Application of optically transparent electrodes

J. Electroanal. Chem., 130 (1981) 351--356

351

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

Preliminary note

APPLICATION OF OPTICALLY T R A N S P A R E N T E L E C T R O D E S P A R T I. ILLUMINATION STEP C H R O N O A M P E R O M E T R Y : ELECTROCHEMICAL STUDIES OF PHOTOCHEMISTRY IN SOLUTION CAUSED BY STEP-FUNCTIONAL ILLUMINATION OF LIGHT T H R O U G H AN OPTICALLY T R A N S P A R E N T ELECTRODE

MASAM!CHI FUJIHIRA

Pharmaceutical Institute, Tohoku University, Aobayama, Sendai 980 (Japan) (Received 28th September 1981)

Recently photoelectrochemistry has been studied very extensively in its relation to solar energy conversion. In some of the devices for such conversion, e.g., in photogalvanic cells, electrochemical behavior of photochemically generated species in solution plays an important role in determining the efficiency of conversion. Consequently, knowledge of t h e fate of the photogenerated species is very important and will be a key to developing a more efficient device. In this note a novel electrochemical m e t h o d is described for studying photochemistry of the species in solution. Attention is paid especially to t h e kinetics of photochemical reactions under illumination whose profile decays according to the Lambert--Beer law with increase in distance from the front face of the solution as shown in Fig. 1A. If the light intensity decays steeply, the concentration profile of the excited species produced by p h o t o n is n o t uniform and changes as a function of the distance (Fig. 1B) in the same way as the light intensity decreases. Consequently the rate equation for such a photo° chemical reaction is related n o t only to the homogeneous chemical reaction A I = I °e-F-cAQ x'l nlO

4t

dc

Io -

dl

dc e

BY

"~

OTE

X

X

Fig. 1. Changes in photon flux I (A) and the evolution rate of excited species dc*/dt (B) as a function of distance x from the OTE---solution interface. 0022-0728/81/0000--0000/$02.75 © 1981 Elsevier Sequoia S.A.

352

b u t also to the diffusional mass transfer process. This effect is significant when the concentration of the light-absorbing species an=l its absorptivity are high. In the present method, light is passed through an optically transparent electrode (OTE) step-functionally and the photocurrent, ip, induced by the photochemical reaction is recorded as a function of time keeping the appliecl electrode potential constant. These are shown schematically in Fig. 2. The m e t h o d can be named as " d o u b l e illumination step c h r o n o a m p e r o m e t r y " analogous to double potential step chronoamperometry. A lo

I I I I I

ip 0

I I I

/

C E t=O

t=t s

Fig. 2. Changes in i n c i d e n t light i n t e n s i t y I ° (A), p h o t o c u r r e n t ip (B), a n d a p p l i e d elect r o d e p o t e n t i a l E (C) as a f u n c t i o n o f t i m e in d o u b l e i l l u m i n a t i o n s t e p c h r o n o a m p e r o m e t r y w h e r e t s is t h e d u r a t i o n o f i l l u m i n a t i o n .

The resulting ip--t curves are analyzed using a digital simulation derived from that originally developed by Feldberg [1]. In this first note, the applicability of the digital simulation is presented b y comparing the observed and the simulated ip--t curves for the simplest case where the photochemical reaction is very rapid and the products are stable. In other words, the ip--t curves are described mainly by mass transfer of the photogenerated products since, the homogeneous photochemical reactions are completed in a period of time which is very much shorter than the time scale of the electrochemical experiments of interest and the back reaction between the photogenerated products is negligible. As an example of such simple photochemical reactions, a wellknown photochemical oxidation of isopropanol to acetone sensitized by photoexcited anthraquinone derivatives was a d o p t e d * [2]. The reaction has already been fully investigated and can be written as * T h e irreversibility o f t h e r e a c t i o n is d u e t o its s p o n t a n e o u s n a t u r e ( A G o < 0), i.e., t h e rea c t i o n is a p h o t o c a t a l y t i c o n e a n d c o n s e q u e n t l y it s h o u l d be pointed out t h a t it is useless for t h e p u r p o s e o f c o n v e r t i n g solar e n e r g y t o c h e m i c a l energy.

353 AQ + CH3CHOHCH3 + hv

-~ AQH2 + (CH3)2CO

(1)

The isopropanol/acetone redox couple is very irreversible while that of hydroanthraquinone/anthraquinone (AQH2/AQ) is reversible. Consequently we can monitor the photochemical reaction by measuring an anodic photocurrent due to the selective oxidation of photogenerated AQH2 back to AQ by setting the potential of OTE at that which is sufficiently positive to oxidize AQH2 at the diffusion controlled rate b u t n o t sufficiently positive to oxidize isopropanol electrochemically. AQH2

-~ A Q + 2 e + 2 H +

(2)

The differential equations describing AQ and AQH2 must account for both diffusion and transformation from AQ to AQH2 by the photochemical reaction described in eqn. (1). Namely, 3CAQ(x,t) = n 3t DA'*

aCAQH~ (x,t) at

32 CAQ(X,t) 0x 2

--A.~H~

+~p

0 2 CAQH~ (x,t) ~X2

3I(x,t) 3x

(3) OI(x,t) aX

(4)

where I ( x , t ) is a flux of photons at locations x at time t, • is the quantum efficiency of the photochemical reaction, and the other symbols are conventional as in Fick's second law. In the derivation of the rate equations for photochemical consumption of AQ and evolution of AQH2 as in eqns. (3) and (4) respectively, we assumed that p h o t o n is absorbed only by AQ and the resulting excited AQ* is converted into AQH2 instantaneously at quantum efficiency ¢b. As the light is passed step-functionally in the present experiments as shown in Fig. 2A, I ( x , t ) can be written as I ( x , t ) = I ° exp [ - e C A Q ( X , t ) x • In 10]

(5)

when illumination is on (0 ~< t ~< ts) and vanishes in the other case (t < 0, t > ts). In eqn. (5), I ° is the flux of the incident photons before entering the solution phase, e is the molar absorptivity of AQ, and CAQ (x, t) is the same concentration of AQ as used in eqn. (3). As initial and boundary conclitions the following equations can be written: CAQ(X,t),= C°AQ, CAQH2 (x,t) = 0

CAQH2(0,t) = 0

(at all t)

(x ~ 0, t < 0)

(6) (7)

Equation (7) was derived since the applied potential is sufficiently positive for AQH2 to be oxidized. In conducting the digital simulation for the present system described by eqns. (1)--(7), only the maximum distance from the electrode surface that must be considered during simulation was modified from the conventional one. For the usual electrochemical systems, a distance 6(Dmaxt) 1~ is adopted as the maximum distance [1,3] since the solution can be regarded to be undisturbed at a distance greater than this ~listance. Dmax is the largest diffusion coefficient involved in the problem, and t is the time

354

elapsed since the initiation of the electrochemical perturbation. On the other hand, the photochemical products in the present system are formed in the same profile as the light intensity profile during illuminations as is evident from Fig. 1B and eqn. (4) and these products diffuse simultaneously in the direction of their lower concentrations. Furthermore, in the successive iterations in the simulation procedure [1,3] to calculate the concentration c of the volume element j in question by iteration k + 1, we must know the concentrations of the volume elements j - 1 and j + 1 adjacent to j at the previous iteration k as well as c at j and k. For example, for AQ: cU, k

+

1) = c(],k)

DAt + -

Ax 2

[c(j + 1,k) - 2 c ( j , k ) + c ( ] - 1,k)] OAt + -

I(j) - I(j - 1) = - e c { j , k ) A x

Ax

[l(j) - I(j -

• In 10 • I ° exp [ - e c { j , k ) j A x

1)I

(8)

• In 10]

(9)

Consequently, one has to start the calculation using the m a x i m u m n u m b e r of volume elements ] m a x which is the sum of conventional m a x i m u m n u m b e r of volume elements at iteration k m a x and the m a x i m u m iteration kmax itself. Jmax = 6 ( D k m a x A t / A x 2 )

'~ + kmax

(10)

-- k

Every iteration, Jmax decreases one by one and finally ]max becomes 6(DkmaxAt/Ax2) 1~ at iteration kmax. Details of the digital simulation will be reported elsewhere. In Fig. 3 are shown the changes in the concentration profiles calculated by [ 600

2

20

400

4 3 2 t=ls 0:1

012

013 X/mm

014

0:5

15 200

0.6

0

i 0.!

0.2

0.3 Xlmm

0.4

0.5

0.6

Fig. 3. Digital s i m u l a t i o n o f c h a n g e s in c o n c e n t r a t i o n p r o f i l e during (1--10 s) a n d a f t e r (10--20 s) i l l u m i n a t i o n in d o u b l e i l l u m i n a t i o n s t e p c h r o n o a m p e r o m e t r y at l o w c o n c e n t r a tion. c = 0 . 1 r a M , D = 4.5 x 10 - 6 c m 2 s - ' , e = 5 X 103 M - ' c m - ' , I ° = 6.0 X 1014 s - ' , t s = 10 s, d~ = 2.0. Fig. 4. Digital simulation of changes in concentration profile in double illumination step chronoarnperometry at high concentration, c = 10 ~ and o t h e r parameters are the same as given in Fig. 3.

355 the present digital simulation for double illumination step chronoamperometric conditions. Since the concentration of light absorbing species (e = 5000 M - ' c m - ' ) is low, the concentration profile of the p r o d u c t formed by a photochemical reaction is nearly uniform and the profile resulting from electrochemistry is more steep. On the other hand, the profiles due to the photochemical reaction also become steep when the concentration of photosensitive species increases a hundredfold keeping e constant as shown in Fig. 4. In these calculations, the radical anion is assumed as the photochemical reaction p r o d u c t as the experiment was carried out in isopropanol saturated with LiOH containing 0.1 M LiC104. In this medium, the following photochemistry is expected in place of eqn. (1): 2AQ±CH3CHOHCH3

+2OH-

+by

-~ 2 A Q : + ( C H 3 ) 2 C O + 2 H 2 0

(11)

A vapor deposited gold film on quartz (ca. 25% transmittance) was used as an OT working electrode. For photoelectrochemical measurements, a light beam from a 500 W high pressure mercury arc lamp was monochromatized by a Shimadzu Bausch & L o m b m o n o c h r o m a t o r with wide slits and then illuminated through the Au OTE. As quinone derivatives naphthacenequinone and 2-methylanthraquinone were used. In Figs. 5 and 6, the simulated ip--t curves are compared with the experi1.0

1.0 E

E

(3.

O.

(3.

0.5

0.5

10 t/s

20

'

lJO

'

2'0

tls

Fig. 5. C o m p a r i s o n o f e x p e r i m e n t a l a n d s i m u l a t e d ip--t c u r v e s o f d o u b l e i l l u m i n a t i o n s t e p chronoamperometry a t l o w c o n c e n t r a t i o n . ( - - ) S i m u l a t e d w i t h t h e p a r a m e t e r s g i v e n in Fig. 3; (o) e x p e r i m e n t a l w i t h n a p h t h a c e n e q u i n o n e , c = 0 . 1 raM, D ± 6 x 1 0 - 6 c m ~ s - 1 , e = 4 . 5 x 103 M - 1 c m - 1 a t 4 0 4 . 7 n m , I ° = 1 . 5 x 1015 s - I , ts = 1 0 s. Fig. 6. C o m p a r i s o n o f e x p e r i m e n t a l a n d s i m u l a t e d ip--t c u r v e s a t h i g h c o n c e n t r a t i o n . ( - - ) S i m u l a t e d w i t h t h e p a r a m e t e r s g i v e n i n Fig. 4; (o) e x p e r i m e n t a l w i t h 2 - m e t h y l a n t h r a quinone, c = 10raM, D = 7 x 10 -~ cm 2 s -I,e = 4 . 4 X 103 M - ~ c m - 1 a t 3 3 4 . 2 n m , I ° = 7 . 8 × 1014 s - 1 , ts = 1 0 s .

mental results. As ordinate, the photocurrent normalized to its m a x i m u m , max, is plotted for the sake of convenience for comparison. The ip--t curve shown in Fig. 5 for the solution containing 0.1 mM o f naphthacenequinone (e = 4500 M -1 ~cm -1 at 404.7 nm) shows almost the same shape as the ip--t curve simulated with the parameters adopted in the calculation in

ip/ip

356 Fig. 3. The shape is c o m m o n for the systems where the Lambert--Beer decay in the light intensity is negligibly small and the concentration profile of the photogenerated product can be regarded to be uniform in the dimension of the diffusion layer thickness. As is evident from Fig. 3, ip decays exactly in the same way as is observed in potential step chronoamperometry after the illumination is switched off (t > ts). In the experiment with the solution containing 10 mM 2-methylanthraquinone (e = 4400 M -1 cm -1 at 334.2 nm), as is shown in Fig. 6, the parameters are almost the same as adopted in the simulation in Fig. 4 where the Lambert--Beer decay cannot be negligible. Consequently, the ip--t curve deviates from the ideal curve shown in Fig. 5, i.e., ip rises more sharply in the initial period b u t levels off at higher rate afterwards under illumination and falls down more steeply after the illumination is switched off. This tendency becomes more obvious with increase in concentration and absorptivity of quinone derivatives and ultimately the ip--t curve changes step-functionally as the illumination-time curve (Fig. 2A), since the penetration depth of illuminated light becomes very much thinner than the diffusion layer thickness, (Dt) 1/~. This situation resembles the photoelectrocatalytic oxidation of isopropanol at the electrode chemically modified with quinone derivatives under step-functional illumination where only surface-bound quinones can absorb photons and be reduced photochemically by isopropanol and reoxidized electrochemically [4]. As the agreement is excellent in these figures, the applicability of the present digital simulation has been verified. Obviously, this indicates that the present m e t h o d can easily be extended to more complicated systems where the photogenerated products react each other back to the starting materials as in photogalvanic cells and their life times are comparable to the duration of the illumination, ts. The m e t h o d described here can be applicable n o t only for photogalvanic cells, but generally to the studies of photochemistry in solution. ACKNOWLEDGEMENT This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education (No. 355436).

REFERENCES 1 S.W. F e l d b e r g in A . J . B a r d (Ed.), E l e c t r o a n a l y t i c a l C h e m i s t r y , Vol. 3, M a r c e l D e k k e r , N e w Y o r k , 1 9 6 9 , p. 1 9 9 2 J.NI. B r u c e in S. P a t a i (Ed.), T h e C h e m i s t r y o f the Q u i n o n o i d C o m p o u n d s , Wiley, 1 9 7 4 , Ch. 9. 3 A . J . Bard and L . R . F a u l k n e r in E l e c t r o c h e m i c a l M e t h o d s , F u n d a m e n t a l s and A p p l i c a t i o n s , Wiley, N e w Y o r k , 1 9 8 0 , p. 6 7 5 . 4 M. F u j i h i r a , S. T a s a k i , T. Osa and T. K u w a n a , in preparation.