1023-1935/01/3701- $25.00 © 2001 åÄIä “Nauka /Interperiodica” 0063
Russian Journal of Electrochemistry, Vol. 37, No. 1, 2001, pp. 63–72. Translated from Elektrokhimiya, Vol. 37, No. 1, 2001, pp. 76–86.
Original Russian Text Copyright © 2001 by Guterman, Nadolin.
INTRODUCTION
In a large number of chemical reactions involving
solid substances, the reaction zone is localized at inter-
faces between the solid reagent and solid product or
between the solid product and solution [1–5]. In turn,
variations in the reaction surface area, which are caused
by the chemical reaction, define the reaction kinetics.
As a rule, the formation of a new phase features the
stage of the nucleation and growth of nuclei. The latter
have a certain size even as early as at the instant of their
formation [1–5]. The rate of such reactions varies with
time in a complicated manner. It depends on specific
features of the formation, distribution, and growth of
nuclei of the reaction’s solid products; variations in the
surface area of the reaction’s interface; diffusion ham-
pering; variations in concentrations of substances that
take part in the reaction; and so on [1–5]. In all electro-
chemical processes, the electrode potential affects the
reaction’s progress virtually at all the reaction’s stages
[4, 5]. If the reaction’s product has an invariant compo-
sition, the measured current is directly proportional to
the amount of the converted substance:
(1)
Therefore, an analysis of the i vs. t dependence (poten-
tiostatic transient of the current) is a convenient way to
study such reactions. The dependence in question may
be obtained by imposing a pulsed potential on the elec-
trode. We note that the heterophase reactions include
different types of electrochemical reactions localized at
the electrode/electrolyte interface or leading to the for-
mation of a reaction boundary in a near-surface layer of
the electrode. Specifically, these are reactions of elec-
trocrystallization of metals; formation of oxide films;
I
nF ρ
M
----------
dV
dt
------. =
and cathodic incorporation and intercalation of metals
into metallic and nonmetallic electrodes, respectively.
1
Kinetic studies of such reactions are frequently based
on mathematical models [6–31]. Thus far, the deter-
mined models [8–24] have failed to account for the
important nucleation features associated with the
mutual influence of the product nuclei on their distribu-
tion over the reagent surface. Moreover, the cumber-
someness of these models makes it difficult to apply
them for analyzing experimental data in real practice.
Stochastic models based on the method of statistical
tests [6, 25–29] are quite competitive with the theoreti-
cal determined models. Of late, the former helped elu-
cidate the role played by the ordering of a nuclei distri-
bution in the kinetics of reactions of electrocrystalliza-
tion [25–28] and electrochemical incorporation of
metals [7]. Their main disadvantage—a considerable
calculation investment—is gradually taken care of with
the development of computers.
Most applied models ignore the size of nuclei at the
instant of their formation. This assumption probably
has no substantial impact on the results of calculations
in the cases where critical nuclei consist of a single
atom or a few atoms, as is the case with the electrocrys-
tallization of some metals at high overvoltages [4, 5].
At the same time, it is obvious that nucleation can also
occur in the cases where critical nuclei comprise doz-
ens and hundreds of atoms, and a tenfold increase in the
nuclei size occurs within a long time period [1–3]. Such
a situation may arise during the nucleation of interme-
1
In the case of the electrocrystallization of metals, values of M and
ρ in (1) refer to the reaction’s product (to the metal of the
deposit); in the case of the electrochemical incorporation of met-
als, to the reagent (the material of the cathode) [6, 7].
Computer-aided Modeling of the Time Dependences
of the Current during Anisotropic Growth of Product Nuclei
V. E. Guterman and K. A. Nadolin
Rostov State University, pr. Stachki 194, Rostov-on-Don, 344104 Russia
Received December 22, 1999
Abstract—A fast computer model, intended for the calculation of the overall reaction rate (current) of aniso-
tropic or nonhomotetic growth of a new-phase nuclei on the basis of the Voronoi diagram, is designed. The
model is used for studying the kinetics of a heterogeneous reaction in the conditions where hemispherical nuclei
of the new phase acquire a semiellipsoid shape in the course of an anisotropic growth. The calculation of current
transients (potentiostatic i vs. t dependences) is substantially complicated in the initial stage of reaction, where
the size of growing nuclei exceeds the critical value by less than an order of magnitude. If semiellipsoid nuclei
overlap, the overall reaction rate is not determined by variations in the overall area of the reaction surface, as
opposed to the growth of hemispherical nuclei. The kinetics of a nonhomotetic nuclei growth may be described
by models designed for an isotropic growth of hemispherical nuclei.