Chirality diffraction pattern

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].

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]. 

I thank Dr D. Schechtman for cooperation in providing me with the X-ray diffraction pattern and for other information, and Professor Barclay Kamb for pointing out to me that an icosahedron becomes chiral when it shares its faces. This investigation was supported in part by a grant from the Japan Shipbuilding Industry Foundation. 

This approach may also be applied to racemic bilayers built up from homo-chiral Langmuir-Blodgett monolayers. By measuring the two-dimensional diffraction pattern from such a bilayer it is possible to deduce the molecular chirality of each of the two monolayers in the order they were inserted to construct the bilayer. This approach can be extended to multilayers. Thus, in principle, we close the circle started in Section IV-G-1. It is possible to assign the absolute configuration of chiral molecules in centrosymmetric crystals provided that one can construct the crystal (in this case the multilayer) by adding homochiral layers one by one. 

In this case, molecules of different chirality are crystallized in a manner of pairing, and crystal structure is different from that of the optically active forms. Therefore, the melting point or solubility of the racemic compound would be lower or higher than those of the corresponding optically active forms (Figure 3). The IR spectrum or the X-ray diffraction pattern in crystal state is different from that of the optically active forms. 

Both Form I (considered later) and Form II can be obtained by epitaxial crystallization. At atmospheric pressure, the unstable, chiral Form II can be forced to crystallize by using an appropriate substrate, namely 2-quinoxalinol, as assessed by the electron diffraction pattern (Fig. 5a) (no AFM images are available) [32], The contact plane is found to be (110)F... 

Fig. 5 (a) Diffraction pattern of sPP crystallized in its chiral Form II on p-quinoxalinol. The presence of reflections characteristic of this form and not observed for Form I confirms that the thin film as a whole is mostly in Form II. Chain axis vertical, (110) contact plane. Reproduced from [32] with permission (b) Illustration of the topographic interactions that induce Form II rather than Form I the hilly surface of the 2-quinoxalinol substrate (left, seen parallel to the contact face) can only accommodate the Form II (110) plane (middle, three chains shown, as seen parallel to the contact plane, chain axis vertical). The (110) plane of Form I (left, also three chains represented) has a profile that is not compatible with that of the substrate contact face... 

Gao etal. have developed a quantitative structure determination technique of SWNT using NED. This, coupled with improved electron diffraction pattern quahty using NED, allows a determination of both the diameter and chiral angle, and thus the chhal vector (n, m), from individual SWNTs. The CNT they studied were grown by chemical vapor deposition (CVD). TEM observation was carried out in a JEOL201 OF TEM with a high voltage of 200 keV. 

To measure chirality from the diffraction pattern, Figure 17 is considered, which shows the geometry of the SWNT diffraction pattern based on the diffraction of the top-bottom graphite sheets. The distances di, d2, d, relate to the... 

The crystallinity of the mesomorphic copolymers was extremely low as judged from the X-ray diffraction pattern, in which only one broad reflection was observed. This may be an essential point with regard to the chain mobility. Since the long side chains are considered to play a role as solvent molecules, the thermotropic system may correspond to a highly concentrated solution. a-Helical main chains embedded in the matrix of side chains take the cholesteric arrangement because of the chirality of the main chain. 

Few drugs make use of X-ray powder diffraction as a regulatory test. However, this method has a unique advantage as a stereochemically specific identity test for chiral drugs. The crystal structure, and therefore the powder diffraction pattern, are necessarily different between the racemate and the enantiomer, except in the case of a racemic conglomerate. Furthermore, published reference data are readily available. In combination with the invariance of the d-spadng measurements, this msy make X-ray diffraction more attractive to the regulatory scientist. 

The dimeric A(LS)2 structure was found remarkably effective even in the case where the unit A is a ionic moiety, such as viologen in 54 [78], or a strongly self-associating group, such as the NAf -disubstituted 3,4,9,10-perylenetetracarboxylic diimide core in 55 [79]. It was foimd that 54 forms a stable gel only in 1-butanol at low concentration (below 1 wt/vol %) of which the CD spectnun displayed the features typical of a chiral, clockwise aggregation of the gelator molecules. X-ray diffraction patterns of the xero-gel of 54 were similar to those of the neat crystal obtained from ethanol. They indicated the formation of a lamellar organization with an interlayer distance of 4.96 nm. The molecules 54 were proposed to exist in an extended conformation in the gel state and to be tilted relative to the normal of the... 

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