Theoretical investigation of the electrochemical deposition of metal involving adsorption and desorption steps

Elecwochimicn Acta. Vol. 38, No. 14, pp. 2043S2050, 1993

0013-4686/93 1.00 + 0.00 Pergamon Press Ltd.

Printed in Great Britain.

THEORETICAL INVESTIGATION OF THE ELECTROCHEMICAL DEPOSITION OF METAL INVOLVING ADSORPTION AND DESORPTION STEPS SYLVIE ROUQUETTE-SANCHEZ, P. COWACHE,P. BONCORPSand J. VEDEL Laboratoire d’Electrochimie(Unit6 Associbs 216 au CNRS) ENSCP, 11, rue Pierre et Marie Curie, 75005 Paris, France (Received 10 March 1993)

Abstract-The objective of this work is the study of a reactional pathway characteristic of an electrodeposition process with adsorption. It involves five limiting steps. The determination of the impedance expression corresponding to this mechanism leads us to give an electrical equivalent circuit. The expression of the real part of the diffusion impedance can be negative when there is adsorption of a competitive species at the electrode. In this case, the shape of the impedance diagram is quite special because the real part of the impedance leads to negative values. The experimental diagrams were realized during the reduction of Te(IV) into Te(0). These diagrams were simulated and the good agreement obtained between the experimental and calculated curves confirms the rate determining steps involved in the reactional pathway proposed. Key words: impedance spectroscopy, electrodeposition, modelization, tellurium, adsorption.

(2) Adsorption

INTRODUCTION The objective of this work is to study the reactional pathway proposed by Sella et &Cl] occurring during the electrochemical reduction of Te(IV) ions into Te(0). The first part of this work is the study of the influence of the kinetic parameters on the shape of the impedance diagrams. The second part shows the first experimental results obtained by reduction of Te(IV) into Te(0).

Ab+ C,,

S +

-

K1

re,

A”+ m

r4

re,

(4) Desorption

To2 (5)

STUDY OF THE REACTION PATHWAY

Five steps are involved in this mechanism: (1) Diffusion A”+ 2

A”+

C*

C,,

Dzcm2s-’

k,=s-’

A”+, s + ne- AA,s

EXPERIMENTAL

THEORETICAL

mol-lcm”s-l

(3) Charge transfer

A,s zA+

The theoretical part of this work and the fitting of the experimental curves were performed on a MacIntosh SE/30 using custom software. The experimental diagrams were obtained with a Solartron 1255 and a potentiostat EGG/PAR 273A driven by an HP Vectra QS/l6S computer. The electrochemical study was realized in a solution of Te(IV) (10e4M) in H#O, (pH 2.2) at 25°C and K,SO, (0.1 M). The working electrode was a rotating disc made of Te(0) (S = 0.08cm’). The potential was monitored against a saturated K,SO, mercury-mercurous sulfate reference electrode (mse). The counter electrode was made of carbon.

K 1 =

s

K,es-’

m

Competitive reaction M C, +

s

LM,s

roe “’ re, *

K,=mol-‘cm3s-’ K;ES_’

K,, K2, K, and K; are the kinetic constant characteristic of each reaction steps. They are supposed to be independent of the potential. M is a species in solution which can be adsorbed at the electrode. The concentration of M in the solution is very important and the diffusion reaction is not considered. In the experimental measurements, M is taken to be K+ cations. The kinetic charge transfer constant k, presents an exponential variation with the potential as shown by the relation: kb = k” exp[b# - E’)] with b, = -anF/RT,, where k” is the intrinsic charge transfer constant, a the charge transfer coefficient, E” the standard potential, n the number of electrons and Tk the temperature. We take F = 96487 C, R = 8.314 J and Tk = 298 K. D is the diffusion coefficient of Te(IV) ions. r is the total number of active sites, s, per area (molcm-*). s is the number of free active sites. A, s the sites covered by A, A”+, s covered by A”+ and M, s covered by M. 0,, t12 and 8, are the proportion of the active surface covered

2043

2044

S. ROUQUE~-SANCHEZ et al.

by A”+,

A and M, respectively. Consequently, 8, = 1 - (0, + 0, + (I,). The electrochemical impedance relation has already been established[2] :

Table 1. Relations between electrical and kinetic parameters 1 - nFSb, k, IX,

Z = R, + Zr/joC, Z,

1 k, 4

(in which R, is the electrolyte resistance and C, the double layer capacitance), with Zr = R, + Sk,

R,TAB,/AIt = R, + Z,

RI

and

kt,Rt

k, R,[(l - K,IY,

Z

(iw + K,

1= jo(l -

K,l3,

c,

TX@ + K,) + K;) + K,C,,(jw + K;)]

T)(jw + K&u

+ K3 Cm + K;)

+ K,C,,(ju

+ K;)(jw + K,)

K2

The corresponding electrical circuit deduced from this relation is given in Fig. la. The relations between electrical and kinetic parameters are given in Table 1. This shows that two electrical circuits are possible depending on the relative values of the kinetic desorption constants K; and K,. If K, is higher than Kj , the inductance L, and the resistance R,, are negative and the electrical circuit can be described with a capacitance C2 and a resistance R, as given in Fig. lb. In both cases, the diffusion impedance is complex and given by the relation: Z, = - TK, I%,, Z, where Z, is the impedance of the electrical circuit given Fig. 1. The expression of Z, is also given in Table 1.

R2

k, R, K&I

R3

k.R,K,C, KAG

R.4

k.R,KsC, Kt’GK - KA k,R,KOCm(K2

RS 4

=- R, + R, k, R,

K,K,

Z.

R, + joL,

Theoretical study of the reaction pathwny

Firstly, for each reactional step, we have defined kinetic constants with the same unity (mol cm -2s-1). Charge transfer: K, = k, r. Diffusion: K,, = (D/6&. Adsorption: K, = K,TC,. Desorption: K, = K, r. Competitive reaction = K, = KAK, with KdlY;/K, C,,,). The numerical

-R:

- K;)

K,C,,K,K;

+

Cc,

R,R,+jaL2R, R, + R, + jwL2

T -K,E’,,

Z*

K’3>KZ Cd

II

R4

I I--------------ZI

L2

WI J

K’3
Fig. 1. Electrical equivalent circuits to the electrochemical impedance.

TZ,

Electrochemical deposition of metal

2- Kg=2OOOO Kg=1 K3=20000 I- K210.1 2- K210.5 3- K2= 10 4- K2=15

Kmt=2.6.10-50

150

Zr 6-Q

zJG-8

0

100

Fig. 2. Influence of the value of the (K,/K;) ratio on the shape of the impedance diagrams: k” = 1 s-‘; a=0.5;Eo=OV;E=-0.05V;D=1.5x10~scm2s~’;R,=1R;C~=10~6F;N=100r.p.m.;C,= 0.01 molcm-“; C, = 10-5molcm-3; r = 10-9molcm-2; K, = log.

values of these constants will determine whether the corresponding reaction step is the rate determining step in the process. Study of the shape of the d@sion impedance as a function of the kinetic parameters The diffusion impedance of the process is different from the classical diffusion impedance, depending on the relative values of K2 and Ks . The real part of the diffusion impedance can even be negative when K, is greater than K; (Fig. 2a and b). The real part of the diffusion impedance can be written as:

ReZ, = K,l%,[ImT*ImZ,

- ReT*ReZ,].

In this relation, ImT and ReT are, respectively, the imaginary and the real part of T (defined in Table 1) and ReZ, and ImZ, the imaginary and the real part of the impedance Z, . From the definition of T, ReT is a negative number and ImT a positive number. ImZ, and ReZ, can be written as: R, R,(R, + R4) + w2L; R, ReZ’ = Rz +

(R, + RJ2 + (wL#

The study of the parameter shows that the necessary conditions to observe a special diffusion impedance are : (1) K2 > K; (as demonstrated previously). (2) The competitive reaction has to be rate determining: K, = KIJ/K3 C, < 1 and t& > 0. (3) The diffusion process has to be rate determining with respect to the adsorption and desorption steps: KDir z K,, c K,, K,. Condition (2) implies that K, = K, Kc c K,. Thus, depending on the value of the K,/K; two cases may be observed :

ratio,

Casel:k,>k;

The influence of the kinetic parameters on the shape of impedance diagrams is illustrated in Figs 3-6. Influence of the rotation rate of the working electrode (Fig. 3). The smaller K,, is, the larger the fre-

quency range for which ReZ, < 0 is. When the ratio 4 2- N = 500 r.p.m.

and

0.1

wL, R: ImZ’ = OL1 + (R, + R,)’ + (wL#

If K, < K; , the electrical circuit equivalent to the impedance is given in Fig. la. In this case, R4 > 0 and L, > 0, consequently: ReZ, > 0, ImZ, > 0, ReZ, > 0, and the impedance diagrams present the shape of classical diffusion with a slope equal to one for middle frequencies values. If K, > K; , the electrical circuit corresponding to the impedance is given in Fig. lb. In this case, R, < 0 and L, < 0. The relations between the kinetic and the electrical parameters show that (R, + R, < 0. Consequently, ReZ, > 0, and ImZ, > 0 or ImZ, < 0. Thus, ReZ, < 0 if ImZ, < 0 and 1ImT*ImZ, I> lReT*ReZ,J. These equations could be solved to determine (i) the frequency range and (ii) the relative values of kinetic parameters to obtain a negative real part of the diffusion impedance.

-20

zr (t-2)

21

Fig. 3. Influence of the electrode rotation rate on the impedance diagrams: k” = Is-‘; a = 0.5; E” = OV; E- -o.osV; D = 1.5 x 10-5cm2s-‘; R, = 1R; C, = C, = 10-5molcm-3; C, = 0.01molcm-3; lO-6 F; T = 10-9molcnt-2; K, = 109; K - 1500; K3 = 20,000; K; = 0.2. ’ -

2046

S. ROIJQUE~-SANCHEZ et al. ? K2=1500 1-K,=10g;K1\=10-5 2-Kt=lO’;K~=lO-’ 3- Kl I 5.106; KA = 5.10v8 KDjf=2.6.10M8 ; KD= 1.5.10s6 : Kc = 1

K,=l@ I- K2 = 1500; KD = 15.104 2-K2=150;K~=l.5.10~~ 3- K2 =50; Kg=5.10-* Krjif=2.6.lO-*;K~=W~;Kc=l

E R

0

Fig. 4. Influence of the adsorption and desorption steps on the impedance diagrams: k” = 1 s- *; OL = 0.5; I?’ = OV; E = -O.OSV; D = 1.5 x 10-5cm2s-‘; R, = 1R; C, = 10b6F; C,,,= 0.01molcm-3; C,= 10-smolcm-3; N = 100r.p.m.; r = 10-9molcm-2;K3 = 20,000; K; = 200. Kurt/K, is greater than 10, the impedance diagrams do not present a special shape for the diffusion impedance. Infuence of the adsorption and desorption steps on the shape of impedance diagrams (Fig. 4a and b). The diagrams given in Fig. 4a were obtained taking the following conditions: the competitive reaction is not rate determining: Kc = 1+ K,, = K,. The desorption step is not rate determining: K, B K,, K,. Curve (1): K JK,, > 10: the impedance diagram single loop is characteristic of the charge transfer step. At low frequencies, the classical diffusion impedance is observed. Curves (2) and (3): K JK,, < 10: one more capacitive loop, characteristic of adsorption step, is observed. The diagrams given in Fig. 4b were obtained taking the following conditions: the competitive reaction is not rate determining: Kc = 1 =S K,, = K,. The adsorption step is not rate determining: Curve (1): KJK,,, > 10: the single KA s &if 9 K,. loop of the impedance diagram single loop is characteristic of the charge transfer step. At low frequencies, the classical diffusion impedance is observed. Curves (2) and (3): KdK,, < 10: one more capacitive loop, characteristic of desorption step, is observed. When Kc = 1 and both the adsorption and desorption steps are rate determining, the shape of impedance diagrams is similar to the one observed in Fig. 4. It shows that when Kc is equal to one, the impedance diagrams show a classical diffusion impedance. In this case, the real part of the diffusion impedance cannot be negative. lntuence of the competitive reaction (Fig. Sac). Figure 5a and b give8 impedance diagrams

obtained with different values of K; (the desorption constant of M). The adsorption and desorption steps are not rate determining: K,, K, 9 K,,. We observe an increase of the size of the impedance diagrams with K; (consequently to an increase of Kc and K,c): the competitive reaction is not rate determining and the only limitation is due to charge transfer and diffusion processes. When Kc < 1 and K, JK,, < 10 (curve8 5-7), the diagram show8 a frequency range for which the real part of the diffusion impedance ReZ, is negative and the special shape of diffusion impedance is observed.

Figure Sb shows the impedance diagram evolution for very low value8 of K3. The diagrams present a capacitive loop characteristic of a charge transfer step and then, for the low frequencies, the impedance leads to a capacitive effect (-Z, leads to an infinite value) (curve 10). This effect was expected taking account of the electrical parameters expressions: K;~K,~(K;-K*)zK,~R,~(-R,)

Impedance diagrams for different values of K, are given in Fig. SC. The curves (1) to (4) were obtained by increasing the value of K, . In all cases, the conditions to obtain a special diffusion impedance are met. However, for high value8 of K,, we observe a capacitive effect for low frequencies and (- ZJ leads to an infinite value ‘as previously observed in Fig. Sb, curve (10). This effect is due to the high value of R, which increases with K, . If the competitive species M is irreversibly adsorbed, the electrode is covered by M (0, -) 1) and the active sites are blocked with respect to the A”+ electrochemical adsorption: the current is nearly equal to zero and the impedance goes to an infinite value. Influence of the number of active sites r (Fig. 6). Impedance diagrams obtained for different value8 of I show a decrease of the diffusion impedance when I increases. Moreover, the time constant wz of the second loop characteristic of adsorption and/or desorption process decreases when I increases. Indeed, we can show that 1 % = (R, + R, + R3)CI K, K. C_, Y

=

r(KDC,

+

r.

.F.

KA C,, + KS C, C, I)

Case 2: K, < K; (A desorption is slower than M desorption) Impedance diagrams obtained when K, is lower than K; present one or two loops (depending on the values of Ku and KA) and a third one characteristic

of the diffusion process (Fig. 7). The special diffusion shape due to the negative value of ReZ, cannot be observed in this case.

Electrochemical deposition of metal 40

40 Kg=20000

1- l- = 103 2- I- = 5.10-10 3- r I 10-10

4- K’3 = 50 : KRC = 2.5.10e6; Kc = 0.25 6- K’3 =0.3 ; KRC = 1.J.10m8 ; Kc = l.S.10s3 8- K’3 = 0.1 ; K ~c = 5.109 ; Kc = S.104 IO- K’3 t 0.001 ; KRC = 5.10v1’ ; Kc = 5.10‘ g I

K~p2.6.10‘*

; Kc = 1

Ci iJ

Kmf= 2.6.10-* ; KD= 1.5.10-6; KA= 10-5

R

.m,,

0

0

.J 40

nm

Fig. 6. Influence of the number of active sites on the impedana diagrams: k”=ls-*; a=O.S; E’=OV; E= -0.05V;D= 1.5 x 10-scm2s-‘; R,=ln; Cd= 1O-6F; C, = 0.001molcm-‘; C, = lo-‘mol entm3; N = 100r.p.m.; K, = 10’; K, = 1500; K; = 200; K, = 20000. electrode

5

and

(Fig. 8). We observed a wave between -0.5 - 1.2V. The limiting current value increase8

with the rotation rate of the electrode. It shows that one of the rate determining steps is the diffusion process. considering that all the reactional step8 are rate determining, the expression of the current is given by:

N

1, = nFSK, Kw K, KD &K&W

0

KA 6

Kuc

GUbir fL KD + KDUKAKuc + KacKA KD + hi, KacKD). +

1C

K w = w4C, with Dl’3

as ia

6 =

2.31 ,/(N)

(N = rotation rate).

l-Kle109;K~=10-s 2- K1 ic 10’ ; KA= lo-’ 3- K1 = 5.10’3; KA= 5.W* Kmf= 2.6.10.* ; KD= l.5.10a ; KRC = KD

0 -20

zl m

80

Fig. 5. Influence of the competitive resction on the impedkO= ls-‘; ana diagrams: a = 0.5; E'=OV; E = -O.OSV; D = 1.5 x 10-scm2s-‘; R, = 1R; C, = 1O-6F; C, = 0.01molcm-3; C, = 10-smo1cm-3; N = 100r.p.m.; I = 10-9molcm-2; K, = 109; K, = 1500.

EXPERIMENTAL STUDY OF THE ELECTROCHEMICAL REDUCTION OF WV) Voltammetric study

Voltammograms were realized with a scan rate of 1 mVs-t for different rotation rates of the working

B ?

0

0

3t

Fig. 7. Influence of the adsorption step on the im diagrams in ease number 2: k” = 1s-i; a = 0.5; P =;; E = -0.05V; D = 1.5 x 10-scmzs-‘; R, = ln; C, = lO+‘F; C,,,= 0.01molcm-‘; C, = lo-’ molcm-3; N = 100r.p.m.; I - 10S9; K, = 1500; K; = 200; K, = mOmI.

S.ROUQUE~-SANCHEZ etal.

2048 0

-l

I - N = 100 r.p.m. 2-N=25Or.p.m. 3-N=MOr.p.m. 4 - N = 750r.p.p.m. 5 - N = 1000 r.p.m.

1 (4

-2E-05

-4E-05 WI

-6E-05

-6.104

-8E-05

-lE-04 -1.25

I

L

-.25

E(V)

Fig. 8. Steady state i-E curves obtained for different rotation rates of the working rde electrode. The measurement of I, is made for potentials for which the current is not limited by the charge trans-

Impedance study

fer process. Therefore, the constant K, is higher than the other ones because Kr varies exponentially with the potential. The expression of the limiting current I, is given by:

Impedance diagrams were performed at different values of the applied potential and for different rotation rates of the working electrode (Fig. 9). An increase of the size of the impedance diagram with the overpotential was observed. The same variation was observed when the rotation rate of the electrode decreases. Knowing that the concentration of Te(IV) ions in the solution is very low (lo-’ molcm-3), the diffusion impedance is necessarily important. Moreover, the volammetric study shows that the system Te(IV)/Te(O) is slow (we do not observe a reoxidation peak of Te(0) before OV). Therefore, the charge transfer resistance decreases with the overpotential. So, the increase of the impedance with the potential is due to the diffusion process and to the other reactions involved in the reactional pathway, except the charge transfer reaction. This assumption is in agreement with the experimental decrease of the diagram size when the rotation rate of the electrode increases. A first simulation of the impedance diagrams has been done (Fig. 9). The kinetic parameters introduced to fit the diagrams are given in Table 2. These first results show that it is possible to interpret the experimental diagrams with the reaction pathway considered. The value of r is about 50 times lower

I, = (nFSK,K,,,K,K,K,JK,(K,,K,K,

+

KDirK,,KtJh

Usually, the variation of I, as a function of fi is studied to calculate coefficient of the diffusional species. But in this case, the expression of the limiting current is too complex and it seems more interesting to study the variation of \F( 1; 1 I) as a function of \F( 1;\R(N)). The expression of \F( 1; I,) is given by: 1 1 1 -_-++ 11

nFSK,,

+ -+-

nFSK,

1

nFSK,,

1 nFSK,

1 = + constant nF8Knir 2.31 = nFSC, D213 + constant. The variation of l/I, as a function of l/p is given in Fig. 8. The variation is linear and we can deduce from the slope of the straight line, the diffusion coefficient of Te(IV) in our experimental conditions. The linear regression gives the equation: y = 15994 - 1.2636 x 10% with a regression coelficient equal to 0.9996. The diffusion coefficient calculated is: D = 1.44 x 10-scm2s-1. This study shows that the diffusion step is one of the rate determining steps in the process and leads us to determine the diffusion coetllcient. But the positive value 15994 given by the linear regression indicates that the steady state is not reached. The limiting current values obtained by the voltammetric study are higher than the steady state one.

Table 2. Kinetic parameters determined by simulation of impedance spectra R, C* k” ; IK, K, K, K; c, cln D N

30051 potential dependent: 1.5 x lO+ to 8 x 10-6F 8 x lo-‘s-’ 0.066-0.07 0.407 v (thermodynamic value) 10-1*molcm-2 1.38 x 108mol-L cm’s_’ 1OOt9-’ 45mol-Lcm3s-L O.oQSS-’ lo-‘mol cme3 2. IO-*molcm-” 1.44 x 10-5cm2s-’ SOO-lOOOtr.min-’

Electrochemical

deposition

of metal

2049

4 N = loo0 r.p.m. l:E=-O.65V 2:E=-O.7V

B E

0 10 10

2oc N = loo0 tp.m. 3-Er0.75V 4-E=O.EV

235 01 3 E=-O.75V S-N=MOr.p.m. 6 - N = loo0 r.p.m.

23500

-3

b3 0

6

Fig. 9. Impedance diagrams obtained for different applied potential values and two rotation rates. + Experimental points; - calculated curve.

than that accepted for Pt(ll1). This should mean that the used tellurium electrode presents less active sites than a well defined Pt surface. The kinetic parameters determined show that all the steps limit the process: KDir = 8 x lo-“, K, = lo-*, K, = 1.4 x lo-‘0, K,, = 6.9 x lo-lo, K, = 5. Because K, > 1 and K, < K,ir, a negative variation of the impedance cannot be obtained. Yet, these results show that Te(IV) is adsorbed before its reduction

and that the adsorption of competitive species (assumed to be sulfate ions) is also part of the process. This is because the low frequency loop can only be obtained in the model when K, < 30 (considering the values of KA, KD and KDir determined by experimental curves fitting). Studying the formation of CdTe in a highly concentrated solution of CdS04, Maurin et a/.[33 observed a negative loop of the diffusion impedance.

2050

S. ROUQIJEITE-SANCHEZ et al.

We plan to investigate whether our for these results.

model

can

account

REFERENCES 1. C. Sella, P. Boncorps and J. k&l, 133.2043(1986).

2. S. Rouquette-Sanchez, Forum

(1990). 3. b. h&An,

0. Solorza and H. Takenouti, .I. electroan&

Chm. 202,323 (1986). J. electrochem. Sot.

P. Roncorps and J. Vedel, 4Montrouge

SW les Imp-+dances Electrochimiques,