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The electrochemistry of silver in KOH at elevated temperatures—IV. AC impedance study
THE ELECTROCHEMISTRY ELEVATED TEMPERATURES-IV.
OF SILVER IN KOH AT AC IMPEDANCE STUDY
BRUCE G. POUND* and DIGBY D. MACDONALD+ Fontana
Corrosion
Center, Department of Metallurgical Engineering, The Ohio State University, Columbus, OH, 43210, U.S.A.
and JOHN W. TOMLINSON Department
of Chemistry, Victoria University of Wellington, Wellington, New Zealand (Received
30 March 1982)
Abstract-The (~c impedance properties of silver in 1 mol kg-’ KOH were studied under potentiostatic conditious over the temperature range 295-478 K. Measurements were obtained over the frequency range 0.5 Hz-5 kHz, and were analyzed in terms of equivalent circuits. It was shown that provision for surface roughness is required for a satisfactory explanation of the impedance data. Values for the double layer capacity and the concentration of AgO- ions at the electrode surface could generally then be obtained. At potentials corresponding to the formation of Ag,O, it is demonstrated that both diffusion in solution and diffusion in the oxide film are operative. At elevated temperatures, the rate of growth of Ag,O centres is controlled partly by diffusion in the oxide and partly by a reaction step at the growing interfaces of the centers. The subsequent formation of Ag,O,, at all temperatures in the range studied, is interpreted on the
basisof an electrocrystallisation impedance.
INTRODUCTION The electrochemical behaviour of silver in 1 mol kg- * KOH over the temperature range 295478 K has been examined previously in terms of the dependence of current and potential on time[l-31. The use of the frequency domain allows surface processes having substantially different relaxation times to be studied. Hence, the time-domain techniques were supplemented with an ac impedance method in which the frequency dispersion of the electrode impedance under potentiostatic conditions was investigated.
components of the ac potential drop across a nonreactive resistor, R,, in the counter electrode circuit were measured by a P.A.R. Model 129A lock-in amplifier operated in its phase-sensitive detector mode. The corresponding real and imaginary components of the impedance were then derived using the following equations: R = cv,,
(1)
x = cvx,
(2)
where C = R, v.d( v’R + v’,),
EXPERIMENTAL The electrochemical cell and the preparation of electrodes have been described previously[2]. The potentials were measured against a non-pressurebalanced external saturated calomel electrode, and therefore had to be corrected for the irreversible contributions arising from the thermal liquid junction and streaming between the WE and RE compartments. Details of the required corrections are given in parts II and III of this study.[2, 31 A constant dc potential modulated by an ac signal (3.2 mVrms) was applied to the working electrode using a Chemical Electronics Type 403A potentiostat coupled to a Brookdeal 9471 signal source. The inphase (real), VR and quadrature (imaginary), V, * Former address: Department
of Chemistry,
of Auckland, Auckland, New Zealand.
+ To whom correspondence
(3)
and Y, is the modulating ar voltage.
University
should be addressed.
Impedance measurements were made on the system over the temperature range 295478K at five potentials in the active and passive regions for each temperature. In addition, the impedance at a potential of 0.5 V (see, 295 K), at which the higher silver oxide, Ag,O,, forms was determined at all temperatures except 478K. At this temperature, OSV lies well into the region of oxygen evolution[3] which completely dominates other electrode processes under these conditions. Hence, the impedance associated with oxide formation was not examined in this case. The ac voltage components were measured at decreasing frequencies from 5 kHz down to (in most cases) 0.5 Hz. In the passive region, measurements were commenced when the dc current, and therefore the rate of film growth, had reached an approximately steady state. At 0.3 V (295 K), the dc current exhibited severe fluctuations after a time which varied with each experiment. In general, the lowest frequency which
1489
BRUCE G. POUND, DIGBY D. MACDONALDAND
1490
could be examined in this case was around 8 Hz, The most likely explanation for this behaviour, which was evident only at 295 K, is the cracking of a thick oxide multilayer.
RESULTS
The impedance components, R and X, at a potential of 0.12 V(sce, 295 K), are plotted in the complex plane in Fig. 1. At 295K, this potential lies in the active region of the steady-state polarisation curve[3]. The impedance of an electrode undergoing dissolution is generally considered to be equivalent to the simple Randles circuit shown in Fig. 2. While the impedance spectrum corresponding to the Randles circuit exhibits a semi-circle at high frequencies, the lack of a distinct semi-circle in Fig. 1 can be explained if the charge transfer resistance, R,, is very small. However, the low frequency line has a slope of 54’ which is greater than the expected value of 45” associated with the Warburg impedance, Zw alone[4]. The electrode impedance, Z’, can be found from (4) where R SO,the solution
W.
R’-jx’,
resistance
(4)
between the working
TOMLINSON
and reference electrodes, is obtained as the high frequency intercept of the impedance locus. Adopting the method of analysis proposed by Sluyters et al. [S, 61, the real and imaginary components of the admittance, A’ and B’, respectively were calculated for unit apparent electrode area. In the case of the Randles circuit, A’ and B’ are given by A’ =
Silver dissolution at 295 K
2’ = Z-R,=
JOHN
~[p2~;p~+2]
(5)
(6)
B’ = ~[p2+:p+Z]+~C.p
where p is the irreversibility coefficient defined by p = R,w”=/a
(7)
and CTis the Warburg coefficient expressed by RT 17= PI~F~(~D)“~C,’
(8)
A’ was found to be linearly dependent on g112 over most of the frequency range shown in Fig. 3a, from which it can be inferred that over this range, at least, p = 0, and the reaction is therefore reversible with A’/& /2= (2~)~‘. However, the apparent double layer capacity, C, (9) was found to be frequency dependent (Fig. 3b).
c.+?= [B’ -A’/@
+ 1)1/w.
(9)
Fig. 1. Impedance spectrum for the dissolution of silver at 0.12 V, 295 K. Frequenciesin Hz are shown for various points.
Fig. 2. Randles equivalentcircuit. R, is the solution resistance between the WE and RE. R, is the charge transfer resistance,Cdl is the double layer capacitanceand Zw, the Warburg impedance.
Therefore, the simple Randles circuit does not adequately represent the electrode impedance. The frequency dependence of Caphas been observed by previous workersC7, S] and was attributed to roughness and/or porosity of the electrode surface. It is know@63 that strong reactant adsorption also gives rise to a frequency-dependent C,, but, in this case, A’/o’/’ is expected to increase with frequency. Hence, it is more likely that surface roughness is responsible for the observed behaviour in the present study since A’/o I” is largely independent of frequency over a wide range (Fig. 3a). Dc Levie[9] has treated the effects of surface roughness on the double layer capacitance. The apparent parallel capacity, Cap, resulting from surface
1491
Ekctrochemistry of Ag in KOH
where Cd, is the true double layer capacity which is assumed to be potential independent when dissolution occurs. The apparent admittance due to roughness effects is given by Y, = &+
jo(gw-
*lz),
(11)
aP =
bw”+jgw’/2,
(12)
where b and g are surface roughness coefficients. This treatment is equivalent to the circuit shown in Fig. 4
Ret
zw
Fig. 4. Equivalentcircuitrepresentingthe impedanceof the silver electrode in the active region. 2, is the apparent impedancedue to roughnesseffects. and this circuit will be used to represent the impedance of a silver electrode undergoing dissolution. The expression for the overall admittance of this circuit is simplified if R,, can be neglected. This approximation is justified by the constant slope of the A’/w’l’ plot over the frequency range and is supported by previous work[7]. The overall admittance can then be expressed as Y’ = (1 +j)o
1’2/2a+ bw” +jgo”’
+jw Cd,, (13)
For which the real and imaginary components of the admittance are
olil
B’ = -+coCd,+gw 20 Fig. 3. Frequencydependenceof the admittancedata for the dissolutionofsilver at O.l2V, 295K. Dependenceof (a) A’on WI’* (b) B’-A’ on w and (c) B’cJJ-“~ on o~“~. roughness was shown to be linearly dependent on CII-‘/~ and this has been supported experimentally[ IO]. In the same frequency region, it was predicted that the apparent parallel resistance, Rap, due to roughness would vary linearly with co- ‘/I. However, other workers[8] found experimentally that for silver in KOH solutions, R,, varies with UJ-” where 0.9 < n i 1.4 and this dependence is used in the present analysis. The apparent double layer capacity may be expressed[7) as
cap= cdl+gw
- l,Z ,
i/2 .
A’ is still predicted to be proportional to wl” with slope (2~)~ 1as shown in Fig. 3a but, at sufficiently high Frequencies,A’ becomes dependent on 0”. However, A clearly is not significantly influenced by surface roughness over the frequency range shown. Equation (15) can be rewritten as
(16) A plot of B’w-“‘against CII~~’(Fig. 3c) was found to be linear. Hence, C, can be determined from the slope while the intercept gives the roughness coefficient after subtraction of (2~)~‘. Since the experimental data were shown to be consistent with the relations predicted on the basis of the proposed equivalent circuit, the parameters, u and Cd, given in Table 1 were calculated. From 0, the equilibrium concentration of AgO-, Co, may be
0.12 0.15 0.18 0.20 0.30 0.50
0.13 0.15 0.18 0.20 0.30 0.50
0.1: 0.15’ 0.18 0.20 0.30 0.50
0.12 0.15 0.18 0.20 0.30 0.50
0.12 0.15 0.18 0.20 0.30
295
348
388
428
478
: 0.6
$ 3.7 3.2 2.5 $
3121
: 0.05 t
$
2766
*
S28 876 1.5 1.3 0.1
59.7 49.4 6.1 3.6 0.4 61
2005 2920 3198 1367 367
16 429 788 1201 2529 846
49 562 3261 7806 26378 305
65 50 4030 3085 13765 49
479 752 3927 5685 36791 722
UT
(Rcm’sm112)
cdl
(FFcm-‘)
us
t t 1680 t 133
16 t t t t 142
49 t 1560 2490 12186 97
65 50 t t 6731 16
479 152 t t 6037 149
(Qcmzs-liz)
_I _. -. ._
* Not present. + IMa not available. $ Interpretation uncertain. 1 Change of slope evident but lower frequency data not available. (1Slopes are taken from plots of B’w-“’ us w-‘/’ [see (32)].
E
09
T
(K)
lO-5 10-S 10-6 lo-’
10-4
10-6 lo-’
10m4 10-4
-
-
-
t t 9.2 x 1O-6 t t
1.3x 10-3 t t t t 2.7 x lo-’
5.3 x t 1.6x 1.0x 2.1 x 2.7 x
5.6 x 7.3 x t t 5.4 x 2.3 x
1.4 x 10-d 8.8 x lo-’ t t 1.1x 10-5 4.4 x lo-4
(moldm-‘)
CO
* I t
* * 7.4 x loms * *
* 1 * t
t 6.5 x lo-” * I
2.2x 10-4 * * 9.2 x lo-’ 1.1 x 10-4 1.2 x 10-4 4.6x 1O-4
t i 3.9 x 1o-5 2.1 x 10-j * * t t 8.4 x 1O-5 1.8 x lo-’
4 i 30754 573 * * 1 7034 33 *
-..
* * *
* I: t
* * t t 1.5x lo-” t P
2.3 x 10m3 2.5 x 10-3
1.5x 1o-3 7.6 x 1O-3 :
: 1518
1 104
t t 4.3 x 10-S t t
1.9 x 1o-3
2.6 x K-”
t *
8.9 x to+ 1.7 x lo-’
t
*
: t 2.8 x 10-3
t t t
*
§ 1721 5316 14192 208
1
* * 3.2 x 1O-3 1.9 x 1o-3 1.6 x IO- 3
t 2.3 x 1O-4 7.4 x 10-5 2.8 x lD-5 1.9 x 10-3
-.
* 1: *
* * * * *
1.6: lo-” * 2.2x lo-‘2 * 1.0x 1o-L1 * * 4.5 x lo-‘0
* 5.0 x lo- ’ 9.2 x 1O-4 7.0 x 10-4 2.1 x 1o-4 2.2 x 1o-3
*
4.6: 10-l”
t
*
* 1 t *
* *
+ *
* *
CT(Ag,O) C(Ag202) (mol cmm2) (mol cm-2)
t&u~ (Scm-2)
X,
(Rc~~s-~‘~)
OF
Table I. Data from impedance and admittance plots
_
Electrochemistry of Ag in KOH obtained using (8). In order to evaluate Co, the diffusion coefficient ofAgO-, D,, was derived for each temperature of interest. Do is a function of temperature as expressed[ 111 by (17).
,
(17)
where E, is the activation energy for diffusion. For aqueous solutions, Z,, - 0.2[12], and for the AgOion in 1 moldm’ KOH at 293 K, D, has been evaluated as 8.6 x i0-6cm2 s-‘[13]. Assuming that E, is independent of temperature, Do can be obtained over the range 295478K (Table 2). Table 2. Diffusion coefficients, D, and Dp, over the temperature range 295-478 K 1O”D (cmZsm’F,
IO’D,
(cm2s~’ 1 295 348 388 428 478
0.8 3.6 8.9 18.2 37.9 -.-_
At 295 K, the roughness coefficient, y, is of the order of 10-3Fcm~2s~1~2 (Table 3), and 0 of the order of 10’ R cm’s _ I”. Using these values, the phase angle is Found to be typically 50 + 5” which is consistent with the experimental value of 54”. Table 3. Surface roughness coefficient, 9, over the temperature range 295428 K
& 295 348 388 428
Film formation
0.4 2.3 6.5
15.1
.---.-
1493
35.5 - ~
The value of Co at 0.12V and 295 K, 1.4 f 0.2 x 10-4 mol dme3, is in reasonable agreement with other values at room temperature obtained by Giles et al. [7] from impedance measurements of electropolished single-crystal electrodes. The double-layer capacity at 0.12 V and 295 K, 59 & 8 ~Fcm-‘, is also consistent with the value of 27 +_ 3 /~Fcm-’ obtained by these workers taking into account the different nature of the electrode surfaces in the two studies. In the case of the equivalent circuit shown in Fig. 4, that is, where surface roughening is present, the phase angle, 4. is not 45” as expected for a Warburg impedance. From (14) and (15), at lower frequencies where Warburg behavior is expected,
c:,
(Fcm-&z)
0.12 0.13 0.12 0.12
(19)
x x x x
10-S 10-a 10-z 10-z
UK 295 K
The impedance spectrum for 0.3 V shown in Fig. 5 is typical of the changes which take place as the potential is increased anodjcally from 0.12 V. The spectra for the film formation region of silver exhibit a “Warburg” (AgOdiffusion) region at high frequencies similar to that at 0.12V. In addition, a linear low frequency region becomes evident -at higher temperatures (see Fig. 10). This second region may well have appeared at 0.3 V, 295 K, if low frequency data had been available. A low frequency Warburg region is predicted from an analysis recently carried out[24] for a point-defect model of film growth. Unfortunately, insufficient data are available to test this model in the present case. Instead, these spectra may be interpreted in terms of a modified Randles circuit as proposed by Armstrong and Edmondson[ 147. Essentially, an additional Warburg impedance is included to account for diffusion of species in the film present on the electrode surface. The total diffusion impedance (Warburg coefficient, a=) is considered to consist ofdiffusion in solution (Warburg coefficient, as) and diffusion in the film (Warburg coefficient, crF) such that UT. = flsf(cd)
= 1+2ug.
1.3 1.9 1.3 1.7
+
UF,
(20)
where f(o) is a complex frequency function which allows for interaction between the ac diffusion layer
Fig. 5. Impedance spectrum for the formation of AgXO at 0.3 V, 295 K.
1494
BRUCE G.POUND,DIGBYD.
and the Nernst diffusion layer at lower frequencies. The faradaic impedance is now given[14] by Zr = R,,+ (1 -j)(uS/w1/2)p(o)+
W. TOMLINS~N
MACDONALDANDJOHN
(1 -j)ar/oii2.
The concentration of diffusing species, C, at the Ag/Ag,O interface can be obtained if it is assumed firstly that for diffusion in the film[l4] car = RTj2 “%I~F~D~’ “C,,
(21) It will be assumed here that R, is negligible. The exchange current density for the formation of Ag,O has been given as 2.8 mA cm-‘[15] so that R,, = 4.6 Dcm’ which is small compared with the real component of the Warburg impedance over most of the frequency range examined. The equivalent circuit as shown in Fig. 4 for the dissolution region can then be used as a model, with a modified Zw, for the electrode impedance for film formation at these potentials. The plot of A’ against w112for 0.3 V at 295 K (Fig. 6a), and particularly at 348 and 388 K (see Fig. 1la) exhibits two regions of linearity. The parameter eT is obtained from the Warburg slope at high frequencies and a, from the Warburgslope at low frequencies[14]. Hence, where possible, ~,can be determined and C,, the concentration of AgO-, calculated (Table 1). Using the same analytical procedure as previously employed on the data for 0.12 V (Fig. 3c), C,, may be obtained at 0.3V as shown in Fig. 6b. Double layer capacitances are listed in Table 1.
(22)
and secondly, that silver ions and not oxide ions are the mobile species in the film. Thediffusion coefficient, D,, for silver in Ag,O is given by[lG] RF = 5.4 x lo-‘exp(
-3503/T), .
(23)
from which D, (Table 2)at each temperature of interest was evaluated. Values of Cr were converted to the fraction of sites, Xr(Table l), occupied by the mobile Ag* ions: XF = C,V&,
(24)
where V, is the molar volume of Ag,O, 32.7 cm3 mol.
Ag,O,
formation
at 295 K
The impedance spectrum in the complex plane at 0.5 V (Fig. 7) exhibits a line at low frequencies having a slope close to 45”. The plot of A’ us w”‘(Fig. 8a) has two linear regions showing that diffusion in the film is still present at 0.5 V. However, B’cu- I/* is clearly not linear with w112 (Fig. 8h) except possibly at higher frequencies. This potential lies in the region for formation of Ag,O, which has been shown[17,18] to occur by an electrocrystallisation process. This process must be considered as part of the overall faradaic electrode reaction and therefore is postulated to correspond to an additional faradaic impedance in series with the Warburg impedahce associated with Ag,O formation. Fleischmann et al.[lB] proposed the following mechanism for the lattice formation of AgO (now generally considered to exist as Ag(I)Ag(lll)O, [19,
201)
0
I
I
I
I
I
20
40
60
so
OH-
1
= OH(ads)+e-,
Ag+ + OH(ads)%
wi,s-’
@a)
AgO + Ht.
(25b)
Since the charge transfer step presumably occurs at a sufficiently fast rate to maintain a pre-equilibrium, it can again be assumed that the charge transfer resistance may be neglected. It is proposed, therefore, that the equivalent circuit shown in Fig. 9 may be used to represent the electrode impedance for rate control by diffusion and crystallization. The impedance associated with electro-crystallization, Z,, was considered in terms of crystallisation on a metal lattice. The faradaic impedance of the series components, Z, and Z,, is given by[21, 221. zr=
zw+z,
= (1 -j)u/w”Z
Fig. 6. Frequencydependenceof the admittancedata for the formation of A&O at 0.3V. 295K. Dependence of (a) A’ on CO”~and (b) B’w-“~
on CU’/~.
(26) +
(Ek:--jEk,O)/(k;+
CO’),
(27)
where E = RT/n’F%k,; k, being the rate constant for crystallization and T, the concentration of adsorbed species. The presence of crystallisation rate control is likely to become evident[22] at high frequencies where the components of the diffusion impedance become relatively small and roughness effects are assumed to be absent. Hence, the case w B k, will be considered and
Electrochemistry of Ag in KOH
1495 0.5
200
-
150
.
-
/
I9
c 5
loo
-
/
.
.7 so
0
-
50
loo
I I50
Fig. 7. Impedance spectrum for the formation of Ag,O,
6
I 2(
at 0.5 V, 295 K.
(a)
I-/i, __ __ __ (b) 3-
Fig. 8. Frequency dependence of the admittanoe data for the formation of AgpOl at 0.5 V, 295 K. Dependence of (a) A’ on ~l’~, (b) B’o-~‘~ on UJI/~(c) A’w-’ on CL-~/’ (d) B’cL-’ on o-“* and (e) B’w-‘I* on w-*“.
(27) can then be rearranged
and inverted
to yield
w2 [ (uw3’2 +ek~)+j(~d~~+~&,w)] Yf = @IiT + akf)l + (ow~‘~ + ek,w)' .
(28)
For s,sufficiently high frequency, only terms containing co3 are retained in the denominator. Hence, the real
BRUCE
1496
G.
POUND,
Fig. 9. Equivalent circuit for the formation component of the overall admittance surface roughness) is given by
DKBY
of
D.
MACDONALD
for
which can be rewritten
(29)
The overall
imaginary
component
(30) is
“2 Ek B’=%+$+~w”~+wC~,, which
can be written
(31)
as (32)
or B’ -_= w
(
1 G+g
>
uJ-1’2+
(33)
&+C,,.
The frequency dependence of the faradaic series components For combined diffusion and crystallisation rate control [see (27)] has been represented diagrammatically by Vetter[22]. A’o-t and B’cu- ’ exhibit a similar frequency dependence to the corresponding impedance components in the absence of surface roughness. In this work, the high Frequency region of the A’w- ‘/w-Liz plot (Fig. Xc) is influenced by the roughness term &_I”-‘. However, the shape of the B’w “’ plot (Fig. 8d) is similar to the curve of the capacitative component, (WC,)-‘, as represented by
r/o-
40
/
-
.fly: 7k
TOMLINSON
The impedance spectrum in the complex plane for each potential changes with increasing temperature as shown by a comparison of Figs 5 and 10. These changes are dependent on the position of the particular potential in the active/passive regions[3] of the current/potential curve at that temperature. The major change is the appearance of a linear low frequency region in the complex plane at potentials in the passive region. The basic equivalent circuits used to represent the electrode impedance at 295 K are applicable at elevated temperatures. However, at potentials in the passive region, it is necessary to modify the equivalent circuit as suggested by the form of the admittance component plots, in particular the low frequency region as shown by the plot of B’o-‘/~ against w112 (Fig. 1 I b). Although some plots of B’w-“Z/w”zin the passive region are linear at high frequencies, generally this is not the case. It is more common for approximately constant values of B’w- ‘I2 to be exhibited at high frequencies probably reflecting very low values of the interfacial capacity at these potentials. However, the scatter of data does not permit an estimation of C,, in most cases. Deviations from the predicted behaviour imply that the equivalent circuit proposed at room temperature is no longer adequate. The observed behaviour may be associated with changes in the kinetics of oxide growth with an increase in temperature. Studies at room temperature by Briggs er al.[17] showed the three-dimensional
as
A &I? 1 -w = 20*,‘/2 +--+-teYr. 2uZw”
W.
of temperature
Effect A’ = g+22;+bw”,
.I~HN
Vetter. The similarity in the curves provides some justification for applying the expression for the crystallisation impedance to the present case. A’ is linearly dependent on o’/*, as predicted, over the frequency range shown in Fig. 8a. The two linear regions allow ur, ,rr, and therefore Co and XF to be obtained. Cdl is determined from the slope B’w- “* us WI” (Fig. gb) which, as might be expected from (32), is linear only at high frequencies. At lower frequencies. the crystahisation component becomes effective and B’W Ii2 as predicted is proportional to we r/r (Fig. Se). This linearity occurs in the frequency region corresponding to ,rr (Fig. Sa) and hence, 8k,/2c$ and c (the surface concentration of OH species in the steadystate) can be determined (Table 1).
Ag,O,.
(allowing
AND
\
--*
05. 680 I
C
‘\
s
if ‘i
30
-
l
l 360
\
\*,p*-‘*
/
8
02
I20 I
20 0
Fig.
50
10.
Impedance
loo
150
I 200
spectrum for the formation of Ag,O
250
at 0.3 V, 388 K
Electrochemistry
of Ag in KOH
1497
Fig. 11. Frequency dependence of the admittance data for the formation of A&O at 0.3 V, 388 K. Dependence of (a) A’ on III”~ (b) B’cI-“~ on w”~ and (c) E~‘w-“~ on w~“~.
growth of Ag,O cm centres formed on a primary layer of the oxide. These workers found that the ratedetermining process occurred not at the expanding interfaces of the growth centres but in the primary layer. However, an increasing rate of diffusion of species through the film with increasing temperature might cause the relative rate of a reaction step at the growing interfaces of the centres to become more significant. Nevertheless, it is likely that diffusion would remain the dominant influence in the overah rate control.
It is proposed that the impedance data at elevated temperatures be analyzed in terms of an equivalent circuit which makes provision for an impedance associated with the formation and growth of the oxide centres. Initially, it is assumed that, as for the formation of Ag,02 at room temperature, the crystallisation impedance required may be represented as having the frequency dependence shown in (27). Hence, the equivalent circuit shown in Fig. 9 is used to represent the electrode impedance under these conditions aithough, Z,, now relates to the growth of Ag,O nuclei.
BRUCE G. HOUND. D~GBY D. MACDONALD
1498
At this higher temperature (388 IL), the dependence of A’ on w”’ exhibits two linear regions at 0.3 V as shown in Fig. Ila. This behavior is simply due to the appearance of the low frequency Warburg region associated with diffusion of ionic species through the oxide layer. It is clear that the roughness term, bo”, must become significant at frequencies beyond those examined. According to (29), it is expected A’ would be proportional to l/w at low frequencies. In some cases, a temporary increase of A’ with a decrease in frequency was observed (see low frequency region of Fig. ila), but generally such a change is brief and a more detailed examination of the data was not possible. At low frequencies, B’w-“~ varies linearly with we’/’ (Fig. ilc), justifying the application of the equations for a crystallisation impedance to the present situation involving oxidecentres. The slope in this region is seen from Fig. 1 la to correspond to solid state diffusion and is given by .?k,/26;. Therefore, c, the surface concentration of adsorbed OH species for Ag,O formation can be evaluated. Equivalent circuit at 0.5 V, 348428
K
The impedance spectrum at 0.5 V, 388 K (Fig. 12) shows distinct changes in its form compared with the spectrumat 0.3 V, 388 K. At 0.5 V, it is likely that Ag,O growth centers will have overlapped to such an extent-
Fig. 12. Impedance
spectrum
+OH(ads)+e-,
adsorption of discharged OH- ions. The removal of the adsorbed species in subsequent steps as given by Hoare would correspond to a reaction impedance[22]. Consequently, inclusion of an impedance, Z0 associated with oxygen evolution, in the equivalent circuit would yield a complicated expression for the overall faradaic admittance. In order to simplify the analysis, it will be assumed that the initial charge transfer step (34) is slow and that the electrode impedance corresponding to oxygen evolution can be represented by a simple charge transfer resistance in the equivalent circuit. Hence, the real component of the admittance is given by
which clearly does not alter the frequency dependence of A’. The expression for the imaginary component as given by (31) remains unchanged. Two linear regions are exhibited by the A’/oi” plot (Fig. 14a), thereby demonstrating the presence of solid state diffusion at 0.5 V for elevated temperatures. Also, as predicted, B’w - ‘I2 is linearly dependent on w- Ii2 at low frequencies (Fig. 14c), thus allowingC (Ag,O,) to be determined for each temperature. From Fig. 14b, it is clear that B’w- ‘I* is not linearly dependent on o”* in the frequency range studied, therefore preventing the determination of Cdl in this case.
these conditions, both the formation of Ag,O oxygen evolution occw.
for 0.5 V, 388 K. Under
that the overall electrode impedance for oxide formation for this potential at elevated temperatures may still be considered in terms of the equivalent circuit in Fig. 9, that is, a Warburg impedance in series with a crystallisation impedance associated with the conversion of Ag,O to Ag,O,. Some modification is required, however, to the equivalent circuit for this potential at elevated temperatures since 0.5 V now lies in the region where oxygen evolution can occur at a significant rate[3]. Since oxide formation occurs simultaneously, oxygen evolution is assumed to take place in parallel as indicated in the equivalent circuit shown in Fig. 13. It has been suggested by Hoare[23] that the mechanism of oxygen evolution in alkaline solutions could involve an initial electrochemical step: OH-
AND JOHN W. TOMLINSON
(34)
which can be considered in terms of a charge transfer resistance, R OHand a pseudocapacity arising from the
and
=, 11,
Fig. 13. Equivalent circuit for OSV over the temperature range 348428 K. Z, is the impedance associated with oxygen evolution.
Electrochemistryof Ag in KOH
1499
Fig. 14. Frequency dependence of admittance data for OSV, 388K. Dependence of (a)A’ on w”’ (b) B’w-‘I’ on wl’z and (cc)B’o-I” on o-I”. DISCUSSION Effect
of potential
The effect of increasing the potential anodically is shown by the changes in the impedance parameters given in Table 1. The interfacial capacity achieves quite low values, particularly at potentials corresponding to film formation; for example, at 0.3 V and 295 K, C,, = 0.4 PFcm-‘. This trend is consistent with the potential dependence of C,, at room temperature
observed by Ciles et af.[7] following the formation ofa monolayer of Ag20. At potentials immediately prior to film formation, the measured capacitance is probably largely an adsorption pseudocapacitance arising from adsorption of OH- ions. When the oxide layer is present, the interfacial capacity is composed of (a) the capacity at the metal/film interphase, (b) the capacity of the film and (c) the capacity at the film/solution interphase. The low value of Cdl measured in this situation very likely reflects a substantial dielectric effect of the oxide.
1500
BRUCE G.POUND,
DIGBYD.
MACDONALDANDJOHN
Wherecomparison of data is possible, both XFand i? (Ag,O) are found to decrease with increasing potential up to 0.3 V. The low values of rare no doubt indicative ofthe extent to which overlap of the growth centres has taken place. At each temperature, uF is greater than Q, where a comparison is possible for a particular potential. This difference is to be expected since the diffusing Ag+ ions in the film have a smaller diffusion coefficient than AgO- in solution (see Table 2). Furthermore, the concentration of Ag+ at the metal/film interface is, for example, 2X,/V,,, = 2 x 3.9 x 10m5/32.7= 2.4 x 1o-6 mol crnm3 at 295 K, 0.3 V compared with 1.1 x 10m5 molcn-3 for CO, that is, approx. five times smaller. However, at 348 K, 0.3 V, C, and CF are comparable ( - 5 x 10m6molcm-3) but this is misleading because a decrease in C, occurs as the potential increases. The concentration of AgO- should remain constant following the formation of bulk Ag,O. Sucha decrease has been reported previously (7) and was attributed to an artifact arising from equating R,, to zero in the Randles circuit. Eflect of temperature As the temperature increases, C, at each potential generally increases except where a shift into the passive region occurs with the temperature change. XF, however, appears to pass through a maximum at 348K. The lack of a distinct crF in the A’/cu”’ plots for potentials up to 0.3 V at 428 K could be attributed to two factors. A higher rate of diffusion at this temperature coupled with a decreased thickness of the film due to a greater solubility of the oxide will reduce the significance of the solid state diffusion impedance. Nevertheless, the oT slope for these potentials does begin to change at low frequencies, thus identifying the commencement ofa (or region. In contrast, a distinct crF is observed at 478 K for 0.18 V. The surface concentration of Ag,O growth centres appears to decrease whereas T: (Ag,O,) exhibits a maximum in the region of 348 K and decreases at 388 and 428 K. This subsequent decrease probably reflects a higher degree of overlap of Ag,O, nuclei at a particular potential due to the increase in temperature. The double-layer capacity at least for the active region increases with temperature. The high values of Cdl at elevated temperatures in this region in which the dissolution reaction is reversible, may be attributed firstly to an increase, in the accumulation of ionic
W. TOMLINSON
species at the electrode surface with temperature (as shown by the values of C,), and secondly, to more extensive roughening of the surface by dissolution. The second factor is reflected in the increased values of the surface roughness coefficient, g (Table 3), which were determined from the plots of B’o- Ii2 tis IU’/~. REFERENCES B. G. Pound, D. D. Macdonald and J. W. Tomlinson, Efectrochim. Acta 24, 929 (1979). 2. B. G. Pound, D. D. Macdonald and J. W. Tomlinson, Elecrrochim. Acta 25. 563 119801. and J. W. Tomlinson, 3. B. G. Pound, D. D. ‘Ma&x& Electrochim. Acra 25, 1293 (1980). 4. E. Warburg, Ann. Physik. 6?, 493 (1899); 6, 125 (1901). 5. M. Sluyters-Rehback and J. ,H. Sluyters, in Electraanalyrical Chemistry (edited by A. J. Bard) 4, 1. Marcel I.
Dekker. New York (1970).
6. B. Timmer. M. Sluters-Rehback and J. H. Sluvters. J. electroanal,. Chem. 18, 93 (1968). 7. R. D. Giles, J. A. Harrison and H. R. Thirsk, J. electraana~, Chem. 22, 375 (1969) 8. B. V. Tilak, R. S. Perkins, H. A. Kozlowska and B. E. Conway, Electrochim. Acto 17, 1447 (1972). 9. R. De J&vie, Electrochim. Acrn 10, 113 (1965). 10. R. De Levic. Adv. Elecrrochem. Electrorhem. Emma I”, 6.329 (1967). ’ 11. H. S. Taylor, .I. them. Phys. 6, 331 (1938). 12. A. C. Riddford. .I. phvs. Chem. 56. 745 (1952). Sac. 117; 491 i1970). 13. B. Miller, .I. &&r&~em. 14. R. D. Armstrong and K. J. Edmondson, J. electraanal. Chem. 53, 371 (1974). 15. T. C. Clark, N. A. Hampson, J. R. Lee, J. R. Morley and 6. Scanlon, Can. J. Chem. 44, 3437 (1968). 16. N. D. Rozenblyum, N. C. Bubyreva, V. 1. Bukhareva and G..Z. Kazakevich, Zh.@ Khim. 40, 2467 (1966). 17. G. W. D. Briggs, M. Fleischmann, D. J. Lax and H. R. Thirsk, Trans. Faraday Sac. 64, 3 120 (1968). 18. M. Fleischmann, D. J. Lax and H. R. Thirsk, Trans. Faraday Sac. 64. 3137 (1968). 19. W. S. Graff and H. H. Stadelmaier, J. electrochem. Sot. 105, 446 (1958). 20. V. Scatturin and P. Betton, J. electrochem. SOC. 108, 819 (1961). 21. H. Gerischer, 2. phys. Chem. 198, 286 (1951). 22. K. J. Vetter, Elertrorhemical Kinetics. Academic Press, New York (1967). 23. J. P. Hoare, The Electrochemistry ofOxygen. Interscience, New York (1968). 24. C. Y. Chao, L. F. Lin and D. D. Macdonald, to be published.
OF SILVER IN KOH AT AC IMPEDANCE STUDY
BRUCE G. POUND* and DIGBY D. MACDONALD+ Fontana
Corrosion
Center, Department of Metallurgical Engineering, The Ohio State University, Columbus, OH, 43210, U.S.A.
and JOHN W. TOMLINSON Department
of Chemistry, Victoria University of Wellington, Wellington, New Zealand (Received
30 March 1982)
Abstract-The (~c impedance properties of silver in 1 mol kg-’ KOH were studied under potentiostatic conditious over the temperature range 295-478 K. Measurements were obtained over the frequency range 0.5 Hz-5 kHz, and were analyzed in terms of equivalent circuits. It was shown that provision for surface roughness is required for a satisfactory explanation of the impedance data. Values for the double layer capacity and the concentration of AgO- ions at the electrode surface could generally then be obtained. At potentials corresponding to the formation of Ag,O, it is demonstrated that both diffusion in solution and diffusion in the oxide film are operative. At elevated temperatures, the rate of growth of Ag,O centres is controlled partly by diffusion in the oxide and partly by a reaction step at the growing interfaces of the centers. The subsequent formation of Ag,O,, at all temperatures in the range studied, is interpreted on the
basisof an electrocrystallisation impedance.
INTRODUCTION The electrochemical behaviour of silver in 1 mol kg- * KOH over the temperature range 295478 K has been examined previously in terms of the dependence of current and potential on time[l-31. The use of the frequency domain allows surface processes having substantially different relaxation times to be studied. Hence, the time-domain techniques were supplemented with an ac impedance method in which the frequency dispersion of the electrode impedance under potentiostatic conditions was investigated.
components of the ac potential drop across a nonreactive resistor, R,, in the counter electrode circuit were measured by a P.A.R. Model 129A lock-in amplifier operated in its phase-sensitive detector mode. The corresponding real and imaginary components of the impedance were then derived using the following equations: R = cv,,
(1)
x = cvx,
(2)
where C = R, v.d( v’R + v’,),
EXPERIMENTAL The electrochemical cell and the preparation of electrodes have been described previously[2]. The potentials were measured against a non-pressurebalanced external saturated calomel electrode, and therefore had to be corrected for the irreversible contributions arising from the thermal liquid junction and streaming between the WE and RE compartments. Details of the required corrections are given in parts II and III of this study.[2, 31 A constant dc potential modulated by an ac signal (3.2 mVrms) was applied to the working electrode using a Chemical Electronics Type 403A potentiostat coupled to a Brookdeal 9471 signal source. The inphase (real), VR and quadrature (imaginary), V, * Former address: Department
of Chemistry,
of Auckland, Auckland, New Zealand.
+ To whom correspondence
(3)
and Y, is the modulating ar voltage.
University
should be addressed.
Impedance measurements were made on the system over the temperature range 295478K at five potentials in the active and passive regions for each temperature. In addition, the impedance at a potential of 0.5 V (see, 295 K), at which the higher silver oxide, Ag,O,, forms was determined at all temperatures except 478K. At this temperature, OSV lies well into the region of oxygen evolution[3] which completely dominates other electrode processes under these conditions. Hence, the impedance associated with oxide formation was not examined in this case. The ac voltage components were measured at decreasing frequencies from 5 kHz down to (in most cases) 0.5 Hz. In the passive region, measurements were commenced when the dc current, and therefore the rate of film growth, had reached an approximately steady state. At 0.3 V (295 K), the dc current exhibited severe fluctuations after a time which varied with each experiment. In general, the lowest frequency which
1489
BRUCE G. POUND, DIGBY D. MACDONALDAND
1490
could be examined in this case was around 8 Hz, The most likely explanation for this behaviour, which was evident only at 295 K, is the cracking of a thick oxide multilayer.
RESULTS
The impedance components, R and X, at a potential of 0.12 V(sce, 295 K), are plotted in the complex plane in Fig. 1. At 295K, this potential lies in the active region of the steady-state polarisation curve[3]. The impedance of an electrode undergoing dissolution is generally considered to be equivalent to the simple Randles circuit shown in Fig. 2. While the impedance spectrum corresponding to the Randles circuit exhibits a semi-circle at high frequencies, the lack of a distinct semi-circle in Fig. 1 can be explained if the charge transfer resistance, R,, is very small. However, the low frequency line has a slope of 54’ which is greater than the expected value of 45” associated with the Warburg impedance, Zw alone[4]. The electrode impedance, Z’, can be found from (4) where R SO,the solution
W.
R’-jx’,
resistance
(4)
between the working
TOMLINSON
and reference electrodes, is obtained as the high frequency intercept of the impedance locus. Adopting the method of analysis proposed by Sluyters et al. [S, 61, the real and imaginary components of the admittance, A’ and B’, respectively were calculated for unit apparent electrode area. In the case of the Randles circuit, A’ and B’ are given by A’ =
Silver dissolution at 295 K
2’ = Z-R,=
JOHN
~[p2~;p~+2]
(5)
(6)
B’ = ~[p2+:p+Z]+~C.p
where p is the irreversibility coefficient defined by p = R,w”=/a
(7)
and CTis the Warburg coefficient expressed by RT 17= PI~F~(~D)“~C,’
(8)
A’ was found to be linearly dependent on g112 over most of the frequency range shown in Fig. 3a, from which it can be inferred that over this range, at least, p = 0, and the reaction is therefore reversible with A’/& /2= (2~)~‘. However, the apparent double layer capacity, C, (9) was found to be frequency dependent (Fig. 3b).
c.+?= [B’ -A’/@
+ 1)1/w.
(9)
Fig. 1. Impedance spectrum for the dissolution of silver at 0.12 V, 295 K. Frequenciesin Hz are shown for various points.
Fig. 2. Randles equivalentcircuit. R, is the solution resistance between the WE and RE. R, is the charge transfer resistance,Cdl is the double layer capacitanceand Zw, the Warburg impedance.
Therefore, the simple Randles circuit does not adequately represent the electrode impedance. The frequency dependence of Caphas been observed by previous workersC7, S] and was attributed to roughness and/or porosity of the electrode surface. It is know@63 that strong reactant adsorption also gives rise to a frequency-dependent C,, but, in this case, A’/o’/’ is expected to increase with frequency. Hence, it is more likely that surface roughness is responsible for the observed behaviour in the present study since A’/o I” is largely independent of frequency over a wide range (Fig. 3a). Dc Levie[9] has treated the effects of surface roughness on the double layer capacitance. The apparent parallel capacity, Cap, resulting from surface
1491
Ekctrochemistry of Ag in KOH
where Cd, is the true double layer capacity which is assumed to be potential independent when dissolution occurs. The apparent admittance due to roughness effects is given by Y, = &+
jo(gw-
*lz),
(11)
aP =
bw”+jgw’/2,
(12)
where b and g are surface roughness coefficients. This treatment is equivalent to the circuit shown in Fig. 4
Ret
zw
Fig. 4. Equivalentcircuitrepresentingthe impedanceof the silver electrode in the active region. 2, is the apparent impedancedue to roughnesseffects. and this circuit will be used to represent the impedance of a silver electrode undergoing dissolution. The expression for the overall admittance of this circuit is simplified if R,, can be neglected. This approximation is justified by the constant slope of the A’/w’l’ plot over the frequency range and is supported by previous work[7]. The overall admittance can then be expressed as Y’ = (1 +j)o
1’2/2a+ bw” +jgo”’
+jw Cd,, (13)
For which the real and imaginary components of the admittance are
olil
B’ = -+coCd,+gw 20 Fig. 3. Frequencydependenceof the admittancedata for the dissolutionofsilver at O.l2V, 295K. Dependenceof (a) A’on WI’* (b) B’-A’ on w and (c) B’cJJ-“~ on o~“~. roughness was shown to be linearly dependent on CII-‘/~ and this has been supported experimentally[ IO]. In the same frequency region, it was predicted that the apparent parallel resistance, Rap, due to roughness would vary linearly with co- ‘/I. However, other workers[8] found experimentally that for silver in KOH solutions, R,, varies with UJ-” where 0.9 < n i 1.4 and this dependence is used in the present analysis. The apparent double layer capacity may be expressed[7) as
cap= cdl+gw
- l,Z ,
i/2 .
A’ is still predicted to be proportional to wl” with slope (2~)~ 1as shown in Fig. 3a but, at sufficiently high Frequencies,A’ becomes dependent on 0”. However, A clearly is not significantly influenced by surface roughness over the frequency range shown. Equation (15) can be rewritten as
(16) A plot of B’w-“‘against CII~~’(Fig. 3c) was found to be linear. Hence, C, can be determined from the slope while the intercept gives the roughness coefficient after subtraction of (2~)~‘. Since the experimental data were shown to be consistent with the relations predicted on the basis of the proposed equivalent circuit, the parameters, u and Cd, given in Table 1 were calculated. From 0, the equilibrium concentration of AgO-, Co, may be
0.12 0.15 0.18 0.20 0.30 0.50
0.13 0.15 0.18 0.20 0.30 0.50
0.1: 0.15’ 0.18 0.20 0.30 0.50
0.12 0.15 0.18 0.20 0.30 0.50
0.12 0.15 0.18 0.20 0.30
295
348
388
428
478
: 0.6
$ 3.7 3.2 2.5 $
3121
: 0.05 t
$
2766
*
S28 876 1.5 1.3 0.1
59.7 49.4 6.1 3.6 0.4 61
2005 2920 3198 1367 367
16 429 788 1201 2529 846
49 562 3261 7806 26378 305
65 50 4030 3085 13765 49
479 752 3927 5685 36791 722
UT
(Rcm’sm112)
cdl
(FFcm-‘)
us
t t 1680 t 133
16 t t t t 142
49 t 1560 2490 12186 97
65 50 t t 6731 16
479 152 t t 6037 149
(Qcmzs-liz)
_I _. -. ._
* Not present. + IMa not available. $ Interpretation uncertain. 1 Change of slope evident but lower frequency data not available. (1Slopes are taken from plots of B’w-“’ us w-‘/’ [see (32)].
E
09
T
(K)
lO-5 10-S 10-6 lo-’
10-4
10-6 lo-’
10m4 10-4
-
-
-
t t 9.2 x 1O-6 t t
1.3x 10-3 t t t t 2.7 x lo-’
5.3 x t 1.6x 1.0x 2.1 x 2.7 x
5.6 x 7.3 x t t 5.4 x 2.3 x
1.4 x 10-d 8.8 x lo-’ t t 1.1x 10-5 4.4 x lo-4
(moldm-‘)
CO
* I t
* * 7.4 x loms * *
* 1 * t
t 6.5 x lo-” * I
2.2x 10-4 * * 9.2 x lo-’ 1.1 x 10-4 1.2 x 10-4 4.6x 1O-4
t i 3.9 x 1o-5 2.1 x 10-j * * t t 8.4 x 1O-5 1.8 x lo-’
4 i 30754 573 * * 1 7034 33 *
-..
* * *
* I: t
* * t t 1.5x lo-” t P
2.3 x 10m3 2.5 x 10-3
1.5x 1o-3 7.6 x 1O-3 :
: 1518
1 104
t t 4.3 x 10-S t t
1.9 x 1o-3
2.6 x K-”
t *
8.9 x to+ 1.7 x lo-’
t
*
: t 2.8 x 10-3
t t t
*
§ 1721 5316 14192 208
1
* * 3.2 x 1O-3 1.9 x 1o-3 1.6 x IO- 3
t 2.3 x 1O-4 7.4 x 10-5 2.8 x lD-5 1.9 x 10-3
-.
* 1: *
* * * * *
1.6: lo-” * 2.2x lo-‘2 * 1.0x 1o-L1 * * 4.5 x lo-‘0
* 5.0 x lo- ’ 9.2 x 1O-4 7.0 x 10-4 2.1 x 1o-4 2.2 x 1o-3
*
4.6: 10-l”
t
*
* 1 t *
* *
+ *
* *
CT(Ag,O) C(Ag202) (mol cmm2) (mol cm-2)
t&u~ (Scm-2)
X,
(Rc~~s-~‘~)
OF
Table I. Data from impedance and admittance plots
_
Electrochemistry of Ag in KOH obtained using (8). In order to evaluate Co, the diffusion coefficient ofAgO-, D,, was derived for each temperature of interest. Do is a function of temperature as expressed[ 111 by (17).
,
(17)
where E, is the activation energy for diffusion. For aqueous solutions, Z,, - 0.2[12], and for the AgOion in 1 moldm’ KOH at 293 K, D, has been evaluated as 8.6 x i0-6cm2 s-‘[13]. Assuming that E, is independent of temperature, Do can be obtained over the range 295478K (Table 2). Table 2. Diffusion coefficients, D, and Dp, over the temperature range 295-478 K 1O”D (cmZsm’F,
IO’D,
(cm2s~’ 1 295 348 388 428 478
0.8 3.6 8.9 18.2 37.9 -.-_
At 295 K, the roughness coefficient, y, is of the order of 10-3Fcm~2s~1~2 (Table 3), and 0 of the order of 10’ R cm’s _ I”. Using these values, the phase angle is Found to be typically 50 + 5” which is consistent with the experimental value of 54”. Table 3. Surface roughness coefficient, 9, over the temperature range 295428 K
& 295 348 388 428
Film formation
0.4 2.3 6.5
15.1
.---.-
1493
35.5 - ~
The value of Co at 0.12V and 295 K, 1.4 f 0.2 x 10-4 mol dme3, is in reasonable agreement with other values at room temperature obtained by Giles et al. [7] from impedance measurements of electropolished single-crystal electrodes. The double-layer capacity at 0.12 V and 295 K, 59 & 8 ~Fcm-‘, is also consistent with the value of 27 +_ 3 /~Fcm-’ obtained by these workers taking into account the different nature of the electrode surfaces in the two studies. In the case of the equivalent circuit shown in Fig. 4, that is, where surface roughening is present, the phase angle, 4. is not 45” as expected for a Warburg impedance. From (14) and (15), at lower frequencies where Warburg behavior is expected,
c:,
(Fcm-&z)
0.12 0.13 0.12 0.12
(19)
x x x x
10-S 10-a 10-z 10-z
UK 295 K
The impedance spectrum for 0.3 V shown in Fig. 5 is typical of the changes which take place as the potential is increased anodjcally from 0.12 V. The spectra for the film formation region of silver exhibit a “Warburg” (AgOdiffusion) region at high frequencies similar to that at 0.12V. In addition, a linear low frequency region becomes evident -at higher temperatures (see Fig. 10). This second region may well have appeared at 0.3 V, 295 K, if low frequency data had been available. A low frequency Warburg region is predicted from an analysis recently carried out[24] for a point-defect model of film growth. Unfortunately, insufficient data are available to test this model in the present case. Instead, these spectra may be interpreted in terms of a modified Randles circuit as proposed by Armstrong and Edmondson[ 147. Essentially, an additional Warburg impedance is included to account for diffusion of species in the film present on the electrode surface. The total diffusion impedance (Warburg coefficient, a=) is considered to consist ofdiffusion in solution (Warburg coefficient, as) and diffusion in the film (Warburg coefficient, crF) such that UT. = flsf(cd)
= 1+2ug.
1.3 1.9 1.3 1.7
+
UF,
(20)
where f(o) is a complex frequency function which allows for interaction between the ac diffusion layer
Fig. 5. Impedance spectrum for the formation of AgXO at 0.3 V, 295 K.
1494
BRUCE G.POUND,DIGBYD.
and the Nernst diffusion layer at lower frequencies. The faradaic impedance is now given[14] by Zr = R,,+ (1 -j)(uS/w1/2)p(o)+
W. TOMLINS~N
MACDONALDANDJOHN
(1 -j)ar/oii2.
The concentration of diffusing species, C, at the Ag/Ag,O interface can be obtained if it is assumed firstly that for diffusion in the film[l4] car = RTj2 “%I~F~D~’ “C,,
(21) It will be assumed here that R, is negligible. The exchange current density for the formation of Ag,O has been given as 2.8 mA cm-‘[15] so that R,, = 4.6 Dcm’ which is small compared with the real component of the Warburg impedance over most of the frequency range examined. The equivalent circuit as shown in Fig. 4 for the dissolution region can then be used as a model, with a modified Zw, for the electrode impedance for film formation at these potentials. The plot of A’ against w112for 0.3 V at 295 K (Fig. 6a), and particularly at 348 and 388 K (see Fig. 1la) exhibits two regions of linearity. The parameter eT is obtained from the Warburg slope at high frequencies and a, from the Warburgslope at low frequencies[14]. Hence, where possible, ~,can be determined and C,, the concentration of AgO-, calculated (Table 1). Using the same analytical procedure as previously employed on the data for 0.12 V (Fig. 3c), C,, may be obtained at 0.3V as shown in Fig. 6b. Double layer capacitances are listed in Table 1.
(22)
and secondly, that silver ions and not oxide ions are the mobile species in the film. Thediffusion coefficient, D,, for silver in Ag,O is given by[lG] RF = 5.4 x lo-‘exp(
-3503/T), .
(23)
from which D, (Table 2)at each temperature of interest was evaluated. Values of Cr were converted to the fraction of sites, Xr(Table l), occupied by the mobile Ag* ions: XF = C,V&,
(24)
where V, is the molar volume of Ag,O, 32.7 cm3 mol.
Ag,O,
formation
at 295 K
The impedance spectrum in the complex plane at 0.5 V (Fig. 7) exhibits a line at low frequencies having a slope close to 45”. The plot of A’ us w”‘(Fig. 8a) has two linear regions showing that diffusion in the film is still present at 0.5 V. However, B’cu- I/* is clearly not linear with w112 (Fig. 8h) except possibly at higher frequencies. This potential lies in the region for formation of Ag,O, which has been shown[17,18] to occur by an electrocrystallisation process. This process must be considered as part of the overall faradaic electrode reaction and therefore is postulated to correspond to an additional faradaic impedance in series with the Warburg impedahce associated with Ag,O formation. Fleischmann et al.[lB] proposed the following mechanism for the lattice formation of AgO (now generally considered to exist as Ag(I)Ag(lll)O, [19,
201)
0
I
I
I
I
I
20
40
60
so
OH-
1
= OH(ads)+e-,
Ag+ + OH(ads)%
wi,s-’
@a)
AgO + Ht.
(25b)
Since the charge transfer step presumably occurs at a sufficiently fast rate to maintain a pre-equilibrium, it can again be assumed that the charge transfer resistance may be neglected. It is proposed, therefore, that the equivalent circuit shown in Fig. 9 may be used to represent the electrode impedance for rate control by diffusion and crystallization. The impedance associated with electro-crystallization, Z,, was considered in terms of crystallisation on a metal lattice. The faradaic impedance of the series components, Z, and Z,, is given by[21, 221. zr=
zw+z,
= (1 -j)u/w”Z
Fig. 6. Frequencydependenceof the admittancedata for the formation of A&O at 0.3V. 295K. Dependence of (a) A’ on CO”~and (b) B’w-“~
on CU’/~.
(26) +
(Ek:--jEk,O)/(k;+
CO’),
(27)
where E = RT/n’F%k,; k, being the rate constant for crystallization and T, the concentration of adsorbed species. The presence of crystallisation rate control is likely to become evident[22] at high frequencies where the components of the diffusion impedance become relatively small and roughness effects are assumed to be absent. Hence, the case w B k, will be considered and
Electrochemistry of Ag in KOH
1495 0.5
200
-
150
.
-
/
I9
c 5
loo
-
/
.
.7 so
0
-
50
loo
I I50
Fig. 7. Impedance spectrum for the formation of Ag,O,
6
I 2(
at 0.5 V, 295 K.
(a)
I-/i, __ __ __ (b) 3-
Fig. 8. Frequency dependence of the admittanoe data for the formation of AgpOl at 0.5 V, 295 K. Dependence of (a) A’ on ~l’~, (b) B’o-~‘~ on UJI/~(c) A’w-’ on CL-~/’ (d) B’cL-’ on o-“* and (e) B’w-‘I* on w-*“.
(27) can then be rearranged
and inverted
to yield
w2 [ (uw3’2 +ek~)+j(~d~~+~&,w)] Yf = @IiT + akf)l + (ow~‘~ + ek,w)' .
(28)
For s,sufficiently high frequency, only terms containing co3 are retained in the denominator. Hence, the real
BRUCE
1496
G.
POUND,
Fig. 9. Equivalent circuit for the formation component of the overall admittance surface roughness) is given by
DKBY
of
D.
MACDONALD
for
which can be rewritten
(29)
The overall
imaginary
component
(30) is
“2 Ek B’=%+$+~w”~+wC~,, which
can be written
(31)
as (32)
or B’ -_= w
(
1 G+g
>
uJ-1’2+
(33)
&+C,,.
The frequency dependence of the faradaic series components For combined diffusion and crystallisation rate control [see (27)] has been represented diagrammatically by Vetter[22]. A’o-t and B’cu- ’ exhibit a similar frequency dependence to the corresponding impedance components in the absence of surface roughness. In this work, the high Frequency region of the A’w- ‘/w-Liz plot (Fig. Xc) is influenced by the roughness term &_I”-‘. However, the shape of the B’w “’ plot (Fig. 8d) is similar to the curve of the capacitative component, (WC,)-‘, as represented by
r/o-
40
/
-
.fly: 7k
TOMLINSON
The impedance spectrum in the complex plane for each potential changes with increasing temperature as shown by a comparison of Figs 5 and 10. These changes are dependent on the position of the particular potential in the active/passive regions[3] of the current/potential curve at that temperature. The major change is the appearance of a linear low frequency region in the complex plane at potentials in the passive region. The basic equivalent circuits used to represent the electrode impedance at 295 K are applicable at elevated temperatures. However, at potentials in the passive region, it is necessary to modify the equivalent circuit as suggested by the form of the admittance component plots, in particular the low frequency region as shown by the plot of B’o-‘/~ against w112 (Fig. 1 I b). Although some plots of B’w-“Z/w”zin the passive region are linear at high frequencies, generally this is not the case. It is more common for approximately constant values of B’w- ‘I2 to be exhibited at high frequencies probably reflecting very low values of the interfacial capacity at these potentials. However, the scatter of data does not permit an estimation of C,, in most cases. Deviations from the predicted behaviour imply that the equivalent circuit proposed at room temperature is no longer adequate. The observed behaviour may be associated with changes in the kinetics of oxide growth with an increase in temperature. Studies at room temperature by Briggs er al.[17] showed the three-dimensional
as
A &I? 1 -w = 20*,‘/2 +--+-teYr. 2uZw”
W.
of temperature
Effect A’ = g+22;+bw”,
.I~HN
Vetter. The similarity in the curves provides some justification for applying the expression for the crystallisation impedance to the present case. A’ is linearly dependent on o’/*, as predicted, over the frequency range shown in Fig. 8a. The two linear regions allow ur, ,rr, and therefore Co and XF to be obtained. Cdl is determined from the slope B’w- “* us WI” (Fig. gb) which, as might be expected from (32), is linear only at high frequencies. At lower frequencies. the crystahisation component becomes effective and B’W Ii2 as predicted is proportional to we r/r (Fig. Se). This linearity occurs in the frequency region corresponding to ,rr (Fig. Sa) and hence, 8k,/2c$ and c (the surface concentration of OH species in the steadystate) can be determined (Table 1).
Ag,O,.
(allowing
AND
\
--*
05. 680 I
C
‘\
s
if ‘i
30
-
l
l 360
\
\*,p*-‘*
/
8
02
I20 I
20 0
Fig.
50
10.
Impedance
loo
150
I 200
spectrum for the formation of Ag,O
250
at 0.3 V, 388 K
Electrochemistry
of Ag in KOH
1497
Fig. 11. Frequency dependence of the admittance data for the formation of A&O at 0.3 V, 388 K. Dependence of (a) A’ on III”~ (b) B’cI-“~ on w”~ and (c) E~‘w-“~ on w~“~.
growth of Ag,O cm centres formed on a primary layer of the oxide. These workers found that the ratedetermining process occurred not at the expanding interfaces of the growth centres but in the primary layer. However, an increasing rate of diffusion of species through the film with increasing temperature might cause the relative rate of a reaction step at the growing interfaces of the centres to become more significant. Nevertheless, it is likely that diffusion would remain the dominant influence in the overah rate control.
It is proposed that the impedance data at elevated temperatures be analyzed in terms of an equivalent circuit which makes provision for an impedance associated with the formation and growth of the oxide centres. Initially, it is assumed that, as for the formation of Ag,02 at room temperature, the crystallisation impedance required may be represented as having the frequency dependence shown in (27). Hence, the equivalent circuit shown in Fig. 9 is used to represent the electrode impedance under these conditions aithough, Z,, now relates to the growth of Ag,O nuclei.
BRUCE G. HOUND. D~GBY D. MACDONALD
1498
At this higher temperature (388 IL), the dependence of A’ on w”’ exhibits two linear regions at 0.3 V as shown in Fig. Ila. This behavior is simply due to the appearance of the low frequency Warburg region associated with diffusion of ionic species through the oxide layer. It is clear that the roughness term, bo”, must become significant at frequencies beyond those examined. According to (29), it is expected A’ would be proportional to l/w at low frequencies. In some cases, a temporary increase of A’ with a decrease in frequency was observed (see low frequency region of Fig. ila), but generally such a change is brief and a more detailed examination of the data was not possible. At low frequencies, B’w-“~ varies linearly with we’/’ (Fig. ilc), justifying the application of the equations for a crystallisation impedance to the present situation involving oxidecentres. The slope in this region is seen from Fig. 1 la to correspond to solid state diffusion and is given by .?k,/26;. Therefore, c, the surface concentration of adsorbed OH species for Ag,O formation can be evaluated. Equivalent circuit at 0.5 V, 348428
K
The impedance spectrum at 0.5 V, 388 K (Fig. 12) shows distinct changes in its form compared with the spectrumat 0.3 V, 388 K. At 0.5 V, it is likely that Ag,O growth centers will have overlapped to such an extent-
Fig. 12. Impedance
spectrum
+OH(ads)+e-,
adsorption of discharged OH- ions. The removal of the adsorbed species in subsequent steps as given by Hoare would correspond to a reaction impedance[22]. Consequently, inclusion of an impedance, Z0 associated with oxygen evolution, in the equivalent circuit would yield a complicated expression for the overall faradaic admittance. In order to simplify the analysis, it will be assumed that the initial charge transfer step (34) is slow and that the electrode impedance corresponding to oxygen evolution can be represented by a simple charge transfer resistance in the equivalent circuit. Hence, the real component of the admittance is given by
which clearly does not alter the frequency dependence of A’. The expression for the imaginary component as given by (31) remains unchanged. Two linear regions are exhibited by the A’/oi” plot (Fig. 14a), thereby demonstrating the presence of solid state diffusion at 0.5 V for elevated temperatures. Also, as predicted, B’w - ‘I2 is linearly dependent on w- Ii2 at low frequencies (Fig. 14c), thus allowingC (Ag,O,) to be determined for each temperature. From Fig. 14b, it is clear that B’w- ‘I* is not linearly dependent on o”* in the frequency range studied, therefore preventing the determination of Cdl in this case.
these conditions, both the formation of Ag,O oxygen evolution occw.
for 0.5 V, 388 K. Under
that the overall electrode impedance for oxide formation for this potential at elevated temperatures may still be considered in terms of the equivalent circuit in Fig. 9, that is, a Warburg impedance in series with a crystallisation impedance associated with the conversion of Ag,O to Ag,O,. Some modification is required, however, to the equivalent circuit for this potential at elevated temperatures since 0.5 V now lies in the region where oxygen evolution can occur at a significant rate[3]. Since oxide formation occurs simultaneously, oxygen evolution is assumed to take place in parallel as indicated in the equivalent circuit shown in Fig. 13. It has been suggested by Hoare[23] that the mechanism of oxygen evolution in alkaline solutions could involve an initial electrochemical step: OH-
AND JOHN W. TOMLINSON
(34)
which can be considered in terms of a charge transfer resistance, R OHand a pseudocapacity arising from the
and
=, 11,
Fig. 13. Equivalent circuit for OSV over the temperature range 348428 K. Z, is the impedance associated with oxygen evolution.
Electrochemistryof Ag in KOH
1499
Fig. 14. Frequency dependence of admittance data for OSV, 388K. Dependence of (a)A’ on w”’ (b) B’w-‘I’ on wl’z and (cc)B’o-I” on o-I”. DISCUSSION Effect
of potential
The effect of increasing the potential anodically is shown by the changes in the impedance parameters given in Table 1. The interfacial capacity achieves quite low values, particularly at potentials corresponding to film formation; for example, at 0.3 V and 295 K, C,, = 0.4 PFcm-‘. This trend is consistent with the potential dependence of C,, at room temperature
observed by Ciles et af.[7] following the formation ofa monolayer of Ag20. At potentials immediately prior to film formation, the measured capacitance is probably largely an adsorption pseudocapacitance arising from adsorption of OH- ions. When the oxide layer is present, the interfacial capacity is composed of (a) the capacity at the metal/film interphase, (b) the capacity of the film and (c) the capacity at the film/solution interphase. The low value of Cdl measured in this situation very likely reflects a substantial dielectric effect of the oxide.
1500
BRUCE G.POUND,
DIGBYD.
MACDONALDANDJOHN
Wherecomparison of data is possible, both XFand i? (Ag,O) are found to decrease with increasing potential up to 0.3 V. The low values of rare no doubt indicative ofthe extent to which overlap of the growth centres has taken place. At each temperature, uF is greater than Q, where a comparison is possible for a particular potential. This difference is to be expected since the diffusing Ag+ ions in the film have a smaller diffusion coefficient than AgO- in solution (see Table 2). Furthermore, the concentration of Ag+ at the metal/film interface is, for example, 2X,/V,,, = 2 x 3.9 x 10m5/32.7= 2.4 x 1o-6 mol crnm3 at 295 K, 0.3 V compared with 1.1 x 10m5 molcn-3 for CO, that is, approx. five times smaller. However, at 348 K, 0.3 V, C, and CF are comparable ( - 5 x 10m6molcm-3) but this is misleading because a decrease in C, occurs as the potential increases. The concentration of AgO- should remain constant following the formation of bulk Ag,O. Sucha decrease has been reported previously (7) and was attributed to an artifact arising from equating R,, to zero in the Randles circuit. Eflect of temperature As the temperature increases, C, at each potential generally increases except where a shift into the passive region occurs with the temperature change. XF, however, appears to pass through a maximum at 348K. The lack of a distinct crF in the A’/cu”’ plots for potentials up to 0.3 V at 428 K could be attributed to two factors. A higher rate of diffusion at this temperature coupled with a decreased thickness of the film due to a greater solubility of the oxide will reduce the significance of the solid state diffusion impedance. Nevertheless, the oT slope for these potentials does begin to change at low frequencies, thus identifying the commencement ofa (or region. In contrast, a distinct crF is observed at 478 K for 0.18 V. The surface concentration of Ag,O growth centres appears to decrease whereas T: (Ag,O,) exhibits a maximum in the region of 348 K and decreases at 388 and 428 K. This subsequent decrease probably reflects a higher degree of overlap of Ag,O, nuclei at a particular potential due to the increase in temperature. The double-layer capacity at least for the active region increases with temperature. The high values of Cdl at elevated temperatures in this region in which the dissolution reaction is reversible, may be attributed firstly to an increase, in the accumulation of ionic
W. TOMLINSON
species at the electrode surface with temperature (as shown by the values of C,), and secondly, to more extensive roughening of the surface by dissolution. The second factor is reflected in the increased values of the surface roughness coefficient, g (Table 3), which were determined from the plots of B’o- Ii2 tis IU’/~. REFERENCES B. G. Pound, D. D. Macdonald and J. W. Tomlinson, Efectrochim. Acta 24, 929 (1979). 2. B. G. Pound, D. D. Macdonald and J. W. Tomlinson, Elecrrochim. Acta 25. 563 119801. and J. W. Tomlinson, 3. B. G. Pound, D. D. ‘Ma&x& Electrochim. Acra 25, 1293 (1980). 4. E. Warburg, Ann. Physik. 6?, 493 (1899); 6, 125 (1901). 5. M. Sluyters-Rehback and J. ,H. Sluyters, in Electraanalyrical Chemistry (edited by A. J. Bard) 4, 1. Marcel I.
Dekker. New York (1970).
6. B. Timmer. M. Sluters-Rehback and J. H. Sluvters. J. electroanal,. Chem. 18, 93 (1968). 7. R. D. Giles, J. A. Harrison and H. R. Thirsk, J. electraana~, Chem. 22, 375 (1969) 8. B. V. Tilak, R. S. Perkins, H. A. Kozlowska and B. E. Conway, Electrochim. Acto 17, 1447 (1972). 9. R. De J&vie, Electrochim. Acrn 10, 113 (1965). 10. R. De Levic. Adv. Elecrrochem. Electrorhem. Emma I”, 6.329 (1967). ’ 11. H. S. Taylor, .I. them. Phys. 6, 331 (1938). 12. A. C. Riddford. .I. phvs. Chem. 56. 745 (1952). Sac. 117; 491 i1970). 13. B. Miller, .I. &&r&~em. 14. R. D. Armstrong and K. J. Edmondson, J. electraanal. Chem. 53, 371 (1974). 15. T. C. Clark, N. A. Hampson, J. R. Lee, J. R. Morley and 6. Scanlon, Can. J. Chem. 44, 3437 (1968). 16. N. D. Rozenblyum, N. C. Bubyreva, V. 1. Bukhareva and G..Z. Kazakevich, Zh.@ Khim. 40, 2467 (1966). 17. G. W. D. Briggs, M. Fleischmann, D. J. Lax and H. R. Thirsk, Trans. Faraday Sac. 64, 3 120 (1968). 18. M. Fleischmann, D. J. Lax and H. R. Thirsk, Trans. Faraday Sac. 64. 3137 (1968). 19. W. S. Graff and H. H. Stadelmaier, J. electrochem. Sot. 105, 446 (1958). 20. V. Scatturin and P. Betton, J. electrochem. SOC. 108, 819 (1961). 21. H. Gerischer, 2. phys. Chem. 198, 286 (1951). 22. K. J. Vetter, Elertrorhemical Kinetics. Academic Press, New York (1967). 23. J. P. Hoare, The Electrochemistry ofOxygen. Interscience, New York (1968). 24. C. Y. Chao, L. F. Lin and D. D. Macdonald, to be published.