Helicoidal structures

In the cis complexes, the torsion angle is usually smaller than that in trans complexes (Tables 16 and 17), leading to decreased antiferromagnetic coupling. In this case, the chains are helical and the compactness of this helix is a further factor that needs to be considered the more compact the helicoidal structure, the greater the antiferromagnetic coupling. 

Bheda et al. ( ) showed that cellulose triacetate forms a mesophase in dichloroacetic acid. Navard and Haudin (18) examined the thermal behavior of liquid crystalline solutions of CTA in TFA. Navard et al. (23) studied the isotropic to anisotropic transitions of solutions of cellulose triacetate in TFA using differential scanning calorimetry. Navard and Haudin (S2) studied the mesophases of cellulose and cellulose triacetate calorimetrically. Navard et al. (83) report similar studies. Meeten and Navard (97) showed the twist of the cholesteric helicoidal structure of CTA and secondary cellulose in TFA is left-handed. 

Vo and Zugenmaier (105) determined the pitch of cellulose tricarbanilate (CTC, D.P. = 100) in 2-pentanone and methyl ethyl ketone (MEK) and ethyl cellulose (EC) in glacial acetic acid as a function of temperature, concentration, solvent, and degree of polymerization. The pitch of the helicoidal structure of CTC/MEK and CTC/2-pentanone is right-handed but EC in glacial acetic acid is left-handed. This is the first report that the substituent will influence the sense of the cholesteric superhelicoidal structure. 

As Guo and Gray (114) point out, the relationship between the handedness of the supramolecular helicoidal structure and the molecular structure 01 cellulose derivatives and solvents is not at all understood" at the present time. 

Giasson et al. (117) give direct electron microscopy evidence for the helicoidal structure of films of the cellulose acetates and of cellulose regenerated from the GTA films by aqueous ammoniiun hydroxide. 

The chains of isotactic polymers (in which the dimensions of R are much greater than those of the hydrogen atom) have the tendency to assume a helicoidal configuration with a pitch which depends on the dimensions of the R group. There is evidence that a helicoidal structure has the tendency to exist also (at least partially) in the amorphous state. It is detectable. 

Figure 2. Helicoidal structure of Amadori-lype sugar derivatives of poly-L-lysine.

In difference from the analysis performed in Ref. [11] for a one-parametric potential, the peculiarity of the relations obtained here is the opportunity to distinguish between the ordering temperature of the magnetic system (p21 0 at H = 0) and the temperature of formation of the helicoidal structure (q 0). The helicoidal magnetic structure exists in a temperature interval (TqU Tql) given by ... 

Cholesteric mesophases form only from molecules having chiral centers. Since the helicoidal structures of cholesterics are supramolecular, the chiral centers in... 

It is possible to conceive of situations where the chemical linking of molecular components around a template is not as crucial as the formation of defined, non-covalent interactions during templating. This may be exemplified by the polymerisation of a nematic liquid crystalline crosslinker in the presence of a template, a non-polymerisable cholesteric mesogen [23]. The chiral dopant forces the crosslinker to form a cholesteric phase. After polymerisation of the crosslinker, the polymer still exhibits a helicoidal structure which is stable over a wider temperature range than the initial cholesteric phase. It is not reported in this work whether extraction of the chiral mesogen has been attempted or not. 

Frank [5.50] was the first to recognize the major role of screw dislocations in the process of the growth of real crystals. Due to the helicoidal structure of this crystal imperfection, a step originates from the point where the screw dislocation line intersects the surface of the crystal face (Fig. 5.26b). This step is constrained to terminate at the dislocation emergence point and winds up into a spiral during the growth process (Fig 5.27). 

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). 

Lyotropic liquid crystalline cellulose derivatives exhibit unique optical properties because of their helicoidal supramolecular structure.The chiro-optical properties of the helicoidal structure can be described by a pitch p (or its inverse, the twist p ) p = 2o/fi, where is the reflection wavelength and h is the mean refractive index of a sheet, and the corresponding handedness of the twist right-handed helicoidal structure being assigned to a positive pitch p > 0) and left-handed helicoidal structures to a negative pitch p < The nematic mesophase can be... 

The observed handedness and pitch of the helicoidal structure is not only sensitive to temperature, but also depends on the concentration and structure of the... 

As seen in Fig. 10, the larger the pitch, the slower the rate the modulus evolution. The modulus of the right-handed mesophase (AEC-4) developed faster than that of the left-handed mesophase (AEC-1) with similar pitch. The difference in relaxation behavior of the AEC solutions may be because of the smaller driving force to reform helicoidal structures of chiral nematic phases from flow-induced nematic mesophases for the mesophases with larger pitch (nematic-like). 

Fig. 5.10.1. (a) Helicoidal structure of the ferroelectric smectic C phase, (b) a poled sample with the helix unwound by an electric field applied normal to the... 

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... 

Lyotropic cellulosics mostly exhibit chiral nematic phases, although columnar phases have also been observed. The molecules in the thermotropic state also form chiral nematic order, but it is sometimes possible to align them in such a way that a helicoidal structure of a chiral nematic is excluded. Upon relaxation they show banded textures. Overviews on lyotropic LC cellulosics are... 

At the selective reflection wavelength, a component of linearly polarized light, e.g., right-handed or left-handed circularly polarized light, is totally reflected without a phase reversal by a twisted helicoidal structure at a wavelength correlated to the pitch P. An oblique incident of light is presumed onto the substrate plane or nematic sheet (see Fig. 3)... 

The Kramers-Kronig [15] transformation relates the optical rotation (ORD) to the circular dichroism (CD). This spectroscopic method is widely used for the determination of the pitch as well. Figure 5 shows examples for left- and right-handed helicoidal structures of cellulosics as they appear in ORD and CD measurements. 

All spectroscopic methods for an evaluation of the pitch lead to the size of the repeat distance of the supermolecular LC structure and the handedness of the twisting, although in UV-VlS spectroscopy, circularly polarized light has to be used. With some skill, the Cano technique may also result in the twisting sense of the helicoidal structure. 

The optical properties of chiral nematic phases are closely related to their supermolecular Structures, as stated by the considerations of de Vries. In particular, the planar textures exhibit beautiful colors correlated to the pitch P of the helicoidal structures by Eq. (1), if the selective reflection wavelength lies in the visible range, and many examples are shown in Fig. 2. 

Figure 23. Spectra by ORD (a) at 140 °C and CD, (b) at 152 °C of a thin layer of ethoxypropyl cellulose that forms a thermotropic right-handed helicoidal structure (adapted from [2]).

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