of the melt‐isothermal crystallization rate, which showed an anomalous peak at around 110–118°C [1, 50]. The DSC thermogram showed double melting peaks in the cold‐crystallization process [51]. Simultaneous DSC and WAXD measurement was performed as shown in Figure 6.6. The unoriented δ form sample was heated gradually, during which the 1D X‐ray diffraction profile was measured stepwise. When the temperature increased to 148–165°C, the 203 and 116 diffraction peaks, which were originally single peaks, changed to double peaks and the relative intensity of these two peaks was exchanged, as indicated by the arrows. This indicates that these two phases are coexistent during the transition, implying a thermodynamically first‐order transition. Besides, several peaks (210 and 213) started to appear, which were assigned to the diffraction peaks of the α form. In this way, the δ form is the crystal form thermodynamically independent of the α form.
FIGURE 6.5 (a) Comparison of the observed 00l reflection profile with the calculated curves for both of P212121 and P1211 models and for the disordered domain model.
Source: Reproduced from Wasanusuk et al., Macromolecules 2011, 44, 6441–6452.
(b) PLLA domain model (several tens Å size along the a axis).
FIGURE 6.6 Temperature dependence of the 1D WAXD profile measured in the phase transition from the δ (α’) to α form of the unoriented PLLA sample (heating process).
Source: Reproduced from Zhang et al., Macromolecules 2008, 41, 1352–1357.
FIGURE 6.7 Observed X‐ray 00l reflection profiles of PLLA α and δ forms.
Source: Reproduced from Wasanasuk and Tashiro, Polymer 2011, 52, 6097–6109.
The crystal structure of the δ form was proposed by analyzing the 2D X‐ray diffraction pattern shown in Figure 6.2b, where the sample was prepared by stretching the melt‐quenched sample followed by annealing at ca. 100°C. In contrast to the α form, the X‐ray diffraction pattern is not very clear and consists of only the 41 broad diffraction spots. In addition, the diffuse streaks are detected relatively strongly along the layer lines, suggesting the existence of the remarkable disorder of the unit cell structure [9]. The orthogonal unit cell was proposed with the parameters a = 10.80 Å, b = 6.20 Å, and c (chain axis) = 28.80 Å. As seen in the 00l profile (Figure 6.7), the 0010 peak is quite strong, but the others are appreciably broad and diffuse, which is different from the sharp 00l peaks observed for the α form. This indicates that the chains takes the 10/3 helical conformation, but they are deformed to more extent than the α form (Figure 6.3). The detailed analysis of the X‐ray diffraction data revealed that not only the conformational disorder but also the chain packing disorder occurs in the crystal lattice of the δ form. In particular, the relative height between the neighboring chains is appreciably random compared with the α form, as seen from the more remarkable streaks along the layer lines of the 2D X‐ray diffraction pattern [9]. Besides, the aggregation of the domains is also more highly disordered than the α form (see Figure 6.5b). The X‐ray‐coherent crystallite sizes, as evaluated from the half width of the various diffraction peaks using Scherrer’s equation [52], are appreciably smaller than those of the α form (see Section 6.3.1).
6.2.4 Crystal Structure of the β Form
As for the structure of the β form, the two types of the crystal structure were previously proposed by the X‐ray or electron diffraction data analysis: model (i) the orthorhombic type: a = 10.31 Å, b = 18.21 Å, and c (chain axis) = 9.00 Å, in which the six chains of 3/1 helical conformation are packed [17], and model (ii) the trigonal type with a = b = 10.52 Å and c (chain axis) = 8.80 Å, in which the three upward helices of 3/1 conformation are related by the space group symmetry P32 [18]. The present authors measured the 2D X‐ray diffraction pattern using a Mo‐Kα beam and analyzed it thoroughly (Figure 6.2d). The several diffraction peaks intrinsic to the β form could not be indexed reasonably by using the model (ii). Besides, the observed 000l reflections along the chain axis do not satisfy the extinction rule requested for the P32 space group (the appearance 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:
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.
Then, the chain packing structure of the α form was used as an initial model of the β form, which was enlarged three times along the b‐axis. The thus‐constructed model consists of the alternate packing of the upward (U) chains and downward (D) 3/1 chains. The positions
