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3D structure of nano-oriented crystals of poly(ethylene terephthalate) formed by elongational crystallization from the melt



We studied the elongational crystallization of poly(ethylene terephthalate) (PET) from the melt using polarizing optical microscope and X-ray observation. We verified that the structure and morphology discontinuously changed from conventional stacked lamellae of folded chain crystals (FCCs) to nano-oriented crystals (NOCs) when the elongational strain rate (\(\dot \varepsilon \)) exceeded a critical value of \((\dot \varepsilon ^*) \cong 10^2\,{\mathrm{s}}^{ - 1}\). Therefore, the universality of NOC formation was verified. We found that the NOCs of PET show a novel three-dimensional (3D) structure and morphology: (i) nanocrystals (NCs) were arranged in a monoclinic lattice, which is a specific morphology for NOCs of PET, compared to iPP, and (ii) the unit cell structure of NOCs was a triclinic system with biaxial orientation. We showed the important role of the primary structure of the plate, such as a benzene ring, in the formation of a novel 3D structure and the morphology of the NOCs of PET. We also clarified that the NOCs of PET showed high performance, such as a high heat resistance temperature (Th)\(\ \cong\ \)281 °C, a high melting temperature (Tm)\(\ \cong\ \)285 °C, high maximum tensile stresses for the machine direction (MD) and transverse direction (TD)\(\ \cong\ \)2.8 × 102 and 74 MPa, respectively, and high Young’s moduli for MD and TD \(\ \cong\ \)5.4 and 1.7 GPa, respectively.

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The synchrotron radiation experiments were performed at BL03XU (Proposal Nos. 2014A7222, 2014B7272, 2015A7221, 2015B7273, 2016A7223, and 2016B7271) of SPring-8 with the approval of the JASRI. A part of this work was supported by Grants-in-Aid for Scientific Research of the Japan Society for the Promotion of Science (KAKENHI No.26410222). We thank M. Hikosaka and S. Hikosaka, Hiroshima University, for assistance in experiments.

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Correspondence to Masamichi Hikosaka.

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Formulation of \(\dot \varepsilon \) in elongation of the melt by rolls

We will formulate \(\dot \varepsilon \) in the compression and elongation using the roll system. We focus on a range from the start (position A) to the end (position B) of compression and elongation of the supercooled melt (Fig. 11a). Hereafter, we refer to this as “range AB”. Here, O is the center of Roll 1, ω is angular velocity, L is the thickness of the supercooled melt at any given position in the range AB and Lobs is the thickness of the sheet at position B. θ is an angle of \(\angle \)COB,

$$\theta \ll 1$$
$$R_{{\mathrm{roll}}} \gg L_{{\mathrm{obs}}}$$
Fig. 11
figure 11

Schematic illustration for formulation of \(\dot \varepsilon \) in elongational crystallization of roll system. a Principle of the roll system. b Schematic illustration of \(\dot \varepsilon _{{\mathrm{xx}}}\) against x, which corresponds to a. (Color figure online)

We consider a microvolume (\(\phi _{{\mathrm{vol}}}\)) at any given position in the range AB, consider an origin at the center of \(\phi _{{\mathrm{vol}}}\), and take the x-axis, y-axis, and z-axis along MD, TD, and ND, respectively. We approximate \(\phi _{{\mathrm{vol}}}\) with a rectangular parallelepiped, and each lateral length of \(\phi _{{\mathrm{vol}}}\) is x, y, and L. As the width of a sheet y is large enough compared to x and L, y does not change during compression and elongation of the supercooled melt, i.e., \(y \cong {\mathrm{const}} \gg x,L\) (A3). Therefore, the supercooled melt should be compressed along the z-axis and elongated along the x-axis in the elongational crystallization via the roll system.

It is obvious that the tensor component of \(\dot \varepsilon \) along the x-axis (\(\dot \varepsilon _{{\mathrm{xx}}}\)) and z-axis (\(\dot \varepsilon _{{\mathrm{zz}}}\)) should satisfy the following relationship,

$$\dot \varepsilon _{{\mathrm{xx}}} = - \dot \varepsilon _{{\mathrm{zz}}}$$

based on Eq. A3 and the mass conservation law with respect to \(\phi _{{\mathrm{vol}}}\), \(\phi _{{\mathrm{vol}}} \cong xyL = {\mathrm{const}}\) (A5). Here, \(\dot \varepsilon _{{\mathrm{zz}}}\) is defined by

$$\dot \varepsilon _{{\mathrm{zz}}} \equiv \frac{1}{L} \cdot \frac{{{\mathrm{d}}L}}{{{\mathrm{d}}t}},$$

where t is time.

From Fig. 11a, L is written as

$$L = 2R_{{\mathrm{roll}}}\left( {1 - {\mathrm{cos}}\theta } \right) + L_{{\mathrm{obs}}}.$$

Since cosθ is approximated by \({\mathrm{cos}}\theta \cong 1 - \frac{1}{2}\theta ^2\) (A8) from Eq. A1, we can obtain, using Eqs. A7 and A8,

$$L = R_{{\mathrm{roll}}}\theta ^2 + L_{{\mathrm{obs}}}.$$
$$\therefore \theta = \left( {\frac{{L - L_{{\mathrm{obs}}}}}{{R_{{\mathrm{roll}}}}}} \right)^{1/2}$$

Here, \(\omega \equiv - \left( {\frac{{{\mathrm{d}}\theta }}{{{\mathrm{d}}t}}} \right)\) (A11) and \(\omega = V_{\mathrm{R}}/R_{{\mathrm{roll}}}\) (A12). From Eqs. A4, A6, A9, A10, and A11, we have

$$\dot \varepsilon _{{\mathrm{xx}}} \cong 2\omega \sqrt {\frac{{R_{{\mathrm{roll}}}}}{L}\left( {1 - \frac{{L_{{\mathrm{obs}}}}}{L}} \right)} .$$

As \(\dot \varepsilon _{{\mathrm{xx}}}\) has a maximum (\(\dot \varepsilon _{{\mathrm{xx}}}^{{\mathrm{max}}}\)) at L = 2Lobs (A14), from Eqs. A13 and A14, we obtain

$$\therefore \dot \varepsilon _{{\mathrm{xx}}}^{{\mathrm{max}}} \cong \omega \sqrt {\frac{{R_{{\mathrm{roll}}}}}{{L_{{\mathrm{obs}}}}}} .$$

To form NOCs (Fig. 11b), it is a necessary condition that \(\dot \varepsilon _{{\mathrm{xx}}}^{{\mathrm{max}}}\) is larger than \(\dot \varepsilon ^*\).

Here, we define Eq. A15 as \(\dot \varepsilon \), i.e., \(\dot \varepsilon \equiv \dot \varepsilon _{{\mathrm{xx}}}^{{\mathrm{max}}}\) (A16). Therefore, from Eqs. A12, A15, and A16, we can obtain

$$\therefore \dot \varepsilon = \frac{{V_{\mathrm{R}}}}{{\sqrt {R_{{\mathrm{roll}}}L_{{\mathrm{obs}}}} }}.$$

Inclined two-point patterns in SAXS patterns for edge-view

We observed the inclined two-point pattern of 100 with an angle of \( \pm \phi \) in the SAXS pattern for the edge-view (Fig. 12). The dominant inclined two-point patterns in Fig. 12a, c were asymmetric and mirrored one another. In contrast, the image of b shows a symmetric pattern. Therefore, the monoclinic arrangement of NCs, shown in DISCUSSION, partly showed an inside-out pattern with low probability.

Fig. 12
figure 12

Schematic illustration of sample edge-view and SAXS patterns. Tc = 241 °C and \(\dot \varepsilon \) = 3.2 × 102 s−1. ac X-ray was irradiated on the corresponding position in the sample. (Color figure online)

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Okada, K., Tanaka, Y., Masunaga, H. et al. 3D structure of nano-oriented crystals of poly(ethylene terephthalate) formed by elongational crystallization from the melt. Polym J 50, 167–176 (2018).

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