Revisit the Gibbs-Thomson Equation Fitting of Poly(butylene succinate) Based on Oligomer Extended-Chain Crystals

Na Li; Yu-Pei Tian; Tian-Yu Wu; Qiong Zhou; Hai-Mu Ye

doi:10.1007/s10118-025-3270-5

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Revisit the Gibbs-Thomson Equation Fitting of Poly(butylene succinate) Based on Oligomer Extended-Chain Crystals

RESEARCH ARTICLE | Updated：2025-01-23

- Revisit the Gibbs-Thomson Equation Fitting of Poly(butylene succinate) Based on Oligomer Extended-Chain Crystals
- Chinese Journal of Polymer Science Vol. 43, Issue 2, Pages: 392-398(2025)
- Affiliations：
  
  College of New Energy and Materials, China University of Petroleum, Beijing 102249, China
- Author bio：
  
  yehaimu@cup.edu.cn
- Funds：
- DOI：10.1007/s10118-025-3270-5
  CLC：
- Received：14 October 2024，
  
  Revised：2024-11-14，
  
  Accepted：19 November 2024，
  
  Online First：17 January 2025，
  
  Published：01 February 2025
- Accepted：
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Li, N.; Tian, Y. P.; Wu, T. Y.; Zhou, Q.; Ye, H. M. Revisit the gibbs-thomson equation fitting of poly(butylene succinate) based on oligomer extended-chain crystals. Chinese J. Polym. Sci. 2025, 43, 392–398

Na Li, Yu-Pei Tian, Tian-Yu Wu, et al. Revisit the Gibbs-Thomson Equation Fitting of Poly(butylene succinate) Based on Oligomer Extended-Chain Crystals[J]. Chinese Journal of Polymer Science, 2025, 43(2): 392-398.
Li, N.; Tian, Y. P.; Wu, T. Y.; Zhou, Q.; Ye, H. M. Revisit the gibbs-thomson equation fitting of poly(butylene succinate) based on oligomer extended-chain crystals. Chinese J. Polym. Sci. 2025, 43, 392–398 DOI： 10.1007/s10118-025-3270-5.

Na Li, Yu-Pei Tian, Tian-Yu Wu, et al. Revisit the Gibbs-Thomson Equation Fitting of Poly(butylene succinate) Based on Oligomer Extended-Chain Crystals[J]. Chinese Journal of Polymer Science, 2025, 43(2): 392-398. DOI： 10.1007/s10118-025-3270-5.

摘要

The advantages of a fixed surface structure and large thickness of the oligomer ECCs make them ideal for validating the Gibbs-Thomson equation of PBS oligomer ECCs in comparison with the folded-chain lamellae data from previous literature.

Abstract

The equilibrium melting point (

) is a crucial thermodynamic parameter for characterizing the crystallization and melting behavior of semi-crystalline polymers. However

the direct measurement of

poses a significant challenge because of the difficulty in physically fabricating fully-extended chain crystals of high-molecular-weight polymers. Therefore

various extrapolation equations for

have been proposed that utilize the thermal properties of ordinary folded-chain lamellae. Among these

the Gibbs-Thomson equation is one of the most commonly employed for modeling. Despite its widespread use

there are notable variations in the

values obtained by different research groups

en when based on similar samples. This raises questions about the validity and accuracy of using the Gibbs-Thomson equation to linearly extrapolate

. In this study

we prepared a series of oligomer extended-chain crystals (ECCs) of poly(butylene succinate) (PBS) and used their properties for Gibbs-Thomson fitting. The results reveal a perfect linear relationship

with an extrapolated

value of 136.08 °C. The basal surface free energy of the oligomer ECCs was calculated as 0.084 J/m

which is approximately twice that of folded-chain lamellae. This difference is attributed to the aggregation of highly mobile free tails on the crystal surface. The two structural features of oligomer ECCs—large thickness and fixed surface—better fulfill the conditions for applying the Gibbs-Thomson equation

ensuring its validity and accuracy. Therefore

we believe that the Gibbs-Thomson fit can produce reliable results when sufficient high-quality data are used.

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references

Hoffman, J. D.; Davis, G. T.; Lauritzen, J. I. The Rate of Crystallization of Linear Polymers with Chain Folding. In Treatise on Solid State Chemistry; Springer: Boston, MA. 1976 , 497−614..

Flory, P. J.; Vrij, A. Melting points of linear-chain homologs. the normal paraffin hydrocarbons. J. Am. Chem. Soc. 1963 , 85 ,3548−3553..

Xu, J.; Heck, B.; Ye, H. M.; Jiang, J.; Tang, Y. R.; Liu, J.; Guo, B. H.; Reiter, R.; Zhou, D.-S.; Reiter, G. Stabilization of nuclei of lamellar polymer crystals: insights from a comparison of the Hoffman-weeks line with the crystallization line. Macromolecules 2016 , 49 , 2206−2215..

Hoffman, J. D.; Weeks, J. J. Melting process and the equilibrium melting temperature of polychlorotrifluoroethylene. J. Res. Natl. Bur. Stand A Phys. Chem. 1962 , 66A , 13−28..

Xie, Z. N.; Ye, H. M.; Chen, T.; Zheng, T. Z.; Xu, J.; Guo, B. H. Melting and annealing peak temperatures of poly(butylene succinate) on the same Hoffman-Weeks plot parallel to T m = T c line. Chinese J. Polym. Sci. 2021 , 39 , 745−755..

Gan, Z.; Abe, H.; Kurokawa, H.; Doi, Y. Solid-state microstructures, thermal properties, and crystallization of biodegradable poly(butylene succinate) (PBS) and its copolyesters. Biomacromolecules 2001 , 2 , 605−613..

Miyata, T.;Masuko, T. Cryst allization behaviour of poly(tetramethylene succinate). Polymer 1998 , 39 , 1399−1404..

Qiu, Z.; Ikehara, T.; Nishi, T. Miscibility and crystallization in crystalline/crystalline blends of poly(butylene succinate)/poly(ethylene oxide). Polymer 2003 , 44 , 2799−2806..

Papageorgiou, G. Z.; Bikiaris, D. N. Crystallization and melting behavior of three biodegradable poly(alkylene succinates). A comparative study. Polymer 2005 , 46 , 12081−12092..

Höhne G. W. H. Another approach to the Gibbs-Thomson equation and the melting point of polymers and oligomers. Polymer 2002 , 43 , 4689−4698..

Pandey, A.; Toda, A.; Rastogi, S. Influence of amorphous component on melting of semicrystalline polymers. Macromolecules 2011 , 44 , 8042−8055..

Toda, A.; Taguchi, K.; Nozaki, K. Gibbs-Thomson, thermal Gibbs-Thomson, and Hoffman-Weeks plots of polyethylene crystals examined by fast-scan calorimetry and small-angle X-ray scattering. Cryst. Growth Des. 2019 , 19 , 2493−2502..

Wunderlich, B.; Arakawa, T. Polyethylene crystallized from the melt under elevated pressure. J. Polym. Sci., Part A: Gen. Pap. 1964 , 2 , 3697−3706..

Geil, P. H.; Anderson, F. R.; Wunderlich, B.; Arakawa, T. Morphology of polyethylene crystallized from the melt under pressure. J. Polym. Sci., Part A: Polym. Chem. 1964 , 2 , 3707−3720..

Li, Y.; Tang, S.; Pan, M. W.; Zhu, L.; Zhong, G. J.; Li, Z. M. Polymorphic extended-chain and folded-chain crystals in poly(vinylidene fluoride) achieved by combination of high pressure and ion-dipole interaction. Macromolecules 2015 , 48 , 8565−8573..

Siegmann, A.; Harget, P. J. Melting and crystallization of poly(ethylene terephthalate) under pressure. J. Polym. Sci., Part B: Polym. Phys. 2010 , 18 , 2181−2196..

Ye, H. M.; Chen, X. T.; Liu, P.; Wu, S. Y.; Jiang, Z.; Xiong, B.; Xu, J. Preparation of poly(butylene succinate) crystals with exceptionally high melting point and crystallinity from its inclusion complex. Macromolecules 2017 , 50 , 5425−5433..

Ye, H.-M.; Chen, X.-T.; Li, H.-F.; Zhang, P.; Ma, W.; Li, B.; Xu, J. Industrializable and sustainable approach for preparing extended-chain crystals of biodegradable poly(butylene succinate) and their applications. Polymer 2019 , 160 , 93−98..

Tian, Y. P.; Wu, T.; Meng, X.; Ye, H. M. Thermodynamic features of extended-chain crystals of poly(butylene succinate) and its random copolymers with adipic acid. Macromolecules 2022 , 55 , 5669−5674..

Ye, H. M.; Song, Y. Y.; Xu, J.; Guo, B. H.; Zhou, Q. Melting behavior of inclusion complex formed between polyethylene glycol oligomer and urea. Polymer 2013 , 54 , 3385−3391..

Ye, H. M.; Li, H. F.; Wang, C. S.; Yang, J.; Huang, G.; Meng, X.; Zhou, Q. Degradable polyester/urea inclusion complex applied as a facile and environment-friendly strategy for slow-release fertilizer: Performance and mechanism. Chem. Eng. J. 2020 , 381 , 122704..

Ichikawa, Y.; Kondo, H.; Igarashi, Y.; Noguchi, K.; Okuyama, K.; Washiyama, J. Crystal structures of α and β forms of poly(tetramethylene succinate). Polymer 2000 , 41 , 4719−4727..

Chen, J. Y.; Li, N.; Wang, S.; Wu, T.; Meng, X.; Ye, H. M. Boosting solvent resistance and structure stability of degradable polyester through extended-chain crystal structure: A preliminary case of oil/water separation membrane. J. Environ. Chem. Eng. 2024 , 12 , 113507..

Yao, S. F.; Chen, X. T.; Ye, H. M. Investigation of structure and crystallization behavior of poly(butylene succinate) by Fourier transform infrared spectroscopy. J. Phys. Chem. B 2017 , 121 , 9476−9485..

Righetti, M. C.; Di Lorenzo, M. L.; Cinelli, P.; Gazzano, M. Temperature dependence of the rigid amorphous fraction of poly(butylene succinate). RSC Adv. 2021 , 11 , 25731−25737..

Chen, S. H.; Su, C. H.; Su, A. C. Sun, Y. S.; Jeng, U.; Chen, S. A. Gibbs-Thomson analysis of crystalline poly(9,9-di- n -octyl-2,7-fluorene). J. Appl. Cryst. 2007 , 40 , s573−s576..

Baratian, S.; Hall, E. S.; Lin, J. S.; Xu, R.; Runt, J. Crystallization and solid-state structure of random polylactide copolymers: poly( L -lactide- co - D -lactide)s. Macromolecules 2001 , 34 , 4857−4864..

Supaphol, P.; Spruiell, J. E.; Lin, J.-S. Isothermal melt crystallization and melting behaviour of syndiotactic polypropylene. Polym. Int. 2000 , 49 , 1473−1482..

Wang, C.; Cheng, Y. W.; Hsu, Y. C.; Lin, T. L. Lamellar morphology and equilibrium melting temperature of syndiotactic polystyrene in β -crystalline form. J. Polym. Sci., Part B: Polym. Phys. 2002 , 40 , 1626−1636..

Yamada, K.; Hikosaka, M.; Toda, A.; Yamazaki, S.; Tagashira, K. Molecular weight dependence of equilibrium melting temperature and lamellar thickening of isotactic polypropylene with high tacticity. J. Macromol. Sci., Part B. Phys., Part B-Phys. 2003 , 42 , 733−752..

Hocquet, S.; Dosière, M.; Thierry, A.; Lotz, B.; Koch, M. H. J.; Dubreuil, N.; Ivanov, D. A. Morphology and melting of truncated single crystals of linear polyethylene. Macromolecules 2003 , 36 , 8376−8384..

Schönherr, H.; Frank, C. W. Ultrathin films of poly(ethylene oxides) on oxidized silicon. 2. In situ study of crystallization and melting by hot stage AFM. Macromolecules 2003 , 36 , 1199−1208..

Yin, J.; Raegen, A.; Idziak, S. H. J.; Forrest, J. A. Crystallization and melting of highly monodisperse poly(ethylene-oxide). Soft Matter 2020 , 16 , 7958−7969..

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