On porous electrodes in electrolyte solutions—IV

Electrochimica Acta. 1964. Vol. 9, pp. 1231 to 1245. Pergamon Press Ltd. Printed in Northern Ireland

ON POROUS

Laboratory

ELECTRODES

IN ELECTROLYTE SOLUTIONS-IV*

R. DE LEVIES for Electrochemistry, University of Amsterdam, Amsterdam, Holland

Abstract-The simple theory proposed on the basis of a transmission-line model is shown to account fully for the ac behaviour of a brush electrode. Conversely,, the rate-determining process at such an electrode may conveniently be studied either by direct comparison with theoretical predictions for a pore or by using a squared representation, leading to the sarne plots as obtained from flat electrodes. Experiments with sintered powder electrodes indicate that the theory is also applicable to these systems. R&urn&Proposition d’un modi?le simple pour rendre compte du comportement d’une electrode poreuse en courant alternatif. La theorie est applicable aux resultats expkrimentaux obtenus avec des tlectrodes g poudres frittCes. Zusammenfassung-Es wird gezeigt, dass die einfache Theorie, welche fiir das Wechselstromverhalten einer Biirstenelektrode auf Grund des hierfiir vorgeschlagenen Modells einer irbertragungsleitung erhalten werden kann, zutreffend ist. Im Gegensatz dazu wird der geschwindigkeitsbestimmende Vorgang an einer solchen Elektrode mit Vorteil entweder durch Vergleich der experimentellen Daten mit den an der Pore entwickelten theoretischen Beziehungen ermittelt, oder es kann ein entsprechendes Model1 derart gewahlt werden, dass sich die fiir die ebene Elektrode geltenden Bezeihungen verwenden lassen. Experimentelle Untersuchungen an gesinterten Pulverelektroden zeigen, dass die Theorie such auf diese Systeme anwendbar ist. INTRODUCTION

the past few years considerable progress has been made in solving the problem of potential and current distribution within a porous electrode.1-28 Most authors have focussed their attention on the dc case, which is of major importance for the practical application of porous electrodes in batteries, accumulators and fuel cells. Recently some papers have appeared dealing partly or wholly with the ac case.5,7~17-1s,25,27~28 Working in the latter field, the present author2’s2* found that some very simple formulae relate the ac behaviour of a pore to that of a corresponding flat electrode. Only a brief account of the theory will be given here, and the emphasis will lie on the experiments which both confirm the calculations and illustrate their applicability. DURING

THEORETICAL 1.

Assumptions underlying the calculations The (1) (2) (3) (4)

model used assumes that pores are of uniform cross-section and of semi-infinite length, homogeneously filled with electrolyte, and without cross-links;

* Presented at the 14th meeting of CITCE, Moscow, August 1963; manuscript received 16 November 1963. Parts I-III: Ekcfrochim. Acta 8, 751 (1963). t Present address: Coates Chemical Laboratory, Louisiana State University, Baton Rouge, La., U.S.A. 1231 fi

R. DE LEVIE

1232 (5)

a large amount of inert electrolyte is present, the electrode material has no resistance, and finally any curvature of the equipotential surface:s within the pores may be neglected.:

2. Equivalent model On the above Fig. 1. It should depends both on (eg in the case of

assumptions each pore may be represented by a transmission line, be noted that the impedance Z of the electrode interface in general potential (eg in the case of a slow electrode reaction) and on time diffusion control).

electrolyte

fEr)&:g

__ (double layer and foradaic

capacitance impedance)

FIG. 1. The equivalent circuit of a pore.

3. Transient response to step functions When a potentiostatic or galvanostatic pore, the potential or the current within slowly, as a result of the damping of the double layer capacitance). Consequently transient response is very complicated.

step function is applied to the orifice of a the pore follows the sudden change but pulse by the capacitive part of 2 (eg the the mathematical analysis of the resulting

3. Steady state response to ac When however a small amplitude alternating voltage is used, and only the steady state harmonic response is considered, a simple analysis is possible. For small amplitudes (G 5 mV) Z is dependent on the angular frequency cc) only, and one deduces for the infinitesimally small section dz of Fig. 2 that de = -iRdz

di=

: This assumption

-i&

can be justified.22

so

so

de

;it + iR = 0,

di dr+;=O>

(1)

On porous electrodes in electrolyte solutions-IV

FIG. 2. An infinitesimally

1233

small section dz of the model.

in which e is the potential, i the current, z the direction the ohmic resistance of the pore per unit pore length electrolyte-electrode interface per unit pore length. On combining (1) and (2) one obtains d2i --dz2

R

d2e --dz’

R

Z

along the axis of the pore, R and 2 the impedance of the

i = 0,

(3)

e = 0.

(4)

and Z

which are the basic differential equations of the model. It is immaterial whether proceed with (3) or (4); in terms of e(z) we have for the semi-infinite pore

we

e(co) = 0,

(5a)

e(0) = E

(5b)

e(x) = E exp (--&R/Z) i(z)

=

_

f

%

(6)

gRexp [-&R/Z]

=

E i(o) = Tz So the pore behaves impedance Z,. 5. Representation

as an impedance

The corresponding

scalar

2/Z

which we shall call the apparent

pore

in the impedance plane

As Z, and likewise ZR, in the complex impedance capacitive part of the total of length jZ1 (its absolute p.

.\/ZR,

and -\/ZR

is a complex quantity, this result is most easily visualized plane, Fig. 3, in which the axes are the ohmic* and the In this plane Z is represented by a vector cell impedance. magnitude or modulus) and of phase angle (argument)

vector z/z

has length

diZ

and phase

only differ in their vector-length.

angle 4~;

Therefore,

as R is a

as long as the

* In the figures the ohmic axis is indicated by R, not to be confused with the electrolyte resistance R per unit pore length used in the formulae.

1234

R.

curvature culations

DE LEVIE

of the electrode surface within the pore has no influence lead to the following conclusions:

on Z, the cal-

1. the phase angle of the impedance of a porous electrode is half that of the equivalent flat electrode and 2. the absolute magnitude of the impedance of a porous electrode is proportional to the square root of that of the equivalent flat electrode.

1

t -1 ilz

impedance flat

-1 WC

of

electrode

c impedance porous

.\

electrolyte

FIG.

6. Curvature

\

resistance 3.

The representation

electrolyte

of

electrode

resistance

outside

pore

in the impedance plane.

of the electrode surface

When the shape of the electrode surface within the pores is taken into account, eg when the pore is assumed to be a circular cylinder, its influence on Z may be evaluated. It turns out that, for the frequencies commonly employed in ac measurements, diffusion in such a circular cylindrical pore often behaves as plane diffusion (ie diffusion towards and from a flat electrode).27 7. Penetration

depth

Equation (7) suggests the use of the reciprocal of the real part of d/R/Z as a quantity characteristic of the fraction of the pore effectively involved in the ac measurements; accordingly we shall define the “penetration depth” A as (9) Some maximum

values for fl are given in Table

1.

For shallow pores of depth 1 we must solve eq. (3) or (4) with appropriate boundary conditions, eg if we neglect the impedance of the bottom-end of the pore we may use (4) and (5b) with

(W

0, from which Z, = 4ZR

cotanh

1R _ . %iZR

On porous electrodes in electrolyte solutions-IV

1235

TABLE 1. THE PENETRATIONDEPTH ,I, IN cm, OF A CIRCULAR CYLINDRICAL PORE, CALCULATED WITH ,%= v’z ra: radius of the pore, !Lrn. p : specific electrolyte resistance, fi cm; K : double layer capacitance, taken to he 20 yF/cm2.

w : angular frequency, taken to be 500 s-l (approx. 80 Hz). If other components of 2 are present besides the double layer capacitance, 1 will be smaller than indicated below x

1 10 100 1000

If I >

0.03 0.01 0.003

10

100

1000

0.1 0.03 0.01

0.3 0.1 0.03

1 0.3 0.1

34 the cotanh term may be neglected,

so then the pore behaves

--

as a semi-infinite

one.

8. Finite electrode resistance A

non-zero

will lead electrolyte given 9.

or

above

the

electrode

porous

and of the flat external the influence

Moreover

are valid

irrespective

the resistance

in either

case

the

of either

simple

the

treatment

system

will

always

up vectorially

surface. it should of

any

cases however,

is negligible

be noted pore

a comparatively

the impedances

In many

surface

have

size distribution.

size

flat

Both

of the differently especially

external

effects

may be

sized pores

at low frequencies,

and the pore size distribution

that the conclusions distribution

is often

at the end of Section

provided

that

all pores

5

can be

as semi-infinite.

Cross-links If parallel

then for other. from

pores of equal diameter

reasons

of symmetry

So, although

both

there

are interco.nnected will be no flow

pores

show

the links,

a wide

pore

is linked

by perpendicular

of current

they behave

from

cross-links,

one pore

as if electrically

to the isolated

one another.

If on the other almost Therefore

exclusively

hand

be that

we assume

that

of the wider we

may

pore,

safely

to a narrow just

one,

the impedance

as in the absence

exclude

EXPERIMENTAL 11.

in the mode1,14~28 which

however

size distribution

of the external

unknown.

10.

and

there may be some pore

for by adding

considered

be incorporated Often

predominates

electrode

and moreover

accounted

may

formulae.

surface andpore

real

surface,

resistance

complicated

is appropriate.

External A

electrode

to more

any

cross-links

will

of cross-links.

from

the model.

VERI.FICATION

Apparatus The

measurements

were

made

with

a

Radiometer

slightly

modified

so as to have more low-frequency

directly

indicates

the absolute

magnitude

(4

GB

measuring

1 “/o i

11 impedance

points.

meter,

This instrument

0.1 Sz) and the phase angle

(+

1”)

with

an

of the cell impedance. The

amplitude

of the alternating

voltage

across

the cell

was monitored

1236

R.

DE

LEVIE

oscilloscope (Philips GM 5606, sensitivity 10 mV/cm) and kept as low as possible, usually below 5 mV top-to-top. The fixed frequencies used were calibrated several times with an electronic counter (Philips GM 4810) with preamplifier (Philips HF 302) and stopwatch, and found to be constant up to 1 per cent. 12. Presentation of results Experimental results are given in graphs in which the measured cell impedances are plotted in the complex plane. We strongly recommend the general use of this presentation for impedance measurements at flat as well as at porous electrodes.2g-32 In our opinion it is preferable to the usual plot of ohmic and capacitive parts separately against wet for the following reasons: (a) Our presentation does not imply any apriori assumptions as to the dependence of the electrode impedance on frequency. (b) Experimental points of a single system are represented (no correction whatsoever applied) in a single curve, which promotes surveyability. Moreover there can be no ambiguity whether the components are plotted in series or parallel representation. (c) The information that we consider most essential for a qualitative interpretation of the curves, viz the phase angle of the electrode impedance and its frequency dependence, can be gained at first glance. 13. Chemicals All solutions were made shortly before the measurements from analytical grade reagents (moreover K,Fe(CN), and K,Fe(CN), were recrystallized from H,O) and conductivity water which had boiled just before use. Furthermore tank nitrogen was led through the solutions prior to the measurements. The cell was thermostated at 25 f 0.1 “C. 14. Platinum brush electrode The following experiments were performed with a brush electrode made of approximately 2000 platinum wires of 50 pm diameter, each about 10 mm long, held together with a Pt wire which also served to make the electrical contact. The electrode was embedded in a tube of Jena 16/III glass, Fig. 4. In order to clean and rinse it The electrode was cleaned with solution was pumped up and down the electrode. between successive measurements aqua regia before every series of measurements; the electrode was left in the solution which had been measured last, and was washed with the fresh solution immediately before each new experiment. A large (55 cma) cylindrical platinum foil surrounding the brush served as auxiliary and counter electrode. In the experiments with. pure KC1 solutions a 10 cm2 Ag/AgCl electrode was also immersed in the solution and connected to the Pt foil. 15. Base electrolyte only Measurements were made in KC1 solutions of different concentrations (0.01-l M). Some typical results are given in Fig. 5, in which the total cell impedance is plotted as it was measured (no corrections applied). The lines drawn are 45” lines (with a flat electrode the double layer capacitance

1237

On porous electrodes in electrolyte solutions-IV

-

1 cm silver powder, sintered at 6OO’C for 15 min Pt wire. 0.5 mm @

Ag wire /

lmm#

/ Pyrex glass

Jena ‘YE glass

A

/

/

/

u

Pt wire,03 mm pr tightly wound around brush

approx. 2000 ,parollel Pt wires 5OP$

FIG. 4. Electrodes.

60.

60-

/

,;/

R,

n --I

220

FIG. 5. Measured cell impedance (lines drawn with slope 45”).

240

260

1238

R.

DE LEVIE

would give a vertical line, 97 = 90”), not passing through the origin as a result of the ohmic series resistance of the electrolyte between brush- and counter-electrode, see Fig. 3. As a further test of the validity of the theory we multiplied the absolute magnitude of the apparent electrode impedance by the square root of the frequency used. This product should be constant. The results calculated for the three solutions of Fig. 5 are given in Table 2. As can be seen, within -the limits of accuracy of the impedance meter used, the results tally with the theory. Note that the double layer capacitance at a porous electrode behaves as a “Warburg” impedance at a flat electrode surface. TABLE 2. ABSOLUTEMAGNITUDEjZ,j OF TNE APPARENTELECTRODE IMPEDANCE (IN a) FOR SOME EXPERIMENTS IN SECTION 15, AND I.& TIMES THE SQUARE ROOT

OF THE

FREQUENCY

FREQUENCIES

f

(IN

k_[Z;

ARE INDICATED

IN

IN

THE ILLUSTRATIONS

ROUND

FIGURES)

The accuracy offand IZ,I is &l per cent and +2 per cent respectively, so the corresponding accuracy of lZ,\ f 1 is 2.5 per cent. The concentrations of the KC1 are indicated on top of the columns Frequency

1M

l-4

.f 71.4 61.4 52.0 43.1 36.7 30.3 20.7 14.5 10.4

19.6 27.1 39.4 56.9 79.7 117 250 503 1004

TABLE

3.

0.1 M

0.3 M

316 319 327 325 327 328 327 325 329

ABSOLUTE

MAGNITUDE

l&l f”

125.2 106.8 88,‘9 73.9 62.9 51.8 35.5 25.1 17.9

lZ,l

556 556 556 557 561 560 561 562 567

OF

THE

APPARENT

979 978 982 982 982 978 988 1005 1044

2208 1877 1566 1302 1100 904 625 448 330

ELECTRODE

16, AND I_&] TIMES THE FOURTH ROOT OF THE FREQUENCY ,f (IN Hz) The concentrations c of the ferrocyanide and ferricyanide ions are indicated on top of the columns. In the calculations of the mean value of lZ,l ft the poor accuracy of the high-frequency points (as lZ,l is &2% + 0.2Q) is not taken into account. In the bottom row the product lZ,l fact (in R s-i molf 1-i) is calculated IMPEDANCE

Frequency -____--

(IN

a)

FOR SOME EXPERIMENTS

10 mM ________---

f 19.6 27.1 39.4 56.9 79.7 117 250 503 1004 mean value: mean value times

IN

SECTION

1mM

3mM

l.%

P-aIf%

IZi

lZ”l.ff

4.3 4.0 3.7 3.2 3.0 2.7 2.2 1.8 1.6

9.1 9.1 9.3 8.8 8.9 8.8 8.7 8.5 8.9 8.9 0.089

8.1 7.4 6.7 6.2 5.6 4.9 4.1 3.4 2.8

16.9 16.8 16.5 17.2 16.7 16.1 16.4 16.1 15.8 16.5 0.090

cf

14.8 13.5 12.3 11.1 10.2 9.1 7.5 6.2 5.1

31.2 30.8 30.7 30.6 30.4 29.8 29.8 29.3 28.7 29.9 0.095

On porous electrodes in electrolyte solutions-IV

X mM Fe (CN)i-/ in

;iTT,

,s’

1M KCI,Pt

measured

1239

Fe (cN)~-

brush,25”C

cell impedance

x=10 .----, R, 12 64-

14

16

18

R

20 -&----%

T 3, -1 s-a

2-

-+-R. 0 10 8-

6-

12

14

18

20

R

22

24

c

26

T -1 WC, '

4-

2-

R,

R-

0

10

12

14

16

18

20

22

24

26

28

FIG. 6. Measured cell impedance (lines drawn with slope 25”). 16. D@usion control was performed on the system [Fe(CN)J4-/[Fe A second series of experiments (CN),13- in 1 M KCl, in which case diffusion c:ontrol was to be expected. In Fig. 6 some measured cell impedances are plotted. The phase angle of the apparent electrode impedance is slightly larger than 22*5”, which latter value may be expected for pure diffusion control. The results are in fair accordance with the theoretical prediction for diffusion control only (see Table 3), even without taking into account the double layer capacitance and specific adsorption possibly present. 17. Reaction control Since so many practical applications of porous electrodes are to be found in systems with slow electrode reactions, a thorough investigation was made of one of in 5 M HCI. Some typical cell impedances are shown these, viz the system Few/Few in Fig. 7.

1240

R.

DE LEVIE

In the foregoing sections, with either capacitance or diffusion control predominating, the experimental impedance plots are linear and it is easy to check the theoretical results both in a qualitative and in a quantitative way. When however reaction control prevails the form of the experimental impedance plots is not so simple, so that then the easiest way to obtain graphs in which a straightforward comparison with the theory can be made is to use the “squared impedance plane”. This means that we must plot in plane polar co-ordinates the square value of the experimentally determined vector length (ie the cell impedance minus the electrolyte resistance outside the pores, which we obtained from measurements up to 100 KHz) with, as

8-

6 t 4. -1 WC. n 2+R, 01

0

2

4

6

8

FIG. 7.

10

12

14

16

16

20

R 22

Measured cell impedances.

argument, twice the value of the corresponding phase angle found. Such a squared apparent pore impedance should behave like the impedance of the equivalent flat electrode, Fig. 3. The squared impedance plane Fig. 8 corresponding to the experiments of Fig. 7 shows that the points fall nicely on semi-circular plots, as may be expected for the combined effects of double layer capacitance and totally reaction-controlled electrode mechanism.2g-32 Moreover the radii of the semi-circles in Fig. 8 are inversely proportional to the concentrations, as required by theory. It should be noted that it is impossible to obtain the value of the rate constant from these measurements without a knowledge of the mean diameter r,, of the pores; this situation is quite analogous to that at flat electrodes, where the electrode surface must be known. The dependence of the rate constant on potential or temperature however can be determined from impedance measurements only. This is illustrated in Fig. 9 where the radii of the semi-circles in the squared impedance plane are plotted as obtained in a series of measurements with the concentration of one component of the Fe”/Fe3+ couple kept constant and the other varied.* * Control measurements have revealed that the reaction rate of the Fea+/Fe3+ couple and the corresponding value of 0: strongly depend on the pre-treatment of the electrode. Consequently Fig. 8 should be regarded as illustrating the applicability of the method rather than as a reliable source of information for the numerical value of a.

On porous electrodes in electrolyte solutions-IV

X mM squared

Fe2+/2X

mt.?

Fe’+

impedance

rn 5M

plane

HCI ,

(after

Pt

brush

electrode,

correction

for

1241

25°C

electrolyte

resistance)

X=I

‘1

/’

/

radius circle

/ I’X

/ I

/’ ,/’

/

206

/

/

/

/

2.5 5 10

/

I

,

1

mol

_-*’

25d

cln-3

of

product

207.5 83 11.5 22

.2075

R

R

+l

2075 t2.5 207525 220 +I0 mol

cm-3

300

FIG. 8. Squared apparent electrode impedances.

18. Use of the squared admittance plane

A still more rigid test for a completely reaction-controlled electrode mechanism is to plot the squared apparent electrode admittance instead of the squared impedance. In such a graph all points will lie on a rectangular network provided the double layer capacitance is the same for all measurements: as all points from one single experiment have the same “charge transfer resistance” parallel to the double layer capacitance, they will lie on a vertical line; as isofrequent points from different experiments all have the same value of angular frequency til times double layer capacitance C, these will lie on horizontal lines. Taking into account the inaccuracy of the impedance meter used and the mathematical manipulations involved, the experimental points come close to vertical lines, Fig. 10. There is a rough quantitative agreement of the identification of the vertical co-ordinates of points in the squared admittance the other hand isofrequent points from different circle plane,

20concentration 10 05

1”” o-7

1

of FeZt,

I

I

I I11111

2

3

L5

7

mM I

10

FIG. 9. Determination

20 of l-a.

--+ III

30 10 50

1242

R. DE LEWE

004-

x=10

n-2 r w3-

X=2-5

x=1

w

.

“-

.

wz-

..

c; 041.

*

01 b 0

c

*

of accuracy.as for apparent impedance

to.2 R ,kl”

calculated from radius of best-fitting circle in squared Impedance plane

A

001

FIG.

limits

calculated electrode

w2

003

10. Squared apparent electrode admittance.

concentrations definitely do not fall on horizontal lines. Apparently the increase in the double-layer capacitance is approximately proportional to the concentration. This points to adsorption of at least one of the electroactive species. TABLE 4. THE CAPACITIVE PART (Yz)" OF THE SQUARED APPARENT ELECTRODE ADMITTANCE (IN fi-a)FROM FIG. 10, x = 25, AND THE SAME QUANTITY DNIDED BY THE FREQUENCY f (IN Hz)

f

-___ (Yy -__ (YZ)“lf

19.6

0.0029 0~00015

27.1

0.0037

39.4

0.0045 ____ 0~00014 0~00011

56.9

-___ 0.0064 -__0~00011

250

79.7

117

0.0082

0.0122

0.0265

0~00010

0~00010

0~00011

In order to determine whether Fe2+ or F&if or both are adsorbed one may turn to the squared admittance planes for Fe2+ constant, Fe3+ varied and vice versa. It turns out that varying the Fe2+ concentration has but a small effect, which may be ascribed to a slight variation in the double layer capacitance of the base electrolyte itself, as the potential now changes somewhat from one experiment to another. On varying the Fe3f concentration, however, the effect is strongly marked, FeCI,, is strongly adsorbed at Pt. As so apparently some Fe3+ species, presumably this adsorption appears mainly to influence the double layer capacitance33-35 we have disregarded a more elaborate treatment.36-38 19. Silver powder electrode Some experiments were performed with electrodes made of spherical silver particles of nearly uniform diameter, which were kindly supplied by Dr H. G. Plust of Brown,

On porous electrodes in electrolyte solutions-IV

1243

Boveri et Cie, Baden, Switzerland. The electrodes consisted of a bent Pyrex glass tube, inner diameter 3.5 mm, narrowed at about 15 mm from the end to enclose roughly a l-mm + silver wire serving to make electric contact. The cup thus formed was filled with the silver powder and sintered in air in an electric furnace for 15 min at about 600°C. The powder and silver wire then cohered, although microscopic observation revealed that the powder particles had remained perfectly spherical even after prolonged sintering. The grain size ranged from approximately 70-100 ,um 4. The electrodes thus prepared (see Fig. 4) were manipulated in a rubber stopper so that they would not be wetted by the solution under investigation. In this position both

ZO-

15-

lo-

50

FIG. 11. Measured cell impedances (line drawn with slope 45”). TABLE 5. APPARENT ELECTRODE IMPEDANCE lZ,l (ABSOLUTE MAGNITUDE, IN a) AT A SINTERED SILVER POWDER ELECTRODE, 0.3 M KC1 (COMPARE TABLE 2) AND lz,/ TIMES THE SQUARE ROOT OF THE FREQUENCYf(IN Hz)

f

19.6

27.1

39.4

56.9

79.7

l-4

34.0

29.1

24.0

19.9

16.8

IZlf *

151

152

151

150

150

117 13.9 151

250 9.5 150

503 7.0 156

1004 4.8 151

the cell and the electrode were evacuated, the latter through the tube containing the silver wire. Then the powder electrode was lowered into the solution and the vacuum over the cell was gradually diminished by letting in nitrogen. The solution consequently entered the powder electrode. When these precautions were omitted there often remained some gas bubbles in For every new experiment a fresh the electrode which caused irregular behaviour. electrode was used, as it proved difficult completely to remove the solution from a preceding experiment. 20. Experimental

results

Measurements were made in KCl, Fig. 11 and Table 5. A loo-cm2 cylindrical silver foil served as reference and counter electrode, of which 20 cm2 had been covered

1244

R.

DE

LEVIE

electrolytically with AgCl. Measurements were also made on Fe2+/Fe3+ in 0.5 M potassium oxalate, Figs. 12 and 13. Here too there seems to be no difference between the ac behaviour of a brush and a powder electrode. For these measurements we used a 55-cm2 cylindrical Pt foil as reference and

Ag

powder

electrode,25”C,measured

cell

impedance

25-T -1

a.’

20.

LO

60

a

30

60 120 250

15. 50 0

5

10

15

20

25

30

35

40

45

50

R. n 55

60

65

FIG. 12. Measured cell impedances.

25

2ooot

mM

squared

Fe2’/Fe3’

in

impedance

T

0.5 M Potaswm-oxolate,

Ag

plane

powder squared

elactrade.25°C admittance

plane

.

WlO-

KOO:

I 0006.

I

t 0

0-i

I I I I I I I I --+ 5-22 I 500

IO00

1500

2cQO

0006.

0004-

0002.

OLi 0

FIG. 13. Squared apparent electrode impedances and squared apparent electrode admittances.

counter electrode, which prevented the silver from reacting with Fe3f. To this end the Pt electrode was short-circuited to the powder electrode before the latter was lowered into the solution, the short-circuit not being removed until connexions had been made to the impedance meter (which has a low dc resistance).

On porous electrodes in electrolyte solutions-1V

1245

AcknowIedgements-I wish to thank Prof. Dr J. A. A. Ketelaar for his stimulating interest in this research and Dr G. H. J. Broers for many discussions on the topic. The present investigations have been carried out partly under the auspices of the Netherlands Foundation for Chemical Research (S.O.N.) and with financial aid from the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 2). 30. 31. 32. 33. 34. 35. 36. 37. 38.

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