Stereo-selective swelling of imprinted cholesteric networks

Molecular chirality, and the chiral symmetry breaking of resulting macroscopic phases, can be topologically imprinted and manipulated by cross-linking and swelling of polymer networks. We present a new experimental approach to stereo-specific separation of chiral isomers by using a cholesteric elastomer in which a helical director distribution has been topologically imprinted by cross-linking. This makes the material unusual in that is has a strong phase chirality, but no molecular chirality at all; we study the nature and parameters controlling the twist-untwist transition. Adding a racemic mixture to the imprinted network results in selective swelling by only the component of "correct" handedness. We investigate the capacity of demixing in a racemic environment, which depends on network parameters and the underlying nematic order.     

Light-induced instabilities driven by competing helical patterns in long-pitch cholesterics

We study theoretically the dynamical reorientation phenomena when a long-pitch cholesteric liquid-crystal film with homeotropic alignment is illuminated by a circularly polarized lightwave. In the present case, the natural cholesteric pitch is of the order of (or larger than) the film thickness. The helical cholesteric structure is thus frustrated by the boundary conditions without illumination. However, above a light intensity threshold reorientation occurs and the bifurcation scenario depends strongly on the natural cholesteric pitch. Recalling that a long-pitch cholesteric is achieved in practice by adding a small amount of chiral agents in a nematic liquid crystal, the observed dynamics can be viewed as the result of the competition between intrinsic and extrinsic unidimensional helical patterns. The intrinsic part consists of the helical deformations induced by the chirality of the dopant, whereas the extrinsic part is related to the chirality induced by the optical field through the non-uniform angular momentum transfer of light to a nematic. The all-optical analog in the case of a pure nematic (without chiral dopant), is also discussed.     

The role of Frank elasticity in cholesteric elastomers

The effect of Frank elasticity on deformations of cholesteric elastomers by mechanical stress applied perpendicular to the helix axis is studied by numerical minimization of the free energy. Above a critical strain, a solution with an only oscillating director is found to be stable in comparison to a distorted helix. At the critical strain, the contractions perpendicular to stress change discontinuously. The critical strain is found to increase with increasing Frank elasticity contribution to the free energy density, and to diverge when the conformation anisotropy of the polymer backbone vanishes. The results are compared with recent experiments which indicated that, in case of weak conformation anisotropies, the Frank elasticity contribution to the free energy cannot be neglected.     

Chiral molecular imprinting in liquid-crystalline network<Superscript>⋆</Superscript>

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.     

Theory of chiral imprinting

We present a continuum model for a nematic elastomer network formed in a chiral environment, for instance, in the presence of a chiral solvent. When this environment is removed, the network can retain some memory of its chiral genesis. We predict the residual chiral order for a number of possible scenarios, and examine the robustness (stability) of the imprinted chirality. We show that a twist-untwist transition can take place, which determines whether the imprinting has been successful. A transition is via a coarsening of the helical director pattern and a lengthening of its pitch. Finally, the effect due to a subsequent swelling by an achiral solvent, or by a solvent of differing chirality, is considered.     

Nonlinear “brightening” of a film of nonabsorbing chiral nematic under selective reflection conditions

A strong decrease in the reflection coefficient of a film of a nonabsorbing chiral nematic (cholesteric) is observed experimentally in the region of selective reflection under the action of a powerful beam of circularly polarized light. The independence of the effect from the average power density (and its dependence only on the peak power density) allow it to be attributed to an increase in the pitch of the cholesteric helix to such a degree that it is completely unwound, an effect previously observed only in static and low-frequency electric and magnetic fields, in the strong field of the light wave. These are the first experiments in which, on account of the specially chosen irradiation conditions, the changes produced in the pitch of the helix by the field of the light wave can accumulate over time, so that a nonthermal mechanism can be invoked to explain the nonlinear brightening of a mirror made of a chiral nematic. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 403–407 (25 March 1996)     

Cholesteric–nematic transitions induced by a shear flow and a magnetic field

The untwisting of the helical structure of a cholesteric liquid crystal under the action of a magnetic field and a shear flow has been studied theoretically. Both factors can induce the cholesteric–nematic transition independently; however, the difference in the orienting actions of the magnetic field and the shear flow leads to competition between magnetic and hydrodynamic mechanisms of influence on the cholesteric liquid crystal. We have analyzed different orientations of the magnetic field relative to the direction of the flow in the shear plane. In a number of limiting cases, the analytic dependences are obtained for the pitch of the cholesteric helix deformed by the shear flow. The phase diagrams of the cholesteric–nematic transitions and the pitch of the cholesteric helix are calculated for different values of the magnetic field strength and the angle of orientation, the flow velocity gradient, and the reactive parameter. It is shown that the magnetic field stabilizes the orientation of the director in the shear flow and expands the boundaries of orientability of cholesterics. It has been established that the shear flow shifts the critical magnetic field strength of the transition. It is shown that a sequence of reentrant orientational cholesteric–nematic–cholesteric transitions can be induced by rotating the magnetic field in certain intervals of its strength and shear flow velocity gradients.     

Untwisting of a cholesteric elastomer by a mechanical field

A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There are similarities with the classical problem of an electric field applied to a cholesteric liquid crystal but also differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is between the director being helically anchored to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis.     

Nematic ordering in anisotropic elastomers: Effect of frozen anisotropy

Nematic ordering in anisotropic non-Gaussian elastomers is considered theoretically using mean field approximation. We focus on the effect of anisotropy during network cross-linking on the system elasticity and, in particular, on the so-called soft deformation mode. As the main result, we calculate the dependence of the elastomer free energy on the angle between the axis of “frozen” anisotropy and the nematic director. The dependence of the isotropic-nematic transition point on the orientational field acting on the monomers during the cross-linking process is also calculated. Received: 5 November 1997 / Revised and Accepted: 29 June 1998     

Strongly anisotropic elastic moduli of nematic elastomers: Analytical expressions and nonlinear temperature dependence

Exact formulae for the elastic moduli of the nematic elastomers are obtained by the implicit function method based on somewhat general energy functions. The formulae indicate that both the moduli parallel and perpendicular to the director of the nematic elastomers are smaller than the modulus of the classical elastomers because of the mechanical-nematic coupling. Moreover, the moduli are generally anisotropic due to the biaxiality induced by stretching the nematic elastomers perpendicular to the director. Then we get the explicit analytical expressions of the parallel and perpendicular moduli by making use of the Landau-de Gennes free energy and the neo-classical elastic energy. Very different from the classical elastomers, they are both strongly nonlinear functions of the temperature in the nematic phase. Furthermore, their ratio, the degree of anisotropy, changes with the temperature as well. The results agree qualitatively with some experiments. Better quantitative agreement is obtained by some modifications of the constitutive relation of the elastic energy.     

Phase chirality and stereo-selective swelling of cholesteric elastomers

Cholesteric elastomers possess a macroscopic phase chirality as the director rotates in a helical fashion along an optical axis z and can be described by a chiral order parameter . This parameter can be tuned by changing the helix pitch p and the elastic properties of the network at formation. The cholesterics also possess a local nematic order, changing with temperature or during solvent swelling. In this paper, by measuring the power of optical rotation , we discover how these two parameters vary as functions of temperature or solvent adsorbed by the network. The main result is a finding of pronounced stereo-selectivity of cholesteric elastomers, demonstrating itself in the retention of the correct chirality component of a racemic solvent. It has been possible to quantify the amount of such stereo-separation, and the basic dynamics of the effect.Received: 18 August 2003, Published online: 5 February 2004PACS: 33.55.Ad Optical activity, optical rotation; circular dichroism - 61.30.Vx Polymer liquid crystals - 87.80.Pa Morphometry and stereology     

Field-temperature phase diagrams in chiral tilted smectics,evidencing ferroelectric and ferrielectric phases

Usual ferroelectric compounds undergo a paraelectric-to-ferroelectric phase transition when the susceptibility of the electric polarization density changes its sign. The temperature is the only thermodynamic field that governs the phase transition. Chiral tilted smectics may also present an improper ferroelectricity when there is a tilt angle between the average long axis direction and the layer normal. The tilt angle is the order parameter of the phase transition which is governed by the temperature. Although the electric susceptibility remains positive, a polarization proportional to the tilt appears due to their linear coupling allowed by the chiral symmetry. Further complications come in when the chirality increases, as new phases are encountered with the same tilt inside the layers but a distribution of the azimuthal direction which is periodic with a unit cell of two (SmC(A)*, three (SmC(Fi1)*, four (SmC(Fi2)* or more (SmC(alpha)* layers. In most of these phases, the layer normal is a symmetry axis so there is no macroscopic polarization except for the SmC(Fi1)* in which the average long axis is tilted so the phase is ferrielectric. By studying a particular compound with only a SmC(Fi2)* and a SmC(alpha)* phase, we show that we recover the uniformly tilted ferroelectric SmC* when applying an electric field. We are thus led to build field-temperature phase diagrams for this class of compounds by combining different experimental techniques described here.     

Phase transition in liquid crystal elastomers—A Monte Carlo study employing non-Boltzmann sampling

We investigate nematic-isotropic transition in liquid crystal elastomers employing a variant of Wang-Landau sampling. This technique facilitates calculation of the density of states from which other thermodynamic properties can be obtained. We consider a lattice model of a liquid crystal elastomer and a Hamiltonian which accounts for interactions among liquid crystalline units and interaction of local nematics with global strain. We investigate the effect of varying the strength of coupling between nematic and orientational degrees of freedom. When the local director is coupled strongly to the global strain, the transition is strongly first order. When the strength of the coupling decreases the transition becomes weakly first order. The transition temperature decreases when the coupling becomes weaker. We also report for the first time results on variation of free energy as a function of average energy at different temperatures and coupling constants.     

The elastic anisotropy of nematic elastomers

We examine the robustness of order in nematic elastomers under mechanical strains imposed along and perpendicularly to the director when director rotation is prohibited. In contrast to electric and magnetic fields applied to conventional nematics, mechanical fields are shown theoretically and experimentally to greatly affect the degree of nematic order and related quantities. Unlike in liquid nematics, one can impose fields perpendicular to the director, thereby inducing biaxial order which should be susceptible to experimental detection. Nematic elastomers with unchanging director and degree of order should theoretically have the same elastic moduli for longitudinal and transverse extensions. This is violated when nematic order is permitted to relax in response to strains. Near the transition we predict the longitudinal modulus to be smaller than the transverse modulus; at lower temperatures the converse is true, with a crossover a few degrees below the transition. The differences are ascribed to the different temperature dependence of the stiffness of uniaxial and biaxial order. We synthesised side chain single-crystal nematic polymer networks, performed DSC, X-ray, birefringence, and thermo-mechanical characterisations, and then obtained linear moduli from stress-strain measurements. Received 29 September 2000     

铁电液晶螺旋结构的理论近似研究

由铁电液晶（FLC）手性近晶C相下螺旋结构的理论近似计算得出FLC一个螺距内平均折射率的表达式,根据表达式可得出一个螺距内的FLC分子作为一个整体可以看成一个向列相液晶分子模型的结论.当FLC沿螺旋轴方向的厚度等于FLC螺距的整数倍时,液晶盒内垂直取向的FLC分子可看作向列相液晶模型组成的集合.ZLI-3654型FLC与5CB型向列相液晶的实验结果验证了上述结论,理论结果和实验结果一致.这一理论可为畸变螺旋FLC和垂直排列畸变螺旋FLC器件的制备以及FLC的应用提供理论指导和更深的认识. 关键词： 铁电液晶 螺距 平均折射率 向列相液晶     

Elastic energies for nematic elastomers

We discuss several elastic energies for nematic elastomers and their small strain expansions both in the regime of large director rotations, and in the case that director changes are small. We propose two fully non-linear model anisotropic energies and compare the behavior they predict with the currently available experimental evidence.     

Nematic ordering in a cell with modulated surface anchoring: effects of flexoelectricity

We have analyzed molecular ordering in a nematic sample sandwiched between two parallel substrates, characterized by a periodically varying anchoring easy axis. If the periodicity lambda is smaller than the Debye screening length l(D) and the nematic material possesses flexoelectric properties, it is necessary to take into account also the electrostatic and flexoelectric contributions in the thermodynamical potential when the actual director field is determined. In this framework, for small deviations from the homeotropic alignment we have derived analytical expressions for the tilt angle (theta) and the electrical potential. To establish a connection with experimentally observable quantities, we have related the theta profile to the average and investigated its behavior for different values of lambda, the flexoelectric coefficient, and the anchoring strength w. Our results indicate that in a nematic with pronounced flexoelectric properties for small enough lambda, a kind of subsurface deformation appears, which substantially decreases . Therefore, effects of flexoelectricity cannot be neglected in treating nematic cells with modulated anchoring which allows bistable ordering.     

Structural and optical investigations of TGBA and TGBC mesophases exhibiting cylindrical and cone-like domain textures

The characterization by optical microscopy, X-ray diffraction and differential scanning calorimetry of two new liquid crystalline compounds is presented. The compounds under consideration incorporate in their molecules two chiral centres (one asymmetric carbon and one asymmetric sulphur of a sulphinate group). While the carbon chirality is fixed in the R configuration the sulphur chirality may be either in the S or in the R configuration. A mesophase in a large temperature domain is evidenced for one of the two diastereomers, while both and mesophases are observed in a similar temperature domain for the other one. For both diastereomers and in both mesophases it is possible to observe the coexistence of two different types of optical textures, namely planar cholesteric textures and developable domains. The latter are coiled in a different way than proposed in an earlier publication. More precisely, they form cylindrical or cone-like domains with double-twist properties as observed in the blue phases. The pitch of the helix in the TGB mesophases is evaluated by means of optical reflection observations in samples exhibiting the planar cholesteric textures. For both diastereomers it is also possible to evaluate structural parameters related to the organization within the mesophases. Finally, the induced phase transition - is studied by the application of an AC electric field. Received: 16 June 1997 / Revised: 17 October 1997 / Accepted: 20 November 1997