Enantiomorphous helices

Hence, without loss of generality, we can consider only the chain of the Scheme 2.1a and the enantiomorphous helices corresponding to the intersections (a) and (a), which are shown in Figure 2.8. 

Intercalates Only recently, the occurrence of a second class of SPS co-crystals, defined as intercalate, has been established [22-24]. This new class of co-crystal presents two features being in common with the 8 clathrates (a) the same close packing of enantiomorphous helices in the ac plane (Fig. 10.2a) (b) a monochnic Plj/a symmetry. However, the guest molecules are not isolated into host cavities but contiguous inside layers intercalated with the monolayers of enantiomorphous polymer helices. 

Figure 10.2 Top (a) and lateral views (b) of the ac layer of s (2/1)2 parallel helices of SPS, that is, the high-density and low-energy structural feature that is common to the 5-nanoporous form and to the corresponding co-crystalhne (both clathrate and intercalate) forms. The minimum interchain distance (0.87 nm) is achieved by alternating enantiomorphous helices (R and L stand for right-handed and left-handed, respectively). (c-e) Molecular models showing the three simplest orientations of the ac layers with respect to the film surface. The plane of the figure is assumed as parallel to the film plane. Arrows indicate the absence of axial orientation, (c) Both a and c axes are parallel to the film plane (otu Cil) (d) a parallel and c perpendicular to the fihn plane a Ci) (e) a perpendicular and c parallel to the film plane (a C ).These three tmiplanar orientations can be achieved for y, 8, and most co-crystalline phases of SPS. (See color insert.)...

It has been recently suggested that the structural feature determining these three different kinds of uniplanar orientations is the layer of close-packed alternated enantiomorphous helices [75] that characterizes the 8 phase of SPS, as well as all related clathrate and intercalate co-crystalline phases with low-molecular-mass guest molecules. 

The model of Figure 10.8d,e is characterized by channel-shaped cavities crossing the unit cells along the c axis and delimited, along b axis, by two enantiomorphic helical chains. 

Albunia, A. R., Rizzo, P, Tarallo, O., Petraccone, V., Guerra, G. Layers of close-packed alternated enantiomorphous helices and the three different uniplanar orientations of syndiotactic polystyrene. Macromolecules, 41,8632-8642 (2008). 

Figure 2.8 Side views and projections along chain axis of two enantiomorphous hypothetical helices of isotactic polymer having unit height of 2 A and unit twist t = 144°, corresponding to intersection points of Figure 2.7a a, left-handed helix with s(5/3)l symmetry and t = —144° = 216° a, right-handed helix with s(5/2)l symmetry and t = 144°.27 (Reproduced with permission from Ref. 27. Copyright 1992 by the Societa Chimica Italiana.)...

Anticlined enantiomorphous chains the conformation of A corresponds to a (TG ) , bond succession (right-handed helix). The conformation of B corresponds to a (G T) . bond succession (left-handed helix). 

The assignment of screw-sense in other helix-forming polypeptides is based on studies of the dispersion of optical rotation and in most cases it has been found to be right-handed for the L-enantiomorph (Urnes and Doty, 1961). Notable exceptions are poly-/8-benzyl-L-aspartate and poly-1-benzyl-L-histidine which form somewhat unstable helices of opposite screw-sense. 

Support for this general picture comes from the electron diflFraction observations on the collapsed monolayer. If the sharp reflection at 5.36 A is a true meridional reflection (better orientation is necessary to be certain), it can be indexed as 005 and the 1.489 A meridional reflection as 00,18 for a hexagonal cell with c = 26.8 A. An 005 reflection would not be produced by a perfect helix, but it can probably be accounted for assuming a distorted a-helix, the distortions being caused by the unsatisfactory packing of the two forms. The reduced axial increment per residue, 1.489 A compared with 1.495 A in the enantiomorphic form, shows that the packing causes the helix to shorten slightly. 

Williams et al. [62] also studied the copolymerization of D- and L-enantiomorphs in dioxan solution and obtained transition points similar to those shown for the L-NCA in Fig. 8. However, in these systems the transition occurred at lower P (Fig. 9), a result which is contrary to that expected if a coil-helix transition were responsible for the change in rate. Kinetic analysis was carried out in terms of simultaneous polymerization in both phases following prior adsorption of monomer. (The general procedure was similar to that of Biihrer and Elias [63] (p. 615 et seq.) and was used by them). It was found that only in the associated phase is selectivity essentially complete with no cross-over reactions. The analysis leads to an estimate of Kl d / l l = 1-6 0.6, in reasonable agreement with the value determined directly (p. 615). 

A number of selected crystal structures of polymers are shown in this section in projection along the helix axes. The poly(ethylsilylethylene) of Fig. 5.23 has its silicon atoms marked by solid circles. Neighboring helices are related by a center of symmetry, so that they must be enantiomorphous and also anticlined, i.e., the helix pairs have different handedness (d-RH and f-LH helices) and opposite inclinations of side-groups (up- and down-helices) as discussed in Sect. 5.1.8. The coordination number for the helices is three instead of the expected four because the 31 and 32 screw axes of the 2 3/1 helices match the trigonal lattice symmetry and permit a closer overall packing with CN = 3 rather than 4 (see Fig. 5.21). 

Finally, it may be noted that some polymers have been obtained in which optical activity is ascribed mainly to conformational asymmetry. In these cases there is a predominance of either right-handed or left-handed enantiomorphs of helical polymer molecules, in contrast to the more usual situation wherein equal amounts of the two enantiomorphs are produced and there is no resultant optical activity. Optically active polymers of this type have been obtained from a-olefins possessing optically active side chains, e.g., 3-methylpent-l-ene, 4-methylhex-l-ene and 5-methylhept-l-ene. Isotactic polymers from these monomers have greatly enhanced optical activity compared to the monomer. Since these polymers are vinyl polymers this optical activity cannot be associated with the asymmetry of the carbon atom in the polymer backbone (for the reasons given above). Thus it is supposed that the presence of optically active side groups favours a particular screw sense of the helix so that the resultant polymer shows a large optical rotation. Optical activity of this type has not been observed when the side groups are not asymmetric. 

K22 are zero, and in the nonpolar nonchiral uniaxial nematic Ki, K2, K 2 and K23 are zero and five elastic moduli remain in Eq. (1). In enantiomorphic phases (cholesterics), the nonzero K2 term leads to a spontaneous equilibrium twist =- 2/ 22-There, the unbiased director field forms a helix of pitch length p=lKlq. The sign of K2 gives the handedness of the helix. In the case of a hypothetical polar nematic phase (which has not yet been found experimentally), a nonzero term would lead to spon-... 

Higher values of the ratio r/R, close to V2 -1 (similar to the situation stabilizing NaCl), are obtained in the cases of many vinyl polymers with chains in complex helical conformation s M N) with a fractional ratio MIN, ranging between 3 and 4, such as form I of isotactic poly(4-methyl-l-pentene) (7/2 helix) [38], form II of isotactic poly(l-butene) (11/3 helix) [46], isotactic poly(m-methylstyrene) (11/3 helix) [86], and syndiotactic poly(4-methyl-l-pentene) (12/7 helix) [72]. In these cases, a tetragonal packing of enantiomorphous chains. 

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