Abstract
Self-discharge is an important factor that severely affects the performance of double-layer supercapacitors. This paper studies the self-discharge behavior of double-layer supercapacitors with experimental and modeling methods. The movement of ions, side-reactions, and instability of the double layer are taken into consideration. The influence of various factors, such as the initial voltage, charge duration, short-term history, and current, on the self-discharge is simulated, showing good agreement with experimental data. The simulation of the ion distribution also gives a detailed explanation of the mechanism of self-discharge and verifies the interpretation of the relaxation process proposed in a recent study. It further clarifies the key role of the charging/discharging current in influencing charge redistribution during self-discharge, which was neglected in previous studies. The results show that the relaxation period during which the supercapacitor loses energy very quickly is due to the unbalanced distribution of ions, and it could be avoided by further charging or by applying a small charging current.
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Abbreviations
- \(C_{\rm{dl}}\) :
-
Double-layer capacitance (F/m)
- \(c_{\rm{l}}\) :
-
Electrolyte concentration (mol/L)
- \(D_{\rm{l,eff}}\) :
-
Effective diffusion coefficient of electrolyte
- \(D_{\rm{l}}\) :
-
Diffusion coefficient of electrolyte
- F :
-
Faraday’s constant, 96,484 C/equiv
- \(i_{0}\) :
-
Exchange current density (A/m3)
- \(I_{\rm{cell}}\) :
-
Total current density (A/m2)
- \(i_{\rm{l}}\) :
-
Current density in electrolyte phase (A/m2)
- \(i_{\rm{s}}\) :
-
Current density in solid phase (A/m2)
- \(L_{ + }\) :
-
Thickness of positive electrode (μm)
- \(L_{\rm{e}}\) :
-
Thickness of separator (μm)
- \(L_{ - }\) :
-
Thickness of negative electrode (μm)
- R :
-
Universal gas constant, 8.314 J/(mol K)
- \(S_{\rm{f}}\) :
-
Specific surface area for side-reactions per unit electrode volume (m−1)
- \(S_{\rm{d}}\) :
-
Specific surface area for double-layer capacitance per unit electrode volume (m−1)
- T :
-
Absolute temperature (K)
- t :
-
Time (s)
- \(t_{ + }\) :
-
Transport number
- \(U_{1}\) :
-
Equilibrium potential (V)
- \(\alpha_{\rm{a}}\) :
-
Anodic transfer coefficient of faradaic reaction
- \(\alpha_{\rm{c}}\) :
-
Cathodic transfer coefficient of faradaic reaction
- \(\varepsilon_{\rm{l}}\) :
-
Volume fraction of electrolyte phase
- \(\varepsilon_{\rm{s}}\) :
-
Volume fraction of solid phase
- \(\sigma_{\rm{l,eff}}\) :
-
Effective conductivity in electrolyte phase (S/m)
- \(\sigma_{\rm{l}}\) :
-
Conductivity in electrolyte phase (S/m)
- \(\sigma_{\rm{s,eff}}\) :
-
Effective conductivity in solid phase (S/m)
- \(\sigma_{\rm{s}}\) :
-
Conductivity in solid phase (S/m)
- \(\phi_{\rm{l}}\) :
-
Potential in electrolyte phase (V)
- \(\phi_{\rm{s}}\) :
-
Potential in solid phase (V)
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Acknowledgement
The authors acknowledge financial support from the National Natural Science Foundation of China (NNSFC) (Project No. 50905096).
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The authors declare that they have no conflict of interest.
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Hao, C., Wang, X., Yin, Y. et al. Analysis of Charge Redistribution During Self-discharge of Double-Layer Supercapacitors. J. Electron. Mater. 45, 2160–2171 (2016). https://doi.org/10.1007/s11664-016-4357-0
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DOI: https://doi.org/10.1007/s11664-016-4357-0