Helicoidal structures liquid crystals

Liquid crystalline (LC) solutions of cellulose derivatives form chiral nematic (cholesteric) phases. Chiral nematic phases are formed when optically active molecules are incorporated into the nematic state. A fingerprint texture is generally observed under crossed polarizers for chiral nematic liquid crystals when the axis of the helicoidal structure is perpendicular to the incident light (Fig. 2). 

Cellulose and some derivatives form liquid crystals (LC) and represent excellent materials for basic studies of this subject. A variety of different structures are formed, thermotropic and lyotropic LC phases, which exhibit some unusual behavior. Since chirality expresses itself on the configuration level of molecules as well as on the conformation level of helical structures of chain molecules, both elements will influence the twisting of the self-assembled supermolecular helicoidal structure formed in a mesophase. These supermolecular structures of chiral materials exhibit special optical properties as iridescent colors, and... 

In the most simple chiral polar tilted smectics, ferroelectric liquid crystals, the flexoelectric phenomenon influences the structure of the SmC phase only quantitatively. It affects the elastic and chiral couplings and consequently slightly changes the transition temperature to the tilted phase and the pitch of the helicoidal modulation. 

The ferroelectric smectics C and H are the only liquid-crystal phases with a polar structure that should make possible in them second-harmonic generation (SHG) via the quadratic nonlinearity Up to now, only nonsynchron-ous SHG was reported in a ferroelectric liquid crystal (LC). - We present here the results of an investigation of phase-synchronous SHG in the ferroelectric phase C with untwisted helicoid. The investigated substance was /7-decy-loxybenzylidene-/7-amino-2-methylbutylcinnamate (DO-MAMBC). 

Since chiral nematic liquid crystals phases have a very similar structural morphology i.e. rod-like molecules with a rotating director), the method developed to describe chiral nematic liquid crystals can be applied to the case of a solid helicoidal film. This method examines the electromagnetic response of materials with screw-like rotating electrical axes. The use of... 

In the beetle Chrysina gloriosa, left-handed green colour reflection is observed from the exoskeleton, but without colour variation, and patterns are structurally and optically analogous to the focal conic domains formed spontaneously on the free surface of a cholesteric liquid crystal. More sophisticated helicoidal structures can be found in Plusiotis resplendens. The latter species is capable of reflecting both left and right circularly polarised light. In contrast to Pallia condensate, the right-handed circular... 

The constituent parts that form liquid crystals can exist over a wide range of sizes, from molecules to colloids. At each size scale different forces control the interactions of the liquid crystal constituents, but the principles of liquid crystalline formation remain the same. In order to understand the use of liquid crystals in biomimetic structural colour for helicoidal architectures, a brief introduction into the huge and varied field of liquid crystals is given here. 

Using self-assembly of a chiral nematic phase in a biopolymer liquid crystal of cellulose nanociystals, a well-controlled technique has been developed to create solid helicoidal architectures for structural colour and for further functionalisation. This section describes the self-assembly process and the control parameters of tuneable helicoidal cellulose films, and the prospects for future development. 

G. Chilaya, Physical properties and applications of liquid crystals with induced helicoidal structure, Metsniereba, Tbilisi, 1985 (in Russian). 

The occurrence of ferroelectricity in the chiral smectic C phase was already predicted by Meyer in 1975 [21]. From symmetry arguments, he concluded a polarization of a smectic layer perpendicular to the layer normal and to the director. Unwinding of the helicoidal structure causes macroscopic ferroelectric properties of the phase [22], [23]. Unlike low molar mass liquid crystals or linear liquid crystal polymers, the unwinding of the helicoidal structure is performed by applying an electric field or by surface effects. 

One optical feature of helicoidal structures is the ability to rotate the plane of incident polarized light. Since most of the characteristic optical properties of chiral liquid crystals result from the helicoidal structure, it is necessary to understand the origin of the chiral interactions responsible for the twisted structures. The continuum theory of liquid crystals is based on the Frank-Oseen approach to curvature elasticity in anisotropic fluids. It is assumed that the free energy is a quadratic function of curvature elastic strain, and for positive elastic constants the equilibrium state in the absence of surface or external forces is one of zero deformation with a uniform, parallel director. If a term linear in the twist strain is permitted, then spontaneously twisted structures can result, characterized by a pitch p, or wave-vector q=27tp i, where i is the axis of the helicoidal structure. For the simplest case of a nematic, the twist elastic free energy density can be written as ... 

From the above it is clear that the optical response of helicoidal structures of liquid crystal molecules depends on the pitch, and in order to relate these optical properties to molecular structures, the dependence of pitch on molecular structure must be considered. 

The dramatic variation of liquid crystalline properties with respect to temperature has resulted in the widespread use of cholesteric (chiral nematic) liquid crystals for thermography. The property that has been exploited most in liquid crystal thermography is the critical temperature dependence of the selective reflection from cholesteric liquid crystals, though other temperature dependent properties of mesophases have been utilized (e.g. the birefringence of nematic systems and selective reflection from other chiral phases). The helicoidal structure of cholesteric materials results in the selective reflection of visible light within a band of wavelengths of width AX, centered at a wavelength Xq, such that ... 

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