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Mathematical modelling of electrode growth

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Abstract

It is known that during electrodeposition or dissolution electrode shape change depends on the local current density (Faraday's law in differential form). Assuming that concentration gradients in the bulk of the solution may be neglected, the current distribution in an electrochemical system can be modelled by a Laplace equation (describing charge transport) with nonlinear boundary conditions caused by activation and concentration overpotentials on the electrodes. To solve this numerical problem, an Euler scheme is used for the integration of Faraday's law with respect to time and the field equation is discretized using the boundary element method (BEM). In this way, and by means of a specially developed electrode growth algorithm, it is possible to simulate electrodeposition or electrode dissolution. In particular, attention is paid to electrode variation in the vicinity of singularities. It is pointed out that the angle of incidence between an electrode and an adjacent insulator becomes right (π/2). This is confirmed by several experiments.

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Abbreviations

x i :

coordinates of a point i belonging to a boundary (m)

t :

time (s)

h:

thickness variation at a point belonging to an electrode (m)

M :

molecular weight (kgmol−1)

ϱm:

specific weight (kgm−3)

z :

charge of an ion (C)

F :

Faraday's constant (C mol−1)

R a2 :

impedance of the linearized activation overvoltage on cathode (S2 cm−2)

θ:

efficiency of the reaction

σ:

electric conductivity (Ω−1 m−1)

U :

electric potential (V)

\(\bar u\) :

rate of mechanical displacement of a point (m s−1)

V :

applied potential on an electrode (V)

W :

Wagner number defined as the ratio of the mean impedance of the reaction \(\left. {\frac{{\partial \eta }}{{\partial J}}} \right|_{Jav}\) and the mean ohmic resistance of the cell given by L/σ with L a characteristic length of the cell.

η:

overvoltage (V)

η1 :

overvoltage on anode (V)

η2 :

overvoltage on cathode (V)

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Deconinck, J. Mathematical modelling of electrode growth. J Appl Electrochem 24, 212–218 (1994). https://doi.org/10.1007/BF00242886

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Keywords

  • Field Equation
  • Boundary Element Method
  • Current Distribution
  • Charge Transport
  • Differential Form