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Non-isothermal crystallization kinetics of polyethylene terephthalate: a study based on Tobin, Hay and Nakamura models

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Abstract

Appropriate knowledge of non-isothermal crystallization kinetics of polyethylene terephthalate is vital in producing final polymeric parts with a certain degree of crystallization. Hence, PET was synthesized through a two-step esterification and polycondensation method. The structure of prepared PET was examined using FTIR and NMR tests. Due to the practical applications of the crystallization process, non-isothermal crystallization of PET was studied from the melt state under various cooling rates (\(\Phi\)) between 5 and 40 K/min using DSC, demonstrating a wide range of \(\Phi\). The experimental results revealed that the crystallization reaches its final value for the cooling rates of 5 and 10 K/min. However, a partial crystallization occurred under higher cooling rates. The recrystallization of these samples during heating was confirmed. Empirical data showed no meaningful change in Tg and Tm with cooling rate. However, TC and the final degree of crystallization varied linearly with cooling rate. Crystallization kinetic models are classified into two types: nonlinear and those that can be converted to linear. Due to the secondary crystallization of PET, the Avrami model could not make a good prediction. Among the linearizable models, Tobin model fitted the results very well. Among the nonlinear forms, the recently developed Hay model has an excellent ability to describe non-isothermal kinetics. Moreover, the integral type of Nakamura model was fitted instead of the normal differentiation form. A two-step optimization method is presented to achieve a high regression coefficient for nonlinear fitted models.

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References

  1. Hafsia KB, Ponçot M, Chapron D, Royaud I, Dahoun A, Bourson P (2016) A novel approach to study the isothermal and non-isothermal crystallization kinetics of poly (ethylene terephthalate) by Raman spectroscopy. J Polym Res 23:1–14

    Article  Google Scholar 

  2. Gaonkar AA, Murudkar VV, Deshpande VD (2020) Comparison of crystallization kinetics of polyethylene terephthalate (PET) and reorganized PET. Thermochim Acta 683:178472

    Article  CAS  Google Scholar 

  3. Heidrich D, Gehde M (2022) The 3-phase structure of polyesters (PBT, PET) after isothermal and non-isothermal crystallization. Polymers 14:793

    Article  CAS  Google Scholar 

  4. Jog JP (1995) Crystallization of polyethylene terephthalate. J Macromol Sci C 35:531–553

    Article  Google Scholar 

  5. Van Antwerpen F, Van Krevelen DW (1972) Influence of crystallization temperature, molecular weight, and additives on the crystallization kinetics of poly (ethylene terephthalate). J Polym Sci B 10:2423–2435

    Google Scholar 

  6. Jabarin SA (1987) Crystallization kinetics of polyethylene terephthalate: I)isothermal crystallization from the melt. J Appl Polym Sci 34:85–96

    Article  CAS  Google Scholar 

  7. Jabarin SA (1987) Crystallization kinetics of polyethylene terephthalate: II)dynamic crystallization of PET. J Appl Polym Sci 34:97–102

    Article  CAS  Google Scholar 

  8. Phillips PJ, Tseng HT (1989) Influence of pressure on crystallization in poly (ethylene terephthalate). Macromolecules 22:1649–1655

    Article  CAS  Google Scholar 

  9. Jiang XL, Luo SJ, Sun K, Chen XD (2007) Effect of nucleating agents on crystallization kinetics of PET. Express Polym Lett 1:245–251

    Article  CAS  Google Scholar 

  10. Deetuam C, Samthong C, Choksriwichit S, Somwangthanaroj A (2020) Isothermal cold crystallization kinetics and properties of thermoformed poly (lactic acid) composites: effects of talc, calcium carbonate, cassava starch and silane coupling agents. Iran Polym J 29:103–116

    Article  CAS  Google Scholar 

  11. Wang G, Chen Y (2018) Isothermal crystallization and spherulite morphology of poly (ethylene terephthalate)/Na+-MMT nanocomposites prepared through solid-state mechanochemical method. J Therm Anal Calorim 131:2611–2624

    Article  CAS  Google Scholar 

  12. Thamizhlarasan A, Meenarathi B, Parthasarathy V, Jancirani A, Anbarasan R (2021) Effect of nucleating agents on the non-isothermal crystallization and degradation kinetics of poly (ethylene terephthalate). Polym Adv Technol 32:766–778

    Article  CAS  Google Scholar 

  13. Sohrabi A, Rafizadeh M (2022) Non-isothermal crystallization and thermo-mechanical properties of poly (butylene adipate-co-ethylene terephthalate) random copolyesters. Thermochim Acta 2:179252

    Article  Google Scholar 

  14. Mohammadi Avarzman A, Rafizadeh M, Afshar Taromi F (2021) Branched polyester based on the polyethylene tere/iso phthalate and trimellitic anhydride as branching agent. Polym Bull 79:6099–6121

    Article  Google Scholar 

  15. Kahkesh S, Rafizadeh M (2020) Flame retardancy and thermal properties of poly (butylene succinate)/nano-boehmite composites prepared via in situ polymerization. Polym Eng Sci 60:2262–2271

    Article  CAS  Google Scholar 

  16. Topkanlo HA, Ahmadi Z, Taromi FA (2018) An in-depth study on crystallization kinetics of PET/PLA blends. Iran Polym J 27:13–22

    Article  CAS  Google Scholar 

  17. Groeninckx G, Berghmans H, Overbergh N, Smets G (1974) Crystallization of poly (ethylene terephthalate) induced by inorganic compounds: I)crystallization behavior from the glassy state in a low-temperature region. J Polym Sci B 12:303–316

    CAS  Google Scholar 

  18. Johnson JE (1959) X-ray diffraction studies of the crystallinity in polyethylene terephthalate. J Appl Polym Sci 2:205–209

    Article  CAS  Google Scholar 

  19. Fielding-Russell GS, Pillai PS (1970) A study of the crystallization of polyethylene terephthalate using differential scanning calorimetry and X-ray techniques. Die Makromol Chem 135:263–274

    Article  CAS  Google Scholar 

  20. Elsner G, Koch MHJ, Bordas J, Zachmann HG (1981) Time resolved small angle scattering during isothermal crystallization of unoriented poly (ethylene terephthalate) using synchrotron radiation. Die Makromol Chem 182:1263–1269

    Article  CAS  Google Scholar 

  21. Engelbrecht S, Tybussek KH, Sampaio J, Böhmler J, Fischer BM, Sommer S (2019) Monitoring the isothermal crystallization kinetics of PET-A using THz-TDS. J Infrared Millim Terahertz Waves 40:306–313

    Article  CAS  Google Scholar 

  22. Menczel JD, Prime RB (2009) Thermal analysis of polymers: fundamentals and applications. Wiley, New Jersey

    Book  Google Scholar 

  23. Mohammadi S, Taremi FA, Rafizadeh M (2012) Crystallization conditions effect on molecular weight of solid-state polymerized poly (ethylene terephthalate). Iran Polym J 21:415–422

    Article  CAS  Google Scholar 

  24. Lemanowicz M, Mielańczyk A, Walica T, Kotek M, Gierczycki A (2021) Application of polymers as a tool in crystallization: a review. Polymers 13:2695

    Article  CAS  Google Scholar 

  25. Wang ZG, Hsiao BS, Sauer BB, Kampert WG (1999) The nature of secondary crystallization in poly (ethylene terephthalate). Polymer 40:4615–4627

    Article  CAS  Google Scholar 

  26. Lu XF, Hay JN (2001) Isothermal crystallization kinetics and melting behaviour of poly (ethylene terephthalate). Polymer 42:9423–9431

    Article  CAS  Google Scholar 

  27. Chen Z, Hay JN, Jenkins MJ (2016) The effect of secondary crystallization on crystallization kinetics—polyethylene terephthalate revisited. Eur Polym J 81:216–223

    Article  CAS  Google Scholar 

  28. Verhoyen O, Dupret F, Legras R (1998) Isothermal and non-isothermal crystallization kinetics of polyethylene terephthalate: mathematical modeling and experimental measurement. Polym Eng Sci 38:1594–1610

    Article  CAS  Google Scholar 

  29. Balamurugan GP, Maiti SN (2008) Nonisothermal crystallization kinetics of polyamide 6 and ethylene-co-butyl acrylate blends. J Appl Polym Sci 107:2414–2435

    Article  CAS  Google Scholar 

  30. Meng C, Liu X (2022) Isothermal crystallization kinetics of bio-based semi-aromatic high-temperature polyamide PA5T/56. Iran Polym J 31:605–617

    Article  CAS  Google Scholar 

  31. Yao H, Li W, Zeng Z, Wang T, Zhu J, Lin Z (2022) Non-isothermal crystallization kinetics of poly (phthalazinone ether sulfone)/MC nylon 6 in-situ composites. Iran Polym J31:869–882

    Article  Google Scholar 

  32. Mahalakshmi S, Kannammal L, Tung KL, Anbarasan R, Parthasarathy V, Alagesan T (2019) Evaluation of kinetic parameters for the crystallization and degradation process of synthesized strontium mercaptosuccinate functionalized poly (ε-caprolactone) by non-isothermal approach. Iran Polym J 28:549–562

    Article  CAS  Google Scholar 

  33. Sánchez-Arrieta N, De Ilarduya AM, Alla A, Muñoz-Guerra S (2005) Poly (ethylene terephthalate) copolymers containing 1, 4-cyclohexane dicarboxylate units. Eur Polym J 41:1493–1501

    Article  Google Scholar 

  34. Charles J, Ramkumaar GR (2009) FTIR and thermal studies on polyethylene terephthalate and acrylonitrile butadiene styrene. Asian J Chem 21:4389–4398

    CAS  Google Scholar 

  35. Chang SJ, Chang FC (1999) Synthesis and characterization of copolyesters containing the phosphorus linking pendent groups. J Appl Polym Sci 72:109–122

    Article  CAS  Google Scholar 

  36. Han Z, Wang Y, Wang J, Wang S, Zhuang H, Liu J, Tang J (2018) Preparation of hybrid nanoparticle nucleating agents and their effects on the crystallization behavior of poly (ethylene terephthalate). Materials 11:587

    Article  Google Scholar 

  37. Smith CW, Dole M (1956) Specific heat of synthetic high polymers: VII) polyethylene terephthalate. J Polym Sci 20:37–56

    Article  CAS  Google Scholar 

  38. Phang IY, Pramoda KP, Liu T, He C (2004) Crystallization and melting behavior of polyester/clay nanocomposites. Polym Int 53:1282–1289

    Article  CAS  Google Scholar 

  39. Lin CC (1983) The rate of crystallization of poly (ethylene terephthalate) by differential scanning calorimetry. Polym Eng Sci 23:113–116

    Article  CAS  Google Scholar 

  40. Torrens-Serra J, Venkataraman S, Stoica M, Kuehn U, Roth S, Eckert J (2011) Non-isothermal kinetic analysis of the crystallization of metallic glasses using the master curve method. Materials 4:2231–2243

    Article  CAS  Google Scholar 

  41. Ozawa T (1971) Kinetics of non-isothermal crystallization. Polymer 12:150–158

    Article  CAS  Google Scholar 

  42. Heidarzadeh N, Rafizadeh M, Afshar Taromi F, Puiggalí J, del Valle LJ (2019) Nucleating and retarding effects of nanohydroxyapatite on the crystallization of poly (butylene terephthalate-co-alkylenedicarboxylate) s with different lengths. J Therm Anal Calorim 137:421–435

    Article  CAS  Google Scholar 

  43. Tobin MC (1974) Theory of phase transition kinetics with growth site impingement: I. homogeneous nucleation. J Polym Sci B 12:399–406

    CAS  Google Scholar 

  44. Tobin MC (1976) The theory of phase transition kinetics with growth site impingement. II Heterogeneous nucleation. J Polym Sci B 14:2253–2257

    CAS  Google Scholar 

  45. Tobin MC (1977) Theory of phase transition kinetics with growth site impingement: III) mixed heterogeneous-homogeneous nucleation and nonintegral exponent of the time. J Polym Sci B 15:2269–2270

    CAS  Google Scholar 

  46. Ravindranath K, Jog JP (1993) Polymer crystallization kinetics: poly (ethylene terephthalate) and poly (phenylene sulfide). J Appl Polym Sci 49:1395–1403

    Article  CAS  Google Scholar 

  47. Chen Z, Jenkins MJ, Hay JN (2014) Annealing of poly (ethylene terephthalate). Eur Polym J 50:235–242

    Article  CAS  Google Scholar 

  48. Chen Z, Hay JN, Jenkins MJ (2013) The effect of secondary crystallization on melting. Eur Polym J 49:2697–2703

    Article  CAS  Google Scholar 

  49. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J Optim 9:112–147

    Article  Google Scholar 

  50. Nakamura K, Watanabe T, Katayama K, Amano T (1972) Some aspects of nonisothermal crystallization of polymers: I. Relationship between crystallization temperature, crystallinity, and cooling conditions. J Appl Polym Sci 16:1077–1091

    Article  CAS  Google Scholar 

  51. Nakamura K, Katayama K, Amano T (1973) Some aspects of nonisothermal crystallization of polymers: II. Consideration of the isokinetic condition. J Appl Polym Sci 17:1031–1041

    Article  CAS  Google Scholar 

  52. Seo J, Zhang X, Schaake RP, Rhoades AM, Colby RH (2021) Dual Nakamura model for primary and secondary crystallization applied to nonisothermal crystallization of poly (ether ether ketone). Polym Eng Sci 61:2416–2426

    Article  CAS  Google Scholar 

  53. Hoffman JD, Davis GT, Lauritzen JI (1976) In: Hannay NB (ed) Treatise on solid state chemistry. Springer, Boston

  54. Marand H, Xu J, Srinivas S (1998) Determination of the equilibrium melting temperature of polymer crystals: linear and nonlinear Hoffman–Weeks extrapolations. Macromolecules 31:8219–8229

    Article  CAS  Google Scholar 

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Sheikh Nezhad Moghadam, A., Rafizadeh, M. & Afshar Taromi, F. Non-isothermal crystallization kinetics of polyethylene terephthalate: a study based on Tobin, Hay and Nakamura models. Iran Polym J 32, 125–137 (2023). https://doi.org/10.1007/s13726-022-01109-w

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