Boston UniversityOpenBU http://open.bu.eduTheses & Dissertations Dissertations and Theses (pre-1964)

1961

A pulsed pool mercury electrode

https://hdl.handle.net/2144/25996Boston University

BOSTON UNIVERSITY GRADUATE SCHOOL

Dissertation

A PULSED POOL MERCURY ELECTRODE

by

Stein Deron

Submitted in partial fulfillment of the requirements for the degree of

Master of Arts 1961 ..,.._

Approved

by

First Reader ••• /. •• ~~ . • /{ 1.: ./A. ~ .

Second Reader .... &.~~ .. /?1 · ~.(...I"Y\-................

\

ACKNOWLEDGMENTS

The author is deeply .indebted to Dr. Arno H.A.Heyn

for his guidance and constant help during the course of this work.

He wants also to express his gratitude to Dr .Ronald M.

Milburn for his advice in preparing this dissertation .

CONTENTS

SUMMARY

INTRODUCTION

STUDY OF THE PULSED MERCURY POOL ELECTRODE

I) Generalities

II) Some diffusion controlled mercury electrodes

III) Equipment and solutions

IV)

V)

A- Solutions

B- Electrodes lo

C- Pulse Generator /~

D- Transmission of the pulse to the mercury pool lk

E- Projection Of the electrode I~

F- Polarograph lb

Procedure

Results A- Squeezing device

l Influence of the voltage scanning rate

2 Influence of the frequency and amplitude

of the pulses

3 Conclusion

B- Piston Device

1 Influence of the cadmium concentration

2 Resistance of the cell

3 Reversibility of the system Cd/Cdl+

4 Influence of the pulse frequency

5 Influence of the pulse amplitude

6 Influence of the distance of the electrode

surface from the capillary tubing 3~

7 Oscillations of the electrolysis current ~~

VI) Comparison with Rosenberg's results ; 4

A- Diffusion current and sensitivity

B- Reversibility

C- Equipment

D- Theoretical Equation for the diffusion current

VII) Conclusion and suggestions for completing the study.

ALTERNATING CURRENT POLAROGRAPHY

I) Discussion of the technique

II) Improvements of the t echnique

III) Proposed circuits

A- Cir.cuit Impedance

B- Alternating potential source

C- Polarizer

D- Recording

E- Amplifier and Standardization

I V) · Conclus ion

41 s-1.

5'4

~4

Slf

S"4

~~

f~

BIBLIOGRAPHY

LIST OF ILLUSTRATIONS

1- Boundary layer

2- Pulsed mercury pool electrode with squeezer

3- Cathodic compartment and geometrical parameters

4- Pulse generator

5- Various squeezing devices

6- Pulsed mercury pool with electromagnetic piston

7- Optics for projection of the electrode

8- Tank

9- Shape of the electric pulse

10- Polarogram with stepwise increase of the voltage

11- Polarographic maximum

12- Influence of the voltage scanning rate on the polarographic

·- maxima

4. _9

IO ~

n ~

\4

14-

15'

J,o

17

13- Thickness of the boundary layer and the polarographic maxima 'l\

14- Cathodic compartment with "square " profile 14

15- Good polarogram l~

16- Influence of the concentration of cadmium ion on the diffusion

current

17- Influence of the resistance drop on the half wave potential

determination of the resistance of the cell

18- Determination of the slope of the polarographic wave

19- Influence of the frequency of the pulses on the diffusion current

20- Influence of the frequency of the pulses on the amplitude of the

pulses of the pool

21- Influence of the amplitude of the pulses of the pool on the

diffusion current

22- Variation of the diffusion current with aJ/&

23- Variation of log re..,wi th log a •

24- Piston

25- Solenoid holder

26- New cell

27- Cell holder

28- Optics for " Sshlieren" experiment

29- Classical polarography and alternating current polarography

30- The four regions in the electrolytic solution

31- First harmonic and second harmonic polarography

32- Circuits for the modified Sargent Polarograph XXI ~

33- Circuits for alternatingvpolarography

LIST OF TABLES

I) Average area and thickness of diffusion layer for some electrodes 7

II) Correction of potentials for resistance drop ~~

III) Influence of the distance of the pool from the capillary tube !O

on the diffusion current

IV) Variation of log I~with log a.

SUMMARY

A pulsed mercury pool electrode is described and the influence

of various factors on its polarographic behavior has been studied. Curves

are given showing the influence of the concentration of the reducible spe-

cies, the frequency and the amplitude of the pulses on the diffusion current.

The electrode appears to be diffusion controlled; its sensitivity

is confirmed to be 0 .18 A/M,i .e .about

.t+/ mercury electrode . The system Cd Cd

a 100 times larger than the dropping

behaves reversibly at this electrode .

The resistance of the electrolytic cell was estimated to be 1300il.

The study of other factors and various devices are suggested .

The derivation of a theoretical equation for the diffusion current

at the pulsed mercury pool electrode is considered. The method of derivation

could be checked by measuring the thickness of the diffusion layer by" Schlie

-ren photography" . Figures illustrates the proposed set up . It is planned to

apply the electrode to analytical determination by alternating current pola-

rography method .

For that purpose circuits and cell of minimum resistance are des-

cribed.

A PULSED MERCURY POOL ELECTRODE

INTRODUCTION

When an electrolysis cell is polarized under a direct current

potential E, this yields a direct current of intensity I . The diagram

of I versus E is called a polarogram; the technique is regula r polaro-

graphy .

If we superimpose on the direct~potential E an alternating po-

tential, the electrolysis current has an alternating component . In

alternating current polarography we record tha amplitude of the alter-

nating component of the current versus the direct potential E of pola -

rization .

Alternating current polarography has been used with both drop-

ping mercury electrode and solid electrodes . The alternating currents

-~ -4 are of the order of 10 pA for 10 - 10 M concentrations of the electro-

active species . It is of interest to try more sensitive electrodes .

For that purpose a pulsed mercury pool electrode was chosen.

An electrode of that type was studied by Rosenberg W (1). In a first

part the properties of Rosenberg's electrode were confirmed and it is

planned to apply it to analytiual determination by the alt~rnating cur -

rent polarography technique .

Note : Only aqueous solutions with an excess of supporting electrolyte

will be used so that the migration of the electroactive species is

negligible .

STUDY OF THE PULSED MERCURY POOL ELECTRODE

I) GENERALITIES.

Mercury has some very strong advantages concerning its use as an

electrode for studying electrochemical reactions.

As examples:

- the high hydrogen overvoltage of mercury enables us to study a

wide range of reduction reactions

- electrochemical reactions are very much dependent on the nature

of the electrode surface; that is why a liquid electrode, like mercury, havin~

a well defined and easily renewable surface, cangive very reproducible resul~.

Therefore mercury electrodes are extensively used and polarogra -

phy is done mostly at the dropping mercury electrode.

Classical polarography makes use of diffusion controlled electro-

lysis: one shows that when the rate of electrolysis is limited by the rate of

diffusion of the reducible species to the cathode, the polarizing potential E

is in linear relationship with log Ict..-I . For example, in the case of a ra-I

pid and reversible redox system

lG) E = C -J- 'RT ~ f,} + 'RT J.o(I:_-I rt4( 18jt. ~A. 0 ;V.( Ju;e L

where E 0 is the " standard potential" for the system

K0

and K~ are the diffusion coefficients for the oxidized and the

reduced species.

n is the number of electrons involved in the reaction per molecule

I is the current intensity

I;..,. the " diffusion current" proportionnal to the bulk concentration

of the reducible species

fO , f(o\ ,are the activity coefficients for the oxidized andl.

the reduced species

/ / //

/ / // //

':J"L.mdary ~.J'er

.....,. V::::.O

Solution

Bul;~ solution

.... -; t L nee :fror.. the electrode

A usual way t o obtain diffusion controlled electrolysis is to have

the electrode and the solution moving with respect to each other. It is known

from hydrodynamics that at the boundary between the solution and the electr~

exists a layer~solution, the "boundary layer 11 ,(fig . l), which does not move

in respect to the electrode surfa ce .

Let b0 be the thickness of this layer. In the bulk of the solution

(x ) \ ) the concentration of solute is kept constant by conveotLon due to

the motion (assuming that the consumption of solute by electrolysis is ne-

gligible compared to the amount in solution); diffusion takes place only in

the boundary layer (x < ao). When this layer is stable and well defined the

electrolysis is diffusion controlled, if the rate of the electrochemical

reaction is large compared to the rate of diffusion.

This is an oversimplified but useful picture. ( For example the

boundary layer and the diffusion layer do not coinc ide entirely(2) ; what is

actually important is the gradient of concentration at the surface of the

electrode itself.) According to Fick's law on diffus i on, we can tell that 1i.

the diffusion current and then the sensility will increase when we decrease ~

Another point to bear in mind is that whenever the shape and / or

area of the electrode change with time, as with the dropping mercury electro

-de , or when the polarizing potential is varied continuously, as in automa-

tic recording, a capacitive charging current adds itself to the pure fara-

daic current , This limits the sensitivity of many types of electrodes. For

example, you can indeed increase the diffusion current at t he dropping mer-

cury electrode by increasing the rate of t he mercury flow according to

Ilkovic's equation (3) 1/~ l./; 1- 1{1:,

IdP."= 607 n D C tW1 )1...

D diffusion constant ( CJM." / ~)

m mercury rate flow (~/s)

t drop time lA ) (_ C..O"AcwX~~ l~W- M It)

but at the same time the charging current increases more rapidly .

- '4~ t:'~ I. e.. = o.o '5 ,, c~ ~ A

CF capacitance for the double layer

Th~e~ were underlying ideas that guided us in this work.

II) SOME - DIFFUSION CONTROLLED MERCURY ELECTRODES

Because of its simplicity the dropping mercury elctrode is the

most common electrode . It gives especially reliable results because of

the continuously renewed surface . It has a thin diffusion layer (40-6o ~ )

l However , its sensitivity is limited by its small area (0 .02cm) and the

importance of the charging current ; moreover the growth of the drop du -

ring its lifetime and the discontinuities when the drop falls give an

electrolysis current withvery large amplitudes.

Many electrodes have been designed to overcome the limitations of

the dropping mercury electrode while keeping its advantages .

Some use a fixed electrdde in agitated solution (4a).

- Delahay and Kublik used suspended drop electrodes.

- Lyalikov and Cooke used bubble electrodes .

- Komyaty,Maness , Vaughn agitated the solution by a glass tube

which rotates rapdtly concentrically with a micro pool electrode .

- Other used a moving electrode in a solution with may or

may not be ag~tated: (1) (4a).

- Heyrovski ' s streaming electrode

-Lee's rotating dropping mercury electrode groove electrode

- Kalthoff's rotating dropping mercury electrode

- Barendrecht's rotating suspended drop electrode

-Leveque's controlled jet electrode

-Griffiths' and Parker's flowing electrode (5) .

TABLE :n:

Average Areas and Thickness of Di f fusion

:ayer for some electrodes

Electrode

droppi ng mer cury electrode

rot2ting mercury drop elec .

( 200-300 t /min.)

rotating mer cury oove el.

( 1000 t /min . )

pulsed mercury pool electrode

rota ting Pt electrode

( 600 t /min . )

Area

0. 02cm.L

0. 08 cm.2.

1. 0 cr.r:: ~

2.0 cmL-

0 . 2 C!llL

40-60p

l0-l5p

l0-l5p

50p

3p

- a vibrating dropping electrmde in agitated solution

- a multiple tip dropping electrode

- a dropping electrode for which only the maximum current of each

drop is recorded

- other tricks to eliminate the spiky current at the dropping

mercury electrode

-Rosenberg's pulsed mercury pool electrode (the pool is pulsed

by squeezing mechanically a closed pocket of air which pushes

the mercury at each time ).

Most of these electrodes are much more sensitive than the drop-

ping mercury electrode. Table I gives some idea of the improvwement and

compares the results with the data for a solid electrode.(4a)

However these electrodes either do not have J renewable surface,

or are difficult to build or adjust.

The pulsed mercury pool electrode does not have a completely re-

newable surface but with a simplified design, it was easy to build. Besi-

des,the increase in sensitivity it yields, over the drmpping mercury elec-

trode is satisfactory (about alOO fold ) and its adjustment did not seem

critical.

III) EQUIPMENT and SOLUTIONS

A) The solutions

To test the pulsed mercury pool electrode we chose the redox system

.t+ CdiCd ,known to be rapid and reversible (6a) (7).

Reagents were Baker Chemicals, "Analyzed " grade .

A stock solution 0.0726 M in CdJ t was obtained by dissolving the

adequate amount of anhydrous cadmium chloride, Cd Cl~ in a solution of

supporting electrolyte, 1M or 10M in potassium chloride. The cadmium chlo

-ride was dried at ll0°C for at least 2 hours. Subsequent dilutions of the

stock solution with

sr:JeFzed t:b.:..n.z

~ I ~2lf> t11i : "' ~ I

Coil

J t1be

- :~:--. 0 i d

rt g RJLSED MERCURY POOL ELECTRODE reser\'o ir

Squeezing device Figure 2

Cathode N 2 !

dJ

supporting electrolyte lead to the ptoper concentrations in CdL+

B) The electrodes

The reference electrode was a saturated calomel electrode of about 2 crrr

area prepared according to the directions given by Charlot (4b).

The liquid junction was obtained by a short agar agar bridge ( length ~

2. 4 cm;~section about 1.5cm) still prepared according Charlot's directions.

\

I

Geometrical Parameters

fig. 3

One model of cathodis compartment

is described on figure 2a; it is

directly derived from the one de-

signed by Rosenberg. The diffe-

rent factors defining the state

of the electrode ar~ indicated on

the figure 3· It was built so

that we could interchange catho-

die compartment. In that way we

are able to study the influence

of the diameter d. of the pool, of

the diameter d/ and length 1 of

the capillary.

The U tube I and stop~~ permitted to adjust the mercury level,i.e.

the distance x between the pool and the capillary.

The siphon was used successively as a drain for emptying and rinsing

the electrode and as gas inlet for nitrogen bubbling, using the three ways

.11 , 1 .st~u,J.,

IO.,..t

D

) r

q ~ 0 0 -

0 0

- -- l

-t

r· ·J! /l'r•r i I

! I

J

r1 ...-

''

....) 1

'{" ~

n \,. . ... !

I I I

f r ~ .J <;

•..\ u "' 0 ' ')

J c.~

- -c :::-, :::. 0

~, 0

I _ -t-~ ---11 r I I I

L p.. '-.)

- 1 0

-r d ~

C) The Pulse Generator lfigure 4)

Available equipment was used . No doubt a more simple pulse gene-

rator could have been designed .

The circuits are shown on figure 4.

A rectifier, R, supplies the power to a mutivibrator, M, the fre-

quency of which is adjusted by the two variable coupled resistance, r ,

and is stabilized by the tube S.

The multivibrator generates a square wave signal which is diffe -

rentiated by a condenser C. The derivative of the- signal is then ampli-

fied and the power tube P delivers the intensity pulses to the solenoid .

Using an oscillograph we

could study the shape of the pul -

se and measure the maxima voltage

and intensity at the solenoid.

The frequency was measured by coun-

ting the number of pulses per

minute1using a stop watch. ~--------------------~~

D) Transmission of the pulse to the pool .

l) Squeezing device .

Several designs were studied.

A thin rubber tubing of the type used in biology for liquid trans -

fusion could be s~ueezed ,between the armature of the solenoid and its coil . ~ ..,_ - -~ -·

The rubber tubing was closed at one end and connected to the cathodic mer-

cury pool on the other. It contained air or mercury .

When the rubber tubing was squeezed the mercury in the pool was rai ­

-sed and it receded again when the tubing was released .

It

r><J'

solenoid

to Hp; reservoir reservoi r

Pocket of air

design 1

====-mrubber t11bing

¢ closed rubber tubing t ""'rc ury level

directly pinched me rcury

design 2

Hg reservoir

t u Hg re se rvo1 r

pinched mercury with intermediate

figure

air pocket

design 3

5

I

Figure 5 shows 3 different ways to pulsate the electrode,which

were tested.

The amplitude of the pulses could be adjusted by varying the

volume of the air pocket in design l and 3, or by varying the length of

tubing which was squeezed, in design 2.

2) Pulsing device with electromagnetic piston.

Figure 6 describes the device.

The piston is made of plexi-

glas to the top of which is attached a

soft iron core. It is driven by the ma-

gnetic pulses from the solenoid. The am-

plitude of the pulses here was determi­c.oU.

ned by the distance between the iron~and

the solenoid.

figure 6 l 1'1

f l

_)

J

screen

light electrode source

I ~- / -- - ~- I ' /

0 ~' - - -:>1---

""' / '

figure 7 E) Projection

Most of the geometrical parameters of the electrode (d,l,x,a )

(fig.3) were measured on an enlarged image of the electrode projected on

a screen.

The optics are described on figure 7·

I

' 'I~

tJ "', -tlt I

I Ill• I

"' I'll Ill I, I oil

'·'' II.\

•' I'

Ill Jl; I ,,, I I I ,,, 'II

1 1rt 'II I'

•II ' '

II I 1,11

1,1

'I I I

Ill

I

II ' •' I I' ~ :I

"' :II I 1!1 ,II

' I I, I

, I

r I,

I, ,,I

·r 'I

f'/1, ~l'tf 'I'

''·' Ill Ill

' II ' 11·1

I :Ill •' I

Ill , I' I Ill

I• Ill ,,1 ,, •I

I ,,1 '!I' 1,, ~ --_1-_T , I

' I ' I

'" ' I ' ' ,, ,, ' ' I ,1, '• ' ,--' I I ~ '"1 L ' I I

I '

I

~ - COv!?._ a. I '!: :!, '' ;I. ,,

t '' ~~i II

:~ ,-" '< ... _LJ. ,,

I I LJ

coure. a

AQUARIUM

Figure 8

They includes an "aquarium" (fig.8) in which the cathode was im-

mersed in order to decrease optical aberrations.

The set up was "standardized " by dipping in..Xo the cathodic com-

partment a 2mm gauge.If J was the size of the image of the gauge, y the

length to be measured, Y the size of the image of y ,We obtain the relation:

enlarging factor J

F) The Polarograph we used was an automatic Sargent XXI Polarograph.

rv- ffiOCEDURE .

Rosenberg(l) noticed that, because of ....... wetting of the

glass walls of the cathodic compartment by mercury, the electrolysis current

was very irregular. According to his suggestion, we coated the cathodic

compartment with Desicate in order to eliminate these fluctuations.

The mercury was admitted into the cathodic compartment up to the

top of the capillary tube .The cell was then rinsed with the solution, filled,

and nitrogen was bubbled through the solution for 15-20 minutes.

The dis tance x of the mercury pool from the capillary tube was

adjusted and the solenoid fixed at the proper distance from the iron core to

give the chosen pulse amplitude .

The pulse generator was turned on and the polarogram taken with

or without nitrogen bubbling .

After each experiment the cathode surface was renewed by expel-

ling 2- 3 drops of mercury over the top of the capillary tube; the mercury

level being kept at the top of the capillary, the cell was then emptied

through the siphon and rinsed with distilled water.

The polarograms were taken with continuous scanning or with step-

wise increased polarization potential .

I max

pA

\<;"o

loo

5o

Influence of the voltage scanning rate on the polarographic maxima

s -:::.0.5 v

L 1.5

.1.+ Cd l.45xl0-j M

2 .0

EJ S ::: 2.0 V

figure 12

2.5

(scanning rate

3 . 0 mV 1 h . 8 V.t.

) '/~

-.I

POLAROO HIIC MAXIMA

. ---- . ..,. -- ---- -~----· ·--~00 ---

: . --------- -;----~ ----·----- - -·- --- -~- ·- - - -· -bO --

. I

' l : . L. :

. -~- 1

·- · 1

Folaro - a \vi th stepl.rise increase of the voltage

I

Cd 1. Lf-5xlo-2> ~:

d t.o em

df 0 .2 cm

1 0.4cm

X 0.2cm

a 0.05CB

f lOOp/min .

figure 10

-E

-0.5 - 0 . 6 - 0.7 - 0. 8 - 0 . 9V

\

Figure 9

V) RESULTS.

A) Squeezing device

The electric pulses had the shape shown in figure 9 and lasted

for 1/3 to 1/5 of the period. The maximum potential was 400V and the maxi­

mum intensity 4A.

The coil ceased to respond to pulses of a frequency higher than

250 per minute.

The results were not satisfactory.

i) Influence of the scanning rate:

When the voltage was increased stepwise the polarogram showed a

steady step (fig.lO ). Still this was not very reproducible.

When the continuous scanning was used, a maximum appeared (fig.ll)

The maximum intensity of the electrolysis current I max is a li­

near function of the square root of the scanning rate (fig.l2).

This is identical to the effect used by Streuli and Cooke (9) in

the linear chronoamperometric technique (amperometry because the current in­

tensity is measured, linear because the voltage is linearly increased with

time ) . The technique allows determination of concentrations down to 10-7 M.

.2o

polarograp*

maxima

c

max l rllC!

L-----+-----~ X

small bo: mda ry lflyer

figure · - 13

Cooke used a motionless mercury pool electrode. The conditions wer~

such that the electroactive species is brought to the electrode only by dif-

fusion.While the electrolysis is in progress the diffusion layer expands.

Thus when the voltage increases the rate of the electrochemical reaction1in -

creases but the rate of the diffusion, inversely proportionnal the thickness

of the diffusion layer decreases ; the electrolysis current pass1es through a

maximum and decreases to zero when the diffusion rate gets lower than the e-

lectrolysis rate. The remaining current represents only the charging current

for the double layer capacitance.

In our case, instead of observing the passage of the electrolysis

current b~ a maximum and then its decrease to the charging current, we noti-

ced a steady step after the maximum. This step was due to the fact that we

dealt not only with diffusion transport but also with mechanical convection

due to the motion of the electrode.

Figure l J explains the relation between the thickness of the boun­

dary layer and the occurrence of the maxima: (4d).If the boundary layer thick

-ness ~ is too large the reaction rate gets greater than the diffusion rate 0

before the diffusion layer has expanded to the limit of the boundary layer

~ and we observe a maximum in the electrolysis current.

2) Influence of pulse frequency and amplitude.

According to what was said above, the boundary layer thickness

had to be decreased to suppress the maxima. This was expected to be benefi-

cial on two points : the thinner the boundary layer would be the larger the

diffusion current; but also the smaller d0 , the higher scanning rate could ~~

be ~without occurence of a maximum.

Cd l . l~)

;~ 0 . ~em

sensitivity 0 . 2 p ' /mi •J .

t )3 pj.a · n

~ ' .

1 ' ' )

j I

l I

------ -------·-· +------- ·j ( (

I

I j

t

l i !

l ·y i

I

f I

lo

X

- 0. 55 - 0. 6

De t ermi nation o f tho slope of he

po 1 ro r pt i c l ve

I cL 25 .1 pA

E '/'J... o . 623V (mos ~-I :::.o)

d '· 0 c..v.,

d 1 0.2cm

1 o.027cm

x O.lcm

a .0. 032cm

f l20p/ m1n.

slope o. 026 t T = 22 ° C

f 1cure 1

X

E versus E s .c,E.

- 0. 65 - 0. 7 v

Increases in frequency andjor increases in the amplitude of the

pulses are both equivalent to an increase in the cathode surface velocity

and therefoke were expected to lower the boundary layer thickness ~ •

A low voltagescanning rate was used with a total span S:0.5V.

Increase in the frequency could suppress the maximum, but as the

frequency increased the amplitude decreased and none of the devices described

in fig.5 gave us adequate means of keeping the amplitude constant , so at

high frequencies the maximum reappeared.

In general when the frequency and amplitude were increased the char

-ging current increased also more rapidly with the voltage.

3~ Conclusion.

The upward pulses given by the squeezing device yielded large de-

formations of the electrode surface, and were responsible for the high char-

ging current.

The lack of adjustability of the amplitude limited very much our

possibility of decreasing the boundary layer thickness.

The results could thus not be satisfactory improved and the device

was abandonned.

B) Piston Device.

The characteristics of the pulses I were the same as for the squeezing device.

The iron coil was below the sole-

noid so that the pulses pulled the mercury

pool down (downwa~dpulses).

I 14 l figure Good polarograms(fig.l5) were ob-

tained with a cathodic compartment with a

profile as "square" as possible.(fig.l4)

E_versus S. C. E.

- 0 . 58 v

- 0 . 59

- 0 . 60

- {). 61

- 0 . 62

- 0 . 63

- 0. 64

- 0. 65

- 0 . 66

- 0 . 67

- 0 . 68

- 0 . 69

- 0 . 70

- 0 . 71

T LE II

I RI E p.A mV

0. 2 0 . 26 - 0 . 580

0. 8 1. 04 - 0. 589

1. 7 2. 2 - 0 . 598

3 . 55 4. 6 - 8 . 605

6. 7 8 . 2 - 0 . 612

9. 8 12 . 7 -0 . 617

13 . 5 17 . 5 - 0. 623

16 . 5 21. 4 - 0 . 629

19. 2 25 - 0 . 635

21. 4 27 . 8 - 0 . 642

22 . 5 29 . 3 - 0.651

23 . 3 30 . 3 - 0 . 660

24 . 8 32 . 2 - 0 . 668

25 . 1 32 . 6 - 0 . 677

E t =. - 0 . 622 V versus s . c.E.

s l ope 0 . 026 at 22°C

Cd .!.+ C: 1. 27xl0-ll 1 in 0.1 l~ KCl

log Id-I I.

2 . 096

1. 490

1. 140

0 . 785

0 . 441

0 . 196 -1. 937 -1. 720 -1 . 489

1 . 243

-1. 072

2 . 838

2 . 149

1'7

I

)

). 625

Influence of the IR drop on t he half wave potential

Determination of the resistance of the cell

slope R ;:::. 1300 SL

correct half wave potential E'h.:::; -0. 621 V

Cd !.-t

d I.OCJ,..o...

d' 0.2cm

1 0,27cm

X O.lcm

a 0.032cm

f 120 p/min .

-~ 3.63xl0 M

figure 17

E versus ci.c.E.

-o. 630 -0.635 v

,1

Influence of the concentration of cadmium ion on the diffusion

currem.t

d \ .o c.w

d ' o.ecm I&_

1 0 . 27cm

X O.lcm

a 0.032cm

1 102p/min.

figure 16

)

c 10 1

1) Influence of the concentration

-4 -5"' In the range 10 10 M the diffusion current is proportional to

the concentration (fig.l6).

2) Resistance of the cell

The approximate resistance can be evaluated from the variation of

• I the apparent half wave potent~al , E 'k , with the concentration (10).

If R is the cell resistance and I~the diffusion current, the slofe

of figure 17, E 1t;~ versus Id/2, is equal to thea resistance of the cell.

This resistamce was found to be very large.

R -:: 1300 Sl

-The reasons for this are especially:

- the presence of the capillary tube

- t he liquid junction between the anode and cathode

- the low concentration of supporting electrolyte (~0 M KCl ~

3) Reversibility

Knowing the cell resistance, the potentials were corrected for the

IR drop (table II) .

The slope of the curve 18,

is 0 .026 V AT 2tc, which agrees only

from the equation

corrected potential E versus log T~-I , T

fairly with the theoretical value, a.o.t~

f _ E '/;. + 1?T ~ IJ-I lA flJQ. T

The measured half wave potential E '/J. -=: - O. G.t V

is about 3% lower than the value -0.60 V reported by Meites (10). The dif-

ference is believed to come from discrepancy between the potentials of the

reference electrodes.

T · LE III

X

mm

3 . 1 38 . 1

2. 16 35 . 3

1. 87 37

1. 15 37

0 . 55 44 . 7

0 . 4 46 . 7

0 . 13 53

Influence , on the diffusion current,o f

t h e distance bet ween the electrode surface

and the top of cathodic compartment .

..,_.

Influence of the amplitude of the pulses on the diffusion current I&_.

\ll-l -s-

Cd 1.5 X 10 M /

d I .o elM /

d' 0. 2cm // )(

l 0 .27 em ~/ X

X o. lcm

~.0 ~ f llOp/min.

\.c; figLlre • .2. I

a C rom

0 0 .10 0.20 0.30 o.4o

Influence of the frequency of the pulseson the diffusion

I - current . !-

~ Cdlt 1.27xlo-4- M X X X d t. o ~

d' Q"'.~m

1 0. 27cm

X O.lcm

X

X X figure 19

X

X

100 150 200 p/min.

Influence of frequency on t he amplitude of t he pulses

X >< X 5

fi gure 20

X X

f

100 150 200 p/min .

4) Influence of the frequency.

The variation of the pulse frequency showed a ·~esonance " pheno-

menon . But this may be entirely due to the unavoidable decrease of the ampli ­

tude for the ~frequencies (fig .l9 -20).

5) Influence of the amplitude

The increase of the diffusion current with the amplitude comfirmed

our conclusion about the influence of the frequency .

The variation is linear for amplitudes a~ 0 . 32rom (fig .21).

The departure from linearly for amplitudes a>0 -32mm can have two

reasons:

- larger errors in the amplitude measurements at these high velocities

of the electrode surface give greater uncertainty in the points)

more likely, the boundary layer thickness is expected to decrease to

a lower limit with increased stirring due to increased frequency; thus also

a limiting value of the current would be reached .

6) Influence of the distance x of the electrode surface from the

capillary.

The study of this factor did not give conclusive r esults as yet .

(table III)

However, as expected, the diffusion increased rapidly when the

distance x became very small: the turbulence which may appear inthe solution

contributes to decrease the thickness of the boundary layer.

7) Oscillations of theelectrolysis current.

Due to the slight periodical deformations of the electrode surfa-

ce, the current was oscillating.

However 'when the recorder was used with the damping switch on po -

sition 1, the oscillations of the recorder pen were not larger than lOmm

while the diffusion current corresponded to a deviation of 200mm.

(~ . COMPARISON WITH ROSENBERG 'S RESULTS (10).

A) Diffusion current and sensitivity.

Rosenbe~' s device and t .e one described here both gave diffusion

controlled electrodes. The value reporeed by Rosenberg was 18.7pA for a 10-4M

SOLUTION at a frequency of 170 per minute, and an amplitude a~o.o6cm.

-4 Our results are similar to his: ~~18.4fA for a 10 M solution

at a frequency 110 per minute and an amplitude a ~ 0.03cm.

It is unlikely that these results can be improved very much by in-

creasing the frequency and amplitude, because t he increase of the charging

current will limit the sensitivity.

B) Reversibility

Rosenberg fonnd a slope of O.o36V for the curve E ~ f (logT~-T) t I

This would indicate that at Rosenberg 's electrode the reduction

of cadmium was less reversible than ours, for which the slope was 0.026V.

This is not probable because the nature of the electrodes and of

the solutions was the same in both cas~.

Furthermore such a conclusion may not be justified because this ~

way of checking the reversibility of a reaction is~very approximate one,

especially when the corrections of the IR drop are so large.

C) Equipment.

The piston device described here is much simpler than the mecha-

nical squeezing device used by Rosenberg . Our device also has the a~antage

that it introduced no disturbing vibrations ~ in contrast to Rosenberg's set-

up .

Rosenberg however was not troubled by the drop of amplitude with

an increase in the frequency of the pulses observed in this work . The iner-

tia of the piston prevented response at higher frequency pulses. The fact

that the squeezing device was mechanically connected to a motor in Rosenberg ~

device avoided such a trouble.

D) Theoretical Equation For The Diffusion Current .

Rosenberg applied the Ilkovic's equation for the dropping mercury

electrode to his electrode.

He equated the drop time, t, of the dropping mercury electrode to

the time between two pulses at the pulsed mercury pool electrode. So we sub -

stitute in Ilkovic 's equation

TABLE IV

a I;L log a log Iol mm pA

0 . 027 3 2 . 43136 2 . 47712

0 . 08 8 2 . 90309 2 . 90309

0 . 15 15 l.l760S' 1 . 17609

0 . 22 20 1 . 34242 1 . 30103

0 . 32 30 1 . 50515 1 . 47712

0 . 37 32 1. 56820 1. 50515

0 . 45 37 1. 65321 1 . 56820

saope 5. 8 9 'l +- -s-

Cc.l C ~ 1 . 5 x 10 1 in 0. 1 M l(Cl .

Variation of the diffus ion current vlith ai./&

IIJ._ pA ccft -ti 1.5x10 1

0 d l '0 Cl..vt

d' () : 2om

1 0.27cm

X 0.1cm

f 110p/min .

0 figure 22

01 I

I I

0 I I a i/a

I

0 0.1 0.2 0.3 0.4 0.5 0. 6 rnrn 'i/'b

,<&

Variation of log ~with log a

slope 0. 9

log I,t Cd.2.-t -~

1.5xl0 Iv1

d \. 0 cu.,

d' 0.2cm

1 0.27cm

X O.lcm

f llOp/min.

0

figure 23

log a

0.5 1.0 1.5.

Calculated values for various amplitudes reported by Rosenberg

are in fair agreement with the experimental data.

Besides, the variation in a2/3 is not too far from a linear va-

riation of the diffusion current at the amplitude reported by Rosenberg .

When the diffusion current Id is plotted versus the 2/3 power of

the amplitude, a, (fig.22) we see that Id is not proportional to a 2/3 . But

when a) 0. 32 , the variations of Id may be closer to a linear function of at;,_,

Jll than proportional to a the first power of the amplitude a.

A plot of log Id versus log a (fig.23) shows that the diffusion

current fits nicely the law

O. G\ Id :::::. k a :.--"

which is intermediate between the linear function in a to the first power

and the linear function in a to the 2/3 power .

The principle of the dropping mercury electrode is not similar

to the one of the pulsed mercury electrode. With the dropping mercury elec-

trode a quasi diffusion controlled state is obtained because the decrease of

the concentration of the reducible species near the electrode is compensated

by an increase in the area of the electrode and by the motion of the electro-

de surface toward the bulk of the solution during the growth of the drop.

The very small oscillations of the current for the pulsed mercury pool show

that one of these effects, the change in the electrode area, is a minor one.

The pulsed mercury pool electrode is certainly closer to a real diffusion

controlled state than the dropping mercury electrode.

Although at this time, no quantitative relation can be given, it * is felt that the major cause for the "diffusion control" at the pulsed mercu-

ry pool electrode is due to the existence of a thin steady boundary layer at

the surface of the electrode . This layer is stabilized by the circulation of

the solution through the capillary at each pulse. The circulation of the so­of the solution near the electrode,by convectio~.

lution thus assures a renewal~~ecause of the reproducibility of the flow, it

assures a steady boundary layer '

where the controlling diffusion takes place . (see page 5"' )

solution

Although the maximum Reynolds number for the motion of the

\\Yet Re -:::. - with ~

\J 1\J 5o ~s velocity o~A w ~~ I

d._::. o.2. CJJ., capillary diameter

v;;. 10~) kinematic viscosity o{ woJrex.,

is only about 1000, i.e . 0 . 4 of the critical value Re ::.2400 for turbulent ~tw .

The rapid periodic motion of the mercury pool certainly hinders

any steady laminar flow . So the flow is rather similar to turbulent flow

while at the dropping mercury electrode it is almost perfectly laminar.

As far as we know nobody has ever derived the equation of the dif-

fusion current at an electrode in periodical motion (lla) (6b) .Levich (2) de-

rived an equation for a plane electrode in a turbulent flow, but the flow was

assumed to be parallel to the electrode surface, and in our case the flow mo-

ves perpendicularly to the electrode surface . Agar (12) showed some general

features of dimensional analysis applied to the calculation of the diffusion

current. This method leads us only to a first approximation for the diffusion

layer thickness

where 1 is a geometrical parameter

x the distance we defined above

Re is the Reynolds number

Pr the Prandtl number

k a proportionality coefficient.

The coeff icient k, and the exponents a,b, and c must be determined

experimentally .

This is not very satisfactory .

We must go back again to the general differential equations

defining the electrode state

Navier Stokes equation

equation of continuity

flDlD the solvent

for the solute

~ '\) is the velocity of the solution

~ its density

p its pressure

-"!1 G the force field in which is the solution

y the kinematic viscosity

c the concentration of the electroactive species

D its ._ diffusion Qtlstant

This should be capable of solution if the correct approximations ~

and boundary conditions are found. We have ~succeed to find these as yet• U1)

VII) Conclusion And Suggestions for Further Study

The piston device pulsed mercury pool electrode is a diffusion

controlled electrode. This seems tm be due to the existence of a steady boun-

dary layer at the electrode surface: this boundary layer arises from the tur-

bulence created in the cathodic compartment by the motion of the mercury pool

and the presence of the capillary tube on top of the compartment, close to 1l

the electrode surface.

The diffusion curremt is propottional to the concentration of Cd~+

in the range of concentration we ffudied (10- L# -10-~ M ) . The sensitivity of the

electrode is~ about a hundred fold the sensitivity of the dropping mercury 4~

electrode~ similar to that reported by Rosenberg.

fip:ure 24

I I

\

fi gure 25

I

I . I

+ -

.. ..

: · ,

; : . . . . ~ :. . ". .. . . . . . • .. . ..

Couf' Q. &-

t \ I I I I I I r • 1 1 j ,o I

--€)-:: I • ' I • 0 '"' • • • • I I.

F igur e 26

~·.

•

. I I 1'/ I I ''II. '

~_j4C_If -~ _'4~t:__'_'~ ~ _ ___:__4_~.~ ~

ceQe

Figu:, 27

•

The oscillations in the diffusion current due to the deforma­

tions of the electrode surface are much smaller than for the case of the

dropping mercury electrode (about 5% of IJ.= 20 ) .

Our pulsing device is much simpler than Rosenberg's.

The diffusion current is proportional to the amplitude of the

pulses,increases with the pulse frequency and with decreasing distance

between the surface of the electrode and the capillary tube.

However, the resistance of the electrode is rather high.

The drop of the amplitude at frequencies greater than 200 per/min.

might be avoided by using a larger piston and coil which should increase the

maximum possible amplitude t figure 24).

Suggested chamges in the mounting of the solenoid are shown on

figure 25 : the threaded .portion should allow an easier adjustment of the

distance between the coil and the solenoid and therefore of the amplitude .

For completing the study the optical set up has been simplified

by suppressing the "aquarium" and using the cell and hold~er described on

figure) 26 ,and 2}. A clearer image of the electrode should thus be obtained,

and the accurate measurement of the geometrical parameters and adjustment to

a given value of the amplitude should be facilit~.

The frequency of the pulse can be measured with an electronic

counter connected in parallel with the solenoid.

With this modified equipment t we want to restudy the influence

of the frequency f and of the distance x on the diffusion current.

The influence of the electrode area A, of the capillary diameter

d', and length l remains to be studied.

To complete a pr&tical study of the electrode the reproducibility

of the electr de should be checked. For this all factors must be kept cons­

tant, in particular the distance x and the amplitude a. This can be done

following Rosenberg's procedure:

l~ght

,(

I

OPriC/\L SET -UP :<'OH

SCHLIEHEN EXPI:.HIMENT

f i g ure

image of sr.hliere n fielJ

/

sc reen

The solenoid is not moved and at each experiment the piston, floating on the

mercury, is brought to the level of a notch made on glass 11 tubing.

As we were mostly interested in the pra&ical properties of the el~

- trode , we did not measure the diffusion layer thickness . However,this would

be very interesting in relation with the derivation of a theoretical equation

for the diffusion current . The easiest thing, we suggest, womld be to use

Schlieren Photography (13). The optical set up is described on figure 28 by

means of the knife edges K1 and K~ , any heterogeneity in the refractive in­

dex of the solution in the Schlieren field will produce variation of the illu

-mination of the Schlieren field image. The intensity of illumination is

shown to be proportional to the gradient of the refractive index. While the

electrolysis goes on there is a gradient of concentration at the electrode

surface, and therefore a gradient of refractive index. This method was ap­

plied to the dropping mercury electrode by Antweiler and von Stackelberg

(14) (15).

ALTERNATING CURRENT POLAROGRAPHY

It has been seen that the pulsed mercury pool electrode is a

diffusion controlled electrode and that it is very sensitive. It was thought

desireable to use it in alternating current polarography.

I) GENERALITIES DISCUSSION OF THE TECHNIQUE

Alternating current polarography yields results similar to those

obtained by derivative polarography: the alternating current amplitude varies

with the polarizing potential , • ' E,like the derivative~ of the direct cur-d..E

rent of electrolysis, I, in respect to the polarizing potential ( fig.29 ).

\

~ / I

/ I / I

The peak height is proportional to the

bulk concentration.

The technique of the derivati~~

polarography affords a better selec-

tivity than classical polarography.

Alternating current polarography

has several advantages over regular

derivative polarography .In the lat-

ter method one applies an alternating

polarizing potential of amplitude lar-

ge enough to cover the range of poten-0\A.l-

tials ~is interested in; the current is

differentiated and the derivative ob-

served on an oscilloscope screen .

As the electrode phenomena are very far from the steady state reached in clas

-sical polarography, they are usually no~ easy to interpret quantitatively.

In addition the charging current is very high because of the rapidly changing

potential (4c).

tv In alternating current polarography a small pertubation is applied ,..

to a steady diffusion controlled state. Several different quantitative approa

-ches have been used in discussing the method.

Delahay (llb) considers the cell as a combination of linear cir-

cuit elements and calculates the faradaic impedance of the cell

w is the pulsation of the alternating

potential

k ~ ,fA the heterogeneous rate constant for the )

electrodhemical reaction

Tachi and Senda (16) on one hand, and Breyer and Hacobian (17) ON

the other took a more fundamental approach . Breyer, for example, considers a

plane electrode; he distinguishes four regions in the solution, as indicated

on figure 30. The alternating potential is assumed to disturb only the re -

gions I and II 1 Then the steady state defined by the diffusion layer (region

III ) is not disturbed . He shows that, if the superimposed potential is

.e_ -= e.* c..(t) wt the current contains harmonics (what Delahay's method cannot pre ­(\1

diet). Breyer derive~ equations for these harmonics . A rapid and reversible

system obeys the equation:

s-o

Electrode

0

II

The four regions in the

electrolytic solution

III

Elect~ochemical D-iffusion

Rer tion

Fi gure 30

IV

Bulk

convection

X

'v\- \ (@lw\r~&) l\\-\,\) +Cv\q_'te":~)

We see that when the amplitude,e , of the alternating potential is

small ( K (\) \ - M 'f e 'f ) and when the system is rapid ItT

( ~ :::- 0 ) the two sets, {4.A, ~

of equations are similar : the alternating current is proportional to the

bulk concentration ,c, to the amplitude and square root of the frequency of

the alternating potential .

This was verified by various workers (8) (18) for f( 1000 and •

~*<20mV. Some discrepancies appeared at highervalues . Improved assumptions

lead to more complicated relations which fitted the experimental data clo-

sely .

The influence of the circuit impedance was studied in detail by

Bauer and Elving (8): an increase in the resistance lowers the peak . They

worked out a met hod of correcting for this, taking into account the phase

shifts .

The technique was applied to analytical determinations and ki-

netics measurements (8) (19) (20).Bauer (21) discussed the possiblities of

the technique ;it is limited by the low current intensities (about lOpA).

Amplification is t herefore needed ~ The charging current is also a limiting

factor . The necessary corrections for impedance and phase shift are bother -

some . However , as long as the impedance of t he circuit is lower than 100-

200 ohms, these corrections can be omitted in the case of analytical deter-

minat i ons , because in that case the actual value of the peak is not needed .

-~ -'+ According to Bauer, the useful range of concentration is 10 -10 M with

conventional electrodes ,

II IM:FROVEMENTS OF THE TECHNIQUE

Various solutions were suggested to overcome the limitations of

the technique:

- Barker and Jenkins (22) used a square wave signal for which the

charging current decreased very fast with time. Thus, by not recording during

the

ITS

first instants of the waves ( when the charging current is important ) .to

INFLUENCEIAELiminated. But this requires an electronic timer and switches,

Hamm (23) DESIGNED A Simpler circuit.

-According to Bauer (20), Jessop worked out a phase sensitive mea

-suring device which avoids the bothersomecorrections for impedance drop

and phase shift.

-Walker, Adams and Alden (24) proposed alternatingcurrent polaro-

graphy with controlled potential. The controller compensates for the impedan-

ce drop. They claim that with this system external resistances as high as se-

veral thousand ohms do not lower the peak.

- Several wo• rkers (80 (9) (18) suggested polarography using the

second harmonic. The double layer is a linear element which cannot give any

harmonics; the second harmonic is therefore free from aby background. The

polarograms are identical to curves of the second derivative (fig.31).

~ The two peaks are symmetrical and pro-Second harmonic

portional to the bulk concentration. In

addition, these peaks are narrower than

the single peak of the first harmonic so

that the second harmonic technique is e-

ven more selective than the first harmo-

- nic technique. figure 31

0 . I ..U.

IOOO yX

e I 1 I I

h> 'K.~<J<cltx.._o( --> tH F ~ ~ l J l I

f\.CA ua•·· .. ~~

r W'i ~Ltc..

cmCUITS ALTER TI CURREifi' POLAROGRA:mY

figure 33

..;

However, the intensity of the second

harmonic is only about 10% of the first harmo­

nic intensity,thus very low noise amplifiers

are required to detect these currents.

III) ffiOPOSED CIRCUITS ( figure 33)

The pulsed mercury pool electrode with its high sensitivity should

ameliorate the amplification problem.

A- Circuit Impedance

We know that the resistance of the electrode is very high . Althoug~

the resistance can be lowered by using a liquid junction of lower resistance

using a reference electrode of larger area, or increasing the concentration

of supporting electrolyte, we do not expect to obtain a resistance lower

than 100 ohms because of the presence of the capillary.

The impedance for the alternating current can be further minimized

to some extend by by-passing it to an auxiliary anode (figure 33) .

Nevertheless, the electrode can probably not be used conveniently

for kinetic measurements unless the potential is controlled. It is still ve­

ry interesting to apply it to analytical determinations and possibly extend

t he useful range of the technique toward lower concentrations.

B- Alternating Potential Source

The alternating signal will be supplied by the' 6o cycle line step­

ped down to about 15mV through the Variac, transformer, and potential divide~ .

C- Polarizer

The direct current polarization will come from the polarizing devi­

ce of the Sargent Polarograph .

T ·•

·- .

....---_..I'--+--·-------

TT'IITi f\L

- ...}. • - • - "- • .l.. I - ' - . - - \, - '"" <1-

•ID "'• IL~ 0 '?- -" ·~ - (:> /(>

..,l _ -~-' _a.._~_

• • • • 0

C mCUITS FOO THE MODIFIED SARGENt' POLAROGRAm

figure 32

D- Recording

The recorder of the polarograph will be used to record the al­

ternating current amplitude . The Sargent Polarograph has been modified for

that purpose (figure 32) .

E- Selective Amplifier

The frequency selective amplifier will include two twins paral­

lel T network tuned to 60 cycles/s .

CONCLUSION

We think that the high sensitivity and good diffusion control of

the mercury pool electrode are well established . So in spite of its high

resistance , the electrode can be applied with profit to alternating polaro ­

graphy .

Alternating polarography is a powerful technique .

Theoretical equations check well with the experimental data .The

existence of higher harmonics is very interesting because this allows the

elimination of the charging current background and so increase the possibi­

lities of the method .

The disadvantage of the high resistance of the electrode could

be overcome when applied to alternating current polarography by controlling

the alternating potential .

The useful range of the alternating current polarography for ana ­

lytical determinat i0ns may be extented to c0ncentration lower than lO~M by

the use of the pulsed pool mercury electrode .

BIBLIOGRAPHY

1 - N.Rosenberg, Thesis, Boston University, (1956)

2- B.Levich, Disc. Far .Sos . ,l,26, 37, (1947)

3- J .Heyrovski, Proc . 1st Internat .Congress Polarog, ,Prague, (1951)

vol.III,p.22

4- G.Charlot, J .Badoz -Lambling, B.Tremillon, les Reactions

electrochimiques, Masson, Paris, (1959)

a) p . 137-146

b) p . l48

c) p . 321-334

5- V.S .Griffiths , W. J . Parker, Anal.Chim.Acta, 14, 194, (1956)

6- J . J .Lingane, I .M.Kolthoff, Polarography, Interscience, New -york

(1952)

a) p . 342

b) P.@O

c) p . 206

7- J .Heyrovski, Anal .Chim. Acta, 2, 538, (1948)

8 - H.H .Bauer, J.P.Elving, Anal .Chem . ..-,30, 334,341, (1958)

9- C~A . Streuli,W . D . Cooke,Anal .Chem.,25,~ 1691,(1953)

10- L.Meites, Polarographic Techniques,(l955) Interscience Publishers,

New-York, p.25,p . 254

11-P.Delahay, New Instrumental Methods in Electrochemistry

Interscience, New -York,(l954)

a~ p . 227

b) p . l54

12-J.N .Agar, Disc .Far . Soc.,~, ) 26, (1947)

13 -Eastman KOdak Cy, Schlieren Photography,booklet,(l960)

14-H.J .Antweiler, Z.Elektrochem . ,43, 596,(37);44, 719 , 831,888, (38)

5"7

15- M.von Stackelberg, ibid.,44, 663, (38); 45, 466, (39)

16- M.Senda,I.Tachi, Bull.Chem.Soc.Jap.,28, 632 , (55)

17- B.Breyer,S.Racobian,Australian J.Chem., 1,225, (54)

18- D.E.Smith, W.R.Reinmuth, Anal .Chem .,33 , 482, (61)

19- van Cakenbergge, Bull.Soc.Chim. belge, 60, 3, (51)

20- B.Breyer, R.R.Bauer , S .RacobianA , Australian,J.Chem., ~, llllr

437,(56)

21- R.R.Bauer,J.Electroanalyt .Chem.,!, 256, (60)

22- G.C.Barker,I.L.Jenkins, Analyst, 77, 685,(52)

23- R.E.Ramm, Anal .Chem.,30, 350, (1958)

24- D.E.Walker, R.N.Adams, J.R.Alden, Anal .Chem.,~ 308,(196l)

25- Frey, Fundamentals of Radiocommunications,Longmans-Green,

New-York,(l944),p .25l.