Helicoidality

Lavery R and H Sklenar 1988. The Definition of Generalized Helicoidal Parameters and of A> Curvature for Irregular Nucleic Acids. Journal of Biomolecular Structure and Dynamics 5 63-91. 

The screw conveyor is one of the oldest and most versatile conveyor types. It consists of a helicoid flight (helix rolled from flat steel bar) or a sectional flight (individual sections blanked and formed into a helix from flat plate), mounted on a pipe or shaft and turning in a trough. Power to convey must be transmitted through the pipe or shaft and is limited by the allowable size of this member. Screw-conveyor capacities are generally limited to around 4.72 mVmin (10,000 ftvh). 

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. 

Organoclay materials with higher-order organization can also be prepared by template-directed methods involving self-assembled supramolecular structures. In this approach, preformed organic architectures in the form of tubes, fibers, hollow shells, gyroids, helicoids, and so on are transferred into hybrid materials exhibiting structural hierarchy, complex form and ordered mesoporosity [47-55]. For example,... 

Fig. 8.4 TEM images showing ethylenediami-nopropyl-functionalized magnesium phyllosi-licate microtubules produced by lipid helicoid templating. In each case the template was removed by washing with ethanol. (A) intact...

The first periodic (in one direction only) minimal surface [12] discovered in 1776 was a helicoid The surface was swept out by the horizontal line rotating at the constant rate as it moves at a constant speed up a vertical axis. The next example (periodic in two directions) was discovered in 1830 by Herman Scherk. The first triply periodic minimal surface was discovered by Herman Schwarz in 1865. The P and D Schwarz surfaces are shown in Figs. 2 and 3. The revival of interest in periodic surfaces was due to (a) the observation[13-16] that at suitable thermodynamic conditions, bilayers of lipids in water solutions form triply periodic surfaces and (b) the discovery of new triply periodic minimal... 

Fig. 17 a One-dimensional electron density distribution of Ca2Al/VBS along the c axis b Gaussian deconvolution of the hydroxide layer c Gaussian deconvolution of the interlayer space and the resulting conformation of VBS molecules in C2/c space group, VBS molecules are related by an helicoidal axis 2 located midway in the interlamellar space... 

The study of mesophases of cellulose and cellulose derivatives is an active field which has expanded rapidly since the initial observation of liquid crystms of hydroxy-propyl cellulose in 1976. There are two areas that warrant turther investigation recent observations regarding the influence of solvent and/or substituents on the cholesteric helicoidal twist await a theoretical explanation there is a lack of careful studies to permit a theoretical treatment of the behavior of ordered celltdose phases. To date, no applications have been developea where the unusual properties of cellulose derivatives are utilized. 

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. 

Guo and Gray (114) foimd that acetylation of the imsubstituted groups in ethyl cellulose changes the sense of the helicoidal cholesteric twist from leff-handed to right-handed in either CHCI3 or m-cresol. 

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. 

Mesophase with a helicoidal superstructure of the director, formed by chiral, calamitic or discotic molecules or by doping a uniaxial nematic host with chiral guest molecules in which the local director n precesses around a single axis. 

See Fig. 3 for an illustration of the helicoidal molecular distribution in a chiral nematic mesophase. 

Mesophase with a helicoidal supramolecular structure in which blocks of molecules, with a local structure of the smectic A type, have their layer normals rotated with respect to each other and are separated by screw dislocations. 

Mesophase with a helicoidal supramolecular structure of blocks of molecules with a local smectic C structure. The layer normal to the blocks rotates on a cone to create a helix-like director in the smectic C. The blocks are separated by plane boundaries perpendicular to the helical axis. At the boundary, the smectic order disappears but the nematic order is maintained. In the blocks the director rotates from one boundary to the other to allow the rotation of the blocks without any discontinuity in the thermomolecular orientation. 

Detonation, Helicoidal. See under Detonation, Spinning or Helicoidal... 

The study, by Dabora et al (Ref 11), of detonating H2-O2 mixtures surrounded by a compressible medium such as an inert gas is mentioned under Detonation, Spin (Spinning or Helicoidal Detonation). In such confinement the detonation proceeds more slowly than if confined by a rigid wall. 

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. 

The well-known helicoidal distortions [70] that even two adjacent base pairs can suffer (role, twist, slide, etc.) suggest that, indeed, the electron/vi-brational couphng should be large in DNA, and therefore that polaron for-... 

In the absence of dynamic and static disorder, all partially filled band systems would exhibit coherent transport over long distances. With static and dynamic disorder, the modulation of the simple molecular orbital or band structure by nuclear effects entirely dominates transport. This is clear both in the Kubo linear response formulation of conductivity and in the Marcus-Hush-Jortner formulation of ET rates. The DNA systems are remarkable for the different kinds of disorder they exhibit in addition to the ordinary static and dynamic disorder expected in any soft material, DNA has the covalent disorder arising from the choice of A, T, G, or C at each substitution base site along the backbone. Additionally, DNA has the characteristic orientational and metric (helicoidal) disorder parameters arising from the fundamental motif of electron motion along the r-stack. 

Helicoidal Fields. Helicoidal fields verify the following set of inequalities ... 

For instance, a velocity field U will be of an helicoidal field if the motion is, itself, helicoidal, too. Indeed, point coordinates of the trajectory have the value... 

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