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Evaluation of the heat capacity of amorphous polymers composed of a carbon backbone below their glass transition temperature

Polymer Journal volume 52, pages 765–774 (2020)Cite this article

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Abstract

Despite being a useful variable for the quantitative analysis of the thermodynamic properties of polymers, the absolute value of heat capacity remains poorly understood for amorphous polymers. This study evaluates the absolute values of the heat capacities of amorphous polymers by using the Tarasov and Einstein equations to calculate the frequencies of the skeletal and group vibration modes, respectively. Moreover, the difference between the heat capacity measured at constant pressure and that obtained at constant volume is added as a correction factor when estimating the heat capacity. The heat capacity that contributes to skeletal vibrations can be expressed using the one- and three-dimensional Tarasov equations, and the contribution of group vibrations can be determined by substituting the absorption frequency obtained from infrared absorption measurements into the frequency value of the Einstein equation. Only three fitting parameters were used to reproduce the absolute value of the heat capacity obtained from the combination of these equations. We used this approach to reproduce the heat capacities of 16 main chain-type amorphous polymers having a carbon backbone. The reproduced and experimental heat capacities of all the samples below their glass transition temperature agreed within less than ±2.5%.

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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;11:2.

    Google Scholar 

  2. Gopal ESR. Specific heats at low temperatures. London: Springer Science & Business Media; 2012.

  3. Wunderlich B. Thermal analysis of polymeric materials. Heidelberg: Springer Science & Business Media; 2005.

  4. Šesták J, Mareš JJ, Hubík P. Glassy, amorphous and nano-crystalline materials: thermal physics, analysis, structure and properties. 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.

    Article  Google Scholar 

  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 der Phys. 1907;327:180–90.

    Article  Google Scholar 

  16. Debye P. Zur theorie der spezifischen wärmen. Ann der 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, Yunitskii GA. Theory of heat capacity of chain and layer structures. Russ J Phys Chem. 1965;39:1109–11.

    Google Scholar 

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

  20. 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 

  21. Wunderlich B. The ATHAS database on heat capacities of polymers. Pure Appl Chem. 1995;67:1019–26.

    Article  CAS  Google Scholar 

  22. Chang SS, Bestul AB. Heat capacities of cis-1, 4-Polyisoprene from 2 to 360 K. J Res Natl Bur Stand A Phys Chem. 1971;75A:113–20.

    Article  Google Scholar 

  23. Dainton FS, Evans DM, Hoare FE, Melia TP. Thermodynamic functions of linear high polymers: part I—polyoxymethylene. Polymer. 1962;3:263–321.

    Article  CAS  Google Scholar 

  24. Bourdariat J, Berton A, Chaussy J, Isnard R, Odin J. Influence of cooling rate on the heat capacity and thermal transitions of amorphous polyhexene-1. Polymer. 1973;14:167–70.

    Article  CAS  Google Scholar 

  25. Furukawa GT, Reilly ML. Heat capacity of polyisobutylene from 0 to 380 K. J Res Natl Bur Stand. 1956;56:285.

    Article  CAS  Google Scholar 

  26. Chang SS. Heat capacity and thermodynamic properties of poly (vinyl chloride). J Res Natl Bur Stand. 1977;82:9–17.

    Article  CAS  Google Scholar 

  27. Lebedev BV, Rabinovich IB, Busarina VA. Heat capacity of vinyl chloride, polyvinylchloride and polyvinylidene chloride in the region of 60–300°K. Polym Sci USSR. 1967;9:545–52.

    Article  Google Scholar 

  28. Lee WK, Choy CL. Heat capacity of fluoropolymers. J Polym Sci. 1975;13:619–35.

    CAS  Google Scholar 

  29. Furukawa GT, McCoskey RE, King GJ. Calorimetric properties of polytetrafluoroethylene (Teflon) from 0 to 365 K. J Res Natl Bur Stand. 1952;49:273–8.

    Article  CAS  Google Scholar 

  30. Lebedev BV, Rabinovich IB, Martynenko LYa. The heat capacity and thermodynamic functions of acrylonitrile and polyacrylonitrile. Polym Sci USSR. 1967;9:1841–9.

    Article  Google Scholar 

  31. Rabinovich IB, Lebedev BV. Thermodynamics of vinyl monomers and polymers. V. Measurement of heat capacity and a calculation of the thermodynamic functions of poly (methyl acrylate), poly-(methyl methacrylate), poly (methacrylamide), poly (α-methylstyrene) and poly (vinyl alcohol). Tr Khim Tekhnol. 1967;2:36.

    Google Scholar 

  32. Pavlinov LI, Rabinovich IB, Okladnov NA, Arzhakov SA. Heat capacity of copolymers of methyl methacrylate with methacrylic acid in the region 25–190 °C. Polym Sci USSR. 1967;9:539–44.

    Article  Google Scholar 

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

  34. Stromberg RR, Straus S, Achhammer BG. Infrared spectra of thermally degraded poly (vinyl chloride). J Res Natl Bur Stand. 1958;60:147–52.

    Article  CAS  Google Scholar 

  35. Krimm S. Infrared spectra of high polymers. Fortschr Hochpolym Forsch Bd. 1960;2:51–172.

    Article  CAS  Google Scholar 

  36. Nallasamy P, Mohan S. Vibrational spectra of cis-1, 4-polyisoprene. Arab J Sci Eng. 2004;29:17–26.

    CAS  Google Scholar 

  37. NIST Chemistry WebBook SRD69. 100 Bureau Drive Gaithersburg, MD 20899. 1901. https://webbook.nist.gov/cgi/cbook.cgi?ID=C592416&Type=IR-SPEC&Index=1#IR-SPEC. Accessed 7 Nov 2019.

  38. Adams MA, Gabrys BJ, Zajac WM, Peiffer DG. High-resolution incoherent inelastic neutron scattering spectra of polyisobutylene and polyisoprene. Macromolecules. 2005;38:160–6.

    Article  CAS  Google Scholar 

  39. Hong JW, Lando JB, Koenig JL, Chough SH, Krimm S. Normal-mode analysis of infrared and Raman spectra of poly (vinyl fluoride). Vib Spectros. 1992;3:55–66.

    Article  CAS  Google Scholar 

  40. Nallasamy P, Mohan S. Vibrational spectroscopic characterization of form II poly (vinylidene fluoride). Indian J Pure Ap Phys. 2005;43:821–7.

    CAS  Google Scholar 

  41. Adams CJ, Downs AJ. The vibrational spectra and structures of selenium tetrafluoride and tellurium tetrafluoride: including a matrix-isolation study. Spectrochim Acta A. 1972;28:1841–54.

    Article  CAS  Google Scholar 

  42. Liang CY, Krimm S. Infrared spectra of high polymers. VII. Polyacrylonitrile. J Polym Sci. 1958;31:513–22.

    Article  CAS  Google Scholar 

  43. Willis HA, Zichy VJI, Hendra PJ. The laser-Raman and infra-red spectra of poly (methyl methacrylate). Polymer. 1969;10:737–46.

    Article  CAS  Google Scholar 

  44. Wei-Fang S. Principles of polymer design and synthesis. Wei-Fang Su, editor. Berlin Heidelberg: Springer-Verlag; 2013. 53.

  45. Bares V, Wunderlich B. Heat capacity of molten polymers. J Polym Sci. 1973;11:861–73.

    CAS  Google Scholar 

  46. Alger M. Polymer science dictionary. London: Springer Science & Business Media; 1996;463.

  47. PolymerProcessing.com. 66 Buckskin Drive Weston, MA 02493 USA. 2001. http://www.polymerprocessing.com/index.html. Accessed 7 Nov 2019.

  48. Yagi T. Heat of fusion and crystallization kinetics of Poly(trifluoroethylene). Polym J. 1980;12:9–15.

    Article  CAS  Google Scholar 

  49. Wunderlich B, Gaur U. Differential scanning calorimetry of flexible, linear macromolecules. ACS Polymer preprints. American Chemical Society. Div Polym Chem. 1981;22:308.

    CAS  Google Scholar 

  50. 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 

  51. 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 

  52. Angell CA, Choi Y. Crystallization and vitrification in aqueous systems. J Microsc. 1986;141:251–61.

    Article  CAS  Google Scholar 

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Acknowledgements

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

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

    Marika Yokota, Kaito Sugane, Itaru Tsukushi & Mitsuhiro Shibata

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  1. Marika Yokota
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Correspondence to Itaru Tsukushi.

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Yokota, M., Sugane, K., Tsukushi, I. et al. Evaluation of the heat capacity of amorphous polymers composed of a carbon backbone below their glass transition temperature. Polym J 52, 765–774 (2020). https://doi.org/10.1038/s41428-020-0317-x

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