Skip to main content

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.

  • Original Article
  • Published:

Prediction of the heat capacity of main-chain-type polymers below the glass transition temperature

Polymer Journal volume 52, pages 1113–1120 (2020)Cite this article

Subjects

Abstract

This study predicts the absolute values of heat capacities from the molecular formula per monomer for main-chain-type polymers below the glass transition temperature. The frequencies of the skeletal and group-vibration modes are calculated using the Tarasov and Einstein equations, respectively, and the heat-capacity differences at constant pressure and constant volume are used to correct the predicted heat capacity. The contributes of skeletal vibrations to the heat capacity can be expressed by one- and three-dimensional Tarasov equations, and the contribution of group vibrations can be determined by summing the group-vibration heat capacities for functional groups and atoms constituting the monomer as obtained from the Einstein equation. The absolute value of the heat capacity is predicted from this combination of equations. The heat capacities of poly(4-methyl-1-pentene) are predicted within an error range of 8.0% from 90 to 180 K and ±2.0% from 180 to 300 K. The heat capacities of poly(vinyl benzoate) are within ±2.0% agreement from 190 to 350 K, while for poly(1,4-butylene adipate), the agreement is within ±2.0% from 80 to 200 K.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

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 Data. 1982;11:1–392.

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  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 8. New York: 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. Kume Y, Muraoka H, Yamamuro O, Matsuo T. Deuteration-induced phase transition in ammonium hexachloroplumbate. J Chem Phys. 1988;108:4090–7.

  9. Miyazaki Y, Wang Q, Sato A, Saito K, Yamamoto M, Kitagawa H, et al. Heat capacity of the halogen-bridged mixed-valence complex Pt2 (dta)4I (dta = CH3CS2−). J Phys Chem B. 2002;106:197–202.

    Article  CAS  Google Scholar 

  10. Yamamura Y, Nakajima N, Tsuji T, Koyano M, Iwasa Y, Katayama S, et al. Low temperature heat capacities and Raman spectra of negative thermal expansion compounds ZrW2O8 and HfW2O8. Phys Rev B. 2002;66:014301.

    Article  CAS  Google Scholar 

  11. Matsuo T, Maekawa T, Inaba A, Yamamuro O, Ohama M, Ichikawa M, et al. Isotope-dependent crystalline phases at ambient temperature: spectroscopic and calorimetric evidence for a deuteration-induced phase transition at 320 K in α-DCrO2. J Mol Struct. 2006;790:129–34.

    Article  CAS  Google Scholar 

  12. Saito K, Sato A, Kikuchi K, Nishikawa H, Ikemoto I, Sorai M. Calorimetric study of metal-insulator transition in (DIMET) 2I 3. J Phys Soc Jpn. 2000;69:3602–6.

    Article  CAS  Google Scholar 

  13. 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 

  14. 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Nernst W, Lindemann FA. Spezifische Wärme und Quantentheorie. Z Elektrochem. 1911;17:817–27.

    CAS  Google Scholar 

  18. Tarasov VV. Heat capacity of anisotropic solids. Zh Fiz Khimii. 1950;24:111–28.

    CAS  Google Scholar 

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

    Google Scholar 

  20. 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

  21. 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 

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

    Article  CAS  Google Scholar 

  23. 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 

  24. 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 

  25. 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 

  26. 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 

  27. Yokota M, Sugane K, Tsukushi I, Shibata M. Evaluation of the heat capacity of amorphous polymers composed of a carbon backbone below the glass-transition temperature, Polym J. 2020. https://doi.org/10.1038/s41428-020-0317-x.

  28. 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. https://doi.org/10.1038/s41428-020-0364-3.

  29. Karasz FE, Bair HE, O’Reilly JM. Thermodynamic properties of poly-4-methyl-pentene-1. Polymer. 1967;8:547–60.

    Article  CAS  Google Scholar 

  30. Pasquini M, Melia TP, Marchetti A. Thermal properties of some substructured poly(vinyl benzoates). Therm Anal Proc Int Conf 4th. 1974;2:65.

    Google Scholar 

  31. Rabinovich IB, Nistratov VP, Babinkov AG, Shvetsova KG, Larina VN. Thermodynamic properties of polybutyleneglycol adipate. Polym Sci USSR 1984;26:826–31.

    Article  Google Scholar 

  32. NIST Chemistry WebBook SRD69. 100 Bureau Drive Gaithersburg, MD 20899, 301-975-2000. 1901. https://webbook.nist.gov/cgi/cbook.cgi?ID=C106989&Units=SI&Mask=80#IR-Spec. Accessed 7 Nov 2019.

  33. Kauzmann K. The nature of the glassy state and the behavior of liquids at low temperatures. Chem Rev. 1948;43:219–56.

    Article  CAS  Google Scholar 

  34. Angell CA, Choi Y. Crystallization and vitrification in aqueous systems. J Microsc. 1986;141:251–6.

    Article  CAS  Google Scholar 

  35. Abramowitz M, Stegun IA. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. New York: Dover Publications; 1965. p. 796.

    Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. Graduate School of Engineering, Chiba Institute of Technology, 2-1-1 Shibazono, Narashino, Chiba, 275-0023, Japan

    Marika Yokota & Itaru Tsukushi

Authors
  1. Marika Yokota
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Itaru Tsukushi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Itaru Tsukushi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yokota, M., Tsukushi, I. Prediction of the heat capacity of main-chain-type polymers below the glass transition temperature. Polym J 52, 1113–1120 (2020). https://doi.org/10.1038/s41428-020-0365-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41428-020-0365-2

This article is cited by

Search

Advanced search

Quick links