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Supernatant Phase in Polyelectrolyte Complex Coacervation: Cluster Formation, Binodal, and Nucleation

Zhang, Pengfei and Wang, Zhen-Gang (2022) Supernatant Phase in Polyelectrolyte Complex Coacervation: Cluster Formation, Binodal, and Nucleation. Macromolecules, 55 (10). pp. 3910-3923. ISSN 0024-9297. doi:10.1021/acs.macromol.2c00340.

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This work studies the structure and thermodynamics of the supernatant phase in polyelectrolyte complex coacervation, a relatively unexplored area. By combining the cluster theory in dilute solution with our recently developed mean-field theory for inhomogeneous polyelectrolyte solutions (Zhang, P.; Wang, Z.-G. Macromolecules 2021, 54, 10994), we systematically investigate the structure of finite-sized clusters formed by oppositely charged polyions in symmetric dilute solutions and how these clusters affect the binodal, spinodal, and nucleation for polyelectrolyte complex coacervation. We find that both the polyion concentration deep inside the cluster and the interfacial tension decrease with increasing the cluster size, reaching their respective bulk coexistence values with corrections inversely proportional to the cluster radius. The polyion concentration in the supernatant phase at coexistence is several orders of magnitude higher than that obtained under the uniform mixing approximation. For most relevant conditions away from the critical point, the supernatant phase consists predominantly of polyion pairs. By examining the nucleation barrier in supersaturated solutions, we can determine a pseudo-spinodal when the barrier is a few multiples of the thermal energy. The location of this pseudo-spinodal is similarly shifted to much higher concentrations than predicted under the uniform mixing approximation. Making the volume approximation for the clusters, we obtain simple analytical expressions for the cluster formation free energy, the modified binodal, and the pseudo-spinodal. In particular, we propose a simple approximate formula for estimating the concentration of the coexisting supernatant phase in terms of the chain length, interfacial tension, and the polyion concentration in the coacervate phase.

Item Type:Article
Related URLs:
URLURL TypeDescription
Zhang, Pengfei0000-0002-4226-1394
Wang, Zhen-Gang0000-0002-3361-6114
Additional Information:© 2022 American Chemical Society. Received: February 15, 2022; Revised: April 13, 2022; Published: May 12, 2022. The authors thank Prof. Isamu Kusaka for valuable discussion on the interfacial tension calculation for finite-sized droplets. P.Z. acknowledges the financial support provided by the National Natural Science Foundation of China (22073016 and 21803011) and the award of Shanghai Dongfang Scholar. Z.-G.W. acknowledges financial support from the Hong Kong Quantum AI Lab Ltd. The authors declare no competing financial interest.
Funding AgencyGrant Number
National Natural Science Foundation of China22073016
National Natural Science Foundation of China21803011
Shanghai Dongfang ScholarUNSPECIFIED
Hong Kong Quantum AI Lab Ltd.UNSPECIFIED
Subject Keywords:Approximation ,Cluster chemistry, Electrostatics, Free energy, Salts
Issue or Number:10
Record Number:CaltechAUTHORS:20220520-388254000
Persistent URL:
Official Citation:Supernatant Phase in Polyelectrolyte Complex Coacervation: Cluster Formation, Binodal, and Nucleation. Pengfei Zhang and Zhen-Gang Wang. Macromolecules 2022 55 (10), 3910-3923; DOI: 10.1021/acs.macromol.2c00340
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114841
Deposited By: George Porter
Deposited On:20 May 2022 22:33
Last Modified:08 Jun 2022 16:41

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