Advertisement

Simulation of Ion Transfer During Electrochemical Shaping by Ultrashort Pulses

  • V. M. Volgin
  • V. V. Lyubimov
  • I. V. Gnidina
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

In the work, an efficient model of the transfer processes in the electrochemical systems was developed for the case that ultrashort current pulses were imposed. The Nernst–Planck equations with the electroneutrality condition were used for calculating the transfer processes in the diffusion layer, and the equilibrium Boltzmann distribution of ions was assumed in the diffuse layer. This provided a high efficiency of the model. The simulation involved the numerical solution of the Nernst–Planck equations for the diffusion layer and the Poisson’s equation for the diffuse layer. Thus, obtained solutions were conjugated in accordance with all boundary conditions. The time dependences of the electrode potential were obtained for the anodic and cathodic processes. The regions, which corresponded to different scales of time and characterized the charging of bulk electrolyte solution, the charging of electrical double layer, and the transfer processes in the diffusion layer, were observed in these dependences. The specific features of transfer processes under the imposition of ultrashort current pulse (a pulse time of the order of tens of nanoseconds) were studied.

Keywords

Ion transfer Ultrashort current pulses The electric double layer Mathematical modeling 

Notes

Acknowledgements

The results of the research project are published with the financial support of Tula State University within the framework of the scientific project No. 2017-67PUBL.

References

  1. 1.
    Schuster R, Kirchner V, Allongue P, Ertl G (2000) Electrochemical micromachining. Science 289:98–101CrossRefGoogle Scholar
  2. 2.
    Kock M, Kirchner V, Schuster R (2003) Electrochemical micromachining with ultrashort voltage pulses—a versatile method with lithographical precision. Electrochim Acta 48:3213–3219CrossRefGoogle Scholar
  3. 3.
    Davydov AD, Volgin VM, Lyubimov VV (2004) Electrochemical machining of metals: fundamentals of electrochemical shaping. Russ J Electrochem 40(12):1230–1265CrossRefGoogle Scholar
  4. 4.
    Malshe AP, Rajurkar KP, Virwani KR, Taylor CR, Bourell DL, Levy G, Sundaram MM, McGeough JA, Kalyanasundaram V, Samant AN (2010) Tip-based nanomanufacturing by electrical, chemical, mechanical and thermal processes. CIRP Ann-Manuf Technol 59(2):628–651CrossRefGoogle Scholar
  5. 5.
    Kenney JA, Hwang GS, Shin W (2004) Two-dimensional computational model for electrochemical micromachining with ultrashort voltage pulses. Appl Phys Lett 84(19):3774–3776CrossRefGoogle Scholar
  6. 6.
    Kenney JA, Hwang GS (2005) Electrochemical machining with ultrashort voltage pulses: modelling of charging dynamics and feature profile evolution. Nanotechnology 16:S309–S313CrossRefGoogle Scholar
  7. 7.
    Hotoiu EL, Van Damme S, Albu C, Deconinck D, Demeter A, Deconinck J (2013) Simulation of nano-second pulsed phenomena in electrochemical micromachining processes—effects of the signal and double layer properties. Electrochim Acta 93:8–16CrossRefGoogle Scholar
  8. 8.
    Bonnefont A, Argoul F, Bazant MZ (2001) Analysis of diffuse-layer effects on time-dependent interfacial kinetics. J Electroanal Chem 500:52–61CrossRefGoogle Scholar
  9. 9.
    Bazant MZ, Thornton K, Ajdari A (2004) Diffuse-charge dynamics in electrochemical systems. Phys Rev E 70(21):021506CrossRefGoogle Scholar
  10. 10.
    Bazant MZ, Chu KT, Bayly BJ (2005) Current-voltage relations for electrochemical thin films. SIAM J Appl Math 65(5):1463–1484MathSciNetCrossRefGoogle Scholar
  11. 11.
    Biesheuvel PM, van Soestbergen M, Bazant MZ (2009) Imposed currents in galvanic cells. Electrochim Acta 54:4857–4871CrossRefGoogle Scholar
  12. 12.
    Van Soestbergen M, Biesheuvel PM, Bazant MZ (2010) Diffuse-charge effects on the transient response of electrochemical cells. Phys Rev E 81:021503CrossRefGoogle Scholar
  13. 13.
    Lim J, Whitcomb J, Boyd J, Varghese J (2007) Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified Stern layer. J Colloid Interface Sci 305(1):159–174CrossRefGoogle Scholar
  14. 14.
    Dickinson EJ, Compton RG (2011) Influence of the diffuse double layer on steady-state voltammetry. J Electroanal Chem 661(1):198–212CrossRefGoogle Scholar
  15. 15.
    Biesheuvel PM, Fu Y, Bazant MZ (2012) Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes. Russ J Electrochem 48(6):580–592CrossRefGoogle Scholar
  16. 16.
    Van Soestbergen M (2012) Frumkin–Butler–Volmer theory and mass transfer in electrochemical cells. Russ J Electrochem 48(6):570–579CrossRefGoogle Scholar
  17. 17.
    Volgin VM, Davydov AD (2001) Numerical modeling of non-steady-state ion transfer in electrochemical systems with allowance for migration. Russ J Electrochem 37(11):1197–1205CrossRefGoogle Scholar
  18. 18.
    Volgin VM, Davydov AD (2007) Numerical simulation of steady state ion transfer to rotating disk electrode: accuracy and computational efficiency. J Electroanal Chem 600(1):171–179CrossRefGoogle Scholar
  19. 19.
    Kumsa D, Scherson DA (2013) Theoretical aspects of pulsed electrochemical micromachining. J Electrochem Soc 160(8):H481–H488CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • V. M. Volgin
    • 1
  • V. V. Lyubimov
    • 1
  • I. V. Gnidina
    • 1
  1. 1.Tula State UniversityTulaRussia

Personalised recommendations