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Analysis of the configurational heat capacity of polystyrene and its monomer and oligomer above the glass transition temperature

Abstract

In this study, we investigated the functions that reproduce the configurational heat capacity (Cconfig) above the glass transition temperature for polystyrene (PS), polyisobutylene (PIB), and their oligomers. The results show that Cconfig can be well reproduced using the power and logarithmic functions based on Landau theory, which explains the vicinity of the critical point. The power and logarithmic functions had four and three fitting parameters, respectively. The error ranges were ~±2% for PS and ±5% for PIB.

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References

  1. Wagman DD, Evans WH, Parker VB, Schumm RH, Halow I, Bailey SM. The NBS tables of chemical thermodynamic properties: Selected values for inorganic and C1 and C2 organic substances in SI units. J Phys Chem Ref Dat. 1982;11:1–392.

  2. Gopal ESR. Specific heats at low temperatures. London: Springer, 2012.

  3. Wunderlich B. Thermal analysis of polymeric materials. Springer, Heidelberg; 2005.

  4. Glassy, amorphous and nano-crystalline materials: thermal physics, analysis, structure and properties. In: Šesták J, Mareš JJ, Hubík P, editors. Hot topics in thermal analysis and calorimetry. vol. 8. Springer Science & Business Media; 2010.

  5. Gibson GE, Giauque WF. The third law of thermodynamics. Evidence from the specific heats of glycerol that the entropy of a glass exceeds that of a crystal at the absolute zero. J Am Chem Soc. 1923;45:93–104.

    Article  CAS  Google Scholar 

  6. Haida O, Matsuo T, Suga H, Seki S. Calorimetric study of the glassy state X. Enthalpy relaxation at the glass-transition temperature of hexagonal ice. J Chem Thermodyn. 1974;6:815–25.

    Article  CAS  Google Scholar 

  7. Tajima Y, Matsuo T, Suga H. Calorimetric study of phase transition in hexagonal ice doped with alkali hydroxides. J Phys Chem Solids. 1984;45:1135–44.

    Article  CAS  Google Scholar 

  8. Jianye W. Heat capacities of polymers in physical properties of polymers handbook. In: James E. Mark, editor. Chapter 9. New York: Springer; 2007. p. 145–54.

  9. Domalski ES, Hearing ED. Heat capacities and entropies of organic compounds in the condensed phase. Volume III. J Phys Chem Ref Data. 1996;25:1–525.

    Article  CAS  Google Scholar 

  10. Pyda M, Bartkowiak M, Wunderlich B. Computation of heat capacities of solids using a general Tarasov equation. J Therm Anal. 1998;52:631–56.

    Article  CAS  Google Scholar 

  11. Wunderlich B. Motion in polyethylene. II. Vibrations in crystalline polyethylene. J Chem Phys. 1962;37:1207–16.

    Article  CAS  Google Scholar 

  12. Pyda M, Nowak-Pyda E, Mays J, Wunderlich B. Heat capacity of poly (butylene terephthalate). J Polym Sci. 2004;42:4401–11.

    Article  CAS  Google Scholar 

  13. Yoshida S, Suga H, Seki S. Thermodynamic studies of solid polyethers. II. Heat capacity of poly(oxacyclobutane), –[–(CH2)3O–]– n, between 1.4 and 330°K. Polym J. 1973;5:11–24.

    Article  CAS  Google Scholar 

  14. Yoshida S, Suga H, Seki S. Thermodynamic studies of solid polyethers. III. Poly(tetrahydrofuran), –[–(CH2)4O–]–n. Polym J. 1973;5:25–32.

    Article  CAS  Google Scholar 

  15. Yoshida S, Suga H, Seki S. Thermodynamic studies of solid polyethers. IV. Poly(octamethylene oxide), –[–(CH2)8O–]–n. Polym J. 1973;5:33–40.

    Article  CAS  Google Scholar 

  16. Yokota M, Nishiyama E, Fujimura J, Tsukushi I. Excess heat capacity for low-molecular-weight amorphous polystyrene below the glass-transition temperature: influence of end groups. Polym J. 2020;52:575–80.

    Article  CAS  Google Scholar 

  17. Yokota M, Sugane K, Tsukushi I, Shibata M. Evaluation of the heat capacity of amorphous polymers composed of a carbon backbone below their glass transition temperature. Polym J. 2020;52:765–74.

    Article  CAS  Google Scholar 

  18. Yokota M, Tsukushi I. Heat capacities of polymer solids composed of polyesters and poly(oxide)s, evaluated below the glass-transition temperature. Polym J. 2020;52:1103–11.

    Article  CAS  Google Scholar 

  19. Einstein A. Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme. Ann der Phys. 1907;327:180–90.

    Article  Google Scholar 

  20. Tarasov VV, Yunitskii GA. Theory of heat capacity of chain and layer structures. Russ J Phys Chem. 1965;39:1109–11.

    Google Scholar 

  21. Debye P. Zur Theorie der spezifischen Wärmen. Ann der Phys. 1912;344:789–839.

    Article  Google Scholar 

  22. Yokota M, Tsukushi I. Prediction of the heat capacity of main-chain-type polymers below the glass transition temperature. Polym J. 2020;52:1113–20.

    Article  CAS  Google Scholar 

  23. Nishiyama E, Yokota M, Tsukushi I. Estimation of the configurational heat capacity of polyisobutylene, isobutane and 2,2,4-isomethylpentane above the glass transition temperature. Polym J. 2021;53:1031–6.

  24. Yamamuro O, Tsukushi I, Lindqvist A, Takahara S, Ishikawa M, Matsuo T. Calorimetric study of glassy and liquid toluene and ethylbenzene: thermodynamic approach to spatial heterogeneity in glass-forming molecular liquids. J Phys Chem B. 1998;102:1605–9.

    Article  CAS  Google Scholar 

  25. Tatsumi S, Aso S, Yamamuro O. Thermodynamic study of simple molecular glasses: universal features in their heat capacity and the size of the cooperatively rearranging regions. Phys Rev Lett. 2012;109:045701.

    Article  Google Scholar 

  26. Gaur U, Wunderlich B. Heat capacity and other thermodynamic properties of linear macromolecules. V. Polystyrene. J Phys Chem Ref Data. 1982;11:313–25.

    Article  CAS  Google Scholar 

  27. Schottky W. The rotation of atomic axes in solids (with magnetic, thermal and chemical applications). Physikalische Z. 1922;23:448–55.

    CAS  Google Scholar 

  28. Kadanoff LP, Götze W, Hamblen D, Hecht R, Lewis EAS, Palciaus VV, et al. Static phenomena near critical point: theory and experiment. Rev Mod Phys. 1967;39:395–431.

    Article  CAS  Google Scholar 

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Acknowledgements

The authors would like to thank Enago (www.enago.jp) for the English language review.

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Correspondence to Itaru Tsukushi.

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Nishiyama, E., Yokota, M. & Tsukushi, I. Analysis of the configurational heat capacity of polystyrene and its monomer and oligomer above the glass transition temperature. Polym J 54, 33–39 (2022). https://doi.org/10.1038/s41428-021-00554-3

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