Electrode Growth Next to an Insulator

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Electrode Growth Next to an Insulator

This example models electrodeposition of copper with a deforming geometry where an electrode surface is placed next to an insulator, initially at an 180 degree angle. This situation is of interest from a benchmark perspective since non-right angles between insulators and growing electrodes may introduce singularities when modeling deforming geometries (Ref. 1).

No concentration gradients in the electrolytes are assumed, and a secondary current distribution is modeled.

The model qualitatively reproduces the results of J. Deconinck (Ref. 1).

Model Definition

The model is made in 2D and consists of a dissolving and a depositing electrode. Only the electrolyte domain is modeled in the geometry. See Figure 1.

Figure 1: Initial modeled geometry.

The electrolyte is assumed to be a 0.8 M CuSO4-0.8 M H2SO4 solution with a conductivity of σ = 0.23Ω-1cm-1, where the H2SO4 is assumed to act as a supporting electrolyte (due to the high conductivity of the protons). Concentration gradients of Cu2+ are neglected in the model and thus a secondary current distribution is assumed.

The electrodes both consist of copper. On the dissolving electrode, copper dissolution occurs

whereas copper is deposited on the depositing electrode

A simplified electrode kinetic model is assumed for both electrodes, with a linear relation between the overpotential, η, and electrode reaction current density, iloc, according to:

By using the copper deposition red-ox reaction as reference potential, the equilibrium potential is set to zero for both electrodes.

The depositing electrode is grounded and a electric potential of 0.778 V is set to the dissolving electrode. All other boundaries are isolated.

Deforming geometry

Due to the dissolution and deposition of copper, the electrode boundaries move during the simulation. The molar flux of copper, NCu (mol/(m2·s)), over the electrodes is described by Faraday’s law according to

where F is Faraday’s constant (96485 C/mol). The stoichiometric coefficients for copper is νCu = 1 for both electrode reactions, and the number of electrons is n = 2.

The depositing velocity, vdep, directed in the normal direction of the electrode into the electrode domain, can be deduced from the molar flux, the density and the molar mass of copper

Results and Discussion

Figure 2 shows a surface plot of the electrolyte potential, and a streamline plot of the electrolyte current density, at 96 h, for the deformed geometry.

Figure 2: Electrolyte potential (surface) and electrolyte current direction (streamlines) at t=96 h.

The electrode growth reaches its maximum close to the insulator-electrode edge, due to the higher electrode currents in this area. Figure 3 shows the profile change of the depositing electrode during the simulation.

Figure 3: Profile of deposited electrode at various times during the simulation.

Notes About the COMSOL Implementation

The model is set up using the Electrodeposition, Secondary interface with a single Electrolyte domain. The depositing and dissolving electrodes are modeled with the External Depositing Electrode boundary nodes.

A time dependent study is used to simulate the electrode growth and dissolution during 96 h.

The default Nondepositing Boundary node is used for the geometry deformation at the insulated boundaries. The boundary condition setting of the feature is changed to Zero Normal Displacement, instead of using the default Zero Normal Velocity. This improves the numerical stability of the geometry deformation on these boundaries.

1. J. Deconinck, “Mathematical modelling of electrode growth,” J. Applied Electrochemistry, vol. 24, pp. 212-218, 1994.

Electrodeposition_Module/Verification_Examples/electrode_insulator_growth

Modeling Instruction

From the menu, choose .

In the window, click

.

1

In the window, click

.

2

In the tree, select .

3

4

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In the tree, select .

6

Draw the geometry using a rectangle and a point.

Rectangle 1 (r1)

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In the toolbar, click

.

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In the window for , locate the section.

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In the text field, type 30[cm].

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In the text field, type 10[cm].

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In the toolbar, click

.

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In the window for , locate the section.

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In the text field, type 20[cm].

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In the toolbar, click

.

Secondary Current Distribution (cd)

Now set up the electrochemical model. Start with the domain settings for the electrolyte.

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In the window, under click .

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In the window for , locate the section.

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From the σl list, choose . In the associated text field, type 0.23[S/cm].

Electrode Surface 1

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In the toolbar, click

and choose .

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Select Boundary 2 only.

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In the window for , click to expand the section.

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Electrode Reaction 1

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In the window, expand the node, then click .

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In the window for , locate the section.

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In the n text field, type 2.

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In the table, enter the following settings:


Species	Stoichiometric coefficient (1)
s1	1

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Locate the section. From the iloc,expr list, choose . In the associated text field, type cd.eta_er1*300[mA/cm^2/V].

Electrode Surface 2

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In the window, under right-click and choose .

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Select Boundary 3 only.

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In the window for , locate the section.

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In the φs,ext text field, type 0.778.

Nondeforming Boundary 1 (ndb1)

The following applies a stronger constraint (than the default condition) for the planar nondepositing walls, in order to enforce a zero boundary movement in the normal direction.

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the window, right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Select Point 3 only.

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Locate the section. Click the button.

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Locate the section. Select the check box.

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In the associated text field, type 0.1[mm].

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Set the solver to simulate 96 hours of deposition, storing the solution every 3 hours.

Step 2: Time Dependent

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the text field, type range(0,3,96).

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In the toolbar, click

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Electrolyte Potential (cd)

A 2D plot of the electrolyte potential and the deformation is created by default. Change the frame of the dataset edges to Geometry in order to show the outline of the original (undeformed) geometry in the figure.

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

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button in the toolbar.

1D Plot Group 6

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In the toolbar, click

and choose .

Use the following steps to create Figure 3.

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In the window for , locate the section.

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From the list, choose .

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In the list, choose , , , , and .

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Click to expand the section. From the list, choose .

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In the text area, type Profile of depositing electrode.

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Right-click and choose .

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Select Boundary 2 only.

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In the window for , locate the section.

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In the text field, type y.

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Locate the section. From the list, choose .

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In the text field, type x.

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Click to expand the section. Select the check box.

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From the list, choose .

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In the table, enter the following settings:


Legends
0 h
24 h
48 h
72 h
96 h

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In the toolbar, click

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