Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Coalescence of two critical points and accelerated phase dynamics in orientational ternary mixtures

Hiroshi Yokota*,†

  • *Contact author: yokotah@tmu.ac.jp
  • †Also at Department of Physics, Tokyo Metropolitan University.

Phys. Rev. E 113, 035405 – Published 4 March, 2026

DOI: https://doi.org/10.1103/85kk-h8ln

Abstract

Motivated by intracellular phase separation, we theoretically investigate how molecular orientation and multicomponent nature affect phase behavior. We construct a minimal model for a ternary mixture composed of isotropic (I), anisotropic (A), and solvent (s) components by combining the Flory-Huggins and Maier-Saupe theories. We obtain two main results from evaluating the phase behavior and the time evolution of the density fields. First, for certain interaction parameters, two distinct binodal lines appear in the plane of the volume fractions of the I- and A-components, and merge through their respective critical points. Second, rapid droplet formation emerges due to a weakly first-order phase transition, characterized by a discontinuity of the spinodal surface. The first result indicates the possibility of continuous transformation between the two phase-separated states. The second result suggests that anisotropic molecules can regulate phase-separation kinetics. These findings might be physically general beyond biological systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (35)

  1. E. W. Martin, T. S. Harmon, J. B. Hopkins, S. Chakravarthy, J. J. Incicco, P. Schuck, A. Soranno, and T. Mittag, Nat. Commun. 12, 4513 (2021).
  2. S. Xu, H. Zhang, B. Qiao, and Y. Wang, Cryst. Growth Des. 21, 7306 (2021).
  3. C. P. Brangwynne, C. R. Eckmann, D. S. Courson, A. Rybarska, C. Hoege, J. Gharakhani, F. Jülicher, and A. A. Hyman, Science 324, 1729 (2009).
  4. C. P. Brangwynne, T. J. Mitchison, and A. A. Hyman, Proc. Natl. Acad. Sci. 108, 4334 (2011).
  5. M.-T. Wei, Y.-C. Chang, S. F. Shimobayashi, Y. Shin, A. R. Strom, and C. P. Brangwynne, Nat. Cell Biol. 22, 1187 (2020).
  6. T. J. Nott, E. Petsalaki, P. Farber, D. Jervis, E. Fussner, A. Plochowietz, T. D. Craggs, D. P. Bazett-Jones, T. Pawson, J. D. Forman-Kay, et al., Mol. Cell 57, 936 (2015).
  7. B. R. Sabari, A. Dall'Agnese, A. Boija, I. A. Klein, E. L. Coffey, K. Shrinivas, B. J. Abraham, N. M. Hannett, A. V. Zamudio, J. C. Manteiga, et al., Science 361, eaar3958 (2018).
  8. A. R. Strom, A. V. Emelyanov, M. Mir, D. V. Fyodorov, X. Darzacq, and G. H. Karpen, Nature (London) 547, 241 (2017).
  9. S. Najafi, J. McCarty, K. T. Delaney, G. H. Fredrickson, and J.-E. Shea, Phase-Separated Biomolecular Condensates: Methods and Protocols (Springer, New York, 2022), pp. 37–49.
  10. S. Shi, L. Zhao, and Z.-Y. Lu, J. Phys. Chem. Lett. 15, 7280 (2024).
  11. J. Berry, S. C. Weber, N. Vaidya, M. Haataja, and C. P. Brangwynne, Proc. Natl. Acad. Sci. 112, 5237 (2015).
  12. W. M. Babinchak and W. K. Surewicz, J. Mol. Biol. 432, 1910 (2020).
  13. C. P. Brangwynne, P. Tompa, and R. V. Pappu, Nat. Phys. 11, 899 (2015).
  14. P.-G. De Gennes and J. Prost, The Physics of Liquid Crystals, 83 (Oxford University Press, Oxford, 1993).
  15. H. Chiu and T. Kyu, J. Chem. Phys. 103, 7471 (1995).
  16. S. K. Das and A. D. Rey, Comput. Mater. Sci. 29, 152 (2004).
  17. J.-i. Fukuda, Phys. Rev. E 58, R6939 (1998).
  18. M. Du and Z. J. Chen, Science 361, 704 (2018).
  19. Y. Lu, B. Weers, and N. C. Stellwagen, Biopolymers 61, 261 (2002).
  20. A. Shakya, S. Park, N. Rana, and J. T. King, Biophys. J. 118, 753 (2020).
  21. A. Maraldo, J. Rnjak-Kovacina, and C. Marquis, Trends Biochem. Sci. 49, 633 (2024).
  22. K. Adachi and K. Kawaguchi, Phys. Rev. X 14, 031011 (2024).
  23. C. Luo, Y. Qiang, and D. Zwicker, Phys. Rev. Res. 6, 033002 (2024).
  24. Y. Qiang, C. Luo, and D. Zwicker, Phys. Rev. Res. 7, 043008 (2025).
  25. A. Gridyakina, N. Kasian, M. S. Chychłowski, M. Kajkowska, and P. Lesiak, Mater. Today Phys. 38, 101258 (2023).
  26. A. Matsuyama and T. Kato, J. Chem. Phys. 105, 1654 (1996).
  27. L. Bottou, F. E. Curtis, and J. Nocedal, SIAM Rev. 60, 223 (2018).
  28. L. Chen and J. Shen, Comput. Phys. Commun. 108, 147 (1998).
  29. R. Koningsveld, W. H. Stockmayer, and E. Nies, Polymer Phase Diagrams: A Textbook (Oxford University Press, Oxford, 2001).
  30. J. Morral and S. Chen, J. Phase Equilib. Diffus. 40, 532 (2019).
  31. Y.-H. Lin, J. P. Brady, J. D. Forman-Kay, and H. S. Chan, New J. Phys. 19, 115003 (2017).
  32. L.-T. Yan and A. C. Balazs, J. Mater. Chem. 21, 14178 (2011).
  33. B. Van Roie, J. Leys, K. Denolf, C. Glorieux, G. Pitsi, and J. Thoen, Phys. Rev. E 72, 041702 (2005).
  34. P. M. Chaikin, T. C. Lubensky, and T. A. Witten, Principles of Condensed Matter Physics, Vol. 10 (Cambridge University Press, Cambridge, England, 1995).
  35. L. Wang, C. Yang, M. Dove, V. Brazhkin, and K. Trachenko, J. Phys.: Condens. Matter 31, 225401 (2019).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation