A rotating-disc electrode for voltammetry and electrochemical impedance measurements

J. Electroanal. Chem., 101 (1979) 153--170

153

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

A ROTATING-DISC ELECTRODE FOR VOLTAMMETRY AND ELECTROCHEMICAL IMPEDANCE MEASUREMENTS APPLICATION TO THE STUDY OF PARTIALLY BLOCKED ELECTRODES

M. ETMAN, E. LEVART and G. SCARBECK

Laboratoire d 'Electrochimie Interfaciale, C.N.R.S., F 92190 Meudon-Bellevue (France) D. SCHUHMANN

Groupe de Recherche de Physicochimie des Interfaces, C.N.R.S., F 34033 Montpellier (France) (Received 10th October 1978}

ABSTRACT A turbulence-free RDE device has been designed for making accurate measurements with low-amplitude electrical signals. Its mechanical construction as well as the drive mechanism with a Hall-effect motor, and the rotation speed control are described in detail. Electrochem ical experiments were effected on platinum electrodes in contact with a solution o f ferri- ant ferrocyanide in 2 M NaOH from 4 to 256 rps and, under transient conditions, for values o f the Laplace parameter up to l 0 s s -1. Excellent agreement was found between the measured Warburg coefficient and the value calculated using diffusion coefficients derived from steady-state measurements of the limiting currents. The whole theoretical concentration impedance spectrum of the RDE was verified using the pulse technique. It is demonstrated by experiments on partially blocked model electrodes that the approximation neglecting lateral convection, which is valid for the uniformly active RDE, is no longer correct.

(1) INTRODUCTION

Since Levich published his theory for the convective diffusion model [ 1 ], the rotating-disc electrode, RDE, became widely accepted for the study of dif5 sion limiting currents under steady-state conditions (the diffusion layer being uniform only with such an electrode). The importance o f RDE systems for elucidation o f mechanisms o f electrode reactions was increased, thanks to the works of Frumkin et al. [2], b y the addition on the same rotating shaft of a ring electrode concentric with the disc one. The electrical responses of the elec trodes were studied under steady-state conditions and then under transient coI ditions [3]. Furthermore, the frequent complexity o f reaction mechanisms ha, led to the development of measurements with a low-amplitude electrical signal It is possible with such a procedure, from the theoretical point o f view, to tak~ into account b o t h the surface p h e n o m e n a and those which take place in the solution in the vicinity of the electrode. Recent theoretical studies [4--7] and experimental results [7--9] have shown that we would possess a powerful analytical tool if it were possible to

154

combine the advantages offered b y the use o f RDE and b y the measurement of electrode impedances. Except in the Warburg region, such measurements impose more stringent technical requirements than in the case o f studies with large amplitude electrical signals. In fact impedance measurements demand very accurate definition of the hydrodynamic layer and hence o f the diffusion layer under fixed-convection conditions. In voltammetry, the performance of RDE is generally perturbed b y current fluctuations, particularly perceptible in the limiting-current domain. These seem to be due to irregularities in the rotation speed and to small turbulences which could be attributed to imperfections in the movement of the disc around its axis of rotation. Other possible sources o f current fluctuations are variations of the resistance due to the moving contact. In contrast, such fluctuations are k n o w n to be entirely absent in streamlined electrolysis cells, when an ideally laminar "free gravity f l o w " is maintained past an appropriate stationary indicat o r electrode [10]. However, it is n o t easy to obtain a diffusion layer with a uniform thickness using such a cell. Many descriptions can be found either o f the mechanical part of the control and the electronic measurement o f rotation speed or, most often, o f the electrode itself. An exhaustive bibliography in this field is given in recent reviews b y Pleskov and Fillinovskii [11] and b y Opekar and Beran [12]. The e~rlier review b y Riddiford [13] also remains useful. In a very recent paper, Ritzler and Gross described an easy-to-build RDE permitting voltammetric measurements with a small-volume cell and with a 2 m m diameter electrode up to 400 rps [14]. We considered it necessary to build a high-precision rotating system in which coincidence b e t w e e n the geometric axis and the axis of rotation would be, if possible, within 1 pm. Moreover its performance must remain constant within a wide range with regard to b o t h the desired speed o f rotation (for instance from a few to a few hundred rps) and to the amplitude and the frequency of the electrical signals applied to the electrode (between 1 mV and 1 V and from 0 to l 0 s Hz). We have attempted to produce a RDE device for accurate impedance and voltammetry measurements in which the causes o f fluctuations are eliminated as far as possible. We have concentrated o u r efforts mainly on t w o essential aspects of the problem. The first is that o f m a x i m u m elimination o f all sources of vibration o f the electrode. The second is regulation o f the speed o f rotation b y means o f a control device o f sufficient accuracy. The present article describes.the equipment constructed in accordance with these requirements, and illustrates h o w t h e y were realized b y giving some significant results obtained under steady-state and transient conditions. (2) MECHANICAL PART

Figure 1 shows a schematic representation of the completed system. The electrolytic cell (1), the electrode-holder ( 5 ) a n d the m o t o r (9) are solidly attached to the supporting block (2) which is rigidly fixed on a metal frame. The supporting block can pivot 90 ° round the shaft connecting it to the frame, thus facilitating positioning of the electrode-holder.

155

~,

13 crn --

~,

Fig. 1. Cross-sectional representation of the rotating-disc electrolytic assembly. (1) Pyrexglass vessel; (2) stainless-steel block supporting the electrode-holder; (3) Kel-F lid; (4) Kel-F cylinder; (5) electrode-holder; (6) Kel-F disc; (7) Kel-F fins preventing movement of the liquid; (8) flexible coupling between the electrode-holder and the motor; (9) Hall-effect motor; (10) brass block supporting the motor; (11) rotating silver contacts; (12) plexiglass cylinder supporting rotating contacts; (13) stroboscopic wheel; (14) magnetic head; (15) water circulation cooling coil. Between t h e cell (1) and the supporting block (2) a Kel-F lid (3) is interposed having in its centre a hollow Kel-F cylinder (4} with internal diameter slightly greater than that o f the electrode-holder. A Kel-F disc (6) is m o u n t e d on the cylinder (4) and supports four fins (7) designed to prevent the liquid mass from being entrained b y the rotating electrode-holder. The disc (6) must be barely immersed in the solution. Under these conditions, even for the highest speeds allowed b y the assembly, movement o f the upper portion o f the solution is slowed down. The laminar flow in the vicinity o f the electrode is therefore not disturbed, which makes it possible to maintain the h y d r o d y n a m i c conditions assumed in yon Karman's theory. Among the experimental requirements of that theory (discussed in detail in a previous paper [15] ), the necessity o f having an effectively infinite liquid volume led us to choose a relatively big electrolyte cell ( ~ 5 0 0 ml). The interior o f the cell is protected against the

156 outside atmosphere by keeping a small excess pressure with a flow of an inert gas which circulates continuously between the supporting block (2) and the lid (3}. This flow is independent of that used for deaerating the electrolytic solution by bubbling. The assembly of the electrode and its support was designed as a "one-piece" structure and adjusted on a truing lathe; it is shown in Fig. 2. A deflector (D) of Kel-F fixed to the upper part of the sleeve (M) covering a stainless-steel tube (T) protects the bearings (B) from splashes of electrolyte. The top end of the tube (T), above the collector (C), enables the shaft of the motor to be connected to the rotating electrode by a flexible coupling. The mechanical accuracy, defined by the maximum distance of a point on the electrode from its mean plane, is of the order of few/~m. This accuracy is not impaired by the successive operations of fitting and removing electrodeholders.

Fig. 2. Details of the electrode-holder. (B) Bearings; (C) rotating silver contacts; (D) KeI-F deflector shielding the bottom bearing; (E) disc electrode; (K) KeI-F electrode support; (L) brass cylinder fitted in the plexiglass support P; (M) Kel-F sleeve tightly covering the immersed part of the electrode-holder; (P) plexiglass cylinder supporting rotating contacts; (T) hollow shaft of the rotating system.

157

Fig. 3. Schematic view of the collector. (1) Carbon-silver microbrushes; (2) plexiglass block supporting fixed contacts; (3) pinchbeck strips connecting microbrushes to their supports; (4) stress-adjusting brass supports; (5) rotating silver contacts.

The transmission of the electric current to the rotating electrode is described in Figs. 2 and 3. An insulated, conducting wire links the electrode(s) (E) to a double silver collector (C) which provides contact with the fixed parts connected to the measuring system via three carbon-silver microbrushes (1, Fig. 3) disposed at 120 ° . A double collector was provided i~ order to make possible contact to two electrodes in the case of a disc and ring system [16,17] or in the case of a double-ring [18--20], This assembly fulfils several conditions which are necessary for proper operation o f the device: low contact resistance, reliability ensured b y the presence of three brushes on each collecting ring, and reduction of resultant forces on the shaft, avoiding premature wear of the bearings and consequent development of excentricity. (3) ELECTRODE-DRIVE AND CONTROL MECHANISM

The drive used is a 30 W Hall-effect collectorless m o t o r (Thomson-C.S.F., P 11 HMC 26/20 Model). If running on no load, its maximum speed is 500 rps. At this speed the power needed to drive the whole electrode system is close to 90 W. Consequently, a water circulation cooling coil (15, Fig. 1) has been installated. The block diagram in Fig. 4 shows the completed assembly: plan (P) contains the diagram of the m o t o r power supply circuit, and plan (R) that of the control loop. The square signals, supplied b y t w o saturated high-again amplifiers (A1), are transmitted to the driver (A2) which assures the periodic reversal of the input voltage of power amplifiers (Az) connected directly to the corresponding m o t o r windings (M). By acting on the control stages, it is possible to interrupt excitation o f the m o t o r periodically and thus to set the chosen speed of rotation. In order to achieve adequate control at low speeds o f rotation, on the shaft o f the m o t o r a stroboscopic iron disc (100 slits) (W) was fitted in

158

\

L. ~

\

li

Fig. 4. Block diagram of rotation speed control system. (A1) High-gain amplifiers of resolver output signals; (A2) drivers; (Aa) motor power amplifiers; (B) monostable flipflop; (C) magnetic head; (D) synchronous demodulator; (E) high-gain differential amplifier; (F} frequency m~eter; (G) information unit (resolver) of the Hall-effect motor; (I) integrator of flipflop output signals; (M) driving unit of the Hall-effect motor; (Ref) d.c. reference voltage; (S) threshold detector; (T) Schmitt trigger.

front o f a magnetic head (C) [21]. This device makes it possible to reduce the lower limit o f the speed o f rotation which can be properly regulated in the proportion of 2/100. However, mechanical friction and other factors introduce non-linear terms into the transfer function, the effect o f which is greater the lower the speed. In order to remedy these shortcomings, a phase control was superimposed on the control described above: the signal supplied b y the Schmitt trigger (T) is applied to a synchronous d e m o d u l a t o r (D), as is also a reference signal provided b y an oscillator (O) whose frequency corresponds to the desired speed of rotation. Continuous monitoring o f the speed o f rotation is obtained with the aid of a frequency meter (F) which displays this speed within a factor o f 100. The addition o f this latter control loop makes it possible, in principle, to obtain an absolute e r r o r o f less than 0.005 rps for all speeds o f rotation. (4) OPERATING TECHNIQUE

In order to assess the extent of the remaining imperfections in the movement of the disc, the image o f a laser beam was thrown on a screen after reflection on the electrode in motion and on an auxiliary mirror. Whatever be the speed of rotation, the play measured under these conditions was found not to exceed +3 #m. The performance of the completed device was tested electrochemically using

159 smooth platinum disc electrodes of diameters varying from 0.4 to 1.0 cm, m o u n t e d in Kel-F supports of different shapes and of external diameters from 0.7 to 1.7 cm. All the measurements reported in the present paper were made in a dark enclosure at 25 + 0.1°C with an equimolar solution o f 0.01 M K4Fe(CN)6 + 0.01 M K3Fe(CN)6 in 2 M NaOH, using Merck's analytical reagents and high-purity water. The rotation speeds used covered the range from 4 to 256 rps according to the external diameter o f the support. The counter-electrode was a platinum plate at t h e b o t t o m o f the cell. The ratio between its area (~ 80 cm 2 for each face) and that o f the RDE was in every case at least 100. A three electrode classical circuitry (SCE as reference) with a potentiostat (Tacussel PRT 40-1X) and a XY recorder (Servogor RE 551) was used for the steady-state measurements. For the reasons previously given [ 15], an ohmicdrop corrector was not used in recording the current-voltage curves. The sweep rate chosen, 5 mV s -x, was far below the limit at which deviations from the steady-state regime occur. The residual current measured in the absence o f electroactive species, was negligible with comparison to the faradaic current for all speeds of rotation used. Measurements of the operational impedance [22,23] were made, with a twoelectrode cell, recording numerically the response t o a small galvanostatic pulse applied to the RDE initially at equilibrium. In every case, the amplitude of the current step was limited so that the final value o f the voltage response did not exceed 10 mV. This actually assures the proportionality between the response function and the perturbation applied. This condition is necessary in order that the behaviour o f the electrochemical system under study may be treated in impedance terms. The data acquisition assembly used operates on the principle already described [24]. It includes in particular an in-store analogue/digital converter (Datalab DL905) enabling several data acquisition speeds from 200 ns to 10 ms to be achieved. The experimental error should not exceed 4 times the accuracy o f the converter used (0.004). The recorded voltage responses on different time scales are normalized with respect to the current and joined together. We have noticed that the value o f the instantaneous resistance measured at a given time was the same within 2% whatever the speed o f the data acquisition used. This error has no significant influence on the value of the impedance finally found, which is derived b y performing numerical Laplace transformation of the voltage and current functions obtained. More details on treatment of the electrode surface as well as on other experimental conditions were described in previous papers [9,15]. (5) RESULTS OF MEASUREMENTS UNDER STEADY-STATE CONDITIONS Crude current-potential curves obtained with a 1.004 cm diameter electrode are shown as an example in Fig. 5. The absence of any fluctuations on these curves gives a first indication of the high mechanical quality o f the device. Figure 6 shows the relation b e t w e e n the limiting current densities found for electrodes o f different diameters and the square root of the rotation speed N. Over the range o f N shown in this Figure, b o t h cathodic and anodic limiting current densities j~ and ]~ are proportional to N 1/2 This proves that laminar

160

""0tZ./mA

3

+C~0

! +211

-SO0

-4.0 ~

-400

-300

-200

-tOO

O0

+300

4

Fig. 5. Steady-state current-voltage curves referred to the equilibrium potential. E q u i m o l a r 0.01 M solution o f ferro- and ferricyanide in 2 M N a O H at 25°C. Platinum disc electrode; area 0.79 cm 2. (1) 16 rps, (2) 64 rps, (3) 100 rps, (4) 144 rps, (5) 169 rps, (6) 196 rps. F o r curves 4, 5 and 6 the ordinate scale is to be multiplied b y 2.

II

15 j®/mA 10

~oJ 0i"'~-. ~ ,.

J 100 N/rev s -1

-5 -10 -15 Fig. 6. Limiting-current densities vs. t h e square r o o t o f t h e r o t a t i o n speed. Platinum disc electrodes: (e) ~el = 0.40 cm, Cext = 0.70 cm; (A) ~bel = 0.71 cm, ~bext = 1.70 cm; (o) eel = 0.98 cm, ~ext = 1.30 cm.

161

flow conditions are maintained. The m a x i m u m divergence from the average straight line (Levich line) was in every case of the order of 0.5%. Results of the study of the ferro-ferricyanide couple under steady-state conditions in the cathodic domain have been analysed recently [15]. The value of the diffusion coefficient for the ferricyanide ion under conditions of the present paper, found from the cathodic slope was Dox = (5.34 + 0.02) X 10 -4 cm 2 s -1. Likewise, the value of the slope of the Levich line obtained from the anodic limiting currents has enabled us to calculate the diffusion coefficient of the ferrocyanide ion. Values of Dox and Dred were obtained by solving the following quadratic equation in which x represents D -~/3 1.612vl/6x 2 + 0.48v-l/6x + 0.23v -1/2 -- nFc(27rN)l/2/Ifl = 0

(1)

derived from the classical expression of the diffusion limiting current density [j~[ = nFDc/6o

(2)

by substituting for the thickness of the diffusion layer 60 its series expansion as a function of Sc -1/3 (where Sc = v/D) limited to the third term (which does n o t affect the precision for values of Sc higher than 1000 [5]). 6o = (v/27rN)l/2(1.612 Sc -1:3 + 0.48 Sc -2/3 + 0.23 Sc -1 + . . . )

(3)

Equation (1) permits a precise calculation o f D knowing the bulk concentration Cox or Cred of the species considered, the corresponding limiting current density j~, the rotation speed N and the kinematic viscosity o f the solution v. Values o f v in various conditions were determined independently [15]. For the solution used in this study, v was found to be (1.27 + 0.01) X 10 -2 cm 2 s -~ at 25°C; this gives finally D r e d = (4,71 + 0.04) × 10 -6 cm 2 s -~. These results are in good agreement with those o f B~zfin and Arvia [25]. (6) ELECTROCHEMICAL TESTS U N D E R T R A N S I E N T C O N D I T I O N S

The current signals AI and the corresponding transient voltage response AE, recorded and normalized as mentioned above, were Laplace transformed Zexp(S) = J 0

A E e x p ( - - s t ) d t / J A I exp(--st)dt

(4)

0

using values o f the Laplace parameter from 0 to l 0 s s -1 to give the crude impedance spectra. Since the transient measurements were accomplished using a two-electrode cell, the measured values o f Zexp represent the sum of the impedances o f both electrodes and the ohmic drop in the solution. Although a very large counter-electrode was used, to maintain its impedance negligible in comparison to that of the RDE at low frequencies, it was necessary to limit the response time according to an a priori calculation [9]. The ohmic resistance R ~ was determined in every case by extrapolating the observed Warburg line to infinite frequency. It should be noticed that, more rigorously, the value of R a , obtained in this way, contains also a possible contribution from the charge transfer process, Rt, and from the double-layer capacity Ca. This latter contribution m a y be replaced to a good approximation

162

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//

Zw÷Rn

Z/£

16

~

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//~/2,1

10

8

/

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/Z.xp ~.

~

~

~

,01 10

s "~/2/se c~/'2

6

04

100 1

25 16 2 3

625 4

4 5

s l s e c "1

6

7

8

S-112/secl/2 Fig. 7. Operational impedance theoretical and experimental spectra. ZW, Warburg impedance, RE, frequency independent cell resistance, Zcell , calculated cell impedance, Zexp; experimentally determined values, s, Laplace parameter. Rotation speed 16 rps; for the other conditions see Fig. 5.

[23] by a constant series resistance Red ~ --O2Cd, where a is the slope o f the Warburg line. In the range o f s up to l 0 s s -1, Rcd is o f the order of 0.01 ~Z cm 2. In these conditions, the charge transfer resistance Rt, whatever its value, m a y be considered as a part o f R~z. Figure 7 shows as an example the crude operational impedance spectrum as a function of s -~/: obtained with an electrode o f 1.004 cm diameter at 16 rps, as well as the corresponding spectrum theoretically calculated. In the high frequency range, we observe a straight-line segment characteristic of the Warburg relationship: Zw

(5)

= os -'2

For a redox solution of equimolar concentration c, the expression of the Warburg coefficient is: a

=

(RT/n2F2Ac)(Do~n

--4. ~JredT~-l/21!

(6)

where A is the area o f the electrode. Introducing in eqn. (6) values o f Dox and Dre d obtained under steady-state conditions, we find o = 30.1 ~ s - i n for A = 1 cm 2. The average value obtained from several series of transient measurements was 29.8 + 0.3. The divergence between those two values is very small and of the order of magnitude of the resolution given by the apparatus used for measuring the transient response. in the Warburg domain, diffusion is the only significant factor determining the transport of the electroactive species; although for low frequencies, con-

163 v e c t i o n m u s t be t a k e n into c o n s i d e r a t i o n . Values o f Zw c a l c u l a t e d a c c o r d i n g to eqn. (5) as well as values o f c o n v e c t i v e d i f f u s i o n i m p e d a n c e Zd c o m p u t e d using a p r e v i o u s l y described p r o g r a m m e [6] are i n d i c a t e d in Table 1. C o m p a r i s o n b e t w e e n Zw and Zd shows t h a t t h e e f f e c t o f c o n v e c t i o n appears f o r values o f s less t h a n a b o u t 50 s -1 f o r t h e speed o f r o t a t i o n in q u e s t i o n . E x t r a p o l a t i o n o f the Warburg line t o infinite f r e q u e n c y gives t h e value o f t h e p u r e l y resistive t e r m R a w h i c h was f o u n d t o be equal t o 2.19 + 0.02 ~2 f o r all r o t a t i o n speeds. In fact, this value varied slightly a c c o r d i n g t o t h e d i a m e t e r o f t h e R D E and t o o t h e r e x p e r i m e n t a l c o n d i t i o n s . T h e m e a s u r e d c r u d e i m p e d a n c e values Zexp were c o r r e c t e d b y s u b t r a c t i o n o f R ~ . Since t h e i m p e d a n c e o f t h e c o u n t e r - e l e c t r o d e is negligible and t h e possible c o n t r i b u t i o n o f R t t o t h e faradaic i m p e d a n c e o f t h e R D E was i n c l u d e d in R a ,

TABLE 1 Values of theoretically calculated Warburg impedance Zw, and of convective-diffusion impedance Z d compared to the experimentally determined values Zex p -- R~2. Rotation speed 16 rps. For the other conditions see Fig. 5.

SIs- 1

ZW]~-~

Z d ]~

(Zexp -- R ~ ) / ~

62500 15625 10000 6000 3000 1500 1000 600 300 200 150 100 75 55 35 20 15 11 9 7.5 5.5 4 3.5 2.5 2 1 0.8 0.6 0.3 0.1 0.01 0

0.120 0.241 0.301 0.389 0.550 0.777 0.952 1.229 1.738 2.13 2.46 3.01 3.48 4.06 5.09 6.73 7.77 9.08 10.03 11.00 12.83 15.05 16.09 19.04 21.3 30.1

0.120 0.241 0.301 0.389 0.550 0.777 0.952 1.229 1.737 2.13 2.45 3.00 3.46 4.03 5.03 6.55 7.47 8.54 9.27 9.95 11.11 12.28 12.75 13.86 14.52 16.12 16.49 16.90 17.55 18.02 18.24 18.27

0.08 0.21 0.30 0.39 0.55 0.77 0.95 1.22 1.74 2.13 2.45 3.01 3.47 4.05 5.03 6.57 7.48 8.57 9.33 10.0 11.2 12.4 12.9 14.0 14.7 16.3 16.7 17.2 17.9 18.4 18.6 18.6

~

164

the values obtained represent the convective
+ 1/I/~c I)

(7)

All our previously published results [9], some o f which are given here as an example, show divergences from the theory of less than 2% (except for the 4 mm diameter electrode for which the error reached 5%). This confirmes once more the appropriateness and reliability o f the device used in the transient regime. (7) APPLICATION TO THE STUDY OF PARTIALLY BLOCKED MODEL ELECTRODES

An a priori calculation of the steady-state attenuation factor p of the diffusion current density for partially covered electrodes was performed first b y Landsberg et al. [26,27] on the basis of Smythe's cylinder model, and more recently b y ourselves using a periodic-lattice model [28]. In b o t h cases, the theory predicts a value of p between 1 and 1 -- 0, where 0 is the fractional surface coverage, approaching 1 if the dimension of the inactive (or active) sites is small, and tending to 1 -- 0 if it is large in comparison with the thickness o f the Nernst diffusion layer. Together with this work, we present a theoretical attempt [29] to deal with the impedance behaviour o f partially covered electrodes. In this theory, the Nernst approximation assumed in the steady-state treatment was replaced b y Levich's convective
165

Fig. 8b

Fig. 8. Microphotographs of m o d e l electrodes. (a) Model electrode No. 1, platinum-araldite, ~ 330 pm, 0 ~ 0.18, ¢ e l = 0.71 cm. (b) Model electrode No. 2, nickel-araldite, X ~ 6 pm, 0 ~ 0.40, picture dimensions ~ 0 . 0 4 x 0.03 cm.

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-14 Fig. 9. R e c o r d e d d.c. v o l t a m m o g r a m s . ( ) U n i f o r m l y active e l e c t r o d e ; ( . . . . . e l e c t r o d e No 1 ; ( . . . . . . ) m o d e l e l e c t r o d e No. 2.

) model

In Fig. 9 one observes that, for the model electrode no. 1 (with a relatively large k) the limiting current values are lower by 5 to 10% than those corresponding to the active one. In contrast, for the electrode no. 2, there are no significant differences between the limiting currents and those for the active electrode, even for the highest rotational speed used (196 rps). The experimental value of p(s) for a model electrode is obtained by dividing its measured admittance by that of a uniformly active one having the same diameter. Experimental and theoretical results giving p as a function of s, for the two electrodes are shown in Figs. 10 and 11. For the electrode No. 1, one can notice (see Fig. 10) t h a t p tends to 1 -- 0 at high frequencies. For the lowest rotational speed, the limiting value, p = 0.82, is effectively attained at s ~ 100 s -1. For t h e electrode No. 2 (see Fig. 11), the limiting value, p = 0.60, is approached only at the highest frequencies experimentally accessible, even for the lowest rotational speed. However, this limit can be obtained by extrapolation in the domain of s between 1 0 3 and l 0 s s -1 . Comparison o f our experimental and theoretical results for model electrodes

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100

s / s ¢ c -~

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gives rise to the following observations: (1) At low frequencies as well as under steady-state conditions, experimental values of p are significantly higher than those predicted by our simplified theory [29]; further they are only slightly affected by the rotation speed of the disc. (2) At intermediate frequencies, deviations from theoretically predicted values of p not only reach 10% but, contrary to the theory, larger values of p are observed at higher rotation speeds. (3) At high frequencies, measured values of p are identical to the theoretical

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4 rev/sec 64 196

6

4

2

36

16

4

1

10000 1600 Fig. 11. A t t e n u a t i o n experimental.

400

s / s e c -~

100

64

f a c t o r p vs. s. M o d e l e l e c t r o d e N o . 2: (

1

0

) theoretical, (......

)

168

predictions within the accuracy o f measurements. To explain the observed deviations from the theory, it is necessary to recall that the lateral components of the convection have not been taken into account. Use of the device described in this paper permitted us to give an: experimental confirmation that these components are effectively negligible in the case of a uniformly active RDE [9]. In contrast, on a partially blocked RDE, lateral convection may not be negligible; it contributes then to the increase of the resulting diffusion current and can lead to experimental values o f p higher than that predicted b y the simplified theory. The higher the rotation speed o f the disc, the more important should be this effect. On the other hand, our theory in which only the normal convection was considered predicts values of p decreasing for higher speeds of rotation. So, the effect of lateral convection on the relation between p and N should be opposite to that of the normal convection; this is in good agreement with our experimental results in the low frequency region when only a slight influence of N on p was observed. In the intermediate frequency region, experimental values of p increase significantly with N. This result indicates that lateral convection would be the predominant factor o f mass transport in this domain. (8) CONCLUSIONS

We have designed a reliable RDE device permitting accurate voltammetry and impedance measurements. Electrochemical tests effected under steadystate and transient conditions prove that this design is successful. Mechanical vibrations and irregularities of the angular velocity as well as other sources of noise have been eliminated. Hence the recorded voltammograms are free from fluctuations and it is possible in particular to measure limiting currents with a precision better than 1%. This result, combined with a careful preparation of the electrode surfaces allowed us to get values of diffusion coefficients with the same accuracy. The precise knowledge of diffusion coefficients is necessary to derive kinetic parameters from the crude experimental data. In this work emphasis was put on combining the use of a RDE and impedance measurements. This permitted us, for the first time, to provide a precise verification o f the convective diffusion model b y operational impedance measurements. The range o f frequencies covered here extends from 0 to l 0 s s -1. This restriction is essentially due to the faradaic impedance, becoming small in comparison to the ohmic drop at high frequencies. This limitation is not very serious in the case of a uniformly active electrode because a sufficiently extended Warburg region is available, even for the highest accessible rotation speeds. This permits an accurate determination of the resistive c o m p o n e n t o f the impedance b y extrapolation to infinite frequency. The situation is quite different in the case of partially blocked electrodes for which the lower limit o f the Warburg region is shifted towards higher frequencies. Similar behaviour is expected in the case of a chemical reaction associated to an electrochemical step [30,31l. The smaller the size o f inactive patches, or the faster the chemical reaction, the sharper will be this effect. The estimation of the ohmic drop b y extrapolation o f the Warburg line will remain possible, but only at very low speeds o f rotation. This was still the case for the

169 model electrodes used in this work, b u t compensation o f the ohmic drop will be necessary in the case of smaller blocking sites. Nevertheless, our RDE device permitted us to confirm that the slope o f the Warburg line does not depend on the dimensions of the blocking patches, b u t only on the surface coverage as predicted theoretically. Since part of our results agree very well with the theory, it is reasonable to suppose that the remaining results are reliable, although at present we have no • precise theory to support them. Thus, the results of impedance measurements on model electrodes lead to the conclusion that lateral convection must be the predominant factor in the intermediate frequency region. At low frequencies, lateral convection would be o f the same order o f magnitude as the normal convection. Equations derived from a new theoretical a t t e m p t (of which it is premature to discuss details here), in which the lateral convection is no longer neglected, show that values o f p increase with the angular velocity, with the diameter o f the disc and also with the dimension o f inactive sites. Such predictions agree with our experimental results. ACKNOWLEDGEMENTS The authors express their gratitude to Mr. L. Demon, Director of the "Service des Prototypes du C.N.R.S." and to his coworkers for mechanical construction o f the RDE device. The study given in this paper was partially performed at the "Commissariat ~ l'Energie A t o m i q u e " where Mr. Etman held a fellowship. The authors are very grateful to Mr. Molina (Service d'Etudes Analytiques, Fontenay-aux-Roses) for the facilities provided during the course of this experimental work, to Mr. Sourrouille (Centre de Marcoule) and to Mr. Defresne (Centre de Saclay) for the preparation of model electrodes. Thanks are due to Prof. Joseph Jordan from the Pennsylvania State University for valuable comments. REFERENCES 1 V.G. Levich, Acta Physieochim. URSS, 17 (1942) 257; 19 (1944) 177; Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, N.J., 1962. 2 A.N. F~_mkin, L.N. Nekrasov, V.G. Levich and Yu. B. Ivanov, J. Electroanal. Chem., 1 (1959) 84. 3 W.J. Albery and M.L. Hitchman, Ring-disc Electrodes, Clarendon Press, Oxford, 1971. 4 J.M. Coueignoux and D. Schuhmann, J. Electroanal. Chem., 17 (1968) 245. 5 E. Levart and D. Schuhmann, Int. J. Heat Mass Transfer, 17 (1974) 555. 6 E. Levart and D. Schuhmann, J. Electroanal. Chem., 53 (1974) 77. 7 C. Deslouis, Thesis, A.O. 11014, Paris, 1975. 8 C. Deslouis, I. Epelboin, M. Keddam and J.C. Lestrade, J. Electroanal. Chem., 28 (1970) 57. 9 M. Etman, E. Levant and G. Scarbeck, C.R. Aead. Sei. (Paris), 287 C (1978) 1. 10 J. Jordan, R.A. Javick and W.E. Ranz, J. Amer. Chem. Soc., 80 (1958) 3846. 11 Yu. V. Pleskov and V. Yu. Filiinovskii, The R o t a t i n g Disc Electrode, Consultants Bureau, N e w YorkLondon, 1976. 12 F. Opekar and P. Beran, J. Electroanal. Chem., 69 (1976) 1. 13 A.C. Rid difo rd in P. Delahay (Ed.), Advances in E l e c t r o c h e m i s t r y and Electrochemical Engineering, Vol. 4, Interscience, New York, 1966, p. 47. 14 G. Ritzler and M. Gross, J. Electroanal. Chem., 94 (1978) 209. 15 M. Etman , R. Molina, D. Schuhmann, E. Levart, O. C o n t a m i n and G. Scarbeck, Analusis, 5 (1977) 11. 16 R.H. Sonnet, B. Miller and R.E. Visco, Anal. Chem., 41 (1969) 1 4 9 8 . 17 G.W. Harcington, H.A. Laitinen and V. Trendafilov, Anal. Chem., 45 (1973) 433.

170 18 19 20 21 22 23 24 25 26 27 28 29 30 31

K.E. Heusler and H. Schurig, Z. Phys. Chem. (Frankfurt), 47 (1965) 117. G. Trimborn, A. Heindricks and W. Vielstich, Messtechnik, 76 (1968) 224. J. Margarit, G. Dabosi and M. Levy, Bull. Soc. Chim. Ft., (1976) 1509. R.K. Dorsch, J. Electroanal. Chem., 21 (1969) 495. E. Poirier d'Ang~ d'Orsay, C.R. Acad. Sci. (Paris), 260 (1965) 5266. E. Levart and E. Poirier d'Ang~ d'Orsay, J. Electroanal. Chem., 19 (1968) 335. O. Dupr~ la Tour, J. Farcy-Bravacos, E. Levart, P. Malaterre and D. Schuhmann, J. Eleetroanal. Chem., 39 (1972) 241. J.C. B~iz~n an d A.J. Atria, Electrochim. Acta, 10 (1965) 1025. R. Landsherg and R. Thiele, Eleetrochim. Aeta, 11 (1966) 1243. F. Scheller, S. M0.Uer, 11. Landsberg and H.J. Spitzer, J. Electroanal. Chem., 19 (1968) 187. E. Levart, D. Schuhmann, O. Contamin and M. Etm a n, J. Electroanal. Chem., 70 (1976) 117. M. E tman, E. Levart and D. Schuhmann, 29th Meeting of I.S.E., Budapest, 1978, E x t e n d e d Abstracts, p. 216; J. Eleetroanal. Chem.. 101 (1979) 141 (this issue). T. Gueshi, K. T o k u d a and H. Matsuda, J. Electroanal. Chem., 89 (1978) 247. O. Contamin, E. Levart and D. Schuhmann, J. Electroanal. Chem., 84 (1977) 271; 88 (1978) 49.