ISSN 1070-4272, Russian Journal of Applied Chemistry, 2006, Vol. 79, No. 11, pp. 1820!1824. + Pleiades Publishing, Inc., 2006.
Original Russian Text + V.I. Karavaev, I.L. Korobova, Yu.V. Litovka, 2006, published in Zhurnal Prikladnoi Khimii, 2006, Vol. 79, No. 11, pp. 1840!
AND CORROSION PROTECTION OF METALS
Calculation of the Most Uniform Electroplated Coating
with Account of Changes in the Concentration
of Electrolyte Components
V. I. Karavaev, I. L. Korobova, and Yu. V. Litovka
Tambov State Technical University, Tambov, Russia
Received May 6, 2006
Abstract-The problem of optimization of the electroplating process by the nonuniformity criterion with
account of the effect of changes in the concentration of electrolyte components on the polarization is formu-
lated and solved.
One of the most important quality parameters of an
electroplated coating is the uniformity of metal distri-
bution over the article surface. The uniformity depends
on the configuration of an electrolytic cell (shape,
size, and relative position of electrodes) and on the
electrochemical component (polarization phenomena).
The effect of these factors on the coating uniformity
has been extensively studied [1, 2]. However, the in-
fluence of the concentration of electrolyte components
on the polarization and, consequently, on the uni-
formity of electroplated coatings has been insufficient-
ly studied. At the same time, the concentration of
electrolyte components varies with time because of the
carry-over of the electrolyte with processed articles,
consumption of these components by electrochemical
and chemical reactions, and electrolyte evaporation.
In many cases, the polarization strongly depends
on the concentration of the electrolyte components.
It was shown in  that the concentration of ammo-
nium ions affects the run of the overall polarization
curves in electrodeposition of a nickel3molybdenum
alloy. In , polarization curves obtained at various
concentrations of lead ions in the cyanide electrolyte
in electrodeposition of gold were reported. It was
demonstrated in  that polarization curves depend
on the concentration of various electrolyte compo-
nents in zinc-, cadmium-, tin-, rhodium-, nickel-, and
silver-plating. In all of these examples, the overvolt-
age changes by 10320% when the concentration of
electrolyte components varies.
In this study, the influence exerted by the concen-
tration of electrolyte components on the coating uni-
formity is examined and electrical parameters of the
electroplating bath that provide the highest coating
uniformity at varied electrolyte concentration are
The coating nonuniformity factor R is defined by
1 d(x, y, z) 3d
is the cathode surface area; d(x, y, z), coating
thickness at a certain point of the cathode, with the
coordinates (x, y, z); and d
, minimum coating thick-
ness on the cathode.
The optimization problem is formulated as follows.
Let the concentration of a component that affects
the polarization be c at a certain instant of time (the
concentration can be measured or calculated in terms
of a mathematical model ). It is necessary to find
the voltage U applied to the bath, at which the coating
nonuniformity (1) is at a minimum.
To relate the criterion R to the concentration c,
we use a set of equations of the mathematical model,
which will have the following form.
The coating thickness at a certain point (x, y, z)on
the cathode surface S
is calculated by the formula
derived from the Faraday law:
Ei(x, y, z)ht
d(x, y, z)=ÄÄÄÄÄÄÄÄÄÄ, (2)