Photogalvanic cells

J. Electroanal. Chem., 107 (1980) 23--35

23

@)Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

PHOTOGALVANIC CELLS PART X. THE T R A N S P A R E N T DISC ELECTRODE A N D THE IRON--THIONINE SYSTEM

W. JOHN ALBERY, PHILIP N. BARTLETT, W. RICHARD BOWEN* F. STEPHEN FISHER and ANDREW W. FOULDS

Department of Chemistry, Imperial College, London SW7 2A Y (England) (Received 25th April 1979; in revised form 9th August 1979)

ABSTRACT The kinetics of the iron--thionine system have been investigated using the transparent rotating disc electrode and flash electrolysis. Using the transparent disc electrode, from the results for the variation of photocurrent with rotation speed and irradiance, we can find the quantum efficiency for the production of semithionine, the efficiency for producing leucothionine from semithionine and the rate constant for the back reaction of leucothionine with Fe(III). This rate constant is also determined from the flash electrolysis experiments. The values of the kinetic parameters are found to be in good agreement with values determined by analysis of the photostationary state, flash photolysis and ac modulation at a transparent disc electrode. The relative merits of the different techniques for investigating photogalvanic systems are discussed.

INTRODUCTION The iron--thionine system has been investigatedas a possible system for photogalvanic cells for solar energy conversion [1--4]. The reaction scheme is: Th ~ Th* Th* + Fe(II) + S" + Fe(III) S" + Fe(III) ~='> Th + Fe(II) k3

S" + S ' - + Th + L

L + Fe(III) k_~ S" + Fe(II) Illuminated electrode: L -+ Th + 2e

Now at Department of Chemistry, Oslo University, Oslo, Norway.

24 Dark electrode: Fe(III) + e -~ Fe(II) where Th is

S" is H

H2N.~'~+'~NH2 and L is H

H~I~'~~+NH3 The reaction scheme may be written more conveniently: Th--

hp

~ S'<

k3

L k3

In this paper we report results on this system using t w o different techniques. The first technique involves dc measurements at a transparent rotating disc electrode. The second technique is flash photolysis with electrochemical detection [5] which we shall call "flash electrolysis". By combining the results from these two techniques with results presented previously from the analysis of the photostationary state [6,7], we can determine the overall quantum efficiency for the production of leucothionine. We also show that the values for the rate constants determined by the different techniques are in good agreement. EXPERIMENTAL The apparatus and technique for the transparent rotating disc electrode has been described previously [8, Part IX, this issue pp. 11--22). The irradiance of the light passing through the electrode with no neutral density filter, I¢ = z, was measured using a Metrologic Radiometer. The diffusion coefficient of thionine was measured using the method of Hitchman and Albery [10]. The flash electrolysis experiments were conducted on the same t y p e of electrode except that it was n o t rotated. The flash was provided b y a Vivitarauto 202 camera flash m o u n t e d directly above the electrode. The current-time transients were recorded on a Gould OS 4000/1 digital storage oscilloscope. The stopped flow experiments were carried o u t using a Nortech SF2A stopped flow spectrometer. All chemicals and solutions were prepared as described previously [ 7 ]. All experiments were carried o u t at 25°C in 50 mM H2SO4 with [Fe(II)]/mM = 10. This concentration is sufficient to trap all of the triplet thionine [7].

25 RESULTS AND DISCUSSION

Typical current voltage curves for the iron thionine system at a transparent rotating disc electrode have been shown in fig. 2 of Part VIII. The photocurrent caused by the photogenerated leucothionine was measured with no added Fe(III) and with [Fe(III)]/mM = 4.35. The irradiance was varied using neutral density filters and the rotation speed was varied from 1 to 50 Hz. Typical results are shown in Figs. 1 and 2. For the iron thionine system the absorbance length, X~ [11], in which the light is absorbed, is always much longer than the other lengths: XJcm

=

(e[Wh]) -1 = 0.13

(1)

where e/dm 3 mmol -~ cm = 129 at X/nm = 598, and [Th]/pmol dm -3 = 60. We can therefore simplify eqn. (10) of Part VIII [12, this issue pp. 1--9] to ob-

/

÷~

5C

"%. 4.0 io/NA

~,

(~= I

+~+-...~o. "0

3.0

2-0

"%,

~ =0-47

~"

@ :o-17

1.(3

oc

0-0

I

I

0.5

1.0

(w/Hz)-v2

Fig, 1. Typical photocurrent--rotation speed curves for solution w i t h n o added Fe(III). Each curve is labelled with the fractional transmittance of the neutral density filter used, ~ . The photocurrents were measured at the potential o f zero dark current: E(vs. S.C.E.) = 3 2 0 i n V . The broken lines connect the observed points; the solid lines connect the points after they have been corrected according to eqn. (15) for reaction of Fe(III) at the electrode. The inset shows that the photocurrents at l o w rotation speed vary w i t h dpw2

26

,,C,'-

O

o

O

3.0 "O,.. . . . .

-(3

1435/IJA

20

1.0

oc

O.O

I

I

0-5

10 (W/Hz)-'i,/2

Fig. 2. T y p i c a l p h o t o c u r r e n t - - r o t a t i o n s p e e d c u r v e s f o r s o l u t i o n w i t h [ F e ( I I I ) ] / m M = 4 . 3 5 . T h e n o t a t i o n is t h e s a m e as f o r Fig. 1. T h e p o t e n t i a l o f t h e e l e c t r o d e w a s 4 0 0 i n V .

tain for the photoelectrochemical collection efficiency, Nhv: i 2(~14~:X~ k Nhv - dPih~, Xe ' f(K)

(2)

where f(~) = cosh(l~) -- exp(--[~: 2) sinh(~)

(3)

t¢ = X D / X ~ , k

(4)

2.k = x-d +

(5)

X a = (DIe 1¢2(1)1. = le)1/2

(6)

Xk = {D/(1 -- q~2)k_2[Fe(III)] }i/2

(7)

XD = 0.64 D 1/3 ul/6 W-i/2

(8)

ihv = A F I ¢ = 1

(9)

I¢ = 1 is the flux of photons per unit area for ~ = 1 ¢1 is the quantum efficiency for the production of semithionine ~b2 is the fraction of semithionine that is converted to leucothionine dPis the fraction of the irradiance transmitted by the neutral density filter. A is the area of the electrode and W is the rotation speed in Hz. The lengths XG, Xk and XD are the generating, kinetic and diffusion lengths respectively [ 11]. The factor 2 in eqn. (2) for the photoelectrochemical collection efficiency arises because leucothionine to thionine is a two.electron oxidation. On the other hand because leucothionine is formed b y the disproportionation of S',

27 i The product ~, ¢2 appears in the definition of XG because to bleach the ¢ 5 < ~, solution one has to turn thionine into leucothionine. Similarly the factor (1 : ¢5) appears in the definition of Xk because it describes the fraction of semithionine that forms thionine. It is convenient to express the flux of photons with no neutral density filter, I¢ =1, as a current ih~, according to eqn. (9). For our experiments: i h v / m A = 1.2

(I0)

D / c m 2 Ms-' = 5.8

(11)

and A/cm 2 = 0.129

(12)

Equation (3) for f(K) reduces to simpler forms when ~ is either << 1 or >> I: < < 1, f(~) ~- ~ and Nhv ~ 2dp,¢2XD/X e

(13)

>> I, f(~) --~ 1 and Nhv ~-- 2~,(P2XG.k/Xe

(14)

when g << 1, XDis much smaller than X~,k and most of the leucothionine photogenerated close to the electrode is lost by convective dilution to the bulk of the solution. From eqns. (8) and (13) the faster the electrode is rotated the lower is the photocurrent, and i should vary with W-'n. It can be seen in Figs. 1 and 2 that this type of behaviour is found for high values of W. When K>> 1 then X~,k is shorter than XD. If Xk is the smallest length, then most of the photogenerated leucothionine is lost by the back reaction; a photostationary state is set up close to the electrode, which is unaffected by the convective dilution and therefore by the rotation speed. If XG is the smallest length, then the solution close to the electrode becomes bleached. The current arises from the absorption of photons close to the electrode by the thionine that is itself the product of the electrochemical oxidation of the photogenerated leucothionine. This is depicted in the following cycle: Electrode

L ~ L + 2 Fe(III) -2e ~ t

hv

hv

T h ~ T h + 2 Fe(II) Distance ~XG < XD

Again the photostationary state does not depend upon X v . Hence when ~ > > 1 the photocurrent becomes independent of the rotation speed. Many of the experimental curves in Figs. 1 and 2 show maxima as W is decreased. These maxima arise because the electrode is n o t perfectly selective between leucothionine and Fe(III). There is some reaction of Fe(III) (and Fe(II)) on the electrode. In both sets of experiments the electrode was potentiostatted at the potential of zero dark current (0.320 V when [Fe(III)] = 0 and 0.400 V when [Fe(III)]/mM = 4.35). Then the contribution to the photocurrent caused by Fe(III) arises entirely from the photogenerated Fe(III). When XG < XD, the generation of Fe(III) close to the electrode by the cycle illustrated above means that the concentration of photogenerated Fe(III) builds up at the electrode surface. This is because the escape of Fe(III) across the diffusion layer, XD, is slower than the consumption of leucothionine at the electrode; the leucothionine has

28

only to diffuse across the smaller distance X6. We can then show that: b. =

iobs(1

+

XDk'/D)

(15)

where i~ = iL -- iFe(II[) and k' is the electrochemical rate constant for the reduction of Fe(III) at the potential of the electrode. Values of k' were estimated from a Tafel plot for the reduction of Fe(III) on the particular electrode used in these experiments. The effect of the correction is shown in Figs. 1 and 2. After making this correction the variation with rotation speed of iL, the photocurrent due to leucothionine, for each irradiance shows a plateau rather than a maximum. For the case with [Fe(III)]/m_M = 4.35 in Fig. 2 the change at ~ -~ 1 between the limiting forms of Nhv takes place for all values of the irradiance at roughly the same value of the rotation speed, W ~ 12 Hz. This t y p e of behaviour is found when XG,k is dominated b y Xk and a single value of W balances XD with Xk. In contrast for the case with no added Fe(III) we find that the switch at ~ = 1 depends on the irradiance, taking place at lower values of W the lower the irradiance. This is the behaviour to be expected if X6,k is dominated by X~, because XD varies with W- in and XG with 4-1/2. This variation of XG with 4 - in means that, as shown in the inset of Fig. 1, the limiting currents vary with ¢1n rather than ¢P. Hence we may conclude that for the results in Fig. 1 the balance is between convective dilution and bleaching. On the other hand for the results in Fig. 2 the size of the limiting currents at low rotating speed are also partly determined by the rate of the back reaction of leucothionine with the added Fe(III). We n o w analyse the data in Fig. 1. With no added Fe(III) the leucothionine is formed efficiently by the disproportionation reaction and ~b2 - 1 With this value and assuming XG.k is dominated by X~ we obtain from eqns. (2), (4), (5), (6) and (9):

i/dp'12 = (¢1 ihvXa,1/Xe)f(l~)

(16)

6.(3

~#~/2/vA

÷

v 4.C

~

x/o

x

v .o

~

xa

~o

t,

x

~ o

ol

o.o 0.0

I

I

0.2

0.4

[ 0.6 q)~/2(w/Hz) -~/2

I

I

0.8

1,0

Fig. 3. All the corrected data for the solution with no added Fe(III) lie on a common curve. The solid line depicts f(/~) calculated from eqn. (3). The values of the transmittance of the neutral density filter, qS, are shown as follows: (o) 1; (X) 0.71; (ix) 0.60; (+) 0.47; ([]) 0.37; (*) 0.24; (~)0.22; (e) 0.17;(0) 0.14; (J) 0.08; (o) 0.06.

29 where (17)

I~ = X D , I ~ I / 2 / X G , 1 W 1/2

and Xv,1 and XG.1 are the values of XD and XG for W = 1 and cp = 1 respectively. Equations (16) and (17) predict that all the current/rotation speed data should lie on a c o m m o n curve when one plots i / ~ in against ( ¢ / W ) ' n . Figure 3 shows that this is indeed true for the 80 points observed for values of 4p between 0.06 and 1.00 and values of W / H z between 1 and 49. From the gradient at low ~, using the approximation f(~) -~ K and eqns. (1), (6), (8), (10), (16) and (17), we find: ¢, = 0.56

From the limiting value at high ~, using the approximation f(~) = 1 and eqns. (1), (6), (10) and (16), we find: ¢, = 0.53 There is good agreement b e t w e e n the two values for ¢,. The error in the: value of 0.53 is larger since the current depends on ¢]/2 rather than ¢,; hence we t a k e ¢, = 0.55

(18)

Furthermore, as shown by the theoretical line in Fig. 3, the slope of the curve agrees with that of the f(~) function for intermediate values of g. Hence these results are in good agreement with the theory for the bleaching at a transparent disc electrode presented earlier [12]. Turning to the results with added Fe(III) we first note that at high values of W there is the same type of W- ' n dependence as in Fig. 1. This rotation speed dependence shows that XD is the shortest length, g < < 1, and eqn. (13) applies. We conclude that there is no bleaching and the leucothionine is stable. However, for the same values of W and • the currents with added Fe(III) are smaller than those with no added Fe(III). For the reaction scheme from eqn. (13) this can only be because ¢2 is less than l a n d semithionine is being lost by reaction with Fe(III) [3,13,14]. As Fe(III) is added, the mechanism shifts from A-2 with an efficient disproportionation reaction to A-l, where the main fate of semithionine is re-oxidation to thionine by Fe(III) [6,7]. We compare the values at W / H z = 49 of the current (see Fig. 2), i4.3s, for [Fe(III)]/mM = 4.35 with the corresponding values of i0 (see Fig. 1) at the same irradiance, where: 2¢2 = (i,~.3s/io)w = 49

(19) •

But from the appendix we find that: 2¢2 =

[(1

+ y)1/2 _

1]/[(1

+ y)l/2 +

1]

(20)

where Y = 8 ¢ , (Pla, = l e k a [ T h ] / ( k _ , [Fe(III)]) 2

(21)

From eqn. (21) we predict (Y/~p) should be constant and eliminating ¢2 between eqns. (19) and (20) we find Y 1V(i°+i4"3sl 2 --1] -~ = "~ L\ i o = i~.3s / w . 49

(22)

30 TABLE 1 Analysis o f d a t a in Fig. 2 Rotation speed/Hz Equation

W = 49 (22)

W = 49 (19)

W= 1 (25)

dp

Y/~P

¢2

Z/PA -1

1.00 0.71 0.61 0.47 0.37 0.29 0.22 0.17

18 21 -27 25 19 18 23

0.33 0.30 0.29 0.27 0.25 0.23 0.21 0.19

0.146 0.123 0.130 0.106 0.120 0.119 0.118 0.133

Mean

22 -+ 1

0 . 1 2 4 -+ 0 . 0 0 4

Values of y/dp are given in Table 1. Reasonable agreement at the different values of ¢P is found and substituting the values from eqns. (1), (9), (10), (12), (18) and (21) we find: (k2_~/k3)/dm 3 mo1-1 s-1 ~ 8.0

(23)

In Table 1 we also give the values of ¢~ calculated from eqn. (19) and the mean value of y/d;. The value of ~2 decreases with the irradianee because the secondorder disproportionation reaction is less favoured compared to the first-order reaction with Fe(III). Returning to t h e data with added Fe(III) we now analyse the results at low rotation speed. Here comparing the typical results in Fig. 2 with those in Fig. 1, the reduction of current is caused not only by ¢2 < ~(see above) but also by the reaction of leueothionine with the added Fe(III). Assuming f(~) = 1, eqn. (2) can be written: =

+

/4.3S

2

,

(24)

(XG ,1)¢~ =

where Xk and XG, X are calculated according to eqns. (7) and (6) with ~b2 = ~. Again comparing values of i4.3s with the corresponding values of i0 at the same irradiance we find that, for no added Fe(III), Xk is long, ¢2 = 4' and from eqn. (16): (¢~?ihv) ,

X~P "2

io

Substitution in eqn. (24) gives 2~2

'nF. 2¢2"

1

l

Values of Z are given in Table 1, where, as predicted by eqn. (25), t h e y are reasonably constant. Substituting values from eqns. (1), (7), (10) and (18) we ob-

31

tain:

k_2/dm 3 mo1-1 s-'

=

560

(26)

The shape of the current/rotation speed curves can be tested in a similar way to that used in Fig. 3. From eqns. (2), (24) and (25) we can show that:

~4"3Sl ~0 '~

= (~)lihv

(I) 112 \i4.35]W

(27)

f(/~)

=1

X e

where XD, 1 /~ ---- ( X G , 1 ) 0 2

2.¢2qb"2( io t

=1

(28)

\i4.3slW=l

W 112

"

Figure 4 shows a plot of the left hand side of eqn. (27) against the variable part of ~. N o t only do all the data lie on a c o m m o n curve b u t also as required the curve is the same curve as in Fig. 3. This arises because the constant terms in eqns. (27) and (28) are the same as those in eqns. (16) and (17). In concluding this section we would like to emphasise the versatility of the transparent disc method. From the data with no added Fe(III) we obtained ¢1 the overall quantum efficiency for semithionine formation b y two different methods. From the data with added Fe(III) at high rotation speeds we obtained ¢2 the efficiency of leucothionine formation from semithionine and at low rotation speeds we measured the rate constant for the reaction of Fe(III) with leucothionine. The flash electrolysis method has been developed by Ohsawa and Aoyagui [5] and independently by ourselves. After the flash the leucothionine and Fe(III) recombine. The progress of this reaction is followed using the limiting current of the reaction of leucothionine on the electrode. A simple analysis using Fick's second law of diffusion [5] shows that

log(it in) = a constant

-

-

k_2[Fe(III)] t

(29)

60 v

~De ÷

¢~,~ o

o

x

~x

o

;° .o ~

g

2.0

..Y 0.0 O0

/

?

I 0.,2

I

I

J

0"4 0"6 0,8 W-1/2 1~1/2(i0/i4.35)W.1 (i4.35/io )W-49 /Hz-1/2

I 1.0

Fig. 4. All t h e c o r r e c t e d d a t a f o r t h e s o l u t i o n w i t h [ F e ( I I I ) ] / m M = 4 . 3 5 lie o n t h e s a m e c o m m o n c u r v e as in Fig. 3. T h e n o t a t i o n f o r t h e values o f (I) is t h e s a m e as f o r Fig. 3.

32

1.5

1-0 i/IJA

t/ms

0.5--

0

I

I

I

50

100

150 t/ms

Fig. 5. Typical current transient for flash electrolysis experiment w i t h [Fe(III)]/mM = 12.5. Inset shows data plotted according to eqn. (29) to find the rate constant from the gradient.

A typical transient is shown in Fig. 5. At short times there is a large maximum in the current because of double layer charging caused by the change in current interacting with the ohmic resistance of the solution and the SnO2 electrode [15,16]. Observations therefore have to be confined to times longer than 10 ms when the charging is complete. Figure 5 also shows the plot of the data according to eqn. (29). The rate constant is found from the gradient. Flash electrolysis

Y

15--

10--

'T

-2.

.j0

0

I

I

I

I

10

20

30

40

Ire <~)]/ram

Fig. 6. Variation of observed first-order rate constant from flash electrolysis experiments, k_2[Fe(III)] , with [Fe(III)].

33 TABLE 2 Results f o r t h e i r o n - - t h i o n i n e S y s t e m in 50 m M H 2 8 0 4 at 25°C (all rate c o n s t a n t s are r e p o r t e d in d m 3 mo1-1 s -1) Method

Ref.

Steady-state photochemistry Flash p h o t o l y s i s

Eqn.

7

l ~ l / d P l k 3 ffi 8 ( k - ~ / k 3 ffi 5

k-2/~bl = 7 6 0 k-2 = 4 3 0 a)

13 17

I~l / k 3 = 3 b k~l/k3=3 c

k.. 2 = 2 6 0 b

S t o p p e d flow T r a n s p a r e n t disc electrode

k-2 = 4 3 0

Flash electrolysis ae m e t h o d

(30) 8

dc m e t h o d , no added Fe(III) added Fe(III) Ideal s y s t e m

k-2 = 4 2 0 c

k_2 = 4 3 0 ~ I = 0.8

( 1 8 ) ¢ I = 0.55 (23) (26) 4

¢1 = 1

k.~i/k 3 = 7

l~l/k3

= 8

k ~ / k 3 < 30

k. 2 = 560 k_ 2 < 10 a

a A s s u m i n g ~bl = 0.57, b T / ° C = 22, c [H2SOa ] = 10 mM.

was carried o u t at concentrations of Fe(III)/mM from 5 to 30. Results are plotted in Fig. 6 and we obtain the value k_2/dm 3

mo1-1 s-1 = 430 + 10

(30)

We n o w collect together in Table 2 results for the iron--thionine system in 50 mMH2SO4 obtained by a variety of different methods. It can be seen that despite the very different nature of the methods, good agreement is obtained for the various parameters. This good agreement further supports the theory of the transparent disc electrode [ 11,12]. We have also included in Table 2 the parameters required for an ideal photogalvanic cell for solar energy conversion [4]. It can be seen that the iron thionine system satisfies the kinetic constraints. However, the fact that ¢1 = 0.57 must reduce the efficiency by this factor. This factor probably arises from inefficient inter-system crossing from the singlet to the triplet. Detailed work at the Royal Institution has measured the efficiency of this stage as ~ = 0.55 [17]. Finally we discuss the value of the different methods in investigating systems for photogalvanic cells. We consider that analysis of the photochemical stationary state is the best way of determining the photochemical mechanism [6,7]. This is because the a m o u n t of bleaching is directly observed as a function of irradiance and composition. There are no electrochemical complications! The rate constant for the back reaction can be determined separately from all other parameters by either of the conventional methods -- stopped flow or flash photolysis -- or by flash electrolysis; the flash eIectrolysis experiment is very simple, cheap, and easy to carry out. The ac methods on the transparent disc electrode [8] is probably the best method of measuring ¢1 since the frequency is high

34

enough for there to be no complications from convective dilution. The ac m e t h o d is also a good technique for measuring the back reaction rate constant providing that it is large enough. The dc method on the transparent disc electrode mimics most closely the situation in the photogalvanic cell. All of the relevant processes can therefore be measured, and this makes it an ideal technique for the screening of new photogalvanic systems. The analysis and separation of the values for the different parameters can however be fairly complicated and the complementary methods are useful in providing a check on the values needed to predict the efficiency of the cell. ACKNOWLEDGEMENTS

We thank BP for research scholarships for PNB, WRB and FSF, and the SRC for a research studentship for AWF. We thank Dr. Harriman for a helpful discussion of his results for ~,. This is a contribution from the Oxford-Imperial Energy Group. APPENDIX

In this appendix we derive the expression for ¢2, the fraction of semithionine that forms leucothionine. From the reaction scheme: ¢2 = k3[S']/(2k3[S'] + kgx)

(A1)

w h e r e / d , = k_, [Fe(III)]. We can apply the steady-state approximation to S" and obtain: khv + k'2[L] = 2k3[S'] 2 + k ' , [ S ' ]

(A2)

where k'2 = k_2[Fe(III)] and khv = ~ , ~ I ~ = l e [ T h ] The steady-state approximation for L gives: k 3 [ S ' ] 2 m (k~ 2 + leD) [ L ] where k D =

(A3)

D/X~.

The first-order rate constant k D describes the loss of L b y convective dilution. Substitution of eqn. (A3) in eqn. (A2) gives a quadratic equation for [S']. Solution of the quadratic and substitution in eqn. (A1) gives: 24~2 =

1+ 1+

4khvk3 (/~,)2

1

+

kD k-2+

~7 ,/2

kD]J

--

~(I+Y)'n--1 (I + y)I/2 + 1 where y-

8khvk3 _

_

(kZ,)2

_

8~bI(PI¢ =i ek3[Th] (k_,[Fe(III)]) 2

We can show that the maximum error in the simplifying approximation is

35

always less than 10%. In our particular set of experiments it was always less than 5%. REFERENCES 1 E. R a b o n o w i t c h , J. Chem. Phys., 8 (1940) 551. 2" W.D.K. Clark and J.A. Eckart, Solar Energy, 17 (1975) 147. 3 N.N. Lichtin in J.R. Bolton (Ed.), Solar Power and Fuels, Academic Press, New York, 1977, p. 119 ff. 4 W~/. Albery and A.W. Fonids, J. Photochem,, I 0 (1979) 41. 5 Y. Ohsawa and S. Aoyagui, J. Electroanal. Chem., 90 (1978) 143. 6 W.J. Albery, W.R. Bowen and M.D. Archer, J. Photochem., 11 (1979) 15. 7 W.J. Albery, W.R. Bowen, M.D. Archer and M.I,C. Ferreira, J. Photochem., 11 (1979) 27. 8 W.J. Albery, W.R. Bowen, F.S. Fisher and A.D. Turner, J. Electroanal. Chem., 107 (1980) 11 (this issue). 9 W J . Albary, M.D. Archer, N.J. Field and A.D. Turner, Faraday DiscusS. Chem. Soc., 56 (1973) 28. 10 M.L. Hitch man and W.J. Albery, Electrochim. Acta, 17 (1972) 787. 11 W J . Albery, M.D. Archer and R.G. Egden, J. Electxoanal. Chem., 82 (1977) 199. 12 W.J. Albery, W.R. Bowen, F.S. Fisher and A.D. Turner, J. Electroanal. Chem., 107 (1980) 1 (this issue). 13 C.G. Harchard and C.A. parker, Trans, Faraday Soc., 57 (1961) 1093. 14 M.I.C. Ferreira and A. Harriman, Faraday Trans. I, 73 (1977) 1085. 15 W J . Albery, A.H. Davis and A.J. Mason, Faraday Discuss. Chem. Soc. 56 (1973) 317. 16 M. Shabrang and S. Bruekenstein, J. Eleetrochem. Soc., 121 (1974) 1439. 17 T.L. Osif, N.N. Lichtin and M.Z. Hoffman, J. Phys. Chem., 82 (1978) 1778. 18 A. Harriman, private c o m m u n i c a t i o n .