Line repetition groups

Recently, a similar analysis of the conformational energy has been performed also for various new syndiotactic polymers.27,47 The conformational energy maps of syndiotactic polypropylene (sPP),48 polystyrene (sPS),49 poly butene (sPB),25 and poly(4-methyl-l-pentene) (sP4MP)26 are reported in Figure 2.12. A line repetition group s(M/N)2 for the polymer chain, and, hence, a succession of the torsion angles. .. 0i, 0i, 02, 02,..., has been... 

All the possible line repetition groups for cis and trans poly dienes compatible with the isotactic or syndiotactic configurations are reported in Figure 2.15,47,68 In order to consider only the possible conformations assumed in the crystalline state, the torsion angle of the central single bond is assumed to be 180° trans) in both the cis and trans polydienes. This condition produces conformations sufficiently extended to be packed in a crystalline lattice for each value of the torsion angles 0i and 02 (Figure 2.15). 

The line repetition group s(M/N) is general for cis and trans polydienes, whichever the A and B substituents, and corresponds to a succession... 

When A A or B B, the symmetry is lower and the only possible line repetition groups are s(M/N) and tc for isotactic and syndiotactic polymers, respectively, in both cis and trans configurations. In these cases, two independent torsion angles in the main chain define the regular conformation (Oi and 02 in Figure 2.15). 

For the isotactic polymer, highly extended chains with chain axis of 7.5-7.6 A can be obtained with a helix repeating after two structural units [s(2/l) line repetition group] when 01 02, and 03 are in the range 180° 8, with 8 being 25-30° and 8i + 82 + 83 0.125 The experimental values of the torsion angles found in the crystal structure of i-STCO123 are indeed 0i = —161.5°, 02 = 155.3°, and 03 = -171.4°. Similar values have been found by conformational... 

To designate linear chain conformations in the crystalline state, the use of line repetition groups [7] is recommended. 

Second and further symbols. The symmetry elements required to define the line repetition group are suggested in Reference [8]. Possible symmetry elements are ... 

The possible line repetition groups are listed below, with examples. (The structure-based name is given first, the source-based name second, in each case.)... 

In the case of syndiotactic polymers with chains in helical conformation, as for sPP, the symbol s(2/l)2 indicates that neighboring structural units are repeated through the operation of twofold axes perpendicular to the chain axis and each pair of units is repeated according to a helix containing two pairs of monomeric units in one pitch. A line repetition group for sPP in the fully extended trans-planar conformation is tcm. In this case the repeating unit comprises two monomeric units [20]. 

Figure 2.15 line repetition symmetry groups and corresponding sequences of torsion angles for cis and trails polydienes. Position of mirror planes (m), inversion centers (i), and binary axes (2) along polymer chain are also indicated. Torsion angle of single bond, CHA-CHA, is assumed to be trails (T) in both cis and lruns polydienes. 

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