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1.
We study the director field around a spherical particle immersed in a uniformly aligned nematic liquid crystal and assume
that the molecules prefer a homeotropic orientation at the surface of the particle. Three structures are possible: a dipole,
a Saturn-ring, and a surface-ring configuration, which we investigate by numerically minimizing the Frank free energy supplemented
by a magnetic-field and a surface term. In the dipole configuration, which is the absolutely stable structure for micron-size
particles and sufficiently strong surface anchoring, a twist transition is found and analyzed. We show that a transition from
the dipole to the Saturn ring configuration is induced by either decreasing the particle size or by applying a magnetic field.
The effect of metastability and the occurrence of hysteresis in connection with a magnetic field are discussed. The surface-ring
configuration appears when the surface-anchoring strength W is reduced. It is also favored by a large saddle-splay constant K24. A comparison with recent experiments [#!itapdb:Poulin1997!#,#!itapdb:Poulin1998!#] gives a lower bound for W, i.e., for the interface of water and pentylcyanobiphenyl (5CB) in the presence of the surfactant sodium dodecyl sulfate.
Received 2 November 1998 相似文献
2.
The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρs ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρs), the interface thickness κ(T,ρs), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4′- cyanobiphenyl and 4-n-heptyl- 4′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1 相似文献
3.
Inclusions in free-standing smectic films are simple model systems for two-dimensional anisotropic dispersions. From theory
and experiment, different topologies of elastic distortions of the embedding liquid crystal are known. Quadrupolar and different
dipolar defect configurations in the vicinity of the inclusion are possible, and these configurations determine the type of
interactions between the inclusions. The quadrupolar configuration is often energetically preferred. We show, however, that
dipolar director configurations around inclusions can be energetically favourable over quadrupolar arrangements in chiral
smectics, as a consequence of a spontaneous-bend term in the elastic-energy formulation. As the inclusion size influences
the selection of the deformation types, the corresponding spontaneous-bend constant can be estimated for the strong anchoring
limit if the c -director fields around inclusions of different diameters are taken into account. 相似文献
4.
H. Stark J. Stelzer R. Bernhard 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(3):515-523
Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a
point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes
a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For
such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental
observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets,
but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order
phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two
boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a
defect between them.
Received 11 December 1998 相似文献
5.
We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 ⩽ x0 ⩽ 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x0 considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x0. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement. 相似文献
6.
We investigated SmC* films sandwiched between silane coated glass plates and observed formation of textures exhibiting a uniform tilt of the smectic
layers with respect to the boundary plates. The layer tilt angle increases from zero to as the sample is cooled from the smectic A phase to room temperature. These films show linear electro-optical effects because
the permanent polarization can be aligned so that it has a component parallel to the applied field without changing the layer
structure. Our analysis indicates that mainly two effects determine the layer tilt. On the one hand, the surface tension tends
to minimise the layer tilt. On the other hand, the surface energy promotes the director to be normal to the boundary plates.
Received 17 July 1998 相似文献
7.
Sebastião PJ Simeão Carvalho P Chaves MR Nguyen HT Ribeiro AC 《The European physical journal. E, Soft matter》2006,20(1):55-61
We present a polarising optical microscopy study of the low-temperature anticlinic-like tilted mesophase of the liquid-crystal
compound octylphenyl-2-chloro-4-(p-cyano-benzoyloxy) (DB8Cl). This mesophase has been described as a bilayer smectic structure in which the molecules within each layer are organised
in an anticlinic way. The optical textures observed in samples with planar orientation show a double stripe pattern, with
the lines aligned parallel to the rubbing direction, characteristic of a double periodic modulation of the refractive index
of the material. The long-period modulation is temperature dependent and disappears for thin sample cells (< 5μm). The short-period
modulation is nearly independent of the thickness of the cells. The experimental results are analysed in terms of a model
which considers that there is a special distribution of the principal optical axis which may be in or out of the polariser-analyser
plane. The observed periodic variation of the principal optical axis could not be interpreted in terms of the original structure
proposed for this phase. DB8Cl presents a structure formed by dimers that can be viewed as flexible bent-core-like molecules, showing similarities with
phases found in banana-like systems, but exhibiting a much more complex structure. 相似文献
8.
9.
We present a simple coarse-grained lattice model for monodomain biaxial liquid-crystal elastomers and perform large-scale
Monte Carlo simulations in the proposed model system. Orientational ordering --uniaxial or biaxial-- reflects in sample deformations
on cooling the system. The simulation output is used to predict calorimetry data and deuterium magnetic resonance spectra. 相似文献
10.
The formation of regular colloid patterns in free-standing smectic films at the transition from the smectic-C to the isotropic
or nematic phase is well known experimentally. The self-organization of isotropic or nematic droplets is caused by their mutual
interaction, mediated by elastic distortions of the local director in the surrounding liquid crystal. These distortions are
related to the anchoring conditions of the director at the droplet border. We describe analytically the energetics of the
liquid crystal environment of a single droplet in one-constant approximation. A method of complex analysis, Conformal Mapping,
is employed. Following a suggestion of Dolganov et al. (Phys. Rev. E. 73, 041706 (2006)), energetics of chain and grid patterns built from the colloids are investigated numerically in order to explain
experimentally observed formations and their director fields. 相似文献
11.
Light traveling through a liquid crystal with disclinations perceives a geometrical background which causes lensing effects
similar to the ones predicted for cosmic objects like global monopoles and cosmic strings. In this paper we explore the effective
geometry as perceived by light in such media. The comparison between both systems suggests that experiments can be done in
the laboratory to simulate optical properties, like gravitational lensing, of cosmic objects. 相似文献
12.
We study numerically the director and orientational order parameter configurations in a nematic liquid crystal around a two-dimensional
spherical particle on the basis of the tensor order parameter formalism. To properly account for the large length scale difference
between the particle and the accompanying orientational defect, we devise an adaptive grid scheme in which the lattice spacing
is automatically and locally adjusted in response to the spatial gradient of the orientational order parameter. This adaptive
grid scheme is useful in studying dynamical as well as static orientational structures. We present a simulation result which
shows how a hedgehog defect of topological charge -1 becomes unstable in two dimensions, and splits into a defect pair of
topological charge -1/2, located symmetrically around the particle.
Received 14 September 2000 and Received in final form 27 December 2000 相似文献
13.
We study numerically the effect of an external magnetic or electric field on the director profiles of a nematic liquid crystal
around a spherical particle. We pay particular attention to the stability of a hyperbolic hedgehog defect accompanying the
particle, which transforms into a Saturn-ring defect encircling the particle under a sufficiently strong external field. We
focus on the particle size dependence of the two important threshold field strengths: the “thermodynamic-transition” field
strength H1 at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H2 at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H1 is non-monotonically dependent on the particle radius R0, H2 monotonically increases with R0 and the dependence of H2 is weak for large R0. The non-monotonic dependence of H1 on R0 can be explained by comparing the energies of the two configurations and assuming the dependence of those energies on a rescaled
field. A crude argument of the energetics of a hyperbolic hedgehog defect under an external field shows that for an asymptotically
large R0 the critical field strength is independent of R0, which agrees with our numerical finding. 相似文献
14.
N.J. Mottram S.J. Elston 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,12(2):277-284
We have theoretically investigated chevron formation in smectic C materials and the transformation of this chevron structure to a tilted layer structure as the cell is sheared. We find a
series of transition temperatures at which the behaviour of the cell critically changes. As the cell is cooled from the smectic
A phase past the first critical temperature there is a second order transition which forms two tilted layer states with lower energy than the smectic A bookshelf structure. Although these low energy tilted structures exist the bookshelf structure is the stable state for zero
shear. However, upon further cooling this bookshelf structure becomes unstable to the formation of a chevron state. Now when
the cell is sheared the chevron structure smoothly transforms into the tilted layer structure. As each further critical temperature
is passed an additional multiple chevron solution is formed which although a high energy, unstable state may be observed transiently. For sufficiently low
temperatures the transition from chevron to tilted layer becomes first order. This first order transition occurs as the chevron
interface merges with the surface alignment region to form the tilted layer structure.
Received 28 December 1998 and Received in final form 8 April 1999 相似文献
15.
16.
We present a study of the effect of weak anchoring on the transition between C1 and C2 chevron structures in smectic-C liquid
crystals. The coexistence of C1 and C2 chevron structures within a single cell causes zigzag defects to occur and may affect
the optical characteristics of the cell. By standard Euler-Lagrange minimisation of the total energy of the system, we obtain
analytical expressions for the equilibrium director cone angle in the two chevron states. These in turn allow us to compare
the total energies of the states and determine the globally stable chevron profile. We show that analytical predictions for
the critical transition temperature, which depends on anchoring strength and pretilt angle, are in good agreement with those
obtained numerically. 相似文献
17.
A cholesteric imprinted elastomer was obtained by cross-linking a nematic side-chain polysiloxane around a chiral template. The template was first linked to some functionalised groups of the polymer via hydrogen-bound interactions, then was removed by washing. The sample was macroscopically oriented during the synthesis; so, both a molecular chirality and a supramolecular phase chirality were topologically imprinted inside the network. Batch rebinding experiments, performed in the presence of the template or of the other enantiomer, showed that the imprinted polymer has a pronounced stereo-selectivity towards the template enantiomer. The rebinding capacity appeared to be greater than an unimprinted mesogenic network as well as than an imprinted non mesogenic one. 相似文献
18.
Fukuda J 《The European physical journal. E, Soft matter》2007,24(1):91-98
It was shown experimentally (P.V. Dolganov et al., Europhys. Lett. 76, 250 (2006)) and by numerical calculations (C. Bohley, R. Stannarius, Eur. Phys. J. E 23, 25 (2007)) that the c -director profile of a two-dimensional chiral smectic-C (SmC) film around a circular inclusion adopts dipolar rather than
quadrupolar configuration observed in achiral SmC films. We give an analytical argument on how spontaneous bend inherent in
chiral SmC liquid crystals influences the configuration of a SmC liquid crystal film around a circular inclusion imposing
tangential anchoring. We find how the angle α between two surface defects seen from the center of the inclusion depends on
the radius of the inclusion R and the strength of the spontaneous bend q . We show, however, that the contribution of the spontaneous bend to the free energy suffers from mathematical ambiguity;
it depends on the mathematical treatment of the outer boundary even when it is at infinity. This might indicate that the shape
as well as the treatment of the outer boundary of the film can significantly influence the equilibrium configuration of the
c -director and the position of the surface defects. 相似文献
19.
We study the role of dislocation loops defects on the elasticity of lamellar phases by investigating the variation of the
lamellar elastic constants, ˉ and K, induced by the proliferation of these defects. We focus our interest on one particular lamellar phase made up of a mixture
of C12E5 and DMPC in water, which is already well-characterised. This lamellar phase undergoes a second-order (or weakly first-order)
lamellar-to-nematic phase transition at about 19°C and dislocation loops are seen to proliferate within the lamellar structure when temperature is decreased below 30°C. The values of both elastic constants of this given lamellar phase are measured as a function of temperature, approaching
the lamellar-to-nematic transition, with the help of Quasi-Elastic Light Scattering (QELS) on oriented lamellar phases. Very
surprisingly we observe a strong and rapid increase in both ˉ and K as the lamellar-to-nematic transition temperature is approached. These increases are seen to start as soon as dislocation
loops can be observed in the lamellar phase. We interpret our results as being the consequence of the appearance and proliferation
of dislocation loops within the lamellar structure. According to a simple model we developped we show that ˉ and K are proportional to the density of dislocation loops in the lamellar phase. 相似文献
20.
The Frank elasticity constants which describe splay (K
1), twist (K
2), and bend (K
3) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations
rest on statistical-mechanical approaches where the absolute values of K
i
(i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined
using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was
obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants
were employed based on different level of approximation about the orientational order and molecular correlations. The best
agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution
function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors
in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the
DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution
is observed for short intermolecular distances.
Received 22 March 2000 and Received in final form 9 June 2000 相似文献