KINETICTHEORY OF INHIBITION AND PASSIVATION I N ELECTROCHEMICAL REACTIONS
of nitroammine complexes of Co(II1) to polystyrenesulfonate were also studied, and the extent of binding was found to be much lower than with the phen complexes and to decrease with decreasing charge of the complex; the Co(en)zpyN0z2+and particularly the Co(bipy),(?;O&+ complex were much more strongly bound, suggesting that the existence of van der Waals forces or hydrophobic bonding's was more important than purely coulombic effects. Binding of phen complexes to the polymethacrylate anion was found to be considerably weaker than to the polystyrenesulfo-
1259
nate ,anion, as expected. Our results indicate that hydrophobic bonding is not an important factor in PVI .Cu(II) 'NTA complexes.
Acknowledgment. This investigation was supported in part by Public Health Service Research Grant GM 02934 from the division of General Medical Sciences, Public Health Service. (18) See, e.g., G. NBmethy and H . A . Scheraga, J. Chem. P h y s . , 36, 3401 (1962).
Kinetic Theory of Inhibition and Passivation in Electrochemical Reactions
by D. Gilroy and B. E. Conway Department of Chemistry, University of Ottawa, Ottawa, Canada
(Received October 19, 1964)
A kinetic theory of inhibition and passivation in anodic organic and metal dissolution reactions is given. Two types of cases arise. The first is one in which the inhibition results from effects of an inhibiting species, produced in a competing reaction, on the free available surface of the electrode and on the activation energy of the primary anodic reaction; the second case is one of self-inhibition which can arise in certain decompositions of adsorbed radicals, e.g., in the oxidation of the formate ion. A reversal of the direction of the log [current ]-potential relation is predicted, and the negative Tafel slope observed in the inhibition of an anodic reaction depends on its mechanism, on the isotherm for the inhibiting species, and on the number of electrons required for its production. Generally, the width, in units of electrode potential, of the region of normal and reverse Tafel behavior is determined by the magnitude of the interaction parameter f(0) in a Temkin type of isotherm for the adsorbed species. The sharpest current-potential relation is observed under Langmuir conditions. Application to several kinds of experimental results including passivation behavior at stainless steel indicates a sufficiently satisfactory agreement between theory and experiment that the general basis of the calculations is supported.
-
Introduction Most anodic reactions including metal dissolution,' organic oxidations, and even the oxidation of hydrogen2 exhibit inhibition or passivation effects. These effects are usually manifested in galvanostatic currentvoltage curves as transition regions3 where there is a relatively abrupt change of the current-potential relation from one Tafel region to another; in potentio-
static determinations they are manifested as limiting currents with reversal of the direction of the currentpotential relation. These effects, e.g., in hydrogen (1) N. Hackerman in "Surface Chemistry of Metals and Semiconductors," ed. by H . G . Gatos, J. W. Faust, and W. A . Lafleur, John Wiley and Sons, Inc., New York, N. Y., 1959, p. 313; see also P. V. Popat and N. Hackerman. J. P h y s . Chem.. 6 5 , 1201 (1961). (2) Ya. M . Kolotyrkin, Z . Elektrochem., 62, 664 (1958); see also M.Breiter, K . Franke, and C. A. Knorr, ibid.. 63, 226 (1959).
V o l u m e 69, Number 4
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D. GILROY AND B. E. CONWAY
1260
ionization,2 can be distinguished from those associated with diffusion limitation o f the rate, by this inversion; thus, diffusion limitation will tend to lead, under most condition^,^ only to a constant limiting current with increasing potential whereas a true passivation under potential control is associated with a region of decreasing- current with increasing- potential following the . attainment of a limiting critical current. The elements of a theory of these inhibition effects have been given in a brief form and it is the purpose of the present paper to examine the kinetic origin of inhibition or passivation effects in more quantitative detail with applications to several anodic reactions. The basis of this treatment will be as follows; an anodic reaction will be considered which is inhibited by the appearance of another species, competing for sites upon the metal electrode surface, the coverage of which by this species can vary with potential. Kolotyrkin2 has regarded the initiation of passivation as being associated with the appearance of a monolayer or less of an inhibiting species; Hackerman, et al.,l have studied the capacitative behavior of passive steel electrodes. In most cases, the inhibiting species will be a “surface” or “adsorbed” oxide, e.g., the entity MOH or RI0889 generated from aqueous solution, but in other cases to be examined, the inhibition may arise in the primary reaction itself; i.e., a self-passivation effect can occur. Of the recent work On electrocatalytic Oxidations has been carried out by nleans of the repetitive Potentiostatic voltage-scanning method1o in which the time- and potential-dependent Faradaic and pseudoFaradaic currents are recorded by means of an oscilloscope. These current-potential relations exhibit peaks which can arise in two ways: (a) fronl charging processes associated with the production or removal of adsorbed intermediate^,^^^" e.g., H, OH, 0, or organic radicals HC()O. , 3 CH~COO.,or CH, , in the Kolbe reaction3 and (b) from kinetic processes exhibiting inhibition effects as the potential is changed. In another paper,” we have dealt with the significance of the adsorption peaks and associated adsorption pseudocapacitance,12 observed in the voltage-sweep method and in the related differential galvanostatic technique.13 Here we shall examine the significance of Faradaic peaks in current-voltage curves and show how they can arise kinetically from inhibition effects in relation to the isotherm for adsorption of the intermediates involved.
Kinetic Relations Case i . A Discharge Step Inhibited b y a Competing Oxide or Similar Species. We consider the general reaction The Journal of Physical Chemistry
X-
+ M +AIX + e
(11
where X is an adsorbed radical produced from the anodic discharge of the ion X- (e.g., in the formate oxidation r e a c t i ~ n ) , ~and ~ l l competition for surface sites occurs between X and the OH species formed (e.g., see ref. 8 and 14) in a reaction such as
111
+ HzO
AIOH
+ H+ + e
(21
Alternatively, the MO species may be involved as considered in case iii. Following previous formulat i o n ~ of~ the ~ ~rate ~ ~equation , ~ ~ for reaction 1 under general Temkin conditionsl2Il6where both the rate and activation energy of reaction 1 depend on coverage through effects associated with the surface availability and interaction effects,” we can write
kT
il = F - KCx-(l - eoHj exp - [AGol* h
PJ‘F
+ (1 - @ f ( W R T
(3)
where f(0) is the Temkin parameterl2ql5 defining the rate of change of apparent standard free energy of adsorption18 of species on the surface with the total
(3) B. E. Conway and M . Dzieciuch, Can. J . Chem., 41, 21, 28, 55 (1963); Electrochim. Acta, 8 , 143 (1963). (4) An apparent exception might arise if, with increasing potential, conditions of diffusion control were initially reached but with further increase of potential, kinetic control were re-established owing to inhibition by competing adsorbed species. Other cases of anomalous Tafel behavior arise in reductions of anions, e . g . , S208 -2, but originate from well-known ionic double-layer effects and are quite different from the effects examined insthis paper. (5) (a) B. E. Conway, “Theory and Principles of Electrode I’rocesses,” Ronald Press. New York, N. Y . , 1964; (b) E. Gileadi and B. E. Conway, “Modern Aspects of Electrochemistry,” ed. by J. O’M. Bockris and B. E. Conway, Butterworth and Co., L t d . , London, 1964, Chapter V. (6) During publication of the work referred t o here,a similar principles have been proposed semiquantitatively by Bagotsky and Vasilev’ for certain organic oxidations and have been developed further in the present paper. (7) V. S. Bagotsky and Y. B. Vasilev, Electrochim. Acta, 9, 869 (1964). (8) J. O’M. Bockris, J . Chem. Phys., 24, 817 (1956); see alsoref. 21. (9) B. E. Conway and P. L. Bourgault, Can. J . Chem., 37, 292 (1959); 38, 1557 (1960); 40, 1690 (1962). (IO) F. Will and C. A. Knorr, Z.Elektrochem., 64, 258, 270 (1960). (11) B. E. Conway, H. A. Kozlowska. and E . Gileadi, J. Electrochem. Soc., in press; H. A. Kozlowska and B. E . Conway, in press. (12) B. E. Conway and E. Gileadi, Trans. Faraday SOC.,58, 2493 (1962); J. Chem. Phys., 39,3420 (1963); see also ref. 18. (13) H. A. Kozlowska and B. E. Conway, J . Electroanal. Chem., 7 , 109 (1964). (14) K. Vetter and D. Berndt, Z . Elektrochem.. 62, 378 (1958). (15) R. Parsons, Trans. Faraday SOC.,54, 1053 (1958). (16) A. N. Frumkin. 1’. Dolin, and B. V. Ershler, Acta Physicochim., 13, 779 (1940). (17) M. Boudart, J. A m . Chem. SOC.,74, 1531, 3556 (1952). (18) B. E. Conway and E. Gileadi, Can. J. Chem.. 42, 90 (1964).
KINETIC THEORY OF INHIBITION A N D PASSIVATION I N ELECTROCHEMICAL REACTIONS
+
coverage 0 ( = Ox @OH) according to the model of B ~ u d a r t ~ which ~ b l ~ we have applied to electrochemical kinetic problemsI2 previously. Also in eq. 3, V is the metal--solution Dotential difference and ionic doublelayer effects have been included in K for brevity (cf. ref. 12). Below the oxygen reversible potential, reaction 2 cannot proceed continuously and a quasiequilibrium will be set up in which the coverage by OH will be dependent on potential according to the electrochemical isotherm 00 H
1-
=
K~ exp
BOH
reaction) and -2RT/F (inhibited reaction). As a function of AV, using eq. 10 ii/ii,max = 2 exp[pAVF/RT]/(l
e x p [ - f ( e ) / ~ ~ l (4)
where Kz is a constant including the activity of the reactant in (2). ex will tend to be small if step 1 is rate-determining with respect to a following desorption step such as
(13)
Temkin Case. Here eq. 7 [cf. eq. 31 is written (cf. ref. 12, 15, 16) il
=
kl(1 - e) exP[pVF/RTl exp[-(l - @f(e)/RT]
and eq. 4 is used for 0. Proceeding as in the Langmuir case, elementary transformations lead to idil,max =
e
1-
1 - Omax
or (5) ii/ii,max =
or
RIX
+ X-+
M
+ Xz + e
=
kl(l -
e) exp[pVF/RT]
1-
(7)
where kl is a combined constant at constant X- and electrolyte concentration and
Then
e
emax
1-
(6)
Langmuir Case. Here eq. 3 is written il
+ exp[AVF/RT])
(14)
[E]
2RfX +x2
1261
(
)’-@
e/(i - e) emaX/(l- e,,,) exp[(2p - l)AVF/RT]
(
@/(I- e) &,,,/(I - e,,)
(15)
)p
~ X[ -P (1 -- 2 p ) f ( e ) / ~ ~ (16) i
which in the usual case of p = 0.5 gives again relations 11 and 12. Here, however, the shape of the il-V curve will not be identical with that obtained from eq. 12 and 13 for the Langniuir case since the variation of 0 from small values toward unity will now occur over a wider potential range20 determined by the magnitude of the general Temkin parameter f(0) in eq. 4 (see ref. 12). Kumerical evaluation of the functions in eq. 13 and 16 leads to the results shown in Figure 1 expressed on a relative current density scale. Case ii. Inhibition in a Heterogeneous Decomposition Step, M X + M Y M Z . Here the reaction scheme considered is
+
where i, is the maximum current in the inhibited process occurring at potential V,,, and coverage emax. Let AV = V - V,,,; then from eq. 8 B =
exp[pAVF/RT]
(10)
and substituting from eq. 9
By differentiation, Omax = p, so that Olnax = 0.5 when fl = 0..5, which leads to the symmetrical relation il/il,,,,
=
2e”2(i -
(12)
so that, the il-V curve is symmetrical with an inversion, i.e., with increasing potential two Tafel regions liniitingly arise with slopes of 2RT/F (normal discharge
+ X- +M X + e + M X RfY + hfZ
AT J!l
(17) (18)
where Y and 2 may subsequently be desorbed to give final products. An example of step 18 may arise in the oxidation of formate3 or in the Kolbe reaction3 (19) I n this representation of t h e origin of coverage-dependent energies of adsorption, the principal effects are attributed to “induced heterogeneity”1’ which can account to a large extent for observed changes of heats of adsorption with coverage. Elsewhere,l2 we have compared the results of such a treatment with those arising when the kinetics are treated in terms of intrinsic heterogeneity. I n the latter case, however, thef(6’) factors can be specific for each of the adsorbed radicals present, and the kinetic analysis is then more complex.9~12 This complication has not, we believe, been examined in the previous w o r k 7 * ’ ~in ~ 1which ~ t h e Temkin isotherm (based on intrinsic heterogeneity) has been used. (20) This potential range will also be related t o the range of potentials over which the adsorption pseudocapacity for OH is appreciable, as treated in our previous papers.12
Volume 69, Number
4 April
1966
1262
c
24-
D. GILROYAND B. E. CONWAY
-
I
f=20
U
2
(L
n
=
k5
KI K2 exp [VF/RT] (27) K2 (1 K2 ~ X ~ [ V F / R T ] ) ~
+
At low coverage by X and OH when K2 exp[VF/ R T ] > 1 and Ox is still ex, i.e., when K 2 (the electrochemical equilibrium constant for step 2) is greater than K1, 1-e+1-eOHand
1 --
e
=
(1
+ K2exp[VF/RT])-l
(25)
and for quasi-equilibrium in step 1
ex
==
K1 exp [VFIRT] Ki = - eoH 1 K2 exp[VF/RT] Ka
+
Hence The Journal of Physical Chemiatry
(26)
Figure 2. Theoretical current-potential relations for inhibition in a heterogeneous decomposition step of the type M MX -., MY MZ (calculated forf = 0, 5, 10, and 20RT).
+
+
The Temkin case corresponding to the above reaction sequence may be considered with reference to the rate equation for step 18 but now written in the form (ef. ref. 12, 18)
is = ksex(l - 6 ) exp[af(B)/RT] X exp[-W - a)f(e)/RTI (28) which gives, when the symmetry factor CY for effects of changing adsorption energy of X, Y, Z, and OH in the induced heterogeneity model” is taken as 0.5
is
=
k58~(1- 8) exp[-f(e)/2RT]
(29)
Following the same principles as before, the currentpotential curve can be. evaluated for this case as shown in Figure 2 for various values of f(0). Inhibition effects are again predicted. The width of the potential range associated with the inhibition effect will be closely related to the potential range over which the coverage by OH and its associated pseudocapacity12 are appreciable; this width will be deteriiiined by f(0) and may be estimated by methods reported previously.
KIFETICTHEORY OF IXHIBITION AXD PASSIVATION I N ELECTROCHEMICAL REACTIONS
(b) Case of Self-Inhibition. The reaction scheme 1, 18 is of special interest in that inhibition effects can also arise without any involvement of a competing species produced in a parallel reaction, e.g. (2). Since experimental behavior which could correspond to this case has been observed” in the oxidation of formate in a completely anhydrous medium (pure HCOOH), this example is of some particular interest. The rate equation is again (cf. eq. 2-2) = k&(l
i5
-
8)
(30)
where 8 refers to the total coverage. Since reaction 18 is rate-determining, BY and 8~ are small and hence 8 BX. Then
+
8
Kl exp [VFIRT]
-
- 1
+ K1exp[VF/RT]
1263
or
AIOH _r R 1 0
+ H+ + e
(37) In either case, the surface concentration of “ N O ” species in reaction 36 or 37 will depend on potential according to exp[2VF/RT], instead of exp[VF/RT] for reaction 2. Such a “higher oxide” species may arise a t higher anodic potentials, e.g., as at platinuin.14.21 If the electrochemical quasi-equilibrium is in favor of “MO,” inhibition will be niainly associated with such species and the Tafel line for an anodic process such as reaction 1 will then have a negative value of 2RT/3F instead of 2RT/F as in case i, i.e., an asginmetric current-potential relation with slope reversal will arise (Figure 4). When hysteresis in oxide formation
(31)
and 1-
e
=
(1
+ K1 exp[VF/RT])-’
(32)
instead of the result given by eq. 25. Hence k5K1 exp[VF/RT]
This result is analogous to eq. 27 and gives limiting Tafel slopes again of R T I F when K1 exp[VF/RT] > 1, i.e., a self-inhibition can arise without competition from a species produced in another reaction. The result under Temkin conditions is analogous and the currentpotential behavior is the same as that for case iia under corresponding conditions. (c) Immediate Desorption of the Reaction Products. Here reaction 18 is to be represented as
RI
+ MX +Y t + ZT
(34)
Two metal sites are considered necessary for decomposition of X as before. This changes the sign of the Temkin term in eq. 29 to give
i5= k58x(l - 8) exp[f(8)/2RT]
(35)
The resulting current-potential curves, shown ’ in Figure 3, are the mirror images, taken about lines of constant potential through the respective i,,,, of those in Figure 2. Case iii. Competition f r o m a Species Arising in a %Electron Quasi-equilibrium. Competitive effects associated with surface oxides may arise8 from equilibria of the type
M
+ HzO
2MOH
+ H+ + e If0 + HzO + h‘I MOH
(2) (36)
LOG [CURRENT DENSITY]
Figure 3. Theoretical current-potential relations for inhibition in a heterogeneous decomposition step of the type XI RIX --* Y Z with desorption of products (calculated for f = 0, 5, 10, and 20RT).
+
+
occurs as a t Pt, the shape of the In [ZI-V curve for a process such as reaction 1 may be different for the ascending (more anodic) direction of potential increase in a potentiostatic experiment and the descending direction, if there is a difference of surface oxide stoichiometry (or oxygen to metal atom ratio in the ad-layer) a t high and a t low potentials. This is the kind of behavior exhibited in a number of oxidations of organic substances, e.g., of formate ion a t P t in aqueous solutions. 11,22 If “higher” oxide formation (e.g., according to a reaction such as (36) or (37)) occurs at higher poten(21) S. Langer and J. Mayell, J . Electrochem. S O L . 111, 438 (1964): see also S. Gilman, Electrochim. Acta, 9, 1025 (1964). (22) A. Kutschker and W. Vielstich, ibid., 8, 985 (1963).
Volume 69, .%-umber
4
A p r i l 1965
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D. GILROYAND B. E. CONWAT
arise. 23 Similarly, under Temkin conditions, the same conclusion holds. When Ox >> OOH, the result is the same as that when no competing reaction is involved, and no inhibition effects arise. I t will be noted, however, that although definite passivation effects are riot predicted for this case, the effect of potential-dependent coverage by another species is to increase the Tafel slope from the value it would normally have (viz. RT/(1 P)F in the above case), i.e., the process is made more irreversible. Relation to Experimental Behaviol.. Elsewhere,y,ll we have examined the kinetics of oxidation of formate ion in aqueous and anhydrous formic acid solutions and discussed the evidence for the mechanisms (19), (20), (21), and the electrochemical desorption of MHCOO. In aqueous solutions at P t , a symmetrical ascending current-potential curve exhibiting inhibition arises” over a range of potential of about 0.8 v. This can be fitted with remarkable exactness by a single value of the parameter f(0) = 1SRT (see Figure 5 ) over a range of 0.8 v.24 Similarly, the data of Bagotsky and Vasilev7 for formic acid oxidation in phosphate buffer pH 4.26 can be fitted with f(0) = 6RT over 0.7 v. (Figure 6). The remarkably good agreement between the form of the experimental and theoretical relations lends strong support to the basis of the present theory of inhibition effects and the significance of the heterogeneity effects taken into account in the theory through the parameter f(O). The fit of the theoretical relation to the experimental points round a curve is a more exacting test of the kinetic equations than comparison of predicted and experimental Tafel slopes. In the aqueous formate oxidation, the descending current-potential line has a smaller negative slope than the ascending one, suggesting a more sensitive dependence of the coverage by oxide species on potential than is the case in the ascending direction. This effect may be associated with the role of a higher oxide (cf. reactions 36 and 37) in the inhibition process, as discussed above. In most inhibition processes involving organic oxidations, a further current-potential relation exists
+
O
1
I
L
0 001
I
ma.
LOG
001 4 mo. (CURRENT
01 I m o i
I I
mol.
DENSITY)
Figure 4. Theomtiqd current-potential relations for inhibition in a diecharge step inhibited by an adsorbed species produced in a two-electron equilibrium.
tials and there is hysteresis with regard to the range of potentials over which such an oxide is formed and reduced, the descending current-potential curve for an oxidation such as (1) should have a lower negative slope in its region of reversal of slope than that observed in the ascending direction. The critical maximum current will also tend to be larger as observed. The exact kinetic behavior for a step such as (1) will obviously depend on the details of the electrochemical isotherm for adsorption of oxide species in the directions of ascending and descending potentials. Case iv. Llischarge of a n Intermediate Radical by a n Electrochemical Mechanism. Here the scheme
X-
+ M -+
MX --t
+e Y+ + Z + e MX
(1)
(38)
is considered. Such a reaction can occur in the electrochemical desorption of formate radicals in formate oxidationa
MHCOO + M
+ H+ + COz + e
(39)
Self-inhibition obviously will not arise in this case. In the case of inhibition by MOH from (2), (eo= >> 0,)
ex
=
K1 exp[VF/RT] 1 K z exp[VF/RT]
+
+
and the rate equation for reaction 38 is
ilo= kloex exp[pVF/RT]
=
+
h0K1exp[(l P)VF/RTl 1 Kzexp[VF/RT]
+
+
(41)
from which it is clear that no passivation effects can The Journal of Physical Chemistry
(23) If a two-electron equilibrium is involved in the production of the passivating competitor, e.g., by steps 36 or 37. then step 38 can he inhibited giving a forward Tafel slope of E T ’(1 p ) ( 0 0 1 aad K2eVF/RT > K2K9e2 As the surface is further oxidized with increasing potential, K2K9e2V F / > K2eVF/RT > l and a Tafel slope of -2RTIF is obtained. Thus step 42 has a critical passivation region which can have the appearance of a “limiting current” when the current-potential peak is broadened under Temkin conditions. Addition of il and ill can therefore explain the experimentaJ results depicted in Figure 5 . At higher potentials, eo 1 and the current for reaction 43 is --+
(25) This conclusion differs from t h a t proposed by Bagotsky and Vasilev,? who regard t h e same reaction as proceeding throughout t h e potential range on a surface the“ properties of which vary with its oxidation. On such a theory, it is difficult t o see how increases of current can arise beyond a region in which current was previously decreasing with more anodic potentials.
Vohme 69, Number
4
April 1966
1266
D. GILROYAND B. E. CONWAY
ilz = klzBoesVF/RTCHCOO -
- klzePVF/RT -
whence (45)
CHCOO -
with a Tafel slope of 2RT/F, as observed." The overall scheme of reactions is then as shown in Figure 7. Case v. Passivation in Metal Dissolution. The present treatment can be extended to metal passivation. As mentioned above, Kolotyrkin2 has argued that the initiation of passivation is associated with a monolayer or less of some species which inhibits the
(53) Kl3K14 exp [2El
+ K13K14K15 exp [ 3 E ]
where K13 and K14 are equilibrium constants for steps 46 and 47, respectively. If coverage only by oxides up to the formal divalent state is involved, then eq. 53 has only the first three terms in its denominator. If step 49 is the process that leads to net dissolution of iron,z8the rate of corrosion is 216
= kl& exp [PEI =
ha13
[exp(l
-I
?
+ P)EI[A + B exp(E) + C exp(2E)
5
ti 0 W
5 [M+ H$ e M O H + H*+ a]
Log i
Figure 7. Over-all scheme of consecutive and alternative reactions in formate oxidation (theoretical).
process of dissolution of metal atoms (or adions26) from the lattice.27 The following scheme for the initiation of passivstion of iron is considered (46)
(48)
(47)
- (el
+ et + el)
e'
J(48)
Fe(OH).,+
e:
+e
de/dt
=
0;c
ea
(46-49)
where FeOH, Fe(OH)2, Fe(OH)3 are the initially inhibiting oxide species at coverages &, 02, and e3 arising in the anodic attack of iron. Denoting VFIRT by E for brevity, the steady-state condition for the corrosion oxidation gives
oi(a)
E; 0
I
50
I
6 2
01 01
E 0.20.2
$
8 0303 ( a ) _I
04 046 -6
-5
-4 -3 -3 LOG [CURRENT DENSITY] aa.cm-' cm-'
-2
(50)
Figure 8. Current-potential relations for passivation of a stainless steel (from Greene and Leonard2Q). Slopes in mv. &s indicated.
(51)
(1961).
kl5& exp[PE] - k-1583exp[- (1 - @ ) E ]= 0
(54)
where i l a and kl6 refer to step 49, and A , B, C, D; are combined constants defined by comparison of eq. 54 with eq. 53. From eq. 54, it is clear that a passivation is accounted for, since, limitingly at high V , the minimum negative Tafel slope is -40 mv., i.e., [- RT/(2 - P ) F ] ,and a t low V , +40 mv., when p = 0.5, i.e., a reversal of slope and a critical current arises. Higher negative slopes may arise depending on the relative values of the terms in the denominator of eq. 54. Relation to Experimental Results. Passivation of 304 stainless steel has recently been examined potentiostatically by Greene and Leonardz9a t various sweep
Fe -+ FeOH --+Fe(OH)2 +Fe(OH)3 1
+ D exp(3E)I-l
I
or
e3 = K15e2exp [El
(26) B. E. Conway and J. O'M. Bockris, Electrochim. Acta, 3 , 340
where the rate constants k16 and k-16, and the equilibrium constant K16 refer to step 48. Similarly
e2 = K1&
exp[E]; e3 = K14K16el expI2EI
The Journal of Physical Chemistry
(52)
(27) Energetically, this may arise because (a) the metal atoms in the surface are stabilized by the presence of the ad-species, and (b) the local field influencing the removal of lattice atoms is changed on account of the dipole potential difference associated with the adsorption of passivating species, e.g., 0, or OH (cf. ref. 3 , 17). (28) J. O'M. Bockris, D . Drasic, and A. R. Despic. Electroehim. Acta,, 4, 325 (1961).
KINETICTHEORY OF INHIBITION A N D PASSIVATION IN ELECTROCHEMICAL REACTIONS
rates in 1 N HZSO, a t 25”. The lower Tafel slope has a value of 40-4*5 mv. and the slope in the current reversal region varies from -50 to -260 niv. depending on sweep rate. The highest sweep rate is 720 v. hr.-l and this gives the highest negative slope (-260 mv.) and the highest critical current (Figure 8). The lowest sweep rate gives reversed slopes of -50 to -62 niv. and lower critical passivation currents. This is as expected; the lower sweep rates allow more time for the inhibiting oxide layer to grow or for the higher valent species to be formed which could lead to lower negative slopes ( c f . eq. 54). The initiation of passivation considered here will be expected to be associated with different effects from those arising with the normally thicker, steady-state passive film on iron, under aqueous aerated conditions. Case vi. Inhibition in a “Chemical” Step. It has been suggestedM that the oxidation of certain hydrocarbons occurs through a “chemical” reaction between the organic substance R and an electrochemi-
1267
cally formed oxide species, cf. reactions 42 and 43. Various special cases can arise for this mechanism depending on coverage by R and the oxide species but when reactions 2, 36, or 37 are involved, an inhibition effect and reversal of Tafel lines will occur in a symmetrical manner (cf., cases i and iia) with slopes of =k RT/F and fRTI2F; such low slopes are, however, not observed in hydrocarbon oxidation at platinum. 30 Acknowledgment. Grateful acknowledgment is made to the Defence Reseafch Board for support of this and related work on organic oxidation reactions on Grant No. 5412-01. We are also indebted to the U. S. Army Research and Development Laboratories for Contract MP 70 AI-63-4 on hydrocarbon oxidation studies. D. G. acknowledges the award of a postdoctoral fellowship. (29) N. D. Greene and R . B. Leonard, Electrochim. Acta, 9, 45 (1964). (30) H . Wroblowa, B. J. Piersma, and J. O’M. Bockris, J. Electroanal. Chem., 6, 401 (1963).
Volume 69, Number 4
April 1965
