Identity period

In the crystalline region isotactic polystyrene molecules take a helical form with three monomer residues per turn and an identity period of 6.65 A. One hundred percent crystalline polymer has a density of 1.12 compared with 1.05 for amorphous polymer and is also translucent. The melting point of the polymer is as high as 230°C. Below the glass transition temperature of 97°C the polymer is rather brittle. 

The poly(5-fnethyl-l, 4-hexadiene) fiber pattern (Figure 6) gave an identity period of 6.3 A, indicating a 3 isotactic helix structure. The X-ray diffraction pattern was not very sharp, which may be due to the difficulty of the side chain with a double bond to fit in a crystalline lattice. The crystallinity was determined to be 15% using the Hermans and Weidinger method (27). A Chloroform-soluble fraction free from catalyst residues showed no improvement in the sharpness of the X-ray diffraction pattern. These data show that the configuration of the 1,2-polymerization units in the homopolymer of 5-methyl-1,4-hexadiene is isotactic. 

Further confirmation of the structure and tacticity of poly/5-methyl-l,4-hexadiene)was obtained from X-ray diffraction and u-NMR data of its hydrogenated polymer (Scheme 2). The hydrogenated polymer sample showed a highly crystalline pattern (Figure 7), with diffraction spots that were well defined. This pattern was identical to that of isotactic poly(5-methyl-l-hexene) as reported in the literature (26) (measured identity period, 6.2 A lit., 6.33 A). 

To denote the stacking sequence of the different structures it is sufficient to give only one identity period of the h, c symbol series. For instance ... 

Isotactic poly(methyl methacrylate), also, is an intricate case, resolved only after a 20-year debate. The repetition period along the chain axis is 10.40 A corresponding to S monomer units the entire cell contains 20 monomer units (four chains). At first, the stmcture was resolved as a 5/1 helix (183) with = 180° and 62 — 108° but no reasonable packing was found using this assumption. Further conformational calculations showed that helices like 10/1 or 12/1 should be more stable than the 5/1 helix. The structure was solved by Tadokoro and co-workers (153b) who proposed the presence of a double helix. Two chains, with the same helical sense and the same direction but displaced by 10.40 A one from the other are wound on each other, each chain having 10 monomer units per turn [i(10/l)] and a 20.80-A repeat period. As a result, the double helix has a 10.40-A translational identity period, identical to that found in the fiber spectmm. The conformational parameters are Of = 179° and 2 = -148°. Energy calculations indicate that the double helix is more stable by 4.4 kcal per-mole of monomer units than two isolated 10/1 helices, a result that is in line with the well-known capacity of this polymer to form complexes in solution (184). 

The crystallographic identity period parallel to the chain axis should preferably be designated c in descriptions of macromolecular crystallography. 

If the number of conformational repeating units along the identity period c is M and the number of turns is N, then ... 

Straight line parallel to the direction of chain extension, connecting the centres of mass of successive blocks of chain units, each of which is contained within an identity period (see Fig. 1). 

Note 1 The chain identity period is usually denoted by c. 

Fig. 1. Side view (above) and end view (below) of the macromolecule of isotactic poly[l-(l-naphthyl)ethane-l,2-diyl] in the crystalline state. The helix symbol is s(2 4/1). The chain axis is shown by the dashed line, and c is the chain identity period. Hydrogen atoms are omitted. [From P. Corradini and P. Ganis. Nuovo Cimento, Suppl. 15, 96 (I960)].

As mentioned earlier, poly(thioformaldehyde) is a highly crystalline polymer, and it has been shown to have a hexagonal crystal structure (14, 24). Thus, poly-(thioformaldehyde) obtained by irradiation of trithiane followed by heating has a hexagonal unit cell with a = 5.07 A and c=36.52 A crossed by one helical chain parallel to the c axis. The chain has an identity period of 36.52 A that comprises 17 —CH2S— units in 9 turns of the helix (14). Poly(thioformaldehyde) made by other methods crystallizes similarly (24). 

Chain-type in crystals of linear polymers. In drawn fibres of these substances the molecules are approximately parallel to the fibre axis, and the unit cell dimension along the fibre axis is also the identity-period of the molecule itself. The fact that it is possible so simply to determine intra-molecular distances has far-reaching consequences. The magnitude of this identity-period may lead directly to a knowledge of... 

The chains of some polymer molecules are not fully extended the identity-periods leave no doubt of that. By rotation round the single bonds the chains are crumpled and shortened. The magnitude of the identity-period may by itself indicate the geometry of the chain, but more probably it will not be possible to draw unambiguous conclusions without the aid of further stereochemical considerations. Examples... 

The distance between the centers of the adjacent helices is equal to the dimension of the a-axis, determined from the (100) spacing of the hexagonal unit cell and the (110) spacing of the triclinic unit cell. The identity period along the c-axis corresponds to ten monomeric units in three helical turns of the polymer. 

Number of monomeric units per turn Identity period referred to one monomeric unit, A Ref. 

In cases where q = 4, e. g., when the positions of substituents on the chain increase the true identity period to four elements, we can show that two other skeletal modes can become potentially active. This of course assumes that the substituents can be neglected and the previous treatment used, an unlikely assumption. Nevertheless the results may serve as crude guides to the location of other possible skeletal frequencies for such polymers. Application of equations (34)—(37) shows that these modes are expected at... 

The basic crystalline chain structure of PTFE has been worked out from x-ray diffraction studies [Bunn and Howells (29)]. It consists of a helical arrangement of CF2 groups along the chain with 13 CF2 groups in the identity period of the helix (see Fig. 8). The two-fold axis of each CF2 group is perpendicular to the helix axis. 

The polymer undergoes a phase transition at 19° C. which seems to be accompanied by a change in the identity period, there now being 15 CF2 groups in the repeat [Pierce,... 

The unique aspect of the structure of PVdC is exhibited by its chain axis identity period of about 4.7 A [Fuller (64) Narita and Okuda (743)]. This indicates that there is more than one monomer unit in the... 

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