A THESIS UNDERTAKEN BY
PHILIP CAPLAIN
IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR
THE DEGREE OF BACHELOR OF SCIENCE
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF
ELECTROCHEMISTRY
JUNE, 1922
INVESTIGATION
AN
THE
INTO
EFFECT
OF
CURRENT
DENSITY
ON
OVERVOLTAGE
V
I30is
SINCERE APPRECIATION
MUST BE EXPRESSED TO
DOCTOR M. KNOBEL
UNDER WHOSE HELPFUL
SUPERVISION THIS THESIS
WAS ACCOMPLISHED,
AND TO WHOM MUST BE
ASCRIBED ANY ORIGINAL
MATTER HEREIN CONTAINED.
1
AN INVESTIGATION OF THE EFFECT OF CURRENT
DENSITY ON OVERVOLTAGE
INTRODUCTION
Overvoltage is defined as the excess of potential
required to liberate hydrogen at any metal electrode
above that required to liberate it
gen electrode;
1.
e.,
at a reversible hydro-
one consisting of platinized plat-
inum saturated with hydrogen gas.
In
electrolysis
there are two other voltage effects
from which overvoltage must be carefully distinguished,
namely: the ohmic drop in
the electrolyte,
and concen-
tration polarization.
In itself, overvoltage has become of great technical importance in recent years.
The success of many
commercial processes depends upon its proper regulation.
Among these may be mentioned the electrolytic separation and refining of metals, and electrolytic oxidation
and reduction processes.
It must be carefully consider-
ed in attempts to develop non-corrodable alloys and protective coatings for metals, for it has been shown to
be a most important factor in corrosion.
2
VARIABLE FACTORS IN OVERVOLTAGE
3
Overvoltage is an irreversible effect, and its magnitude is determined by a number of variable factors,
as
follows:
A. Nature of electrolyte
I. Concentration of the ion in question; this is
actually a question of concentration polarization,
but is properly considered here from the overvoltage
viewpoint; the overvoltage increases with decrease
of concentration.
If, during electrolysis, the
rate of ionization is not sufficient to maintain
constant concentration of the ion, the overvoltage
will rise.
The presence of compounds forming com-
plexes with the ion will affect the overvoltage
by altering its concentration, and the rate with
which it is produced by ionization.
II. Nature of the ion; the nature and hydration of
the ion markedly affect the overvoltage.
(See Page 16)
III. Presence of addition agents, certain specific
substances, usually colloids, increase the overvoltage when present in small amounts.
B. Nature of Metal of the electrode
I. Its compgsition affects the overvoltage.
II. Its surface structure affects the overvoltage.
The overvoltage of cast,
wrought,
and elec-
trodeposited metal decreases in the order
named for a given metal.
I
Its past
-
4
history may -markedlyaffect the overvoltag.
III. Character of surface; a rough surface decreases the overvoltage by increasing the
superficial area.
In addition, the char-
acter of the surface appears to affect specifically the overvoltage by means not yet
understood.
(See Page /i5)
IV. Formation of alloy; If the ion deposited
alloys with the metal of the electrode, the
overvoltage is diminished.
V. Passivity of metal of electrode; under cer-
tain conditions the metal may become more
noble than normal, affecting, thereby, the
overvoltage of ions deposited against it.
C.
Current density; overvoltage increases with
current density.
D.
Temperature;
(See,
however,
Page 1f)
an increase of temperature di-
minishes overvoltage.
E.
Time;
overvoltage does not assume its full mag-
nitude except after a lapse of time, great
with some metals, almost instantaneous with
lead and mercury.
F.
(See, however, Page t5)
Pressure; overvoltage appears to decrease with
increase of pressure.
G.
Presence of a depolarizer; a depolarizer can
act in two ways:
(a) As a catalyzer, increasing the velocity of the slow reaction which is
5
causing irreversibility.
(b) By reducing the energy consumption at
the electrode below the amount corresponding to equilibrium electrode potential.
In the case of cathodic potential,
this is usually accomplished by reduction of the polarizer.
Another view-
point is to consider the depolarizer to
lessen the concentration of the products
of electrolysis at the electrode,
thus
decreasing the back electromotive force.
It
is the purpose of this thesis to investigate
the effects of current density on hydrogen overvoltage,
in the endeavor to confirm and elaborate upon theories
propounded as to the causes of the phenomenon.
6
RESUME OF VARIABLES AFFECTING OVERVOLTAGE
A.
Nature of electrolyte
I. Concentration of the ion in question.
(a) Its concentration
(B) Rate of ionization producing the ion
(c) Presence of complex-forming compounds
II. Nature of the ion.
(a) Its nature
(b) Hydration
III. Presence of addition agents.
B.
Nature of electrode material
I. Composition.
II. Surface structure.
III. Character of surface.
IV. Formation of Alloy between discharged ion and
electrode material.
V. Passivity of electrode.
C.
Current Density
D.
Temperature
E.
Time
F.
Pressure
G.
Presence of a depolarizer
7
THEORIES OF OVERVOLTAGE
8
THEORIES OF OVERVOLTAGE
Broadly speaking, there are four tenable theories
Each theory, as propos-
of overvoltage to be considered.
ed by the various investigators, embodies different modifications, as indicated in the following resume.
I. The Dielectric-Resistance Theory.
was proposed by Haber1
This theory
He postulated the absorb-
in 1902.
tion or occlusion of a layer of gas at the electrodeelectrolyte surface.
low conductivity,
This film acts as a die.lectric
of
thus increasing the potential gradient
to be overcome by the ion in passing from the electrolyte to the electrode.
The thickness of this film de-
pends upon the nature of the electrode material,
thus
causing the different overvoltages observed with different electrodes.
II.
The Surface Tension Theory.
elaborated by Moller 2 in 1909.
This theory was
He found that curves
showing the variation of overvoltage with temperature
bore a very close resemblance to those of surface tension against temperature.
It was also observed that
both curves reached their maximum at 5.30, and that the
greater the value of the maximum,
the greater the slopes
of the curves on each side of the maximum.
cal formula was obtained,
An empiri-
giving overvoltage as a func-
tion of the surface tension of the gas film, or bubbles,
formed at the electrode.
To explain the variation of
overvoltage with the metal employed as cathode, it was assumed that the assistance offered to the electrical forces
fvrming the film varies with the nature of the electrode
material.
Metals possessing a strong attraction for hy-
drogen have a low overvoltage.
This theory has been further elaborated by MacInnes 3
Adler, and Contier1 3 .
A low current density was employed,
so that one bubble of hydrogen was evolved in one or
more minutes.
The overvoltage-time curve was sinuous,
with a sharp break following the maximum values of overvoltage.
The bubble was freed at approximately the min-
imum value, and continued to be evolved at the same
point, seemingly indicating that a nucleous was invari-
ably left behind.
To account for these relationships,
MacInnes took cognizance of the fact that the vapor pressure of a bubble varies inversely as its size, the
smaller the bubble, the greater the vapor pressure.
This
increase of.vapor pressure in turn increases the amount
of hydrogen gas dissolved in the solution for equilibrium with the gaseous phase.
The increase of dissolved
hydrogen increases the decomposition cathodic voltage of
the solution in accordance with the Nernst Theory, and
hence, bg definition, the overvoltage.
Stating these
facts concisely, from the opposite viewpoint we have:
the larger the bubble, the smaller the overvoltage. Hence
as the size of the bubble increases, the overvoltage decreases.
When the bubble is liberated,
the overvoltage
starts to increase, due to the minuteness of the nucleus
10
remaining, and rises to a maximum.
At which point the
bubble again begins to grow, and the process repeats.
The overvoltage of a given metal is determined by the
size of the nuclei which it can absorb, the larger
these nuclei, the smaller the 6vervoltage.
MacInnes
has used microscopic examination, and the pressure var-
iation of overvoltage, (See Page lo ), in support of this
theory.
III. The Monatomic-Hydrogen Theory, first elaborated
by Nernst4 .
Nernst assumed that during electrolysis,
the hydrogen ions penetrate below the surface of the electrode.
There the charge is given up, and the hydogen
exists in the monatomic and molecular forms, in accordance with the equation
2H
==
H2 .
For bubble formation
a certain minimum concentration of the gas H 2 is required.
If the solvent power of the electrode material for the
gasbe low, before this minimum concentration is reached,
the electrode will have become saturated with the gas at
atmospheric pressure.
Due to the slow rate at which the
electrode arrives at equilibrium with the atmosphere, the
electrode must be supersaturated to cause the formation
of bubbles.
This corresponds to an increase of the elec-
trolytic solution pressure of the hydrogen, and a consequent rise of overvoltage.
The variation of overvoltage with many of its determining factors lends verisimilitude to this theory.
Recently Wilson 5 has found that overvoltage decreases with increase of pressure.
sure should cause the reaction
H
An increase of pres+
H
-+
H2
to proceed
11
towards the right with increased velocity, increasing
the concentration of H2 , and bringing the electrode
nearer to the bubbling point, thus decreasing the overvoltage.
For the same reason, an increase of temperature
decreases the overvoltage.
Haber' had found that the applied cathodic poten-
tial is a logrithmic function of the current, which he
E = A logI
expressed thus:
-
B, in which A and B are
the current.
constants, and I is
Tafel later attacked the problem from the view-
point of the monatomic hydrogen theory.
He found that
the cathodic, potential for mercury and lead vary very
nearly as a logrithmic function of the current, but only
approximately so for other metals.
As the causes of the
deviation from the logarithmic curve, he ascribed the
undeterminable influence of three factors, which were
the catalytic influence of the electrode material upon
the reaction
H 1
H -- + H 2 , the influence of time,
), and unknown specific effects of the nature
(See page 4
of the electrode surface.
Tafel evolved the mathemat-
ical derivation following:
In or at the surface of the cathod
the following
reactions are assumed to take place:
1.
H
E=
2.
H
H ==H
H
2
The first reaction, the discharge of the hydrogen
Ion, may take place at a relatively great rate;
but the
second, the association of monatomic hydrogen to molecular hydrogen, requires appreciable time, as determined
12
by the reaction constants, and any catalytic effects
present.
Assume electrolysis to take place under steady
conditions; i. e.,
that the decrease in concentration
of dissolved hydrogen, by evolution as a gas, is balanced, at all moments, by the increase caused by the
association of the hydrogen atoms. Then the concentration
of the dissolved molecular hydrogen remains constant.
In equation (2) let k be the velocity constant of
the reversible reaction.
Let I he the current density,
CH the concentration of dissolved molecular hydrogen,
and CH -the concentration of hydrogen ions.
Then
-d CH
------
2
= k CH
dt
H
For steady conditions of electrolysis
I = K'C
and
CH
=
From Nernst's Formula
E=RT ln CH
F
= RT ln K'I
H*
F
= RT in I + RT ln K
2F
F
qH
E
=
g16gi-a
For reversible reactions this vould be
E = 0.0002T logI
t
a
= C.0001T logI -
a
n
13
For Pb and Hg, at 120, the actual curve was given by
E
a * 0.107 logI ; whereas the forTmula for
the reversible electrode requires
E = a + 0.0285 logI
It
aopears,
therefore,
that the constant b for electrodes
possessing overvoltage is
sible hydrogen electrode.
greater that that for the reverBoth the 4iuantities,
b and a,
were calculated for steady conditions of electrolysis at
temperature T, and are constant only under these conditions.
Summarizing this theory, then, it appears that
overvoltage is due to the slow rate, and the irreversibility, of the reaction
H
+
H
-v
H 2 , and that any
factor which will increase the rate, and reduce the
irreversibility, will decrease the overvoltage.
IV. The fourth theory may be termed the SolidSolution Theory.
This theory of Foerster's? also makes
use of an intermediate stage between the charged ion and
the evolved gas.
It differs from the above described
theory, however, in that it assumes the formation of a
compound or solid solution by the discharged ion within
the electrode material, the concentration of which determines the electrode potential.
The variation of overvoltage with the variable
factors is explained by this theory as follows:
Time:
the longer electrolysis continues, the great-
er the concentration, and hence the greater overvoltage.
The rate of decomposition of the solid solutioa
equals its
rate of formation,
finally
and the cathodic potential
14
becomes constant.
Current Density; the greater the current density,
the greater the rate of formation of the solid solution,
with consequent increase on concentration and rise of
overvoltage.
Temperature;
the higher the temperature,
the more
rapid the rate of decomposition of the solid solution,
with attending decrease of concentration and lowering
of overvoltage.
The investigators Reichenstein , Pring9, and
Curzon1 0 have found evidence indicating that the hydrogen deposited at the cathodspenetrates below the surface.
The previous history of the electrode affects its internal structure, and in connection with the nature of the
surface, determines the amount and depth of penetration.
The internal structure, nature, and the physical condition of the metal thus seems to have a great influence
upon the overvoltage at the electrode, determining to
what extent the liberated gas will dissolve and take part
in the electrode reactions.
In a definite electrode vol-
ume, occupied by the gas through penetration, an inter-
mediate formation of hydrides or other unstable compounds
takes place.
The depth of penetration has been deter-
mined by Pring, by depositing one metal on to another until
no further change in overvoltage resulted.
quired is
given by the last
The depth re-
column of the following table,
indicating the thickness necessary to give the effect of
the massive metal.
wo,
jw
,
-
15
MILLIGRAMS/SQ.CM.
METAL
MILLIMETERS THICK
(From density & weigit)
4 X 10-6
Pt
0.01
Au
0.3
1.6 X 10
Zn
0.3
4.2 X 10~4
Cu
3.0
3.4 X 10~3
Sn
4.0
5.5 X 10-3
Ni
15.0
1.6 x 10-2
Pb
75.0
6.6 x 10
Newberyl,
recently investigating the phenomenon
of overvoltage, has arrived at some very interesting
conclusions.
He employed the vibrator method (See Pagesare)
for measuring the cathodic potential, in order to eliminate any polarization effects due to the presence of a
film of gas surrounding the electrode.
During electrol-
ysis, he believes, the ions penetrate the electrode surface, pass through intermediate stages, and emerge in the
molecular gaseous form, breaking open the surface of the
electrode in doing so.
Microscopic examination revealed
the surface to be pitted with innumerable crater-like
formations, apparently confirming the theory.
It was
found that at high current density the overvoltage of
lead, mercury, and platinum increased with time to a maximum, and then slowly fell.
The maximum overvoltage
Newbery believed to be determined by the mechanical
strength of the surface crystals, and the surface tension
forces (in the case of mercury) which resist the passage
of the molecular hydrogen from the interior of the electrode to the, exterior.
The fall of overvoltage, after
16
reaching the the maximum, was attributed to the increased
permeability of the electrode surface material to the molecular gaseous form, because of the extreme degree of
pitting to which it had been subjected.
Newbery investigated some further factors affecting
overvoltage, arriving at the following conclusions:
(a) Overvoltage was, for the most part, to be ascribed to supersaturation of a superficial volume of the electrode with molecular gas under very high pressure, due to
the permeability of the electrode material to ions, and
non-permeability to molecular gas.
(b) The'hydration ofan ion" affects its overvoltage because of the relatively slow rate of dehydration
during discharge of the inn.
This is particularly true
in the case of iron and related metals.
(c) Colloids, in conjunction with hydrated ions,
are carried into the electrode material during electrolysis increasing the overvoltage.
They have negligible
effect upon non-hydrated ions.
'(d) Townsend12 in 1897 had shown that the gaseous
products of electrolysis, escaping at the electrode, carry
an electric charge.
Newbery believes that the marked fall
of overvoltage, often observed at high current densities,
may be attributed to the inductive action, on the electrode, of the escaping charged gas.
It was found that at
high current densities variations of overvoltage show an
inverse relation to variations in the charge of the gas,
the action being often sufficient to reduce the overvoltage to a negligible quantity.
17
Of the four factors considered, (a),
(b), and (c)
tend to increase overvoltage, whereas (d) decreases it.
For deposition of a metal, (a) is not operative.
At low
current densities factor (a) preponderates, whereas at
high current densities, (b) is the preponderant factor.
Recently Newbery has more thoroughly investigated
factor (a), and has been led carefully to distinguish it
from overvoltage proper.
He calls this mechanical resis-
tance which opposes the passage of the ion from the electrolyte to the electrode, and of the molecular gas from
the electrode to the atmosphere, the transfer resistance
of the cell.
The resistance of a cell is composed of
two parts, that due to the electrolyte, and that due to
the transfer resistance.
Transfer resistance is a variable quantity, as
follows:
I. It is of greatest magnitude where gases are liberated.
II. Of considerable magnitude where ions of a gas
carry the current.
III. Of small magnitude when the current is carried
be metallir ions and ions which dissolve the cathode.
The high transfer resistance is favored by low current density, low temperature, polished electrode surfaces,
and high overvoltage.
Eliminating the effects of gas film resistance (as
indicated previously) and of transfer resistance, Newbery4s
data led him to interesting conclusions.
Cathodic hydrogen pvervoltage of metals apparently
18
places these metals in nine groups, corresponding to
groups one to eight of the periodic table, and under certain conditions, a group of zero overvoltage., Metals appearing in more than one overvoltage group have valences
corresponding to each group.
The overvoltage increases
in two equal steps from group zero to group two, and thereafter decreases gradually from group to group.
In explanation of these results, Newbery assumes
overvoltage, as such, to be due to the high solution pressure of compounds, or solid solutions, formed by the discharged ion within the electrode, the nature of this compound or solid solution being determined by the nature of
the electrode metal, as indicated by its position in the
periodic table.
Passivity of the metal, Newbery explains,
is due to the insolubility and high conductivity of this
compound or solid solution formed at or in the surface of
the electrode.
19
RESUME OF THEORIES OF OVERVOLTAGE
I. The dielectric-resistance theory.
Assumes overvoltage to be due to the electrical resistance of a film of gas formed at the electrode.
II. Surface tension theory.
Assumes overvoltage to be a direct function of the
surface tension of the film of gas,or of the bubble of
gasformed at the electrode.
III. Monatomic hydrogen theory.
Assumes overvoltage to be caused by the slow rate and
irreversibility of the reaction H e- H = H .
2
IV. Solid solution Theory.
Assumes the overvoltage to be due to the high solution
pressure of unstable compounds or solid solutions formed within the electrode surface by the discharged ion
and the material of the electrode.
APPARATUS
AND
METHODS OF PROCEDURE
21
Diagram of the
Dynamic Method
Fig. ( I)
1
Diagram of the
Commutator Method
Fig.(2)
Rt Lead
Cathode
THE CELL
Fig. (3)
-- MINN
Copper
Lead
Platinum
Lead
-a
Glass
Tube
Glass
Tube
Ex>osed
Meftury
Re sevoir
Asphalt
Exposed
Asphalt
'tacking
Surface
'Mercury Cathode
Construction
Fig. (5)
Usta:L. Cathode
Construction
Fig. (4)
THE METHOD.
With the purpose of confirming, or further
modifying existing theories of overvoltage, it is
pu-rposed to investigate the variation of hydrogen
overvoltage with respect to current density, and
against various cathodic materials.
For this
purpose there are to be considered two methods of
procedure, respectively, the commutator method,
and the conventional method,
which will be called
the dynamic method.
A diagram of the connections, and of the
apparatus, employed by each method is shown on
pages
(22 )
and (P I ) respectively.
The Commutator method was employed by Newbury
in the development of the theory outlined on
pages (16)
to ( 18
)
As used by him, the commutator
had a frequency of 2500 cycles per minute; that is to
say,
contact was completed through the circuit of
the applied voltage, and through the potentiometer
circuit for alternating periods of aprroximately
0.012 seconds.
By means of this system the potentio-
meter measures the difference of potential between
the cathode and the reference electrode at periods
during which no polarizing current is flowing in the
cell, for at these times the circuit of the applied
voltage is broken.
The voltage measured is due to
the back electro-motive force of the cathode, caused
by the gaseous hydrogen occluded within its surface.
Since the potentiometer is balanced against the existing difference of potential, there exists a condition
of equilibrium such that no current flows in the
cathode-reference electrode circuit.
This fact causes
the method to possess three important advantages, as
follows:
a)
It
eliminates
the effect of the presence of
gas films on the cathode surface.
If current were
flowing, the film would oppose an ohmic resistance,
and the potential drop thus caused would cause an
additive error in the measurement of the cathodic
potential.
b) It eliminates the effect of the ohmic resis-
tance of the electrolyte.
If current were flowing,
the potential drop in that portion of the electrolyte
completing the circuit between the cathode and the
reference electrode would cause an additional additive
error in the measurement.
c) It eliminates the effect of transfer
existance, as postulated by Newbery (see pagel'7).
This effect obviously is operative only when the
current flows and causes a further additive error
in the measurement.
The commutator method is based on the assumption
that the adsorbed hydrogen of the cathode does not diffuse
away during the short time of the half cycle of the
commutator, the cathodic potential thus remaining
/4
constant during that time.
The work of Le Blanc in
1910, however, seems to throw this assumption into
error of considerable magnitude.
On page (2-a
), fig.
(617), are reproductions
of
oscillograph curves of the terminal voltage of electrolytic cells, as obtained by Le Blanc.
In these curves,
portion (a) represents the voltage at that time during
which the current flows; (b) when the current ceases;
and (c) when the current reverses and flows in the
opposite direction.
An essential difference to be
noted between this and Newbery's work, is that current
is here drawn from the cell to actuate the oscillograph,
whereas, in the commutator method, no current is drawn
at the time of measurement of the cathodic potential.
"U
4Z8
Pt/I-npo, /Pt
(b)
Pt/0.05-n IKI+X1-n HSO/Pt
rig.(7)
Leblano's Oscillograph Curves
of Cell Terminal Voltage
Ordinates =Volts
Abscissae = Tiae
I
Fig. ( 6 ) is the curve obtained with a cell
consisting of 1-n sulphuric acid between platinum
electrodes at low current density.
The shape of the
curve indicates that polarization at the electrodes,
or concentration polarization has taken place.
During
the time (a), the electro-motive force increases, due
to increasing concentration of the products of electrolysis at the electrodes.
During the time (b) current
is drawn from the cell by the oscillograph.
This
current is supplied by the gaseous products of electrolysis which had accumulated at the electrodes, and
now reenter the solution.
As the concentration of
the gases in the electrode material decreases, the
voltage of the cell falls slightly.
It is the
voltage corresponding to that of the part (b) of the
curve that the commutator method measures.
In this
instance, the method would give practically correct
results.
Since the potentiometer draws no current,
the part (b) of the curve would fall off very little,
and would be approximately of the same value as at
the instant at which the current ceased; which is the
desideratum.
30
It must be observed, however, that, in this case, the
current density was low ( 0.0045 amp./ sq.cm.), and
the electrodes were of platinum.
The low current
density, and the high occlusive power of the platinum
tend to keep the concentration, and resultant pressure
bf the gaseous products of electrolysis low.
Conditions, however, are not the same at high
current density, and with electrodes of other nature
than platinum.
Under these conditions the concentration
and the resultant pressure of the gases may be comparatively large.
Indeed, in the case of metals of very
low occlusive power, such as mercury, much gas maybe
absorbed by the layer of liquid in contact with the
electrode surface, instead of by the electrode material
itself.
At high current density the violent bubbling
constantly sweeps away this saturated layer of liquid.
Due to the high gas pressures within the surface of the
electrode, and the violent bubbling at its surface,
diffusion and convection will take place, tending to
rapidly dissipate the adsorbed qas of the electrode.
Hence, at the instant the polarizing current ceases,
the electro-motive force of the cell will fall
a3'
extremely rapidly.
An analogous case is shown by
fig. ('1 ), where, though platinum electrodes were
employed, an abrupt decrease of voltage is shown.
by parts (b) of the curve.
This curve was obtained
by Le Blanc in the electrolysis of a solution of
0.05-n IPKI in 1-n H2 SO4 .
The commutator method,
applied to this, and similar, cases would give results
very much in error.
It is a fact that, whereas, at low
current densities, Newbery's results checks those of
other investigators, at high current densities, they
are of decidedly lower values.
The phenomenon considered must take place with
great rapidity.
In LeBlanc's work the length of time
represented by portion (b) of the curves is 0.019 seconds.
Newbery's commutator, having a frequency of 2500 cycles
/
minute, the length of time is 0.012 seconds.
It is thus seen that the initial assumption of the
conrmutator method, namely, that the cathodic potential
on open circuit does not decrease over a short period of
time, is false, and to a magnitude sufficient to vitiate
the value of the results obtained.
For this reason it was decided to employ the
dynamic method, particularly because it is believed that
the errors present are, or may be made, of small
magnitude, as follows:
Transition resistance, e this factor is a
recent postulate, propounded by Newbery, and still
awaiting confirmation.
Though probably present, it
is likely of small magnitude.
Ohmic resistance of a film of gas, microscopic examination has shown that the gas,
evolved at the cathode, forms, as bubbles, on minute
nuclei,
scattered at various points on the surfaceiw
It is extremely doubtful, if, under ordinary conditions
of electrolysis, that an intact film of gas forms, covering the entire surface, so as to cause the effect
attributed to it.
Ohmic resistance of the electrolyte,- at high
current densities, the reference electrode being' some
distance from the cathode, the error introduced by
this factor may be of considerable magnitude.
In
order to reduce it to a minimum, the tip of the
reference electrode is bent at an angle and closely
pressed against the surface of the cathode, as shown
on fig (p ), page (as),
In the calculaticns cognizance was
taken of the
ohmic drop existing in the conductors between the
exposed surface of the cathode,and the notentiometer
lead.
313
THE APPARATUS
AND
PROCEEDURE.
A diagramatic representation of the cell used
is shown in fig (3 ),
page (a3 ).
The electrolyte used was 2-n sulrhuric acid.
At this concentration the dissociation> of the acid is
about fifty percent, so that an aprroximately normal
solution of the hydrogen ion was 6btained.
The reference electrode was of the mercury mercuric sulphate type.
The mercuric sulphate was
added to excess, so as to saturate the 2-n sulphuric
acid of the electrode.
The solution of the electrode
was of the same acid concentration as that of the
cell so as to avoid concentration difficulties.
It
was found that the value of the reference electrode of
this type with respect to a normal hydrogen reference
electrode was very closely
0.670 volts.
That is
to say, in order to obtain the cathodic potential on
the hydrogen scale, readings with respect to the
mercury-mercuric sulphate electrode must be decreased
by 0.670 volts.
The anode consisted of sheet platinum.
compartment, as shown in fig (3 ),
The anode
was separated from
3 -1
.that of the cathode by a tube, about two centimeters
in diameter, plugged with glass wool, so that oxygen,
evolved at the anode, might not find its way to the
cathode, there to exert a depolarizing effect.
The cathode consisted of one of the substances
against which it was desired to measure the hydrogen
overvoltage.
It was built up with a definite exposed
area, usually of one square centimeter, and save where
a crystalline surface was desired, was carefully
polished to smoothness, finishing up with 0000 emery
paper.
It was found most convenient to build upr the
cathode in the form shown in fig (4
),
page (e-t).
To this effect a heavy copper lead was soldered to, or
tightly,wrapped around a projecting portion of the
sample, a glass tube was slipped over the lead, and
the joint sealed tight with asphalt of grade twelve.
The asphalt was applied by heating a portion in the
flame to incipent fusion, and then rubbing on the
joint, smoothing with the flame, or a heated glass rod.
When using mercury as the cathode, however, the
electrode was built up in the form shown in fig (5
A Ilatinum wire, dipping into the mercury, served as
the lead.
).
It was always endeavored to so place the electrode,
that, the lines of current flow in the electrolyte were
of uniform density, and at right angle to the surface
of the electrode.
To this end the tip of the reference
electrode was placed in contact with the cathode surface
in an extreme upper corner, and the exposed cathode
surface was placed opposite the opening from the anode
chamber, at right angles to the line of current flow.
In the case of the mercury electrode, however, the same
-effect was attained, by immersing the electrode vessel
deeply in the cathode apartment.
Voltage was applied to the cell by means of a
twenty volt drop wire.
In series with the cell there
was connected a; variable high resistance, so as to give
stability to the electrical system.
A milliammeter,
scaled to 0.1 of a milliampere was used to measure
small currents, and an ammeter, scaled to 0.01 of an
ampere to measure large currents.
A Leeds and Northrup
potentiometer, in connection with a Weston standard
cell, was employed to measure the cathode potential.
When it was deemed necessary, as with platinized
platinum, smooth platinum, and palladuim, to aid in the
saturation of the cathode material with hydrogen, this
36
gas was bubbled through the electrolyte, over the
cathode surface, the cathode conpartment being covered,
so as to put the electrolyte under a hydrogen pressure
of an atmosphere.
In all cases, for the same purpose,
a small current, of about 0.2 of a milliampere, was passed
before the run,
for some time, until numerous small
bubbles of hydrogen were evident on the cathode surface.
At high current densities Newbery had found that the
overvoltage falls off, instead of increasing, with increasing current density.
In explanation he offered a
rather complex postulate.
Namely, he attributed the
fall of overvoltage to the inductive effect of escaping
electrically charged gas, though no explanation was given,
in electrical terms, as to the manner in which the effect
is accomplished.
It appears, however, that there exists
a simpler explanation, far more tenable; that is, the
temperature effect.
At current densities of the magnitude
of one ampere per square centimeter, the overvoltage is
usually of the order of a volt.
Since overvoltage is an
irreversible effect the energy it represents must be
dissipated as heat at the surface of the cathode.
At an
area of one square centimeter, there must therefore be
evolved heat energy of the magnitude of a Watt.
This is
a very large amount of heat to be dissipated in such a
small area, and it must cause a comparatively large
increase of temperature at the metal-liquid junction.
An increase of temperature of any considerable magnitude
tends to decidedly decrease the overvoltage.
Since, at
high current density, the overvoltage-current density
curve is very flat, normally increasing but slightly
with increase of current, a decrease of even small
magnitude, caused by the rise in temperature, would
actually cause the curve to fall off.
In the runs a
thermostadt was employed, which, though decreasing the
effect referred to, was found powerless to eliminate it
cempletely.
This is because the temperature rise, due
to the overvoltage, is.extremely
localized, and not
very subject to the influence of the thermostadt.
At low current densities, the current was increased
and readings taken every minute, the lapse of time being
allowed to permit the overvoltage to attain a condition
of approximate equilibrium.
But at current densities
exceeding fifty milliamperes per square centimeter the
adjustments and readings were made as rapidly as possible
(akout every half minute), since the time effect, though
38
present, is greatly overbalanced by the temperature effect
mentioned above.
During a preliminary run against palladium, a black
deposit was observed forming on the surface of the electrode.
The deposit completely covered the surface, was easily
rubbed off, and rapidly dissappeared on exposure to the
air, leaving the surface in its original polished condition.
The deposit is probably a hydride of palladium, which is
oxidized on exposure to the atmosphere.
The data, and the
curves,,are for values obtained against this black deposit.
.
On polishing a sample, the surface is reduced to an
amorphous condition.
In the case of tellurium and of a
duplicate specimen of tin a crystalline surface was obtained by a fresh fracture in the firsV case, and, in the
latter,
by annealing the polished sample at a high temperature.
At high values of current density the deposited
hydrogen vigorously attacked the tellurium, forming hydrogenated tellurium.
The surface of the sample being eaten
away, the reference electrode was no longer in contact
with it.
The ohmic drop of the electrolyte thus caused an
additive error in the readings, and, for this reason, the
curve of the results, given later on,is shown as a dotted
line.
39
THE
THEORY
Room 14-0551
M
ibraries
Document Services
77 Massachusetts Avenue
Cambridge, MA 02139
Ph: 617.253.2800
Email: docs@mit.edu
http://libraries.mit.edu/docs
DISCLAIMER
Page has been ommitted due to a pagination error
by the author.
. - --
I.
THEORY.
The monatomic theory of overvoltage (see page /I )
ascribes the deviation of the overvoltage from a
logarithmic function of the current density to the
influence of several factors, such as catalytic influences; time effect; temperature effect; deviation
of gases from the perfect gas laws, when occluded in the
metal of the electrode; specific effects of the nature
of the electrode surface, such as transition resistance;
etc.
Believing the catalytic influences to be of pre-
dominating importance, Dr. Knobel,
under whose super-
vision this thesis was accomplished, applied its effect
to the mathematical analysis of the phenomenon.
Let the following symbols have the indicated meaning.
n - 2; being the numerical coefficient of the
left hand side of the equation 2 H = H
2
; the specific reaction rate of the equation
H = H
2 2H=H
2
t
; time in seconds.
p
; pressure in atmospheres, the subscript
indicating of what gas.
I
; current in amperes.
R
; the universal gas constant, being equal
to 8.32 joules per degree
T
; temperature in degrees absolute.
'I
42
;value of the Faraday in coulombs,
F
being equal to 96500
C,
; concentration of the hydrogen ion in
the electrolyte.
E
; Overvoltage
kg
; a constant
K5
; specific reaction rate of the reaction
H2 = 2H
On assumption of the monatomic hydrogen theory,
and in accordance with the law of mass action as applied
to the reaction rate,
-
dPHtn
dPH- = kiPH
1 PH
d t
Furthermore, due to the liberation of atomic hydrogen
by electrolysis,
dPH
dt
where k 2 is a constant.
At equilibrium, at any point during electrolysis,
k PHI2 = k 2 r
P 2
H,
3
where k
3
= k
.L
ki
43
In accordance with Nernst's formula,
E
RT
F
in
P
1
where k, is a constant such that
k0.
- RT
F
I
E
RT
F
ln
E
RT
2F
in
E =
8.32 x 298 x 2.303
96500
2
x
where k4
I .RT
2F
in (k C ,)
ln k3 -_RT
F
-AT. ln k
2F
3
-
= PH
ln (klC ,)
log It k,
RT in
-
(tLC
E = 0.0297 log I -t-k4
When E is zero, I is not zero, bnt is a very small
quantity, provided kg is large.
According to the mona-
tomic hydrogen theory, the overvoltage should be zero when
the current is zero.
The discrepancy may be traced to
the neglect of the back reaction, H 2 = 2 H.
Assuming this reaction to take place, then,
reasoning as before,
- d P1
k1 Pj
P
1
2
d t
k2 1
-k
= k1 Pif1
2
- k5
i2
44
2
P
k3 I +k 6
where k
6
E
E
RT
F
ln
= k
P
5
2
k3 It k6 - RT
3.F
0.0297 log (I+k7 )t RT
2F
in (k C
)
in k3 - RT iln (k/C1.)
F
where k7 = k6
E
0.0297 log (Ii1-7 ) t k
4
By definition, k4
k4
.00297 log kc
2
.0297 log k3 - R
F
ln (k C
(a constant)
ik2 is invariable; k1 is larger,the
larger the catalytic rower of the
metal.
Thus k4 is smaller, the
larger the catalytic power of the
metal.
From the equation involving
E, k7 , and k , it is evident that k7
is larger, the larger the catalytic
power of the cathode.
)
At very low current densities, the monatomic
hydrogen, liberated in small amounts, is all adsorbed
by the cathode material, and in the reaction 2H = H 2
is practically completely subjected to the catalytic
influence of the cathode.
This catalytic influence
is constant, and the quantities k
and k
7
invariable.
remain
4
Then, in the equation E - 0.0297 log
(I-k7 )-fk4 ,' since k 7 is very small, the derivative
of E with respect to log I will be a constant of
value 0.0297.
As the current density increases, the amount of
monatomic hydrogen liberated increases.
it is postulated
that the cathode material is not capable of completely
adsorbing and catalysing the increasing amcunts of
the gas liberated, and that the layer of liquid, in
immediate juxtaposition with the cathode enters into
the reaction to aid in that capacity.
Since the catalytic
power of the liquid is not the same as that of the
cathode material, the total effective catalytic influence changes continuously in value, and thus the
values of k7 and h
undergo a continuous change.
At the
46
referred to in the derivation
same time the quantity k
as invariable, no longer remains constant, but the
effect of its change may be thrown over into k7 and
k4 .
Since k7 and k4 are no longer constant, under the
conditions referred to, the derivative of the curve with
respect to log I will cease to be a constant, but will
deviate smoothly from a constant value.
As the current density increases to high values,
however, the part played by the absorbtion and catalytic
powers of the liquid becomes of predominating influence,
the cathode then serving, for the most part, merely as
a conductor, to relieve the ions of their charge.
The
catalytic power of the liquid being constant, the
quantities k7 and k4 approach constancy at high current
densities.
Once more the derivative of the overvoltage
with respect to log I approaches the constant 0.0297.
It is thus to be expected that the curve of over-
voltage plotted against log I will, at low current
densities, deviate from a straight line of slope 0.0297,
and again approach a straight line, of the same slope,
at high current density,
the slope for intermediate
current densities being of a continuously varying value,
always greater than 0.0297.
At very high current densities, it is postulated
that the pressure of the occluded monatomic hydrogen
approaches a value of one atmosphere.
At zero over-
voltage, under conditions of equilibrium, i.e., at
the decomposition cathodic potential, the current
density being zero, the monatomic hydrogen is occluded
at a pressure corresponding to its equilibrium pressure
with the molecular gas existing at a pressure of one
atmosphere; it being understood that the cathodic compartment is under a hydrogen atmosphere of one atmosphere during the electrolysis.
The maximum overvoltage,
approached with increase
of current density, then represents the electro-motive
force necessary to cause an increase of the monatomic
hydrogen pressure from its equilibrium value to that of
one atmosphere.
The change of pressure of the gas
represents a change in the free energy of the system.
Let-AF be the change of free energy represented
by the reaction of two moles of monatomic hydrogen at
one atmosphere pressure to one mole of the molecular
gas at one atmosphere pressure; Emar. be the value of the
maximum overvoltage in volts; and Q be the amount of
electricity in coulombs, passed to liberate two moles
of the monatomic gas.
Assuming the reaction to be
isothermal and reversible, the following equation holds
true, -
A F
= Q Emam.
The average of the value of the free energy,
A
F;
as ascribed by various investigators, such as
Langmuir, Keys , Lewis, and Bohr, is about 67000
calories.
Q is equal to two faradays.
Hence we have, -
Ema
67 000 x 4.2
2 x 96500
1.46 volts
where 4.2 is a factor for the
conversion of calories to joules.
Due to the large differences in the magnitude ascribed
by different investigators to the value of the free
energy change, the value obtained for the maximum overvoltage is open to wide variations.
If the overvoltage
should finally reach its maximum value, the curve,
in accordance with the proposed postulates of the
preceeding derivation, would lose its logarithmic
character, becoming a straight horizontal line.
Summarizing the substance of the preceeding discussion, we obtain the following:Overvoltage is, in effect, a logarithmic function
of the current density.
It departs from a strict logarithmic relation in a
I.
zzz
-
40
fashion such that when plotted against log I,itdeviates
from a straight line of slope 0.0297 at low current
density, and again approaches a straight line of the
same slope at high current density.
At high current densities the overvoltage approaches,
as a limit, a value in the neighborhood of 1.46 volts.
The preceeding statements are independent of the
nature of the electrode under usual circumstances.
RESULTS AND CONCLUSIONS
DATA
OVERVOLTAGE CURVES
AGAINST CURRENT DENSITY
OVERVOLTAGE CURVES
AGAINST LOG.OF
CURRENT DENSITY
DISCUSSION
DATA
I
V
Fe
Chem
electrolyte Metal
OVERVQLAGE
Milli
Log
Milli
Amps.
Amps.
Sn
Sn'
amorph. oryst.
v
Brass
Monel
Metal
Duri-
ron
4
I
.1680
0
-00
.2411
.2704
.2026
.2824
.1
-1..0
.3995
. 5340
. 2183
.3160
.3832
1911
.1710
1
0.0
.8561
.6791
.4036
.6592
.4967
.2754
.1970
2
.3010
.9469
. 7020
.4474
.7249
.5346
.3022
.2136
5
.6990
1.0258
.7515
.5024
.'885
.5960
.3387
.2443
10
1.0
1.0767
.8258
.5571
.8349
.6459
.3832
.2856
50
1.6990
1.1851
.9270
.7000
.9322
.8011
.5345
.5096
100
2.0
1.2230
.9614
.8184
.9696
.9104
.6244
.6129
200
2.3010
1.2342
.9806
.9854
.9989 1.1088
.7108
.7240
500
2.6990
1.2380 1.0031
1.2561
1.0407 1.2318
.8619
.8591
1000
3..0
1.2306 1.0091
1.2915
1.0682 1.2544' 1.0716
1.0205
1500
3.1761
1.2286 1.0186
1.2908
1.0859 1.2491 1.2095
1.1400
k-1
I
V
OVERVOLTAGE
Au.
Milli
Amps.
0
Log
Milli
Ams
Cd
0
Cu
.466
.1
1.0
a,22
.651
.351
1
0.0
.241
.981
.479
2
.3010
5
.6990
.332 1.086
10
1.0
.390 1.134
50
1.6990 .507
1.211
100
2.0
.588
1.216
200
2.3010 .668
1.228
500
2.6990 .770
1000
3.0
1500
3.1761 .807
v
Al
Graphite
Ag
Pt
smooth
Pt
platinized
-
0.000
-
.0034
.499
.3166
.2981
, .0154
.565
.5995
.4751
.024
.0022
.034
.0208
.625
.6520
.5787
.548
.051
.0272
.745
.7250
.6922
.584
.068
.0300
.826
.7788
.7618
.186
.0376
.968
.9032
.8300
.801
.288
.0405
.996
.9774
.8749
.988
.355
.0420
1.176
1.0794
.9379
1.246 1. 186
.573
.0448
1.237
1.1710
1.0300
.798 1.254 1.254
.676
.0483
1.286
1.2200
1.0890
.768
.0495
1.292
1.2208
1.0841
1.257 1.269
\31
(A'
I
v
Milliamp
Log
Milliamp
Milli-
Hg
0V.
amp
II
Log
Millia
amp
Tellurk
ium
Ov .
Milliamp
41
0.00
v
Palladium OV.
-00
.2805
0.00
.5562
.416-0.3809
.0504
.227
0.114
.8488
.832-0.0799
.3505
1.135
.0550
.1392
1.54
.1875
.9295 14667 ..2219
.4162
2.27
.3560
.1820
3.87
.5877
1.0060 4.16
.6191
.4405
4.54
.6571
.2349
7.69
0.8859
1.0361 8.32
.9201
.4530
11.35
1.0550
.3165
38. 7
1. 5877
1.0634 41.6
1.619
.4705
22.7
1.3560
.4034
76.9
1.8859
1.0665 83.2
1.9201
.4733
L13.5
2.0550
.7205
154
2.1875
1.0751 166.7
2.222
.4986
227
2.3560
.8607
387
2.5877
1.1053
416
2.619
.5370
454
2.6571
.9521
769
2.886
1.108
832
2.9201
.5940
1135
3.0550
1.0513
3.0618
1.126
1250
3.0969
.6590
2270
3.3560
1.1168
3400
3.5315
1.1570
-00
0.00
.0769 -1.114
" .769
1153
-
-00
Log
Milliamp
-0.8440
.0546
-
m
-
-
CURVES OF OVERVOLTAGE
AGAINST CURRENT DENSITY
On these curves the
average value oftF
is taken as 67000 cal..
Bohr's value is 61000 cal..
..
.
...
.-
Volts
|
p
I.p
I
1.6
v}
i
ii
-
-------
-
-
1
-
_-
-
-
H-
H
-i
__
{
1.4
"T
1.2
- I -t
1.0
- -
- --
r-
0.8
p4
0.6
*TN*
0.4
-T
T2I
-,H
0.2
Am
AS
t
T
.C2
T"*
0.0
0.1
0.2
0.3
0.4
0.6
0>6
0.7
0.8
C0.9i
1,
1. 1
1.2
1.3
1.4
Amp./Sq.Cm.
1.5
Volts
1.6
1.4
1.2
1.0
0.8
0.4
0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Amp/Sq.Cm.
1.3
1.4
1.5
-
~
24'
~
$I4
iI
IL-4
-
1.6
o 1.4
44
F-[
141
-
-
IL-
1.2
~
1.
V
-F
t",Li
j~r~
_
-Ie-el
e-h
-T
0.8
0.6
0.4
=77
0.2
7~
_
I-,
4
A
~
tt__
__
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.09
1.0
1.1
Amp/Sq .Cm.
1.2
1.3
1.4
1.5
1
6
1.4
0.8
--
0.
I4ItI.J~i= II
-rrard
-
-
--1 -
-
0 .2P-0.6r
0.2
0.1
0.2
0.3
0.4
0-.5
0.6
0.7
0.8
0.9
1.0
1.1 1.2 1.3
Am~p./Sq .Cm.
1.4
1.5
3
H - 1
IT - -
-
-+- -- --
t
- - --
-I--
t
-
-- ,
4--
-
-
1.6
rA
1.4-
Caa
Ye
t ef
11 on
Bn
0
----
1.2
r
1.0
4
-
-t
_
2*
ii..
-r
t
0.8
*
I,
-t
-
L
0.4
VITj
4t~I
I2Tf
0.2
-1-R IFi_EH
It
~JiIj7 §tI
'4.
iZl=f t
14
R
0.2
0.4
0.6
0.6
41-L,
114
17 if
0.3
4Y
4 ~ Th ~f4i~ThTh~T2~4f
0.0
0.1
4___4_
1--
0.7
C_.8
I~i
C.2 1.(0
1
1.2
peres
1.3
.
per Sq.Cm.
-I
-=Now
6/
CURVES OF OVERVOLTAGE AGAINST
THE LOGARITHM OF CURRENT DENSITY
t
r-:-
FL
f , 11
I
''
c
1
I
|771
'4-
2
2
Volts
--
-
-
--
-ii---
---
j
-
1.4
-I-1.2
e4
-
1.0
0.8
------
LL
+. C.j.is
+4...it...>
0.4
-
.:
0.2
A
0.0
0.2
J~
4iI
0.4
0.6
0.8
1.0
1171 17]
1.2
1.4
ift
1.6
1.8
2.0
-I- -~-,-~-~ted-
I
2.2 2.4 2.6
2.8
3.0
Log.of Amp./Sa.Cm.
3.2
FIV
a-~
7~ _
~-
_ii7~
4
Volts
1,6
-
- I
4
-- r - - --- - - - --
1.4
1.2
-b-
-
i
1.0
0.8
0.6
r
0.4
**~0
c
-
S
aW
*DHO.
_
0.2
00
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.8
2.2 2.4 2.6
Log.of Amp./Sa.Cm.
3.0
3.2
-
,
-
,
-
~-.4
. -
-.
~}~tt~4'
'1
itt
-
4
TI *1
;
-.-
7+
th ~±fi~'I
"~1~.1
I
-I
--
4
7
-n
----
4---4
Volts
( very
Zv c l gE
1. 6
gI.gadr
-
.-
Log i.l
+ -4
+ -
-- ~----4-----
-4--4-
172 ii iii
I
_______________
-4-
~'~Ti Y24
P7
'47
4
1
I
K
1.4
a Mf
1.2
f-
--
-1
1.0
Uk 6"Q&
~--
-i Rg.
.
-I-
--I
I-
0.4
-17
-
I-rLL0.2
I-~
'1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1-~4
1.4
-1,
V
-I-
t-Th~
1.6
1.8
2.0
2.2
2.4
2.6
2.&
3.0
3.2
Log.of Amu./Sq.Cri.
44
-I.,
~1i74i~t
I-
I
IK'KJ
Volts
-tj
1.6
It
i4~ti~
II
H-
-U
V
-
I,
t
i
1
LKi
-- I---
I
-~-1-
1.4
-,
7>4,>
-j
-t
4 f
I-
I-4
i -I-
Cv r cIta
4
1.2
FT7
'LaRpst
-I
1.0
______
4I~~-
0 .8
I
A
ii.'
-I-----
-~
-II
I
1
L4~~
ii
I
___
4
0.6
-
0.4
----
- ----
-4--
-V
-
111 ~wm
- -4-
L.mAti~±
I
0.2
-'-if
±
0.2
0.4
4
I-
±
0.0
T_
0.6
0.8
1.0
____
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.
3.0
Log.of Amp./Sq.Cw.
3.2
66
THE RESULTS.
The data obtained, showing the variation of
overvoltage with respect to current density, is given
graphically on the preceeding pages (pagesSa-'4.
The form of the curves is very satisfactory.
exceeds the calculated maximum.
approaching it.
No curve
Many are apparently
Were Bohr's value (61,000 calories)
for the free energy, A F, used, instead of an average
value (67,000 calories), the calculated maximum overvoltage would be 1.33 volts.
This would be a still
more satisfactory limit for the curves obtained.
It
may be expected that at very high current densities, if
other effects (such as the temiperature effect, ect.)
do not interfere, that the tendency of all the curves to
approach the calculated maximum would become very evident.
The curve of the overvoltage with resrect to log.
I are plotted on pages(a-rf).
Points corresponding to
values of current less than one milliampere are not
Plotted, because, in addition to the enormous rate at
which the logarithm varies, the variation of overvoltage
with respect to current density, in this range, is so
rapid that the milliammeter was very far from being of a
-
~
..
-~
67
datisfactory sensitivity or accuracy.
The curves are of
great interest, because, as predicted, they are apparently
deviating from a straight line at low current density,
and approach a straight line at high current density.
Because of the limited range of the curves, it is not
certain whether the ,slope approached are actually of the
calculated value, that is, 0.0297.
The curve obtained with platinized platinum is,
however, an exception, in that it is practically a straight
line throughout.
Apparently the capacity of this cathode
for the adsorbtion, catalysis, and evolution of gas is
so great that the changes in catalytic power, causing the
deviation of the curve from a logarithmic form, do not
take place, the curve remaining very nearly a true
logarithmic function.
Moreover, it is a noticeable fact,
that the slope of the platinized platinum derivative is
only about one half of the calculated value.
46
THE CONCLUSION.
Consideration of the results leads to the
conclusion that, though very satisfactory, a further
extension of the investigation is necessary to make
them
definitely conclusive.
Further mathematical analysis of the theory is
required to explain the low value of the slope obtained
for the overvoltage curve of platinized platinum with
respect to log I.
It would also be desirable to further extend the
range of the data, and of the curves, with the end in
view of obtaining more definite information as to the
existance and the value of the limit approached by
-
a) The overvoltage curves
b) The slope of the overvoltage curves with
respect to log. I.
At low current densities, to attain this end, it
will be found necessary to employ a very sensitive and
accurate milliammeter, for reasons already indicated.
It would also be desirable to evolve a method to more
definitely saturate the cathode material with the gas,
since it is believed that failure to achieve saturation
at low current densities was a factor of consequence
in the results.
At high current density, to further extend the
range, secondary effects, such as the temperature
effect, must be combatted.
It is believed that the
magnitude of the temperature effect may be very
successfully diminished, without introducing any undesirable effects, by causing the electrolyte to have
a positive circulation, continually sweeping the electrode
surface with a cooling stream.
70
REFERENCES
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Haber & Russ
2. Moller
Zt. Electrochem.
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J.A.C.S.
Maclnnes & Con tieri
Nernst
539,
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4.
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Unpublished.Thesis
M.I.T.
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"
"
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Newbery
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12.
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Die Elektromotorischen
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