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
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
USD 39.95
Prices may be subject to local taxes which are calculated during checkout







Similar content being viewed by others
References
Yamakawa H, Yoshizaki, T. Helical Wormlike Chains in Polymer Solutions (Springer, Berlin, 2016).
Fujita, H Polymer Solutions (Elsevier, Amsterdam, 1990).
Flory PJ. Principles of Polymer Chemistry (Cornell University Press, Ithaca, NY, 1953).
Yamakawa H. Modern Theory of Polymer Solutions (Harper & Row, New York, 1971).
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.
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.
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).
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.
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.
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.
Konishi T, Yoshizaki T, Yamakawa H. On the “universal constants” Φ and of flexible polymers. Macromolecules. 1991;24:5614–22.
Konishi T, Yoshizaki T, Yamakawa H. Determination of stereochemical compositions of oligostyrenes by 13C NMR. Polym. J. 1988;20:175–8.
Konishi T, Yoshizaki T, Shimada J, Yamakawa H. Characterization and optical anisotropy of oligo- and polystyrenes in dilute solutions. Macromolecules. 1989;22:1921–30.
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.
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.
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.
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.
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.
Parrinello M, Rahman A. Crystal structure and pair potentials: A molecular-dynamics study. Phys. Rev. Lett. 1980;45:1196–9.
Nosé S. A unified formulation of the constant temperature molecular-dynamics methods. J. Chem. Phys. 1984;81:511–9.
Hoover WG. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A Gen. Phys. 1985;31:1695–7.
Darden TA, York DM, Pedersen LG. Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems. J. Chem. Phys. 1993;98:10089–92.
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.
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).
Berendsen HJC, van der Spoel D, van Drunen R. GROMACS: A message-passing parallel molecular dynamics implementation. Comput. Phys. Commun. 1995;91:43–56.
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.
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.
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.
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.
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).
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.
Jensen F. Introduction to Computational Chemistry, 3rd ed. (John Wiley & Sons, Ltd., West Sussex, UK, 2017).
Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, et al. Gaussian16, Revision A.03. (Gaussian Inc., Wallingford CT, 2016).
Einaga Y, Abe F, Yamakawa H. Second virial coefficients of oligo- and polystyrenes. Effects of chain ends. Macromolecules. 1993;26:6243–50.
Domb C, Barrett AJ. Universality approach to the expansion factor of a polymer chain. Polymer. 1976;17:179–84.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding authors
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.
About this article
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
Received:
Revised:
Accepted:
Published:
Version of record:
Issue date:
DOI: https://doi.org/10.1038/s41428-024-00987-6


