Applicability of Different Double-Layer Models for the Performance Assessment of the Capacitive Energy Extraction Based on Double Layer Expansion (CDLE) Technique
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Operations
3. Theory of Electrical Double Layers
3.1. Gouy–Chapmann–Stern Model
3.2. Modified Poisson–Boltzmann–Stern Model
3.3. Modified Donnan Model
3.4. Booth Correction of Dielectric Permittivity
4. Experimental Results and Model Applications
4.1. Gouy–Chapmann–Stern Model
4.2. Modified Poisson–Boltzmann–Stern Model
4.3. Modified Donnan Model
4.4. Full CDLE Experiment
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
CapMix | Capacitive mixing |
CDP | Capacitive energy extraction based on Donnan Potential |
CDLE | Capacitive energy extraction based on Double Layer Expansion |
SE | Soft Electrode |
EDL | Electric double layer |
PB | Poisson Boltzmann |
GCS | Gouy–Chapman–Stern |
MPBS | Modified Poisson–Boltzmann–Stern |
mD | modified Donnan |
Specific surface area | |
Microporous surface area measurement | |
Total volume of pores | |
Pore thickness | |
Average pore diameter | |
Equilibrium electrode charge per mass, C/g | |
Electric current, A | |
Measured current, A | |
Leakage current, A | |
Mass of total electrodes, g | |
Applied voltage, V | |
Cell potential, V | |
Potential increase due to the double layer expansion, V | |
External resistance, Ω | |
Extracted energy, J/g | |
Electrolyte concentration, mm | |
Electrolyte concentration of freshwater, mol/m3 | |
Electrolyte concentration of seawater, mol/m3 | |
micropore total ion concentration, mol/m3 | |
number concentration of the ith species in diffuse layer, 1/m3 | |
number concentration of the ith species at the bulk solution, 1/m3 | |
number concentration of ith species in the micropores of the electrode, 1/m3 | |
elementary charge, C | |
valence of the ith species | |
Boltzmann constant, J/K | |
free space permittivity, F/m | |
relative permittivity of the electrolyte solutions | |
electric potential, V | |
surface potential, V | |
electric potential drop across the stern layer, V | |
electric potential difference across the diffuse layer, V | |
surface charge density, C/m2 | |
total differential capacitance of the double layer | |
differential capacitances of the stern layer, F/m2 | |
differential capacitances of the diffuse layer, F/m2 | |
average excluded volume per ion, m3 | |
d | spacing of counterions near a highly charged surface, m |
Debye length, m | |
Bjerrum length, m | |
volumetric charge density, C/m3 | |
excess chemical potential, kT | |
volumetric capacitance of the Stern layer, F/ m3 | |
volumetric capacitance of the Stern layer (low charge limit), F/ m3 | |
Parameter to describe nonlinear part of Stern capacity, F∙m3/mol2 | |
E | energy parameter, kT mol/m3 |
size of micropore, m | |
index of refraction of the electrolyte at zero electric field frequency | |
dipole moment of the solvent molecule and in the case of water, D(Debye) | |
effective specific electrode area, m2/g |
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Materials | (m2/g) | (m2/g) | (cm3/g) | (cm3/g) | (nm) | (nm) |
---|---|---|---|---|---|---|
Raw Activated Carbon | 1659.457 | 1176.362 | 0.835 | 0.502 | 0.427 | 3.805 |
Fabricated Electrode | 1272.124 | 906.254 | 0.649 | 0.387 | 0.427 | 4.043 |
Models | Parameters | |||||
---|---|---|---|---|---|---|
(F/m2) | (m2/g) | (nm) | (nm) | |||
GCS | 0.131 | 619.46 | 5.3 | 78.5 | - | |
GCS—B * | 1.0–1.15 | 540.25 | 4.19 | 68.5–78.5 | - | |
MPBS | 0.141 | 580.88 | 4.92 | 78.5 | 0.75 | |
MPBS—B * | 0.09–0.095 | 857.79 | 7.29 | 74.6–78.5 | 1.42 | |
(F/m3) | α (Fm3/mol2) | (F/m3) | (kT mol/m3) | (cm3/g) | ||
mD | 2.1 108 | 10.48 | (2.1–2.24) 108 | 1.18 | - | 0.35 |
i-mD | 2.06 108 | 13.65 | (2.06–2.23) 108 | 0.23–2.76 | 436.7 | 0.367 |
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Zou, Z.; Liu, L.; Meng, S.; Bian, X.; Li, Y. Applicability of Different Double-Layer Models for the Performance Assessment of the Capacitive Energy Extraction Based on Double Layer Expansion (CDLE) Technique. Energies 2021, 14, 5828. https://doi.org/10.3390/en14185828
Zou Z, Liu L, Meng S, Bian X, Li Y. Applicability of Different Double-Layer Models for the Performance Assessment of the Capacitive Energy Extraction Based on Double Layer Expansion (CDLE) Technique. Energies. 2021; 14(18):5828. https://doi.org/10.3390/en14185828
Chicago/Turabian StyleZou, Zhi, Longcheng Liu, Shuo Meng, Xiaolei Bian, and Yongmei Li. 2021. "Applicability of Different Double-Layer Models for the Performance Assessment of the Capacitive Energy Extraction Based on Double Layer Expansion (CDLE) Technique" Energies 14, no. 18: 5828. https://doi.org/10.3390/en14185828