An important aspect of electrodeposition is that the total amount deposited is directly related to the amount of charge passed in carrying out the desired reaction, and hence to the thickness of the plated layer. The mass of the deposit is
(13.1)
where Q is the charge passed due to the plating reaction. Assuming that the current density is uniform, the charge, Q, is
(13.2)
where i is the total current density (all reactions, not just the desired reaction) and is the faradaic efficiency for the deposition reaction at the cathode. If the current density, area, and faradaic efficiency do not change with time,
(13.3)
where I is the current, and t is the time since the plating began. Under these conditions, the thickness of the deposited layer, L, can be calculated from the mass
(13.4)
The average deposition rate is L/t.
ILLUSTRATION 13.1
A continuous sheet of copper is made by electrodeposition on a rotating drum of lead. For the conditions given below, what should be the rotation speed of the drum in revolutions per hour?
Cathode current density = 1000 [A·m−2]
Faradaic efficiency = 95%
Desired thickness = 10 μm
Copper density = 8900 kg·m−3
Angle of cathode immersion = 165°
In order to find the revolution speed, we need to know the length of time required to produce the deposit of the desired thickness. From Equation 13.4,
Solving this equation for t yields
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