Spontaneous twist

Chiral nematic Hquid crystals are sometimes referred to as spontaneously twisted nematics, and hence a special case of the nematic phase. The essential requirement for the chiral nematic stmcture is a chiral center that acts to bias the director of the Hquid crystal with a spontaneous cumulative twist. An ordinary nematic Hquid crystal can be converted into a chiral nematic by adding an optically active compound (4). In many cases the inverse of the pitch is directiy proportional to the molar concentration of the optically active compound. Racemic mixtures (1 1 mixtures of both isomers) of optically active mesogens form nematic rather than chiral nematic phases. Because of their twist encumbrance, chiral nematic Hquid crystals generally are more viscous than nematics (6). 

Spontaneously twisted nematics, 15 92 Spontaneous polarization, in compound semiconductors, 22 152 Spontaneous polymerization ofVDC, 25 695... 

Aromatic amines are not the only type of molecule to undergo a spontaneous twist in the excited state, but DMABN is the best-studied example. Other such compounds are stilbene-type molecules, where the double bond twists in the excited state. The electronic structure for both cases, twisting double bonds and twisting single or partly double bonds of 7r-donor linked to 7r-acceptor (TICT molecules), can be related to each other and characterized in the framework of quantum-chemical treatment as described in Section III. 

The cholesteric liquid, which is a spontaneously twisted nematic, behaves like a negative uniaxial crystal, so that light vibrating perpendicular to the molecular layers shows maximum velocity. Linearly polarized light transmitted perpendicular to the molecular layers shows rotation of its electrical vector along a helical path. 

We now consider defect structures in the cholesteric liquid crystal. Treating the cholesteric as a spontaneously twisted nematic,... 

As we shall see further on, the terms linear in dnjdx, allow us to discuss not only conventional nematics with Dooh symmetry but also some biased nematic phases. For example, we can discuss the phases with a spontaneous twist (cholesterics with broken mirror symmetry) or a spontaneous splay (uniaxial polar nematics with broken head-to-tail symmetry, n -n). For a standard nematic only quadratic terms will remain. 

It is reasonable to assume that the hne shapes shown in Fig. 13 reflect the presence of helical structures in cholesteric LCs even in the strong magnetic field, and it can safely be assumed that the helical structure directions were perpendicular to the magnetic field, as proposed by Meyer [14]. At first, Eq. (18), in which uniaxial rotation is assumed, was used to simulate the hne shapes in Fig. 13. According to the field effect on cholesteric LCs, in which, macroscopically, cholesteric LCs are spontaneously twisted nematics, Eq. (18) was integrated in terms of / l, which should have provided the pseudo-line shapes of helical structures in the magnetic field. However, it was very difficult or nearly impossible to reasonably reproduce the experimental line shape with our analysis. Therefore, the concept of biaxiality for... 

In addition to the effect of the surface interaction, smectic C liquid crystals prefer to form a spontaneous twist and bend form of the director based on the chiral properties. Although the helix is suppressed by the substrate surfaces, the... 

For the spirally wound fibre composite tube of Problem 6.10. estimate the coefficients of linear thermal expansion parallel to and perpendicular to the fibres. If the temperature of the tube were raised from 20 C to 50 C, show that it would spontaneously twist, and predict the relative rotation of the ends of the tube. Also predict the changes in length and diameter. 

Observation of the electrospun fibers by means of scanning electron and atomic force microscopies showed that the electrospxm fibers exhibited a spontaneous twist along the fiber axis that is not present in fibers electrospxm from the isotropic phase. Fibers with a twist are shown in Figxires 8.13 and 8.14. 

V. M. Pergamenshchik, Surfacelike-elasticlty-induced spontaneous twist deformations and long-wavelength stripe patterns in a hybrid nematic layer, Phys. Rev. E, 47,1881 (1993]. 

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 ... 

The analog of the magnetic intensity H (produced by external currents) would be an external field coupled to the two components of curl n. A local microscopic source of bend [23] is not easy to imagine. On the other hand, chirality is naturally coupled to twist chiral mesogens develop a spontaneous twist in the nematic phase. The cholesteric is thus analogous to a normal metal in a magnetic field. 

Experiments show that the introduction of chirality (chiral mesogen or chiral dopant) in a nematic phase generates a spontaneous twist of the director, n = (cos27Cz/P, sin 2 nz IP, 0) for instance for a helical twist of pitch P along the direction z. The higher the chirality (i.e. fraction of chiral dopant for instance), the higher the twist (i.e. the shorter the pitch). It is thus clear that twist is a structural response coupled to the microscopic constraint chirality. How can these two physical quantities be linked in a quantitative way The covariant expression of the local twist, commonly used in the... 

The purely orientational order of nematics leads to discontinuities that are discrete structures in the form of points and thin threads. Continuous defects also exist, but some of these cannot be deformed continuously into the monocrystal and therefore should be classified as genuine defects. The presence of a spontaneous twist in a nematic liquid facilitates such situations, the main example being that of thick threads forming interlocked rings [48, 49, 53,73],... 

The spontaneous twist in the cholesteric phase, in particular the field-induced nematic-cholesteric transition, can be exploited for the experimental determination of the twist constant [61, 62]. 

If we insert the new twist term according to Eq. (116) into Eq. (96), the free energy attains its minimum value for nVxn=-q if splay and bend are absent (the cholesteric ground state). It means that we have a spontaneous twist in the ground state. This is connected to the fact that we now have a linear term in the free energy. For, if we expand the square in the twist term we could write the free energy as... 

In the same way, if we expand the bend term (Eq. 117) we get the linear term -K B [nx(Fx i)] in the free energy. With both these linear terms present, the liquid crystal thus has both spontaneous twist and spontaneous bend. 

The new chiral terms are of first order and therefore describe spontaneous deformations. The Dj term means that there is a tendency for the c-vector to bend in the plane of the layer, which means that a coupled ferroelectric polarization (see next chapter) will have a tendency for a spontaneous splay. The D3 term is a spontaneous twist, describing the helical order of the SmC ground state. In the ground state, there is a pure twist in c. This means that c-Vxc = -q, and consequently,/c Vxc = 0. This reduces (4.60) near the equilibrium to ... 

All these terms are easy to interpret. The term expresses the fact that there is a spontaneous bend Dj/Bj in this plane. The second term describes the splay. It does not couple to other deformations, and there is no spontaneous splay. The third term describes the twist between c in successive layers and recalls the fact that in a chiral material there is a spontaneous twist equal to -D3/B3. Finally, the cross term, Bjj, describes the bend-twist coupling. 

There is one pecularity concerning the helix structure which should be mentioned. In contrast to the cholesteric helix, the chiral smectic C helix contaim a spontaneous bend in addition to the spontaneous twist (7]. This leads to a local Oexoelet tic polarization which adds up to the ferroelectric polarization (8]. Beresnev et al. (9] have claimed that the latter contribution clearly dominates, but the flexoelectric term may become significant tot materials with a short helix period p < I tun. 

The cholesteric blue phase (ChBP) appears in a very narrow temperature range (usually within 1 °C) just below the isotropic phase in short helical pitch material. Recently it was found by Kikuchi et al. that the temperature range can be expanded by polymer stabilization [62], and application in high-speed displays is anticipated. In ChBP, the helices produced by the spontaneous twist of the director form a cubic lattice with a regular three-dimensional alignment. However, it cannot fill the space continuously, and defect lines called discbnations are embedded in the cubic lattice structure. 

The production of thermotropic APC cellulose derivatives micro fibers is reported (Canejo et al. 2008) for the electrospinning of APC. These were obtained from a lyotropic solution of APC at room temperature. Scanning Electron Microscopy (SEM) observations showed that the APC electrospun fibers exhibit a spontaneous twist along their axis. 

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