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Published May 7, 2022 | Accepted Version + Published + Submitted
Journal Article Open

Thermodynamics of electrolyte solutions near charged surfaces: Constant surface charge vs constant surface potential


Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational—that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson–Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.

Additional Information

© 2022 Author(s). Published under an exclusive license by AIP Publishing. Submitted: 24 February 2022; Accepted: 07 April 2022; Accepted Manuscript Online: 08 April 2022. D.B. acknowledges support from the NDSEG Fellowship Program. C.B. is supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship, under Award No. DE-SC0020347. Z.-G.W. acknowledges financial support from the Hong Kong Quantum AI Lab. The authors have no conflicts to disclose. Author Contributions: D.B. and C.B. contributed equally to this work. Data Availability: The data that support the findings of this study are available from the corresponding author upon reasonable request.

Attached Files

Published - 174704_1_online.pdf

Accepted Version - 174704_1_online-acc.pdf

Submitted - Manuscript.pdf


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October 9, 2023
October 24, 2023