III. THE EXPERIMENTAL SITUATION REGARDING THE TEMPERATURE DEPENDENCE OF TAFEL SLOPES
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Electrochemical Reaction Rates and the Tafel Equation
117
to: (1) the supposed linear proportionality of b to T (i.e., a is a
constant, temperature-independent parameter); and/or (2) the form
of b with respect to T. These experimental facts are central to the
topic of the present paper.
In this section the bases of the above remarks are documented
from previous literature and from new results recently reported.
2. Documentation and Examples of the Experimentally Observed
Dependence of b on T and the Behavior of a with T
(i) The H2 Evolution Reaction at Hg
Historically, the h.e.r. has often been taken as a prototype
process for discussions of the principles of electrode
kinetics;I317'18'2O'21U however, the behavior of this process at
various metals is far from that represented by Eqs. (1) or (4) with
(5). For the h.e.r. at Hg, four sets of relevant data that are to be
considered reliable from the point of view of system purity and
experimental technique,39'40 and cover a wide range of temperature,
are available for discussion: the work of Post and Hiskey41 in
aqueous HC1; the work of Conway et al2 in methanolic HC1 from
173 to 353 K; the work of Bockris et al43 in methanolic HC1 above
and below the mp of Hg; and the work of Conway and Salomon42
in methanolic HC1 and MeOD/DCl, also down to low temperatures.
Following the first indication in the work of Stout48 that b can
be independent of temperature, Bockris and Parsons,11 and Bockris
et al43 showed that a similar effect arose in the h.e.r. at Hg in
methanolic HC1 between 276 and 303 K; below these temperatures,
b apparently varied in the conventional way with T. However, the
derived a values showed a considerable spread. Variations of the
temperature effect in b were discussed in terms of the possible
influence of impurities but an overall assessment of all other, more
recent, observations of the dependence of b on T for various types
of reactions leads to the conclusion that the "unconventional"
dependence is not due to some incidental effect of impurities. In
fact, in another paper, Bockris and Parsons11 suggested that the
temperature dependence of fi for the h.e.r. at Hg arose because of
expansion of the inner region of the double layer with temperature.
They also noted that, formally, for b to be independent of T, the
entropy of activation should be a function of electrode potential,
118
Brian E. Conway
0 13
H 2 EVOLUTION AT Hg
H2O/HCI(POST*«HISKEY)
(a)
0 10
MeOH/HC
(CONWAY et ol)
b(CLASSICAL)'2 3RT/O5F
Br2 EVOLUTION AT C/CH5CN
L
0 07
005
180
200
220
240
260
280
300
320
340
360
T/K
b and a as f(T) at Hg
0 62
0-60
Solid Hg
0 54
052
(b)
011
010
0 09
0 08
0 07
0 06
203
. Solid Hg
223
243
263
T/K
283
303
Electrochemical Reaction Rates and the Tafel Equation
119
but the matter was not pursued further until the treatment of
Conway et al2 referred to in more detail elsewhere in this article.
In Fig. 3a, the Tafel slopes from these authors' works are
plotted comparatively as a function of temperature T. It is evident
that the Eq. (5) for b a s / ( T ) , commonly assumed, is not followed,
and the T dependence of b is fitted2 by an equation of the form
RT
0+*
rather than that of Eq. (5) with a s p. (Note, that for Hg, almost
all authors, with the exception of Horiuti,44 agree that the ratecontrolling step in H2 evolution at Hg from acidic solutions is the
discharge of the hydronium ion, H 3 O + , or the related species H9C>4,
so that a = fi; cf. Section II.) The data of Bockris et al43 are
somewhat different (Fig. 3b) and (3 appears to be dependent on T
over part of the T range investigated.
Thus from Refs. 2,41, and 42, b has a temperature-independent
component, X, which for the h.e.r. at Hg has the value 40 mV. Here,
in Eq. (14), /3' is the symmetry factor which must be evaluated
from the derivative of b with respect to T; thus
db/dT= R/p'F
(15)
P' = (R/F)[l/(db/dT)]
(16)
so that
The data of Fig. 3a show that p' is constant with T but has a value
appreciably different from 0.5 ± 0.05 usually obtained using Eq. (5)
at T =* 298 K. It is evident, and important to note, that for the h.e.r.
results at Hg it is incorrect to evaluate j3 from Eq. (5) at some
particular values of T since, in fact, that equation erroneously
represents the form of b with T; it is Eq. (14) that must be employed,
using Eq. 16.
It is certainly a remarkable coincidence that (3 evaluated from
Eq. (5) at the "laboratory temperature" —298 K comes out very
Figure 3. (a) Tafel slopes b for the h.e.r. at Hg in aqueous and methanolic acid
solutions as a function of temperature (from data of Post and Hiskey, Conway et al.,2
and Conway and Salomon42). Comparison with behavior for Br2 at graphite also shown
(see Fig. 8). (b) Tafel slopes b for the h.e.r. at liquid and solid Hg from the results of
Parsons and Bockris11 in methanolic HC1 (from Ref. 43).
120
Brian E. Conway
near the conventionally "expected" value of 0.5; a similar point
has been emphasized by Yeager et al.45b (see below) with regard
to his results for O2 reduction at Pt in H3PO4 over a wide temperature
range. However, it evidently just is a coincidence since it is quite
evident that the true "/3", written as j3' in Eq. (14), must be evaluated
from Eq. (16) rather than from Eq. (5). If /3 is evaluated from Eq.
(5) it has an apparent temperature dependence, the origin of which
is clear if Eq. (5) is coupled with Eq. (14), which truly represents
the results of Fig. 3a, namely
£!?
Then j8 is evidently given by
1//3 = l/p' + KF/RT
(18)
or
(19)
so that p is apparently T dependent; thus it is seen that fi apparently
increases with T as has been noted empirically in some earlier
works using Eq. (5) with experimental b values. We emphasize
again that the symmetry factor for the h.e.r. at Hg must be evaluated
from Eq. (14); then the true /3, written as /3', is found to be
independent of T and the Tafel slope has the form represented by
Eq. (14) which is fundamentally different from that normally
assumed [Eq. (5)]. We shall comment on possible nontrivial explanations for the form of Eq. (14), including the significance of K,
in Section IV.
(«) The H2 Evolution Reaction at Ni
Conway et al.2 also studied the h.e.r. at Ni under high-purity
conditions in methanolic HC1 over a wider range of temperature.
Under these conditions, the "Tafel lines" appear as two linear
segments,t the slopes of each of which depend on T as shown in
Fig. 4. Comparative data for the D2 evolution reaction (d.e.r.) from
MeOD/DCl are shown in Fig. 5.
t In aqueous HC1, lines with a small degree of curvature are usually observed with
b = 0.10 ±0.005 V a t 298 K.
Electrochemical Reaction Rates and the Tafel Equation
121
Ni/HCI-MeOH
-0.6
-0.5
-0.4
Log [CURRENT DENSITY] amp cm"
Figure 4. Tafel relations for the h.e.r. at Ni in methanolic HC1 over a wide range
of temperature (from Ref. 2). Note that upper-region slopes increase with increasing
T, while lower-region slopes decrease for the same electrode process.
The two linear Tafel regions at Ni in methanolic HC1 vary
with T in a continuous and complementary way: one has a slope
that increases with T while the slope of the other simultaneously
decreases with T (Fig. 4), so there is a singular temperature at
which the Tafel relation is one line over the whole c.d. range.2 The
directions of change of the slopes of the two Tafel lines at each
temperature, other than at the singular temperature, correspond
apparently to reaction mechanisms that are consecutive ( ^ ^ 0
or parallel (/""""). However, we believe, based on new data
obtained from potential-decay experiments,77 that the two regions
correspond to desorption mechanisms in the h.e.r. taking place
through different populations of adsorbed H which have different
dependencies of their coverage on T and rj.
It is evident that the 7-dependence of b again does not follow
that conventionally assumed [Eq. (5)] and, moreover, for the same
reaction at the same metal, Ni, the two Tafel-line segments have
slopes that vary in opposite directions with temperature; Fig. 4
shows that this is a systematic variation and not the result of some
122
Brian E. Conway
"bv_
D(Ioweri)
0 26 -
^ D C ! MeOD
(a)
Ui
^HCI-MeOH
022 -
X
O
CL
o
D(upperTT^?S
^^^^^S^Mupper ' O \
^^"^^^^-^
a
0.14 -
H (lower i)
" ^
0.10 -
160
220
T/K
260
300
C/) 0.09 150
190
230
270
310
T/K
Figure 5. Tafel slopes for the d.e.r. at Ni in d-methanolic DC1 over a wide
range of temperature in comparison with those for the h.e.r. in ethanolic HC1
(from Ref. 2).
arbitrary comparison of the behavior at say just two different
temperatures. It is interesting that in methanolic HC104, made up
from the 70% aqueous acid, so that the methanolic solution contains
an unavoidable small mole fraction of H2O, two Tafel regions are
not observed. Hence the behavior in anhydrous methanolic HC1
may be connected with anion adsorption effects in that solvent [see
Section IV.9]. As will be discussed in that section, the influence of
temperature on the effects of adsorbed anions on the kinetics of
Electrochemical Reaction Rates and the Tafel Equation
123
an electrode process must always be recognized as a possible reason
for unconventional temperature variation of Tafel slopes, unless
conditions otherwise preclude the possibility of such effects, e.g.,
as at Hg at appreciable overpotentials in the h.e.r. where anion
adsorption is known to be insignificant.93'94
(Hi) The H2 Evolution Reaction at Cd
Data for the h.e.r. at Cd were also found2 to behave unconventionally.
(it?) The H2 Evolution Reaction at Electrocatalytic Ni-Mo Alloys
Recently, much interest has centered on the electrocatalytic
behavior of Ni-Mo alloyst (prepared electrolytically or by thermal
reduction of oxide or molybdate mixtures) for cathodic H2 evolution
in alkaline-water electrolyzers or as cathodes in electrolytic Cl2
cells. The h.e.r. at these electrode materials exhibits46 remarkably
low Tafel slopes, in the range 22-26 mV, at elevated temperatures,
~363 K. This is one of the reasons for their excellent behavior as
electrocatalysts for the h.e.r. However, the Tafel slopes exhibited
by these materials depend on temperature in a most unusual way,
decreasing with increasing temperature, as do some of the results
at Ni2 (Fig. 4).
The rj vs. In [current-density] relations (Fig. 6) exhibit two
linear regions (as with Ni under certain conditions—see Fig. 4),
each of which has a slope that decreases with T as shown in Fig.
7. This is not seemingly due to some change of mechanism as
temperature is increased since the decrease of the slopes with T is
evidently (see Fig. 7) a continuous one for both regions of the In i
vs. rj relations as is seen from Fig. 7.
This behavior must correspond to variation of a with a power
of T > 1 in the relation b = RT/a(T)F in order for b to decrease
with increasing T, or b is of the form b = K' - cT for the particular
case where b decreases linearly with T as in some experiments.
$ There is some question whether these are true equilibrium metallic alloys (it is
unlikely) and also what is the state of Mo—is it metallic or in the form of MoO
in a Ni-metal host structure.
Brian E. Conway
124
0.4
©
0.3
Q2
0.1
-3
log i (mA cm
Figure 6. Tafel relations for the h.e.r. at Ni-Mo electroplated electrocatalysts at
several temperature curves (1-4), 341, 319, 298, and 278 K, compared with behavior
of metallic nickel (curve 5) (Real apparent area factor for Ni-Mo coated electrode
450 x ); electrolyte is 1.0 M aqueous KOH (from Ref. 46, see also Fig. 19).
(v) Redox Reactions at Electrodes Involving Werner Complex Ions
The behavior of b as /(T) for ionic redox reactions at electrodes, especially those processes that involve only outer-sphere
changes of state, and both red and ox species which are not
specifically adsorbed, is of great interest. From some of Weaver's
work107108 information on the dependence of b on T for such
reactions is available and some attempts have been made, e.g., by
Parsons and Passeron,7 to establish if the potential-dependent factor
in the electrochemical rate equation in fact includes a quadratic
term in rj as well as the usual linear one; however, this is a different
question (cf. Ref. 8) related to the harmonicity or, otherwise, of
the fluctuations involved in the activation process.14
Later in this article, we refer to Weaver's work107108 on the
evaluation of real entropies of activation of some one-electron redox
reactions of complex metal ions at Hg, and corresponding data on
Electrochemical Reaction Rates and the Tafel Equation
125
150
NJ:Mo:Cd I
7 9 2 0 : I I TAFEL SLOPES
IMNaOH
HIGH b REGION
100
It!
3
u- 50
<
280
LOW b REGION
290
300
T/K
310
320
330
Figure 7. Decrease of slope b for h.e.r. at Ni-Mo electrocoated cathodes with
temperature: (O) upper c.d. region, and (x) lower c.d. region (from Ref. 46).
temperature variation of the transfer coefficient. These results are
of great interest.
The problem with redox reactions of this type is that their rate
constants are usually too large for regular steady-state techniques
to be reliably applied, a or (3 then have to be determined through
the reaction order or by some method such as Faradaic rectification.
Usually, such methods require evaluation of the double-layer
behavior in order to make "double-layer corrections." This is often
an unsatisfactory business, especially when corrections would be
required over a range of temperatures. We conclude that for this
important class of electrochemical reactions more data for
examination of b(T) or a(T) are required. However, for certain
ionic redox reactions that are sufficiently slow, Weaver107 has been
able to evaluate a as /(T) from Tafel plots over a range of 0.3 ~
0.4 V: a is in fact found to be independent of T for these cases (see
p. 179), an important result.
The Tafel-slope behavior as /(T) for solvated electron formation47 in, e.g., liquid NH3 or HMPA solutions would be another
interesting case for investigation.
126
Brian E. Con way
(vi) Anodic N2 Evolution from N3-ion at Pt
Probably the earliest, well-documented case of unconventional
behavior of the Tafel slope with temperature was reported by Stout48
for the anodic evolution of N2 from discharge of azide ion at Pt in
aqueous solutions. The overall reaction is
2N3 -> 3N2 + 2e
(20)
but detailed steps in the reaction have not been characterized;
presumably the N3 radical is an intermediate but whether its
decomposition to N2 is homogeneous or heterogeneous is as yet
unknown and the question of recombination to give an unstable
(and probably chemically unlikely) N6 species is unresolved.
For the azide discharge reaction at Pt, b in Eq. (5) is found
to be independent of T so that a itself is apparently linear in TI
This case can be regarded qualitatively as different from that for
the h.e.r. at Hg or limitingly as a special case of Eq. (14) where
K » RT/ p'F. Theoretical aspects of this type of case will be treated
in Section IV.
Although very little is known about the surface electrochemistry of the azide discharge reaction, analogies with the
situation in Cl~ or R.COO"36 discharge from aqueous solutions
would suggest that N^ is discharged at Pt on a surface covered or
partially covered by discharged OH or O species (cf. Ref. 49) with
possible coadsorption of N^ ion (regarded as a pseudohalogen).
Then the state of surface oxidation of the Pt and the temperature
dependence of the state of surface oxidation will determine, in part,
the temperature dependence of the Tafel slope of the N^ discharge
process. That a process occurring on a surface oxide is involved is
indicated by the unusually high Tafel slopes of —ART/F (as in
the Kolbe reaction36) characteristic (cf. Refs. 50 and 51) of charge
transfer across a barrier-layer film. Competition between specific
adsorption of N^ and electrodeposition of OH and O species49 may
be expected in this reaction. In this case, it is difficult to assign any
single reason for the independence of b on temperature. Qualitatively, a tends to become smaller with increasing film thickness but
greater with increasing film conductivity. The surface electrochemistry involved (cf. Ref. 49) is obviously complex and little
is known about its temperature dependence except that surface
Electrochemical Reaction Rates and the Tafel Equation
127
oxidation of Pt is facilitated, as may be expected, by elevation of
temperature ;52 the charge transfer characteristics of the oxide film
are not, however, known as a function of temperature, but conductance measurements were made by Shibata and Sumino53 at room
temperature for thin and thick films in the absence of Cl" or
pseudohalide ions.
(vii) Anodic O2 Evolution at Pt
In studies of the O2 evolution reaction at Pt from aqueous
H2SO4, it is found that the Tafel slopes determined for the steadystate kinetics of this reaction at several temperatures do not correspond to the conventionally expected behavior according to Eq.
(5), so that a is somewhat temperature dependent as in the case
of Section III.2, (ii). However, more work on this case is required,
taking into account the temperature dependence of oxide-film
growth, etc.
(viii) Anodic Br2 Evolution from Br~ in CH3CN Solution
In an experiment designed to determine if unconventional
temperature dependence of Tafel slopes (where a seems to be itself
linear in T) originates in some way on account of the temperature
dependence of the structure54'55 of associated solvents such as H2O
and MeOH (cf. Ref. 2) in the electrode/solution interphase or of
orientation of solvent dipoles of the structured solvent, Conway et
al2 determined b for anodic Br2 evolution at graphite from Br~ ion
in CH3CN over an 80 K temperature range: b was found to be
70 ± 7 mV and independent of T over the whole temperature range
covered so that a is again, for this case, independent of T (Fig.
8a). Since CH3CN, although a strongly polar solvent, is generally
considered to be "unstructured" in the sense that H2O or MeOH
are, it can be concluded that it is unlikely that the temperature
dependence of a can be directly attributed to changes of structure
of the solvent in the double layer or of the structural factor55 in
the solvation of the reactant ion. Recent results from this laboratory
on anodic Cl2 evolution at Pt also show that b (=0.04 V in this
case, prior to a limiting current) is almost independent of T. This
result is surprising since two complicating aspects of the electrodekinetic behavior must be involved: temperature dependence of Cl~