Current-voltage relations for electrochemical thin films

Martin Z. Bazant, Kevin T. Chu, B. J. Bayly

Research output: Contribution to journalArticlepeer-review

227 Scopus citations


The DC response of an electrochemical thin film, such as the separator in a micro-battery, is analyzed by solving the Poisson-Nernst-Planck equations, subject to boundary conditions appropriate for an electrolytic/galvanic cell. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer, which mediates Faradaic reactions with nonlinear Butler-Volmer kinetics. Analytical results are obtained by matched asymptotic expansions in the limit of thin double layers and compared with full numerical solutions. The analysis shows that (i) decreasing the system size relative to the Debye screening length decreases the voltage of the cell and allows currents higher than the classical diffusion-limited current; (ii) finite reaction rates lead to the important possibility of a reaction-limited current; (iii) the Stern-layer capacitance is critical for allowing the cell to achieve currents above the reaction-limited current; and (iv) all polarographic (current-voltage) curves tend to the same limit as reaction kinetics become fast. Dimensional analysis, however, shows that "fast" reactions tend to become "slow" with decreasing system size, so the nonlinear effects of surface polarization may dominate the DC response of thin films.

Original languageEnglish (US)
Pages (from-to)1463-1484
Number of pages22
JournalSIAM Journal on Applied Mathematics
Issue number5
StatePublished - 2005


  • Butler-Volmer reaction kinetics
  • Electrochemical systems
  • Poisson-Nernst-Planck equations
  • Polarographic curves
  • Stern layer
  • Surface capacitance
  • Thin films

ASJC Scopus subject areas

  • Applied Mathematics


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