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:

Excess heat capacity for low-molecular-weight amorphous polystyrene below the glass-transition temperature: influence of end groups

Polymer Journal volume 52, pages 575–580 (2020)Cite this article

Subjects

Abstract

In this work, we analyze the absolute heat capacity below the glass-transition temperature Tg for two types of amorphous polystyrene with differing low-molecular weights. Both amorphous polystyrenes have excess heat capacities that cannot be reproduced by skeletal and group vibrations from 70 K to Tg, which differs from the results for amorphous polystyrene with large molecular weights. The excess heat capacity is analyzed using the Schottky model. The ratio of the degrees of freedom of the Schottky model NSC for PS-A300 and PS-A500 (NSC,PS-A300/NSC,PS-A500) is 1.6, which reflects the ratio of the end groups per molecule ((i.e., the number of monomer units of PS-A500/the number of monomer units of PS-A300 = 5/3) = 1.7), and the resulting excitation energy (=31 meV) is consistent with that determined using inelastic neutron scattering (=30 meV).

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

Access options

Buy this article

  • Purchase on SpringerLink
  • 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

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 Dat. 1982;11:1–392.

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

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

  4. Šesták J, Mareš JJ, Hubík P, editors. 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, Mitani T, Sorai S. 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, Saito K, Sorai S. Low temperature heat capacities and Raman spectra of negative thermal expansion compounds ZrW2O8 and HfW2O8. Phys Rev B. 2002;66:014301.

    Article  Google Scholar 

  11. Matsuo T, Maekawa T, Inaba A, Yamamuro O, Ohama M, Ichikawa M, Tsuchida T. 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) 2I3. 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. 1988;52:631–56.

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  16. Yokota M, Sugane K, Tsukushi I, Shibata M. Evaluation of heat capacity below the glass-transition temperature of amorphous polymers composed of carbon backbone. Polym J. (in press).

  17. Westrum Jr. EF, Furukawa GT, McCullough JP. Adiabatic low-temperature calorimetry. In McCullough JP, Scott DW, editors. Experimental thermodynamics, Vol. I, calorimetry of non-reacting systems. London: Butterworths; 1968. p. 133–214.

    Chapter  Google Scholar 

  18. Wunderlich B, Pyda M. Thermodynamic properties of polymers. Encycl Polym Sci Technol. 2002;12:165–207.

    Google Scholar 

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

    Article  CAS  Google Scholar 

  20. Tsukushi I, Yamamuro O, Sadanami K, Nishizawa M, Matsuo T, Takeda K. Construction of a top-loading adiabatic calorimeter and enthalpy relaxation of glassy (1,3-propanediol)(0.5)(1,2-propanediamine)(0.5). Rev Sci Instrum. 1998;69:179–84.

    Article  CAS  Google Scholar 

  21. Inoue K, Kanaya T, Kiyanagi Y, Shibata K, Kaji K, Ikeda S, Iwasa H, Izumi Y. A crystal analyzer type inelastic spectrometer using the pulsed thermal neutron source. Nucl Instrum Method A 1993;327:433–40.

    Article  Google Scholar 

  22. Fujimura J, Nishiyama E, Tsukushi I, Shibata M. Enthalpy relaxation of low-molecular-weight amorphous styrene oligomers measured with an adiabatic calorimeter. J Therm Anal Calorim. 2019;135:1813–7.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  28. NIST chemistry WebBook SRD69. 301-975-2000, 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.

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

    Article  Google Scholar 

  30. Karasz FE, Bair HE, O’reilly JM. Thermal properties of atactic and isotactic polystyrene. J Phys Chem. 1965;69:2657–67.

    Article  CAS  Google Scholar 

  31. 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 

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

    CAS  Google Scholar 

  33. Westrum Jr, Edgar F. Lattice and Schottky contributions to the morphology of lanthanide heat capacities. J Chem Thermodyn. 1983;15:305–25.

    Article  CAS  Google Scholar 

  34. Uchida A, Moriya Y, Kawaji H, Atake T, Fukuhara M, Kimura H, Inoue K. Low temperature heat capacity and thermodynamic functions of Zr0.55Al0.10Ni0.05Cu0.30. J Chem Eng Data. 2009;54:2033–37.

    Article  CAS  Google Scholar 

  35. Yamashita S, Nakazawa Y, Oguni M, Oshima Y, Nojiri H, Shimizu Y, Miyagawa K, Kanoda K. Thermodynamic properties of a spin-1/2 spin-liquid state in κ-type organic salt. Nat Phys. 2008;4:459–62.

    Article  CAS  Google Scholar 

  36. Marshall W, Lovesey SW. Theory of thermal neutron scattering. Oxford: Clarendon; 1971.

  37. Kubota H, Kaneko F, Kawaguchi T. Inelastic neutron scattering study on the polytypism of even-numbered n-alkanes. J Cryst Growth. 2005;275:e2181–86.

    Article  CAS  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, Eri Nishiyama, Jun Fujimura & Itaru Tsukushi

  2. Department of Mathematics and Science, School of Science and Engineering, Kokushikan University, 4-28-1 Setagaya, Setagaya-ku, Tokyo, 154-8515, Japan

    Eri Nishiyama

  3. Research Center for Thermal and Entropic Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka, 560-0043, Japan

    Jun Fujimura

Authors
  1. Marika Yokota
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eri Nishiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Fujimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. 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., Nishiyama, E., Fujimura, J. et al. Excess heat capacity for low-molecular-weight amorphous polystyrene below the glass-transition temperature: influence of end groups. Polym J 52, 575–580 (2020). https://doi.org/10.1038/s41428-020-0310-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41428-020-0310-4

This article is cited by

Search

Advanced search

Quick links