06/01/2007
The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [ VieillardBaron J. Chem. Phys. 56 4729 (1972); Perram and Wertheim J. Comput. Phys. 58 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals.
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06/01/2007
The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [ VieillardBaron J. Chem. Phys. 56 4729 (1972); Perram and Wertheim J. Comput. Phys. 58 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals.
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02/01/2000
The most frequently observed focal conic domains (FCD’s) in lamellar phases are those based on confocal paris of ellipse and hyperbola. Experimentally, the eccentricity of the ellipse takes a broad range of values 0<~eeisolated FCD reaches a minimum only at e⃗1 (under the constraint of a fixed major semiaxis of the ellipse); exceptions include situations with large saddlesplay elastic constant and small domains where the applicability of the elastic theory is limited. In realistic cases, a value of eccentricity smaller than 1 is stabilized by factors other than the curvature energy: by dislocations emerging from the FCD’s with e≠0, compression of layers and surface anchoring.
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01/21/2002
The critical divergence of the smecticorder correlation lengths parallel and perpendicular to the director, ξ∥,⊥, and the susceptibility, σ0, near the nematictosmecticA phase transition has been measured in a 5 T magnetic field. The high magnetic field reduced the mosaicity and improved the effective transverse resolution by almost 2 orders of magnitude and permitted measurements nearly over four decades of reduced temperature. The results provide important new insights into mosaicity correction. The values of the critical exponents of ξ∥,⊥ and σ0 were ν∥ = 0.79±0.02, ν⊥ = 0.68±0.02, γ = 1.45±0.04, respectively. They become smaller for a narrower nematic range.
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04/01/1998
The nematic (N) to lamellar (Lα) phase transition in binary mixtures of cesiumperfluorooctanoate (CsPFO) and water has been studied by highresolution synchrotron xray scattering at 46.6 weight % CsPFO. The longitudinal correlation length ξ∥ and the susceptibility σ associated with the lamellar phase fluctuations in the N phase, measured over three decades of reduced temperature, diverge with critical exponents ν∥=0.86±0.04 and γ=1.37±0.11, respectively. These results show that the N to Lα phase transition is quantitatively similar to the N to smecticA phase transition of thermotropic liquid crystals with a wider nematic range.
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04/15/1995
Two compounds of the 1(4’alkoxyphenylamino3[5’’(2’’menthylpirydil)]propen1one3 (PIRn) series that exhibit the hexaticB (HexB) to smecticA (SmA) and the crystalB (CryB) to HexB phase transitions were studied by high resolution ac calorimetry. The HexB–SmA phase transition was found to be of first order and continuous for PIR7 and PIR9, respectively. The tricritical point was located at the concentration for which TCryB–HexB/THexB–SmA =0.980±0.004, i.e., a hexatic range of 7 K. At both sides of the tricritical point, nonclassical and nonthreedimensionalXY specific heat exponents α were observed. The CryB–HexB phase transition was of first order and was associated with a small or immeasurable Cp anomaly.
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02/24/2011
Simultaneous and direct xray measurements of the smectic layer spacing, molecular tilt, and orientational order in the de Vries smectic A (SmA) and C (SmC) phases of two organosiloxane mesogens reveal that (i) the SmC (tilt) order parameter exponent beta = 0.26 +/ 0.01 for 2nd order SmASmC transitionin excellent agreement with the tricritical behavior, (ii) the siloxane and hydrocarbon parts of the molecules are segregated and oriented parallel to the director with very different degree of orientational order, and (iii) thermal evolution of the effective molecular length is different in the two phases.
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12/01/1994
Smallangle neutron scattering was employed to study the effect of shear flow on the nematic (N) and lamellar (L(alpha)) phases in aqueous solutions of cesium perfluorooctanoate. Shear rates as high as similar to 4000 s(1) were used. The N phase was found to align with the director in the direction of the gradient velocity. The L, phase oriented with lamellae parallel to the shear plane. This change in equilibrium orientation is attributed, primarily, to changes in the value of the Ericksen viscosity parameter at. Subtle shearratedependent director reorientations were also observed in the proximity of the NtoL(alpha) phase transition.
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11/15/2002
Previous studies of critical behavior at the nematic to smecticA transition by highresolution xray scattering were performed using low magnetic fields of 0.10.8 T. In those studies, the transverse resolution was limited by the sample mosaicity which complicated data analysis. In order to understand the effect of sample mosaicity on the measured values of critical exponents, the divergence of the smectic order correlation lengths xi(parallel to,perpendicular to) and susceptibility sigma(o) was studied in a magnetic field ranging from 0.25 to 5 T. The use of high (5 T) field reduced the sample mosaicity and improved the effective transverse resolution by almost two orders of magnitude. Three liquid crystals, two mixtures of 6th and 7th homologs of 4,4(')dialkylazoxybenzene (DnAOB) and 4noctylcyanobiphenyl (8CB) were studied. 15 wt% (D6.15AOB) and 40 wt% (D6.4AOB) mixtures of D7AOB in D6AOB have a wide nematic range, while 8CB has a narrow nematic range. Analysis of the data at different fields revealed a different and proper way to apply the mosaicity correction. The Gaussian mosaicity correction was found to be temperature independent but significantly (similar to3.5 times) smaller than the width of the sharpest q(perpendicular to)scan, which has traditionally been used for mosaicity correction in all previous studies. The values of the critical exponents measured over almost four decades of reduced temperature were: nu(parallel to)=0.79+/0.02, nu(perpendicular to)=0.69+/0.02, gamma=1.46+/0.04 for D6.15AOB; nu(parallel to)=0.79+/0.02, nu(perpendicular to)=0.67+/0.02, gamma=1.44+/0.04 for D6.4AOB; and nu(parallel to)=0.70+/0.02, nu(perpendicular to)=0.52+/0.02, gamma=1.24+/0.04 for 8CB. The results for the two mixtures suggest that in wide temperature range nematics, far from the tricritical point, the exponents may be material independent. No significant effects of mosaicity on the values of the coefficient c of the fourthorder term in the structure factor were observed.
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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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11/15/1997
Reentrant nematic phases and smectic antiphases occur as intermediate states between two onedimensionally ordered frustrated smectic phases, characterized by two competing and, in general, incommensurate smectic density waves. Using highresolution xray diffraction, we have examined the evolution of the two density waves as a function of temperature in all phases of a mixture of polar liquid crystals octyland decyloxyphenyl nitrobenzoyloxy benzoate (47.4 mol% DB8ONO2+52.6% DB10ONO2). This mixture exhibits at temperatures below 127 degrees C the liquidcrystal phase sequence: smecticA(d), reentrant nematic phases Nd and N1, smecticA(1), tilted antiphase (C) over tilde, smecticA(2), and smecticC2 phases. Detailed investigations of several orderdisorder transitions and the evolution of fluctuation effects in this system are reported.
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11/28/2011
A method of achieving homeotropic alignment of liquid crystals (LCs) by ultraviolet light induced phase separation of LC from its mixture with photocurable prepolymer is reported. Vertical polymer columns and microfibrils developed during the phase separation promote homeotropic alignment of the LC director (i.e., alignment perpendicular to the LCsubstrate interface), suitable for devices based on LCs possessing negative dielectric anisotropy. These vertical structures extend between two substrates and permit the fabrication of highly flexible electrooptical devices with high contrast coupled with fast response times. This simple singlestep technique eliminates the need for the traditional polymer alignment layer predeposited on substrates. (C) 2011 American Institute of Physics. [doi:10.1063/1.3663966]
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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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07/15/1991
The results of a highresolution xraydiffraction study of the smectic phases in mixtures of DB7OCN and 8OCB show that the incommensurate smecticAi2 phase, previously reported in this mixture, is in fact a coexistence of the partially bilayer smecticAd and the bilayer smecticA2phases at a firstorder phase transition between them.
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07/13/1992
The structure of frustrated smectic phases exhibited by binary mixtures of 4noctyloxyphenyl4'cyanobenzoyloxybenzoate (DB8OCN) and 4noctyloxybenzoate4'cyanoazobenzene (8OBCAB) have been studied by highresolution xray diffraction. This system was previously reported to exhibit three incommensurate smecticA phases. These incommensurate smectic A(i1) A(i2), and the soliton A(i2) phases are found to be coexistences of A(d) and A1; A(d) and A2; and A(d), A1, and A2 phases, respectively. As of now, there are no known incommensurate smecticA phases.
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10/01/2009
The dye sunset yellow (SY) forms columnar aggregates via ππ stacking in aqueous solutions. These aggregates develop orientational and translational order at elevated concentrations to exhibit the nematic (N) and columnar (C) mesophases. Positionalorder correlation lengths of the aggregates in the directions parallel and perpendicular to the stacking direction were measured as functions of temperature, concentration, and ionic content of solutions with synchrotron xray scattering in magnetically aligned samples. Average length of aggregates (i.e., the number of SY molecules in an aggregate) grows monotonically with concentration while their effective transverse separation decreases. The scission energy, E, determined from the Arrhenius thermal evolution of the longitudinal correlation length, is found to be 4.3±0.3 kBT and 3.5±0.2 kBT, in the N and C phases, respectively. Temperature and concentration dependence of E suggests that chromonic aggregation is not an isodesmic process. The aggregate length decreases with decreasing pH when HCl is added to the solution.
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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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01/01/2003
The first examples of achiral bentcore molecules consisting of an azo linkage and five aromatic rings exhibiting bentcore mesophases are reported. They exhibit B1 and B2 phases as identified by optical microscopy, differential scanning calorimetry, Xray diffraction, and electrooptical techniques. The B2 phase of these materials is identified to be the anticlinic–antiferroelectric, SmCAPA phase. The mesophases of these compounds have relatively low transition temperatures and wide temperature ranges. The observation of bentcore phases in azo compounds assumes significance from the fact that the introduction of the –NN– linkage adds a new dimension, namely photochromism, to this field.
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01/01/2006
A homologous series of shapepersistent Vshaped molecules has been designed to form the biaxial nematic phase. Phenyleneethynylene moieties are attached to a bent fluorenone unit to create an apex angle of about 90°, which is determined from the single crystal structure. Two mesogens, one symmetric and another unsymmetric, have been synthesized by attaching a cyano group to one or both of the peripheral phenyl units, respectively. These groups introduce local dipoles essential for the formation of the nematic phases. The tendency to form a crystalline phase is reduced by laterally substituted hexyloxy chains which allow the nematic phase to be supercooled to a glassy state. Two of the three fluorenone derivatives exhibit a transition from the uniaxial nematic to the biaxial nematic phase. This transition has an undetectably small transition enthalpy, but the Xray diffraction, polarizing optical microscopy, and conoscopy reveal the presence of the biaxial order in the low temperature nematic phase.
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04/01/2001
A novel method for liquid crystal alignment using insitu exposure to linearly polarized ultraviolet (LPUV) light during imidization of polyimide has been devised. The alignment layers prepared by this method exhibit higher thermal stability than the conventional method that employs LPUV exposure after imidization. Multidomain cells can be easily fabricated with the use of a photo mask and multistep insitu LPUV exposure during hard bake. With this method, it is also possible to generate pretilt angle using twostep LPUV exposure during imidization.
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02/16/1998
We explore the SaffmanTaylor instability of a gas bubble expanding into a shear thinning liquid in a radial HeleShaw cell. Using Darcy's law generalized for nonNewtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip splitting, and produce fingers which oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis.
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03/24/2003
We report on the development of a dilute suspension of ferroelectric particles in a nematic liquidcrystal(LC) host. We found that the submicron particles do not disturb the LC alignment and the suspension macroscopically appears similar to a pure LC with no readily apparent evidence of dissolved particles. The suspension possesses enhanced dielectricanisotropy, and is sensitive to the sign of an applied electric field.
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