Chiral patterns

Remarkable chiral patterns, such as those in Figs. IV-15 and XV-8, are found in mixtures of cholesterol and 5-dipalmitoyl PC (DPPC) on compression to the plateau region (as in Fig. XV-6). As discussed in Section IV-4F, this behavior has been modeled in terms of an anisotropic line tension arising from molecular symmetry [46-49]. 

The results surveyed in the preceding two sections provide a first clue to the origin of chirality chiral patterns can emerge spontaneously in an initially uniform and isotropic medium, through a mechanism of bifurcations far from thermodynamic equilibrium (see Figs. 4 and 5). On the other hand, because of the invariance properties of the reaction-diffusion equations (1) in such a medium, chiral solutions will always appear by pairs of opposite handedness. As explained in Sections III.B and III.C this implies that in a macroscopic system symmetry will be restored in the statistical sense. We are left therefore with an open question, namely, the selection of forms of preferred chirality, encompassing a macroscopic space region and maintained over a macroscopic time interval. 

For the inherently chiral (R,R)- and (S, S)-TA, a zigzag distortion has been confirmed experimentally via XPD [25]. DFT calculations, however, predicted also for achiral (R,S)-TA and SU on Cu(110) a chiral zigzag conformation after deprotonation of both carboxyl groups (Fig. 11) [26]. Indeed, observations of long-range chiral patterns suggest this geometry [27-29]. 

Fig. 1. Typical ED pattern of polychiral MWCNT. The pattern is the superposition of the diffraction patterns produced by several isochiral clusters of tubes with different chiral angles. Note the row of sharp oo.l reflexions and the streaked appearance of 10.0 and 11.0 type reflexions. The direction of beam incidence is approximately normal to the tube axis. The pattern exhibits 2mm planar symmetry [9].

Fig. 3. (a) Diffraction pattern of a well formed rope (superlattice) of armchair-like tubes. Note the presence of superlattice spots in the inset (b). The broadening of the streaks of 1010 type reOexions is consistent with a model in which the SWCNTs have slightly different chiral angles. 

The diffraction patterns due to different isochiral clusters are superimposed and well separated in a polychiral MWCNT diffraction pattern, suggesting that interference between waves scattered by tubes with different chiral angles can be neglected. It is therefore meaningful to discuss only isochiral clusters of tubes. Such clusters are only compatible with a constant intercylinder spacing c/2 for pairs of Hamada indices satisfying the condition = L +M +LM - (nc/a). Approximate solutions are for instance (8, 1) and (5, 5) [16,17]. 

Fig. 11. Simulated diffraction space of a chiral (40, 5) SWCNT. (a) Normal incidence diffraction pattern with 2mm symmetry (b),(c),(d) and (e) four sections of diffraction space at the levels indicated by arrows. Note the absence of azimuthal dependence of the intensity. The radii of the dark circles are given by the zeros of the sums of Bessel functions [17].

Several sections of the diffraction space of a chiral SWCNT (40, 5) are reproduced in Fig. 11. In Fig. 11(a) the normal incidence pattern is shown note the 2mm symmetry. The sections = constant exhibit bright circles having radii corresponding to the maxima of the Bessel functions in Eq.(7). The absence of azimuthal dependence of the intensity is consistent with the point group symmetry of diffraction space, which reflects the symmetry of direct space i.e. the infinite chiral tube as well as the corresponding diffraction space exhibit a rotation axis of infinite multiplicity parallel to the tube axis. 

Using HRTEM the chiral angle can also be deduced from the moird or coincidence pattern formed in the central area of the tube image between "front" and "back" surfaces of the tube. 

The diffraction patterns of isochiral clusters of tubes with different chiral angles in MWCNTs are superimposed in the composite pattern, the different chiral angles can be measured separately by diffraction contrast imaging [26]. 

NMR signals for difluoromethylene moieties range from -85 to -111 ppm (excluding difluorocyclopropyls), with viunal 7jjp values similar to the primary cases More compbcated sphttmg patterns arise from diastereotopic fluorines when a chiral center IS present in the gemmal difluonde Diastereotopic fluonnes may differ in chemical... 

Stereoregular polymer (Section 7.15) Polymer containing chirality centers according to a regular repeating pattern. Syndiotactic and isotactic polymers are stereoregular. 

In 1980, Katsuki and Sharpless communicated that the epoxidation of a variety of allylic alcohols was achieved in exceptionally high enantioselectivity with a catalyst derived from titanium(IV) isopropoxide and chiral diethyl tartrate. This seminal contribution described an asymmetric catalytic system that not only provided the product epoxide in remarkable enantioselectivity, but showed the immediate generality of the reaction by examining 5 of the 8 possible substitution patterns of allylic alcohols all of which were epoxidized in >90% ee. Shortly thereafter. Sharpless and others began to illustrate the... 

The AE reaction has been applied to a large number of diverse allylic alcohols. Illustration of the synthetic utility of substrates with a primary alcohol is presented by substitution pattern on the olefin and will follow the format used in previous reviews by Sharpless but with more current examples. Epoxidation of substrates bearing a chiral secondary alcohol is presented in the context of a kinetic resolution or a match versus mismatch with the chiral ligand. Epoxidation of substrates bearing a tertiary alcohol is not presented, as this class of substrate reacts extremely slowly. 

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