Skip to main content
SpringerLink
Log in

A mathematical model of nanoparticulate mixed oxide pseudocapacitors; part II: the effects of intrinsic factors

  • Original Paper
  • Published:
Journal of Solid State Electrochemistry Aims and scope Submit manuscript

Abstract

Our previously reported mathematical model for a mixed oxide nanoparticulate-based supercapacitor containing RuO2·xH2O and MO2·yH2O (M being another suitable transition metal) was analyzed. Both double-layer and faradaic processes responsible for charge/discharge were considered. The effects of the intrinsic factors, unit cell length, state of charge, and the exchange current densities of the electrochemical processes of the constituents on the performance of the model supercapacitor were clarified. Compensation effects where each constituent compensates the shortcomings of the other at specific conditions of discharge are analyzed in the light of the model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

E :

Local electrode potential, V

E 0 :

Initial local electrode potential, V

\( \bar{E} \) :

Dimensionless local electrode potential, E/E 0

h Ru :

Length of crystal lattice on the RuO2·xH2O surface, cm

h M :

Length of crystal lattice on the MO2·yH2O surface, cm

i 0,Ru :

Exchange current density for the faradaic reaction of RuO2·xH2O, A cm−2

i 0,M :

Exchange current density for the faradaic reaction of MO2·yH2O, A cm−2

i C :

Double-layer current per unit volume of electrode, A cm−3

i cell :

Cell current density, A cm−2

i f :

Faradaic current per unit volume of electrode, A cm−3

\( {\bar{i}_C} \) :

Dimensionless double-layer current, i C L/i cell

\( {\bar{i}_f} \) :

Dimensionless faradaic current, i f L/i cell

L :

Thickness of the electrode, cm

S V :

Specific surface area per unit volume of the electrode, cm2/cm3

t :

Time, s

t d :

Discharge time, s

V 0 :

Initial potential before charge, 0.5 V (vs. SCE)

x :

Position coordinate, cm

X M :

Volume fraction of MO2·yH2O in the electrode

δ Ru :

State of charge of RuO2·xH2O

δ M :

State of charge of MO2·yH2O

Φcell :

Cell potential or the matrix potential difference between the two current collectors, V

\( {\bar{\Phi }_{cell}} \) :

Dimensionless cell potential, \( \frac{{{\Phi_{cell}}}}{{2{V_0}}} \)

θ :

Fraction of oxidized species in the faradaic reaction

ξ :

Dimensionless position coordinate, x/L

References

  1. Farsi H, Gobal F (2009) J Solid State Electrochem 13:433

    Article  CAS  Google Scholar 

  2. Farsi H, Gobal F (2007) J Solid State Electrochem 11:1085

    Article  CAS  Google Scholar 

  3. Farsi H, Gobal F (2007) Comput Mater Sci 39:678

    Article  Google Scholar 

  4. Rodrigues S, Munichandraiah N, Shukla AK (2000) J Power Sources 87:12

    Article  CAS  Google Scholar 

  5. Blood PJ, Sotiropoulos S (2002) J Power Sources 110:96

    Article  CAS  Google Scholar 

  6. Pop V, Bergveld HJ, Notten PHL, Op het Veld JHG, Regtien PPL (2009) Measurement 42:1131

    Article  Google Scholar 

  7. Milocco RH, Castro BE (2009) J Power Sources 194:55

    Article  Google Scholar 

  8. Zhongxue L, Jie C (2008) Microelectron Eng 85:1549

    Article  Google Scholar 

  9. Tseng CY, Lin CF (2005) J Power Sources 147:282

    Article  CAS  Google Scholar 

  10. Ng KS, Mooa CS, Chen YP, Hsieh YC (2009) Appl Energy 86:1506

    Article  CAS  Google Scholar 

  11. Lee S, Kim J, Lee J, Cho BH (2008) J Power Sources 185:1367

    Article  CAS  Google Scholar 

  12. Çadirci Y, Özkazanc Y (2004) J Power Sources 129:330

    Article  Google Scholar 

  13. Hansen T, Wang CJ (2005) J Power Sources 141:351

    Article  CAS  Google Scholar 

  14. Plett GL (2004) J Power Sources 134:252

    Article  CAS  Google Scholar 

  15. Plett GL (2004) J Power Sources 134:262

    Article  CAS  Google Scholar 

  16. Plett GL (2004) J Power Sources 134:277

    Article  CAS  Google Scholar 

  17. Hammouche A, Karden E, De Doncker RW (2004) J Power Sources 127:105

    Article  CAS  Google Scholar 

  18. Blanke H, Bohlen O, Buller S, Doncker RW, Fricke B, Hammouche A, Linzen D, Thele M, Sauer DU (2005) J Power Sources 144:418

    Article  CAS  Google Scholar 

  19. Conway BE (1991) J Electrochem Soc 138:1539

    Article  CAS  Google Scholar 

  20. Conway BE, Pell WG (2003) J Solid State Electrochem 7:637

    Article  CAS  Google Scholar 

  21. Conway BE, Briss V, Wojtowicz J (1997) J Power Sources 66:1

    Article  CAS  Google Scholar 

  22. Pell WG, Conway BE (1996) J Power Sources 63:255

    Article  CAS  Google Scholar 

  23. Mahon PJ, Paul GL, Keshishian SM, Vassallo AM (2000) J Power Sources 91:68

    Article  CAS  Google Scholar 

  24. Wakihara M, Yamamoto O (Eds) (1998) Lithium ion batteries—fundamentals and performance. Wiley–VCH, Weinheim

  25. Shriram S, Renganathan NG, Ganesan M, Dhananjeyan MVT (2005) J Electroanal Chem 576:43

    Article  CAS  Google Scholar 

  26. Lin C, Ritter JA, Popov BN, White RE (1999) J Electrochem Soc 146:3168

    Article  CAS  Google Scholar 

  27. Jow TR, Zheng JP (1998) J Electrochem Soc 145:49

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, University of Birjand, P.O. Box: 97175-615, Birjand, Iran

    Hossein Farsi

  2. Department of Chemistry, Sharif University of Technology, P.O. Box: 11365-9516, Tehran, Iran

    Fereydoon Gobal

Authors
  1. Hossein Farsi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fereydoon Gobal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hossein Farsi.

Additional information

This paper has been presented in International Battery Materials Association (IBA) 2007 Conference, Shenzhen, China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farsi, H., Gobal, F. A mathematical model of nanoparticulate mixed oxide pseudocapacitors; part II: the effects of intrinsic factors. J Solid State Electrochem 15, 115–123 (2011). https://doi.org/10.1007/s10008-010-1072-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10008-010-1072-2

Keywords

Search

Navigation