J Electroanal. Chem , 111 (1980) 287--294 287 © Elsevmr Sequoia S.A., Lausanne -- Printed in The Netherlands

A PRECISE COTTRELL CELL

HARUKO IKEUCHI, YUMIKO SHIWA, HIROKAZU TSUJIMOTO, MASATO KAKIHANA, SAKUE TAKEKAWA and GEN P. SATC)

Department of Chemistry, Faculty of Scwnce and Technology, Sophia University, Kioicho, Chiyoda-ku, Tokyo 102 (Japan)

(Received 22nd January 1980)

ABSTRACT

A precise Cottrell cell with glassy carbon electrode for chronoamperometric determination of diffusion coefficients is described The validity of the measurement was demonstrated by comparing the observed diffusion coefficient of thallium(I) ions in 0.5 mol dm -3 KNO3 solu- tion at 25°C with the standard value previously determined by the thin-walled hanging mercury drop electrode method. The essential points for successful measurement are a right choice of the material and a precise finish of that part of the cell where the diffusion is made to occur.

INTRODUCTION

The Cottrell cell, in which the depolarizer diffuses linearly in the direction normal to the electrode surface, has long been studied since the classical work by Laitinen and Kol thoff [ 1 ]. The diffusion coefficients of a number of depolarizers obtained by Von Stackelberg et al. with a Cottrell cell [2] have been cited as standard values. Some other experimental studies of the Cottrell cell technique are found in the literature of the 1950s [3,4]. Owing to the slow response of the current-measuring devices then available, these workers had to use long electrolysis times ranging from 1 to 30 min, and the results were inevitably subject to convective disturbance in spite of their careful experi- mentation, as indicated by relatively poor constancy of the i x/t values tabulated by the authors [ 1,2 ]. Furthermore, it was impossible for them to demonstrate the validity of the measurements because of the lack of reliable standard values for the diffusion coefficients.

In chronoamperometr ic and chronopotent iometr ic techniques which make use of a stationary electrode such as the spherical unshielded disk, cylindrical or tubular electrode, analysis of the results becomes difficult owing to the effect of the non-linearity of the diffusion pattern. In fact, much effort has been expended in evaluating the correction terms in these techniques for the contr ibut ion made by the non-linearity at certain electrode configurations [5--12].

It is desirable that an accurate Cottrell cell method be established which can cover the usual time ranges of chronopotent iometr ic and chronoamperometr ic techniques, i.e. from a few milliseconds to several seconds. The diffusion

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pattern of this type of cell is the simplest, and the data are more easily amen- able to theoretical analysis, even when the electrode process is complicated. Moreover, the electrode area can be much larger, and the measurement can be carried out at lower depolarizer concentrations.

This report describes the construction of a Cottrell cell and evaluation of its performance. The evaluation was made in terms of comparison between the diffusion coefficient of TI(I) ions measured with the Cottrell cell and the standard value determined by means of the thin-walled hanging mercury drop electrode (TW-HMDE) method [13,14].

EXPERIMENTAL

Cottrell cell

The design of the present Cottrell cell is shown in Fig. 1. The electrode was a disk of glassy carbon (Tokai Carbon, GC-2000) of ca. 3 mm thickness and ca. 10 mm diameter. The end serving as the electrode surface was ground with a series of emery papers of increasing fineness, then with diamond paste (average grain size, 3 pm) and finally polished with aluminium oxide (average grain size, 0.3 pm) on a turntable. The disk was then washed thoroughly with water and dried in a desiccator.

The diffusion was made to take place in a precisely machined cylindrical cavity of the cell piece [Fig. 1(4)]. The upper end of the cell piece was care- fully finished so as to achieve a perfect contact with the electrode surface. No

3 ~ e-- 2 o r 3 m m

r2: Fig. 1. Cottrell cell (1) holders; (2) brass push rod; (3) glassy carbon disk; (4) cell piece.

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sealing material was used. The surface area of the electrode was calculated from the inner diameter of the cavity rc, which was determined by microscopic mea- surement to a precision of I pm.

The electrode disk was pushed onto the cell piece by means of a brass push rod [ Fig. 1(2)] by tightening the screw of the holders. During this operation the push rod was held in place so that no torque would be exerted on the disk: if the disk is allowed to slip against the cell piece, the upper edge of the cell piece may be damaged. The lower end of the rod was machined to a spherical form in order to facilitate flat and even contact between the electrode surface and the edge of the cavity. The body of the cell was made of poly(methyl methacrylate) (PMMA).

Chronoamperometric apparatus

A potentiostat (Fuso Seisakusho, Model 311) was used with a double poten- tial step accessory constructed by the same manufacturer, which permitted switching from a predetermined potential to another by manual operation without introducing chattering noise by means of a combination of relays and FET switches. The current signals were either recorded by a high-speed pen recorder (Riken Denshi, Model SP-G3) or stored in a digital memory (Bioma- tion, transient recorder, Model 802). In the latter case the signal was retrieved by a digital printer.

The electrolysis vessel was an all-Pyrex glass beaker similar to that described previously [13]. The test solution was thermostated to 25.0 + 0.1 ° C, and the temperature fluctuation during the measurement was <0.01 ° C. The solution was deoxygenated with a stream of argon.

Reagents

The water used in the present experiments was obtained by passing deionized water through a column of active charcoal and distilling it in an all- glass apparatus. Thallium(I) nitrate solution was prepared gravimetrically from a dried 99.9% sample (Yamada Kagaku-Yakuhin K.K.). Potassium nitrate was recrystallized from water. The other chemicals were of reagent grade (Wako Pure Chemical Industries) and used without further purification.

Procedure

When the Cottrell cell was assembled, the electrode surface was conditioned at the beginning of a series of measurements by cyclic polarizations in a deoxygenated supporting electrolyte solution, first between 0 and --1.8 V vs. SCE. The potential range was then narrowed to between 0 and --0.6 V and the conditioning continued until practically no faradaic current was observed on the cyclic voltammograms. During this process the solution in the diffusion cavity was continuously flushed by means of a small J-shaped pipette with a rubber bulb. The conditioning was usually completed within 1 h. Then the cell assembly, after being rinsed with portions of deoxygenated test solution, was placed in the electrolysis vessel containing the deoxygenated test solution.

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The electrode was first brought to the lowest positive potential at which no reduction occurred, and then the potential was stepped up to that at which the diffusion current was measured. The chronoamperogram was corrected for the residual current, which was recorded under the same conditions in the corre- sponding supporting electrolyte solution.

RESULTS AND DISCUSSION

When the diffusion current at the Cottrell cell Lid, c l is plot ted against t - in , t being the electrolysis time, a straight line passing through the origin should be obtained according to the Cottrell equation,

]Id,cl = FSnc(D/Trt) in (1)

where F is the Faraday constant, S the surface area of the electrode (S = urn), n the charge number of the electrode reaction, c and D the bulk concen- tration and the diffusion coefficient of the depolarizer respectively.

The experimental plots were quite linear as shown by the example presented in Fig. 2, and their intercepts Ac were practically zero as shown in Table 1 *. The D values were calculated from the experimental slope Bc (= 7rl/2Fr~ncD 1/:) with the known values of the other factors and are listed in the last column of the table. The agreement between them and the standard value is satisfactory. It is therefore concluded that the present Cottrell cell method is capable of determining diffusion coefficients with a precision comparable to that of the TW-HMDE method.

The above experiments covered a time range from about one-half to several seconds. At longer and shorter times of electrolysis, deviation from the linear diffusion was observed. This will be bet ter shown by the example of the hexacyanoferrate(III)--KC1 system, since in the case of TI(I) ions prolonged electrolysis resulted in erratic chronoamperograms, presumably owing to some irregularity of the deposited metal layers.

In Fig. 3, IId,cl tln/ncr~ is plot ted against t In. If the diffusion current follows the Cottrell equation, the plot should be a horizontal line. This is the ease for the experimental plot (the circles) at moderate electrolysis times. The diffusion coefficient corresponding to this constant value is 7.84 × 1 0 -1° m 2 s -1. Unfortunately, no standard value is ye t available for comparison [14]. Towards both ends the plot deviates. The excess current flowing after ca. 150 s is at tr ibuted to convection as in the case of TW-HMDE [13]. But with the Cottrell cell this deviation was insignificant until the thickness of the Nernst diffusion layer 5 reached ca. 0.6 ram, a value much thicker than that for TW- HMDE (ca. 0.15 mm) in a similar system [13], reflecting a more stable diffu- sion layer in the Cottrell cell.

At t < 0.1 s, the current was in excess. The leak or infiltration of the solu- tion through the top of the cell piece would bring about such an effect. This

* Somet imes a small faradaic cur ren t was observed at --0.7 V, the voltage at which the e lec t rode was main ta ined before c o m m e n c e m e n t o f electrolysis. In such cases the results were less reproduc ib le and t h e y are n o t inc luded in the table. This p h e n o m e n o n will be descr ibed in detail e lsewhere.

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10

8

"~6

d 4

2

0

Fig 2. I d , c vs. t -~/2 plot

/ ///Z , , , r i * , i i I i

0 05 10 ( t l s )-I,,2

1.0 tool m -3 TINO3 in 0.5 mo l d m -3 KNO3, 25 °C, r c = 1 .018 m m .

occurred when the contact between the upper edge of the diffusion cavity and the electrode surface was incomplete. However, in this case, it was indicated at once by a very large spurious current already flowing in the conditioning stage, and the cell was in fact unusable.

The roughness of the electrode surface may be partly responsible for the excess current. Observation with a scanning electron microscope and X-ray microanalyser showed that crater-like holes were scattered over the smooth sur- face (Fig. 4), and aluminium was detected in the holes. Some particles of aluminium oxide had not been washed ou t of the holes. These holes, which

T A B L E 1

Di f fu s ion coe f f i c i en t o f TI(I) ions in 0.5 tool d m -3 KNO3 a q u e o u s s o l u t i o n at 25°C mea- su red wi th a Cot t re l l cell (r C = 1 .018 r am; t he u n c e r t a i n t y is 95% c o n f i d e n c e l imi ts )

n c / m o l m -3 Elect ro lys is Po ten t i a l N u m b e r 1 0 6 A c / A 10 l° D i m 2 s -1

t ime range / s vs. SCE/V of r u n s

1 .0750 0 . 8 2 - - 8 . 2 0 - - 0 . 7 0 - * - - 1 . 1 0 9 - - 0 . 0 4 - - ¢ 0 . 0 1 18.4 +- 0.1 1 0750 0 .7 2 - -8 .20 - -0 .70 ~ - - 1 . 1 0 3 ---0.01-- 0 .00 18.5 -+ 0.4 1 . 0750 0 72 - -8 20 - -0 .70 -+ - -1 .15 3 - -0 02-- 0 .00 18.5 -+ 0.3 4 . 4 9 9 0 0 5 1 - -8 .80 - -0 .73 ~ - - 1 . 1 0 4 - - 0 . 2 4 - - + 0 . 0 1 18.7 + 0.2

average = 18.5 -+ 0.1 a

a S t anda rd value (ob t a ined wi th TW-HMDE [13 ] ) = (18.7 + 0.3) × 10 - l ° m 2 s -1.

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" i "

E "T

Tn

4

0

o--OA o o

~ . - - A - - _ _ - f t -

I I I

5 10 15

( t / S )~/2

Fig 3. Time dependence of Id,ctl/2/ncr~ 1 mol m -3 K3Fe(CN)6 in 1 mol dm-3 KC1, 25°C.

Fig. 4. The surface of glassy carbon electrode. The length of the bar is 5 #m.

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may probably be the pores in glassy carbon cut open by grinding, would certainly increase the true surface area and consequently the diffusion current, if their inside walls have electrode function. However, in view of the depth of the holes, at most 4 pm, it seems improbable that this effect would remain noticeable until 6 reached a few tens of micrometres. In fact, at the unshielded microdisk electrodes, with the glassy carbon surface finished in the same way as the present one, the excess current decayed much more rapidly [15]. Therefore, the observed excess current cannot be attributed entirely to the roughness effect.

This experiment was carried out with a cell piece made of PMMA. Micro- scopic observation revealed that the upper edge of the diffusion cavity was slightly rounded. When the edge touches the electrode surface, there should be an intervening thin dead space containing an excess of solution, and the current will be larger than expected until the diffusion layer has grown suffi- ciently far beyond this region. This view is corroborated by an experiment in which a cell piece made of more easily deformable material was used. The triangles in Fig. 3 were obtained by using a polyethylene cell piece. It seems that the cross-section of the diffusion cavity increased along the distance from the electrode surface after passing through a minimum point. The cell piece was observed under a microscope after the experiment; the upper edge of the cavity was rounded and bent inward so that the upper part of the cavity was narrowed.

Although no quantitative assessment was possible, these facts indicate the importance of the right choice of material for the cell piece: too soft a cell piece is easily deformed, but it should not be so hard that the electrode surface is damaged. In addition, good workability and adequate elasticity are required. For glassy carbon electrodes, PMMA was found to be most suitable among the several plastics examined, but it was a little too hard for the platinum elec- trode.

CONCLUSION

The present results demonstrate that a properly constructed Cottrell cell can realize the ideal linear diffusion with reasonable accuracy. The time window of the present Cottrell cell, 0.1--150 s, covers that of the usual chronoampero- metric and chronopotentiometric techniques. In order to extend the time window toward shorter times, it seems essential to find the right combination of materials for the electrode and cell piece and to refine the mechanical finishing techniques.

ACKNOWLEDGEMENTS

The authors are greatly indebted to Dr. J. Yamada of the National Chemical Laboratory for Industry and to Mr. K. Noguchi of the Department of Mechani- cal Engineering of this university for their indispensable help in designing and machining the cells. They also thank Dr. Jean Michalec of the Life Science Institute of this university, for correcting the manuscript.

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