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Published September 6, 2022 | Published + Supplemental Material
Journal Article Open

Driving force and pathway in polyelectrolyte complex coacervation

  • 1. ROR icon California Institute of Technology


There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation–polyanion complexation and polyion pair–pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

Additional Information

© 2022 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). This research is supported by funding from Hong Kong Quantum AI Lab Ltd. We thank the general computation time allocated by the resources of the Center for Functional Nanomaterials, which is a US Department of Energy Office of Science User Facility, at Brookhaven National Laboratory under Contract DE-SC0012704. We thank Prof. M. Muthukumar for bringing our attention to his forthcoming book. Author contributions: S.C. and Z.-G.W. designed research, performed research, analyzed data, and wrote the paper. The authors declare no competing interest.

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Published - pnas.2209975119.pdf

Supplemental Material - pnas.2209975119.sapp.pdf


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August 22, 2023
November 16, 2023