j^CTROLyTIC SEPARATION OF HYDROGEN AND DRUT^ RTUM
AT A MERCURY CATHODE
DISSERTATION
Submitted in partial fulfilment
of the requirements for the
degree of
DOCTOR OF PHILOSOPHY
at the
POLYTECHNIC INSTITUTE OF BROOKLYN
by
MARTIH HOME
August 1951
Approved:
Head of Department
Approved by the Guidance Committee:
Chairman:
Clarence F. His y
Associate Professor of 'Chemistry
Major: Physical Chemistry
Frank C. Collins
Professor of Chemistry
Minor; Analytical Chemistry
Jo
igman
Assistant Professor of Chemistry
Minor: X Ray Diffraction
Isidor Fankuchen
Professor of Applied Physics
bthor was
oi
TO MT WIFE
The author is deeply indebted to "Professor C. F.
Hiskey for his patient and helpful guidance throughout
the course of this investigation.
He also wishes to thank
Professor F. C. Collins for his help with the section on
diffusion, Dr. Benjamin Post for his frequent help and
advice, and Dr. Leopold May for sharing the maintenance
of the mass spectrometer throughout most of this study.
In this paper are described, the design of an
electrolytic cell, the techniques and determination of
the Reparation factor of hydrogen and deuterium at a
mercury cathode, by means of a hier type mass spectro­
meter.
Reparation factors have been determined over a
range of current densities from 10”^ to 3 x 10”^
amps/cm^ and at temperatures from 0° to 96.5°0.
The
reproducibility for the lower current densities is
less than one percent, and the accuracy less than
three percent.
For the two higher current densities
the precision of measurement is 1 to 2 percent.
Diffusion effects have been evaluated for the two
higher current densities at 25°.
Calculation of the activation energy of separa­
tion was made on the basis of the measurements in
this paper at 950, 1000 and 1100 mv. overvoltage.
This value, by method of least squares is 0.14 t .01
kcal.
TABLL OF COÛTANTS
rage
I.
Introduction
A.
Hydrogen - Deuterium Electrolytic
Separation ...
B.
II.
1
Background of lhis Investigation ...
3
Bxpe rimental Te clinique s
A.
Electrolysis Cell........................... 5
3.
Purification of Materials
.....
8
C.
Mass Spectrometer ........
9
1. Description .........
9
2. nineties of Ion Formation
3. Operation.
.......................... .12
4. Impurity Effects
D.
11
....
Standard Samples
...................... 14
15
........
III. Experimental Results
A.
Variation of Separation Factor with
Temperature and Current Density
IV.
...
17
B.
Errors of measurement...................... 18
C.
Contamination
............................. 19
Discussion of Results
A.
General Considerations
................
24
B.
Diffusion Effects ........
27
C.
Separation Factor from Overvoltage
Data.................. 58
D.
Separation Factor and Temperature .
.
.
39
E.
Separation Factor and Current Density
.
44
TABLE Qg COKTLKTS
(continued)
Page
V.
Summary and Conclusions .
47
VI.
References
49
INTRODUCTION
I.A. Hydrogen - deuterium Electrolytic Separation
During the electrolysis of an aqueous solution,
the lighter isotope of hydrogen is preferentially
liberated at the cathode.
The relative rate of evol-
uation of the isotopes of hydrogen is defined as the
separation factor.
11)
,
.
&
=
^0»
1,0.
where 0^ and
are the concentrations of the lighter,
i.e., hydrogen, and of the heavier, i.e., deuterium,
isotope, respectively.
The value of this separation factor has been re­
ported to vary between S and 20 (1) and is strongly
dependent upon the nature of the cathode material.
Following the discovery of heavy hydrogen,
(2)
and its concentration in aqueous solution by electrolysi
(d) there has been a great deal of interest in the
mechanism of hydrogen discharge.
particular int^rcsn
has centered about the electrolytic method of separation
wnich has proved to be the most efficient and most
generally used.
In jcneral, cstlioüe materials appear to ial±
distinct groups with regard to separation
into
lactor.
(4) Group I, which includes the n^uEls of Ion
overvoltage, nicxel,
iron, coppor, l^ad
(in alhaline
solution), join silvery smooth platinum, and palladium,
exhibit a hiyh separation factor,
of mercury, tin,
.-roup II is composed
me. load (in acid solution), metals
which exhibit hiju hydrop^m cvervoltape.
experimental determination of the separation factor
of mercury, which serves as an example of Group II
metals, is iar from conclusive and agreement amonn the
Cable I is a resume of rhe
several authors is poor.
existing experimental work for mercury.
Table 1
^esum e oi ^e portexi ^epc .ration _acûor i or
i.e:rcurj
Author
i( amps/cm
Copley
C-.
Oyriuj
7 x 10-^
20
10
1 5
55
95
h^^O^
Cl:
p
'
-'
m
1‘
2.7
p
30
to
50
HOI
and
KOI
gl
L5
CgmO^ 1.511
6
LguO^ O.li,
3.1
u.5
O« K
i
.1
•1
"!
r- !
Cuken L 5 x 10 I
Bratzler C x 10~^
(7)
error
■st*
-zL
.,alton c. 5 x 10 ~
^olienden to,
10" "
(o )
electrolyte
uoriuti
Okamoto
_
This study repi'ssents one phase of a
carried
out et the Polytechnic Institute of tne intejr&uCd
problem of hydrogen isotopes overvoltage and electro­
lytic separation.
The"separation factor which repre­
sents the relative rate of liberation of hydrogen isotopes
at a cathode is et least partially due to the difference
in overvoltage of hydrogen and deuterium.
jnen no
interaction is present between the evolved gas and gne
electrolyte, the energy difference as reflected by the
overvoltage should govern the ret es of discharge of
liberated gases.
tne
Conversely, a knowledge of the separa­
tion factor should permit the evaluation of the overvoltage
difference with high precision since it deals with a
small difference between large numbers.
x._er cur y, because of its non— cataly
gic
nt. uur-*.,
exhibits no interchange between the evolved gas and the
solution (8) and therefore represents a suitable choice
for this study.
The following is an outline of the objectives in this
investigation of the electrolytic separation at a mercury
cathode:
1)
The design of an electrolytic cell and the develop­
ment of the technique for obtaining reproducible separa­
tion factors.
2)
The determination of the separation factors over a
range of temperature and current density,
5)
and
The determination of the slope of the separation
factor against the reciprocal of the absolute temperature
at constant overvoltages in order to evaluate the activa­
tion term of separation.
4
SXPEBBIEwTAL TSCHMI^S
II.A. Slectrolysis Cell
The essential feautres of the electrolysis cell
are :
a)
^11 pyrex glass construction
b)
In situ distillation of both the mercury and the
electrolyte
c)
Elimination of back diffusion of oxygen from the
anode chamber to the cathode, and
d)
A long'path length between the sample take off and
the cathode chamber to prevent contamination by stopcock
grease.
Description and Operation:
Previously treated mercury is
placed in the mercury still of the electrolytic cell (figure
1) A, which is then sealed with a torch.
A vacuum from
D through stopcock B and dust trap C is used for the distill­
ation of the mercury from à, which is rapped with nichrome
ribbon, to reservoir E.
After distillation, the vacuum,
is replaced by an inert atmosphere of eith nitrogen or
helium through 11, B, and C.
The electrolyte is placed in F which is likewise
sealed with a torch and electrically heated by means of
nichrome ribbon.
The electrolyte is distilled over into
compartment G, the anode chamber.
with a 19/24 standard taper joint;
The top of G is fitted
this serves to connect
a small still through the male member of the joint.
•
electrolysis cell
The electrolyte, to which separately distilled sulfuric
acid had been added at compartment G, passes into the
cathode chamber I through the fritted glass at H.
in
inert gas is then bubbled through the solution which is
now tenth normal with respect to
by means of the
ungreased stopcock J, turned to the proper position.
When the solution has been thoroughly deoxygenated, mer­
cury is placed in the platinum connecting wells of the
cathode and anode, K and L respectively.
I polarizing
potential is then applied through these connections.
Stopcock J is then turned 180 degrees and the mercury from
K is permitted to flow into the bottom of 1.
The polari­
zing current is increased to 5 x 10“^ amps/cm2.
This
condition of pre-electrolysis is maintained for five to
ten hours in order to plate out any reducible impurities.
Following the pre-electrolysis treatment, the mercury
from the cathode chamber is discarded through the lower
arm of stopcock 5.
Fresh mercury from reservoir F is
permitted to flow into the cathode chamber.
It this point, the entire cell is immersed in a
constant temperature bath,
kt all settings above room
temperature, cooling water was circulated through condenser
N in order to prevent condensation of the electrolyte
in the capillary section.
Dry ice was kept at point 0 in
order to freeze any grease from the sample take off stop­
cock r.
The volume of the capillary section between h
6
and 1 is small compared to the volume of a sample, which
is approximately three ml, so that the hold up is negligible
and the flushing between samples a simple matter.
The electrolyte is permitted to rise in the cathode
chamber up to the point at which the capillary section
begins.
The gas generated at the cathode forces the level
of electrolyte down,
hn adequate sample is ready when the
level is down to the bottom of the condenser IL
The sample
bulb is attached to point Q through the standard taper 7/25
joint, and evacuated through the three way stopcock f, and
D.
f is then turned to permit the gas from the cathode
chamber to fill the evacuated space up to the sample bulb
stopcock.
I is then closed and the gas between the two
stopcocks permitted to enter into the sample bulb.
By
filling the sample bulb in stages, finer control of the
amount of gas taken off is achieved .
If necessary, the
procedure is repeated, until the electrolyte again rises
to the junction of the capillary in the cathode chamber.
7
II.B. Purification of HattriaIs
Hercury
The mercury was first air busDied in a ten per­
cent mercurous nitrate - dilute nitric acid solution 1 or
48 to 72 hours by means of a fine stream of dust iree
air.
The rate of agitation was such as to cause intimate
mixing.
The mercury was then washed several times with dis­
tilled water and dried.
under vacuum.
It was then distilled three times
The triply distilled mercury was uhen uimis
ferred to the mercury still in the electrolytic cell.
i2eavy rater
fhe heavy water wes received 1ro^i bue .^-ru^rg
Oxygen Co. in 25 ml sealed vials assayed as
density measurements,
by
Tne contends of the vials wei e
distilled from HinO 4 - mH
unuer vacuum.
A us disrilla-
tion res crrri^u ous .m a rwo srage sui^i uy
n
receiver end with dry ice and .ceeping the rest of the still
at room temperature.
The elctrolyte, prepared by weight dilution of the
heavy water was placed in the elctrolyte still of the
electrolysis cell and distill 1 ad in situ.
8 -
Ii.U, usss spectrometer
1. Description.
The instrument usee in this investig­
ation is a Kier GO degree null type instrument (9) whose
essential features are:
:
a)
1 fixed magnetic field of.^lnico magnets.
b)
separate collector plates and feedback amplifiers
for mass 2 and mass 5.
c)
h direct reading ratio of the resultant ion currents
of the two masses.
d)
A null detector by means of a wall type galvanometer.
Gas sample bulbs are connected to the gas inlet system
of the mass spectrometer through the 7/25 standard taper
joints; the female member on the inlet system and the male
member on the sample bulb.
The space up to the stopcock
of the sample bulb is evacuated by the inlet system i'orepump.
Approximately twenty five percent of the three ml-
atmospheres of sample gas is admitted in uo une inlet sys­
tem and through an adjustable leak into the mass spectro­
meter tube.
The size of the leak is such as to permit
gas to enter the evacuated mass spectrometer tube at the
rate of one cc per twenty four hours.
The leak is located
in a 20 inch length of l/8th inch copper tubing which is
used to provide the necessary path length for a steady
state concentration at the leak.
9
This prevents fraction-
S’ ,
c°v
SPECTROMETER
TUBE
2
SHIELD
ELECTRON TRAP
3
ION
I
REPELLE R
DRAWING
5
OUT PLATES
FOCUS
6 FOCUS
BEAM
CENTERING
BEAM CENTERING
ELECTRON
BEAM
6
/
FIGURE 2
0 RtOU VD
4
at ion of the hydrogen isotopes into the mass spectrometer
tube.
A tungsten filament (1/1000 inch x 4 mm) heated by
a current of 4.0 amperes, emits a total spectrometer
current of ten milllamps.
These emitted electrons which
are aligned by a 100 Gauss magnet, ionize the incoming gas
to a mixture of:
Hg,
HD***,
HD^* , and
;
the latter two, however, represent a negligible fraction
of the total ions at the deuterium content used.
The positive ions, once formed, are repelled by the
potential on plate 3 of the mass spectrometer tube
(fig. 2)
and then drawn out by a small negative potential on plate
4, at right angles to the plane of the mass spectrometer
At this point, the ions, which have practically zero
tube.
velocity in the direction along the length of the tube, are
subjected to a large electrostatic field (620 volts) and
accelerated into the magnetic analyser.
This field of 800
Gauss is so shaped as to refocus the ions at the collector
plates.
The collector plates of hydrogen and deuterium re­
spectively feed into separate preamplifiers which are
situated in a shielded housing adjacent to the mass spectometer tube.
The voltages, developed across 2 x 10^° and
4 x 10^0 ohm resistors by the ion currents from each collect­
or plate, are fed into separate
amplifiers.
regenerate feedback
A fraction of the hydrogen voltage is bal­
anced against the total output from the deuterium amplifier
10
by accurate decade resistances,
^hen balance, as indicat ­
ed by a null reading on the wall galvanometer, is obtain­
ed , the ratio of the two masses is read directly.
2. kinetics of Ion Formation.
Bleakney (10) determin­
ed the kinetics of the production of the positive ions
of masses two and three in the mass spectrometer.
formation of
and
The
was found to be first order with
respect to the gas pressure behind the leak and tuat of
That is, a plot of either hh
second order.
or of
(mass c )
(mass 2) against pressure in rhe foresystem
would yield a straight line passing through zero; like­
alone, if such were possible, to obtain
wise , a plot of
would presumably also give a straight line against the
square of the pressure.
*
Inasmuch as H and HD cannot be detected indeoendb
ently, it was suggested (10) that the ratio of mass b to
mass 2, i.e. ,
(HD^
)/H^ , be plotted as a function of
pressure in the foresystem and extrapolated to zero pressure
The intercept at this point is the ratio of HD* to H*.
On the instrument at the Institute a straight line
of the above function of ratio vs. pressure was obtained
with only tank hydrogen (isotopic content approximately
1 part in 5000).
In the range generally used, one to two
percent HD, the curves were of the shape shown in figure L.
This behavior, however, is not unique.
s imilar functions.
11 -
nier (t) reported
—a actual practice, it uas found, convenient no
operate in the region of the curve above o volt^ as
read on the mass tuo amplifier.
_he nnss 2 voltage is
proportional to the pressure in the foresysten aid there­
fore used
tl..
ctccmmu^
.1,. ratio of the mfcnoivn
sample is cjuparad to tint oi p stancarc san;!^ of similar
isotopic contenu at the sam mass 1 voltage.
3. operation,
the pattern of operation is as follows:
vUhnonn ^as is admitted in order to flush out bus system.
This is evacuates until ont:
the background reading is lefu.
^ninonn ^as of sufficient pressure (7 to 6 cmi. ol' mercury)
is admitted to give s reading of at least seven and a half
volts on mass ... voltmeter.
/art of this ^as is urained
off' until a reading of approximately seven volts is rejster-
ed.
The standard potentiometers are adjusted until a null
is indicated on the jelvanometer at its hignest sensitiv­
ity.
The ratio is recorded and gas partially drained
until a reading of 5 to six volts is registered on mass a
amplifier.
Again the voltage and the ratio of mass 3 to
mass 1 is noted.
The unknown gas is evacuated to back­
ground reading of mass 2 amplifier and the standard sample
admitted to flush out the system.
The same process is
repeated for the standard sample and readings taken at the
same voltages.
After the standard gas has been evacuated, the high
voltage and the three focusing potentials in the mass spec­
trometer tube are readjusted for maximum sensitivity, i.e.,
maximum reading on mass t amplifier for a given background.
ro
VARIATION OF MASS SPECTROMETER
TO
WITH VOLTAGE OF MASS 2 AM PLIFIER
O)
RATIO
30
O
CD
>
CO
2
>
z
o
X 10 3
RATIO SfH
h3
The same procedure of
the samples is aGaim
carried out except that the standard sample is run first.
The time for the total operation is kept to approximate­
ly fifteen minutes.
In the event that this is not
possible, the high voltage is shut down after the first
set of readings of unknown and^standard samples, and the
amplifiers rezeroed.
It was found that fifteen minutes is the shortest
period for low frequency drift of significant variations
in the DO amplifiers,
when the period of drift for a
two percent error is less than fifteen minutes the
machine is considered to be unstable and the determina­
tion rejected.
The sample is run again at a different
t ime =
The practice of initially admitting a higher pressure
of gas than iu read on the machine was instituted in or­
der to permit the rapid attainment of concentration
gradients at the leak.
When this procedure was not
followed the voltage reading would gradually rise at a
given pressure, with a corresponding increase in the
ratio as indicated on the galvanometer.
The time re­
quirement for the attainment of a constant voltage and
ratio under these conditions is more than fifteen min­
utes for a combination of unknown and standard samples.
The determination of the ratio before a constant reading
is attained introduces an error greater than that inherent
in the machine.
It was found that a steady state is ob­
tained in much less time when goin^ from a higher to a
lower pressure than in the reverse order.
4. Impurity effects.
The amount of moisture dis­
solved in the gas evolved at the cathode is generally
regarded to be negligible.
In an effort to check this,
gas samples were run on the mass spectrometer with the
foresystem adapted with a dry ice - trichlorethylene trap.
No detectable difference was found in the results when
the dry ice trap was removed and the gas sample run at
ro om temperature.
The effects of gross impurities of nitrogen and air
(twenty percent) were determined by Nier (9).
The
effects of smaller percentages of air contamination were
determined during the course of this investigation.
It
was found that the sensitivity, i.e., volts of mass 2 per
cm pressure behind the leak, was markedly decreased and
the ratio of deuterium to hydrogen increased.
The net
effect on the reading of the mass spectrometer of air in
the samples is to raise the mass three to mass two ratio
and therefore decrease the separation factor observed.
Because of the first effect of air impurity, i.e.,
the marked decrease in sensitivity, contaminated samples
are readily detected, and rejected.
A quantitative eval­
uation of the effects of impurities of air, nitrogen and
water vapor is now in progress at the Institute.
- 14
11.D. standard Samples.
Standard samples ^ere generated
by the action of enriched water on magnesium at 47b° 0.
A diagram of the pyrex glass standard sample reaction
vessel is shown in figure 4.
magnesium in the form of,small turnings is admitted
into the vessel through the top of 1 which is then sealed
with a torch,
h heater of nichrome ribbon wound around
an insulated metal form is embedded in refractory C, and
fits over B, the lower extension of the vessel, in which
the magnesium is deposited,
fhe magnesium and the reaction
vessel is degassed under vacuum for several hours,
stop­
cock D is kept closed and between I and 11 ml of enriched
water is placed in the sidearm n through its top which is
then sealed with a torch.
the enriched water is then
frozen by means of a dry ice trap; stopcock D is opened and
the sicearm evacuated.
The stopcocic is again closed and
the dry ice trap removed.
Inis process of freezing down
and then evacuating the dissolved air is repeated several
times until the air has been entirely removed,
stopcock
F is then closed, D left open and the magnesium brought up
to temperature will cm is read bp means of a c bromol - axumel
thermocouple placed between the neater and the extension m.
reaction time is between 10 and 20 hours and completion
is determined by a constant reading on the manometer
sealed into the manifold.
itandard samples generated from the same water in
— Ia —
STANDARD SAMPLE
5
D
D
O
<
>
CD
FIG U R E
REACTION BULB
IU
UI
o
2
z
<
3
r
r
EXPKRIüüKTAL RESULTS
RESULTS
u
71
17
111.3. Errors of neasurernent
The absolute error in separation factor is less than
three percent ; this represents the square root of the sum
of the squares of the individual errors due to sampling,
dilution, preparation of the electrolyte, and calibration
of the mass spectrometer.
The relative error of the separation factor for the
four lowest current densities is less than 1 percent.
The
relative error for the values at the two highest current
densities is between 1 and two percent,
home of the values
in Table II, particularly those at 250, represent as many
as sixty five separate determinations on the mass spectro­
meter relative to a standard gas sample.
The precision of
measurement, which is the average deviation of the mean
value divided by the square root of the number of determin­
ations, is therefore reduced to a very small number rel­
ative to the two percent figure for the reproducibility
of the mass spectrometer.
18
111.^. Contamination
One of the criteriea for an acceptable run was that
a separation factor obtained for a given set of conditions
of temperature and current density at the inception of
a run be reproduced at the same conditions at the termina­
tion of the run.
In the instances where this was not
realized, the entire run was rejected.
Almost without
exception, the terminal values were lower than the in­
itial values for a rejected run.
The variation of the separation factor from a con­
taminated solution, at three successive surfaces, with time,
is shown in figure 5.
The value approached by the separation
factor obtained during a run which had gone bad appears
to be independent of temperature and is somewhat less than
3.0.
This corresponds to the value of the separation fact­
or obtained when stopcock grease was added to the electro­
lyte, Table III.
Contamination is therefore said to be
due to the creep of grease from stopcock P into the sol­
ution and the interface of mercury and the solution.
The average time length of a run was about a week
but sometimes ran as high as two weeks.
The appearance of the mercury surface during electro­
lysis was found to be a sensitive indication of contam­
ination.
Under normal conditions of proper cleanliness
of the electrolyte and the mercury, a single bubble of
19
LU
UJ
CK
X
UJ
Z
O
CM
rO
LU
O
<
LL
X
ZD
en
LU
O
<
LL
œ
D
C/)
04
O
O
O
<r
ro
IO
yoiovd
O
04
NOiivyvdas
TIME
IN
HOURS
LU
Q
<
LL
CK
D
(O
gas leaves the edge of the mercury surface and rapidly
moves toward the center of the surface, to the point of
maximum curvature.
In succession, and generally over
the same path, bubbles race to this preferential point
and there collect to form a bubble large enough to leave
the surface.
This pattern remains substantially the
same with changes in temperature and current density,
except that at higher current strengths, the point of high­
est curvature where the bubbles leave the surface, shifts
further away from the center.
Then the rate of evolution
is high, this mode of bubble evolution is supplemented
by a fine mist of bubbles rising uniformly from the
surface.
When contaminated, a steady state of small bubbles
appear on the mercury surface extending from an arc
at the edges and directed toward the point of departure.
The greater the degree of contamination, the larger the
segment of mercury covered with small bubbles.
Upon in­
creasing the current density, the size of the segment
diminishes; if contamination is slight, a very high
current density, i.e., greater than 10“^ amps/cm2,
creates the impression of wiping the surface clean,
however, during advanced stages of contamination, the sur­
face cannot be cleared of bubbles at even the highest
current density used.
20
None of the samples generated during the time in
which the surface exhibited these characteristics of con­
tamination were used in the evaluation of the separation
factors in Table II.
The temperature was kept constant by means, of a mer­
cury thermal regulator and a constant temperature bath to
well within one degree.
21
Table IV
Sample Data
mass Spectremete;r:
Filament Current
emission Current
mcLeod Gauge
4.0 amps
10.0 ma
IQ-5 mm 1 is
Electrolyte
HD0/H20
H^oO^
0. 0541
0. 12 k
Standard Sample :
V-6
Sample
D-71
3%.
m-
HD/Hg
mlvoHs)
(Background SO mv. V_ )
-^2
25
2x10'5
7.6
Ô.0
V-6
7.5
5.8
0.0120
:Ratio (ZD/%)
0.00944
0.00915
0.O1200
0.01169
3.62
3.65
(refocus and rezero, background 25 mv.)
V-6
D -71
8.1
6.0
0.01209
0.01138
8.1
6.0
0.00914
0.00893
3.76
3.78
(refocus and rezero, background 20 mv.)
25
8,i
6.0
0.00997
0.00956
V-6
8.2
6.0
0.01288
0.01233
V-6
8.0
6.0
0.01317
0.01270
8.0
6.0
0.U0999
0.00945
0-72
2x10-5
D-72
22
5.66
3. 66
3.74
3.82
Sample
T^C
C
Vd (volt s)
Hetio (ED/HS)
(seiocus and re^ero, dadground 20 mv.)
ü-121
80
10-5
V-6
7.5
6.0
0.00932
0.00959
7.5
6.0
0.01243
0.01210
3.60
3.59
(^eloeus and re zero, bac. ground 20 mv.)
D-151
T-ô
25
2:110-5
7.5
6.0
0.00956
0.00920
7.5
6.0
0.01246
0.01215
3.70
3.75
(mefocus and re zero, bac].ground 20 mv.)
7-6
D-151
7.o
6.0
0.01230
0.01207
7.5
6.0
0.00933
0.00896
3.74
0.82
DISCUSSION OF RESULTS
^v.a. vénérai uonaiaeraüioa&
***"'*— ^n—■—■in» in m»im । mu ■ irmm.
Reported separation factors at a number of different
metal cathodes indicates uno distinct cLasses.
the sep­
aration factor of one group appears to be consistently
high, in the neighborhood of 7, whereas the second
group exhibits a factor around three.
(11)
the several theories (11) regarding the mechanism
of the electrode process are inconsistent rich each other
and nona is applicable to all metals.
rhe departure iroa
a unique mechanism use made by Zoriuti and ohamoto (6)
uho evaluated the possible mechanisms as follows:
1)
the neutralization of both hydrogen ions to form
chemisorbed hydrogen atoms on the electrode, followed by
the union of the two atoms to form a molecule which is th
desorbed.
1)
the neutralization of a hydrogen ion uhich is then
approaches by another hydrogen ion to form ? molecule con
currently with neutralization.
5a)
Independent neutralization of tau ions in solution
and the formation of a molecule without bsin_ absorbed on
the electrode.
ub)
-imultanoous neutralization and molecule formation
in solution by too ions without bsing absorbed on the
electrode.
because of the energy considerations of a pair of
three oossiblities are:
I. Neutralization of two ions, nhich goes rapidly, follow­
ed by the rate ^overnius recombination of the absorbed
Q
<X A
G*. U xJ i—1 !—) *
*#**P4@
I
-J
W
II. Neutralization of a single ion as the rate detemin-
.., . » 1 a f 2a,1 b
in^ step.
III. Neutralization of the coupled
ÏÏ—povernin^
the rate.
............
2b
A discussion of the various mechanisms and a review
of the literature is found in Butler, "^lectrocapillarity-.
The classification of the existing theories in light of
the above three generalized mechanisms is given by Okamoto
who has evaluated the following scheme.
cases
(15)
mercury represents the group oi metals exhinitin^
the lower separation factor and nickel tne ^roup nitn
the higher separation factor.
The assignment of mechan­
ism I to mercury requires the hydrogen ion to go through
the absorbed state,
uince the dissociation energy of
EgE is very small, the energy requirement for this acti­
vated state ^as considered too great for a reasonable
rate.
Cases 1 and 2 more therefore eliminated from con­
sideration.
Theoretical considerations of cases 3 and 4
yielded a separation factor (5) entirely inconsistent ^ith
experimental results.
This leaves the assignment of mech­
anism III to mercury, whereas consideration of the instant­
aneous anodic current (13)
mechanism I to nickel.
called
(15) led to the assignment of
The proposed mechanisms were
'electrochemical' in tne case or mercury and the en­
tire group it represents, and * catalytic* in the case of
the group of metals exhibiting the higher separation
factor and represented by nickel.
A calculation of the separation factor for mercury
in which the configuration of the activated complex was
considered to consist of a hydrogen atom and a. hydrogen
ion bounded in a colinear fashion by a mercury atom from
the electrode and an oxygen atom from the electrolyte,
was made by Horiuti and his coworkers.
(13)
The value of
the separation factor by this method of calculation was
given as 3.4 at 20°C.,
(13) however, in a later paper,
— 26 —
the value was reported at the same temperature as 3,8.(16)
These values, particularly the latter one, agree remark­
ably well with the observed values in Table II.
IV.B. Diffusion Effects
Though the diffusion process is generally not con­
sidered at low and intermediate current densities in high
overvoltage problems, it is apparent that at high current
densities the diffusion process becomes increasingly im­
portant .
At current densities in the neighborhood of
10”2 amps/cm^, diffusion competes with the activation
step as the rate determining step.
When the rate of diffusion of the ions up to an
electrode is less than the rate of discharge, a concentra­
tion gradient will be built up.
At some distance from
the electrode equal to a diffusion layer thickness,
the ionic concentration is equivalent to that of the
bulk of the solution, and, as the electrode is approached
this concentration drops to G , the concentration at the
electrode.
In the consideration of the effect of diffusion on
the observed separation factor, 30bS, the ratio of hydro­
gen and deuterium ions at the electrode will be compared
to that ratio in the bulk of the solution, since it is
the latter ratio which is used in the experimental sep­
— 27 —
aration factor.
This separation factor may be written
as
iH/iD
(2)
^obs
g/nD\
'
'sol
T)
P"
where i x and i
are the total hydrogen and deuterium
currents and
and CD the concentrations of the hydrogen
and deuterium ions, respectively.
The subscript sol refers
to the bulk of the solution.
In the following treatment it is assumed that the
problem consists of two parts, a) the diffusion up to the
electrode, and b) the discharge at the electrode which
is governed solely by the relative activation energies.
That is, a true separation factor may be obtained if the
observed factor is corrected for the electrode concentra ­
tion ratio.
The corrected separation factor is
E
D
°cor
where the subscript el refers to the ratio at the electrode.
The corrected factor is related to the observed separa­
tion factor by
28
(C^O^Jsol
(4)
scor
(Ch/GD)el
^obs
One method of determining the ratio of the hydrogen
and deuterium ion concentrations at the electrode is by
means of Fick's first law of diffusion
(5)
Rate of diffusion
A
=
(Csol - Cel)
s
However, solution by this method requires a know­
ledge of
£ , the diffusion layer thickness, which cannot
be readily determined without ambiguity.
Another
method
involves Fick's second law
(6)
:
D
St
O X2
where t is the time in seconds, D the diffusion coefficient
in cm/sec2, and x the distance from the electrode in cm.
The concentration C is expressed in moles/cm^.
The boundary and initial conditions are
(Ôc/dt)x,o
= #c. ;
29
(t=O)
co
where
Ô
is the transmission coefficient.
The solution to this equation has been determined
by Collins (17) and is
(7)
eri ——
/4Dt
where
dz
erf y
and
erf c y
dz
The flux in moles/cm2 is given by the expression
CoD
(8)
exp
Dt
F
erf c
Dt
X
The method then, for determining the role of diffusion
as applied to the separation factor may be outlined as
follows:
a)
An experimental determination of the flux into the
30
sink (electrode ), as a function of time, i.e., the current
density variation with time at a fixed potential across
the cell and at constant temperature.
b)
Hatching this experimental curve with one calculated
by means of expression (8) with-different values of the
transmission coefficient, and thereby finding the proper
for a particular current density.
c)
Utilization of the transmission coefficient of b) in
expression (7) in order to obtain the concentration at
the electrode for different values of the time.
From this,
a time average of the electrode concentration is evaluated
during the interval of sample generation.
d)
The time average electrode concentration due to diffusion
is then used to find an overall concentration ratio at
the electrode for use in expression (4).
The total observed polarizing current through the
cell, i, is composed of two components which cannot be
separately measured: the migration current im, and the
diffusion current id.
This situation differs from the
usual diffusion studies in that the migration current is
not reduced to a negligible value by the introduction of
a large excess of indifferent electrolyte, but rather con­
stitutes a major portion of the total current.
.For the case of the H ions
—
of
is the total hydrogen ion current, i^ and i^
where
the hydrogen ion current due to migration and diffusion
respectively,
i
however, is
H
+
(10)
but since
ir~
( iHtiD)
i?
and
TT
where t^;
is the transference number of the hydrogen ion
and is readily determined from the concentration and mobil­
ity of the constituent ions in the solution;
t
- "—QU—
? ciui
L is the mobility.
The diffusion current of the deuterium ion is de­
fined in the same manner as that of the hydrogen ion:
substituting in the above for i$ from expression (2)
and for the transference number of the deuterium ion,
the diffusion component 01 the deuterium ion current
becomes,
(14)
^obs
heglecting the contribution of G^Uin the denominator
since it is small compared to the rest of the denominator,
the term in the brackets becomes,
(15)
^obs
•
since
H
G
'V
z
“SO A
0s 4
expression (15) may be written as
The term now left in the bracket is independent of
current density and initial concentrations.
OD
—
By substituting
the values of the ionic mobilities and the two extremes
of the observed separation factors, the bracket becomes,
25.8
3.83
which is always less than zero and therefore leads to a
negative value of the deuterium diffusion current.
Since
this has no physical significance it has therefore been
D
'
shown that i^ is exactly zero for all cases considered.
It then follows that
(17)
CD
^sol
°el
D H
and the increased (G /C )Q1
D F
over (G /G ^)sol is entirely
due to the variation of the hydrogen ion diffusion current.
By means of expression (17), expression (4) becomes,
(18)
8
cor
S
”
C sol
obs -- --CHel
in consideration of the diffusion effects, we are then,
34
O
O EXPERIMENTAL
O
O
o
6.75
13
60
56
FIGURE 6
o
48
5
10
15
20
TIME
25
30
IN
35
40
45
50
SECONDS
55
60
only concerned, with that portion of the current which is
due to diffusion, i.e.,
The experimental curve
(1 - t^ )i.
in figure 6 is based upon (1 - t^)i equal to one.
The
two accompanying curves are calculated from expression (8)
with values of 1/^
taken as 6.75 and 13.
The ordinates
for the calculated curves were based upon
(t :OO)
:
1
An examination of (8) will show that
may be
determined directly from the value of the flux at t - 0
with a knowledge of the bulk concentration and the diffusion
coefficient of the hydrogen ion.
The former is readily
obtained from the pH of the solution and the initial per­
centage concentration of deuterium; the latter however,
cannot be determined precisely under the conditions of the
experiment.
Expression (8) st t : 0 reduces to
Consequently, an error in D results in a relatively
large error in the transmission coefficient.
the original expression of the flux,
2
However, in
(8), D appears
% and
and the slope of the flux with time at a given
value of
is practically unaltered by a small error in D.
Figure 6 indicates that there is good agreement be-
tween the experimental function at current density of
3 x 10
T = 25°C, and that calculated with
1/
Therefore, using this value of the trans­
equal to 13.
mission coefficient, the concentration of the hydrogen
ion at the electrode due to diffusion was determined by
means of expression (7) at x : 0 for time
equal to 30,
70, 100, and 140 seconds.
These values of the concentration are expressed as
the ratio of the electrode diffusion concentration to
the bulk diffusion concentration and are given in Table V.
Table V
The Ratio of the Concentration at the Electrode to that of
the Bulk of the Diffusive Component of the Hydrogen Ion
Current
i -
3 x 10”2 amps/cm2
T =
25°C.
( C )
[ °o)dif
t in seconds
0
1.000
30
0.536
70
0.421
100
0.374
140
0.328
36
PERCENT DIFFUSIVE FLUX
o
o
no
o
variation
N>
O
o
v
o
o
in
—
FD
o
8§
<0
o
o
_
œ
o
diffusive flux
0)
O
o
A plot of the above Table and the time average value,
f, determined throughout the generation interval of the
sample
(160 seconds), and indicated by a broken line, is
given in figure 7.
The total electrode concentration of hydrogen ions
relative to the total concentration of hydrogen ions in
solution, may be expressed as :
fel
(19)
C%ol
=
+ r(i - 4)
By means of expressions (18) and (19), 8
for
T = 25°, i = 8 x 10~2 amps/cm'5 was found to be 3.53.
The same procedure was used for determining 8^
T Z 25°, i : 5 x 10 S amps/cm 2.
for
The value was found to be
3.66.
A plot of the separation factor vs. the log of the
current density including the corrected values for the two
current densities exhibiting diffusion effects, at 25°
is shown in figure 8.
- 37
SEPARATION FACTOR
bi
Ui
O
04
•
CD
OJ
(D
O
O
bi
CD
O
LOG CURRENT DENSITY
(amps
no
/ cm=)
m
m
c
30
X)
m
U) o
m
m
m o
m 3
o
5
no
CD
o
IV.C. Separation Factor from Overvoltage Data
The overvoltage relationship expressed in the form
of the Tafel (18) equation is
a + b log i
Y =
(20)
is the overvoltage in millivolts, a and b are
p
constants and i is the current density in amps/cm .
where
For hydrogen and deuterium at a mercury cathode the over­
voltages are (19)
:
1416
+
116 log i
A
=
^2
1485
+
119 log i
The above expressions are not temperature independent and
hold for T z 20°.
The separation factor from a solution of equal hydro­
gen and deuterium content is the ratio of the respective
currents at a given overvoltage, therefore,
g
=
a
=
%2
iDg
1 " sHa
e
bH2
JLz.fBa
6
- 38 -
bD2
Substituting the values for a and b of hydrogen and deuter
ium, the separation factor at 20°, from the above exprès-
sion, is found to be 5.1.
From the above it can be seen
that the separation factor is strongly dependent upon
the value of the slope, b, which is given as
b
z
2.503 RT/ol F
The uncertainty in the constant <X
which results in an error in b of 2.4.
current density, i, at
is 0.01 (21)
The error in the
■equal to 1000 mv is
a ' 4
rib
0.435 b2
which is equal to 0.16 i.
The error in the separation factor calculated from
P
overvoltage data due to the error in both i^
1.2, which is of the order of 55^ of 3.
and i
D
is
Because of such
a large error inherent in the separation factor calculated
by this method, any attempt to predict the small tempera­
ture dependence of 3 from overvoltage data is futile.
IV. D. Separation Factor and Temperature
The first approximation of the order of the temper­
ature dependence of S, which does not take into consid-
39
eration the nature of the electrode, is an exponential
relationship
(21)
A e
where E is the activation energies of the two isotopic
species.
Since the entropy change for the two isotopes
is about the same and the reaction path taken to be identical,
the activation energy difference is assumed to be equal
to the difference in zero point energy.
of the order of 1400 cal.
E is therefore
(20)
The theoretical determination of the variation of
the separation factor with temperature calculated by
assuming the 'electrochemical' mechanism for mercury is
likewise given in the form of expression (21 ).
T is
again the absolute temperature and E in calories determines
the degree of temperature dependence of 3.
E was found
to be 0.66 kcal, by Okamoto (13) which is small compared
to 1.29 kcal for nickel, calculated by assuming the
'catalytic' mechanism.
Temperature dependence of S is generally evaluated at
constant overvoltage where the energy barrier is the same.
By means of generalized Tafel equations of overvoltage
for hydrogen and deuterium (19)
(21) and Table II, the
separation factor has been determined at overvoltages of
40
04
m
o
CM
œ
o
CM
0)
O
T
ro
a>
o
04
O
O
w
ro
O
O
Z
<
OJ
A
O
V
O)
O
O
O
O
a>
m
O
Z<
950, 1000, and 1100 mv., as a function of temperature.
Table VI
Variation of Separation Factor at Constant Overvoltage
with T emperature
»
Ov ervo.lt age in mv.
1000
1100
T°C.
950
0
==— —
3.83
3.76
25
5.78
3.74
3.68
50
3.74
3.70
3.62
74
3.67
3.64.
3.58
96.5
3.62
3.57
3.54
The value of E determined in this investigation
by the plot of the separation factor at constant overvoltage,
(Table VI) against 1/T (absolute ) between 0 and 96.5°C. is
given in figure 9 and is 0.14 kcal, t .01.
This value is
well within the precision of measurement of the separa­
tion factor and is considerably smaller than the theoret­
ical value.
In the overvoltage determinations, the value of oQ ,
which is in the expression for the slope, b, was found to
increase with a rise in temperature for both hydrogen and
deuterium.
(19)(21)
This change in
has been said to
indicate the aquisition of weak catalytic properties by
the mercury cathode.
(22)
41
The value of
for hydrogen
remains constant in the temperature range from 0 to 260
at 0,50 and then rises to value of 0.55 at 91.3°.
A value of 0,80 for
(21)
, which is exhibited by platinum,
palladium and copper under certain conditions,
(23) has
been taken to indicate a different mechanism of hydrogen
discharge equivalent to the catalytic mechanism of Horiuti
Assuming a linear shift in the change of mechanism as
indicated by the rise in <%, a weighted separation factor
composed of a component due to the 'electrochemical'
mechanism and a component due to the 'catalytic' mechanism
may be calculated.
In order to make this calculation, the following
information is needed:
a)
A knowledge of the degree of shift in mechanism from
'electrolytic' to catalytic.
b)
The value and temperature coefficient of S for a pure
'electrochemical' mechanism, and
c)
The value and temperature coefficient of 8 for a pure
'catalytic' mechanism.
The degree of shift is indicated by the rise in
The departure of
oC
from its constant value of 0.50
between 0 and 260 toward a value of 0.80 is taken as a
measure of the change in mechanism.
The value of S for a pure electrochemical mechanism
is taken from the observed values in this investigation in
the region where
is constant, between 0 and 260.
The temperature dependence of the 'electrochemical'
42
mechanism is due to Okamoto.
(13)
The value of 8 for a * catalytic* mechanism has been
determined for copper by Horiuti (4).
The temperature
coefficient of the * catalytic * mechanism has been calculat ­
ed by Okamoto.
(13).
This information is given in Table VII below.
Table VII
The Weighted Separation Factor for Mercury
r
T°C.
OC.
degree shift
in mechanism
Scat
calc.
-elec
calc.
8
weighted
25
0.50
0.00
7.4
3.74
3.74
50
0.52
0.07
6.2
3.41
3.64
75
0.54
0.13
5.4
3.18
3*4^
100
0.56
0.20
4.9
2.98
3.40
where
Weighted
is,
r ^cat
$wsighted
(1 - r)
r is the degree of shift in mechanism.
The positive temperature coefficient of the separa­
tion factor for tin (24) is apparently due to the same
shift in mechanism, but presumably to a much greater ex­
43
tent.
The separation factors reported for mercury at two
temperatures and at constant overvoltage by Walton and Wolf-
enden (6) are,
150
950,
3.5&
D.4
The overvoltage corresponds to a current density
between 5 x 10"^
and 10”^ amps/cm^ at the higher temp­
erature and is in the neighborhood of 800 mv.
ulated from these values is 0.1 kcal.
(20) E calc­
Agreement with the
value of E determined in this investigation at overvolt ­
ages of 950, 1000, and 1100 mv. is good.
IV.3.
Separation Factor and Current Density
The slope of the separation factor with increased
current density is small but definitely negative.
This
slope remains constant even at high currents when the cor­
rection for diffusion effects is applied.
The decrease
in S at 15° was reported as seven percent for a twenty
fold increase in current density from 5 x 10"^ to
6 x 10"4 amps/cm^
(6)
at 950 the same authors reported
no change in separation factor with the same variation in
current density.
44
The variation in separation factor in this invest­
igation was found to be three to three and a half per­
cent for a twentyfold change in current density, from
10
to 2 x 10 $ amps/ cm^ at all observed tempera­
tures .
:
Despite the large error inherent in the evaluation
of the separation factor for mercury from overvoltage
data, the sign of the slope of S with current density,
may however be determined.
The slope of the overvoltage against the log of
the current density for both hydrogen and deuterium
has been determined at a mercury cathode.
The slope
for deuterium was reported to be consistently higher than
that for hydrogen; the difference in slopes, though
small, is beyond the range of experimental error.
(19)
Inasmuch as the separation factor is the ratio of the
currents of the two isotopes at a given overvoltage, a
larger slope of overvoltage vs. current density for
deuterium indicates an increasingly larger difference
in current for the two isotopes with an increase of cur­
rent density.
This is in direct contradiction to the
observed results of this investigation.
In view of the fact that the ground state of the
isotopes in dilute deuterium mixtures is somewhat differ­
ent, particularly for the heavy isotope, than in the respect­
ive solutions of pure heavy and light water from which the
-
45
overvoltage measurements were made, a continuation of
this study of separation factor is suggested.
An evaluation of the separation factor at a mercury
cathode over the entire range of isotopic content of
the electrolyte would be desired in order to resolve
this apparent contradiction between overvoltage data and
the observed separation factor.
—
V, Summary and Conclusions
' '* »*»**<IWI ■!> >»m»xwi «
Â-
Wj; naw ।
Techniques have been developed and a cell designed
and constructed for the measurement of the hydrogen -
deuterium separation factor by means of a mass spectromet­
er, in a reproducible manner.
B-
The separation factor has been determined over a
range of current density from 10"^ to 5 x 10"^ amps/cm^
and at temperatures from 0° to 06.5°C. from solutions of
1.5 to 2.5^ D%0.
C-
The precision of met sûrement for the lower current
and the error less than three
densities is less than
percent.
D-
The precision of measurement for the two higher
current densities is one to 2 percent.
Diffusion effects
at these current densities have been evaluated at 25°.
The slope of d vs. current density was found to be con­
stant when corrections for diffusion effects were
made.
B-
The separation factor from overvoltage data for
mercury was calculated and found to be in the range of
the observed values, however, the precision of this
method is of the order of 35^ of the calculated separa­
tion factor.
47
F-
à determination of the activation energy of sep­
aration "was made by means of a plot of separation fact­
or against the reciprocal of the absolute temperature.
1 vias found to be 0.14 ±.01 kcal,
A calculation from the only reported temperature
data of separation factor at a mercury cathode, Walton
and .Volf end en, (ô ) indicated a value of 1 of 0.1 kcal.
48
(1)
Gleswtooe, "Introduction to Electrochemistry",
1) . Van Lbstrand, heu York, 1942, p. 477
(2)
(3)
urey, Erickwedde, c. murphy, rhys. Lev. , 39,
164,
(1932)
(a)
hashburn, L trey, kroc. Nat. Acad, hci.,
18, 496,
(b)
Levis, cc Lacdonald ? J. Chea.
341,
(4)
(1952)
hys*, 1.,
(1933)
Horiuti, a Okamoto,
ci. Papers Inst, of zhys.
ano Che in., ne s., Tokyo, 28, 231,
(1936)
(5)
Topley, c- Tyring, J. Chen, zhys., 2, 217,
(6 )
j alt on, e: golf end en, Trans. Far, ooc., 34,
436,
(1934)
(1938)
(7)
Taken & Bratzler, k. phys. Chem., n!74, 27L,
(8)
Hirota, k Horiuti, oci.Oarers Inst, of 1hys.
and Chern. Res, a Tokyo, _30, 151,
(9)
(1935)
(1936)
Tier, Inghram, Jtevens, & Rustad, university of
Hinnesot^ 0 ELI sr - 149
(10)
Bleakney, Thys. Rev., 41, 32,
(11)
(a )
(b)
(1932)
. Topley, dû Tyring, Nature, 133, 292,
Horiuti, u. Okamoto, ici, racers Inst, of
Thys. end Chern. Hes., Tokyo, 28, 231,
(c )
(1934)
(1936)
Halton, L kolfenden, Trans. Far, roc.,
34, 436,
(1938)
- 49
(18)
Reviews :
(a)
Wirtz, w. llektrochem., 44, 303,
(b)
Butler, Ioid, 44, 55,
(c)
Butler, Electro capillarity"', Che rai g al
(1933)
(1933)
publishing Co. hew York, 1940, Chapter VI
(13)
Okamoto, J, Fac. 3ci. Hokkaido Imp. Univ.', mer. Ill,
2, 115,
(14)
(1958)
Butler, "Blectrocapillarity", Chemical Publishing
Co., New York, 1940, p. 130
(15)
Horiuti, & Okamoto, Bull. Chern. Soc. Japan, 13,
216,
(1938)
(16)
Horiuti, & Nakamura, J. Chern. Phys., 18, 395,
(17)
Collins, J. Col. Sci., 5, 499,
(18)
Tafel, Z. Ihysik. Chern., 50, 641,
(19)
lost, & Hiskey, J.N.C.S., 73, 161,
(20)
Glasstone, Laidler, R Byring, "Theory of Rate Process­
(1950)
(1950)
(1905)
(1951)
es", lUGraw-Hill, New York, 1941, p. 594
(21)
Post, c Hiskey, J.A.C.8., 72, 4203,
(22)
Post, Dissertation, "Hydrogen Overvoltage on Hercury
(1950)
Cathode", Polytechnic Inst, of Brooklyn, June 1949,
p. 36
(23)
Glasstone, Laidler, & Nyring, Ref.
(24)
Walton, & Rolfenden, Nature, 138, 468,
50
(19), p. 592
(1936)
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