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Investigation of Dielectric Decrement and Correlation Effects on Electric Double-Layer Capacitance by Self-Consistent Field Model

Part of:ChemistryPartial differential equations, boundary value problems

Published online by Cambridge University Press:  21 July 2016

Manman Ma,
Shuangliang Zhao and
Zhenli Xu
Manman Ma*
Affiliation:
Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Shuangliang Zhao*
Affiliation:
State Key laboratory of Chemical Engineering, East China University of Science and Technology, 200237, Shanghai, China
Zhenli Xu*
Affiliation:
Institute of Natural Sciences, Department of Mathematics, and MoE Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
*
*Corresponding author. Email addresses:mmm@sjtu.edu.cn (M. Ma), szhao@ecust.edu.cn (S. Zhao), xuzl@sjtu.edu.cn (Z. Xu)
*Corresponding author. Email addresses:mmm@sjtu.edu.cn (M. Ma), szhao@ecust.edu.cn (S. Zhao), xuzl@sjtu.edu.cn (Z. Xu)
*Corresponding author. Email addresses:mmm@sjtu.edu.cn (M. Ma), szhao@ecust.edu.cn (S. Zhao), xuzl@sjtu.edu.cn (Z. Xu)

Abstract

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The differential capacitance of electric double-layer capacitors is studied by developing a generalized model of the self-consistent Gaussian field theory. This model includes many-body effects of particles near the interface such as ionic sizes, the order of water alignment and electrostatic correlations, and thus can present more accurate predictions of the electric double-layer structure and hence the capacitance than traditional continuum theories. Analytical simplification of the model and efficient numerical method are introduced, in particular, the approximation of the self-Green's function which describes the self energy of a mobile ion. We show that, when the applied voltage on interfaces is small the dielectric effect of the electrode materials plays an important role. For large voltage, this effect is screened, but the dielectric saturation due to the alignment of the nearby water is shown to be essential. For 2:1 electrolytes, abnormal enhancement on the capacitance due to the dielectric electrode is observed, which is due to the interplay of the image charge effect and Born solvation energy in the self energy of ions.

Keywords

Supercapacitormany-body effectsGreen's functioncontinuum theory

MSC classification

Secondary:65Z05: Applications to physics65N06: Finite difference methods92E99: None of the above, but in this section

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016, pp. 441 - 458
Copyright
Copyright © Global-Science Press 2016 

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