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PreprintCC BYChemRxiv

Nucleation of Condensates and Voids: A Generalised Critical Cluster Equivalence Principle for Phase Separation in Liquid Mixtures

  • Lunna Li1,2
  • Erik E. Santiso3,4
  • Matteo Salvalaglio1,2
4 affiliations
  1. 1Thomas Young Centre and Department of Chemical Engineering
  2. 2UniversityCollegeLondon
  3. 3Department of Chemical and Biomolecular Engineering
  4. 4NorthCarolinaStateUniversity
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Abstract

The assembly, number density, and size distribution of biomolecular condensates are central to their biological functions, but the nucleation kinetics that precede growth and coalescence remain difficult to characterise experimentally and in simulations. In this work, we develop a theoretical framework to apply the critical cluster equivalence principle (CEP), which builds on the thermodynamic equivalence between stable clusters in confined systems and critical clusters in open systems, to multicomponent liquids undergoing phase separation into solvent-and solute-rich phases. We first test the proposed approach in a symmetric Lennard-Jones mixture, where nucleation rates agree with large-scale Yasuoka–Matsumoto simulations and the predicted critical cluster sizes match independent seeding results. We then use the validated approach to investigate a homopolymeric chainsolvent system, introducing concepts intrinsic to biomolecular condensates such as chain rigidity and connectivity. Here, the CEP predicts the coexistence composition and interfacial tension for both the forward nucleation of dense condensates and the reverse formation of dilute voids, indicating that the curvature dependence is consistent in both directions, thereby uncovering a forward/reverse relationship that has primarily been studied for single-component droplets and bubbles, now demonstrated for a compositionally mixed liquid phase separation. Overall, the CEP-based workflow employs smaller systems and shorter simulations than conventional nucleation methods. These findings indicate a comprehensive methodology for quantitatively examining biomolecular condensate nucleation in explicit solvent.

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Cite

BibTeXRIS
BibTeX
@misc{li2026nucleation,
  title = {{Nucleation of Condensates and Voids: A Generalised Critical Cluster Equivalence Principle for Phase Separation in Liquid Mixtures}},
  author = {Lunna Li and Erik E. Santiso and Matteo Salvalaglio},
  howpublished = {ChemRxiv},
  year = {2026},
  month = sep,
  doi = {10.26434/chemrxiv.15009057/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009057/v1},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - Nucleation of Condensates and Voids: A Generalised Critical Cluster Equivalence Principle for Phase Separation in Liquid Mixtures
AU  - Lunna Li
AU  - Erik E. Santiso
AU  - Matteo Salvalaglio
PY  - 2026
DA  - 2026/09/18
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15009057/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009057/v1
AB  - The assembly, number density, and size distribution of biomolecular condensates are central to their biological functions, but the nucleation kinetics that precede growth and coalescence remain difficult to characterise experimentally and in simulations. In this work, we develop a theoretical framework to apply the critical cluster equivalence principle (CEP), which builds on the thermodynamic equivalence between stable clusters in confined systems and critical clusters in open systems, to multicomponent liquids undergoing phase separation into solvent-and solute-rich phases. We first test the proposed approach in a symmetric Lennard-Jones mixture, where nucleation rates agree with large-scale Yasuoka–Matsumoto simulations and the predicted critical cluster sizes match independent seeding results. We then use the validated approach to investigate a homopolymeric chainsolvent system, introducing concepts intrinsic to biomolecular condensates such as chain rigidity and connectivity. Here, the CEP predicts the coexistence composition and interfacial tension for both the forward nucleation of dense condensates and the reverse formation of dilute voids, indicating that the curvature dependence is consistent in both directions, thereby uncovering a forward/reverse relationship that has primarily been studied for single-component droplets and bubbles, now demonstrated for a compositionally mixed liquid phase separation. Overall, the CEP-based workflow employs smaller systems and shorter simulations than conventional nucleation methods. These findings indicate a comprehensive methodology for quantitatively examining biomolecular condensate nucleation in explicit solvent.
ER  -