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Approximate evaluation of cell resistance with resistive electrodes

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Abstract

The resistance of a cell composed of a resistive anode and a conductive cathode has been theoretically calculated by solving the two-dimensional Laplace equation for the solution phase where the anode has an overpotential of a linear type. Conditions were evaluated under which the cell resistance could be obtained on the assumption that the direction of the current flowing in solution was perpendicular to the electrode. These were not strongly dependent on the ratio of the interelectrode distance to the height of the electrodes. The main parameters which determine the conditions were the Wagner number and the ratio of the electrode resistance to the solution resistance.

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Abbreviations

a :

linear overpotential coefficient

b :

linear overpotential coefficient

d :

interelectrode distance

h :

height of the electrode

i :

current density flowing in the solution

i av :

average current density

i max :

maximum current density

I :

current fed to the anode

r :

cell resistance

r ap :

cell resistance obtained on the assumption that current lines are normal to the electrodes

r Lp :

cell resistance calculated from the Laplace equation

t :

thickness of the anode

V :

cell voltage

V eq :

open circuit inner potential difference between the anode and cathode

w :

width of the electrodes

Wa :

Wagner number given by Equation 12

x :

axis normal to the electrode surface

y :

axis in the direction to the electrode height

β:

ratio of solution resistance to anode resistance

η:

overpotential

θ:

dimensionless parameter defined by Equation 18

ϱ:

resistivity

ϕ:

inner potential of the solution

ψ:

inner potential of the electrode

ψ T :

inner potential of the electrode at the terminal

a:

anode

c:

cathode

s:

solution

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Authors and Affiliations

  1. Department of Electronic Chemistry, Graduate School at nagatsuta, Tokyo Institute of Technology Nagatsuta, Midori-ku, 227, Yokohama, Japan

    Koichi Aoki, Koichi Tokuda & Hiroaki Matsuda

  2. Research and Development Center, Permelec Electrode Ltd, 1159 Ishikawa, 252, Fujisawa, Japan

    Yoshinori Nishiki

Authors
  1. Koichi Aoki
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  2. Yoshinori Nishiki
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  3. Koichi Tokuda
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  4. Hiroaki Matsuda
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Aoki, K., Nishiki, Y., Tokuda, K. et al. Approximate evaluation of cell resistance with resistive electrodes. J Appl Electrochem 17, 552–558 (1987). https://doi.org/10.1007/BF01084129

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  • DOI: https://doi.org/10.1007/BF01084129

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