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FIGURE 6.2 2D‐WAXD patterns of PLLA (a) mesophase, (b) δ form, (c) α form, and (d) β form.

      Source: (a)–(c): Reproduced from Wasanasuk et al., Macromolecules 2011, 44, 9650–9660; (d): Wang et al., Macromolecules 2017, 50, 3285–3300.

      6.2.2 Crystal Structure of the α Form

      The crystal structure of PLLA α form proposed at first was of the orthorhombic unit cell of a = 10.7 Å, b = 6.45 Å, c (chain axis) = 27.8 Å [15], which contains the two chains of 10/3 helical conformation [13, 48], where 10/3 indicates that the 10 monomeric units are contained and the 3 turns in the repeating period. The internal rotation angles of the skeletal chain are approximately expressed as the repetition of TTG where T and G are trans and gauche bonds, respectively. The crystal structure was refined by Sasaki et al. by assuming the space group symmetry P2₁2₁2₁ [13]. However, several unsolved problems are still relevant in the abovementioned crystal structure analysis of the α form. For example, if the structure of the P2₁2₁2₁ space group is assumed correct, the molecular chain must be deformed more or less from the regular and uniform 10/3 helical conformation, since the unit cell possesses only the 2₁ screw symmetries. If the 2₁ screw axis passes through the center of the molecular chain along the c axis, the five monomeric units should form one crystallographically asymmetric unit. The total number of the atomic coordinates to be determined is remarkably large, making the structure analysis greatly difficult. A more serious problem is the usage of the space group P2₁2₁2₁ itself.

      The observed X‐ray diffraction pattern shows a series of 00l reflections containing the odd l values (003, 007 etc.) in addition to the even 00l peaks. This is not consistent with the extinction rule (00l with even l values) required for the space group P2₁2₁2₁.

      In the X‐ray structure analysis of the α form, the total number of the adjustable parameters of one asymmetric unit (i.e., the coordinates and thermal factors of the atoms in one asymmetric unit) is 101 for C and O atoms of isotropic thermal factors, and 306 for C, H, and O atoms of anisotropic thermal factors. So, for the determination of the accurate crystal structure of the α form, we need to collect the X‐ray diffraction spots of about two to three times larger than the number of the parameters, i.e., 600–900 spots. The usage of an X‐ray beam of a shorter wavelength is useful for this purpose. For example, the X‐ray beam of 0.328 Å wavelength, generated from the synchrotron radiation facility, was incident to the ultra‐drawn PLLA α form sample [14]. From the collected 2D‐WAXD pattern, 700 independent diffraction spots were recognized, which are high enough when compared with the above‐mentioned number of the adjustable parameters. The quantitative analysis was performed manually by reading the positions and integrated intensities of all the observed diffraction peaks. By taking the above‐mentioned problems into consideration, the space group was reduced to the P12₁1 of the monoclinic system, which is lower than the space group P2₁2₁2₁. The following unit cell parameters were obtained.

The finally refined crystal structure, which can be assumed as the most accurate crystal structure of the α form, is shown in Figure 6.3. The two antiparallel L‐helices are packed in the unit cell. The chain conformation is approximately a repetition of TTG sequences. But, the individual chain is not symmetric. The two chains are connected by the 2₁ screw symmetry along the b axis to give the structure of the alternately upward and downward chains along the c axis. This model can reproduce the observed X‐ray diffraction profiles along all the layer lines quite well as shown in Figures 6.4 and 6.5a.

FIGURE 6.3 Crystal structure of PLLA α form. The space group is P12₁1. No symmetry is existent along the chain axis. The helical chains are packed upward and downward along the chain axis alternately.

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