Second harmonic ac polarography of strongly adsorbed electroactive species

J. Electroanal. Chem., 117 (1981) 17--28

17

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

SECOND HARMONIC AC POLAROGRAPHY OF STRONGLY ADSORBED ELECTROACTIVE SPECIES

D. LELIEVRE * and D. SAUR

Institut fiir anorganische und analytische Chemie, Johannes Gutenberg-Universiffit, Postfach 3980, D-6500 Mainz (F.R.G.) E. LAVIRON

Laboratoire de Polarographie Organique Associd au C.N.R.S. (LA33), Facultd des Sciences Gabriel, 6, Boulevard Gabriel, F-21 100 Dijon (France) (Received 28th May 1980; in revised form 28th July 1980)

ABSTRACT The second harmonic ac current is calculated for the case of a quasi-reversible surface redox system: both species are strongly adsorbed according to a Langmuir isotherm and the kinetics of the process are controlled by the electron transfer. The current is measured with a phase-sensitive detector and the variation of the in-phase and quadrature components vs. the frequency leads to the surface rate constant k s. The experimental results obtained for benzo(c)cinnoline are in good agreement with the theoretical predictions and with the results of impedance measurements. The advantages of the two methods are compared.

(I) INTRODUCTION

Second harmonic ac polarography measurements have been applied successfully to chemical analysis [1--5] and to the determination of heterogeneous charge-transfer rate parameters for quasi-reversible systems [6--8], as well as to the study of systems coupled with homogeneous chemical reactions [9--13]. We present in this paper the theoretical expression of the second harmonic polarogram, calculated in the case of the phase-sensitive detector method, for a reversible or quasi-reversible electrochemical reaction O + n e ~ R when both O and R are strongly adsorbed according to a Langmuir isotherm. The experimental results obtained for the benzo(c)cinnoline--dihydrobenzo(c)cinnoline system are in accord with the theory and the parameters calculated are in good agreement with those obtained by faradaic impedance studies [14,15] (II) THEORY

Let us Consider the surface electrochemical system: Gads "b n e ~ Rad s * Permanent address: Laboratoire de Chimie Analytique des Milieux R~actionnels Liquides, E.S.P.C,I., 10, rue Vauquelin, F-75231 Paris Cedex 05, France. 0022-0728/81/0000--0000/$ 02.50, © 1981, Elsevier Sequoia S.A.

18

where both O and R are strongly adsorbed according to a Langmuir isotherm. Let Fo and FR be the superficial concentrations of O and R. As shown by one of us in previous papers (see ref. 14 and references therein) we have for a dropping mercury electrode in the case of a reduction (only O is present in the solution): Fo + FR = FT = 0.74 c o D ~ n t '/2 For a reversible or quasi-reversible reaction, Fo and FR obey a relation which has the form of the Nernst equation: Fo/FR = e x p ( n F / R T )

(E - - E °') -~ ~7

in which the standard surface potential E °' is related to E ° by E °' = E ° - - ( R T / n F ) l n ( b o / b R )

bo and bR being the adsorption coefficients. As in a previous paper [14], we will assume that the double-layer capacitance does not vary when the potential is changed. If both O and R are neutral species, as is the case here, this is justified by the fact that the total coverage is constant; benzo(c)cinnoline has indeed been shown to conform to that type of behaviour [14]. The current response of the system to an alternating potential E + AE = E + J~EI sin cot is i(E + A E ) = I o ( E ) + A E d i / d E

+ 0.5 AE 2 d 2 i / d E 2 + "'"

(1)

The first harmonic of the current is given by AE d i / d E and the second by 0.5 A E 2 d2i/dE 2 since AE 2 is a function of 2co according to: AE 2 = IAEI: sin2cot = 0.5 fAE[2 {sin(2cot--~/2) + 1}

(2)

Let us designate by i, and i: the amplitude of the first and second harmonic current, we have thus: i: = 0.25 d i , / d E

(3)

(in eqn. 2, the term 0.5 [AEf2 leads to the faradaic rectification). In the case of strongly adsorbed electroactive species, one of us [14] has already established the equation of the current for the first harmonic. With a dete, tion angle ~, il is given by the relation (eqn. 34, ref. 14): il = (F2/RT) n2A Iz~kE]FT 69 sin ~0, cos(~9, - - X ) 77(1 + ~7) -2

(4)

in which ¢1 is the phase shift of the current: tan ~01 = (ksco-1)0? -a + ~71-,)

(5)

where k s is the rate constant of the electrochemical reaction, a the transfer coef ficient and the other symbols have their usual meaning. According to eqn. (2), the expression for the second harmonic results from the derivative of ii with an additive phase shift of u/2 (~ = 0 ° corresponds to the c o m p o n e n t in-phase with the potential): i2 = ( F 3 / R : T 2) n3A

I~LEI2FTXI/2

(6)

19 with q~: = ~(1 + V)-3co sin ~ ( [ a -- (1 -- a) ~] cos ~ol s i n ( 2 ~ -- k) + (~ -- 1) s i n ( ~ -- k)}

(7)

The current function ~2 depends only on E, co, ks and a. The total phase shift ~2 of the second harmonic does not appear in eqn. (7); ~2 may be calculated from: cot ~2 = i2(0 ° )/i2(90 ° ) = ~2(0 ° )/~P2(90 °)

(8)

but the analytic expression of cot ~2 is n o t simple and it is more convenient to leave ~01 (phase shift of the first harmonic) in the expression of ~2. The ac polarogcam corresponding to the second harmonic may be decomposed into two terms: (1) An amplitude factor i2/~J2 = (naF~/R2T~) A F w ]L~EI2 which depends only on the experimental conditions IAEI, A, F w. (2) A current function @2 which represents the influence of the parameters co, ks and a on the polarogram (co is the angular frequency of the alternating potential AE and not that of the current i2). This function of 77 has two peaks (Figs. 1 and 2) and is antisymmetric with respect to the point E = E °' (~? = 1) if a = 0.5.

-5O E - EV,~v

Fig. 1. T h e o r e t i c a l variations o f t h e s e c o n d h a r m o n i c c u r r e n t f u n c t i o n w i t h t h e f r e q u e n c y . k s = 103 s - l , (~ = 0.5, n = 2, d e t e c t i o n angle k = 0 °. (1) 1 0 0 Hz; (2) 1 5 0 Hz; (3) 2 5 0 Hz; (4) 500 Hz; (5) 103 Hz.

20

T ~

50

E -E c

_ 5~0

~5G

-

100

Fig. 2. Same conditions as in Fig. 1 with k = 90 °.

(II. 1) Effect of the frequency on the current function T h e s h a p e o f t h e p o l a r o g r a m d e p e n d s o n t h e value o f t h e d e t e c t i o n angle. Figure 1 r e p r e s e n t s t h e v a r i a t i o n o f t h e in-phase c o m p o n e n t w i t h t h e p o t e n t i a l (k = 0 ° ), f o r t h e case k s = 103 s -1 a n d a = 0.5. T h e q u a d r a t u r e c o m p o n e n t (k = 90 °) is s h o w n in Fig. 2. When t h e f r e q u e n c y increases b o t h t h e h e i g h t ~ a n d t h e p o t e n t i a l Ep o f t h e p e a k change, as s h o w n in Fig. 3. T h e in-phase c o m p o n e n t presents a maximum, whereas the component for ~ = 0°increases and tends t o w a r d s a limit.

(II.2) Influence of the rate constant T h e v a r i a t i o n s o f ~ p a S a f u n c t i o n o f k s are s h o w n in Fig. 4 f o r t h e case N = 3 0 0 Hz (co = 1 8 8 5 s -1) a n d ~ = 0.5 : ~ p ( 0 ° ) increases a n d t e n d s t o w a r d a limit, while ~ p ( 9 0 ° ) p r e s e n t s a m a x i m u m w h e n k s increases.

2]

/

/

/

/

tO0

i

i

50

4O

I'

b

20

/

i

N/H~

i

i

500

1000

D

500

I 1000

N/Hz

Fig. 3. V a r i a t i o n s o f t h e p e a k h e i g h t ( c u r v e a) a n d t h e p e a k p o t e n t i a l ( c u r v e b ) , in t h e s a m e c a s e as in Figs. l a n d 2 . ( )k=0°;( ..... )k=90 ° .

(H.3) Influence of the transfer coefficient The curves s h o w n in Figs. 1 and 2, calculated for a = 0 . 5 , are antisymmetric. This is n o longer true w h e n ~ ¢ 0.5 (Figs. 5 and 6): for a > 0.5, t h e potential

200

100

102

.

103

~

"

~

104

~s~S-1-

Fig. 4. V a r i a t i o n s o f t h e p e a k h e i g h t o f t h e c u r r e n t f u n c t i o n w i t h t h e r a t e c o n s t a n t v a l u e . N = 3 0 0 H z , 0~ = 0 . 5 , n = 2. ( ) k = 0 ° ; (. - - • ~ - ) ~ = 9 0 ° .

22

,oot*' 5O

_75

,

_2s

/mV~

-100~

Fig. 5. I n f l u e n c e o f t h e v a l u e o f t h e t r a n s f e r c o e f f i c i e n t o n t h e s h a p e o f t h e c u r r e n t f u n c t i o n k s = 103 s -1 , N = 2 5 0 H z , n = 2. T h e v a l u e o f o~ is s h o w n o n t h e c u r v e s ; ~ = 0 °.

50

-7

215

50-

Fig. 6. S a m e c o n d i t i o n s as in Fig. 5 w i t h ~ = 9 0 °.

75

23

I

~.\~ \.

"

o

J/

\y,

-5'o

il

~

~

~

__-- d, = 0.5

I --

I"

s/

5'o d=0.6

E - E°'/mV

....

-" d, = 0,'/

Fig. 7. Variations of the phase shift of the second harmonic polarogram where ksCO:1 = 1.84: influence of the transfer coefficient. Experimental points for benzo(c)cinnoline, pH = 12.7, N = 64 Hz, are superimposed on the curve a = 0.6. The best fit is obtained for E °' = --922 mV vs. Ag/AgCl.

s h i f t s n e g a t i v e l y f o r )~ = 0 ° a n d p o s i t i v e l y f o r )~ = 9 0 ° a n d t h e t w o p e a k s b e c o m e unequal.

(H.4) Calculation of the phase angle of the second harmonic T h e p h a s e a n g l e ~2 c o r r e s p o n d i n g t o t h e s e c o n d h a r m o n i c c a n b e c a l c u l a t e d n u m e r i c a l l y f r o m e q n . ( 8 ) ; ~2 is a f u n c t i o n o f t h e p o t e n t i a l a n d d e p e n d s o n t h e v a l u e s o f k s c o -1 a n d o f ~ ( F i g . 7). A s s h o w n in t h i s f i g u r e , t h e v a r i a t i o n s o f c o t ~2 w i t h t h e p o t e n t i a l a r e c h a r a c t e r i s t i c o f a n a v a l u e . T h e d e t e r m i n a t i o n o f t h e e x p e r i m e n t a l v a l u e s o f c o t ~ = f ( E ) f r o m t h e p o l a r o g r a m a t )~ = 0 ° a n d k = 9 0 ° a n d t h e c o m p a r i s o n w i t h t h e t h e o r e t i c a l c u r v e s give a v e r y p r e c i s e m e a n s o f studying a system of this kind by using the whole polarogram. For example,

•.

d =0.6

~

8

J ~

1 i

2 i

4 i

~

6 i

k s ~-1

Fig. 8. Variations of the peak ratio pH = 12.7, N = 32, 64 and 128 Hz.

w i t h ksO9 -1 .

Experimental points for benzo(c)cinnoline,

24 TABLE 1 pH

E°'/mV (Ag/AgCI)

~

k s exp/s -1

11 11.7 12.2 12.7

820 870 900 920

0.6 0.6 0.6 0.6

65 255 480 775

-+ 5 ± 10 ± 10 ± 25

e x p e r i m e n t a l p o i n t s are s h o w n in Fig. 7 in t h e case o f b e n z o ( c ) c i n n o l i n e at p H = 12.7 f o r N = 64 Hz; the s u p e r p o s i t i o n is o b t a i n e d f o r E °' = - - 9 2 2 m V , k s ~ -~ = 1.84 and a = 0.6. If o n l y t h e rate c o n s t a n t ks is n e e d e d , t h e use o f t h e curve c o t ~02 = f(E) is a t e d i o u s task and is u n n e c e s s a r y since t h e height o f t h e peaks can give the value o f k s v e r y rapidly, as s h o w n in S e c t i o n (II.5). (II.5) P e a k ratio as a f u n c t i o n o f ks¢o -~

A c c o r d i n g t o eqns. (5) and (7), ~2 should be a c o m p l i c a t e d f u n c t i o n o f 69 and o f ks ; calculations show, h o w e v e r , t h a t t h e ratio in2(O ° )/ip2(90 °) = ~p2(O ° ) / ~ n 2 ( 9 0 °) o f t h e p e a k heights f o r X = 0 ° and 90 ° is a linear f u n c t i o n o f ks¢o -1 (Fig. 8); t h e slope o f t h e straight line d e p e n d s slightly on a. It is t h u s v e r y easy t o d e t e r m i n e ks : t h e e x p e r i m e n t a l ratio r is first calculated, a n d ks¢o -I is d i r e c t l y d e d u c e d f r o m Fig. 8. (III) EXPERIMENTAL First and s e c o n d h a r m o n i c p o l a r o g r a m s were r e c o r d e d with an a p p a r a t u s previously described [ 1 6 , 1 7 ] . T h e a m p l i t u d e o f t h e sinusoidal p o t e n t i a l can vary f r o m 0 t o 128 m V and its f r e q u e n c y f r o m 32 t o 1 0 2 4 Hz {i.e. t h e f r e q u e n c y 2¢o o f the c u r r e n t f r o m 64 t o 2 0 4 8 Hz). In this w o r k t h e f r e q u e n c y i n d i c a t e d is always t h a t o f the p o t e n t i a l . T h e c u r r e n t is m e a s u r e d with a phase-sensitive d e t e c t o r and t h e d e t e c t i o n angle X can v a r y f r o m 0 t o 360 ° ; t h e m e a s u r e m e n t s c o r r e s p o n d t o an i n t e g r a t i o n o f t h e c u r r e n t at t h e e n d o f t h e d r o p life during 0 . 1 2 5 s whatever t h e d r o p time. T h e p o t e n t i a l s were m e a s u r e d with respect t o an Ag/AgC1, sat. KC1 e l e c t r o d e . T h e d r o p t i m e o f t h e m e r c u r y e l e c t r o d e was T = 0 . 5 - - 4 s and t h e flow rate m = 6.3 × 10 -4 g s -1 . T h e auxiliary e l e c t r o d e was a p l a t i n u m .wire. T h e m e a s u r e m e n t s were carried o u t in a q u e o u s b u f f e r e d solutions ( B r i t t o n - - R o b i n s o n buffers with 0.1 M KNO3 as s u p p o r t i n g e l e c t r o l y t e ) . T h e a p p a r a t u s was t h e r m o s t a t e d at 20.0 + 0.1 °C. (IV) RESULTS B e n z o ( c ) c i n n o l i n e in basic m e d i a and p h e n a z i n e in n e u t r a l m e d i a w e r e studied b y s e c o n d h a r m o n i c ac p o l a r o g r a p h y in o r d e r t o verify t h e applications

25

r~

E

,100mY ,

!~ tLI ! !

"o!

li

0°

_

90 °

Fig. 9. E x p e r i m e n t a l s e c o n d h a r m o n i c p o l a r o g r a m s o f b e n z o ( c ) c i n n o l i n e a t p H = 1 1 . 7 (...... ); 1 2 . 2 ( ); 1 2 . 7 ( . . . . . ); w i t h N = 6 4 H z w h e r e k = 0 ° a n d ~ = 9 0 ° ; c = 10 -s M. T h e t h e o r e t i c a l p o i n t s c o r r e s p o n d t o : ( 4 ) ksCO -1 = 0 . 6 2 ; ( e ) ksCO -1 = 1 . 1 8 ; (m) ksO9 -1 = 1.84.

! / P lO

15 pH

Fig. 10. R a t e c o n s t a n t o f t h e s u r f a c e e l e c t r o c h e m i c a l r e d u c t i o n f o r b e n z o ( c ) c i n n o l i n e p o t e n t i a l . ( * ) T h i s w o r k ; (¢~) f a r a d a i c i m p e d a n c e m e a s u r e m e n t s [ 15 ].

vs.

26

of the m e t h o d and to compare its possibilities with those of fundamental harmonic ac polarography and of faradaic impedance measurements. Examples of polarograms are given in Fig. 9 in the case of benzo(c)cinnoline; we have verified that for benzo(c)cinnoline as well as for phenazine, the current is proportional to IAEI 2 and to VT/6 as predicted by eqn. (6) (AFT ~- T7/6). The value of k s has been determined b y using the procedure described above in Section (II.5); the points obtained at pH 12.7 for N = 32, 64 and 128 Hz are shown in Fig. 8. The values of ks¢o -1 found are respectively 3.96, 1.84 and 0.94, whence ks = 7 7 5 + 2 5 s -1. By using these values of ks, the theoretical current has been calculated for different potentials along the polarogram; as shown in Fig. 9, the agreement with the experimental data is good. When the pH increases, the in-phase component increases, while the quadrature c o m p o n e n t decreases. This p h e n o m e n o n is due to a variation of k s with the pH (because of the complex nature of the reaction [15], the apparent standard potential is noted here Eeq instead of E °' and the rate constant ks exp). Once ks.ex , is known, Eeq and a can be determined by comparing the experimental and theoretical variations of cot ~2 with the potential until the best fit is obtained (Fig. 7). DISCUSSION

We have shown that second harmonic ac polarography can be used for a rapid determination of the electrochemical parameters, k s and E °', in the case of

I

0.3125 nA

j

i i j

i

i

o

\ \

0 I

~4

°i' - E/v

v, .,,,/A.c. !

I1.2S nA

i

22"50

Fig. 11. F i r s t h a r m o n i c p o l a r o g r a m f o r a 10 - s M p h e n a z i n e s o l u t i o n : i n f l u e n c e o f t h e d o u b l e l a y e r c a p a c i t a n c e , p H = 4 . 6 5 , T = 2 9 3 K, N = 64 Hz, 1" = 0.5 s. ( . . . . . ) X = 0°; ( ) )t = 22.5 ° .

27 0°

90 °

! \ 0

-E/V

O'2 \

'\.

\

" .

0 ~

i0. 2

\

I I I

i Fig. 12. Second harmonic polarogram for the same solutions as in Fig. 11, T = 1 s. ( . . . . . k = 0°; ( ) k = 90 ° .

)

strongly a d s o r b e d electroactive species. T h e advantage o f using t h e s e c o n d harm o n i c r a t h e r t h a n t h e f u n d a m e n t a l lies in t h e f a c t t h a t t h e i n f l u e n c e o f t h e capacitive c u r r e n t is m u c h smaller, so t h a t t h e precision is b e t t e r : Figs. 11 and 12 r e p r e s e n t t h e first and s e c o n d h a r m o n i c polarograms f o r a p h e n a z i n e solution. It is easily seen t h a t t h e d e t e r m i n a t i o n o f t h e p e a k ratio is m o r e precise f o r t h e s e c o n d h a r m o n i c t h a n f o r t h e first (in this case, it was n o t even possible t o o b t a i n t h e c o m p o n e n t k = 90 ° f o r t h e first h a r m o n i c ) . By c o m p a r i n g t h e s e c o n d h a r m o n i c and t h e faradaic i m p e d a n c e [ 1 5 ] , we can say t h a t f o r the d e t e r m i n a t i o n o f k s t h e precision is equivalent for b o t h m e t h o d s , b u t t h e faradaic m e a s u r e m e n t s lead also to t h e value o f R and Ca. ACKNOWLEDGEMENTS We are grateful t o C.N.R.S. ( F r a n c e ) a n d D . F . G . (Federal R e p u b l i c o f Germ a n y ) , w h o s e j o i n t s u p p o r t m a d e this w o r k possible. REFERENCES 1 H.H. Bauer, J. E l e c t r o a n a l . Chem., 1 ( 1 9 5 9 / 6 0 ) 256. 2 R. Neeb, M i k x o c h i m i e a A c t a , Vol. I, V i e n n a , 1 9 7 8 , p. 305. 3 L. Metzger, G. Willems a n d R. Neeb, F r e s e n i u s Z. Anal. C h e m . , 288 ( 1 9 7 7 ) 35.

28 4 5 6 7 8 9 10 11 12 13 14 15 16 17

W. R a n l y a n d R . N e e b , F r e s e n i u s Z. A n a l . C h e m . , 2 9 2 ( 1 9 7 8 ) 2 8 5 , 3 7 0 . A.M. B o n d , J. E l e c t r o a n a l . C h e m . , 3 5 ( 1 9 7 2 ) 3 4 3 ; 3 6 ( 1 9 7 2 ) 2 3 5 . J.E.B. Randles and D.R. Whitehouse, Trans. Faraday. Soc., 64 (1968) 1376. T . G . M e C o r d a n d D . E . S m i t h , A n a l . C h e m . , 4 0 ( 1 9 6 8 ) 2 8 9 ; 41 ( 1 9 6 9 ) 1 3 1 ; 4 2 ( 1 9 7 0 ) 1 2 6 . D.E. Smith, C.R.C. Crit. Rev. Anal. Chem., 2 (1971) 248. J. D e v a y , T. G a r a i a n d L. M e s z a r o s , A c t a . C h i m . A c a d . Sci. H u n g . , 76 ( 1 9 7 3 ) 51. D . E . S m i t h 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. 1, M a r c e l D e k k e r , N e w Y o r k , 1 9 6 6 p. 1. T . G . M c C o r d a n d D . E . S m i t h , J. E l e c t r o a n a l . C h e m . , 26 ( 1 9 7 0 ) 6 1 . T . G . M c C o r d a n d D . E . S m i t h , A n a l . C h e m . , 4 1 ( 1 9 6 9 ) 1 4 2 3 ; 4 2 ( 1 9 7 0 ) 2. K.R. Bullock and D.E. Smith, Anal. Chem., 46 (1974) 1567. E. L a v i r o n , J. E l e c t r o a n a l . C h e m . , 9 7 ( 1 9 7 9 ) 1 3 5 . D. Lelievre, V. P l i c h o n a n d E. L a v i x o n , J. E l e c t r o a n a l . C h e m . , 1 1 2 ( 1 9 8 0 ) 1 3 7 . D. S a u r , F r e s e n i u s Z. A n a l . C h e m . , 2 9 0 ( 1 9 7 8 ) 2 1 7 , 3 7 2 . D. S a u r a n d R . N e e b , F r e s e n i u s Z. A n a l . C h e m . , 2 9 0 ( 1 9 7 8 ) 2 2 0 , 3 7 4 .