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Supercapacitors with carbon electrodes. Energy efficiency: modeling and experimental verification

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Abstract

In the paper, charging–discharging processes in symmetric electrochemical supercapacitors with activated carbon electrodes were studied. Mathematical modeling and experimental verification of these processes were performed. Such factors as the charging of the electric double layer, diffusion–migration transport of species in pores of the electrodes and separator, quasi-reversible Faraday redox reactions of surface groups, kinetics of which is related to the Butler–Volmer type, and porous structure of the electrodes with hydrophobic–hydrophilic characteristics were taken into consideration. The dependencies of energy efficiency on time of charging and discharging, current, and thickness of the electrodes have been calculated. These relations are very important when supercapacitors are applied to smoothing of peak load of electrical networks. The dependence of the efficiency on current is characterized by a maximum and a minimum. The optimal operating modes for the supercapacitors have been found to depend on device parameters. It is important to note that the efficiency value is close to 100 % for supercapacitors under certain conditions, but this magnitude is unattainable for batteries.

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Abbreviations

A 1 and A 2 :

Parameters, see Eqs. (4) and (5)

C :

Specific capacitance

c :

Concentration of electrolyte

c 10 :

Initial concentration of electrolyte

D :

Diffusion coefficient

D eff :

Effective diffusion coefficient

E :

Overpotential

E 0 :

Equilibrium potential

F:

Faraday number

i 0 :

Exchange current density

j ad :

Adsorption current

j C :

Charging current of EDL

G :

Rate coefficient of adsorption energy

k :

Conductivity of electrolyte

k eff :

Effective conductivity of electrolyte

L ele :

Electrode thickness

L sep :

Separator thickness

Q θ :

Specific molar capacitance of adsorption

q i :

Electrode charging factor

r :

Pore radius

r*:

Effective pore radius

S :

Surface density

T :

Time

t + :

Transfer number

X :

Coordinate

Α :

Wetting angle

Β :

Transfer coefficient

φ e :

Electric potential of electrolyte

φ s :

Electric potential of solid phase

θ 0 :

Initial fraction of the covered surface

σ eff :

Effective conductivity of the electrode

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Acknowledgments

We thank Dr. Yu. S. Dzyazko deeply for the helpful notices regarding this work.

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Authors and Affiliations

  1. A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leniskii Pr. 31, 119071, Moscow, Russia

    Yu. M. Volfkovich, D. A. Bograchev, A. Yu. Rychagov & V. E. Sosenkin

  2. Department of Physical Chemistry, Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia

    M. Yu. Chaika

Authors
  1. Yu. M. Volfkovich
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  2. D. A. Bograchev
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  3. A. Yu. Rychagov
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  4. V. E. Sosenkin
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  5. M. Yu. Chaika
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Correspondence to D. A. Bograchev.

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Volfkovich, Y.M., Bograchev, D.A., Rychagov, A.Y. et al. Supercapacitors with carbon electrodes. Energy efficiency: modeling and experimental verification. J Solid State Electrochem 19, 2771–2779 (2015). https://doi.org/10.1007/s10008-015-2804-0

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  • DOI: https://doi.org/10.1007/s10008-015-2804-0

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