Long pitch

Figure 8. (Continued). As described above, the packing of myosin molecules into the thick filament is such that a layer of heads is seen every 14.3 nm, and this reflection is thought to derive from this packing. Off the meridian the 42.9 nm myosin based layer line is shown. This arises from the helical pitch of the thick filament, due to the way in which the myosin molecules pack into the filament. The helical pitch is 42.9 nm. c) Meridional reflections from actin. Actin based layer lines can be seen at 35.5 nm, 5.9 nm and 5.1 nm (1st, 6th, and 7th layer lines)and they all arise from the various helical repeats along the thin filament. Only the 35.5 nm layer line is shown here.The 5.9 nm and 5.1 nm layer lines arise from the monomeric repeat. The 35.5 nm layer line arises from the long pitch helical repeat and is roughly equivalent to seven actin monomers. A meridional spot at 2.8 nm can also be seen, d) The equatorial reflections, 1,0 and 1,1 which arise from the spacings between crystal planes seen in cross section of muscle.

It can also be described as a right-handed two-start helix in which two chains of subunits coil around one another with a long pitch (Fig. 7-10). 

Fig. 5a-c. Granulator screws, a Uniform long pitch b variable long pitch c with conical core... 

IR or UV reflecting cholesterics are colorless in the visible region of the spectrum. Therefore, retardation plates can be realized for STN displays using a long pitch material. Also UV reflecting LC siloxanes are of interest for retardation plates because they exhibit behavior like an optical negative uniaxial material. 

The model has been refined by two lines of study (Ohtsuki, 1974). The first refinement was made by analysis of the troponin-tropomyosin relationship in the paracrystalline structure (discussed in Section II,E,2). The analysis has confirmed that troponin lies approximately two-thirds of the molecular length (i.e., 27 nm) from one end of a filamentous tropomyosin molecule of 40-nm length. Another refinement was based on consideration of the arrangement of actin molecules in the thin filament. Corresponding molecules in two long-pitched strands of actin in the filament are shifted relative to each other by a distance of half the... 

Maps of Limulus thin filaments reveal actin monomers whose bilobed, two-domain shape and monomer-monomer connectivity are typical of F-actin (Lehman et al., 1994). In addition, longitudinally continuous strands of density, presumably tropomyosin, follow long-pitch actin helices and are evident in reconstructions carried out on filaments both in the absence and in the presence of Ca2+. Filaments in Ca -free buffer show the tropomyosin strands following successive actin monomers in contact with the extreme inner edge of their outer domains, whereas in Ca + the strands are closely associated with the inner domain of... 

Both smooth and skeletal muscle actin filaments are saturated with tropomyosin (Sobieszek and Bremel 1975). Both exhibit the same characteristic stoichiometry of binding of 1 molecule of tropomyosin interacting with 7 monomeric units of F-actin on each of the two strands of F-actin (Hartshorne 1987). The length of tropomyosin molecules (284 amino acids) and their periodicity in smooth and striated muscles is the same (Matsumura and Lin 1982). In both tissues, tropomyosin exists as a dimeric a-helical coil (Caspar et al 1969). Individual tropomyosin molecules bind in an end to end fashion to form a continuous strand on the thin filament that lies along the long-pitch of the double helix formed by the actin monomers (Moore et al 1970, OBrien et al 1971, Spudich et al 1972, Milligan et al 1990). 

In summary, the presence of elastic anisotropy favours one particular value of the constant c for a disclination pair. This may have a bearing on the structure of disclination pairs in long-pitched cholesterics in which each layer may be regarded as nematic-like. Since each layer is allowed only one value of c, and the layers themselves are rotated about the twist axis, disclination pairs may be expected to adopt helical configurations as illustrated schematically in fig. 3.5.24. As we shall see in 4.2.1, this conclusion seems to be in agreement with experimental observations. 

As already indicated briefly in 3.5.8 the effect of elastic anisotropy has some interesting implications for cholesterics, especially for long-pitched structures. We have seen that disclination pairs in nematics have angular forces in the presence of elastic anisotropy. For all practical purposes, the solutions that were obtained for nematics will hold good for each nematiclike cholesteric layer, except that the layers now twist continuously in the... 

Fig. 4.4.2. A spherical drop of a long-pitched cholesteric liquid crystal showing the characteristic /-line (from Robinson ). The structure of this defect was explained...

Microtubular haemoglobin has been observed in erythrocytes in sickle cell anaemia. After deoxygenation and addition of thermal energy, the mutant molecules of haemoglobin (HbS) stack to form monomolecular filaments. Six strands assemble into a heli-coidal microtubule showing six helices of long pitch (review in 19). These microtubules form a cholesteric packing (6). 

If a chiralized nematic with a long pitch ( 27r/g) and positive Ae is... 

Fig. 13.21 Classification and structure of ferro-, ferri and antiferroelectiic phases. The third column represents the number (m) of the smectic layers / in a unit cell (for SmC abbreviation IC means incommensurate). In the right column the orientation of the dielectric ellipsoid is presented for different layers within the unit cell viewed along the z-axis. The long-pitch helical structure due to the molecular chirality is igntued for clarity, although it slightly influences the value of angle (p for the ellipsoids in the xy plane for each structure, see the next figure...

Note that in our simplified picture the molecular chirality is ignored and its role in the formation of long-pitch helix wiU be discussed below. The structure and properties of the phases pictured in Fig. 13.21 may be summarised in order of increasing temperature ... 

Fig. 13.22 Chiral antiferroelectric SmC A phase. Alternating tilt plane (a) and layer polarization (b) and the long-pitch helical structure (c). Note that the unit cell consisting of two layers rotates as a whole forming two geared helices of the same handedness. This type of rotation is controlled by molecular chirality inherent in all phases shown in Fig. 13.21...

K2 and high P. The significance of using long pitch, i.e., is not apparent from Table 3. However, low K3 and low K2 are most effective when the pitch is not stabilized by a cholesteric additive, i.e., P=< .2... 

Depending on its chemical stmcture, the pitch of a cholesteric liquid crystal could take any value in the region from a few tenths of a micron to infinitely long. The periodicity of a cholesteric liquid crystal with the pitch Pg is PJ2, because n and - n are equivalent. Cholesteric liquid crystals are also called chiral nematic liquid crystals and denoted as N. Nematic liquid crystals can be considered as a special case of cholesteric liquid crystals with an infinitely long pitch. 

In order to find such an approximation we return for a moment to the problem of light propagation in a helical structure. In the foregoing discussion the limit of long pitches, A/p C — n, was excluded. As a matter of fact this limit was considered as early as 1911 by Maugin and was treated by de Vries also. They showed that in this regime the normal modes become linearly polarized one is... 

In long-pitch nemato-cholesteric mixtures oriented homeotropically by cell walls, the bubble domain texture is often observed. A careful investigation of the director distribution in the bubble and striped (fingerprint) domains has been carried out in [3]. 

FIGURE 6.16. Bistable switching in long-pitch cholesterics with a tilt of the director o- (a) Tilted states with n/2 turns in zero field, = 55 . (b) Free energies g as functions of thickness to pitch ratio d/Po at zero field, dlPoY = 0.89 is the operating point, (c) g(d/PoY in an electric field versus reduced volteige U/Ufi Uf is the Frederiks transition threshold, Ae > 0. 

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