ISSN 1023-1935, Russian Journal of Electrochemistry, 2018, Vol. 54, No. 5, pp. 456–458. © Pleiades Publishing, Ltd., 2018.
Original Russian Text © K.V. Rybalka, L.A. Beketaeva, A.D. Davydov, 2018, published in Elektrokhimiya, 2018, Vol. 54, No. 5, pp. 523–526.
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Cathodic Component of Corrosion Process:
Polarization Curve with Two Tafel Portions
K. V. Rybalka*, L. A. Beketaeva, and A. D. Davydov
Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences,
Leninskii pr. 31, Moscow, 119071 Russia
*e-mail: mamaison2000@yandex.ru
Received June 23, 2017; in final form, October 16, 2017
Abstract—A method for the analysis of corrosion process involving two cathodic reactions and one anodic
reaction is proposed. By way of example, this method is used to calculate a particular cathodic polarization
curve with two Tafel portions. The calculated polarization curve coincides with the experimental curve measured on stainless steel in 0.5 M HCl solution.
Keywords: corrosion, cathodic processes, polarization curves, corrosion current
DOI: 10.1134/S1023193518050063
INTRODUCTION
The mechanism and rate of uniform (general) corrosion of metals is frequently studied using the following equation [1–3]:
E − Ecorr ⎞
E − Ecorr ⎞⎤
i = icorr ⎡exp ⎜⎛ −
− exp ⎜⎛
⎟
⎟⎥ , (1)
⎢⎣
bc
ba
⎝
⎠
⎝
⎠⎦
where icorr is the corrosion current density, E is the
electrode potential, Ecorr is the corrosion potential,
bc and ba are the kinetic parameters depending on the
mechanism of electrode reactions.
This equation was derived for the simplest case,
when, firstly, the electrochemical reactions involved
in the corrosion process are described by the Tafel
equation and secondly, the corrosion process is associated with only two reactions: one cathodic reaction
and one anodic reaction.
This work is based on the fact that the corrosion
current density can be determined by the method of
Tafel extrapolation using a single experimental
cathodic polarization curve [1, 2, 4–6].
In many cases, for example, in the aerated acid
solutions or solutions containing salt and acid, two
cathodic reactions can proceed: the reduction of dissolved oxygen and H+ cations. In these cases, equation (1) cannot be used to calculate the corrosion current density.
In [7], the corrosion behavior of a metal was simulated taking into account one anodic reaction and two
aforementioned cathodic reactions. The simulation
was performed irrespective of any corrosion system
and any experimental data. The system of mass-trans-
fer equations for three types of reagent and the electroneutrality equation was solved numerically using the
finite element method for a rotating disk electrode
taking into account the diffusion, migration, and convective transport mechanisms. The calculated
cathodic polarization curves contained two portions
of diffusion limiting current for two cathodic reactions
separated by the Tafel region for the reaction of H+
cation reduction.
At the same time, in the practice of corrosion studies, there are examples where the oxygen reduction proceeds in the mixed kinetic mode, for example, in [8].
The aim of this work is to determine the method for
analyzing the cathodic process, which corresponds to
the polarization curve with two Tafel regions related to
two cathodic reactions.
EXPERIMENTAL PROCEDURE
The experiments were performed using the potentiodynamic method for measuring the cathodic polarization curves at a potential scan rate of 10–3 V/s. A
fragment of wire of AISI 304 stainless steel 0.5 mm in
diameter and 20 cm in length was used as the test electrode. Its surface was preliminarily degreased and,
then, washed with twice-distilled water. The experiments were performed under the conditions of natural
aeration. The potentials were measured and presented
against the potential of saturated silver–chloride reference electrode.
456
CATHODIC COMPONENT OF CORROSION PROCESS
METHOD OF CALCULATING
POLARIZATION CURVES
The cathodic process was simulated using the
equations that take into account one anodic and two
cathodic reactions. The model polarization curve was
calculated using the equation that takes into account
that one cathodic reaction proceeds in the mixed
kinetic mode.
Let us consider the case of linear diffusion of a substance that is reduced on the electrode. In this case,
the concentration of the substance in the near-electrode layer cs at a current i can be expressed in terms of
the bulk concentration c0 and the diffusion limiting
current id:
csi = c0 ⎛⎜1 − i ⎞⎟ .
⎝ id ⎠
Then, at icorr, we obtain:
(2)
i
i
(3)
cscorr = c0 ⎛⎜1 − corr ⎞⎟ .
id ⎠
⎝
The dependences of currents i1 and i1corr for the first
reaction can be written as follows [3]:
E − Er ⎞
i
,
i1 = kcs exp ⎛⎜ −
b1c ⎟⎠
⎝
E − Er ⎞
i1corr = kcsicorr exp ⎛⎜ − corr
⎟,
b1c
⎝
⎠
where k is the coefficient and Er is the equilibrium
potential. Then,
csi
E − Ecorr ⎞
i1 = i1corr icorr
exp ⎛⎜ −
.
b1c ⎟⎠
cs
⎝
From (3) and (4), we obtain:
(4)
i1corrid
E − Ecorr ⎞
exp ⎛⎜ −
i −i
b1c ⎟⎠
⎝
(5)
i1 = d 1corr
.
i1corr
E − Ecorr ⎞
⎛
1+
exp ⎜ −
id − i1corr
b1c ⎟⎠
⎝
The final equation for the total corrosion current is as
follows:
E − Ecorr ⎞
i = (i1corr + i2corr ) exp ⎛⎜
⎟
ba
⎝
⎠
i1corrid
E − Ecorr ⎞
⎛
exp ⎜ −
i −i
b1c ⎟⎠
⎝
(6)
− d 1corr
i1corr
E − Ecorr ⎞
⎛
1+
exp ⎜ −
id − i1corr
b1c ⎟⎠
⎝
E − Ecorr ⎞
− i2corr exp ⎛⎜ −
.
b2c ⎟⎠
⎝
Here, i1corr and i2corr are the first and second cathodic
currents at the corrosion potential, id is the diffusion
limiting current of the first reaction, b1c, b2c and ba are
the parameters that characterize two cathodic reacRUSSIAN JOURNAL OF ELECTROCHEMISTRY
Vol. 54
457
i, µA/cm2
1000
100
10
1
–500
–450
–400
–350
–300
–250
E, mV
Fig. 1. Cathodic potentiodynamic curves (potential scan
rate 1 mV/s) measured on specimen of AISI 304 stainless
steel in 0.5 M HCl solution.
tions and anodic reaction, 2.3b1c, 2.3b2c and 2.3ba are
the cathodic and anodic Tafel slopes, respectively.
RESULTS AND DISCUSSION
Figure 1 shows the measured cathodic polarization
curve for the electrode of AISI 304 steel. The electrode was preliminarily held in 0.5 M HCl solution at
the open-circuit potential (corrosion potential) for
14 days.
Two slopes of the curve in Fig. 1 can be the evidence for two cathodic reactions conjugated with the
reaction of anodic dissolution of metal, for example,
the reduction of hydrogen ions and oxygen dissolved
in the solution. In the general case, other reactions can
be involved in the cathodic process.
Let us determine the corrosion currents i1corr, i2corr
and coefficients b1c, b2c and ba, at which the polarization curve calculated by equation (6) coincides with
the experimental curve presented on Fig. 1.
Here, these values were determined by the fitting
method using the MATHCAD software package.
Table 1 lists the calculated total corrosion current, the
corrosion currents of individual cathodic processes,
the diffusion limiting current, and the parameters
characterizing the dependence of partial currents on
the potential.
Figure 2 shows the experimental and calculated
(model) polarization curves. It is seen that they virtually coincide.
Table 1. Electrochemical parameters of corrosion process
icorr,
μA/cm
57.4
No. 5
i1corr,
2
i2corr,
2
i d,
2
μA/cm
μA/cm
μA/cm
52.3
5.1
90
2018
2
b1c,
mV
b2c,
mV
ba,
mV
153
76
30
458
RYBALKA et al.
In the case that all reactions are controlled by the
charge-transfer stage, the polarization curve can be
calculated by equation (7). Equation (7) is the simplified version of equation (6) for the case that the diffusion current of the first component tends to infinity.
i, µA/cm2
1000
E − Ecorr ⎞
i = (i1corr + i2corr ) exp ⎛⎜
⎟
ba
⎝
⎠
(7)
E − Ecorr ⎞
E − Ecorr ⎞
⎛
⎛
i
− i1corr exp ⎜ −
−
exp
−
.
2corr
⎜
b1c ⎟⎠
b2c ⎟⎠
⎝
⎝
100
10
1
–200
–150
–100
–50
0
E – Ecorr, mV
Fig. 2. Cathodic potentiodynamic curve measured on
specimen of AISI 304 stainless steel in 0.5 M HCl solution
(circles) and the curve calculated using parameters determined by fitting (solid line).
i, µA/cm2
REFERENCES
1000
3
2
100
1
10
–200
CONCLUSIONS
The approach used in this work allows one to analyze the corrosion process, which is characterized by
two Tafel regions in the cathodic polarization curve. A
method for simulating the cathodic polarization curve
is proposed. The method enables one to estimate the
kinetic characteristics of both cathodic reactions and
determine the contribution of each reaction to the
total cathodic current. This makes it possible to determine which of cathodic processes proceeding at the
electrode can determine the corrosion rate of the
metal under investigation.
–150
–100
–50
0
E – Ecorr, mV
Fig. 3. Calculated (1 and 2) partial and (3) total cathodic
polarization curves.
The method enables us not only to calculate the
total polarization curve, which virtually coincides with
the experimental curve, but also to determine the
kinetic parameters of both cathodic reactions and the
diffusion limiting current of the first reaction. Figure 3
gives the partial (1 and 2) and total (3) cathodic polarization curves, which were calculated using the corresponding terms of equation (6) and the data presented
in Table 1.
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RUSSIAN JOURNAL OF ELECTROCHEMISTRY
Translated by T. Kabanova
Vol. 54
No. 5
2018