Decorative Plating

This tutorial example of decorative electroplating models a secondary current distribution with full Butler-Volmer kinetics for both anode and cathode. The thickness of the deposited layer at the cathode is computed along with the surface thickness change on the anode caused by metal dissolution.

A more detailed description of how to build this model, including screenshots, can be found in the Introduction to the Electrodeposition Module book.

Model Definition

The model geometry is shown in Figure 1. The anode is a planar dissolving anode. The cathode represents a furniture fitting that is to be decorated by metal plating.

Figure 1: The model geometry.

The conductivity of the metal of the anode and cathode is very high compared to that of the electrolyte and it is thus assumed that the electric potential in the metal is constant. Variations in the activation overpotential are therefore caused by the potential in the electrolyte at the surface of the electrodes. Under these assumptions, the electrodes are treated as boundaries in the simulations.

Before beginning, one difficulty found in all current density distribution models needs to be discussed. The overpotential,

, for an electrode reaction of index m, is defined according to the following equation:

where

denotes the electric potential of the metal,

denotes the potential in the electrolyte, and Eeq,m denotes the difference between the metal and electrolyte potentials at the electrode surface, measured at equilibrium using a common reference potential. The electric potential of one of the electrodes may be bootstrapped, so that all other potentials are measured with this reference (this bootstrap can actually be achieved by fixing the potential at any point in the cell). In this case, the electric potential of the metal is selected at the cathode as a bootstrap by setting this potential to 0 V. This implies that the electric potential of the metal at the anode is equal to the cell voltage. The potential of the electrolyte floats and adapts to satisfy the balance of current, so that an equal amount of current that leaves at the cathode also enters at the anode. This then determines the overpotential at the anode and the cathode.

Electrolyte charge transport

Use the Secondary Current Distribution interface to solve for the electrolyte potential, φl (SI unit: V), according to:

where il (SI unit: A/m2) is the electrolyte current density vector and σl (SI unit: S/m) is the electrolyte conductivity, which is assumed to be a constant.

Use the default Insulation condition for all boundaries except the anode and cathode surfaces:

where n is the normal vector, pointing out of the domain.

The main electrode reaction on both the anode and the cathode surfaces is the nickel deposition/dissolution reaction according to

Use a Butler-Volmer Expression to model this reaction; this sets the local current density to

The rate of deposition at the cathode boundary surfaces and the rate of dissolution at the anode boundary surface, with a velocity in the normal direction, v (m/s), is calculated according to

where M is the mean molar mass (59 g/mol) and ρ is the density (8900 kg/m3) of the nickel atoms and n is number of participating electrons. Note that the local current density is positive at the anode surface and negative at the cathode surfaces.

On the anode the electrolyte current density is set to the local current density of the nickel deposition reaction:

On the cathode, add a second electrode reaction to model the parasitic hydrogen evolution reaction:

Use a cathodic Tafel equation to model the kinetics of the hydrogen reaction on the cathode, this sets the local current density to

The hydrogen reaction does not contribute to the rate of deposition of nickel, but it contributes to the total current density at the cathode surface:

Solve the model in a time-dependent study, simulating the electroplating for 600 s.

Results and Discussion

Figure 2 shows the change in the total electrode thickness for the cathode surfaces indicating the deposition thickness after 600 s. It can be seen that the deposition thickness is quite non-uniform. The lowest deposition thickness is found at the bottom end of the cathode geometry, farthest from the anode surface. The deposition thickness could be optimized further by changing design parameters such as plating cell geometry, distance between the anode and cathode surface, conductivity of the electrolyte and operational parameters such as applied current or potential.

Figure 2: The simulated results of the change in the total electrode thickness.

Figure 3 shows the local current efficiency over the cathode surface. The efficiency is calculated as the nickel deposition current density divided by the total current density at the cathode. The efficiency is about 97%.