Kinetic study of the chlorine electrode reaction on Ti/RuO2 through the polarisation resistance: Part III: Proposal of a reaction mechanism

Article abstract of DOI:10.1016/S0013-4686(01)00839-8

A kinetic mechanism for the chlorine electrode reaction (ClER) on Ti/RuO₂ electrodes is proposed. The first step is the oxidation of the superficial sites, where the chloride ion is electroadsorbed giving the atomic chlorine intermediate. The later discharge of chlorine can take place either by recombination of two adsorbed intermediates or by the reaction between the intermediate and the chloride ion, being both chemical steps. The expression of the intrinsic polarisation resistance Rp_o as a function of the activity of chloride a_Cl-^o' and the partial pressure of chlorine p?_Cl2 was obtained from the resolution of the kinetic mechanism and it was compared with experimental data. The correlations of the independent experimental relationships Rp_o versus a_Cl-^o' and Rp_o versus p?_Cl2 were remarkably good, giving strong evidence that the ClER takes place through the proposed mechanism on the RuO₂ electrodes. The kinetic constants obtained from the correlations were used for the simulation of the dependences of the current density and the surface coverages on overpotential.

Full text of DOI:10.1016/S0013-4686(01)00839-8

Electrochimica Acta 47 (2002) 1145–1152
www.elsevier.com/locate/electacta
Kinetic study of the chlorine electrode reaction on Ti/RuO2
through the polarisation resistance
Part III: proposal of a reaction mechanism
J.L. Ferna´ndez, M.R. Gennero de Chialvo, A.C. Chialvo *,1
Programa de Electroqu´ımica Aplicada e Ingenier´ıa Electroqu´ımica (PRELINE), Facultad de Ingenier´ıa Qu´ımica, Uni6ersidad Nacional del Litoral,
Santiago del Estero 2829, 3000 Santa Fe, Argentina
Received 2 July 2001; received in revised form 27 September 2001
Abstract
A kinetic mechanism for the chlorine electrode reaction (ClER) on Ti/RuO2 electrodes is proposed. The first step is the
oxidation of the superficial sites, where the chloride ion is electroadsorbed giving the atomic chlorine intermediate. The later
discharge of chlorine can take place either by recombination of two adsorbed intermediates or by the reaction between the
intermediate and the chloride ion, being both chemical steps. The expression of the intrinsic polarisation resistance Rpo as a
o’
function of the activity of chloride a
and the partial pressure of chlorine p¯Cl was obtained from the resolution of the kinetic
−
Cl
mechanism and it was compared with experimental data. The correlations of2the independent experimental relationships Rpo
o’
Cl
versus a
and Rpo versus p¯Cl were remarkably good, giving strong evidence that the ClER takes place through the proposed
−
2
mechanism on the RuO2 electrodes. The kinetic constants obtained from the correlations were used for the simulation of the
dependences of the current density and the surface coverages on overpotential. © 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Chlorine electrode reaction; Ti/RuO2 electrode; Polarisation resistance; Kinetic mechanism
mechanisms proposed for the ClER was carried out
1. Introduction
and described in Part II [2]. The dependences of Rpo on
o’
Cl
a
and p¯Cl for each mechanism were derived and
−
The chlorine electrode reaction (ClER) on Ti/RuO2
electrodes has been studied by the use of the polarisa-
tion resistance (Rp) [1,2]. In part I [1], the conditions
where it is possible to make this analysis were estab-
lished and the results obtained in the measurements of
Rp as a function of pH, the activity of chloride (a
2
compared with the experimental results. It was verified
that the Volmer–Krishtalik mechanism (modified
scheme) partially describes the experimental results,
although another elementary kinetic process should be
involved in the reaction. Therefore, this third part deals
with a proposal of a sequence of elementary steps that
configure a mechanism for the ClER on RuO2, which is
in agreement with the obtained experimental evidences.
o’
Cl
)
−
and the partial pressure of chlorine (p¯Cl ) were reported.
2
It was also possible to explain the effect of acidity
(aoH’+) by means of an inhibition model based in the
superficial acid–base equilibrium of the oxide. Starting
from this model the intrinsic polarisation resistance
(Rpo), independent of the solution pH, was obtained.
For the interpretation of the variation of Rpo on the
operative variables, a theoretical analysis of the main
2. Theoretical aspects
2.1. Proposal of a kinetic mechanism for the ClER on
Ti/RuO2 electrodes
* Corresponding author. Tel: +54-342-457-1164; fax: +54-342-
457-1162.
The first aspect to be taken into account in the
proposal of a mechanism for the ClER on Ti/RuO2
electrodes, which was already mentioned in Part I [1], is
E-mail address: achialvo@fiqus.unl.edu.ar (A.C. Chialvo).
1 ISE member.
0013-4686/02/$ - see front matter © 2002 Elsevier Science Ltd. All rights reserved.
PII: S0013-4686(01)00839-8

1146
J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1145–1152
that there are strong evidences in favour of a change in
the oxidation state of the superficial sites of the ruthe-
nium oxide. They would increase their oxidation state
at slightly smaller potentials than those at which the
ClER takes place [3–5]. Burke and O’Neill [3] demon-
strated that this process is indifferent to the presence of
chloride ions. Thus, the oxidation of these sites can be
written as:
The formation of molecular chlorine should take
place by the reaction of a chlorine adsorbed intermedi-
ate and a chloride ion:
–SClZ+1+Cl− = –SZ+Cl2
(3)
It should be noticed that reactions (1), (2) and (3)
constitute the modified scheme of the Volmer–Krishta-
lik mechanism [2,16], which has been analysed in Part
II [2]. In addition to these steps, it cannot be ignored
the well-known capacity of RuO2 for the adsorption/
desorption of chlorine in aqueous solution [10]. Then,
the possibility of formation of adsorbed chlorine from
the molecular chlorine dissolved in the solution near the
reaction plane should be considered:
–SZ = –SZ+1+e−
(1)
where –SZ and –SZ+1 are the non-oxidised and oxi-
dised superficial sites respectively. It should be noticed
that this step is intrinsic to the oxide, and therefore it is
common to any reaction that can take place in the same
potential region, such as the oxygen electrode reaction.
There are evidences that reaction (1) is only one of
successive oxidation steps, which could lead to the
break-up of the ruthenium oxide, producing species of
high oxidation states like RuO4 or oxichlorides of
Ru(VI) and Ru(VII) at high overpotentials [6–9]. It has
been recently demonstrated [9] that these species exist in
solution in a proportion depending on pH and their
presence can be detected by the application of a fast
potentiodynamic sweep towards the cathodic direction
immediately after the evolution of chlorine, as it is
shown in the voltammograms of Fig. 1.
2–SZ+1+Cl2 = 2–SClZ+1
(4)
Eq. (4) is the Tafel step written in the inverse direc-
tion with respect to that commonly used. The direction
in which this step is taking place at a given overpoten-
tial is governed exclusively by the relative values of the
following relationships: the surface coverage of ad-
sorbed Cl with respect to its value at equilibrium and
the fraction of oxidised sites with respect to its corre-
sponding equilibrium value (see Eq. (21) later on).
Therefore, it is possible that molecular chlorine can be
also produced by recombination of two chlorine ad-
sorbed intermediates. Although the Tafel step is ac-
cepted as taking part in the ClER mechanism on
platinum [11–13], certain doubts were stated about its
existence on oxides, based on the analysis of reaction
orders and Tafel slopes. Nevertheless, the existence of a
non-electrochemical step without the participation of
chloride ions has been emphasised [14] and also evi-
dences of the presence of this step during the ClER on
RuO2 electrodes have been given [15].
The formation of the chlorine adsorbed intermediate
from the chloride ions should take place preferably on
the oxidised sites, which are generated together with the
chlorine evolution:
–SZ+1+Cl− = –SClZ+1+e−
(2)
It should be reasonable to call the resulting kinetic
mechanism, constituted by steps (1–4), as the Volmer–
Krishtalik–Tafel mechanism.
2.2. Theoretical analysis of the
Volmer–Krishtalik–Tafel mechanism
The same generalised treatment described in the Part
II [2] was used here to obtain the expression of the
polarisation resistance for the Volmer–Krishtalik–
Tafel mechanism. As it consists of four elementary
steps and two reaction intermediates, two linearly inde-
pendent routes can be outlined. Making a mass balance
of the global reaction in stationary state, the following
expression for the global reaction rate (V) as a function
of the rates of the elementary steps is obtained:
2V=61+62=62+63=2(61−64)=2(63−64)
Fig. 1. Voltamperometric responses of a Ti/RuO2 electrode after
chlorine evolution at p=0.1 V during 30 s. Sweep rate: 0.5 V s−1
Electrolyte solution: NaCl (4−x) M+HCl xM. T=30 °C. pH: 2.18
(a), 0.91 (b), 0.53 (c), 0.09 (d). (1) First cycle, (2) Successive cycles.
Reference electrode: chlorine electrode (ClE), E vs. SCE=1.092 V.
.
=2(62+64)
(5)
being 6i=6+i−6−i, where the subscripts i refers to the
elementary step (i=1, 2, 3, 4).

J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1145–1152
1147
The following implicit relationships between the rates
of the elementary steps are involved in Eq. (5):
It should be noticed that if the Tafel step is negligible,
6e4=0, Eq. (13) becomes equal to the expression of Rpo
corresponding to the Volmer–Krishtalik mechanism
[2]. Assuming a Langmuirian adsorption for the reac-
tion intermediates, the expressions for the equilibrium
surface coverages (qeI, qIeI) as well as those of the
equilibrium reaction rates of the elementary steps (1),
(2) and (3) are the same as those derived by the
modified scheme of the Volmer–Krishtalik mechanism,
Eqs. (30)–(34) of the Part II [2]. The following relation-
ships between the equilibrium constants of the four
elementary steps are verified:
61=63=62+264
(6)
The corresponding relationships between the electro-
chemical affinity of the global reaction (A) and those of
the elementary steps (Ai) are:
A=A1+A2+A3=2(A1+A3)+A4=2A2−A4
(7)
Combining Eqs. (6) and (7) and taking into account
the relationship between Ai and 6i [17], the following
expressions for the electrochemical affinities of the ele-
mentary steps are obtained:
K1K3K
K2
K22
K4
K1K2K3=e−2fE
;
4=1;
=e−2fE
(14)
2
61e
o
o
(6e4+1)
A1=
A2=
A3=
A4=
A
A
A
A
(8)
(9)
1
1
where Ki is the equilibrium constant of the step i, Eo is
the standard potential of the ClER and f=F/RT.
The equilibrium reaction rate of the step (4) is:
ꢀ ꢁ
1+(46e4+6e2)
+
6e1 6e3
1
1
ꢀ ꢁ
1+26e4
+
6e1 6e3
6e4=k+4(qeI)2p¯Cl =k−4(qIeI)2
(15)
2
1
1
ꢀ ꢁ
1+(46e4+6e2)
+
where qI is the fraction of oxidised sites (–SZ+1), qII is
the surface coverage of adsorbed Cl on the oxidised site
(–SClZ+1), k+i, k−i are the constants of the forward
and backward reaction rates respectively of the step i.
Substituting the expression of qeI in Eq. (15) and taking
into account Eq. (14), the equilibrium reaction rate of
step (4) is obtained as a function of the operative
6e1 6e3
2
63e
(6e4+1)
(10)
(11)
1
1
ꢀ ꢁ
1+(46e4+6e2)
+
6e1 6e3
1
1
ꢀ ꢁ
1−6e2
+
6e1 6e3
variables aoC’l−and p¯Cl
:
2
2fE
2
o
2
1
1
ꢀ ꢁ
1+(46e4+6e2)
+
k
+4K1e p¯ Cl
6e4=
(16)
2
6e1 6e3
[K1efE p¯ C1/l2(1+K2efE p¯ C1/l2)+ao’
]
2
o
o
−
Cl
2
2
where 6ei =6+e i=6−e i is the equilibrium rate of step i.
From the first and fourth term of Eq. (5) and taking
into account Eqs. (8) and (11), the expression of the
global reaction rate is derived:
The expression of Rpo for the Volmer–Krishtalik–
Tafel mechanism is derived by substitution of the corre-
sponding equilibrium reaction rates into Eq. (13):
1/2
Cl
(1−h)/2
Cl
k2ao’2(1−h)
1
1
ao’h
1
p¯
a
4k+4K%p¯
p¯ (1−h/2)
1
k−3
ꢂꢀ ꢁ
−
nꢂ
n
ꢀ
ꢁÂ
Cl
1
Cl
2
Á
Ã
2
+
+
K%
2 (1+K%p¯ C1/l2)+1 +
+
1
2
2
Ã
1/2
Cl
h/2
o’
Cl
RT
k1 k2K%p¯
p¯
Cl
2
k
−3p¯Cl
k1
−
−
Cl
1
2
2
Rpo=
Í
Ì
(17)
and
4F2
k
+4K21%p¯ 2Cl
1
1
ao’h
1
ꢂꢀ ꢁ
−
n
Cl
h/2
2
Ã
Ã
1+
+
+
o’
Cl
1/2
Cl
−[K%p¯ C1/l2(1+K%p¯ 1/2)+ao’
]
−
Cl
k1 k2K%p¯
p¯
k−3p¯Cl
Ä
Å
a
1
2
Cl
1
Cl
2
2
2
2
2
hfE
hfE
fE
o
o
o
where k1=k
e
, k2=k
e
, K% =K1e
1
+1
+2
K% =K2efE . It can be observed that this equation in-
o
1
1
1
ꢀ ꢁ
2
Á
Ã
Â
1+6e4
+
+
Ã
Ì
6e1 6e2 6e3
A
volves the kinetic constants of the forward reaction of
steps (1), (2) and (4) and the kinetic constant of the
backward reaction of step (3), as well as the equilibrium
constants of steps (1) and (2). The other constants can
be calculated from those involved in Eq. (17), taking
V=Í
(12)
1
e
1
1
1
1
RT
ꢂ ꢀ ꢁ n
+
46e4
+
+1
Ã
Ã
+
61 6e3 6e2
6e1 6e3
Ä
Å
The following generalised expression for the polarisa-
tion resistance of the Volmer–Krishtalik–Tafel mecha-
nism is obtained from the relationship between Rpo and
V/A in the limit for the overpotential p tending to zero
[2,17] and taking into account Eq. (12):
into account Eq. (14) and that Ki=k+i/k−i
.
3. Results
1
1
1
46e
1
1
ꢀ ꢁ
4
Æ
Ç
+
+
+
+
Ã
Ã
3.1. Analysis of the experimental data Rpo 6s. p¯Cl and
−
RT 6e1 6e2 6e3 62e 61e 6e3
2
Rpo=
Ã
Ã
(13)
Rpo 6s. ao’
Cl
4F2
1
1
1
ꢀ ꢁ
1+6e4
+
+
Ã
Ã
È
É
6e1 6e2 6e3
The experimental data were correlated with Eq. (17)

1148
J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1145–1152
through the mechanisms already discussed [2], even
using different adsorption isotherms for the description
of the reaction intermediates.
On the other hand, the correlation made on the
experimental dependence Rpo versus ao’ at a chlorine
−
partial pressure equal to 1 atm is illustrCalted in Fig. 2IV,
where it can be also observed that the present mecha-
nism can describe appropriately the experimental data.
The resulting parameter values are shown in Table 1(d).
In the same way, the curves Rpo versus p¯Cl were
2
simulated with these parameters at different chloride
concentrations, which are shown in Fig. 2III. A very
good agreement between the simulations and the exper-
imental responses is again obtained, better than that of
the other mechanisms [2].
It should be noticed in Table 1 the similarity between
the different values of the kinetic constants, which were
obtained from two different sets of experimental data.
Thus, it was possible the calculation of average values,
which are shown in Table 1(e). It should be taken into
account that the parameters used in a simulation were
obtained by correlation of a completely independent
data set. Moreover, the expressions used in both, corre-
lation and simulation respectively, have in common
only the mechanism that originated them. In this con-
text, the excellent agreement between simulations and
experimental data constitutes strong evidence in favour
of the proposed mechanism.
Fig. 2. Correlations of the dependences Rpo vs. p¯Cl (I) and Rpo vs.
2
o’
Cl
o’
Cl
a
(IV), and simulations of the dependences Rpo vs. a
(II) and
−
−
Rpo vs. p¯Cl (III), respectively, by means of the Volmer–Krishtalik–
2
Tafel mechanism. Experimental conditions: NaCl–HCl, CCl−: 2 M
(“), 3 M (ꢀ), 4 M (ꢁ); p¯Cl =1 atm (ꢂ). T=30 °C. Dashed line in
2
(II): simulation with the average constants (Table 1e).
using a non-linear least squares method. The value of
the symmetry factor h was fixed at 0.5 and one of the
o’
Cl
operative variables, a − or p¯Cl , was kept constant. The
2
aim of this correlation was to find the set of kinetic
parameters that better reproduces the experimental
results.
3.2. Simulations of dependences log j, qI and qII 6s. p
The correlations of the experimental dependences
Rpo versus p¯Cl at three different concentrations of
chloride ions a2re shown in Fig. 2I, where it can be
verified that a good correlation is achieved in all cases.
A fitting with this accuracy could not be obtained
through any of the previously analysed mechanisms [2].
The kinetic constants obtained in each correlation are
shown in Table 1(a–c), which are very similar for the
three concentrations. As a self-consistency test, with
The dependence of the current density j on overpo-
tential p for the ClER on a Ti/RuO2 electrode free from
any mass transfer process can be simulated with the
kinetic constants calculated as it was indicated in the
previous item. It should be noticed that, as the kinetic
parameters were obtained from experimental data re-
lated to the real area of the electrodes [1], the simulated
responses correspond to a smooth surface. The expres-
sions of the surface coverages qI and qII and that of the
relationship j vs. p corresponding to the Volmer–
Kristhalik–Tafel mechanism must be derived to carry
out such simulations. Although it is likely that the
variation of the surface coverage of the adsorbed chlo-
these kinetic constants the dependences Rpo versus ao’
−
were simulated. The corresponding curves are shownCiln
Fig. 2II, where a notable agreement between the simu-
lations and the experimental response is observed. A
simulation of this accuracy could not be obtained
Table 1
Kinetic and equilibrium constants of the elementary steps of the ClER obtained from the correlation of the experimental data Rpo vs. p¯Cl (a, b
2
o’
Cl
and c) and Rpo vs. a
(d) by the Volmer–Krishtalik–Tafel mechanism (average values: (e))
−
hfE
o
hfE
o×103
K1efE ×106
K2efE
o
o
k
e
k
e
+2
k
−3×1011
k+4
+1
(a)
(b)
(c)
(d)
(e)
2.2603
2.3237
2.6122
2.6644
2.4652
1.623
1.318
1.212
1.011
1.291
6.954
7.210
5.870
10.407
7.610
157.046
161.116
239.604
121.331
169.774
3.208
3.266
4.653
4.001
3.782
240597.7
244982.8
349019.5
212101.5
261675.4
k9i in mol s−1 cm−2
.

J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1145–1152
1149
1
m2
e e−fp qeIIehfp
(1−qe) qII
!ꢂ
n
rine intermediate on overpotential could be significant,
a Langmuirian behaviour is considered as a first
approximation.
The expressions of the reaction rates of the elemen-
tary steps are:
c=
−
2m4(ehfp+m3)
"
−
[(1−qe)m3+qeII(m3+ehfp)]
(ehfp+m3)
[(1−qe)m3+qeII(m3+ehfp)] (1−qe)
ehfp
(1−q)
qI
qIe
ꢂ
ꢂ
n
×
−
(27)
61=6e1
62=6e2
63=6e3
64=6e4
ehfp
−
e−(1−h)fp
(18)
(19)
(20)
(21)
(1−qe)
It can be demonstrated that only the following root
has a physical meaning:
q
qIe
qII
n
I
ehfp
−
e e−(1−h)fp
qII
−b+ꢃb2−4ac
q
(1−q)
ꢂ n
qI=
(28)
II
−
2a
qeII (1−qe)
From the first and third term of Eq. (5) and taking
into account Eqs. (19) and (20), the expression of V is:
q2
q2
ꢂ n
I
II
−
qeI2
q
e 2
II
6e
qIe
63e
(1−qe)
ꢂ
n
2
2V=
ehfp
+
qI
The following relationship between qI and qII can be
obtained from the first two members of Eq. (6):
1
1
62e
63e
(1−qe)
ꢂ ꢀ ꢁ
n
+ 6e3
+
−
e e−(1−h)fp qII−
(1−qe)
ꢂ
n
qeII 1−qe
qII
(ehfp+m3)−
e−(1−h)fp+(ehfp+m3) qI
qIe
qII=
(22)
(29)
(1−qeI)
e
hfp+m3
The relationship j versus p is obtained replacing Eq.
(22) into Eq. (29) and taking into account that the
current density is j=2FV:
qeII
1
1
62e
ꢂ ꢀ ꢁ
n
qeII(63e +61eehfp) 63e
+
−
e e−(1−h)fp
qII
qeII 1−qe
63e
(1−qe)
j/F=
−
[(1−qe)6e3+qIeI(6e3+6e1ehfp)]
qe
ꢂ ꢀ ꢁ
II
?
n
6e3 1+
−6e2e−(1−h)fp [6e1(1−q)e−(1−h)fp+qIe(63e +6e1ehfp)]
qIe
1−qe
qI
qIe
!
+ 6e2ehfp+6e3
−
(30)
(1−qe)
[63e(1−qe)+qIeI(63e +6e1ehfp)]
where mi=6ei /6e1. Then, from the first and last members
where qI is defined by Eqs. (25)–(28).
of Eq. (6):
The expressions of the limiting anodic and cathodic
kinetic current densities, as well as the limiting values of
the surface coverages can be also obtained:
1
1
q
(e−fp+m2)
1
ꢀ ꢁ ꢂ
n
2m4
−
q2I +
+
e
hfpqI
qeI2
qIe
(1−qe)
e 2
II
1
m2
e e−fp
ehfp
qI(+)= LimqI=0; qI(−)= Lim qI=0
(31)
(32)
ꢂ
n
hfp
+
−
e
q −
II
=0
(23)
p“ꢀ
p“ −ꢀ
(1−qe) qII
(1−qe)
qII(+)= LimqII=1; qII(−)= Lim qII=0
p“ꢀ
p“ −ꢀ
The expression for qI is obtained substituting Eq.
(22) into Eq. (23):
2F
qeII
6e
qeII
2F6e3
(1−qe)
ꢀ ꢁ
4
Limj=
6e3+
;
Lim j= −
(33)
p“ꢀ
p“ −ꢀ
aq2I +bqI+c=0
(24)
Taking into account the dependence of the experi-
mental current density ( j*) on pH, Eqs. (9) and (12) in
Part I [1], using the average kinetic constants given in
Table 1(e) and the Eqs. (22), (25)–(28) and (30), the
curves log j* versus p and qi versus p were obtained at
different conditions (T=30 °C). From the analysis of
the variation of Rp on pH, it can be concluded that the
fraction of non-inhibited surface area is independent of
potential in the range of the experimental measure-
ments (DEB0.05 V) [1]. This invariance was considered
to be valid in the range of overpotentials used in the
simulations (Dp=0.35 V). Fig. 3 shows the effect of the
chloride ions concentration at a given pH while Fig. 4
illustrates the effect of the chlorine partial pressure.
where
2
2m
(1−qe)e−(1−h)fp+qIe(m3+ehfp
)
! ꢂ
n"
4
qeI2
a=
1−
(1−qe)m3+qIeI(m3+ehfp
)
(25)
(e−fp+m2)
1
qe
1
m2
!
ꢂ
n
II
b=
+
−
−
e e−fp
qIe
(1−qe) qIe (1−qe) qII
(1−qe)e−(1−h)fp+qIe(m3+ehfp
)
ꢂ
n"
×
ehfp
(1−qe)m3+qIeI(m3+ehfp
)
2m4(ehfp+m3)[(1−q)e−(1−h)fp+qIe(m3+ehfp)]
+
qeI[(1−qe)m3+qeII(m3+ehfp)]2
(26)

1150
J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1145–1152
Fig. 3. Simulations of the dependences log j*, qI and qII vs. p. p¯Cl =1
Fig. 5. Simulations of the dependences log j*, qI and qII vs. p.
CCl =3 M, p¯Cl =1 atm, pH: 1.0 (a), 0.75 (b), 0.5 (c), 0.25 (d).
2
atm, pH 0.75, CCl (M): 0.5 (a), 1 (b), 2 (c), 3 (d), 4 (e).
−
−
2
Furthermore, the effect of the pH value is shown in
Fig. 5. As it is already stated, these dependences
represent the behaviour that should have a RuO2
electrode with a smooth surface operating under
activated control in stationary state. It should also be
very interesting to visualise the magnitude of the
contribution of each elementary step to the total
response. Fig. 6 illustrates the dependences of the rates
of each step and that of the global reaction on p.
mental results reached by means of the modified VK
mechanism, leaded to the proposition of a new possible
sequence of elementary steps. In this context, two facts
are decisive in order to achieve the final outline. One of
them is the almost unquestionable simultaneity of two
processes, the superficial oxidation of the electrode
material and the chlorine evolution. This fact had al-
ready been recognised two or three decades ago [5,18],
when the formation of a reaction intermediate in an
oxidised state was proposed. Later on, the advances
achieved in the understanding of the superficial be-
haviour of oxides introduced several improvements
[14,16,19]. Thus, it was considered reasonable to pro-
pose the oxidation of the superficial sites as the first
step, which should fulfil two boundary conditions. One
is related to its independence on the chloride ion con-
centration, based in experimental evidence [2]. The
other is the independence on pH, since the resulting
4. Discussion
The aim of improving the description of the experi-
Fig. 6. Simulations of the dependences of the global reaction rate
V=j/2F (a) and of the rates of the elementary steps 1 (b), 2 (c), 3(b)
Fig. 4. Simulations of the dependences log j*, qI and qII vs. p.
CCl =3 M, pH 0.75, p¯Cl (atm): 1 (a), 0.75 (b), 0.5 (c), 0.25 (d).
and 4 (d), on p for the Volmer–Krishtalik–Tafel mechanism. CCl =
−
1 M, p¯Cl =1 atm. Inset graph: enlarged scale.
−
2
2

J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1145–1152
1151
mechanism should not involve this last variable. Then,
the active surface is occupied by oxidised and non-oxi-
dised sites and the formation of the adsorbed chlorine
intermediate will take place on those that minimise the
global energy of the system. Moreover, it seemed to be
that this oxidation step makes possible the chlorine
evolution, as it is more likely that the adsorbed interme-
diate is formed on the oxidised sites.
on p, after the derivation of the corresponding analyti-
cal expressions, and the obtained results were illustrated
in Figs. 3–5. It can be observed that the fraction of
oxidised sites tends to zero in both anodic and cathodic
directions (Eq. (31)), going through a maximum slightly
up the equilibrium potential. Besides, the surface cover-
age of the adsorbed chlorine goes respectively to zero
and one in the cathodic and anodic direction (Eq. (32)).
The dependence log j* versus p presents three remark-
able characteristics. One of them is the non-existence of
rigorous Tafelian regions, reaching quickly limiting ki-
netic current densities in both directions (Eq. (33)).
Another aspect is the low current densities, which does
not overcome 10−3 A cm−2, which contrasts with the
usually reported values between 0.1 and 1 A cm−2
[3,7,15,16,20–32]. Nevertheless, it should be bear in
mind that in general these values correspond to appar-
ent current densities (related to the geometric area),
being obtained on electrodes with roughness factors
ranging between 100 and 1000 [33–38]. Therefore, if the
polarisation curves described here are referred to the
geometric area of an electrode with such roughness
factor, they will be increased in two or three orders of
magnitude. Moreover, some curves obtained on smooth
surfaces show similar current densities to those of the
present simulations [39]. The third characteristic is the
presence of a non-diffusional maximum in the cathodic
region, which magnitude decreases when the concentra-
tion of chloride increases and when the chlorine partial
pressure decreases. After that, a limiting kinetic current
is achieved. The presence of such cathodic maximum in
the ClER on ruthenium oxide based electrodes was
reported by Erenburg et al. [18], who referred it to
changes in the oxide surface with time. Likewise, the
existence of the limiting kinetic current was clearly
demonstrated by Evdokimov et al. on RuO2 rotating
disc electrodes [19,20]. It should be taken into account
that the simulated curves represent the responses of a
smooth RuO2 electrode where the ClER operates exclu-
sively under activated control in the whole interval of
the evaluated overpotentials, a fact that is rather
difficult to be fulfilled in this type of materials. Finally,
from the observation of the resulting dependences for
the rates of the elementary steps on p, it can be
concluded that steps (1), (2) and (3) take place in the
proposed direction, but step (4) occurs in the inverse
direction and thus molecular chlorine is generated by
recombination of two adsorbed chlorine atoms.
At this point, the second decisive aspect is the way in
which the chlorine intermediate is formed, being the
most common the electroadsorption of chloride ions
(Volmer step). Nevertheless, it should also be natural to
outline the possibility of the adsorbed chlorine forma-
tion from the dissolved molecular chlorine. There are
evidences that this dissociative adsorption takes place
at cathodic potentials [10]. On the other hand, the
formation of molecular chlorine through the recombi-
nation of two adsorbed chlorine (Tafel step) occurs on
metals like platinum [11–13] and it should also take
place on RuO2. Therefore, it was considered appropri-
ate to include step (4) in order to take into account the
interrelation between the adsorbed atomic chlorine and
the molecular chlorine. It should be emphasised that
the direction indicated for a given step is not necessarily
the correct one, as it is established for the sign of the
corresponding reaction rate at a given overpotential.
Step (3) consists in the combination of adsorbed
chlorine with the chloride ions in solution, producing
molecular chlorine and regenerating the non-oxidised
sites (step 3). In place of this chemical step, the interac-
tion between the adsorbed chlorine and the chloride ion
through the Heyrovsky step, regenerating the oxidised
site with the transfer of one electron could be proposed.
In such case, the site oxidation should be at equilibrium
without participating of the reaction mechanism. This
scheme would correspond to the Volmer–Heyrovsky–
Tafel mechanism, with an acid–base and a redox equi-
librium previous to the kinetic mechanism [14].
However, it has been demonstrated in part I [1] that
only the acid–base equilibrium is external to the reac-
tion mechanism and explains itself the dependence of
the reaction rate on pH.
The expression of the polarisation resistance as a
o’
Cl
function of a
and p¯ was obtained from the resolu-
Cl
2
−
tion of the kinetic mechanism formed by the four
elementary steps and then it was compared with the
experimental data. It has been demonstrated that the
correlation of both independent experimental plots Rpo
o’
Cl
versus a
and Rpo versus p¯Cl was remarkably good.
−
2
Furthermore, these results can be reproduced through a
unique set of kinetic constants of the elementary steps.
This is a very restrictive test that the mechanism could
overcome and therefore is a strong evidence that the
ClER takes place through it on the RuO2 electrodes.
The kinetic constants obtained from this analysis
were used to simulate the dependences log j*, qI and qII
5. Conclusions
On the basis of the use of the polarisation resistance,
a complete kinetic analysis was carried out, giving solid
evidences about the mechanism through which the

1152
J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1145–1152
´
[8] A.A. Uzbekov, V.S. Klement’eva, Elektrokhimiya 21 (1985) 758.
[9] J.L. Ferna´ndez, PhD Thesis, Universidad Nacional del Litoral,
Santa Fe, Argentina, 2001.
chlorine electrode reaction takes place on Ti/RuO2
electrodes. This involve the following sequence of steps:
´
–SZ+H+ = –SHZ+1
–SZ = –SZ+1+e−
–SZ+1+Cl– = –SClZ+1+e−
–SClZ+1+Cl− = –SZ+Cl2(g)
2–SClZ+1 = 2–SZ+1+Cl2(g)
[10] V.P. Chviruk, O.V. Linyucheva, Elektrokhimiya 32 (1996) 1212.
[11] F. Li, A.R. Hillman, S.D. Lubetkin, Electrochim. Acta 37 (1992)
2715.
[12] B.E. Conway, G. Ping, J. Chem. Soc. Faraday Trans. 87 (1991)
2705.
[13] B.E. Conway, D.M. Novak, J. Electroanal. Chem. 99 (1979) 133.
[14] R.G. Erenburg, Elektrokhimiya 20 (1984) 1602.
[15] H.J. Heidrich, L. Mu¨ller, G. Schatte, Elektrokhimiya 26 (1990)
´
´
´
905.
[16] L.I. Krishtalik, Electrochim. Acta 26 (1981) 329.
[17] M.R. Gennero de Chialvo, A.C. Chialvo, J. Electroanal. Chem.
415 (1996) 97.
[18] R.G. Erenburg, L.I. Krishtalik, I.P. Yaroshevskaya, Elek-
trokhimiya 11 (1975) 1072.
The first is an equilibrium step independent of the
ClER, being an intrinsic property of the oxide. This
step explains the dependence of the electrode behaviour
on pH. The following four steps configure the mecha-
nism of the ClER, that can be denominated the
Volmer–Krishtalik–Tafel mechanism. This involves a
first step of oxidation of the superficial sites, which
generate the active sites where the adsorbed chlorine
intermediate is formed from the chloride ions. The later
discharge of chlorine can occur either by the recombi-
nation of the adsorbed intermediates or by the reaction
of an intermediate with a chloride ion.
´
´
[19] S. Trasatti, Electrochim. Acta 32 (1987) 369.
´
´
[20] R.G. Erenburg, L.I. Krishtalik, N.P. Rogozhina, Elektrokhimiya
20 (1984) 1183.
´
[21] S.V. Evdokimov, V.V. Gorodetskii, Elektrokhimiya 22 (1986)
782.
[22] S.V. Evdokimov, M.I. Yanovskaya, Yu.E. Roginskaya, E.N.
´
Lubnin, V.V. Gorodetskii, Elektrokhimiya 23 (1987) 1509.
[23] G. Faita, G. Fiori, J. Appl. Electrochem. 2 (1972) 31.
´
´
[24] R.G. Erenburg, L.I. Krishtalik, V.I. Bystrov, Elektrokhimiya 8
(1972) 1740.
[25] I.E. Veselovskaya, E.K. Spasskaya, V.A. Sokolov, V.I.
´
Tkachenco, L.M. Yakimenko, Elektrokhimiya 10 (1974) 70.
Acknowledgements
[26] D.A. Denton, J.A. Harrison, R.I. Knowles, Electrochim. Acta
24 (1979) 521.
[27] M.M. Pecherskii, V.V. Gorodetskii, S.V. Evdokimov, V.V. Lo-
The financial support of Consejo Nacional de Inves-
tigaciones Cient´ıficas y Te´cnicas (CONICET), Agencia
Nacional de Promocio´n Cient´ıfica y Tecnolo´gica (ANP-
CYT) and Universidad Nacional del Litoral (UNL) is
gratefully acknowledged.
´
sev, Elektrokhimiya 17 (1981) 1087.
[28] N.Y.a. Bune´, M. Yu. Portnova, V.P. Filatov, V.V. Losev, E
´
lek-
trokhimiya 20 (1984) 1291.
[29] S.V. Evdokimov, V.V. Gorodetskii, V.V. Losev, Elektrokhimiya
´
21 (1985) 1427.
[30] J.A. Harrison, S.D. Hermijanto, J. Electroanal. Chem. 225
(1987) 159.
´
[31] S.V. Evdokimov, K.A. Mishenina, V.V. Gorodetskii, Elek-
References
trokhimiya 24 (1988) 1475.
[32] S.V. Evdokimov, V.V. Gorodetskii, M.I. Yanovskaya, Y.E.
´
[1] J.L. Ferna´ndez, M.R. Gennero de Chialvo, A.C. Chialvo, Elec-
trochim. Acta 47 (2002) 1129.
[2] J.L. Ferna´ndez, M.R. Gennero de Chialvo, A.C. Chialvo, Elec-
trochim. Acta 47 (2002) 1137.
[3] L.D. Burke, J.F. O’Neill, J. Electroanal. Chem. 101 (1979) 341.
[4] T. Hepel, F.H. Pollak, W.E. O’Grady, J. Electrochem. Soc. 133
(1986) 69.
Roginskaya, Elektrokhimiya 23 (1987) 1516.
[33] A.T. Kuhn, C.J. Mortimer, J. Electrochem. Soc. 120 (1973) 231.
[34] L.D. Burke, O.J. Murphy, J. Electroanal. Chem. 96 (1979) 19.
[35] R.F. Savinell, R.L. Zeller III, J.A. Adams, J. Electrochem. Soc.
137 (1990) 489.
[36] A. Restovic, G. Poillerat, P. Chartier, J.L. Gautier, Electrochim.
Acta 39 (1994) 1579.
[5] J. Augustynski, L. Balsenc, J. Hinden, J. Electrochem. Soc. 125
(1978) 1093.
[37] J.L. Ferna´ndez, C.A. Marozzi, M.R. Gennero de Chialvo, A.C.
Chialvo, J. Electroanal. Chem. 457 (1998) 109.
[6] R. Ko¨tz, H.J. Lewerenz, S. Stucki, J. Electrochem. Soc. 130
(1983) 825.
[38] P. Nkeng, S. Marlier, J.F. Koenig, P. Chartier, G. Poillerat, J.L.
Gautier, Electrochim. Acta 43 (1998) 893.
[7] F. Hine, M. Yasuda, T. Noda, T. Yoshida, O. Okuda, J.
Electrochem. Soc. 126 (1979) 1439.
[39] E.J. Kelly, D.E. Heatherly, C.E. Vallet, C.W. White, J. Elec-
trochem. Soc. 134 (1987) 1667.