Kinetic study of the chlorine electrode reaction on Ti/RuO2 through the polarisation resistance: Part II: Mechanistic analysis

Article abstract of DOI:10.1016/S0013-4686(01)00838-6

A new methodology for the kinetic treatment of electrode reactions is presented. It is based on a theoretical analysis of the predictive capability of different mechanisms for the dependence of the polarisation resistance on the different operative variables. This procedure is applied in this case to the analysis of the chlorine electrode reaction on Ti/RuO₂, for which the variation of the polarisation resistance on the activity of the chloride ions and on the partial pressure of the chlorine gas is derived. The descriptive capability of the mechanisms under discussion at present for this reaction is discussed and the theoretical dependences are compared with experimental data.

Full text of DOI:10.1016/S0013-4686(01)00838-6

Electrochimica Acta 47 (2002) 1137–1144
www.elsevier.com/locate/electacta
Kinetic study of the chlorine electrode reaction on Ti/RuO2
through the polarisation resistance
Part II: mechanistic analysis
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 new methodology for the kinetic treatment of electrode reactions is presented. It is based on a theoretical analysis of the
predictive capability of different mechanisms for the dependence of the polarisation resistance on the different operative variables.
This procedure is applied in this case to the analysis of the chlorine electrode reaction on Ti/RuO2, for which the variation of the
polarisation resistance on the activity of the chloride ions and on the partial pressure of the chlorine gas is derived. The descriptive
capability of the mechanisms under discussion at present for this reaction is discussed and the theoretical dependences are
compared with experimental data. © 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Chlorine electrode reaction; Ti/RuO2 electrode; Polarisation resistance; Kinetic mechanisms
The present analysis is focused in the ClER on
1. Introduction
Ti/RuO2, as the experimental dependences of Rp on the
o’
Cl
activity of the chloride ions (a −) and the partial
The polarisation resistance (Rp) has been occasion-
ally used for the kinetic analysis of electrode reactions
that can be studied around the equilibrium potential,
pressure of chlorine (p¯Cl ) were determined [8]. The
2
theoretical relationships Rp=Rp(ao’ −,p1k,...,pnk) and
Rp=Rp(p¯Cl ,pk1,...,pnk) are derived forCldifferent mecha-
such as those of hydrogen (HER) and chlorine (ClER)
on several electrode materials like noble metals [1–3]
and oxides [4–6]. The expression relating the polarisa-
tion resistance with the elementary kinetic parameters
involved in the Volmer–Heyrovsky–Tafel (VHT)
mechanism has been recently derived for the HER [7].
However, the potentiality of this variable for a com-
plete kinetic study of an electrodic reaction has not
been explored yet. Therefore, a complete aprioristic
analysis of the descriptive capability of a given mecha-
nism, guided to obtain the functionality of the polarisa-
tion resistance with the operative variables, should be
of interest.
2
nisms, being pki the kinetic parameters of the elemen-
tary steps corresponding to the k mechanism. On this
basis, the kinetic parameters pki are evaluated by regres-
sion of one type of experimental data, for example Rp
o’
Cl
versus
a
.
Then, substituting them in Rp=
−
Rp(p¯Cl ,pk1,...,pnk), the Rp versus p¯Cl dependence is pre-
dicted 2and compared with the experimental results. This
procedure, which can be also applied viceversa, gives
strong evidence in order to validate a given kinetic
mechanism, much more accurate than the simple corre-
2
lation of experimental data.
The ClER depends directly on the variables a
o’
Cl
and
−
p¯Cl , as it is already stated. However, it is known that
2
the reaction rate is also influenced by pH [8,9]. On this
sense, it has been demonstrated that the effect of this
variable can be satisfactorily explained on the basis of a
surface model that takes into account the inhibition of
active sites by protons [8]. Therefore, the mechanisms
* Corresponding author. Tel.: +54-342-4571-164; fax: +54-342-
4571-162.
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)00838-6

1138
J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1137–1144
under study are Volmer–Heyrovsky–Tafel and
Volmer–Krishtalik, which do not involve protonated
intermediates.
being 6i=6+i−6−i, where the subscript i refers to an
elementary step.
2.2.2. Dependence of the polarisation resistance on the
equilibrium parameters
The expression of Rpo as a function of the equi-
librium reaction rates has been previously obtained for
the HER [7] and is identical for the ClER:
2. Theoretical analysis
2.1. Fundamentals
RT
46eT+6eH+6eV
ꢀ
ꢁ
Rpo=
(3)
The expression of the intrinsic polarisation resistance
(Rpo), independent of pH, as a function of the equi-
librium reaction rates can be obtained from the deriva-
tive of the theoretical expression of the dependence of
the current density on overpotential. This is derived
from the mass balances of the global reaction in sta-
tionary state [10], assuming a given behaviour for the
adsorption of the intermediate species, as it was carried
out for the HER under the mechanism of VHT [7].
Nevertheless, this expression can also be deduced from
a general treatment based on the formalism of the
Thermodynamics of the irreversible processes [11]. Basi-
cally, the relationship between the rate (V) and the
electrochemical affinity (A) of the global reaction is
obtained through the relationships between the rates
and affinities of the elementary steps, respectively [7,11].
In this context, the following equality is considered [7]:
4F2 6eV6He +6Ve 6Te +6He 6eT
where 6ei is the equilibrium reaction rate of the step i.
2.2.3. Dependence of the polarisation resistance on the
operati6e 6ariables
From the dependences of the reaction rates of the
elementary steps on the electrode potential [12] and
considering a Langmuir type adsorption for the reac-
tion intermediate, the expressions of the corresponding
equilibrium reaction rates can be written as:
e
6eV=k+V(1−qe)ao’ −ehfEe =k−Vqee−(1−h)fE
(4)
(5)
(6)
Cl
6eH=k+Hqeao’ −ehfEe =k−H(1−qe)p¯Cl e−(1−h)fE
e
Cl
2
6eT=k+T(qe)2=k−T(1−qe)2p¯Cl
2
where k+i and k−i are, respectively, the constants of
the forward and backward reaction rates of the step i,
h is the symmetry factor (supposed equal for all the
elementary steps), f=F/RT, Ee is the equilibrium po-
tential, qe is the equilibrium surface coverage of the
adsorbed Cl intermediate.
V
A
1
Lim
=
(1)
p“0
(nF)2Rpo
where p is the overpotential, n is the number of trans-
ferred electrons and F is the Faraday constant. There-
fore, applying Eq. (1) to a given kinetic mechanism the
expression of Rpo as a function of the equilibrium
reaction rates is obtained. Finally, from the correspond-
ing expressions of the reaction rates of the elementary
steps [12], the dependences of Rpo on the operative
variables can also be derived.
The dependence of qe on the chlorine partial pressure
can be obtained from Eq. (6):
1/2
p¯
Cl
qe=
(7)
2
p¯ 1C/l2 +K1T/2
2
The linking relationships between the equilibrium
constants of the elementary steps can be also derived
considering a Nernstian behaviour of the equilibrium
potential:
2.2. Volmer–Heyro6sky–Tafel mechanism
2.2.1. Reaction rate on steady state
KVK
KH
KH
T=1, KVKT1/2=e−fE°
,
=e−fE°
(8)
K1T/2
The application of the mechanism of Volmer–Hey-
rovsky–Tafel (VHT) to the ClER involves the follow-
ing elementary reaction steps:
where Ki=k+i/k−i is the equilibrium constant of the
step i and E° is the standard potential of the ClER.
Rearranging Eqs. (4)–(6), substituting Eq. (7) in
them and taking into account the relationships (8), the
expressions of the equilibrium reaction rates are ob-
tained as a function of the variables a
–SZ+Cl− = –SClZ+e−
(V)
(H)
(T)
–SClZ+Cl− = –SZ+Cl2(g)+e−
–SClZ+ −SClZ = 2–SZ+Cl2(g)
o’
Cl
and p¯Cl :
−
2
aoC%(l1−h)p¯ h/2
−
Cl
2
6eV=k+VKTehfE°
(9)
The following relationships between the global reac-
tion rate and the corresponding rates of the elementary
steps was obtained by means of a mass balance of the
reaction in stationary state [10]:
(p¯ 1C/l2 +K1T/2
(1+h)
)
2
o’(1−h)
−
Cl
2
a
p¯ Cl
2
hfE°
6eH=k
e
+H
(10)
(p¯ 1C/l2 +K1T/2
)
2V=6V+6H=2(6H+6T)=2(6V−6T)
(2)
2

J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1137–1144
1139
p¯Cl
6eT=k+T
(11)
the global reaction rate and the corresponding reaction
rates of the elementary steps are [14]:
2
(p¯ 1C/l2 +K1T/2 2
)
2
The corresponding expression of Rpo, obtained re-
placing Eqs. (9)–(11) into Eq. (3), is:
2V=61+62=61+63=62+63=261=262=263
(13)
(1−h/2)
Cl
kVao’(1−h)
k
+Tp¯
k
ꢀ ꢁ
Æ
Ã
Ç
Ã
2
4
+(p¯ 1C/l2 +K1T/2
)
2
Hp¯ 1C/l2 +KT
(p¯ 1C/l2 +K1T/2
)
2
2
RT
kV
−
Cl
(1−h/2)
Rpo=
Ã
Ã
(12)
4F2
k
+Tp¯
k
kH
kV
kVKTao’(1−h)p¯ h/2
Cl
Cl
2
ꢀ ꢁ
−
Cl
2
Ã
Ã
4
Hp¯ 1C/l2 +KT
+
p¯ Cl (p¯ 1C/l2 +KT1/2
1/2
)
È
É
kVao’(1−h) kV
2
2
2
−
Cl
hfE°
where kV=k
e
and kH=k+HehfE°. Eq. (12) con-
+V
tains the constants of the forward reaction rates of the
elementary steps and the equilibrium constant of the
Tafel step. The other equilibrium constants are related
to this through the relationships (8).
where the subscript is referred to the step oi or mi
(i=1, 2, 3).
2.3.2. Dependence of the polarisation resistance on the
equilibrium rates
2.3. Volmer–Krishtalik mechanism
The relationship between the electrochemical affinity
of the global reaction rate and those of the elementary
steps is:
The mechanism of Volmer–Krishtalik (VK) is
known in two kinetically equivalent schemes [13], which
will be called original (o) and modified (m) respectively.
A=A1+A2+A3
(14)
The relationship between A and V is obtained from
Eqs. (13) and (14) and taking into account the relation-
ship between the affinity and the reaction rate of an
elementary step when the system is near the equilibrium
state [11]:
–SClZ = −SClZ+1+e−
–SZ+Cl− = –SClZ+e−
–SClZ+1+Cl− = –SZ+Cl2(g)
–SZ = −SZ+1+e−
–SZ+1+Cl− = –SClZ+1+e−
–SClZ+1+Cl− = –SZ+Cl2(g)
(o1)
(o2)
(o3)
(m1)
(m2)
(m3)
1
1
1
ꢀ ꢁ
A=RT
+
+
V
(15)
6e1 6e2 6e3
Finally, the expression of the polarisation resistance
as a function of the equilibrium reaction rates for both
schemes of the VK mechanism is achieved from Eq. (1)
to Eq. (15):
Ignoring the nature of the involved species, it is
verified that step (o1) is equivalent to (m1), steps (o2) to
(m2) and steps (o3) to (m3). Therefore, both mecha-
nisms lead to the same expressions for the surface
coverage of the intermediate species and for j versus p,
which were previously obtained [14]. The corresponding
equations for the polarisation resistance as a function
of the equilibrium reaction rates are also the same.
Nevertheless, it should be taken into account that the
surface coverages are referred to different species.
Moreover, the equilibrium constants and thus Rpo have
different dependences on the experimental variables. It
can be observed that both outlines consider a step of
oxidation of the superficial sites, (o1) and (m1) respec-
tively, and the difference among them resides in their
nature. While in the modified scheme the loss of elec-
trons takes place in an empty site generating an active
site, in the original the site with the intermediate al-
ready adsorbed is oxidised.
RT 1
1
1
ꢀ ꢁ
Rpo=
+
+
(16)
4F2 6e1 6e2 6e3
Eq. (16) can also be obtained evaluating the deriva-
tive at p=0 of the expression of the current density on
overpotential [14].
2.3.3. Dependence of the polarisation resistance on the
operati6e 6ariables. Original scheme
The expressions of the equilibrium reaction rates of
the elementary steps are:
e
6e1=k+1qeIehfEe =k−1qIeIe−(1−h)fE
(17)
(18)
(19)
e
6e2=k+2(1−qe)ao’ −ehfEe =k−2qeIe−(1−h)fE
Cl
6e3=k+3qIeIaoC’l− =k−3(1−qe)p¯Cl
2
where qI is the surface coverage of adsorbed Cl on the
non-oxidised sites (–SClZ), qII is the surface coverage of
adsorbed Cl on the oxidised sites (–SClZ+1), q=qI+
qII, (1−q) is the fraction of non-oxidised free sites
(–SZ) and the superscript e is referred to equilibrium
values.
2.3.1. Reaction rate on steady-state
For each one of the schemes under analysis, the
reaction mechanism has three elementary steps and two
intermediate species, so that only one linearly indepen-
dent route can be considered. The relationship between

1140
J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1137–1144
o’
The corresponding equations of the surface coverage
and the polarisation resistance as a function of a
Cl
−
of the intermediate species can be derived from Eq. (17)
to Eq. (19):
and p¯Cl were obtained by the procedure described
previous2ly:
1/2 o’
Cl Cl
2
K2e fE°p¯
a
1/2
2
K1e fE°p¯
−
qeI =
(20)
(21)
Cl
qeI =
(30)
(31)
K2e fE°p¯ 1/2(ao’ − +K e fE°p¯ 1/2)+ao’
K1e fE°p¯ 1/2(1+K e fE°p¯ 1/2)+ao’
−
Cl
Cl
1
Cl
2
Cl
2 K1K2e2fE°p¯Cl
2
−
Cl
2
Cl
2
Cl
qeII=
2
K1K2e2fE°p¯Cl
K1e fE°p¯ 1/2(1+K2e fE°p¯ 1/2)+ao’
qeII=
−
Cl
2
Cl
Cl
2
2
K2e fE°p¯ 1/2(ao’ − +K e fE°p¯ 1/2)+ao’
−
Cl
Cl
1
Cl
2
Cl
2
hfE° o’(1−h) h/2
Cl
k
+1e
a
p¯ Cl
2
−
6e1=
(32)
as well as the following linking relationship between the
equilibrium constants of the elementary steps:
K1e fE°p¯ 1/2(1+K2e fE°p¯ 1/2)+ao’
−
Cl
Cl
2
Cl
2
1+h
2
K1K2K3=e−2fE°
(22)
(1+h)fE° o’(1−h)
−
Cl
k
+2K1e
a
p¯ Cl
2
6e2=
(33)
(34)
Rearranging Eqs. (17)–(19), substituting Eqs. (20) and
(21) in them and taking into account Eq. (22), the
expressions of the equilibrium reaction rates as a func-
tion of the operative variables are derived:
1+h
K1e fE°p¯ 1/2(1+K2e fE°p¯ 1/2)+ao’
−
−
Cl
Cl
2
Cl
2
o’
k
a −p¯Cl
−3 Cl
2
6e3=
K1e fE°p¯ 1/2(1+K2e fE°p¯ 1/2)+ao’
Cl
Cl
2
Cl
2
(1+h)fE° o’(1−h)
ao’h
1
2
k
+1K2e
a
p¯ Cl
RT
1
1
ꢂꢀ ꢁ
−
n
−
Cl
Cl
h/2
2
Rpo=
+
+
6e1=
6e2=
6e3=
(23)
(24)
(25)
4F2 k1 k2K%p¯
p¯
Cl
k−3p¯Cl
1/2
Cl
1
K2e fE°p¯ 1/2(ao’ − +K e fE°p¯ 1/2)+ao’
hfE° o’(2−h) h/2
2
2
2
−
−
−
Cl
1
Cl
2
Cl
Cl
2
1/2
Cl
p¯
a
ꢂ
n
k
+2e
a
p¯ Cl
K%
2 (1+K%p¯ 1C/l2)+1
(35)
−
Cl
1
2
2
2
o’
Cl
−
K2e fE°p¯ 1/2(ao’ − +K e fE°p¯ 1/2)+ao’
Cl
1
Cl
2
Cl
Cl
2
where k1=k+1ehfE°, k2=k+2ehfE°, K% =K1e fE° and
o’
−3 Cl
1
k
a
−p¯Cl
2
K% =K2e fE°. It should be noticed that Eq. (35) estab-
K2e fE°p¯ 1/2(ao’ − +K e fE°p¯ 1/2)+ao’
2
Cl
1
Cl
2
Cl
Cl
lishes different dependences of Rpo on aoC’l− and p¯Cl with
respect to the original scheme. It should be menti2oned
that the linking relationship between the equilibrium
constants of the elementary steps is the same as the
original scheme, given by Eq. (22).
2
Finally, replacing Eqs. (23)–(25) into Eq. (16) and
grouping constants, the corresponding expression of the
polarisation resistance for the original scheme of the
VK mechanism is obtained:
o’
Cl
RT
a
1
1
ꢂ
−
n
(26)
Rpo=
+
+
(1−h)/2
Cl
4F2 k1K%p¯
k2aoC’l−p¯ hC/l2
k
−3p¯Cl
2
2
2
2
3. Analysis of the descriptive capability of the studied
mechanisms
p¯Cl
ꢀ
ꢁ
K%K%
2 +K%p¯ 1C/l2 +1
1
2
2
2
o’
Cl
a
−
where k1=k+1ehfE°, k2=k+2ehfE°, K% =K1e fE° and
Holding one of the two variables (a −or p¯Cl ) con-
o’
Cl
1
2
K% =K2e fE°
.
stant, particular expressions of Eqs. (12), (26) and (35)
are obtained. The descriptive capability of each one of
these equations was evaluated for different values of the
kinetic parameters in the range of Rp values less than
10 kV cm−2, which corresponds to the domain of
experimental determinations. Some of these simulations
are shown in Fig. 1 for the three mechanisms under
study. It should be noticed that for a given set of
constants, each mechanism establishes unique depen-
2
It should be noticed that although Eq. (26) involves
only some of the kinetic and equilibrium constants of
the elementary steps, the other can be calculated by Eq.
(22).
2.3.4. Dependence of the polarisation resistance on the
operati6e 6ariables. Modified scheme
The equilibrium reaction rates of the elementary
steps are:
dences Rpo versus aoC’l−and Rpo versus p¯Cl
.
It has been determined that all mechani2sms have the
capability to describe increasing or decreasing depen-
6e1=k+1(1−qe)ehfEe =k−1qeIe−(1−h)fE
6e2=k+2qeIao’ −ehfEe =k−2qIeIe−(1−h)fE
(27)
(28)
(29)
e
e
dences of Rpo on p¯Cl in the range of pressures analysed,
Cl
2
but it is not so for the dependences Rpo versus ao’ −. In
this case, the mechanism VHT can only preCdlict a
decreasing behaviour of Rpo on ao’ −, independently of
the values assigned to the parametCelrs. Meanwhile, both
schemes of the VK mechanism can predict also decreas-
ing responses, which can present a minimum depending
on the values of the kinetic parameters.
6e3=k+3qIeIaoC’l− =k−3(1−qe)p¯Cl
2
In this case qI is the fraction of oxidised sites (–SZ+1
while qII and (1−q) have the same meaning as in the
original scheme.
The following expressions of the surface coverages of
the intermediate species, the equilibrium reaction rates
)

J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1137–1144
1141
Fig. 1. Simulations of the dependences Rpo vs. p¯Cl (C =2 M) and Rpo vs. ao’ (p¯Cl =1 atm) for the ClER through the Volmer–Heyrovsky–
−
Cl
−
Cl
2
2
Tafel, original Volmer–Krishtalik and modified Volmer–Krishtalik mechanisms. T=30 °C. Kinetics parameters: VHT: kV=10−15, kH=10−5
+T=10−6, KT=103 (a), 4×103 (b), 7×103 (c), 104 (d); original VK: k1=103, k2=103, k−3=10−10, K% =1012, K% =5×10−14 (a), 10−13
,
k
1
2
(b), 2×10−13 (c), 5×10−13 (d); modified VK: k1=1, k2=103, k−3=2×10−10, K% =2×10−13, K% =1013 (a), 5×1012 (b), 1012 (c), 1011 (d).
1
2
ki in mol s−1 cm−2
.
4. Analysis of experimental results
can be considered acceptable. The corresponding ki-
netic constants obtained from these correlations are
shown in Table 1(a, b and c). Nevertheless, when
In the first part [8], the experimental measurements
of the polarisation resistance were described. It was also
analysed the influence of pH, so that the calculated
starting from these results the dependence Rpo versus
o’
Cl
a
at p¯Cl =1 atm is predicted (Fig. 3II), the resulting
−
2
values of Rpo are free from the influence of this vari-
values of Rpo are almost independent of ao’ −, although
they are in the order of the experimental vCallues. Corre-
lations were also carried out with other values of h, but
o’
Cl
able. The dependences of Rpo on p¯Cl and a
are
−
shown in Fig. 2. It can be observed an2 increase in the
polarisation resistance as the activity of chloride ions
increases, seeming that the curve passes through a
o’
Cl
minimum in the range 0.1Ba − B 1.
4.1. Analysis by the Volmer–Heyro6sky–Tafel
mechanism
It has been indicated in a previous item that Eq. (12)
cannot predict an increasing dependence of Rpo on
o’
Cl
a
−, as it is observed experimentally, independently of
the values assigned to the constants. Consequently, this
mechanism should be discarded for the description of
the ClER on Ti/RuO2 electrodes.
4.2. Analysis by the Volmer–Krishtalik mechanism
(original scheme)
Following the proposed methodology, the parame-
ters involved in Eq. (26) were evaluated by fitting the
o’
Cl
experimental dependences Rpo versus p¯Cl at a
con-
−
2
stant, taking the symmetry factor h=0.5. It can be
observed in Fig. 3I that the correlations corresponding
to three different chloride concentrations (2, 3 and 4 M)
o’
Cl
Fig. 2. Experimental dependences Rpo vs. p¯Cl and Rpo vs. a
for
−
2
the ClER in NaCl–HCl solutions saturated with Cl2(g). CCl− =2 M
(“), 3 M (ꢀ), 4 M (ꢁ); p¯Cl =1 atm (ꢂ). T=30 °C.
2

1142
J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1137–1144
Fig. 3. Correlations of the experimental dependences Rpo vs. p¯Cl (I)
Fig. 4. Correlations of the experimental dependences Rpo vs. p¯Cl (I)
2
2
o’
Cl
−
and Rpo vs. ao’ (IV) for the ClER by the modified VK mechanism,
and Rpo vs. a
(IV) for the ClER by the original VK mechanism,
−
Cl
and their corresponding simulations of the dependences Rpo vs.
and their corresponding simulations of the dependences Rpo vs.
o’
o’
a
−(II) and Rpo vs. p¯Cl (III) using the kinetic parameters obtained
a
−(II) and Rpo vs. p¯Cl (III) using the kinetic parameters obtained
Cl
from each fitting (Table 21). Correlations: CCl− = 4 M (a), 3 M (b), 2
Cl
from each fitting (Table 22). Correlations: CCl− =4 M (a), 3 M (b), 2
M (c); p¯Cl =1 atm (d). Simulations: p¯Cl =1 atm (a, b, c); CCl− =4
M (c); p¯Cl =1 atm (d). Simulations: p¯Cl =1 atm (a, b, c); CCl− =4
2
M (d1), 32M (d2), 2 M (d3).
2
M (d1), 32M (d2), 2 M (d3).
the descriptive capability of Eq. (26) were not
improved.
4.3. Analysis by the Volmer–Krishtalik mechanism
(modified scheme)
On the other hand, if the order of the analysis is
inverted, that is the experimental Rpo versus ao’ −plot is
correlated, the results are good (Fig. 3IV) Cal nd the
corresponding values of the obtained constants are
indicated in Table 1(d). However, the simulations of the
The correlation of the experimental data through Eq.
(35), following the proposed methodology, are shown
in Fig. 4I, IV. The corresponding values of the kinetic
parameters are illustrated in Table 2. The response of
this mechanism in relation to the correlation of the
dependence Rpo versus p¯Cl (Fig. 3III) with these
2
parameters are unacceptable. The range of variation of
the simulated values of Rpo (ꢀ0.038 kV cm2 atm−1) is
almost one order of magnitude less than that of the
corresponding experimental values. Moreover, for the
highest concentrations of Cl−, the simulations cannot
even describe the experimental decreasing variations.
It should be noticed that the equilibrium surface
coverages qeI and qIeI evaluated from Eqs. (20) and (21)
have a maximum variation of DqeI B0.1 and DqIeIB0.1
dependence of Rpo on p¯Cl is similar to that of the
2
original scheme. The description of the experimental
Rpo versus aoC’l−plot with the parameters obtained in the
previous correlation is again not acceptable. Neverthe-
less, the correlation of the experimental data Rpo versus
o’
Cl
a
−is good and the resulting parameters lead to a
description of the dependence Rpo versus p¯Cl much
more accurate than that of the original scheme,2 espe-
cially at the higher values of p¯Cl . This should be due to
2
in the whole range of p¯Cl and ao’ values.
the parameters were calculated at 1 atm. The equi-
−
Cl
2
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 original VK mechanism
−
hfE
hfE
K1e fE
K2e fE
o
o
o
o
k e
+1
k e
+2
k−3
(a)
(b)
(c)
(d)
7.25×1025
2.11×1025
1.41×1029
6.78×10−10
5.51×106
1.20×107
8.65×109
2.39×10−4
1.26×10−10
1.38×10−10
2.49×10−10
1.61×10−5
362.70
2.29
92.66
10−18
1.1×10−17
2×10−18
0.07245
23417.12
k9i in mol s−1 cm−2
.

J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1137–1144
o’
1143
librium surface coverages qeI and qIeI evaluated from
Eqs. (30) and (31) have a maximum variation of DqeI B
−
Cl
a − and p¯Cl were derived for the Volmer–Heyrovsky–
Cl
2
Tafel mechanism and for both schemes, original and
modified respectively, of the Volmer–Krishtalik mecha-
nism. It has been considered a Langmuirian behaviour
for the adsorbed intermediates. Taken into account that
the variation of the equilibrium surface coverages in the
experimental conditions was not significant, the reac-
tion kinetics should be almost indifferent to the be-
haviour of the adsorbed intermediates. Therefore, the
use of another adsorption isotherm should not intro-
duce changes in the results obtained.
10−7 and DqeIIB0.1 in the whole range of p¯Cl and ao’
2
values.
5. Discussion
A kinetic study carried out on porous electrode mate-
rials such as oxides obtained by thermal decomposition
is intrinsically complex. Therefore, it should be done
under special conditions, such as near the equilibrium
potential of the reaction under evaluation. The polari-
sation resistance is the appropriate kinetic variable for
this case, as it can be measured directly and free of any
aprioristic restriction. However, the kinetic expressions
habitually used for describing the j versus p plot were
derived under a series of approaches, such as rate-deter-
mining step criteria or quasi-equilibrium assumption,
which make these equations inapplicable near the equi-
librium conditions. Nevertheless, kinetic expressions
can be obtained in the framework of an analysis with-
out the classical approximations [7,10]. Such expres-
sions were derived and applied to the most important
mechanisms outlined for the ClER on RuO2 electrodes.
The theoretical dependences of the polarisation resis-
tance on the variables that influence the electrodic
reaction were obtained for each mechanism under
study. On this basis, an aprioristic analysis of the
predictive capability of a given mechanism can be car-
ried out in order to determine if it is intrinsically
accurate for the correlation of experimental data. From
the independent fitting of the variation of Rp on one of
these variables, a set of kinetic parameters (pki ) is
obtained. Then, it is verified if this set can reproduce
appropriately the experimental variations of Rp on the
other variables. This procedure introduces a strong
restriction that makes this methodology highly reliable,
as it is unlikely that an inappropriate mechanism can
overcome this test successfully.
It has been proved that the VHT mechanism is
unable to reproduce the observed behaviour, particu-
larly the experimental Rpo versus a
o’
Cl
plot, which
−
shows a minimum. This solid argument confirms that
this mechanism is not appropriate for the ClER on
RuO2 electrodes. The main failure should be that the
oxidation of the superficial sites of ruthenium dioxide
at the potentials of the ClER [15,16] is not taken into
account. Precisely, this step is the main difference be-
tween the mechanisms VHT and VK, being the nature
of these oxidised sites the difference among the two
schemes of this last mechanism. Both of them are
qualitatively able to predict the observed behaviour of
Rpo as a function of aoC’l− and p¯Cl . A good agreement is
2
achieved between the experimental and the theoretical
response for the dependence Rpo versus aoC’l−by means
of the original scheme, from which a set of kinetic
constants were calculated through least squares (Table
1d). Nevertheless, the self-consistency is not achieved
on the description of the relationship Rpo versus p¯Cl
,
2
since the simulation using the kinetic constants ob-
tained from the correlation of the Rpo versus. ao’ −data
is not in agreement with the experimental resuCltls. On
the other hand, the set of parameters (Table 2d) ob-
tained with the modified scheme reproduces fairly well
both dependences. The main failure of this scheme is
the description of the dependence Rpo versus p¯Cl , espe-
2
cially for the lower values of p¯Cl . This result suggests
that there are probably certain as2pects in the modelling
of the effect of the chlorine partial pressure that were
not appropriately taken into account. On this sense, the
improvement of the predictive capability of the
modified VK mechanism was intended through the
adoption of a Frumkian behaviour for the adsorbed
intermediates. However, the correlations were only
On this context, taking into account that experimen-
tal data of the intrinsic polarisation resistance as a
function of the chloride ions concentration and the
chlorine partial pressure were obtained and described in
the part I [8], expressions of the dependences of Rpo on
Table 2
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 modified VK mechanism
−
hfE
hfE
o
K1e fE
K2e fE
o
o
o
k
e
k
e
k−3
+1
+2
(a)
(b)
(c)
(d)
1.44×10−7
4.74×10−8
1.29×10−8
4.23×10−9
6.6×10−4
6.4×10−4
8.4×10−4
6.9×10−4
1.15×10−7
1.07×10−7
1.35×10−7
3.67×10−7
4.738×10−7
4.641×10−7
5.624×10−7
5.0×10−7
10176.1
9845.1
9272.7
46371.3

1144
J.L. Ferna´ndez et al. / Electrochimica Acta 47 (2002) 1137–1144
scarcely improved, needing an extremely high value of
the interaction coefficient (ꢀ6000), which is meaning-
less. Besides, the self-consistency in the simultaneous
description of both dependences was again not
achieved. These facts indicate that the change of the
adsorption isotherm only adds one fitting parameter,
which improves the description of both dependences,
but do not modify the descriptive capability of the
mechanism. Therefore, it is likely that a more complete
mechanism, involving the modified scheme of the
Volmer–Krishtalik mechanism should describe accu-
rately the chlorine electrode reaction.
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.
References
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6. Conclusions
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variables. Its application to different mechanisms pro-
posed for the ClER on Ti/RuO2 electrodes was de-
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concluded that the Volmer–Krishtalik mechanism, par-
ticularly the modified scheme, could partially describe
the experimental dependences of the polarisation resis-
tance on the operative variables. However, certain defi-
ciencies were observed indicating that another
elementary process could take place simultaneously.
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Acknowledgements
The financial support of Consejo Nacional de Inves-