Simulation of the Cyclic Voltammetric ... - ACS Publications

6

S i m u l a t i o n of the C y c l i c V o l t a m m e t r i c C h a r a c t e r i s t i c s of a S e c o n d O r d e r EC C a t a l y t i c

Downloaded by UNIV OF ARIZONA on December 17, 2014 | http://pubs.acs.org Publication Date: July 2, 1982 | doi: 10.1021/bk-1982-0192.ch006

Mechanism DENNIS M. DIMARCO, PAUL A. FORSHEY and THEODORE KUWANA Ohio State University, Department of Chemistry, Columbus, OH 43210 This paper describes a general method for the elucidation of rate parameters for second order homogeneous ec catalytic reactions, using cyclic voltammetry as the diagnostic electrochemical tool. It is being written so that others besides the everyday practitioners of electrochemistry can relate the mechanistic aspects to the diagnostics, and hence, can appreciate the beauty of the ec mechanism for the design of catalytic electrodes. In doing so, i t assumes that cyclic voltammetry remains a convenient and powerful diagnostic tool for the study of this mechanism, that the ec catalytic mechanism is a viable approach to the design and fabrication of catalytic electrodes, and that redox mediators serving as catalysts can be thoroughly characterized in a solution coupled ec mechanism and then transferred to the electrode surface via their immobilization. Previous reports invoking the ec mechanism have been well documented both in this lab (1-4) and others (5). In this paper we w i l l restrict our discussion to the homogeneous case. Cyclic voltammetric current-potential profiles were computer simulated for the ec catalytic reduction of molecular oxygen by water-soluble iron porphyrin. These profiles were in good agreement with experimental ones for a mechanism involving oxygen reduction to water through hydrogen peroxide in a series pathway. The reaction sequence of an ec c a t a l y t i c regeneration mechanism i s i l l u s t r a t e d , for a reduction by reactions 1 and 2: 0097-6156/82/0192-0071 $7.75/0 © 1982 American Chemical Society In Chemically Modified Surfaces in Catalysis and Electrocatalysis; Miller, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICALLY MODIFIED SURFACES

72

sM M

M

ox

r

+

(1)

V

(2)

+ S


where M

, denotes the redox mediator and S , represents ox/r ox/r the solution reactant species (hereafter referred to as the reactant). The electrode reaction of S / i s shown i n r e ox/r action 3. r

When k „ i s large, the concentration r a t i o M /M i s Nernstian. 'The equilibrium constant, K , of reaction 2 i s q

g

r

0

determined by E ^ and E°g values of reactions 1 and 3, respectively ( K

e q

= exp((E°^ - E°^)F/RT) when r ^ - n

g

- 1.

For some of the less complex ec processes, c y c l i c v o l t ammetry (i-E) waves have been used to show, q u a l i t a t i v e l y , the effects of the follow-up reaction (reaction 2). The model f i r s t developed for this scheme consider only pseudo f i r s t order conditions where the heterogeneous process was either reversible (.6,7) or i r r e v e r s i b l e (7,8). Accordingly, when the homogeneous rate constant was very large, the i-E scan appeared similar to a conventional polargraphic wave without any peaks. The complications of Nicholson and Shain (J), provide c y c l i c i-E data that can be compared d i r e c t l y to experimental results. While these data can be used to f i t the case represented by equations 1 and 2 (n^ = 1), more complex schemes involving second or higher order homogeneous reactions, conditions of unequal diffusion c o e f f i c i e n t s , and mechanisms in which k i s i n the quasi-reversible regime have not been g M

described i n d e t a i l . More recently Andrieux et. a l . (5a,5b) have described a procedure for computer simulation of a second-order ec catal y t i c mechanism. In their work c y c l i c voltammetric data were calculated while changing the rate and r e v e r s i b i l i t y of the follow-up reaction. Using the implicit finite-difference method

In Chemically Modified Surfaces in Catalysis and Electrocatalysis; Miller, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

6.

DIMARCO ET AL.

Second Order EC Catalytic Mechanism

these authors calculated voltammetric waves for dimensionless homogeneous rates (kf*C ) as large as 5 x 10 M s . The results were then applied to cases where n 10 for the conditions shown above). To explain t h i s further, consider the t o t a l current to be a sum of contributions from the mediator and the reactant. An i-E plot of the reactant contribution i s shown i n F i g . 2B. This contribution was obtained by subtracting the current due to the reversible mediator from the t o t a l current for the c a t a l y t i c process (i.e. that shown i n F i g . IB or 2A). The reactant contribution w i l l be related to the rate of the homogeneous reaction (reaction 2).


f

RATE = k *c(M )*C(S ) f

r

(4)

ox

When k j i s small and C(S ) i s r e l a t i v e l y constant within the diffusion layer, the maximum rate occurs when C(M ) approaches the bulk mediator concentration. Under Nernstian conditions t h i s w i l l occur negative of the E of the mediator. As k^ increases, C(S ) i n the diffusion** layer i s no longer constant for the duration of the voltage scan. The i-E wave of the reactant c o n t r i bution now resembles that of a normal c y c l i c wave with i t s peak potential dependent on k^. This i s shown i n F i g . 2B when y^ i s greater than 0.1. The maximum current contributed by the reactant w i l l s t i l l occur when C(S )»C(M ) i s the largest, but t h i s product w i l l be maximized at successively lower values of C(M ) that i s , e a r l i e r i n the i^E scan. The maximum current contributed by the reactant exceeds i Q for y^ greater than 5.0. This agrees with results whosn r e c i n t l y by Andrieux et a l . (5b). With very large values of k^ the reactant i s depleted (and i t s current contribution has reached i t s peak) before the current due to the mediator i s s i g n i f i c a n t . At t h i s point the dual peak phenomenon i s observed and the reactant peak i s separated from the mediator peak. When the mediator i s under Nerstian control the two peaks w i l l increase i n separation as k continues to increase (5b). Thus for effective catalysis both k^ and k must be large. Thermodynamic considerations highlight the advantage of having a x

f

g

positive value of E°'

- E°'

for catalysis of a reduction (17).


80


The transition from the reversible to the i r r e v e r s i b l e case i s demonstrated i n F i g . 2C. The changes incurred as k ^ dereases are: 1) the s h i f t of the peak potential i n the negative direction and, 2) the disappearance of the dual peak phenomena. In curve 1 of F i g . 2C, the voltage i s scanned with overvoltage i n creasing i n the negative (reducing) direction. At the foot of the wave, the current i s limited by the heterogeneous rate of electron transfer to the mediator. The reactant w i l l not be depleted u n t i l significant concentrations of M are formed; thus both mediator and reactant w i l l be depleted a i approximately the same time. Compare t h i s to the case where k ^ i s large and there i s no l i m i t ation by heterogeneous charge transfer. Without k limitation the reactant can be depleted prior to depletion of the mediator, resulting i n the formation of two peaks. In the transition from the reversible to the irreversible case, behavior intermediate to the two preceeding cases i s displayed. To summarize, i n order to observe the double peak wave, both dimensionless rate constants, k^ and k , need to be large, and


M

g M

the Og/C^ r a t i o approximately equal to unity. DIAGNOSTICS Introduction The method of overlaying d i g i t a l l y calculated i-E curves with experimental ones i s frequently used as a v e r i f i c a t i o n of the proposed mechanism f o r the reaction involved. In order to use the simulated data diagnostically, the behavior of a certain mechanism must be calculated over a wider range of conditions. In the course of these simulations one finds which parameters are most useful and then quantitates their dependence on changes i n such variables as rate constants, scan rates, and concentration r a t i o . In this section we w i l l f i r s t display the dependence of the peak current and peak potential on the two rate constants, k^ and k « Then g M

the effects of experimentally variable parameters (i,e. scan rate and concentration ratio) w i l l be examined. The data i n this section w i l l deal with a single electron transfer reaction followed by a second order c a t a l y t i c regeneration step, as shown by r e actions 1 and 2. Dimensionless rate constants were calculated using nominal experimental values incorporated into the appropriate dimensionless groups (see Table 1). Effects of kThe dependence of i ^

c

on k^ i s shown i n F i g . 3. At low values

of k^ the peak current depends solely on k » g M

l

rate increases (100 < k- < 5 x 10* M~

l

As the homogeneous

s~ ) the i

increases



DIMARCO ET AL.


Mox • e

M * S —> ox S R

log y -2.6 -16 -6

.4

f

0x

14

M

+

R

24

F/gwre 5. Normalized peak current as a function of the homogeneous rate constant. Data for three values of k are shown. Other parameters are the same as for Fig. 1. 9


82


smoothly with k .

The decrease i n i

f

p

with k

c

l

f

> 5 x 10* M~

1

s*

i s due to the double peak phenomena as already discussed. When k i s small there i s no actual separation of the two waves. g

M

Note that when the two peaks actually separate, the f i r s t peak (i.e. that due to the reduction of the reactant) i s used i n the i pc versus k^r plots, The s h i f t i n with k i s shown i n F i g . 4. At very high f


values of y~, E s h i f t s positive of E°' Some aspects of this r pc M behavior have also been shown previously (5b,19). Effects of k

s,M u

The effects of k

on E can be seen i n F i g . 5. At large s,M pc ° values of y s , Epc i s constant as long as fy- i s constant. As y^ s decreases and the heterogeneous reaction becomes i r r e v e r s i b l e , the J

&

u

&

9

y

peak potential changes by 120 mv per decade change i n y dependence of i

i s independent of k

(7).

g

The

^ under reversible and i r r e -

g

versible conditions. For the highest value of k^ the peak current decreases as k

increases due to the double peak formation (cf,

g

Fig. 2). Comparison of Fig. 3 to F i g , 6 shows that the peak current of the catalyst wave i s much more dependent on k^ than on k « A similar comparison of Figs. 4 and 5 shows the following characteri s t i c s : 1) When k i s large the peak s h i f t depends only on g

g

M

M

changes i n k . Under these conditions, E values positive of E ° f pc pc for the mediator alone can be used for diagnostic c r i t e r i a for k^. 9

r

v

Peak potentials negative of the mediator peak however would produce ambiguous results since they could be generated by more than one value of k_; and 2) under conditions where the catalyst reaction i s not Nernstian, the peak potential i s dependent on both k^ and k ^. g

Thus i n this regime the determination of both rate constants would be d i f f i c u l t . Since k for the mediator i s normally obtained experimenta l l y , a set of working curves for the particular case under consideration can be generated using experimental values for a l l necessary parameters and plotting i ^ and E^ versus k^. It may be necessary to adjust the experimental conditions to obtain useful values of the diagnostic parameters. For example, i f one finds that values of i are very near those for the catalyst alone ( i . e . in F i g . 3, near -> 0.0), then increasing the value of y w i l l g

M

c

c

f

move i ^ to higher (and more diagnostically useful) values.


From


DIMARCO ET AL.

No.

4

1

-.2

1

s

20

2 10" 0 2 0 3 10° ,020 4 10' .002 2

Volts

4

3 o e o o

-.1 Downloaded by UNIV OF ARIZONA on December 17, 2014 | http://pubs.acs.org Publication Date: July 2, 1982 | doi: 10.1021/bk-1982-0192.ch006

y

2 • o

©

1

logkt 1 log Yi -26

o

2 -16

3 -6

4 .4

9I

5 14

6 2.4

Figure 4. Normalized peak potential versus the homogeneous rate constant. Different values of k demonstrate the dependence of peak potential on the heterogeneous rate constant. Other parameters are the same as for Fig. 1. $

o A 0 • O * O

0

0

o A

o

A-3

A A A A A

A

8

8

fC\

8

0

•

Volts -2

*

t

O

a

-.3

•

*

No

k

1

10

2

o

3

o

-.4

4

o

i

Log(ks) -6 Log(ys) -ie Figure 5.

-5 -2.e

-4

-te

-3 Ve

-2 .2

f

Yt

-

.0025 -

10

3

.25

10

5

25

10

6

250 i

i

-1

0

1.2

-

2.2

Normalized peak potential as a function of y . Different values of y are used; other parameters are the same as for Fig. 1. s


f



M

Q X

» e g^*M • S R

No kf/M^-S" y

2

3

•

A

9 ¥ ft *

A

5

_ o

o 4—A

o

t

*

3 •

•

*

•

2-o

o

o

O

0

o

l-o

o

o

O

0

0

o

o

o

6 10« 250 o

D

ft ft

o 4 o

% *

o

•

•

o

°

•

'P.O

1.0

Mpx*

5 4 3 10 10* 3X10 10< 1 0 003 .25 .75 2.5 25 1

1

f

2.0

*~»

Qx

°

o

t

.

O o

o

Log(ks)

-6

Log(y )

-3.8

s

igure 6.

i 1 -5 -2.8

4

1 1 -3

•1.8

-8

-2 .2

-1

1.2

1 0 22

The dependence of i on y is shown for different values of y . Other parameters are the same as for Fig. 1. pc

$


f

6.

DIMARCO ET AL.

Fig.


85 4

1

3 we see that k needs to l i e between 100 and 2 x 10 M" s~

l

f

(for the conditions shown in Fig. 3) for greatest u t i l i t y . The dimensionless homogeneous rate can be increased by either i n creasing the concentration of the reactants, or be decreasing the scan rate (v). Care must be exercised i n changing v as both k^ and k

gM

are related to v through the dimensionless parameters.

In the reversible region (k

large) this i s no problem since

g M

neither ipc or Epc vary much with ks,M* : however i n the quasireversible region or irreversible regime, changes in E^ and/or n

w

c


i

w i l l occur on varying y v i a changes i n v. pc ° ^s,M In general the i i s most diagnostically useful at i n t e r w

mediate values of y^ and the change i n E^ i s more useful for large c

values of k^ C/a.

A good point of delineation i s k^ C/a • 10.

Effects of Scanrate In order to v e r i f y a proposed mechanism i t i s useful to know the behavior of the simulation through a range of experimental variables. Probably most useful i s the correlation of peak pot e n t i a l or current to scanrate (v). Both k and k are related s,M f to v v i a the dimensionless parameters (Table 1). F i g . 7B shows that a decrease i n scanrate increases the contribution of the follow-up c a t a l y t i c process to the peak current. As discussed e a r l i e r the dimensionless homogeneous rate i s inversely proport i o n a l to v. In fact, for large values of k , where the peak current i s independent of k , a plot of i ^ / i ^ Q versus log r

v

1

gM

gM

i

1/v would resemble a plot of

i

p c

/ p

C

Q versus log k

f

(cf. Fig. 3).

Changes in Epc with v likewise r e f l e c t both k s and k-. ° f For the case where k i s large the change i n y generated by varygM

gM

ing v, does not s h i f t E . The resultant s h i f t i n E with v i s pc pc due to the e f f e c t i v e change i n k^. Thus as k^. increases or v decreases, the peak s h i f t s s l i g h t l y negative and then back i n the positive direction. Eventually i t becomes more positive than the E i n the absence of homogeneous k i n e t i c s . This i s similar to the behavior that was shown i n Fig. 4 for the change i n E due to pc k

g

^. When the rate of the heterogeneous process decreases,

changes i n v affect both y

gM

and y^.

The s o l i d lines plotted i n

Fig.

7A depict the s h i f t of E with ln(v) for an irreversible one pc electron transfer wave (7). The simulated points for curves 4 and



Figure 7.

The variation of E (top) and i (bottom) as a function of In (scan rate) is shown. K = 4x 1V/M s. pc

pe

f


6.

DIMARCO ET AL.


87

5 i n F i g . 2A appear to be the sum of the potential s h i f t due to y^ and that due to y . J


s

Diagnostic plots of one parameter as a function of the dimensionless rate are common i n numerical analyses of rate constants. Manipulation of the scan rate i s one way to experimentally change the dimensionless rate constants. Having more than one adjustable rate constants which depend on the scanrate make the determination of rate constants less straightforward. Changes i n v can however, be used to show the qualitative changes i n the i-E scan that are characteristic of the ec mechanism. This w i l l be demonstrated later. Concentration Ratio Effects Another system variable that can be manipulated experimenta l l y i s the concentration r a t i o , C /C . F i g . 8 shows the dependence of normalized reactant peak current on C^/Cg and k^. In F i g . 2 the reactant current was plotted as a function of pot e n t i a l when t h i s concentration r a t i o was equal to unity. In these figures the current i s normalized to i for the subpc,0 M

A

strate.

Increasing either the ^/Cg r a t i o or k^, increases the

turnover of the reactant* When the C /C- r a t i o i s very small, very w

M

b

large values of k^ are required for high turnover of the reactant. The l i m i t of the reactant contribution as k^ gets very large i s 1.351^

approximately

Q, i n agreement with similar results ob-

tained for y approaching 5 x 1 0 M" s"" . Although this discussion has so far been limited to the case where n = n^ « 1, and g / - 1, we can apply the same diagnostics to a wide range of similar cases. For the c y c l i c voltammetric results described herein, the concept of a concentration r a t i o can be expanded to a more general c y c l i c voltammetry "flux r a t i o " 5

1

1

f

D

D

g

M

i x

which would include the n and D ratios of the mediator and r e actant. Thus our previous results for C g / 1 w i l l apply to a l l experimental situations i n which the following r a t i o holds: C

=

M

1 n

Applying t h i s concept to F i g , 8 one can then use ( *

c

s

# D s

i r

s ) /

I n

C

#D

X

i n p l a c e

o f C

C

T h u S

t h i S

a n a l v s i s

f o rt

n

e

s i m

l e

^ M* M M ^ q/ M* P case can be applied to cases i n which D^ i s not equal to D^ and n

g

i s not equal to n^.

These results show that one can determine



88


1.2 1D .8

M

.6

cL

.4 .2

log k 10 range the peak potential s h i f t can also be used to determine the rate constant. According to Andrieux and coworkers the peak potential s h i f t 30 mV per decade increase i n k for very f

large y

f

(5b).

This particular determination i s dependent on

Nemstian response of the mediator. The present work allows the behavior of an ec c a t a l y t i c system to be predicted over the f u l l range of k for the mediator. gM

The variation due to k

was similar to the case of a single

g

electron transfer. The E was independent of k under reverspc s,M i b l e conditions and shifted by 120 mV/decade k under irreversi b l e conditions. In the quasi-reversible region the respective parameters varied smoothly between the two l i m i t i n g cases. The object of the exercise with k ^ has been to understand how i t can effect the diagnostic parameters used for the determination of k^. The f i n a l two parts of t h i s section showed how to experimentally obtain working curves that could be compared to simulated data. Plots of peak current versus v should be used discriminately since b e f f e c t i v e l y varies both y- and y . As long as y » 1 or i s s u

v

gM

g

y

« 1, i

rate.

i s independent of the dimensionless heterogeneous

In addition to t h i s , plots of i *

versus concentration can

PC

be used to match the simulated i versus y~ plots. pc i EXPERIMENTAL AND SIMULATED EC CATALYSIS The Catalysis of Oxygen Electro-reduction A problem that has been prominent for many years has been the catalysis of oxygen electro-reduction. The objective and problem with oxygen are i l l u s t r a t e d by the c y c l i c voltammetric i-E waves shown i n F i g , 9. Curve a i s the computer simulated i-E wave for a reversible, four electron reduction of oxygen to water (E° » +1.23 V vs NHE). The i value i s 8 times the peak height that J

r

f



90


[ .

1.0

.e

E vs

(

*h^^2

NHE

volts

Figure 9. CV i-E scans pertinent to oxygen reduction catalysis. Key: a, simulated, reversible, four electron reduction of oxygen to water; b, simulated ec catalytic mechanism, N = 4 with E °' = 1.23 volts; c, experimental oxygen reduction on glassy carbon; d, experimental FeTMPyP reduction on glassy carbon; and e, experimental oxygen reduction catalyzed by FeTMPyP (on glassy carbon). M


6.

DIMARCO ET

Second Order EC

AL.

91

Catalytic Mechanism

would have been obtained i f oxygen was reduced only to the superoxide ion, an one electron reduction. The factor of 8 appears because the number of electrons, n, i n the reduction of oxygen to water i s raised to a power of 3/2 i n the Randles-Sevcik equation (16). I f i t were possible to mediate ( i . e . catalyze) the reduction of oxygen at the reversible potential using an one electron mediator, the increase i n current by oxygen conversion to water (N = 4) would be a direct multiple of N, the stoichiometric coefficient. Thus for a follow-up reaction l i k e : N»M

+ S

= N»M + S ox ox r the current would be given by:

C6)


r

1

- Si

C7)

+

where i ^ i s the current due to the mediator and i«, i s that contributed by the ec catalysis of the reactant species. Thus for oxygen, an one electron mediator would produce a peak height (N»i p,)b due to oxygen catalysis of curve b i n F i g . 9. For the c

conditions shown, N»i

i s only four times that of the one elecp,o tron reduction of oxygen. One can draw similar conclusions regarding the reduction of oxygen to hydrogen peroxide (N = 2). Curve C i n the same figure i s the experimental i-E curve for the reduction of oxygen at a highly polished glassy carbon electrode i n 0.1M H S0*. This reduction i s highly i r r e v e r s i b l e with the peak potential shifted negative of the reversible peak by about 1.5 v o l t and the peak current i s about one-fifth the height of the reversible peak (curve a). Curve d shows the reversible redox i-E wave for the iron tetrakis(N-methyl-4-pyridyl)porphyrin (abbr: FeTMPyP) which has been shown to be an effective catalyst for the reduction of oxygen on glassy carbon (!)• In e a r l i e r studies in which the FeTMPyP and oxygen concentrations were equal to 2,4 x 10~ M (air-saturated solution), H 0 was concluded to be the product of the oxygen reduction, from the analysis of the CV i-E wave heights (1), Curve e i n F i g . 9 i s the i-E wave for the above conditions. To date a l l of the data are consistent with an ec catal y t i c mechanism for t h i s reduction. Three different ec c a t a l y t i c mechanisms are considered i n the simulation of the i-E curves for oxygen reduction catalyzed by FeTMPyP. These are: 2

k

3

1.

2

e step:

Fe(III)TMPyP + e- = Fe(II)TMPyP

c step:

2Fe(II)TMPyP + 0

2

+ 2H

+

(8)

=

2Fe(III)TMPyP + H 0 2

2


(9)

92


2.

reaction 8 followed by: +

4Fe(II)TMPyP + 0 + 4H = 2

(10)

4Fe(III)TMPyP + 2H 0 2

3.

Reactions 8 and 9 followed by: +

2Fe(II)TMPyP + H 0 + 2H = 2

2

2Fe(III)TMPyP + 2H 0

(11)


2

where reactions 9, 10 and 11 reflect the reactant stoichiometry i n the homogeneous step. The simulated i-E waves showing an N = 2 stoichiometry for oxygen catalysis by Fe(II)TMPyP are given i n Fig. 10 A and B. The experimental k value of 5 x 10" cm s~* i s used i n F i g . 10 A as the value of reaction 9 i s varied, while 3

gM

6

1

l

in Fig. 10 B, the k i s fixed at 2 x 10 M" s~ as the value of f

k ^ i s varied. These values of k^ and K had been previously g

g

estimated from CV data (19). The i

values are about 5 times

pc

greater than those previously seen i n F i g . 2 for similat values of k and k^ because of the larger ratios of^/ ^ ' 2 and g / = 9 for the oxygen/FeTMPyP case. More recently, i t (19) has found that the extent of oxygen catalysis by FeTMPyP was concentration dependent. The i ^ normalized to i (where i ^ i s the peak current for reduction of pc,0 pc,0 oxygen to superoxide ion) was found to approach four at FeTMPyP/ oxygen concentration ratios greater than two. This result suggested that oxygen could be c a t a l y t i c a l l y reduced to water. In this case the overall reaction has a stoichiometry of four. Characterization of this reaction by changes i n the concentration r a t i o i s shown i n F i g . 11, A and B, The results r e f l e c t the large homogeneous rate constant i n two ways: 1) the rapid i n crease i n i with C^, and 2) the s h i f t of E positive of the E{> 0 °^ * d i a t o r . The experimental results can be compared to different mechanisms for mediated oxygen reduction. The peak currents for oxygen reduction are higher than that expected of a two electron process. This model i s therefore considered inappropriate. The simulated peak currents for the mediated N = 4 case are greater than that obtained experimentally. Thus under these conditions the reaction i s somewhere between the two and four electron processes. Of course the peak currents for the four electron stoichiometry can be decreased by decreasing the homogeneous rate; this w i l l be discussed l a t e r . Using mechanism 3 the values of i closely match the experimental results. In add««n

n

D

D

g M

M

c

A

p

t

c

p c

ie m e

c

0


DIMARCO ET AL.

Second Order EC Catalytic Mechanism NO 1 2 3 4 5 6 7 8 9 10

-1


3

0.0

yc 2x10 500 6x10 150 2x10 50 6x10 15 5 2x10 6x10 15 .5 2xK> 6x10 .15 2X10 .05 0 0 6

5

5

4

4

3

3

2

2

-0.4

VOLTAGE

Figure 10. Simulated i-E scans for the ec catalytic mechanism when N = 2, and D /Du — 9. Effects of changing k , with k = 5 X 10 cm/s (top); and k when k = 2 X 1V/M s (bottom). 3

a

f

9tM

f


$tM

94


.1 -


B

1

2

3 C(M)/C(S)

4

5

Figure 11. Dependence of E (top) and i (bottom) on the concentration ratio CM/C . Key: D /D = 9; curve 1,N = 2,k = 1 X 1&/M s, k = 0.01 cm/s; curve 2, N= 4, k = 2 X 10*/M s, k = 0.01 cm/s; curve 3 N = 2 + 2 (scheme three), k (rxn 8) = 5 X i 0 7 M s k (rxn 10) = 5 X 1P/M s k = 0.01 cm/s; and curve 4, experimental reduction of oxygen using water soluble FeTMPyP. po

q

S

pc

M

f

f

t

$

f

f

$

T

t

$


6.

DIMARCO ET AL.


95

i t i o n to t h i s , F i g . 11 B shows the peak potential s h i f t s of the catalyzed wave (with mechanism 1 excluded). The results clearly demonstrate that the peak potentials for mechanism 3 more closely match the experimental peak s h i f t s . The peak currents for mechanism 2 can be lowered to approach the experimental by l ° ~ ering the homogeneous rate constant. However, the concomitant s h i f t of E ^ i n the negative direction makes t h i s lowering of k^ i

f s

w

p c

unacceptable (cf. F i g . 11 B). Further d e t a i l s of the mechanistic pathways for the reduction of oxygen catalyzed by t h i s water s o l uble iron porphyrin w i l l be published (19).


CONCLUSION CV, i-E waves can be used p i c t o r i a l l y to demonstrate the characteristics oa an ec c a t l y t i c mechanism. Wave parameters ( i pc and Epc) can be used diagnostically to obtain shoichiometric ° and k i n e t i c information. Use of these parameters i n conjunction with d i g i t a l l y simulated data can provide qualitative to semiquantitative information on very complex ec mechanisms. The determination of the homogeneous rate constants i s especially usef u l for oxygen catalysis by water-soluble metal porphyrins, which can be transferred to the surface by immobilization for heterogeneous catalysis. There i s evidence already i n the case of immobilized iron porphyrin (4) that the N value does depend on the coverage of the catalyst, i n agreement with the homogeneous results. I t i s our purpose to continue the study of the relation-^ ships between homogeneous and immobilized ec c a t a l y t i c systems and to apply the tools developed i n this study to the diagnosis of surface modified for electrocatalytic purposes. M

M

ACKNOWLEDGEMENTS We gratefully acknowledge the support of t h i s work by grants from the A i r Force Office of S c i e n t i f i c Research (grant No. 783672) and the National Institute of Health (grant No. 19181). The discussions and helpful comments by H.N. Blount of the University of Delaware are gratefully appreciated.


96


Cg

Key to Symbols and Abbreviations n»F»v/(R/T) transfer coefficient f o r an electrochemical reaction bulk concentration of the mediator: M bulk concentration of the reactant: M

CV

c y c l i c voltammetry

D

d i f f u s i o n coefficient of the mediator: cm s~*

a alpha

2

w

1

diffusion coefficient of the reactant: cm s"

E^'M

formal electrode potential of the M , couple ox/r formal electrode potential of the $ / couple

Q

E 'S Downloaded by UNIV OF ARIZONA on December 17, 2014 | http://pubs.acs.org Publication Date: July 2, 1982 | doi: 10.1021/bk-1982-0192.ch006

2

Dg

ec E^

v

ox

Y

designates an e l e c t r o c a t a l y t i c scheme involving an homogeneous step following a heterogeneous electron transfer cathodic peak potential: Volts

F i pc i ~ pc,0 K

equilibrium constant

k^

homogeneous rate constant f o r forward reaction: M"* s*"

k ^

heterogeneous rate constant of the mediator: cm s"

k

heterogeneous rate constant of the reactant: cm s'"

g

Faradays constant: 96500 coulombs peak cathodic current peak cathodic current f o r a l e , reversible reaction

1

1

1

1

S y %y

M , ox/r N

mediator i n ex c a t a l y t i c scheme stoichiometric r a t i o equal to n^/vt^

n^

number of electrons transferred per molecule of

ng

number of electrons transferred per molecule of S /

ox R r S , ox/r T v yy

oxidized form of a redox couple gas constant: 8.314 joules/mole»degree reduced form of a redox couple reactant i n an ec c a t a l y t i c scheme temperature i n degrees kelvin scanrate: V s~* dimensionless homogeneous rate » k-»C/a dimensionless heterogeneous rate = k /d^»a

g

J

M o x

/

QX

J

2

g


r

r

6. DIMARCO ET AL.


97

Literature Cited


ed

1. T. Kuwana, M. Fujihira, K. Sunakawa, and T. Osa, J. Electroanal. Chem., 88 (1978) 299. 2. T. Kuwana and A. Bettelheim, Anal. Chem., 51 (1979) 2257. 3. T. Kuwana, R.J. Chan and A. Bettelheim, J . Electroanal. Chem., 99 (1979) 391. 4. T. Kuwana, R.J. Chan and A. Bettelheim, J . Electroanal. Chem., 110 (1980) 93. 5. For example, see the following papers and the references listtherein: a) C.P. Andrieux, J.M. Dumas-Bouchiat and J.M. Saveant, J . Electroanal. Chem., 87 (1978) 39-53; b) C.P. Andrieux, C. Blocman, J . J . Dumas-Bouchiat, F. M'Halla and J.M. Saveant, J . Electroanal. Chem., 113 (1980) 19-40; and c) M.K. Hanafey, R.L. Scott, T.H. Ridgway and C.N. Reilley, Anal. Chem., 50 (1978) 116. 6. J.M. Saveant and E. Vianello in "Advances in Polarography", I.S. Longmuir (Ed.), Vol. I, p. 367, Pergammon Press. N.Y., 1960. 7. R.S. Nicholson and I. Shain, Anal. Chem., 36 (1974) 706-723. 8. J.M. Saveant and E. Vianello, Electrochim. Acta., 10 (1965) 905. 9. S.W. Feldberg in A . J . Bard (Ed.), "Electroanalytical Chemistry", Vol. 3, Marcel Dekker, New York, 1969, pp. 199-296. 10. D. Britz, "Lecture Notes in Chemistry" Digital Simulation in Electrochemistry", Springer-Verlag Berlin. Heidelberg, New York, 1981. 11. For example the heterogeneous equivalent approximation (12), the unequal box size method (13), the orthogonal collocation technique (14) and the aforementioned implicit scheme all w i l l lead to decreased computer time, although a price is usually paid in generality and/or accuracy, 12. J . Ruzic and S.W. Feldberg, J . Electroanal. Chem., 50 (1974) 153-162. 13. T. Joslin and D. Pletcher, J . Electroanal. Chem., 49, (1974) 171-186. 14. B. Speiser and A. Rieker, J . Electroanal. Chem., 102 (1979) 1-20. 15. Several programs used in this study, as well as added insights into the ec catalytic mechansim were provided by Prof. Henry Blount of the University of Delaware. 16. (a) J.E.B. Randles, Trans. Faraday Soc., 44 (1948) 327, (b) A. Sevcik, Collect. Czech. Chem. Commun., 13 (1948) 349. 17. Recent results by Anson (18) and Saveant (5a) indicate that this driving force i s not necessary as long as a sufficiently rapid follow-up reaction occurs which effectively removes the product (S ) of reaction 2. 18. F . C . Anson, J. Phys. Chem., 84 (1980) 3336-3338. 19. P. Forshey and T. Kuwana, submitted for publication (1981). 20. H. Matsuda and Y. Ayabe, Z. Electrochem., 59, (1955) 494. r

RECEIVED March

19, 1982.


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