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of 000l reflections with l = 3, 6, 9, …) [20]. The 2D X‐ray diffraction pattern was measured again using the incident X‐ray beam of shorter wavelength (λ = 0.711 Å) than before, giving 40–50 observed diffraction spots in total [20]. The indexing of the observed peaks was made using the orthorhombic‐type unit cell:

StartLayout 1st Row a equals 10.41 modifying above upper A with ring comma b equals 18.02 modifying above upper A with ring comma and 2nd Row c left-parenthesis c h a i n a x i s right-parenthesis equals 9.00 modifying above upper A with ring at 23 degree upper C period EndLayout

      The chain takes the 3/1 helical conformation [17, 18], and the six chains are packed in the unit cell, the same as the model (i). The 18 monomeric units are contained in the unit cell. According to the International Table for Crystallography [53], the orthorhombic unit cell must contain four or eight crystallographically asymmetric units. Therefore, if the orthorhombic system is assumed, the 18 monomeric units (or six chains) cannot be divided into the asymmetric units and are difficult to correlate with each other by the symmetric relation. So, the final space group symmetry selected is P1, which reproduced the observed X‐ray diffraction data well. However, it was impossible to determine the packing structure of many such chains uniquely because the observed diffraction peaks are relatively small in number compared with the total number of the adjustable structure parameters. As the hints to construct the crystal structure model, two important phenomena were observed:

      1 The α (or δ) form transforms to the β form by the application of tensile or shear force, wherein the alternate packing structure of the upward and downward chains must be kept between them.

      2 The relationships of the unit cell size among the three crystalline forms are a (α) ≈ a (δ) ≈ a (β), b (α) ≈ b (δ) ≈ b/3 (β), and c (α) ≈ c (δ) ≈ 3c (β), suggesting that the positions of the chains in the cell might not change very much before and after the structural transition from the α to β form.

Schematic illustration of crystal structure of PLLA beta form (model 2).

      Source: Reproduced from Wang et al., Macromolecules 2017, 50, 3285–3300

      6.2.5 Structure of the Mesophase

      The 2D X‐ray diffraction pattern of the uniaxially oriented mesophase, prepared by stretching the amorphous sample around T g, is shown in Figure 6.2a. The pattern is very broad and diffuse. The relative content of the mesophase increases with an increase of tensile drawing ratio of the original amorphous sample [54]. The X‐ray data analysis revealed that the oriented mesophase contains the conformationally disordered 10/3 helical chains, which are gathered together to form the small domains of about 30 Å (c‐axis) × 20 Å (lateral direction) size with low correlation between them [5]. By heating, the mesophase undergoes the stepwise disorder‐to‐order phase transformation to the δ and α forms [5] (refer to Section 6.3.1). These transitions were proposed to occur, not by the solid‐to‐solid process, but by the melt‐recrystallization process, although not yet confirmed [55].

Schematic illustration of comparison of the observed X-ray diffraction profiles with those calculated for the structure model 2 of the beta form.

      Source: Reproduced from Wang et al., Macromolecules 2017, 50, 3285–3300.

      6.3.1 Phase Transition in Cold Crystallization

      6.3.2 Phase Transition in the Melt Crystallization

      As predicted from the phase diagram (Figure 6.1), quenching the melt gives various crystalline phases depending on the quenching temperature. The X‐ray diffraction measurement revealed the details as shown elsewhere [5]. The mesophase was formed when the quenching temperature was near T g. By quenching into 100–120°C, the δ crystal was formed. Cooling to the higher temperature caused crystallization to the α form.

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