Transpassivity of molybdenum in H2SO4 solution

JOURNAL O~

ELSEVIER

Journal of Electroanalytical Chemistry 381 (1995) 123-131

Transpassivity of molybdenum in H 2 S O 4 solution M. Bojinov a, I. Betova a, R. Raicheff b a Central Laboratory of Electrochemical Power Sources, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria b Department of Electrochemical Engineering and Corrosion Protection, Higher Institute of Chemical Technology, 1156 Sofia, Bulgaria Received 31 January 1994; in revised form 24 June 1994

Abstract

The anodic oxidation of molybdenum in H 2 S O 4 solutions (0.5-5.0 M) was studied, emphasizing transpassive dissolution. Voltammetric experiments indicated that transpassive dissolution was kinetically controlled, and that a secondary passivation process took place under transport control. Steady state polarization curves in the transpassive dissolution region exhibited a two-slope Tafel-like behaviour, suggesting the concurrence of two parallel reaction paths. Ac impedance measurements revealed a total of four time constants, implying the existence of three stable reaction intermediates. A quantitative model of the interface, comprising five reaction steps involved in two parallel pathways, is proposed. This model is able to reproduce both the stationary polarization curve and the general features of the impedance spectra.

Keywords: Anodic oxidation; Transpassive dissolution; Molybdenum;

1. Introduction

Molybdenum is one of the most important constituents of stainless steels. It is known to improve the resistance of these alloys to localized corrosive attack in media containing aggressive anions. Although the general cause of localized corrosion is believed to be the rupture of the native passive film on the metal surface, no quantitative mechanism of this process has been proposed. Several years ago, Macdonald and coworkers [1-6] developed the point defect model (PDM) for the growth and chemical breakdown of passive films on metals. This model has been used in attempts to understand the mechanism underlying the effects of alloying elements, such as Mo or W, on the resistance of stainless steels to localized attack, which resulted in the development of the solute-vacancy interaction model (SVIM) [7,8]. In order to obtain more information on the electrochemical behaviour of an alloy, it is useful to study the electrochemistry of the pure metal constituents first. Using this approach, we have obtained useful results for Pb + Sb [9-14] and Pb + Sn [15-17] alloys. The electrochemistry of iron and chromium in acid solutions has been thoroughly studied in both steady state and transient conditions. However, there have been relatively few investigations of the behaviour of 0022-0728/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0 0 2 2 - 0 7 2 8 ( 9 4 ) 0 3 6 7 5 - 6

H 2 S O 4 solutions

molybdenum in acid solutions [18-29]. Koenig and Gohr [18] divided the polarization curve of the metal into three potential regions: in the most negative, hydrogen evolution proceeds on the electrode; in the middle zone a layer of M o O 2, leading to passivity, is formed through which Mo diffuses into the solution; in the high potential region, the M o O 2 layer is transformed to MoO 3 and Mo dissolves to form molybdate ions. H e u m a n n and Hauck [19] and Wikstrom and Nobe [20] proposed that the limiting step of Mo oxidation was the transition from the quadrivalent to the hexavalent state in the anodic layer. Hull [21] performed an extensive study of the electrochemistry of Mo using cyclic voltammetry combined with the rotating ring-disc electrode technique. Hull assumed that, in acid media, the electrode surface was always covered with an oxide film. The active-to-passive transition was attributed to a change in the character a n d / o r the chemical composition of the passive film (according to the p o t e n t i a l - p H diagram [22,32] a transition from M o O 2 to M o O 3 is expected). General mechanisms were postulated by Hull for the "active" region (MoO2-covered electrode), the transition region and the "passive" region (MoO3-based film and soluble molybdate species). According to Hull, two types of surface films and two soluble intermediates were formed in the potential range investigated.

124

M. Bojinov et al. /Journal of Electroanalytical Chemistry 381 (1995) 123-131

Investigations of the electrochemical behaviour of Mo combined with X-ray photoelectron spectroscopy (XPS) analyses of the anodic layer have been conducted by Kozhevnikov et al. [23] and by Olefjord and coworkers [24-26]. The XPS results for the open-circuit corrosion of a (100) single-crystal face of Mo in H 2 S O 4 [26] were interpreted by a chemisorption passivation mechanism; at more positive potentials in the transpassive region, a continuous film of a mixed-valency oxide was formed. These interpretations disagreed with the results of Uergen et al. [27], who claimed that a three-dimensional film was formed both at open circuit and during oxidation in acidic chloride solutions. The cathodic and anodic behaviour of Mo in sulphate solutions over a range of p H values (1-10) has recently been studied by Batrakov et al. [28,29]. A multistep mechanism of oxidation with a rate-determining chemical step was proposed on the basis of steady state polarization measurements. The open-circuit potential of Mo in these media was believed to be consistent with the presence of a M o O ( O H ) 2 oxide on the electrode surface [29]. Impedance measurements of the anodic behaviour of Mo in alkaline media have been performed by Armstrong et al. [31]. A qualitative examination of the results showed that each new type of film (with a valence state between III and VI as determined by XPS measurements [32]) was associated with a different shape of the impedance spectrum [31]. It was assumed that the anodic layers were conductive and that the impedance characteristic was due solely to the film Isolution interface. Thus there is lack of information concerning the detailed mechanism of the processes on the Mo electrode in acidic media during transpassivity and secondary passivation. The aim of this p a p e r is to present experimental data on the transpassive dissolution process which were obtained using linear sweep voltammetry, potentiostatic measurements and ac impedance spectroscopy. A model of the interface during the oxidation of Mo is also presented.

three-electrode cell was used with a large platinum sheet as the counter-electrode and a saturated mercury sulphate electrode as the reference (0.67 V vs. standard hydrogen electrode (SHE)). All the potentials in the present paper are quoted with respect to this reference electrode. The electrolytes (0.5-5.0 M H 2 S O a) were prepared from p.a. H 2 S O 4 and double-distilled water. The experiments were conducted at room temperature (20 _+ I°C) in aerated solutions. 2.2. Apparatus and procedure The steady state potentiostatic measurements and linear sweep voltammetry were carried out using M270 Electrochemical Software (Princeton Applied Research) with a P A R M273 potentiostat and an IBM XT computer. All the values of the potentials were corrected for IR drop. The ac impedance measurements were performed using M378 Electrochemical Impedance Software (Princeton Applied Research) with the M273 potentiostat and a P A R 5301 lock-in amplifier. The frequency range was typically between 0.01 Hz and 100 kHz with an ac signal amplitude of 2 mV (rms). The resulting impedance spectra were numerically processed using the Equivalent Circuit program [33] in order to obtain best-fit values of the circuit elements.

3. Results 3.1. Cyclic uoltammetry A set of cyclic voltammograms for a Mo electrode in aerated 1 M H2SO 4 obtained at different scan rates are presented in Fig. 1.

Mo + 1.8 1.0

2. Experimental

1 M H_S0 4

q

...... 2 0 IIIV/S ...................... 4 0 r n V / s

0.5

100 .

-

. _ - , ~ " ' ~~ " ~~ ' " . , . . . _ ] ' . ' . : ~

,

w

~

~

2.1. Electrodes and electrolytes ~. Wire and disc electrodes made of pure molybdenum (99.9%, Koch) were used. They were insulated in acidresistant epoxy resin such that an area of 0.6 cm 2 was exposed to the electrolyte. Mechanical polishing with fine-grade emery paper, degreasing with ethanol and rinsing with distilled water followed by cathodic polarization in the hydrogen evolution region was found to give the most reproducible results. A conventional

0

-0.05 -0.10 -1.0

' -0'.6

' -0'.2

'

012 E/\'

'

016

'

110

'

114

Fig. 1. Cyclic voltammograms of a Mo electrode in 1 M H2SO 4 obtained at different scan rates. Note the tenfold scale increase for the cathodic currents.

125

M. Bojinoc et al. /Journal of Electroanalytical Chemistry 381 (1995) 123-131

In the positive sweep a fast current rise is observed for potentials above - 0 . 1 V. R e g i o n I, in which the current is i n d e p e n d e n t of sweep rate, is followed by an anodic p e a k II whose height d e p e n d s on sweep rate. T h e current then decreases steeply until it reaches a quasi-constant value (region III). A relatively small peak whose height also increases with sweep rate is observed on the negative scan (note the change in current scale in Fig. 1). T h e current then drops to very small values and hydrogen evolution begins. T h e d e p e n d e n c e s of the characteristic p a r a m e t e r s of the anodic and cathodic peaks (Jpa, Epa, Jpc and Epc) on scan rate in the range 0.01-0.1 V s -1 are shown in Figs. 2 and 3. The regression equations describing these d e p e n d e n c e s are also given in the figures. The height of the anodic p e a k d e p e n d s linearly on the square root of the sweep rate, providing evidence for a transport-limited passivation process (Fig. 2(a)). A similar d e p e n d e n c e is observed for the cathodic peak, indicating that the film reduction is also transport limited (Fig. 3(a)). T h e anodic and cathodic peak potentials d e p e n d linearly on the logarithm of the sweep rate (Figs. 2(b) and 3(b)). These results, together with the existence of a relatively wide potential region in

Mo +

1 M H eSO 4

-jpc = -0.035 + 0.420 v 1/2 100

q 66

33 a

0

0.1

0.i4

0.i8

0.32

0.~6

o'.3

( v / V s - ' )1/2 Epc = - O.064 - 0.054 lnv

0.18 -

>0.12 & UJ

0.06 -4.8

-4.4

-4

-3.6

-3.2

-2.8

-2.4

In ( v / V s - ' )

Mo + 1 M II,$0 4 Jpa = 0.63 + 2.73 v 1/2 1.6E

<

Fig. 3. Dependence of (a) the current density Jpc and (b) the peak potential Epc of the cathodic peak in the voltammograms of Fig. 1 on sweep rate•

a

1.4-

which the current is i n d e p e n d e n t of sweep rate (Fig. 1), suggest a mixed charge t r a n s f e r - d i f f u s i o n m e c h a n i s m for the overall oxidation process.

--...

~- 1.21.00.8 0.1

0.14

0.18

0.22

0.26

0.3

Mo +

1 M n 2S 0 4

(v/Vs-~) I/2 Qc / Qa = - 0.005 + 0 . 0 6 7 5 v 1/2

E

p a

= 1 . 8 8 2 + 0 . 1 8 9 lnv :

0.016

1.4-

>

1.3-

O

0.01

;o

w~- 1.2-

0.005

1.1 1 -4.8

m

-4.4

-4

-3.6

-3.2

-2.8

-2.4

In (v / Vs -1) Fig. 2. Dependence of (a) the current density jp. and (b) the peak potential Epa of the anodic peak in the voltammograms of Fig. 1 on sweep rate•

0.1

0.i4

0.i8

0.22

0.~6

0'.3

(vi/2/Vs-,) I/2 Fig. 4. Dependence of the ratio of the charge Qc in the cathodic peak to the total anodic charge Qa on sweep rate.

M. Bojinov et al. /Journal of Electroanalytical Chemistry 381 (1995) 123-131

126

The dependence of the ratio of the charge Qc in the cathodic peak to the total anodic charge Qa on sweep rate is presented in Fig. 4. This figure shows that the higher the sweep rate, the greater is the amount of oxidation product reduced during the reverse scan. If it is assumed that the cathodic charge is due to the reduction of the anodic film, it can be concluded that the relative amount of solid product formed during the positive sweep is quite small, and does not exceed 1.5% of the total amount of oxidation products (i.e. most of the products formed during the oxidation of Mo are soluble). The apparent Tafel slopes of the anodic passivation and cathodic reduction reactions can be deduced from the dependences of Epa and Eoc on In ~,. The values obtained a r e b a = 0.78 V and b c = 0.25 V, which are quite high and are commonly observed for film-covered electrodes [5].

Typical steady state potentiostatic polarization curves obtained for a Mo electrode in 0.5-3 M H z S O 4 in the transpassive dissolution region are presented in Fig. 5. In the low potential region ( E < 0 V), polariza-

0 . 5 M H2S04

2 M H2S0 4

4

0

0 -2

-1

-0.2

<~,~

-0.1

0 E/V

0.1

-4 0.2 -0.3

-6.1

E/

1 M H2$04

V

o'.1

3 M t12S0 4

2f

©

2

o,18 0.6 0.4 O.

1

11

1

[~

1

3

5

7

9

1,8

2,6

3.4

4.2

5

0.4 0.3 0,4

11

0.2

O.

.1

0.1

1.9

2.3

2,7

31

3.5

39

18"

2

22

2.4

2,6

2.8

2 I

o,1

2.1

2,3

2.5

2.7

2.9

Re(X) / g2 Fig. 6. A set of complex plane impedance spectra for a Mo electrode in 0.5 M H2SO 4 (frequencies in hertz).

3.2. Steady state polarization curves

1

Mo + 0 . 5 M H 2 S 0 4

0 -2

tion for about 1 h is necessary to reach a stationary current density at a given potential, whereas a few minutes are sufficient at higher potentials. At potentials above 0.2 V, the current density was so high that a rapid change in the electrode surface prevented accurate measurement. Thus in this work we restricted our investigations to the potential region below 0.2 V. The polarization curves of Mo in 0.5-3 M H 2 S O 4 are qualitatively similar (Fig. 5). They can be divided in three regions: (1) the first Tafel region ( - 0 . 3 to - 0 . 0 7 V) where the logarithm of the current j varies linearly with potential E; (2) the transition region ( - 0 . 0 7 to 0 V) where a pronounced curvature is observed in the log j - E curves; (3) the second Tafel region (above 0 V) where the current increases slowly with potential. There are some quantitative differences between the acid solutions used: in more dilute solutions the current is somewhat higher in the first Tafel region, whereas in the more concentrated solutions it is slightly higher in both the transition and the second Tafel regions. Tafe! coefficients of 0.05 _+ 0.005 V and 0.20 +_ 0.05 V were calculated from the linear parts of all polarization curves in regions (1) and (3) respectively, suggesting that the Mo oxidation mechanism is independent of acid concentration.

-2

3.3. A c impedance measurements -0.3

-0.2

-0.1 0 E/ V

-4

0.1 -0.3

,

,

,

-0.2

,

,

,

-0.1

,

0

,

0.1

E/V

Fig. 5. Steady state potentiostatic polarization curves in Tafel coordinates for a Mo electrode in 0.5-3.0 M H2SO 4.

Impedance measurements of a Mo electrode in 0.55.0 M H 2 S O 4 w e r e performed in the potential range from - 0 . 3 to 0.2 V after a stationary current density

M. Bojinov et al. /Journal of Electroanalytical Chemistry 381 (1995) 123-131

Mo + 3 M H2SO 4 -200/

l0 -2,

o1' ,5"IL _0.07,,

::y, oo 0

B 400

-1'8 1

0

1

2

4

5

6

7

0.05 V "0' I-0,6 9

"1'21

-0.03 V

10

0~1 ho~ ~

3

,

,,5

2,5

030'~3,5

0 -0,3

-0,6

-0,2

0

0 O

1,5

2

2,5

1k

-0,1

I00

-0,2

1

0.10 V

0.03 V

..0,4

0,5

~

10

lOk 1

0,1

L 10 D B

[

0,2 ~,4'

o',5

' o:3

'

i

'

1,2

Re(Z)

0'20,5 0,6 0,7 0,8

0,9

/

Fig. 7. A set of complex plane impedance spectra for a Mo electrode in 3.0 M H2SO 4 (frequencies in hertz).

had been reached. Once this condition had been satisfied, no significant dependence of the impedance spectra on the polarization time was observed; thus the spectra could be assumed to be stationary. Impedance spectra for the Mo electrode in 0.5 M and 3.0 M H2SO 4 are presented in Figs. 6 and 7. Qualitatively similar responses were found throughout the acid concentration range investigated (0.5-5.0 M). The shapes of the impedance spectra depend strongly on the electrode potential. The existence of the three potential regions proposed above on the basis of steady state measurements is confirmed by these results. At the open-circuit potential ( - 0 . 3 5 _+ 0.05 V, not shown in Figs. 6 and 7) a single capacitive loop A with a large diameter is observed, indicating that the corrosion reaction is very slow. At potentials more positive than - 0 . 2 5 V, an additional low frequency pseudo-inductive loop B is observed (Figs. 6 and 7), suggesting a two-step process with an adsorbed intermediate (first Tafel region). At - 0 . 1 V, a distorted high frequency capacitive loop C appears (transition region). This loop becomes dominant for potentials more positive than - 0 . 0 5 V, and in the same potential range an extra pseudo-inductive loop D appears, which is very evident at E > 0 V (second Tafel region) (Figs. 6 and 7). Thus a total of four time constants--two capacitive (A and C) and two pseudo-inductive (B and D) were observed over the potential range studied. It can be assumed that the appearance of a high frequency capacitive time constant implies a change in the proper-

127

ties a n d / o r chemical composition of the passive film, whereas the lowest frequency time constant is probably due to a further reaction intermediate in the second Tafel-like region. Because the two capacitive semicircles at high frequencies (A and C) overlap significantly, it was not possible to determine their resistances separately with sufficient accuracy. Thus we denote the sum of the resistances of these two capacitive loops as R t (charge transfer resistance), and the resistances of the two low frequency pseudo-inductive loops (B and D) as - R 2 and - R 3 , respectively. The dependences of these resistances on potential for all acid concentrations investigated are shown in Tafel coordinates in Figs. 8 and 9. These dependences provide further confirmation of the potential regions defined above. In the first Tafel region, both log R t and l o g ( - R 2) depend linearly on the applied potential. The curvature observed at higher potentials is directly related to the appearance of the second capacitive time constant (Figs. 6 and 7). The appearance of the third potential region correlates well with the detection of the resistance - R 3 of the second inductive loop (Figs. 8 and 9). The different slopes of the log Rt-E and l o g ( - R z ) - E dependences again sug-

Mo + 0 . 5 M H 2 S 0 4

j/mA.cm .o -R2/Q, Rt/O,

i 4

•

/

/

~

o

°.

o

o

"2

~* : o

i 1

-2

-o.2

-o.i

©

6

o'.i

E/V

o.a

Mo + 1 M HaSO 4 4

~ <

~

•

j / mA.cm "2

~'

" R2]

..~

~2--20 -o.3

£a

£i

6

o.1

E/V Fig. 8. Potential dependences of the resistances R t ( + ) , - R 2 (~) and - R 3 ( & ) in Tafel coordinates for a Mo electrode in 0.5 M and 1.0 M H 2S O 4. The stationary polarization curve ( B ) is included for comparison.

M. Bojinov et al. /Journal of Electroanalytical Chemistry 381 (1995) 123-131

128

Mo + 2 M H 2 S 0 4 • + o

4-

j / mA.em -2 Rt/~ - R2 / ,f],

-2 ~-4

-dl

-0.3

Mo+

2-. o

E/V 3 M tt2S0 4 • + o

4 .

'

%

oh

j / mA.em -2 Rt / ' f ) ' - R~) / g),

0-

-4

-0a

-0'2

-dl

6

01

E/V Fig. 9. P o t e n t i a l d e p e n d e n c e s o f t h e r e s i s t a n c e s R t ( + ) , - R 2 (O) a n d - R 3 ( ~ ) in T a f e l c o o r d i n a t e s f o r a M o e l e c t r o d e in 2.0 M a n d 3.0 M H 2 S O 4. T h e s t a t i o n a r y p o l a r i z a t i o n c u r v e (11) is i n c l u d e d for

ing soluble species of the metal in its highest valence state. A model of the interface during the transpassivity of Mo in H 2 S O 4 solutions must be consistent with the following experimental observations: (1) a two-slope Tafel-like steady state polarization curve suggesting two parallel reaction paths, one dominant below - 0 . 1 V and the other dominant above - 0.03 V; (2) a total of four time constants in the impedance spectra, suggesting the existence of three stable reaction intermediates; (3) a change in the shape of the impedance spectra from that characteristic of two time constants to those characteristic of three and four time constants which occurs at the transition potentials between the three regions of the polarization curve ( - 0.1 V and - 0 . 0 3 V respectively); (4) an effective lack of dependence of both steady state and impedance results on pH and H z S O 4 c o n c e n t r a t i o n , implying that neither H + nor SO 2+ influence the transpassive dissolution mechanism. Several models have been tested according to the procedure described by Keddam et al. [37] and Bai and Conway [38,39]. The model which was able to reproduce both the steady state polarization curve and the general features of the impedance spectra was found to be: Mo

oV):d . <

comparison.

kl

. gest that these resistances are identified with different stages of the oxidation process. The Tafel coefficients of the corresponding stages were calculated from the products 2.3RtI and - 2 . 3 R 2 I (both products are independent of electrode potential within experimental precision) and were found to be b t = 0 . 0 5 0 - t - 0 . 0 2 g and b 2 = 0.035 + 0.01 V. The resistance R 3 slowly decreases with potential in the second Tafel region.

4. D i s c u s s i o n

4.1. A physical model of the interface during transpassive dissolution Both the literature data and the results reported here indicate the complexity of the processes taking place during the oxidation of Mo in acid solutions. It is frequently claimed [34-36] that transpassivity of metals is due to a change in the nature a n d / o r chemical composition of the passive film leading to the formation of conductive layers which then dissolve, produc-

> Mo(III)

' Mo(IV).~

k~'

Mo(VI)sol

k% -2 Mo(V)a d Since neither the steady state data nor the impedance spectra provided any information about the chemical nature of the species involved, in accordance with the suggestions of Bai and Conway [38] we preferred to use this skeletal presentation of the model. A physical model consistent with the above scheme is proposed below. (1) It is assumed that, at open circuit, the Mo is almost completely covered with a Mo(III) species (either a chemisorbed layer or a thin oxide-hydroxide film [23-29,32]) which is oxidized to Mo(IV) (step (1) in the reaction mechanism. (2) At small positive overpotentials there is a continuous increase in the formal coverage 01 of Mo(IV). (3) At potentials of - 0 . 2 V and above further oxidation of Mo(IV) to Mo(V) begins, leading to a decrease of 01 with potential (equivalent to a pseudoinductive loop in the impedance diagram). (4) At potentials close to - 0 . 1 V the coverage 02 of Mo(V) reaches a maximum and the second reaction pathway manifests itself. The increase in the coverage

M. Bojinov et al. /Journal of Electroanalytical Chemistry 381 (1995) 123-131

03 of Mo(V)aj with potential in the transition region is indicated by the extra capacitive loop in the impedance spectra. (5) At potentials more positive than -0.03 V 03 reaches a constant value, whereas both 01 and 02 continue to decrease (appearance of two inductive loops in the impedance diagrams (Figs. 6 and 7)). This physical description is converted into a quantitative model by using the procedure of Bai and Conway [38,39], based on the concepts of Armstrong and coworkers [40,41], which leads to analytical expressions for both the steady state polarization curve and the ac impedance data. The following assumptions are made. (1) The rates of steps (1)-(5) in the model follow a Tafel dependence on the overpotential r/(defined with respect to the open-circuit potential of the Mo electrode ( - 0 . 3 5 V) [38]): ki=k

? exp(bi~)

i = 1 .... ,5

(1)

(2) The adsorption of the intermediates follows a Langmuir isotherm (the assumption of Frumkin isotherms gives analogous results but the calculations are more complicated [42]). (3) The rates of the backward reactions of (4) and (5) are neglected because the calculations are performed for overpotentials greater than 0.1 V [38]. (4) The standard rate constants k~ are independent of the change in the coverages of the intermediates. The following notation proposed by Bai and Conway [38] is used throughout this section: r i = F i ( d O i / d t ) is the net rate of production of the intermediate species i, 0i is a formal fractional quantity analogous to surface coverage [38] and /] is the maximum surface excess of the intermediate. Thus 01, 02 and 03 are the formal coverages of the surface with Mo(IV)~d, Mo(V)ad and M o ( V ) ~ d respectively. For small sine perturbations of the type

129

In the model presented above, the current I and the rates of production of intermediates of steps (1)-(5) are expressed by I = F(t h

+ 2v 2 + v 3 + v4 +

r~ = F l ( d O J d t

) = v I - u3

r2 =

)

IF'2(dO2/dt

r 3 =F2(dO3/dt

=

3Vs) (4)

U2 -- U4

) = v3

In view of the autocatalytic character of steps (2) and (5) [38]

Mo(II1) + Mo(IV). d ~ Mo(V)a d 4- Mo(IV)a d q- 2eMo(V)~ d + Mo(III) --* Mo(VI)~o, + Mo(V)~ d + 3e the rates of steps (1)-(5) are given by [38] kl(1 - 01 -

U1 =

02

-

03)

-

k_lO 1

c,2 = k201 - k _ 2 0 2

303

c' 3 = k301 - k

U4

(5)

k402

:

b,5 = ksO 3

a

©

<

0

% © -2

-3-

r&c = ] r/I exp(jwt)

0ac = 10l exp(j~ot)

-4

(2)

-o.3

i

-o'.2

Iac = III exp(j~ot)

+ ( I)0101,~ + ( I)ozO2a c + ( I)0303,~

i

6

i

o'.1

&, >

c 0.6 :J

cj

0.4

~t, 0 . 2

+ (rl)O303ac F 2 ( j o ) O 2 a c ) = ( r 2 ) E E a c + (r2)olOlac 4- (r2)o202ac

~ 0,8

C

F,(jo~0,ac) = ( r , ) EE.~ + ( rl)o,Ola c q- ( rl)O202a c

(3)

+ (r2)o303ac

r3(jo)02.~) = (r3)EE.c

-o'.1 E / V

where j = fZ-_ 1, the rate expressions in potential and coverage can be expanded in Taylor series, neglecting the higher-order terms [38]: I,o = ( I ) E E , c

i

+ (r3)OlOlac q- (r3)o202ac

+ (r3)o303ac

where ( )e denotes O/OE, and ( )o, denotes 0 / 0 0 i [38,39].

-0.3

-0.2

-0.1 E/

0

0.1

V

Fig. 10. Experimental results (points) and curves simulated using the reaction model (see text) ( ) for the Mo + 5 M H z S O 4 system: (a) stationary polarization curve; (b) development of the formal coverages of the intermediates with the electrode potential.

M. Bojinoc et al. /Journal of Electroanalytical Chemistry 381 (1995) 123-131

130

By setting all the derivatives in Eq. (4) to zero (steady state regime) it has been shown [38] that the equation describing the steady state polarization curve is of the type

Table 1 Kinetic parameters of the proposed model used to simulate both the steady state polarization curve (Fig. 10(a)) and the ac impedance diagrams (Fig. 11) for the system M o + 5 M H z S O 4 Kinetic parameters

Values

I = 3 F ( k 4 0 2 + k503)

k 1 / m o l c m 2s 1 k t/molcm2s 1

1 × 1 0 13 1×10 It 8 × 1 0 13 1 x l O 14 2 × 1 0 12 3 × 10 s 8 × 1 0 t3 12× 10 s 50 22 18 25 7 l X 10 -8 2 x 10 s 1×10 s

where the steady state coverages with Mo(V)ad and Mo(V)dd are given by 0 2 = klk2k_3/(k_

2 + k4)D

0 3 = klk3/D

D = klk_ 3 + klk2k_3/(k_

2 + k4) + klk 3 + k_lk_

3

The impedance response can then be evaluated by simultaneous solution of Eqs. (3) where the partial derivatives are calculated from Eqs. (5). Details of the derivation are given in [38]. A numerical procedure developed by one of the authors and outlined in more detail in [16] was used for the computer simulation of both the steady state polarization curve and the impedance spectra. No fitting algorithm was used, but the values of the parameters were adjusted manually to reproduce the experimental

~

-300

-200

-100

?o c

0' 200

0

400

600

-3 10

~~.o

-2 "N.

o

- d 1K

o.'.,, ~ ; 0 . 1 E =

0.06 V

2

4

6

k2/molcm2s

i

k _ 2 / m o l c m 2 s -1 k 3 / m o l cm2 s - I k 3 / m o l cm 2 s 1 k4/molcmZs i k s / t o o l cm 2 s - l

bl=b_i/V 1 b z = b 2 / V -~ b 3 = b 3 / V -1 b4 / g - 1 b5 / V 1 F 1 / m o l cm 2 F 2 / m o l cm 2 F 3 / m o l cm 2

results. The results of the simulation for the Mo + 5 M H2SO 4 system are presented in Figs. 10 and 11, and the kinetic parameters are listed in Table 1. The close agreement between the experimental data and the calculated curves in Figs. 10(a) and 11 demonstrates the ability of the model to reproduce the observed results, i.e. to explain the general features of the transpassive dissolution of Mo in H z S O 4 media. As the number of parameters involved in the model is quite large, it is possible that another parameter set could give an equally good or even better fit to the experimental data. Therefore the values of the rate constants obtained here will not be discussed further. The development of the formal surface coverages 0 i with potential are shown in Fig. 10(b). These dependences seem to confirm the general physical picture of transpassive dissolution outlined above. Further work is now in progress with the aim of elucidating the impact of different factors, such as solution pH, the type and concentration of acid anions and the molybdate concentration, on the kinetics of transpassive dissolution of Mo in acidic media.

-0,4

5. Conclusions -0,2

~

~

.

-

100

E = 0.03 \" 0.4

0,6

0.8

1.0 1

I

] 1,2

Re(Z) / .q, Fig. 11. Experimental results (points) and curves simulated using the reaction model ( ) for the system M o + 5 M H2SO4: ac impedance spectra (frequencies in hertz).

The anodic behaviour of pure Mo in H 2 S O 4 solutions was studied using steady state, voltammetric and ac impedance methods. The following general conclusions can be drawn from the results. (1) The anodic polarization curve of Mo in H 2 S O 4 solutions can be divided into three regions: a Tafel-like region, a transition region in which there is pronounced curvature in the log j - E dependence and a second TafeMike region in which the current increases more slowly with potential.

M. Bojinov et al. /Journal of Electroanalytical Chemistry 381 (1995) 123-131

(2) Cyclic voltammetric results indicate that the current is independent of sweep rate in the Tafel region. An anodic peak is observed in the positive sweep, followed by a cathodic peak in the negative sweep. The dependences of the peak currents and potentials on sweep rate are consistent with a mass-transfer-controlled dissolution reaction. (3) The steady state polarization curves and ac impedance spectra at a given potential are almost independent of acid concentration in the range 0.5-5.0 M, precluding any role for the acid anion in the overall oxidation process. (4) A quantitative model of the oxidation of Mo in H2SO 4 solutions, including two parallel reaction pathways and three stable intermediates, was proposed. It is consistent with literature data and is able to reproduce both the steady state polarization curve and the general features of the ac impedance spectra in the transpassive dissolution region.

Acknowledgement The authors are grateful to The National Foundation for Scientific Research of the Bulgarian Ministry of Science and Education for financial support of this work.

References [1] C. Chao, L. Lin and D.D. Macdonald, J. Electrochem. Soc., 128 (1981) 1187. [2] L. Lin, C. Chao and D.D. Macdonald, J. Electrochem. Soc., 128 (1981) 1194. [3] C. Chao, L. Lin and D.D. Macdonald, J. Electrochem. Soc., 129 (1982) 1874. [4] D.D. Macdonald and M. Urquidi-Macdonald, J. Electrochem. Soc., 137 (1990) 2395. [5] D.D. Macdonald and S.I. Smedley, Electrochim. Acta, 35 (1990) 1949. [6] D.D. Macdonald, J. Electrochem. Soc., 139 (1992) 3434. [7] M. Urquidi and D.D. Macdonald, J. Electrochem. Soc., 132 (1985) 555. [8] M. Urquidi-Macdonald and D.D. Macdonald, J. Electrochem. Soc., 136 (1989) 961. [9] D. Pavlov, M. Bojinov, T. Laitinen and G. Sundholm, Electrochim. Acta, 36 (1991) 2081. [10] D. Pavlov, M. Bojinov, T. Laitinen and G. Sundholm, Electrochim. Acta, 36 (1991) 2087.

131

[11] T. Laitinen, H. Revitzer, G. Sundholm, J. Vilhunen, D. Pavlov and M. Boiinov, Electrochim. Acta, 36 (1991) 2093. [12] M. Bojinov and D. Pavlov, J. Electroanal. Chem., 315 (1991) 201. [13] M. Bojinov and D. Pavlov, J. Electroanal. Chem., 346 (1993) 339. [14] M. Boiinov and D. Pavlov, J. Electroanal. Chem., 364 (1994) 195. [15] M. Bojinov, K. Salmi and G. Sundholm, J. Electroanal. Chem., 347 (1993) 207. [16] M. Bojinov, K. Salmi and G. Sundholm, J. Electroanal. Chem., 358 (1993) 177. [17] M. Bojinov, K. Salmi and G. Sundholm, Electrochim. Acta, 39 (1994) 719. [18] M. Koenig and H. Goehr, Ber. Bunsenges. Phys. Chem., 67 (1963) 837. [19] T. Heumann and G. Hauck, Ber. Bunsenges. Phys. Chem., 71 (1967) 404. [20] L. Wikstrom and K. Nobe, J. Electrochem. Soc., 116 (1969) 525. [21] M.N. Hull, J. Electroanal. Chem., 38 (1972) 143. [22] M. Pourbaix, Atlas d'Equilibres Electrochimiques ?~ 25°C, Gauthier-Villars, Paris, 1963. [23] V. Kozhevnikov, T. Tzenta, V. Knyazheva and Y. Kolotyrkin, Prot. Met. (USSR), 19 (1983) 699. [24] I. Olefjord and B.O. Elstroem, Corrosion (Houston), 38 (1982) 46. [25] I. Olefjord, B. Brox and U. Jelvesdam, J. Electrochem. Soc., 132 (1985) 2854. [26] B. Brox, W.T. Hua and I. Olefjord, J. Electrochem. Soc., 135 (1988) 2184. [27] M. Uergen, U. Stolz and R. Kirchheim, Corros. Sci., 30 (1990) 377. [28] V. Batrakov, N. Simonova and I. Gorichev, Prot. Met. (USSR), 29 (1993) 549. [29] V. Batrakov, I. Gorichev and N. Simonova, Prot. Met. (USSR), 29 (1993) 554. [30] W. Yang, R. Ni, H. Hua and A. Pourbaix, Corros. Sci., 24 (1984) 691. [31] R.D. Armstrong, M.F. Bell and A.A. Metcalfe, J. Electroanal. Chem., 84 (1977) 62. [32] A.F. Povey and A.A. Metcalfe, J. Electroanal. Chem., 84 (1977) 73. [33] B. Boukamp, Equivalent Circuit, University of Twente, The Netherlands, 1989. [34] R.D. Armstrong and M. Henderson, J. Electroanal. Chem., 40 (1972) 121. [35] I. Epelboin and M. Keddam, Electrochim. Acta, 17 (1972) 177. [36] M. Keddam, H. Takenouti and N. Yu, J. Electrochem. Soc., 132 (1985) 2561. [37] M. Keddam, O.R. Mattos and H. Takenouti, J. Electrochem. Soc., 128 (1981). [38] L. Bai and B. Conway, J. Electrochem. Soc., 137 (1990) 3737. [39] L. Bai and B. Conway, J. Electrochem. Soc., 138 (1991) 2897. [40] R. Armstrong, J. Electroanal. Chem., 34 (1972) 387. [41] R. Armstrong and K. Edmondson, Electrochim. Acta, 18 (1973) 937. [42] J.-P. Diard, B. Le Gorrec and C. Montella, J. Electroanal. Chem., 326 (1992) 13.