, with negative dielectric anisotropy, have a positive Kerr constant. The Landau–de Gennes model was obeyed for these compounds.

Electro-optical Kerr effect of two high birefringence nematic liquid crystals

A new tolane-base liquid crystal, 4′-heptyl-3-fluoro-4-isothiocyanatotolane (7TOLF), and a biphenyl-base nematogen, 4′-heptyl-3-fluoro-4-isothiocyanatobiphenyl (7BF), have been investigated for the first time to determine their electro-optical behaviour and third order non-linearity using the static Kerr effect method. Both the nematic compounds have a fluorine atom attached to the phenyl-NCS moiety. They possess the same polar head group (-NCS) and alkyl tail (-C7H15). So the effect of the tolane group of nematogen on the electro-optical behaviour was investigated and compared. The temperature dependence of the electric Kerr constant in the isotropic phase and the pre-transitional behaviour has been investigated for these high birefringence compounds in the isotropic phase. Both the compounds have a positive and large Kerr constant which increases with decrease in temperature. The Landau–de Gennes model was obeyed for these compounds. For 7TOLF, the observed value of susceptibility, χ3 is about 228 times higher than that of CS2. The experimental Kerr effect data were also compared with those of the well-studied nematic liquid crystals.

Waves at the Nematic-Isotropic Interface

ABSTRACT We examine surface modes at the nematic-isotropic interface in polymer-liquid-crystal mixtures using the dynamical Landau-de Gennes model for the orientational (non-conserved) order parameter coupled with Cahn-Hilliard equation for concentration (conserved order parameter) and with hydrodynamic degrees of freedom. The generalized dispersion relation is obtained and analyzed in particular cases. Orientational order parameter relaxation dominates in the short wavelength limit, while in the long wavelength limit viscous damping becomes important. The effect of polymer is to increase the surface tension and as a consequence the relaxation rate in the hydrodynamic limit. Finally, we discuss how to measure experimentally the dispersion relation.

Pretransitional fluctuations in the isotropic phase of a lyotropic chromonic liquid crystal

We have studied isotropic-to-nematic pretransitional fluctuations in an aqueous solution of disodium cromoglycate (cromolyn) by static and dynamic light scattering. Cromolyn is a representative of lyotropic chromonic liquid crystals with building units being elongated rods formed by aggregates of disk-like molecules. By combining light-scattering and viscosity measurements we have determined the correlation length and relaxation time of the orientational order-parameter fluctuations and estimated the size of the cromolyn aggregates. The pretransitional behavior of light scattering does not completely follow the classic Landau-de Gennes model. This feature is most probably associated with the variable length of cromolyn aggregates. We have observed a dramatic increase of the shear viscosity near the transition to the nematic phase, the fact which correlates with the idea of growing supramolecular aggregates. The steep temperature dependence of the viscosity is accompanied by a practically temperature-independent translational diffusion coefficient.

The static Kerr effect of two nematic mixtures comprised of pentyl and heptyl cyanobiphenyls in the isotropic phase

Electro-optic Kerr effect and the pretransition behaviour was investigated for the 5CB and two of pentyl and heptyl nematic mixtures, (F1 [71% 5CB:29% 7CB] and F2 [51% 5CB:49% 7CB]), at temperatures above the nematic-isotropic transition temperature. The Kerr constant of these liquid crystals was found to be very high at the nematic-isotropic transition temperatures. The linear dependence of ( T− T*) −1 on the Kerr constant is found to be in good agreement with the predications of the Landau–De Gennes model.

Effect of spontaneous polarization and polar surface anchoring on the director and layer structure in surface-stabilized ferroelectric liquid crystal cells.

We use the Landau-de Gennes model to study theoretically the effect of the magnitude of the spontaneous polarization (P(S)), the ratio (r) between the equilibrium layer tilt and the smectic cone angle, the thickness of the insulating alignment layers and the strength of the polar and nonpolar surface anchoring on the director and layer structure in surface-stabilized ferroelectric liquid crystal cells with the chevron structure of smectic layers. The system shows a surprising number of stable structures, accompanied by one or two metastable ones. At P(S) greater than the critical value only quasimonostable structures, which can exhibit the thresholdless (V-shaped) switching, exist at all r and both at weak and strong polar surface anchoring. At lower P(S) bistable and monostable structures can coexist. Bistable structures can be expected at high r, low P(S) and if polar surface anchoring is weaker than the nonpolar one. Lowering the ratio r and/or increasing the strength of polar anchoring promotes the stability of monostable structures. Thicker insulating alignment layers also drive the system into the monostable state. Polar surface anchoring induces a large surface electroclinic effect. As a result the nematic deformations close to the surfaces are very strong and the stress is relieved by bending of the smectic layers. This leads to the formation of a double chevron structure which is stable at very large polar anchoring and due to the surface electroclinic effect it is metastable also at lower values of polar anchoring.

Rotational dynamics of nondipolar and dipolar solutes in an isotropic liquid crystal: Comparison with an isotropic liquid

Rotational dynamics of a nondipolar solute, 2,5-dimethyl-1,4-dioxo-3, 6-diphenylpyrrolo[3,4-c]pyrrole (DMDPP) and a dipolar solute, coumarin 6 (C6) has been studied in the isotropic phase of a liquid crystal, 4′-methoxybenzylidene-4-n-butylaniline (MBBA) to understand the influence of pseudonematic domains on the dynamics of dopant molecules. The reorientation times of both DMDPP and C6 follow the Stokes–Einstein–Debye hydrodynamic model instead of the Landau–de Gennes model, which is used to describe the rotational relaxation of neat isotropic liquid crystals. However, comparison of the data for both DMDPP and C6 in MBBA to that in an isotropic solvent, 1-decanol reveals that the probes are rotating considerably slower in the liquid crystal. These results indicate that ordered local structures of the liquid crystal exert more friction on the rotating solute molecule compared to an isotropic liquid.

Symmetry and pattern formation for a planar layer of nematic liquid crystal

Using equivariant bifurcation theory, and on the basis of symmetry considerations independent of the model, we classify square and hexagonally periodic patterns that typically arise when a homeotropic or planar isotropic nematic state becomes unstable, perhaps as a consequence of an applied magnetic or electric field. We relate this to a Landau–de Gennes model for the free energy, and derive dispersion relations in sufficient generality to illustrate the role of up/down symmetry in determining which patterns can arise as a stable bifurcation branch from either initial state.

Biaxial melting of the nematic order under a strong electric field.

We study the action of a strong electric field on a nematic, topologically stabilized with director n perpendicular to E. Above a threshold field the nematic order on the cell midplane is "melted" and rapidly reconstructed with n axially E. In a Landau-de Gennes model, we show that the observed transient "melted" state is a biaxial nematic and not an isotropic liquid.

Nematostatics of triple lines.

The Landau-de Gennes model for nematic liquid crystal bulk and interfaces has been extended to nematic triple lines involving the intersection of two isotropic fluids and one nematic liquid crystalline phase. A complete set of bulk, interface, and triple line force and torque balance equations has been formulated. The triple line force and torque balance equations have linear, interfacial, and bulk contributions. The bulk contributions appear as junction integrals, the surface contributions as junctions sums, and the line contributions as gradients of stresses. Reduction of dimensionality from three to one dimensional creates the following effects: (a) bulk terms enter interfacial balances as surface jumps and line balances as junction integrals, and (b) surface terms enter linear balances as junction sums. Line stress and torque equations are derived using classical liquid crystal models. The correspondence between line stress and line torque and their surface and bulk analogs is established. The triple line force and torque balance equations are use to analyze the contact angle in a nematic lens lying at the interface between two isotropic fluids, when the preferred surface orientation is tangential. The effect of anisotropy and long range elasticity on triple line phases is established. Under weak anchoring the contact angle is shown to be a function of the anchoring energy at the nematic-isotropic interface, while under strong anchoring conditions the contact angle is a function of the Peach-Koehler force that originates from bulk long range elasticity and acts on the triple line. The use of the complete set of balance equations removes the classical inconsistency in force balances at a contact line by properly taking into account long range (bulk gradient elasticity) and anisotropic (interfacial anchoring elasticity) effects.

Nonlinear dynamics of a nematic liquid crystal in the presence of a shear flow

In this paper we study a Landau-de Gennes model of a nematic liquid crystal in a model shear flow employing a range of analytical and numerical techniques. We use asymptotic methods and numerical bifurcation theory to provide a comprehensive description of the different in-plane modes that exist in terms of the temperature and imposed shear rate, as well as determining their stability to in-plane disturbances. We show that there are two physically distinct solution branches, one of which corresponds to an in-plane director (denoted IPN). The other branch corresponds to the director being aligned perpendicular to the shear plane, i.e. so-called log-rolling states. We find both tumbling and wagging time-dependent modes. The mode structure is organized by a Takens-Bogdanov point, at which a family of Hopf bifurcation points and a family of limit points coincide. At low strain rates tumbling occurs as a transition from the IPN branch. In addition, we show that at larger values of the strain rate the wagging modes emanate from a Hopf bifurcation on the IPN branch and evolve continuously into tumbling modes. Moreover, we show analytically that this boundary between tumbling and wagging corresponds to a state in which the distribution function is cylindrical in the shear plane. This provides confirmation of the tumbling-wagging transition mechanism observed by Tsuji and Rey in numerical calculations relating to a confined geometry.

Theoretical and Computational Rheology for Discotic Nematic Liquid Crystals

This paper presents an analysis of the role of orientation on the rheology of discotic nematic liquid crystals. The shear rheological properties exhibited by flow-aligning discotic mesophases are calculated by using a complete generalized nonlinear second-order tensor Landau-de Gennes model that takes into account short-range order elasticity, long-range elasticity, and viscous effects. A unified expression for the extra stress tensor is given. The second-order tensor Landau-de Gennes model was reduced to the uniaxial Leslie-Ericksen to obtain limiting rheological material functions valid at low and high shear rates. Analytical results are able to predict the material functions computed by the full Landau-de Gennes model for nonhomogeneous flow-aligning discotic nematic liquid crystals. Experimentally reported changes in the sign of the first normal stress differences with shear rate are captured by the model. A new Carreau-Yasuda liquid crystal model has been used to characterize the shear rheology for characteristic boundary conditions, and a viscosity power law exponent of 0.5 and a normal stress coefficient power law exponent of 0.44 have been obtained.

Capillary Thermodynamics of Nematic Polymer Interfaces

The Cahn-Hoffman capillarity vector thermodynamics formalism for curved anisotropic interfaces is adapted to soft liquid crystalline polymer-isotropic fluid interfaces. The Cahn-Hoffman formalism in conjunction with the interfacial Landau-de Gennes model is used to derive compact expressions for the capillary pressure, tangential Marangoni force, and interfacial torque. It is shown that the interfacial thermodynamics of nematic polymers can be analyzed in terms of three distinct modes: (i) area size change, (ii) area rotation, and (iii) tensor order parameter curvature. The formalism allows to clearly identify the nature and magnitude of these three contributions. Characteristic cases biaxial and uniaxial nematic ordering states are analyzed. Anisotropic liquid crystal surfaces display a number of novel interfacial effects: (a) capillary pressure even for flat surfaces, (b) tensor order parameter-dependent renormalization of the tension coefficients due to anchoring energy, (c) tensor order parameter-driven transitions between classical Laplace pressure and non-classical behavior, (d) Laplace-like capillary pressure due solely to orientation curvature, (e) generation of Marangoni forces through interfacial order and/or orientation gradients, and (f) surface torques generation. Schematic of the geometry considered in this article.

Electro-Optic Kerr Effect Investigations in a New Homologous Series of Liquid Crystal

Measurements are reported for the first time for the D.C. Kerr response and the pretransitional behaviour of a new homologous series of liquid crystal 4′-(trans-4′-alkylcyclohexyl)-benzonitrile(for n=5 to 9) at and above the nematic-isotropic phase transition temperatures. The real part of the third order nonlinear susceptibilities(χ(3)) have been determined for this homologous series of liquid crystals from the Electro-optic Kerr effect (EOKE) experiments at and above the nematic-isotropic phase transition temperatures. The variation of the Kerr constant with temperature has been discussed on the basis of the Landau-de Gennes model of nematic-isotropic phase transition. The Kerr relaxation time and other statistical parameters concerned with a nematic-isotropic phase transition like the latent heat of transition have also been determined using the Landau-de Gennes' theory of phase transition. The variation of the Kerr constant, the values of the third order nonlinear susceptibilities, the Kerr relaxation time and the latent heat of transition with the number of carbon atoms in the alkyl chain within the series have been discussed on the basis of an interesting effect called the “ODD-EVEN” effect. The results and discussions are presented.

The Electro-optical kerr effect in eutectic nematic mixtures of E7 and E8

Abstract Electro-optic Kerr effect and the pretransition behaviour investigated for the eutectic nematic mixture liquid crystals E7 and E8 at temperatures above the nematic-isotropic transition temperature (in the isotropic phase). The Kerr constant of these liquid crystals found to be very high at the nematic-isotropic transition temperatures as the molecules are expected to be highly ordered close to phase transition temperatures. The linear dependence of (T - T*)−1 on the Kerr constant is found to be in good agreement with the predications of the Landau-De Gennes model.

Stability of a pixel in surface stabilized smectic-c chevron cells

We use Landau-de Gennes model to find the minimum width of a switched stripe in a surface stabilized smectic-C cell. The dependence of the critical width on temperature and on values of the nematic and smectic elastic constants is estimated analytically. The results are compared with numerically obtained critical widths. We also find characteristic times in which the wall between two switched regions is formed.

Kerr effect investigations in a liquid crystal

Measurements are reported for the d.c. Kerr response and the pretransitional behaviour of a new liquid crystal, 4-cyanophenyl 4-pentylbenzoate at and above the nematic-isotropic phase transition temperature. The real parts of the third order nonlinear susceptibilities chi(3) at and above the nematic-isotropic transition temperatures are determined for the new liquid crystal from the electro-optic Kerr effect (EOKE) experiments. The variation of the Kerr constant with temperature is discussed on the basis of the Landau-de Gennes model of the nematic-isotropic phase transition. The susceptibility values are also compared with that of the well known liquid crystal 4'-pentyl-4-cyanobiphenyl (5CB). The effect of the linking group of the liquid crystal on the suceptibility value is also discussed.

Structure and energy of the wall separating two states in surface-stabilized smectic C chevron cells

We use a Landau-de Gennes model to study the structure of the wall formed between two oppositely switched areas (pixels) in surface stabilized smectic C cells with uniform chevron direction. We find the width of the wall and calculate the energy associated with its formation. This approach also allows us to determine the effect of the temperature on the pixel wall properties. We predict analytically and calculate numerically that both the wall energy and the wall width obey a power law dependence on temperature with the exponents 3/2 and 1/2, respectively.

Classification of Static Field Effects in Smectic A Mesophase

Bifurcational analysis of the extended Landau-de Gennes model of smectic A (A) liquid crystal in external field is performed. Topological classification of phase diagrams of the system in “field-temperature” coordinates is made. Depending on mesogeneous properties the following static field effects are demonstrated to realize: a) suppression of the nematic (N)-paranematic (pN) phase transition in the critical end point (CEP) (the Wojtowich-Sheng effect); b) induction of an intermediate nematic phase (the Rosenblatt effect) followed by its suppression (the induced Wojtowich-Sheng effect); c) induction of tricritical point (TCP) on the A-N phase transition line (the Rosenblatt-Hama effect); d) induction of the A-nonspontaneous nematic (NSN) TCP in combination with the induced Wojtowich-Sheng effect; e) induction of the A-pN TCP in combination with the induced Wojtowich-Sheng effect (the Lelidis-Durand effect); f) induction of the A-NSN-pN triple point (TP) by an arbitrary weak field; g) coincidence of the A-NSN-pN TP and the A-NSN TCP under the influence of the field (field analogue of the Achard-Sigaud-Hardouin effect); h) realization of the A-pN TCP in combination with prohibition of the induced Wojtowich-Sheng effect. Conditions are formulated leading to realization and prohibition of effects listed above.

Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K22 and K33 are the largest, and decrease to zero in the infinite-frequency limit. The correction to K11 is negative, and vanishes in both limits. The absolute value of the correction to K11 is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation.