Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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

## Abstract

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.

This is a preview of subscription content, access via your institution

## Access options

\$32.00

All prices are NET prices.

## References

1. Okada K, Washiyama J, Watanabe K, Sasaki S, Masunaga H, Hikosaka M. Elongational crystallization of isotactic polypropylene forms nano-oriented crystals with ultra-high performance. Polymer J. 2010;42:464–73.

2. Kakudo M, Kasai N. Kobunshi xsen kaisetsu. Tokyo, Japan: Maruzen publishing Co. Ltd.; 1968. p. 75–96.

3. Okada K, Tagashira K, Sakai K, Masunaga H, Hikosaka M. Temperature dependence of crystallization of nano-oriented crystals of iPP and the formation mechanism. Polymer J. 2013;45:70–8.

4. Price FP. Nucleation. In: Zettlemoyer AC, editor. Ch. 8. New York, NY: Marcel Dekker Inc.; 1969.

5. Daubeny R, de P, Bunn CW, Brown CJ. The crystal structure of polyethylene terephthalate. Proc R Soc Lond. 1954;A226:531–42.

6. Ikeda M, Mitsuishi Y. Studies on thermal behavior and fine structure of polyethylene-terephthalate. I. Equilibrium melting temperature and surface free energy. Koubunshi Kagaku. 1967;24:378–84.

7. Fakirov S, Fischer EW, Hoffmann R, Schmidt GF. Structure and properties of poly(ethylene terephthalate) crystallized by annealing in the highly oriented state: 2. Melting behavior and the mosaic block structure of the crystalline layers. Polymer. 1977;18:1121–9.

8. Mehta A, Gaur U, Wunderlich B. Equilibrium melting parameters of poly(ethylene terephthalate). J Polymer Sci Polymer Phys. 1978;16:289–96.

9. Dörscher M, Wegner G. Poly(ethylene terephthalate): a solid state condensation process. Polymer. 1978;19:43–7.

10. Alexander LE. X-ray diffraction methods in polymer science. Ch. 4. Kyoto, Japan: Kagaku-Dojin Publishing Company Inc.; 1973.

11. Hahn T, editor. International tables for crystallography. Vol. A. 4th ed. Dordrecht, Netherlands: Kluwer Academic Publishers; 1996. p. 106–7.

12. Asano T, Seto T. Morphological studies of cold drawn poly(ethylene terephthalate). Polymer J. 1973;5:72–85.

13. Kan-no T. Plastics processing databook. Tokyo, Japan: Nikkan Kogyo Shimbun, The Japan Society for Technology of Plasticity; 2002. p 39.

14. Fischer EW, Fakirov S. Structure and properties of polyethyleneterephthalate crystallized by annealing in the highly oriented state. Part 1 Morphological structure as revealed by small-angle X-ray scattering. J Mater Sci. 1976;11:1041–65.

15. Tatsumi T. Ryutairikigaku. Tokyo, Japan: Baifukan Co. Ltd.; 1982. p. 171.

16. Kassner K. Science and technology of crystal growth. In: van der Eerden JP, Bruinsma OSL, editors. Dordrecht, Netherlands: Kluwer Academic Publishers; 1995. p. 193.

## Acknowledgments

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.

## Author information

Authors

### Corresponding author

Correspondence to Masamichi Hikosaka.

## Ethics declarations

### Conflict of interest

The authors declare that they have no competing interests.

## APPENDIX

### APPENDIX

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,

$$\theta \ll 1$$
(A1)
$$R_{{\mathrm{roll}}} \gg L_{{\mathrm{obs}}}$$
(A2)

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,

$$\dot \varepsilon _{{\mathrm{xx}}} = - \dot \varepsilon _{{\mathrm{zz}}}$$
(A4)

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

$$\dot \varepsilon _{{\mathrm{zz}}} \equiv \frac{1}{L} \cdot \frac{{{\mathrm{d}}L}}{{{\mathrm{d}}t}},$$
(A6)

where t is time.

From Fig. 11a, L is written as

$$L = 2R_{{\mathrm{roll}}}\left( {1 - {\mathrm{cos}}\theta } \right) + L_{{\mathrm{obs}}}.$$
(A7)

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,

$$L = R_{{\mathrm{roll}}}\theta ^2 + L_{{\mathrm{obs}}}.$$
(A9)
$$\therefore \theta = \left( {\frac{{L - L_{{\mathrm{obs}}}}}{{R_{{\mathrm{roll}}}}}} \right)^{1/2}$$
(A10)

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

$$\dot \varepsilon _{{\mathrm{xx}}} \cong 2\omega \sqrt {\frac{{R_{{\mathrm{roll}}}}}{L}\left( {1 - \frac{{L_{{\mathrm{obs}}}}}{L}} \right)} .$$
(A13)

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

$$\therefore \dot \varepsilon _{{\mathrm{xx}}}^{{\mathrm{max}}} \cong \omega \sqrt {\frac{{R_{{\mathrm{roll}}}}}{{L_{{\mathrm{obs}}}}}} .$$
(A15)

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

$$\therefore \dot \varepsilon = \frac{{V_{\mathrm{R}}}}{{\sqrt {R_{{\mathrm{roll}}}L_{{\mathrm{obs}}}} }}.$$
(A17)

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.

## Rights and permissions

Reprints and Permissions

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). https://doi.org/10.1038/s41428-017-0003-9

• Revised:

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41428-017-0003-9