The Journal of Supercomputing

, Volume 75, Issue 12, pp 7790–7798 | Cite as

Parallel implementation of a three-dimensional cellular automaton model of the electrochemical oxidation of carbon “Ketjenblack EC-600JD”

  • A. E. KireevaEmail author
  • K. K. Sabelfeld
  • E. N. Gribov
  • N. V. Maltseva


The paper presents a three-dimensional cellular automaton model of electrochemical oxidation of the carbon. The sample of the electro-conductive carbon black “Ketjenblack EC-600JD” consisting of granules of carbon is simulated. The electrochemical oxidation of the carbon granules occurs through a few successive stages. Parallel implementation of the three-dimensional cellular automaton model of carbon corrosion is developed. The efficiency and speedup of the parallel code are analyzed. The portions of surface carbon atoms and atoms with different degree of oxidation are computed by the parallel code. Based on the obtained values of atom portions the electrochemical capacity is calculated. The results of computer simulation are compared with the experimental data.


Parallel implementation Cellular automaton Domain decomposition Connected component Electrochemical oxidation Carbon corrosion 



K. K. Sabelfeld and A. E. Kireeva kindly acknowledge the support of the Russian Science Foundation under the Grant \(\hbox {N}^{\underline{\mathrm{o}}}\) 14-11-00083 on the computer simulation algorithm development. E.N. Gribov and N.V. Maltseva carried out the experimental work under the support of the budget project AAAA-A17-117041710087-3 of Boreskov Institute of Catalysis.


  1. 1.
    Toffoli T, Margolus N (1987) Cellular automata machines: a new environment for modeling. MIT Press, Boston, p 259CrossRefGoogle Scholar
  2. 2.
    The US DRIVE Fuel Cell Technical Team Technology Roadmap
  3. 3.
    Capelo A, Esteves MA, de S AI, Silva RA, Cangueiro L, Almeida A et al (2016) Stability and durability under potential cycling of Pt/C catalyst with new surface-functionalized carbon support. Int J Hydrogen Energy 41(30):12962–12975CrossRefGoogle Scholar
  4. 4.
    Gribov EN, Kuznetzov AN, Golovin VA, Voropaev IN, Romanenko AV, Okunev AG (2014) Degradation of Pt/C catalysts in start-stop cycling tests. Russ J Electrochem 50(7):700–711CrossRefGoogle Scholar
  5. 5.
    Li L, Hu L, Li J, Wei Z (2015) Enhanced stability of Pt nanoparticle electrocatalysts for fuel cells. Nano Res. 8(2):418–440CrossRefGoogle Scholar
  6. 6.
    Shrestha S, Liu Y, Mustain WE (2011) Electrocatalytic activity and stability of Pt clusters on state-of-the-art supports: a review. Catal. Rev. Sci. Eng. 53:256–336CrossRefGoogle Scholar
  7. 7.
    Gribov EN, Kuznetsov AN, Voropaev IN, Golovin VA, Simonov PA, Romanenko AV et al (2016) Analysis of the corrosion kinetic of Pt/C catalysts prepared on different carbon supports under the “Start-Stop” cycling. Electrocatalysis 7:159–73CrossRefGoogle Scholar
  8. 8.
    Chen J, Siegel JB, Matsuura T, Stefanopoulou AG (2011) Carbon corrosion in PEM fuel cell dead-ended anode operations. J Electrochem Soc 158(9):B1164–B1174CrossRefGoogle Scholar
  9. 9.
    Pandy A, Yang Z, Gummalla M, Atrazhev VV, Kuzminyh NYu, Vadim IS, Burlatsky SF (2013) A carbon corrosion model to evaluate the effect of steady state and transient operation of a polymer electrolyte membrane fuel cell. J Electrochem Soc 160(9):F972–F979. arXiv:1401.4285 [physics.chem-ph]CrossRefGoogle Scholar
  10. 10.
    Meyers JP, Darling Robert M (2006) Model of carbon corrosion in PEM fuel cells. J Electrochem Soc 153(8):A1432–A1442CrossRefGoogle Scholar
  11. 11.
    Gallagher KG, Fuller TF (2009) Kinetic model of the electrochemical oxidation of graphitic carbon in acidic environments. Phys Chem Chem Phys 11:11557–11567CrossRefGoogle Scholar
  12. 12.
    Golovin VA, Maltseva NV, Gribov EN, Okunev AG (2017) New nitrogen-containing carbon supports with improved corrosion resistance for proton exchange membrane fuel cells. Int J Hydrogen Energy 42:11159–11165CrossRefGoogle Scholar
  13. 13.
    Gribov EN, Maltseva NV, Golovin VA, Okunev AG (2016) A simple method for estimating the electrochemical stability of the carbon materials. Int J Hydrogen Energy 41:18207–18213CrossRefGoogle Scholar
  14. 14.
    Maltseva NV, Golovin VA, Chikunova YuO, Gribov EN (2018) Influence of the number of surface oxygen on the electrochemical capacity and stability of high surface Ketjen Black ES 600 DJ. Russ J Electrochem 54(5):489–496CrossRefGoogle Scholar
  15. 15.
    Kireeva AE, Sabelfeld KK, Maltseva NV, Gribov EN (2017) Parallel implementation of cellular automaton model of the carbon corrosion under the influence of the electrochemical oxidation. In: Malyshkin V (ed) PaCT 2017, LNCS, vol 10421, pp 205–214. Google Scholar
  16. 16.
    Meier JC, Katsounaros I, Galeano C, Bongard HJ, Topalov AA, Kostka A et al (2012) Stability investigations of electrocatalysts on the nanoscale. Energy Environ Sci 5:9319–9330CrossRefGoogle Scholar
  17. 17.
    Bandman OL (2010) Cellular automata composition techniques for spatial dynamics simulation. In: Simulating complex systems by cellular automata. In: Hoekstra AG et al (eds) Understanding complex systems, Berlin, pp 81–115Google Scholar
  18. 18.
    Abubaker A, Qahwaji R, Ipson S, Saleh M (2007) One scan connected component labeling technique, signal processing and communications. In: ICSPC 2007. IEEE International Conference, pp 1283–1286Google Scholar
  19. 19.
    Godsil C, Royle GF (2001) Algebraic graph theory. In: Graduate texts in mathematics, vol 207, 443 P. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics SB RASNovosibirskRussia
  2. 2.Boreskov Institute of Catalysis SB RASNovosibirskRussia
  3. 3.Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations