Helical pitch

Figure C 1.4.7. Spatial variation of the polarization from tire field resulting from two counteriDropagating, circularly polarized fields witli equal amplitude but polarized in opposite senses. Note tliat tire polarization remains linear but tliat tire axis rotates in tire x-y plane witli a helical pitch along tire z axis of lengtli X.

Very recently, it has been reported that SWCNT can be synthesized by decomposition of benzene with Fe catalyst [27]. It would be of most importance to establish the controllability of the diameter and the helical pitch in this kind of synthesis of SWCNT toward the development of novel kinds of electronic devices such as single molecule transistor [41]. It can be said that this field is full of dream. 

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.

The helical pitch was calculated to correspond to 0 = 0.397rt and 0.399rt for the chains with R = Et and i-Pr, respectively. The decrease in xT at low temperature is justified by the fact that adjacent Gd3+ spins are almost antiparallel in these derivatives. A much smaller pitch, 0 = 0.206rc and 0.17.5re, was estimated for R = Me and Ph, respectively x> h1 agreement with the increase of the xT at low temperature. 

The Helfrich-Prost model was extended in a pair of papers by Ou-Yang and Liu.181182 These authors draw an explicit analogy between tilted chiral lipid bilayers and cholesteric liquid crystals. The main significance of this analogy is that the two-dimensional membrane elastic constants of Eq. (5) can be interpreted in terms of the three-dimensional Frank constants of a liquid crystal. In particular, the kHp term that favors membrane twist in Eq. (5) corresponds to the term in the Frank free energy that favors a helical pitch in a cholesteric liquid crystal. Consistent with this analogy, the authors point out that the typical radius of lipid tubules and helical ribbons is similar to the typical pitch of cholesteric liquid crystals. In addition, they use the three-dimensional liquid crystal approach to derive the structure of helical ribbons in mathematical detail. Their results are consistent with the three conclusions from the Helfrich-Prost model outlined above. 

In order to further experimentally probe the hard-core model of polysilane aggregate chirality, a series of poly-[(alkyl)alkylphenylsilylene]s, differing in phenyl ring-substituent position and chain length were synthesized, designed such that the polymer chain diameter, d, and helical pitch, p, in the hard-core model were varied.343... 

Fig. 7. Illustrating the structure of a chiral smectic C mesophase P = helical pitch)...

A series of bridged [7]thiaheterohelicenes 131 with a variety of helical pitches have been prepared from 2,13-bis(chloromethyl)thiaheterohelicene 130 with alkyl dithiols (Equation 34) <2002JOC1795>. 

The secondary structure of poly(iV-alkynylamides) is influenced by the position of the chiral center and amide group.The position of the chiral center mainly affects the helical pitch, which becomes short when the chiral center is positioned away from the main chain. The stability of the helical structure is also influenced by the position of the amide group. Based on molecular orbital study, it is concluded that poly(iV-propargylamides) with right-handed helical structure display a plus Cotton effect around 390 nm. This is also confirmed by the exciton chirality method using porphyrin as a chromophore. ... 

When an anode contains an appropriate amount of metals (or metal oxide), novel carbon materials such as SWNTs, metallofuJlerenes, filled nanocapsules, bam-boo -shaped tubes (23), nanochains (10), and MWNTs filled with metal carbides (24,25) are formed. Especially SWNTs are now attracting a great deal of interest from researchers in physics and materials science, because exotic electronic properties that vary between semiconducting and metallic states depending on how a graphene sheet is rolled (i.e., diameter and helical pitch of a tube) are predicted theoretically (26-28) and because unique quantum effects are revealed experimentally (29,30). 

Subsequent studies on the chiral nematic phase of 8 and 10 showed the influence of complexed salts on the liquid crystalline properties. In the complexes (Scheme 5), the helical pitch was strongly affected by the complexed cation and the counterions [29]. 

Crown ether binaphthyl derivatives 128-131 (Scheme 71) were synthesized and investigated by Akagi [139], Compounds 128-131 were used to induce chiral nematic phases (N ) in liquid crystals. It was found that the helical twisting power increased with decreasing ring size. Helical polyacetylenes were synthesized in the N phases. It was found that the interdistance between the fibril bundles of the helical polyacetylene was equal to the half-helical pitch of the N liquid... 

Fig. 3 Inverse structural pitch (1/nP) as a function of dopant ratio. Bent-shaped molecule P12-0-PIMB enhances the twisting power, which is proportional to 1/nP, whereas rod-shaped molecule TBBA gives just a dilution effect the helical pitch increases...

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