Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 47, Issue -, Pages 188-203Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2018.10.011
Keywords
Size-modified Poisson-Boltzmann equation; Electrostatic free energy; PDE-constrained variational methods; Electric double layer
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Funding
- National Natural Science Foundation of China [11701576, 11501053]
- Foundation of Education Department of Hunan [15C0026]
- Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science Technology)
- Central South University
- National Science Foundation, USA [DMS-1226259]
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In this paper, an improved electrostatic free energy functional is presented as an extension of the one proposed in Xie and Li (2015) to reflect ion size effects. It is then shown to have a unique minimizer, resulting in the solution existence and uniqueness of one commonly-used ion size-modified Poisson-Boltzmann equation (SMPBE). As for applications, SMPBE is used to calculate the electrostatic solvation free energy with the new derived well-defined formula and simulate an electric double layer numerically to demonstrate the advantage of SMPBE over the classic Poisson-Boltzmann equation in the prediction of ionic concentrations. (C) 2018 Elsevier Ltd. All rights reserved.
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