07/15/2008
Recent experiments report that the longlookedfor thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations, we concentrate on some elementary theoretical issues concerned with the classical sixthorder Landaude Gennes free energy expansion in terms of the symmetric and traceless tensor order parameter Q(alpha beta). In particular, we fully explore the stability of the biaxial nematic phase giving analytical solutions for all distinct classes of the phase diagrams that theory allows. This includes diagrams with triple, critical, and tricritical points and with multiple (reentrant) biaxial and uniaxial phase transitions. A brief comparison with predictions of existing molecular theories is also given.
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11/17/2006
Dynamic light scattering from orientational order fluctuations in a liquid crystalline tetrapode reveals successive, weakly firstorder isotropic to uniaxial and uniaxial to biaxial nematic phase transitions. The order parameter relaxation rates exhibit temperature dependences consistent with Landau–de Gennes mean field theory. Combined with previous evidence of a secondorder uniaxialbiaxial transition in a closely related tetrapode, the present study supports the existence of a nematicnematic tricritical point in thermotropic liquid crystals.
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11/16/2006
Dynamic light scattering from orientational order fluctuations in a liquid crystalline tetrapode reveals successive, weakly firstorder isotropic to uniaxial and uniaxial to biaxial nematic phase transitions. The order parameter relaxation rates exhibit temperature dependences consistent with Landau–de Gennes mean field theory. Combined with previous evidence of a secondorder uniaxialbiaxial transition in a closely related tetrapode, the present study supports the existence of a nematicnematic tricritical point in thermotropic liquid crystals.
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10/15/2006
The combined effects of the tendency of cholesterol to order lipids in the liquid phase and the coupling between lipids in the two leaves of a bilayer are investigated theoretically utilizing a Landau free energy. We show that as a consequence of these combined effects, lateral phase separation in the outer leaf between cholesterolrich and poor liquids causes a similar, but weaker, phase separation in the inner leaf. Just as the areal density of lipids in the outer leaf increases in the cholesterolrich regions, so the areal density of lipids also increases in the inner leaf. Thus, the areal density in the inner leaf varies spatially, reflecting spatial variations of the areal density in the outer leaf. This provides a mechanism for proteins attached to the inner leaf via a hydrocarbon tether to respond to variations in the composition of the outer leaf. We also note that the effect of coupling between the leaves should be observable in artificial bilayers.
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09/15/2002
We report specificheat measurements for a series of liquid crystals imbedded in a porous cylindrical geometry. Above the nematictoisotropic transition and dependent on nematic width (or chain length), the specific heat shows a small peak. In analogy to known ellipsometry results, the peak is believed to be the signature of a nematic prewetting transition.
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06/15/2002
Two examples of the director structure and electric field in patterned electrode liquid crystal cells are studied using a recently developed calculational model. First, a display cell that exhibits a homeotropic to multidomainlike transition with twist wall structures has been considered for a liquid crystal with positive dielectric anisotropy. The model elucidates the behavior of the electric field. Calculations show good agreement between the model and direct computer solution of the EulerLagrange equations, but the model is at least 30 times faster. Second, the possibility that a cell has +/1/2 disclination lines instead of a wall defect is probed. A temperature dependent estimate for the size of the defect core is given, and the total free energy of the cell with disclination lines was calculated and compared with the corresponding value for the same cell with wall defect structure. (C) 2002 American Institute of Physics.
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12/01/2001
We investigate theoretically the pseudoCasimir force between parallel plates immersed in a chiral nematic liquid crystal. We focus on smallseparation limit where the director configuration between the plates inducing strong homeotropic anchoring is uniform. We find that the force is attractive at separations smaller than the crossover distance and repulsive otherwise, and that it diverges logarithmically at the critical distance where the uniform structure is replaced by a distorted structure. We also analyze modifications to the force introduced by magnetic field and comment on the possible detection of the effect.
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05/01/2001
A model for describing properties of a liquid crystal display which combines the concepts of inplane switching and vertical alignment is proposed. There is good agreement between the results of this model and direct computer calculation of the director and the light transmittance. The usefulness of the model lies in the faster speed of calculations compared to direct computer solution of the Euler–Lagrange equations.
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02/15/2001
A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquidcrystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a nonwet layer having a small deviation from bulk order, and a different nonwet layer with a large deviation from bulk order that decays nonmonotonically as the distance from the wall increases. In particular, the large deviation nonwet layer is a feature of systems at the Lifshitz point and also those systems having only homogeneous bulk phases.
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03/01/2000
We study the Landau model of the class of incommensurate systems with a scalar order parameter where the modulated phase is driven by a gradientsquared term with negative coefficient. For example, theoretical studies of cholesteric liquid crystals in a field (electric or magnetic) suggest that such an modulated phase should exist at high chirality. The bulk phase diagram in the presence of a bulk external field which couples linearly to the order parameter exhibits a modulated phase inside a loop in the temperaturefield plane, and a homogeneous phase outside. On analyzing the same model for a semiinfinite system, we find a surprising result; the system exhibits surface states in a region where the bulk phase is homogeneous (but close to the modulated region). These states are very different from the wellknown surface states induced either by a surface field or by enhanced interactions at the surface, for they exist and are energetically favored even when the sole effect of the surface is to terminate the bulk, as expressed by free boundary conditions taken at the surface. Near the surface, the surfacestate order parameter is very different from the bulk value (in fact, it has the opposite sign). When the temperature or the bulk field are varied to move away from the modulated state, we find a surface phase transition at which the surface states become energetically unfavorable, though they continue to exist as metastable states. We then study how a surface field changes the surface phase diagram.
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01/15/2000
An approximate analytical approach for describing properties of a liquid crystal display associated with a homeotropic to multidomainlike transition for a liquid crystal with a positive dielectricanisotropy was developed. The electrode and surface coating of the display are prepared in such a way that in the absence of an electric field (dark state) the liquid crystal alignment is homeotropic. The bright state corresponds to a situation when a high voltage is applied to the interdigitated electrodes located on both substrates, which causes a director deformation of a multidomain type. Approximate solutions for the three dimensional electric field and director configuration in the case of strong homeotropic anchoring were obtained to describe the bright state. It was found that two different defect structures are possible for the director configuration: one corresponds to a wall defect and the other to two disclination lines. A first order phase transition between the two structures is predicted at a particular value of the voltage. An estimate of this critical voltage is obtained.
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09/15/1998
The mechanism of liquid crystal pretilt angle generation on photoreactive polymer films doubly exposed to linearly polarized ultraviolet (uv) light has been investigated. The first exposure for time; tau(1) is normal to the surface, and the film is subsequently irradiated for time tau(2) With obliquely incident uv light with a plane of polarization rotated by 90 degrees with respect to that of the first uv light. The state of the polymer film after two exposures was characterized with a tensor order parameter, which then served as a boundary condition for the surface state of the nematic liquid crystal. The bulk liquid crystal behavior was investigated using Landaude Gennes theory extended to include the possibility for weak surface interactions linear in the tensor order parameter. The pretilt angle was calculated as a function of both tau(1) and tau(2), and as a function of the second uv light angle of incidence. The calculated behavior of the pretilt angle was found to be in qualitative agreement with experimental observations. Conclusions about the strength of the anchoring have also been made.
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07/27/1998
The electroopticproperties of a liquidcrystal display associated with a homeotropic to multidomainlike transition for a liquid crystal with a positive dielectricanisotropy have been investigated. The cell plates are prepared in such a way that, in the absence of an electric field, the liquidcrystal alignment is homeotropic. an electric field created by interdigitated electrodes on both substrates causes a director deformation of a multidomain type. The display shows wide viewing angle, excellent color characteristics, and a fast response time. The molecular director configuration, together with the electrooptic characteristics of the device, are discussed in this letter.
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02/16/1998
The electrooptic properties of a novel liquid crystal device associated with a homogeneous to twistedplanar (HTP) transition have been investigated. The cell plates are prepared in such a way that in the absence of an electric field the liquid crystal orientation is uniform throughout the cell, and thus between crossed polarizers the cell appears black (off state). When an electric field of a particular configuration is applied, a 90° twist is imposed, and the cell transmits light (on state). It was found that the HTP device exhibits wide viewing angle and excellent color characteristics. The dependence of the electroopticeffect on rubbing directions and cell gap has also been investigated.
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08/15/1997
The phase diagram of a bull; cholesteric liquid crystal in an electric or magnetic field applied perpendicular to the pitch axis is studied. This is an example of a system which exhibits different types of phase transitions between various modulated and homogeneous states. Possible transitions are of three types: (1) first order, (2) continuous and described as a condensation of solitons with repulsive interaction, or (3) continuous but characterized by a small order parameter. The detailed behavior of the temperaturefield phase diagram is found to be strongly dependent on the intrinsic chirality, where the existence of an undulating state is predicted at high chirality. The relevant temperature, electric field, and chirality ranges are experimentally attainable.
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04/15/1997
We calculate the thermodynamic phase diagram of a semiinfinite nematic liquid crystal system above its bulk ordering temperature for the case of planar boundary conditions. The latter are assumed to favor a uniaxially ordered surface state, characterized by a negative orientational order parameter, at sufficiently high temperatures. All symmetryallowed terms either linearly or quadratically proportional to the tensor order parameter characterizing the transition to a biaxially ordered surface stale are included in the analysis. The EulerLagrange equations obtained by minimizing the Landaude Gennes free energy expression are solved exactly by numerical methods, we find that both first and secondorder transitions are possible; they occur in different sections of the thermodynamic phase boundary separated by a line of tricritical points. In the secondorder region, we evaluate the effect of fluctuations on this quasitwodimensional system by introducing the BerezinskiiKosterlitzThouless mechanism, and calculating its effect on the phase boundary and nature of the transition. Possible ways of observing this phase transition experimentally are considered and some potentially useful techniques noted.
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02/01/1997
The liquid crystal orientation on a poly(vinyl cinnamate) or poly(vinyl 4methoxycinnamate) coated solid substrate exposed to linearly polarized UV light has been studied. The angular distribution of the polymer side chains and the photoreaction products was derived as a function of exposure time using a simple assumption about the probability for crosslinking of two side chains. The liquid crystal was assumed to be weakly anchored to the surface but have a degree of order and orientation determined from those of the polymer side chains. The polar and the azimuthal surface coefficients were estimated as a function of exposure time using the Landau–de Gennes theory and the behavior of a twist cell with polymer plates was studied for the values of the calculated surface coefficients.
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10/15/1995
Phase transitions in finitethickness nematogenic materials bounded by two planar surfaces and characterized by identical surface interactions linearly proportional to the order parameter have been studied theoretically by solving the coupled nonlinear EulerLagrange equations. The surface interaction was assumed to favor molecular orientation in the surface plane with no rubbed or preferred direction. The related problem of a semiinfinite film having a single surface has been studied previously at temperatures above the bulk nematicisotropic phase transition point TNI. For that geometry and physically relevant elastic constants, it was shown that, in addition to the bulk transition, there is a second transition at higher temperatures between biaxial and uniaxial ordering of the surface layer when the strength of the surface coupling is not too weak. It is shown here that this double phase transition reduces to a single one for sufficiently thin layers.
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03/01/1995
We explore the interplay between various interaction and hopping terms, in particular the effect of OO hopping, tppo on the charge instabilities and phase separation in the threeband extended Hubbard models. Within a weakcoupling meanfield approach, we find that in two dimensions (2D), tppo moves the phase separation boundary appreciably to higher dopings. This would increase the window of doping over which chargetransfermediated superconductivity can occur. Considering a larger phase space, we also obtain a more complete picture of the coexistence lines and spinodal decompositions, and determine the chargetransferinstability critical point. We also consider the 1D case: tppo is found to play a similar role, but the phase separation occurs at significantly lower dopings compared to 2D. This may be of interest to recent Monte Carlo calculations.
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04/15/1994
Surfacelayer transitions in nematogenic materials characterized by a preferential planar surface interaction linear in the order parameter have been studied theoretically at temperatures above the bulk transition (T(NI)). The coupled EulerLagrange nonlinear differential equations obtained from the Landaude Gennes free energy were solved exactly by numerical integration. This problem had been studied previously employing various limits and approximations with several differences in the phase diagram reported. The exact results allow one to determine which of these differences are artifacts of the approximations used and which are dependent upon the ratio of elastic constants. It is found, for physically relevant elastic constants, that there is always a uniaxially ordered surface layer at sufficiently high temperatures. For weak surface coupling, no surface phase transition occurs and the uniaxial layer remains the stable state until T(NI) is reached. When the surface coupling is increased, there is a single firstorder (prewetting) transition from uniaxial to biaxial surface ordering as the temperature is reduced towards T(NI). This transition boundary becomes second order (by way of a tricritical point) when the surface coupling is further increased. We also find that the meanfield boundary is suppressed due to BerezinskiiKosterlitzThouless (BKT)type phase fluctuations. Also, these fluctuations can result in the reentrant (with increasing surface coupling strength) uniaxialbiaxial phase boundary terminating on the bulk transition line rather than becoming asymptotic to it.
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08/15/1993
For a surface interaction linear in the order parameter and favoring an orientation in which liquidcrystalline molecules lie parallel to the surface (but which is independent of whether the orientation is uniaxial or isotropic in the bounding plane), a symmetrybreaking phase transition in a surface layer is possible at temperatures above that of the bulk isotropic to nematic transition. At the surface transition, the hightemperature inplane isotropic state becomes unstable with respect to a biaxial phase, the transition being continuous and therefore ofthe BerezinskiiKosterlitzThouless (BKT) type, It is expected to occur for intermediate surface couplings but not at very weak or very strong couplings. The bulk phase always remains disordered. The BKT transition boundary is calculated explicitly and the results are compared with earlier theoretical studies on systems with linear or quadratic surface interaction potentials. Numerical estimates indicate that systems having the required linear surface potentials can be prepared and possible techniques for observing a BKTtype phase transition are discussed.
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06/15/1992
The measurement of the saddlesplay surface elastic constant K24 in a nematic liquid crystal is reported based on two independent deuterium nuclearmagneticresonance (2HNMR) experiments. Fifty years after the pioneering work of Oseen and Zocher, these measurements were made from observations of nematic directorfield configurations and a configuration transition discovered in submicrometersized cylindrical cavities of Nuclepore membranes under selected surface preparations and wall curvatures. The experimental difficulties in separating the effect of anchoring energy from surface elastic energy (inherent in small confining volumes) were overcome by a unique use of NMR and the ability to predict stable nematic structures with elastic theory. Direct comparison of calculated 2NMR spectral patterns to experiment is very sensitive to the details of the stable nematic directorfield configuration in cylindrical cavities. Small differences in the director configuration imposed by the curvature or elastic properties of the nematic liquid crystal are strongly reflected in the shape of the spectral pattern. Different nematic structures with preferred perpendicular anchoring conditions such as the escaped radial and planar polar show markedly different patterns. Theoretical analysis reveals that a planarpolar structure is preferred in cavities with a high degree of curvature or sufficiently weak anchoring conditions at the cavity boundary. The features of the planarpolar structure are described in terms of the dimensionless parameter RW0/K, where R is the radius, W0 is the molecular anchoring strength, and K is the bulk elastic constant in the oneconstant approximation. At a sufficiently large radius or substantially strong anchoring conditions, the escapedradial structure is favored and sensitive to the dimensionless surface parameter σ=RW0/K+K24/K1. The 2NMR technique unambiguously distinguishes between these two stable nematic directorfield configurations and is sensitive to the surface parameters σ and RW0/K. Theoretical analysis also reveals that the relative magnitude of the bend (K33) and splay (K11) bulk elastic constants plays a vital role in determining the molecular anchoring angle at the cavity wall of the escapedradial configuration. As K33/K11 increases, the molecular anchoring angle is shown to deviate further from its preferred perpendicular orientation in the presence of finite molecular anchoring to alleviate the expensive bend deformation. Experimentally, point defects occur in the escapedradial configuration where the direction of bend is changed, resulting is a series of alternating hyperbolic and radial defects. An analytical trial function is constructed that describes these defect structures in the region of interest.
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09/09/1991
Analysis of the Frank free energy for nematics confined to cylindrical regions indicates that the director pattern is dependent on the surface elastic constant K24 if there is weak normal anchoring and escape along the cylinder axis. Using deuterium nuclearmagneticresonance techniques on samples of submicrometersize cavities in Nuclepore membranes, we report the first measurement of K24.
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08/15/1991
The directorfield configuration of a nematic liquid crystal confined to cylindrical cavities of polycarbonate Nuclepore membranes ranging from 0.3 to 0.05mum in radius is determined using deuterium nuclear magnetic resonance (H2 NMR). Spectral patterns from cavities of radius 0.3mum reveal the escapedradial configuration with singular point defects, but as the cylinder size is decreased, the elastic energy imposed by the curvature of the confining walls competes with the anchoring energy to tilt the directors away from their preferred perpendicular anchoring direction, preventing the expected transition to the planarradial configuration. A surface fitting parameter is directly determined by simulating H2NMR line shapes, and by studying a series of samples with different radii, the molecularanchoring strength W0 and surface elastic constant K24 are extracted.
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03/15/1991
Possible phases in a nematic liquid crystal confined to a spherical submicrometer droplet embedded in a solid polymer are analyzed in terms of a Landaude Gennes theory. For a droplet with a radial structure we show that the strength of the nematicpolymer interfacial interaction affects the nematicparanematic (partially ordered isotropic phase) phase transition and may in addition induce a boundarylayer nematic phase. This boundary layer phase exists only in a narrow (approximately 0.1 K) temperature interval above the nematic phase for a restricted range of interfacial interactions. Also in the radial structure the degree of ordering is suppressed close to the center of the droplet where a defect is located. As the size of the droplet decreases, the relative size of this region of suppressed ordering increases. Below a critical radius R(c) (0.22mum for 4npentyl4'cyanobiphenyl), if the surface interaction is above a critical value (q(max) = 1.85 x 10(3)), the transition between the nematic phase and the paranematic phase no longer occurs. A threedimensional phase diagram is presented to demonstrate the effect of the surface interaction strength, droplet radius, and sample temperature on the stability of phases within a droplet.
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12/26/1988
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12/07/1987
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05/01/1982
A simple extension of McMillan's meanfield model of the nematic and smecticA phases is reported. Specifically, terms proportional to fourthorder Legendre polynomials are included in the mean field. For a reasonable range of parameter choices this mean field can restrict the most probable directions of the long axis of a molecule in a smectic layer to a cone with the axis of the cone parallel to the optic axis. This result is related to recent quadrupolemagneticresonance observations of molecular order, and also to xray experiments which find that the repeat distance of the smectic layers is less than the alltrans length of the molecule. Finally, a possible connection to recent theories of the smecticA—smecticC transition is pointed out.
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06/15/1981
The LandaudeGennes theory is used to study the isotropicnematic phase transition of a semiinfinite system having a wall which induces local nematic order. Analytic solutions are obtained and it is found that (1) for sufficient surface order, the briefringenceinduced optical phase shift diverges at the transition rather than at the supercooling limit, and (2) the regions of superheating and supercooling are severely restricted.
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06/15/1980
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10/01/1979
The results of direct measurements of the principal indices of refraction in the smecticA and smecticC phases of two homologous liquid crystals are reported. These results are compared qualitatively with the orientational model of Straley and with a model based on anisotropic nematic fluctuations due to coupling between orientational and translational order.
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06/15/1979
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06/15/1978
A simple formulation i presented for the analysis of nuclear quadrupole spectra in biaxial liquid crystals based on orientational order parameters. The analysis contains no tilt angle or other modeldependent parameters not directly measured in NMR experiments. The observability and effect of various order parameters on the asymmetry of the electric field gradient η is discussed. It is shown that η is insensitive to rotational freezeout of the variety expected to be observed in some biaxial phases. Nuclear quadrupole resonance experiments are described which are expected to yield rotational freezeout parameters.
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01/01/1978
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06/15/1977
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06/15/1977
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