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:

A combined study on intermolecular interactions between polystyrene and d-limonene utilizing light-scattering experiments and computational simulations

Abstract

To quantitatively evaluate the solvent quality of d-limonene for polystyrene, light-scattering experiments were performed on polystyrene in d-limonene. Molecular-level information on the intermolecular interactions between the repeat unit of polystyrene and d-limonene was obtained by means of computational simulations. From the light-scattering experiments, the mean-square radius of gyration 〈S2〉 values for atactic polystyrene (a-PS) with weight-average molecular weights ranging from 3.73 × 104 to 2.87 × 106 in d-limonene at 25.0 °C were determined to be between those in toluene, a good solvent, and those in cyclohexane, a poor solvent. Moreover, the second virial coefficient A2 values of a-PS in d-limonene were smaller than half of those in toluene. The 〈S2〉 and A2 values were analyzed according to the helical wormlike chain model, and the binary-cluster integral β, representing the magnitude of the excluded volume between constituent segments of a-PS, was found to exhibit an intermediate value between those in toluene and cyclohexane, confirming that d-limonene is a medium solvent for a-PS. The intermolecular interaction energy between cumene as a model compound representing the repeat unit of polystyrene and d-limonene, which was obtained from the computational simulations, supported the estimated solvent quality for polystyrene.

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

Access options

Buy this article

USD 39.95

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

Similar content being viewed by others

References

  1. Yamakawa H, Yoshizaki, T. Helical Wormlike Chains in Polymer Solutions (Springer, Berlin, 2016).

  2. Fujita, H Polymer Solutions (Elsevier, Amsterdam, 1990).

  3. Flory PJ. Principles of Polymer Chemistry (Cornell University Press, Ithaca, NY, 1953).

  4. Yamakawa H. Modern Theory of Polymer Solutions (Harper & Row, New York, 1971).

  5. Noguchi T, Miyashita M, Inagaki Y, Watanabe H. A new recycling system for expanded polystyrene using a natural solvent. Part 1. A new recycling technique. Packag. Technol. Sci. 1998;11:19–27.

    Article  CAS  Google Scholar 

  6. Noguchi T, Inagaki Y, Miyashita M, Watanabe H. A new recycling system for expanded polystyrene using a natural solvent. Part 2. Development of a prototype production system. Packag. Technol. Sci. 1998;11:29–37.

    Article  CAS  Google Scholar 

  7. Hattori K. Recycling of expanded polystyrene using natural solvents, in Recycling Materials Based on Environmentally Friendly Techniques (ed. Achilias, DS) Ch 1 (IntechOpen, London, 2015).

  8. Ozeki T, Ida D, Osa M. A quantitative evaluation of solvent quality of an environmentally friendly solvent ‘d-limonene’ for polystyrene. Polym. J. 2024;56:121–5.

    Article  CAS  Google Scholar 

  9. Abe F, Einaga Y, Yoshizaki T, Yamakawa H. Excluded-volume effects on the mean-square radius of gyration of oligo- and polystyrenes in dilute solutions. Macromolecules. 1993;26:1884–90.

    Article  CAS  Google Scholar 

  10. Yamakawa H, Abe F, Einaga Y. Second virial coefficient of oligo- and polystyrenes. Effects of chain stiffness on the interpenetration function. Macromolecules. 1993;26:1898–904.

    Article  CAS  Google Scholar 

  11. Konishi T, Yoshizaki T, Yamakawa H. On the “universal constants” Φ and of flexible polymers. Macromolecules. 1991;24:5614–22.

    Article  CAS  Google Scholar 

  12. Konishi T, Yoshizaki T, Yamakawa H. Determination of stereochemical compositions of oligostyrenes by 13C NMR. Polym. J. 1988;20:175–8.

    Article  CAS  Google Scholar 

  13. Konishi T, Yoshizaki T, Shimada J, Yamakawa H. Characterization and optical anisotropy of oligo- and polystyrenes in dilute solutions. Macromolecules. 1989;22:1921–30.

    Article  CAS  Google Scholar 

  14. Berry GC. Thermodynamic and conformational properties of polystyrene. I. Light-scattering studies on dilute solutions of linear polystyrenes. J. Chem. Phys. 1966;44:4550–64.

    Article  CAS  Google Scholar 

  15. Wang J, Wolf RM, Caldwell JW, Kollman PA, Case DA. Development and testing of a general AMBER force field. J. Comput. Chem. 2004;25:1157–74.

    Article  PubMed  CAS  Google Scholar 

  16. Bayly CI, Cieplak P, Cornell WD, Kollman PA. A well-behaved electrostatic potential based method using charge restrains for determining atom centered chargers: The RESP model. J. Phys. Chem. 1993;97:10262–80.

    Article  Google Scholar 

  17. Cornell WD, Cieplak P, Bayly CI, Kollman PA. Application of RESP charges to calculate conformational energies, hydrogen bond energies, and free energies of solvation. J. Am. Chem. Soc. 1993;115:9620–31.

    Article  CAS  Google Scholar 

  18. Berendsen HJC, Postma JPM, van Gunsteren WF, DiNola A, Haak JR. Molecular-dynamics with coupling to an external bath. J. Chem. Phys. 1984;81:3684–90.

    Article  CAS  Google Scholar 

  19. Parrinello M, Rahman A. Crystal structure and pair potentials: A molecular-dynamics study. Phys. Rev. Lett. 1980;45:1196–9.

    Article  CAS  Google Scholar 

  20. Nosé S. A unified formulation of the constant temperature molecular-dynamics methods. J. Chem. Phys. 1984;81:511–9.

    Article  Google Scholar 

  21. Hoover WG. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A Gen. Phys. 1985;31:1695–7.

    Article  PubMed  CAS  Google Scholar 

  22. Darden TA, York DM, Pedersen LG. Particle mesh Ewald: An Nlog(N) method for Ewald sums in large systems. J. Chem. Phys. 1993;98:10089–92.

    Article  CAS  Google Scholar 

  23. Essmann U, Perera L, Berkowitz ML, Darden T, Lee H, Pedersen LG. A smooth particle mesh Ewald method. J. Chem. Phys. 1995;103:8577–93.

    Article  CAS  Google Scholar 

  24. Bekker, H, Berendsen, HJC, Dijkstra, EJ, Achterop, S, van Drunen, R, van der Spoel, D, et al. Gromacs: A parallel computer for molecular dynamics simulations. in Physics Computing 92. (ed. de Groot, RA & Nadrchal, J) pp. 252-6 (World Scientific, Teaneck, 1993).

  25. Berendsen HJC, van der Spoel D, van Drunen R. GROMACS: A message-passing parallel molecular dynamics implementation. Comput. Phys. Commun. 1995;91:43–56.

    Article  CAS  Google Scholar 

  26. Lindahl E, Hess B, van der Spoel D. GROMACS 3.0: A package for molecular simulation and trajectory analysis. J. Mol. Model. 2001;7:306–17.

    Article  CAS  Google Scholar 

  27. van der Spoel D, Lindahl E, Hess B, Groenhof G, Mark AE, Berendsen HJC. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005;26:1701–18.

    Article  PubMed  Google Scholar 

  28. Hess B, Kutzner C, van der Spoel D, Lindahl E. GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theory Comput. 2008;4:435–47.

    Article  PubMed  CAS  Google Scholar 

  29. Pronk S, Páll S, Schulz R, Larsson P, Bjelkmar P, Apostolov R, et al. GROMACS 4.5: A high-throughput and highly parallel open source molecular simulation toolkit. Bioinformatics. 2013;29:845–54.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  30. Páll, S, Abraham, MJ, Kutzner, C, Hess, B & Lindahl, E Tackling exascale software challenges in molecular dynamics simulations with GROMACS. in Solving Software Challenges for Exascale (ed. Markidis, S & Laure, E) pp. 3–27 (Springer International Publishing, Berlin, London, 2015).

  31. Abraham MJ, Murtola T, Schulz R, Páll S, Smith JC, Hess B, et al. GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX. 2015;1–2:19–25.

    Article  Google Scholar 

  32. Jensen F. Introduction to Computational Chemistry, 3rd ed. (John Wiley & Sons, Ltd., West Sussex, UK, 2017).

  33. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, et al. Gaussian16, Revision A.03. (Gaussian Inc., Wallingford CT, 2016).

  34. Einaga Y, Abe F, Yamakawa H. Second virial coefficients of oligo- and polystyrenes. Effects of chain ends. Macromolecules. 1993;26:6243–50.

    Article  CAS  Google Scholar 

  35. Domb C, Barrett AJ. Universality approach to the expansion factor of a polymer chain. Polymer. 1976;17:179–84.

    Article  CAS  Google Scholar 

  36. Abe F, Einaga Y, Yamakawa H. Second virial coefficient of oligo- and poly(methyl methacrylate)s. Effects of chain stiffness and chain ends. Macromolecules. 1994;27:3262–71.

    Article  CAS  Google Scholar 

  37. Tokuhara W, Osa M, Yoshizaki T, Yamakawa H. Second virial coefficient of oligo- and poly(α-methylstyrene)s. Effects of chain stiffness, chain ends, and three-segment interactions. Macromolecules. 2003;36:5311–20.

    Article  CAS  Google Scholar 

  38. Horita K, Abe F, Einaga Y, Yamakawa H. Excluded-volume effects on the intrinsic viscosity of oligo- and polystyrenes. Solvent effects. Macromolecules. 1993;26:5067–72.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Daichi Ida or Masashi Osa.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sato, T., Chikuba, N., Ida, D. et al. A combined study on intermolecular interactions between polystyrene and d-limonene utilizing light-scattering experiments and computational simulations. Polym J 57, 171–179 (2025). https://doi.org/10.1038/s41428-024-00987-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Version of record:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41428-024-00987-6

Search

Quick links