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The design and development of a condenser for determining dielectric comstants of conducting solutions

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THE DESIGN AND DEVELOPMENT OF A CONDENSER
FOR DETERMINING DIELECTRIC CONSTANTS
OF CONDUCTING SOLUTIONS
A Thesis
presented to
the Faculty of the Department of Chemistry
The University of Southern California
In Partial Fulfillment
of the Requirements for the Degree
Master of Science in Chemistry
by
Elbert D. Bostrom
January
1941
UMI Number: EP41527
All rights reserved
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T h is thesis, w r it t e n by
......... . E L B E M . . D M K E . . M 3T R 0M .........
u n d e r the d i r e c t i o n o f h%$.. F a c u l t y C o m m it te e ,
a n d a p p r o v e d b y a l l its m e m b e r s , has been
presented to a n d accepted by the C o u n c i l on
G ra d u a t e S t u d y a n d Research in p a r t i a l f u l f i l l ­
m e n t o f the r e q u ir e m e n ts f o r the degree o f
MASTER OP SCIENCE
ecretary
F acu lty Com m ittee
..
V
C hairm an
TABLE OF CONTENTS
i
CHAPTER
PAGE
INTROD U CTION............. ..
I.
THE INSULATED CONDENSER
Circuit
. . . -.
. . . . . .
. .............
III.
.........
1
1
. . . . .
1
Calibration of experimental condensers . . .
4
M e a s u r e m e n t s ................................
5
THE ELECTROLYTIC L E A K ...................
DISCUSSION OF RESULTS ' . .
.................
Use of insulated condenser . . .
IV.
iii
. . . . . . . . . .
Experimental condenser ...........
II.
.
26
32
.........
32
Current compensation experiments * .........
32
Further problems . . . . . . . . . . . . . .
35
SUMMARY OF R E S U L T S ............................
B I B L I O G RAPHY.....................
37
38
INTRODUCTION
Dielectric constants are useful in the study of the
structure of matter.
Although the subject is not a new.one,
it has received the attention of numerous investigators and
considerable progress has been made within the last twenty
years.
One of the most interesting problems as well as the
most difficult is the determination of the dielectric con­
stant of conducting solutions.
There have been many methods
devised for studying conducting solutions and there have
been many results.
Whereas the results of some investi­
gators have shown an increase in the dielectric constant of
salt solutions over that of pure water, others have found an
initial decrease and then a rise up to the strongest sqlution
that could be measured with their apparatus.
The latter re­
sult agrees with the mathematical theory advanced by DeBye
and Falkenhagen.^
The purpose of this thesis has been to study some of
the experimental difficulties attendant to the determination
of the dielectric constants of conducting solutions, and to
see if the initial dip could be obtained as predicted by the
DeBye theory.
A study was also made concerning the feasibility of
1 Physik. Z., 29, 401 {1928).
coating the metal parts of an experimental condenser with
insulating materials such as glass or hard rubber in order
that the dielectric constants of materials which might react
with metal surfaces could be studied.
Throughout the experiments emphasis was placed upon the
apparatus and its design rather than the gathering of actual
dielectric constants, as the accurate measurements of con­
stants was regarded as beyond the scope of this thesis.
-
CHAPTER I
THE INSULATED CONDENSER'
I. . CIRCUIT
The circuit used was the resonance "current tuning"
type.
It consisted of a crystal-controlled oscillator func­
tioning at twelve hundred kilocycles, a receiving circuit
containing a General Radio type 722-B precision condenser,
and a detector circuit read by means of an ordinary tenmilliampere meter (Pig. 1).
The advantages of a resonance
circuit lie not only in its simplicity, but also in the ac­
cessibility of the experimental condenser, and the ease with
which this part of the apparatus may be connected in or out
of the circuit.
II.
EXPERIMENTAL CONDENSER
The experimental condenser consisted of an outer brass
cylinder, one inch in diameter and four inches long with the
bottom narrowed down and connected to a pet-cock which
drained the condenser (Pig. 2).
The inner electrodes were
brass rods four inches long, with diameters ranging from 1/8
to 1/2 inch.
For each inner electrode there was a series of
1 Rev. Sci. Inst., II (No. 3), 105 (1940).
2
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tightly fitting rubber sheaths.
Each sheath had a different
wall thickness from all others in a series.
The brass rods
were bolted to a hard rubber cap, which fitted tightly over
the outer cylinder.
This cap. was drilled to admit liquid,
and' the height of the liquid in the condenser was read by
means of a glass side.arm, fitted in the outer cylinder near
its top.
To avoid errors due to capillary effects, a large
bulb was blown in the glass side arm, and the liquid brought
up to the mark on the bulb.
The connecting wire to the pre­
cision condenser was held in place between nuts that screwed
to the upper end of the inner electrode which extended
through the hard rubber cap.. A joint was made in this wire
about two inches away from the inner electrode so that con­
nections between the condenser and the circuit could easily
be made with the minimum capacity change.
of the condenser was permanently grounded.
The outer cylinder
The temperature
of the experimental condenser was thermostatically controlled
at 25° C . ± 0.1°.
With such a design many different capacitances could
be established with minimum effort.
The A C vs. dielectric
constant curves, for high and low capacitances containing
insulating sheaths, could be compared.
III. CALIBRATION OF EXPERIMENTAL CONDENSERS
Ordinary condensers give linear functions of the
5
replaceable capacitance.
This is not the case with condensers
containing insulating material.
In order to construct A C
vs. dielectric constant curves for the various condensers,
solutions having known dielectric constants were made up from
dioxane and water.
This was made possible, by the previous
2
work of Akerloff and Short.
Throughout this work commercial
dioxane, and commercial distilled water, were used without
further purification.
IV. MEASUREMENTS
Measurements were made as follows.
When the circuit
had warmed up for several hours, and the water bath was func­
tioning properly at 25° 0., the condenser was assembled by
inserting the desired core with or without a hard rubber
sheath of known thickness.
The resonance curves were taken
in the customary manner, by selecting’ successive settings on
the milliampere meter dial and reading the setting of the
precision condenser.
Both the maximum current when the cir­
cuit was sharply tuned, and the minimum current with the cir­
cuit detuned, were recorded.
Resonance curves were obtained from all possible con­
denser combinations, as listed in Table I, for air, for water,
and for a 60 per cent by weight solution of dioxane in water.
2 J. Am. Ohem. Soc., 58, 1242 (1936).
6
TABLE I
Core Diameter
1/2"
Thickness of Hard Rubber Sheaths
.034"
3/S"
1/4"
.033"
1/8"
.042"
.060"
.042"
.061"
.040"
.062"
.042"
.081"
The tuning curves are shown in Figures 3a to 3e.
In every
case the precision condenser reading has teen plotted
against the corresponding millammeter reading.
The position
of the maximum point of each curve was calculated by averag­
ing several pairs of points on the opposite sides of the
curve.
Examination of the tuning curves showed that the
higher the capacity of a given experimental condenser, the
greater the damping for any given solution, and that the
thicker the hard rubber sheath the less the damping.
This
' is illustrated for the one-half inch core in Table II.
In
general as the cores became smaller, the maximum currents
became higher...
It was also noted that the anti-damping
effect of the hard rubber sheaths tapered off with increas­
ing thickness of the sheaths.
It is easy to see that con­
densers of high capacity would cause more damping in the
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TABLE I I
Sheath
Water
Maximum Current
60$ Dioxane
.034”
6.5
5.9
.042”
6.9
• 6.5
.060”
7.05
6.7
indicator circuit tlian those of low capacity, "because the
conductivity would be greater#
The anti-damping effect of
the hard rubber sheaths will be discussed later.
In Figure 4, the capacity vs. dielectric constant
curves are shown.
The ideal curve would be a straight line,
such as is obtained from non-insulated condensers.
Otherwise
the curve must be steep enough at all points so that it may
be readily used.
Figure 5 shows the difference in capacity,
when the dielectric constant varies from 26.9 to 78.7, for
various condensers having a given thickness of hard rubber.
It is greatest for the 3/8 inch core.
One can see that this
superiority would not hold for the bare cores.
However, it
was not determined by experiment at what thickness of hard
rubber the 1/2 inch core would overtake the 3/8 inch core in
relative positions as shown by Figure 5.
From Figure 6 it is seen that for the given thicknesses
of hard rubber on the metal cores, the greatest total
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difference in capacity will be for the condenser having the
largest original capacity.
If the hard rubber were of such
thickness as to occupy all of the available-space in one con­
denser,- that condenser would have no change in capacity.
It must also be remembered, as previously mentioned,
that the larger the metal core is, the more damping takes
place in the indicator circuit, and for a •given thickness of
hard rubber on any of the cores, the larger the core the more
damping will take place (Fig. 7).
Due to the above considerations it seemed advisable to
continue further experiments using the 3/8 inch core.
Thus
two new rubber sheaths of .020" and .010" thickness were made
carefully to fit the 3/8 inch core.
obtained for each case.
Calibration curves were
The results obtained using the .010"
sheath seemed at first quite remarkable.
curve came very close to being linear.
The calibration
Its capacity increase
was 172 units as compared with 66 units for the .020” sheath.
Later the .010” sheath had to be discarded, as small holes
were detected in it.
To test further the .020,” 'hard rubber
sheath a series of water-dioxane solutions were made up for
use in obtaining a more completely calibrated curve.
Instead
of the usual three points there were eight (Fig. 8 ).
To examine the effect of introducing a strongly con­
ducting solution into an insulated condenser, a .001 normal
solution of potassium chloride was put into the condenser and
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the circuit balanced.
It was found that the circuit could be
easily balanced, i.e., the indicator circuit did not com­
pletely damp out as would occur with uninsulated metal plates.
The capacity read would not fit on the calibrated curve, if
3
G-rubb and Hunt's value for the dielectric constant of .001H
potassium chloride were accepted.
Therefore, though sheath­
ing the metal cores with hard rubber increased the current
maximum in the indicator circuit such a device did not make
it possible to determine dielectric constants of strongly
conducting solutions.
In order to secure a more complete idea as to the be­
havior of the experimental condensers containing strongly
conducting solutions, tests were run on potassium chloride
solutions of the following concentrations:
saturated, one
normal, one-tenth normal, one-hundredth normal, and .001
normal.
It will be seen from figure 9 that the heights of
the resonance curves depended upon the conductivity of the
salt solution, and the thickness of the hard rubber sheath.
To explain the rather odd behavior, such that onetenth normal and stronger solutions gave high and sharp res­
onance curves, whereas the one-thousandth normal salt solu­
tion gave a low flat resonance curve, it was necessary to
3 J. Am. Chem. Soc., 61, 565 (1939)
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H E A D IN G OF PRECISION C O N D E N S E R
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21
assume that the rubber sheaths caused the experimental con­
denser to act as though there were two condensers in series.
Then one condenser, which in this case is the one formed by
the two surfaces of the hard rubber sheath, would function
without leakage.
The other condenser would have various
degrees of leakage, depending upon the conductivity of the
solution in it.
On such a basis it is seen that with highly
conducting solutions, such as tenth-normal or stronger, that
the resonance curve obtained would be only for the hard rub­
ber sheath acting as a condenser, whereas for a solution of
.001 normal potassium chloride, the current in the indicator
circuit would be damped, due to the effect of a leaky, but
not completely ineffective, condenser in the circuit.
To test the above assumption the circuit was altered
in many ways.
First of all, a five hundred m m f . condenser
was connected into the circuit as shown in Figure 10.
Figure 10
22
This circuit was found unsatisfactory as damping was too pro­
nounced for the various solutions.
An increase in the capa­
city of the fixed condenser produced greater damping.
Accord­
ingly the five hundred mmf. condenser was replaced-by a fifty
mmf. condenser.
It now was possible to obtain readings, not
only on water and dioxane solutions, but also on a .01 normal
potassium chloride solution.
The results are shown in
Figure 11.
Second, commercial inductance-free carbon resistances
were connected across the experimental condenser to cause
leakage, as shown in Figure 12.
Figure 12
Here it was noted that from very high resistances allowing
practically no leakage, the ohmic resistance could be re­
duced to a point such that maximum damping occurred, and
then if the resistance were further reduced the current in
the indicator circuit began to increase.
This behavior was
like that of salt solutions in the insulated condensers.
No
o .01 N K C t
W a t e r
#2
P /£ L £ C V R / C
UNITS
ty
t J G . li
24
change was obtained by using the carbon resistance, other
than that already mentioned.
When the insulated condensers were mathematically
treated as two condensers in series, close agreement was ob
tained between the calculated and experimental values of AC
for water and 60$ dioxane as shown in Table III.
• TABLE III
'Water
Experimental Calculated
60$ Dioxane
Experimental Calculated
Core
Sheath
1/2 "
.034"
83.0
82.1
64.7
60.1
1/ 2 "
.042"
66.5
64.9
53.7
53.1
1/2 ”
.060"
50.5
46.9
43.6
40.6
3/8"
.020"
66.0
63.9
48.5
48.0
To treat an insulated condenser as two condensers in
series, the following method was employed.
The measurements
of the space available for the liquid was substituted into
the equation:
Cx - IL*..i!.
2 'lnr,
rA
Then the experimental value of the capacity of the sheaths
obtained from the measurements on saturated solutions of
potassium chloride was used, instead of calculating the capa­
city.
This gave two capacities which were combined according
25
to the series law—
Example:
i = i + i
C
°1
2
1/2” core and .034” sheath.
c sheath -691.5
-587.5
=104.0
^
air
sat. KCL
mmf.
" 78.5 10 = 692 mmf.
Sin/'1000^
\ 568/
1 _ _1_ , _ 1 _ _
796 : C 2 = 90.2 mmf.
C " 692 * 104 ~ 71,800
Coir =
— = 8.8 mmf.
air
2*ln/1000\
i 567/
£ = T35 + 8Ts ; °1 = 8-1 “»*•
Cg - C1 = a c
90.2
8.1
=82.1 mmf.
—
CHAPTER II.
THE ELECTROLYTIC LEAK
It was believed that a current compensation device
could be used in order to obtain the dielectric constants
of dilute salt solutions.
Accordingly the next experiments
concerned the compensation of the current in the indicator
circuit so that it would always have the same maximum, re­
gardless of the conductivity of the solution in the experi­
mental condenser.
For this purpose a condenser was constructed of plati­
num wire electrodes, which were coiled in such a manner that
the capacity of the condenser could be increased or decreased
by merely springing the coils, eloser or farther apart.
capacity could be changed easily from .2 to .4 mmf.
Its
The
electrodes were finally set for a capacity of .36 mmf.
For the first experiment a one-half-wave rectifier
vacuum tube was connected in parallel with the experimental
and precision condenser.
By adjusting the current in the
tube, the current in the milliammeter was controlled.
But
it was found that the capacity effect of the tube varied in
a non-reproducible manner, and so it was discarded.
In the second set of experiments, induction-free carbon
resistances were connected in parallel with the experimental
and precision condenser.
By choosing the proper ohmic value,
27
the current in the meter was increased or decreased.
This
method was discarded because the experimentally determined
capacity effect of a resistance was useful only with that
resistance in the circuit.
No interpolation could be made
between two resistances giving different current maxima.
Therefore, a considerable number of resistances would be re­
quired to obtain all current values.
An attempt to make a variable resistance, by means of
a thread wet with a solution of potassium chloride was dis­
carded, as no control could be kept over the resistance of
the thread.
Another method was tried which consisted of loading a
roughened glass plate with graphite.
Copper clips on the end
of the glass plate made contact with the graphite.
But re­
moving and adding the graphite caused the capacity to change
in an unreproducible manner.
Because of the difficulties encountered in the above
methods, an electrolytic leak was tried.
This leak was con­
structed exactly like the experimental condenser except that
the platinum wires were held about two centimeters apart and
were not coiled.
This was so as to have the smallest capa­
city obtainable from the leak.
In this connection, the design
of the leak is important, as it was found that drawing the
platinum wires farther apart in the leak to a distance of five
centimeters did not change the capacity of the leak, from its
original value of .02 mmf.
This suggests that the capacity
of the leak was due largely to the design of the lead as a
unit and not just the distance between the ends of the plati­
num wire electrodes.
The capacity effect of the leak was ‘
carefully ascertained with the following solutions in it:
water,
.0005JI, .001N, .0025N,
chloride.
.005N, and .01N potassium
This was done with the experimental condenser con­
taining first air and then water.
From Figure 13' it is seen
that as the leak caused the current in the indicator circuit
to drop, its own capacity decreased at first and then after
quickly going through a minimum, began to increase.
To test this particular circuit,
.0005 potassium
chloride was introduced into the experimental condenser and
distilled water was put into the leak.
The circuit was then
balanced and the maximum.current in the indicator circuit
noted.
Then pure water was put into the experimental con­
denser and the maximum current in the indicator circuit
brought down to the previous value by use of the appropriate
strength of potassium chloride solution in the leak.
The
difference in the two current maxima was small and a correc­
tion was made from Figure 13.
By this method the capacity of
the experimental condenser when filled with .0005 normal
potassium chloride was very close to that of its capacity
when filled with water.
Similarly, data were obtained for
.0002N potassium chloride.
29
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The dielectric constants of the .0002N and .0005N
potassium chloride solutions were calculated from the experi­
mental data in the regular manner, and are compared with
values from Grubb and Hunt"*" in Table IV.
TABLE IV
Experimental
Grubb and Hunt
.0002N KCL
76.6
78.19
.0005N KCL
75.8
78.01
Solution
Calculation of dielectric constant of .0005N KCL from experi­
mental data by the usual method is shown below.
Resonance Point
Max. Current
With air
693.93
2.42
.07 mmf. to 2.10
With water
665.80
2.37
.06 mmf. to 2.10
With .0 0 0 5 N K C L
666.70
2.10
None
Air
693.86
Air
693.86
.0 0 0 5 N K C L
666.70
Water
665.74
A01 =
37.16
.
E g - 1 = (SX - 1 )_£C2
^
,
Dk
.0005N KCL * E g
=
AC2 *
- i s
Correction (Fig. 13)
28.12
27.19
(78.5 - 1) 28.12
75.8
1 J. Am. Chem. Soc., 61, 565 (1935)
31
The results given by this method would bear out the conclu­
sion that initially, dielectric constants of salt solutions
decrease below that of pure water, and are opposed to the
results obtained by Jezewskis and others who claim that the
dielectric constant of salt solutions always increase above
that of pure water.
2 Physik. Z. , 34, 88 (1933)
CHAPTER III
DISCUSSION OF RESULTS
I. USE OF INSULATED CONDENSERS
The information obtained from condensers containing
insulating materials can be used to advantage in the study
of liquids that would corrode ordinary metal to metal con­
densers.
It would also be of advantage for those liquids
which must not be exposed to air, such as those that are
prepared in all glass systems and cannot be removed from
their containers.
The curves shown in Figure 4 are steepest in the low
dielectric constant range.
Experimental accuracy is dependent
upon the steepness of such curves.
One might think that these
curves would be useful only for liquids of low dielectric con­
stant.
However as insulated condensers can be treated as two
condensers in series, it is possible to predetermine the slope
of such curves at any point.
II. CURRENT COMPENSATION EXPERIMENTS
One might question whether it is necessary to know
the dielectric constants of the solutions used in the leak.
It is necessary only to know the capacity effect of the solu­
tion in the leak.
However, using potassium chloride solutions,
33
it is possible to construct curves as in Figure 13, which can
be used to interpolate for values not experimentally deter­
mined.
This would not be possible if one used many solutions
varying widely in dielectric constants.
The accuracy of the calculated setting of the preci­
sion condenser when the circuit is tuned depends upon the
sharpness of the resonance curve as well as the precision of
the instruments.
From Figure 14 it is seen that these "com­
pensated" curves are very flat.
These curves would have been
about ten times sharper if the liquid in the experimental con­
denser had been nonconducting.
However, the accuracy ob­
tained was suitable for general results.
If a DiAsonval gal­
vanometer replaced the meter used, accuracy would be
immensely improved.
Further experiments would have to be carried out with
a more accurately controlled circuit.
It would be very im­
portant to keep the circuit at constant temperature by means
of an air bath.
A resonance "potential tuning" circuit, in which the
conductivity of the liquid being studied is immaterial, has
been described by Lattey and Davies.^- But the data presented
for the dielectric constants of salt solutions were not re­
assuring, and further, showed, no decrease as predicted by the
1 Phil. M a g . , .12, 1111 (1931)
M I L L J A M P jS
34
PREC/SlQ/v
CONDENSER
S E T T / A / O S
35
DeBye theory.
III. FURTHER PROBLEMS
The experimental results given in Table IV show a dis­
crepancy from those of Grubb and Hunt's.
But Grubb and Hunt
were vx>rking at 8 x 10 cycles, whereas the experimental re­
sults were obtained at 1.2 x 10 cycles.
This suggests that
experiments be carried out to determine the effect of differ­
ent wave lengths on the value of the dielectric constants.
Other problems, dealing with the behavior of water and
dioxane during mixing, presented themselves.
For instance,
it was noted, that when the two liquids were mixed the tempera­
ture rose, and also a volume shrinkage occurred.
From time
to time small bubbles were seen to collect and rise in the
glass side arm of the insulated condenser, but these bubbles
were not noticed when the solution was in the mixing beaker.
Most interesting from the point of this thesis is the problem
arising from a maximum conductivity occurring in the region
of a 20 per cent concentration (by weight) of dioxane in
water (Fig. 15).
36
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CHAPTER IV
SUMMARY OF RESULTS
It has been found that condensers having either one
or both electrodes sheathed with an insulating dielectric
such as glass or hard rubber do not give straight line func­
tions for capacity vs. dielectric constant curve.
Many
thicknesses, of sheaths have been tested on many different
sized cores, assembled within a cylinder of one inch di­
ameter, and the results given.
From these results one con­
denser was selected as having the best dimensions for prac­
tical experiments.
Although the sheaths improved the
sharpness of resonance curves, they cannot be used as an
effective device for studying the dielectric constants of
strongly conducting solutions.
A suggestion has been made
for the application of condensers having insulated elec­
trodes.
Mathematically, insulated condensers may be treated
as two condensers in series.
Other experiments were made concerning the compensa­
tion of the current in the circuits so that for differently
conducting solutions in the experimental condenser the cur­
rent in the indicator circuit would always have the same
maximum.
By this method the results Indicated that the di­
electric constant of dilute salt solutions is less than that
of water.
Further experiments along this line would have to
be conducted with a more carefully controlled circuit.
BIBLIOGRAPHY
I. PERIODICALS
Akerloff and Short, Journal of the American Chemical Society,
Vol. 58, 1936.
DeBye and Ealkenhagen, Physikaliche Zeitschrift, -Vol. 29,
1928.
Grubh, H. M . , and H. Hunt, Journal of the American Chemical
Society, Vol. 61, 1939.
Jezewski, Physikaliche Zeitschrift, Vol. 34, 1933.
Lattey and Davies, Philosophical Magazine, Vol. 12, 1931.
Williams, D. T . , and C. S. Copeland, Review of Scientific
Instruments, Vol. 11, No. 3, March, 1940.
II. BOOK
Smythe, R. P . , Dielectric Constants and Molecular Structure,
New York: The Chemical Catalog Company, 1931.
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