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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