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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.
Recommended