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ABSTRACT

STATIC ELECTRIFICATION OF FILAMENTS:
EFFECT OF FILAMENT DIAMETER IN A NYLON-TANTALUM SYSTEM

‘V

By

Lawrence W. Hantel

A systematic study was made of the effect of filament
diameter on the charge transferred between filaments rubbed together
under controlled ambient and mechanical conditions. Nylon mono-
filaments of various diameters (9.2-32-mils) specially prepared
from the same batch of polymer were rubbed against tantalum wires
of various diameters (7-62-mils) at different normal forces between
filaments. The charge transferred was found to be more or less
proportional to the square root of the normal force between the
filaments, in agreement with earlier findings. The charge transferred
followed no simple law with respect to filament diameter, however.
At constant diameter of tantalum, the charge was nearly independent
of nylon filament diameter. At constant diameter of nylon filament,
the charge increased with increasing diameter of tantalum wire for
small diameters, but then fell off. The complexity of the dependence

of charge on filament geometry suggests that a simple mechanism

is unlikely to be able to describe the process of charge transfer,

and it is proposed that further progress will be made by working

with precisely-defined materials, such as alkali halides and

transition-metal oxides, under simple and well—defined mechanical

conditions.

STATIC ELECTRIFICATION OF FILAMENTS:
EFFECT OF FILAMENT DIAMETER IN A NYLON-TANTALUM SYSTEM

By;,

Lawrence W.’Hantel

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Physics and Astronomy
1962

_) j

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I

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I,
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ACKNOWLEDGMENTS

I wish to express my sincere appreciation to
Prof. D. J. Montgomery, for his suggestion of this problem, and
for his unwavering encouragement and advice during the execution
of this work.

Mr. Larry Knapp took significant portions of the data in
the later stages of the experiment. His careful work is greatly
appreciated.

Mr. Jerry Tomecek is responsible for the diagrams in
this thesis and I am indebted to him for his careful work.

The assistance extended by Dr. Robert G. Brown and
Mr. J. W. Regester of the Polychemicals Department, Research and
Development Division, E. I. Du Pont de Nemours and Company, in
obtaining the nylon samples, and Mr. F. J. Harrington, Fansteel
Metallurgical Corporation, in obtaining the tantalum samples was
invaluable.

Sincere thanks are extended to Mr. Charles Kingston,

ii

supervisor of the machine shOp in the Department of Physics and
Astronomy, for his help in modifying and maintaining the apparatus.
Financial support for this work, for which I am very

grateful, has been provided by the Chemstrand Research Center.

W1:

iii

TABLE OF CONTENTS

CHAPTER Page
I 0 INTRODUCTION 0 O O O O O O O O O O O O O O O O O O 1
II. EXPERIMENTAL CONSIDERATIONS . . . . . . . . . . . . 6

A. Samples . . . . . . . . . . . . . . . . . . . 6
B. Apparatus .

III. RESULTS . . . . . . . . . . . . . . . . . . . . . . 12

Sample Schedule . . . . . . . . . . . . . . . 12
Rub Schedule . . . . . . . . . . . . . . . . l3
Reproducibility . . . . . . . . . . . . . . . 14
Effect of Velocity . . . . . . . . . . . . . 14
Effect of Normal Force . . . . . . . . . . . 16
Effect of Filament Diameter . . . . . . . . . l8
. Long-term Results (L) . . . . . . . . . . . . l8

EQWHUOWP

Short-term Results (8) . . . . . . . . . . . 19

IV. DISCUSSION 0 O O O O O O O O O O O O O O O O O O O 21

LIST OF FIGIJRES O O O I O O O O O O O O O O O O O O O O O O 26

REFERENCES CITED . . . . . . . . . . . . . . . . . . . . . 47

iv

CHAPTER I
INTRODUCTION
The effects of static electrification have been observed

from ancient times (1). But until 1600, when Queen Elizabeth's
Surgeon, Dr. William Gilbert, published Dgyfiaggggg (2), the
phenomena of static electricity were thought to occur only rarely.
Gilbert published a list of some twenty substances in addition to
the traditional and precious amber, diamond, and jet, that could be
electrified. He did not, however, establish the existence of two kinds
of electricity. The basis for this discovery was laid by experimenters
such as von Guericke, who, before 1672, discovered that electricity
can repel as well as attract. It was left to DuFay, in 1733, to
establish definitely that there are two kinds of electricity. Later
the law of conservation of charge was suggested by the experiments of
Franklin in about 1750, and of Priestley in 1767, and finally the
law of force between localized charges was established by Coulomb
after anticipatory experiments by other workers. The foundations for

quantitative treatment of electricity were thus laid. Fruitful

investigation of the relation between the chemical and physical nature

of materials and their electrical properties had to wait upon
development first of atomic theory and then upon the develOpment

of solid-state theory. Even then, not much attention was devoted

to this field until industrial interest demanded it. Effects of static
electricity are beneficial in such applications as spray painting,
insecticide dusting, dust precipitation, fiber orientation, electro-
static imaging, and some other highly specialized uses. Electrostatic
effects are harmful in the textile processing mills, in plastic
processing and utilization, and in photographic film processing.
Technological development in all these instances has been slowed

down by the dearth of fundamental knowledge concerning the charge
transfer between solids.

Problems in textile technology, specifically those attendant
upon the increase in processing speeds for the hydrOphilic and there-
fore readily conducting fibers (cotton, wool, silk, and rayon), and
upon the increase in electrical resistivity for the hydrophobic
fibers (nylon and most of the other synthetics), have motivated
several groups to undertake fundamental studies on the static electri-
fication of fibers. The Textile Research Institute in Princeton,

New Jersey, in 1951 started a program based on measuring the charge

transferred between filaments rubbed together under controlled
ambient and mechanical conditions (3). The program, with refinements
of apparatus and techniques, was continued at Princeton (4) and was
developed further at Michigan State University (5,6 ).

In the studies up to the present one, certain regularities
were observed. Cunningham and Montgomery (6,7), in an effort to
systematize the data, developed an expression for the net charge q
remaining on one object when two objects are rubbed together and

then separated. The expression is given as

q=qof ,

where qo is the total charge transferred during contact, and f is
the fraction of the total charge retained after separation. One then
attempts to study qo and f separately. The fraction f approaches a
constant value, presumably unity, with increasing rub speed and
increasing resistivity. Therefore by working under suitable conditions
it is possible to keep f constant and study qo separately.

The charge qo has been decomposed formally into the pro-
duct of two terms, a factor b dependent on the atomic parameters of

the material (5), and a factor g, dependent on the geometry of the

sample and mechanics of contact. By working with specimens of identical

chemical composition, it is h0ped to keep b constant and thereby be
able to study g. Cunningham in fact started such measurements with
nylon against tantalum, but his results were inconclusive because
there was some question as to the chemical identity of the nylon
from one filament to another of different diameter.

In the study of static electrification of solids the effect
of the size of the objects, specifically of the diameters of filaments,
is important because of its value in making clearer the process of
charge transfer. The work of Cunningham showed the likelihood of
a diameter effect, but it was suspected that its source might be
difference in chemical composition of the samples, rather than
difference in the diameters. To try to resolve this question, a
study of the effect of the diameter of nylon in rubbing nylon on
tantalum and on polyethylene was undertaken by Montgomery, Smith,
and Wintermute (8). For nylon against tantalum the charge transferred
was found to be proportional to the square root of the product of the
normal force and the diameter. For the nylon against polyethylene,
the charge was found to be pr0portional to the square root of the
normal force, but nearly independent of the diameter of the nylon.

An explanation pr0posed for the observed effects suggested the

desirability of performing experiments where the diameter of not
only the nylon filament but also of the tantalum filament is varied.
The present thesis i§_concerned with the study of the effect of

varying the diameter of the tantalum filaments ell as the diameter

lg
a

 

‘3: the nylon filaments,gg the charge transferred between the filaments

when rubbed together under controlled mechanical and ambient conditions.

CHAPTER II

EXPERIMENTAL CONSIDERATIONS

A. Samples

In this experiment we are concerned with tantalum wires
rubbed on nylon filaments. The nylon samples, specially prepared from
nylon-66 obtained from the Polychemicals Department, E.I. Du Pont
de Nemours and Company, had the following diameters; 62, 32, 17, and
9.2 mils. These filaments, though not all from the same melt, were
from the same bag, to insure uniformity with respect to chemical
composition. The diameters were measured and found to vary less
than 10% from the mean values stated.

The tantalum wire, annealed, was obtained from the Fansteel

Metallurgical Corporation in the following diameters and tolerances:

Diameter (mils) Tolerance (mils)
3.0 0.2
7.0 0.25
14.0 0.3
33.5 0.4
62.0 0.8

B. Apparatug

An apparatus was designed by Cunningham for rubbing two
filaments together under controlled mechanical and ambient conditions.
He describes the apparatus in detail in his thesis (6). Many mech-
anical details of the apparatus have been modified for the present
experiments, but the principle of the experiment remains the same.
Accordingly a detailed description is omitted here.

In short, the apparatus rubs two filaments together,
measures the charge left after separation on one filament, and then
neutralizes the system to prepare it for a succeeding rub. The
apparatus may be placed on automatic cycling, wherein the fibers are
rubbed together and then neutralized, or they may be rubbed together
as many times as desired without neutralizing. The system may be
described in four parts; (1) a rubbing mechanism; (2) a control
system; (3) a measuring device; (4) and a neutralizing mechanism.

The rubbing mechanism rubs the filaments together at a
fixed orientation and velocity. Figure l is a photograph of the

filaments in the rubbing mechanism. Three standard orientations are:

0 O

0 - 90 , 90o - 0°, and 450 - 45°. This nomenclature refers to the

top filament with respect to the bottom filament (See Figure 2).

Thus in the 00 - 9Oo rub the surface of contact of the top filament
stays the same and the bottom filament presents a constantly changing
surface of contact. In the 900 - 0o rub the top filament saws across

the bottom filament, which presents the same surface during the rub.

In the 450 - 45o rub, the orientation chosen for this work, the

axis of each filament is at an angle of 450 to the direction of

motion of the top filament holder or top yoke, and at an angle of

900 with respect to the axis of the other filament. In this orientation
the only one used in the present work, each filament presents a fresh
surface to the other during an individual rub.

The rubbing is accomplished by a pair of master-slave selsyn
motors that drive the rubbing mechanism through a roller chain. The
bottom filament remains stationary while the top filament is rubbed
across it at a given speed for a predetermined length of rub. The
"overlap" of the two filaments when in contact is controlled by
the vertical coordinate of the bottom filament, which can be changed
at will (p£,Figure 3). When the two filaments are directly over one
another, the t0p filament is lowered to push against the bottom one
by means of two rotary solenoids that rotate a shaft on which the top

filament holder rides. The top filament is lowered to the same point

each time, whence, as mentioned, the overlap is determined by the
vertical height of the bottom filament. The shaft is then raised
after the filaments have rubbed for the predetermined distance.

After the shaft is raised, the top filament holder proceeds along

the shaft and stops at the end, at the point of maximum separation

and therefore minimum capacitance. A system of cams and microswitches
connected to the shaft driving the master selsyn motor determines the
length of rub and the point where the top filament assembly stops at
the completion of a rub.

The control system has the function of regulating the
variables connected with the experiment. These variables may be
considered in two parts, the mechanical and the ambient. The mech-
anical part of the system is the pppppppip control, consisting of-

a set of three cams that are run by a l-rpm motor and a set of
microswitches actuated by the cams. This arrangement enables the
apparatus to cycle by itself. In the present experiment it is
necessary to neutralize the bottom filament after every rub. The
neutralizing mechanism accomplishes this. A radioactive source
(polonium) is lowered over the bottom filament so that enough ions

are created in the air surrounding the filament to neutralize any

10

charge that has accumulated on the bottom filament. The first cam in
the automatic control closes a microswitch that allows the radioactive
source to be lowered over the filament for a given length of time,

and then the second cam closes another switch to raise the source

out of the path of the upper yoke. A few seconds after the source is
raised, the third cam closes a switch to activate the drive motor and
begin another rub. A complete cycle takes one minute.

The ambient variables-—temperature, pressure, and composition-
are controlled as follows. The apparatus is inclosed in an insulated
box. The humidity is maintained at 33.5% by placing open trays of
magnesium chloride inside the box. The humidity is monitored by
measuring the a-c resistance of a calibrated humidity-sensitive
element (salt-impregnated plastic). The temperature is controlled
with light bulbs as heaters turned on by a relay tripped by a device
sensitive to the height of the Hg column in a thermometer in the test
chamber. The temperature was maintained at 30: 0.500.

The charge-measuring system shows the charge left on the
bottom filament. The top filament is grounded and the bottom filament
is connected to a plate insulated from the rest of the system by

four polystyrene stand-off insulators. The filament itself is close

11

to the plate, and the system behaves almost as a Faraday ice-pail.
To the plate is connected the input to a Keithley electronic
electrometer, Model 210. The electrometer measures the voltage
change on the bottom-filament assembly, and sends a signal to an
Esterline-Angus recording milliammeter to provide a continuous
record.

The capacitance of the system and the leakage resistance
are determined by observing the voltage decay when known high
resistances are connected between the electrometer input and ground.
From the observed time constants the capacitance and resistance can

be directly obtained.

CHAPTER III

RESULTS

A. Sample Schedule

The combinations of nylon and tantalum available to us
for the present experiment are shown in the diagram below.
Although it was intended to test all available combinations,
this was found to be impractical. The very thin tantalum wires
cut into the nylon severely and the very heavy nylon filaments
could not be stretched straight with reasonable loads, so these
were eliminated from experimental consideration. The combinations
actually tested are indicated in the diagram by L for one type of

test and by S for another, in accordance with a scheme to be

described below.

 

 

 

 

 

 

 

 

 

A 62 -

(0

t:

5 32 L,S L,S L,S
I:

3

,5 ..

z 17 . L,S L,S L,S L,S
S

4..)

g 9 L,S L,S L,S L,S
m

w

Q

 

7 14 33.5 62
Diameter Tantalum (mils)

12

13

B. Rub Schedule

 

Figure 4 shows the results for a typical combination
of samples for a long series of rubs with neutralization between
rubs. As can be seen there is a rather rapid rise in the charge
transferred for the first few rubs and then a leveling off. As
has been discussed in reference 7, p. 164, the behavior with successive
rubbing is complicated, and it is necessary to choose a somewhat
arbitrary rubbing schedule. In general, the charge generated changes
only slightly with successive rubs after fifty to a hundred rubs,
There will be very slow changes over periods of hundreds or thousands
of rubs, as a result of wearing and ageing effects. However we
believe that such changes reflect primarily mechanical rather
than electrical effects, and we do not concern ourselves with them
here. Hence the region of primary interest is around one hundred
rubs, which we designate as long-term behavior, or for short, L
behavior.

The short-term behavior, too, is of interest, both in
itself and a means for shortening testing procedures. Since there
appears to be a slowing down of the variation after a dozen or so
rubs, this number was chosen to characterize the short-term behavior

denoted by S.

14

C. Reproducibility

Reproducibility - Eppfippjppp. As can be seen from Figure 4, the rub-
to-rub reproducibility with a set of rubs for a given pair of fila-
ments is within 3% of the mean course of the curve envelope. This
finding is in accord with earlier experience.

Reproducibility - ”set-p -set' for a given pair of filaments ("day-

to-day”). A repetition of a set of rubs of the type depicted in
Figure 4 usually gives the same L or S value within 10%.
Reproducibility - pamplgfgp-sample ("Filament-Ep-Filamgpg").
Replications of an experiment with different sections of the material
from the same spool give results for the L values within 17% and
the S values within 14%.
D. Effect pf Velocity

Cunningham and Montgomery (6) conjectured, on dimensional-
analysis arguments, that the fraction f of the charge retained would
depend on the ratio of to, a time characteristic of the charge-transfer
process, to 17 , a time characteristic of the charge-distribution
relaxation. The time to would be given by some characteristic
distance.lg within the filament divided by the rub velocity.nr .

The time ’0' would be equal to the dielectric constant 6 multiplied

by the electrical resistivity f . Thus f would be a function of Zr.

15

Moreover, f should attain an upper limiting value for small values
of(’L/‘¢e). Cunningham and Montgomery tested this conjecture by
measuring the charge transferred from a nylon filament to a tantalum
wire as a function of velocity, with the electrical conductivity as

a parameter fixed by controlling the ambient temperature while hold-
ing the relative humidity constant. The results showed that this
conjecture could be maintained, and that f attained its limiting
value easily within the capabilities of the apparatus (rub velocities,
2-10 cm/sec.), even for relative humidity as high as 75% and temperatures
up to 35°C, where the volume resistivity of nylon is 1010 ohm-cm.

In the present experiments, typical conditions were 33% relative
humidity and 30°C, under which conditions the volume resistivity of
nylon is 2 x 1012 ohm-cm. Hence f would appear to be at its limiting
value, so that small variations in rub speed or in electrical pro-
perties of the material would not change it. This point was checked
directly at 40% relative humidity and 30°C for 32-mil tantalum on
l7-mil nylon by varying the speed from about one-fifth the normal
value used in the experiment to the normal value. As seen in Figure 5,

the charge produced was constant to within the rub-to-rub reproducibility.

This finding made it possible for us to relax certain of

16

the experimental conditions with respect to temperature and relative
humidity, in order to obtain data more rapidly and conveniently.
Some of the later data have been obtained at room temperature (24-
28°C) and room humidity (15-45%).

E. Effect pf Normal Force

The normal force between the filaments is controlled by
the weight W hung on the lower filament, in conjunction with the
geometrical arrangement of the apparatus. Consideration of Figure 3
shows that the normal force between the filaments is given approximately
by twice the tension (equal to the weight W under the conditions of
the experiment) multiplied by the ratio of the overlap to half the
span of the lower yoke, so long as the upper filament is at high
enough tension that its deflection is negligible.

It has been found (4,6,8) that almost always an increase in
the normal force increases the charge transferred, typically as F to
some power between % and l. A set of representative data is shown in
Figure 6, where the points show the measured values of q against F
for a l4-mil tantalum wire rubbing against a l7-mil nylon filament.

The solid curve shows the relation qr\IF%.

It is easier to visualize the functional dependence with the

l7

aid of logarithmic plots, and we use such plots henceforth. The
fundamental data are conveniently presented in this form, and since
their precision is not high, it is sufficient to use these graphs
instead of tables. The data for the long-term behavior (L) are

given in Figures 7a-d. and for the short-term behavior (S) in

Figures 8a-d. For each set of figures a pair of parallel lines of
slope one-half is drawn to bracket the data and permit easy eval-
uation of the adequacy of this power-law representation. For the L
set, the lines are drawn at a separation corresponding to a ratio

of 2:1. Virtually all the data for a given figure are included
between these limits. For a given diameter of nylon filament the
points lie pretty well parallel to the bracketing lines. For the S
set, where the spread in the data is much greater, it is necessary to
draw the bracketing lines of slope one-half at a separation corresponding
to a ratio of 3:1. The set of points for a given combination of fila-
ment diameters does not always lie parallel to the bracketing lines:
indeed with the 9.2-mil nylon filaments a line of lepe unity fits
the data better. Moreover with these samples the filament-to-filament

variability is higher.

18

F. Effect pf Filament Diameter

Although the postulation q1~'F% is far from perfect, it
can be used to reduce the mass of data to more nearly manageable
proportions. To illustrate the techniques of this reduction, Figure 9
shows a logarithmic plot of q against F for the data of Figure 6.
There are shown also the values of q/F%, which is seen not to
deviate far from a constant over the whole range of varying force.
We can then take this constant as a parameter to describe the electro-
static behavior of this particular combination of filament diameters
over the whole range of varying force. This parameter can then be
studied as a function of filament diameter. We shall adopt this
procedure to show the behavior of charge transferred with filament
diameter, instead of merely making crossplots of the data in
Figures 7 and 8.
G. Longeterm results CE)

35

Figure 10 shows a plot of q/F against dTa’ the diameter of

the tantalum wire, with dNy’ the diameter of the nylon filaments, as

%

a parameter. Individual values of q/F are shown, their spread along

the vertical representing both the departure from constancy for a given

dNy’ and the variation from one d to another. The dependence on

NY

19

dNy is so slight that coding of the points for the separate nylon
diameters is not practical. We note that q/Fg increases at first

with increasing d roughly as the square root (represented by the

Ta
dashed line of slope one-half), and then falling off at the largest
diameter of tantalum used. Here a few points lie nearly on the dashed
line, but they are remote from the main body of points and we do not
believe that their existence can be taken to justify maintaining

the square-root law. Perhaps there occurs sporadically electrical
breakdown or rolling rather than sliding of one filament on another,
to reduce the charge below normal; but we have no evidence to support
this conjecture.

Figure 11 shows a plot of q/Fg against dNy’ with dTa now
serving as parameter. Of course, no new information is contained in
this plot, but the effect of nylon diameter is easier to visualize.
We see that q/F$5 varies little with dNy’ as we knew implicitly from
Figure 10. The vertical spread of the points reflects of course the

variation with d that appeared explicitly in Figure 10.

Ta
H. Shgggrterm results SS)

Figure 12 shows a plot of q/Fg against dTa’ the diameter

of the tantalum wire, with dNy’ the diameter of the nylon filament,

20

35

as a parameter. Individual values of q/F are shown, their spread
along the vertical again representing both the departure from
consistancy for a given dNy’ and the variation from one dNy to
another. The dependence on dNy is appreciable, but to code the

points on the scale of the drawing is again impractical. We note that

there is very little dependence on dTa

L
Figure 13 shows a plot of q/F2 against dNy’ with dTa now
serving as parameter. We might note a tendency for a maximum at
intermediate diameters, but one would be hard put to certify its

reality.

CHAPTER IV

DISCUSSION

The dependence of transferred charge on filament diameter
has significant technological and scientific consequences. Hence
considerable effort is justified in establishing this dependence.
The history of the diameter effect is very confusing. Hersh (4),
in his exploratory experiments on size effect, reported no depen-
dence. Cunningham (6), in later and more refined experiments, found
that the charge transferred decreased with increasing filament
diameter, on rubbing 8-mi1 nylon on varying diameters of poly-
ethylene. He warned, however, that possible difference in chemical
composition from diameter to diameter might be masking the true
diameter dependence. Montgomery, Smith, and Wintermute (reference
8, hereinafter referred to as MSW) sought to eliminate this possi-
bility by working with Special samples extruded from the same melt
and therefore chemically identical. In running 12-mil tantalum
against several different diameters of nylon, MSW found that the
charge transferred was proportional to the square root of the nylon

diameter. In running 12-mi1 polyethylene against nylon, they

21

22

found no effect of nylon diameter. To explain these findings, MSW
suggested an explanation based on detailed consideration of the
area of true contact as influenced by the diameters of the fila-
ments. They proposed that their conjecture be tested by studying
a wider range of nylon diameters and by varying diameters of tan-
talum or polyethylene. It was the intention of this work to test
the conjecture of MSW. Several changes were made in the apparatus
to give better control over the mechanical variables. The fluctua-
tions in charge measured from rub to rub were thereby brought to
less than 3%, as compared with the 5% reported by MSW. The varia-
bility from filament to filament was brought to 17% for the long-
term runs and to 14% for the short-term runs, as compared with the
20% reported by MSW.

So far as dependence of charge on normal force is con-
cerned, most of the results in the present work are in agreement
with earlier findings that the charge increases more or less as
the square root of the force, as can be seen in Figures 7 and 8.
As pointed out in Chapter III, such a simple relationship makes
it possible to assess any diameter effect readily. But when the

dependence of charge on diameter of the nylon filament is considered,

23

the results for the L tests of the present work fail to agree with
the results of MSW, as can be seen from Figure 11. Here, instead of
the increase of charge as the square root of the diameter, a ggcrease
is found at the largest diameter (following a slight increase at the
smaller diameters). Hence, we cannot apply the conjectures of MSW

to the present data.

For the dependence of charge on diameter of the tantalum
filament, there is evidence in the L runs for the square-root law
for 7-mil, l4-mil, and 32-mil wires, but not for 62-mil wire, as
seen in Figure 10. It is difficult to say whether the few points
at the highest diameter represent an artifact or not.

Concerning the S tests - which are not supposed to be
described by the MSW explanation - we note that the diameter of the
nylon filament exerts almost no effect on the charge transferred. In
conjunction with the L tests for the smaller-diameter filaments, the
S tests indicate that the charge transferred during the first few rubs
does not depend on the filament diameter, but that with increasing
number the charge builds up to a limiting value prOportional to the
square root of the diameter. Such circumstances render understandable
some of the conflicting findings and opinions about the diameter
effect. So far as effect of diameter of tantalum wire is concerned,

no strong trend appears.

24

It becomes increasingly clear that the complexity of
the geometric effects is so great that they cannot be unraveled
without resort to simpler experimental arrangements. Closer examination
of the dependence of charge on normal force bears out this conclusion
For example, the behavior of charge-versus-force for the 9.2-mil
nylon filament is better described by a first-power law rather than
a square-root law (pf, Fig. 7a). This finding is quite consistent
and reproducible. Indeed, earlier works did obtain some curves not
following a square-root law, but they believed that the effect was
spurious in view of the lower degree of refinement in their apparatus
and procedures (8). Hence we conclude that our studies have reached
the stage where the changes in the electrostatic behavior due to
different origin of material, changing normal force, and varying
filament diameters, all demand better defined substances and better
defined conditions for their elucidation (10).

Specifically, materials of precisely-defined chemical
composition (such as alkali halides, but especially transition-metal
oxides) of well-defined geometry (probably circular cylinders) need
to be studied in carefully- controlled atmospheres (including vacua,

and inert gases at high and low pressures) with well-defined

25

mechanical conditions (say with solidly-backed specimens in precisely-
loaded holders). We fear that the cost of such an apparatus makes

it impractical to consider its development at this time.

FIGURES

7a.

7b.

7c.

7d.

8a.

26

LIST OF FIGURES

Photograph of Rubbing Apparatus.
Schematic Diagram of Rub Type.

Diagram to Illustrate Geometrical Configuration of

Filaments.

Reproduction of Chart Record of Electrometer Voltage

V as a Function of Rub Number.

Logarithmic Plot of Electrometer Voltage Against Rub
Velocity .

Linear Plot of Voltage V Against Weight W on Lower

Filament . . . . . . . . . .

Logarithmic Plot of Voltage Against Weight on Lower
Filament, for 7-mil Tantalum Wire Rubbing on Nylon

Filaments of Various Diameters (Long-term) .

As in Figure 7a, but for 14-mil Tantalum Wire.
As in Figure 7a, but for 32-mil Tantalum Wire.
As in Figure 7a, but for 62-mil Tantalum Wire.

Logarithmic Plot of Voltage Against Weight on Lower
Filament, for 7-mil Tantalum Wire Rubbing on Nylon

Filaments of Various Diameters (Short-term.) .

Page

28

29

30

31

32

33

34

35

36

37

38

FIGURES

8b.

8c.

8d.

10.

11.

12.

13.

27

As in Figure 8a, but for l4-mil Tantalum Wire .
As in Figure 8a, but for 32-mil Tantalum Wire .
As in Figure 8a, but for 62-mi1 Tantalum Wire .

Logarithmic Plot of Voltage V, and of V/W95
Weight W for 14-mil Tantalum Against 17-mi1 Nylon .

Against

Logarithmic Plot of V/W3 Against dTa’

of Various Diameters. (Long-term.).

for Nylon Filaments

Logarithmic Plot of V/W25 Against d for Filaments of

Ny’
Various Diameters dTa' (Long-term.) .
Logarithmic Plot of V/W3

Against d for Nylon Filaments

Ta’
of Various Diameters. (Short-term.) .

Logarithmic Plot of V/W$5 Against d for Filaments of

Ny’
Various Diameters dTa' (Short-term.).

Page

39

40

41

42

43

44

45

46

28

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30

! (1)3}, "Tap
A?“ l/ Filament
$53-$31 ,’ (Tantalum or
,l’ Polyethylene)
l/l I:’:'.4" I i
/ x V, /
. 9 ,1

o
@030

 

 

/____’_ _
T ,' z;_ 1,, §___f._;l_;1.

, ,, _+ 1 ‘1

Bottom ) ® l_/i

Filament
(Nylon)

 

 

 

 

 

 

 

 

 

Top
Filament

 

  

 

 

Filo ment

Figure 3. Diagram to illustrate geometrical con-
figuration of filaments. The tension T on the
bottom filament, equal to the weight W, acts to
press the bottom filament against the top fila-
ment through a length of contactl. The overlap
is the vertical distance between the center lines
of the two filaments. (After Montgomery, Smith,

and Wintermute 1961 . )

31

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32

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b 38.1mm ~(A) aSsaIOA

Voltage V(v)rv q

50

20

H
O

U!

34

 

 

 

 

 

L 7-mi1 Ta (-)
/
. /
/
/
.. /
/ /
/
/ /
/
/
/
/
/
(+)
0‘ 9.2-m11_Ny
/ / .x 17.~0-mil_Ny
V] I I l
i0 20 . so 100 200 p 500

Weight (g)~ F
Figure 7a. Logarithmic plot of voltage.V (prOportional to
charge q) against weight W on lower filament (prOportional
to normal force F), for 7-mil tantalum wire rubbing on nylon

filaments of various diameters as shown. (Long-term.)

50

20

3'10

3

;>

0)

OD

CU

:1

g 5
2
l

35

 

L l4-mil Ta <-) /

 

 

 

 

l , I
/ / ('1')
i / ' a 9.2-mil Ny
/
X 17.0-mil Ny

.. A 3.2.0-mil Ny

_l‘ n r - '1 l
10 20 - 50 , 100 200 500

Weight (g)~ F
Figure 7b. As in Figure 7a, but for l4-mil tantalum wire.

(Long-term. )

Voltage V(v) N q

50

36

 

 

 

 

 

 

/
1”‘
L 32-mi1 Ta (-)
/
/
(+)
/ 0. '9.2-mi1 Ny
‘x 51.7.0-mil Ny
A '32.0-mi,1 Ny
l' l 1 ~ I
10 _2o 50 100 200 500

Weight (g)~ F

Figure 7c. As in Figure 7a, but for 32-mil tantalum wire.

(Long- term. )

37

 

 

 

 

 

50
L 62-mil Ta (-)
20
0'
10
2
2
:>
o
co
m
4.)
‘3
> 5
/ ('1')
A O 1.9.2-mil Ny
X 17.0-mil Ny
2 ..
A 32.0-mil Ny
1 l' l L 1
10 20 - 50 100 200 500

~ Weight (g)~ F
Figure 7d. As in Figure 7a, but for 62-mil tantalum wire.
(Long-term.)

Voltage V<V>av q

38

 

50

20

10

 

 

/ 0

X 17. O-mil Ny

S 7-mil Ta (-) /

(+)

9. 2-mil Ny

 

i n n n

 

5
2 .—
1

10

20 ' 50 100 200 500

Weight (g)~F .
Figure 8a. Logarithmic plot of voltage V (proportional to
charge q) against weight W on lower filament (proportional
to normal force F), for 7-mil tantalum wire rubbing on nylon

filaments of various diameters as shown. (Short-term.)

Voltage V(v)~ q

50

20

H
O

U!

39

 

 

 

S 14-mi1 Ta (')

 

 

/
/
/
/,/
/
(+)
/ a 9.2-mil Ny
/ x l7-.-0-mil Ny
.. A 32-.0-mi1 Ny
Ii J '4 l
10 20 50 100 200 500
Weight (g)~F
Figure 8b. As in Figure 8a, but for l4-mil tantalum wire.

(Short-term.)

Voltage V(v )N q

50

20

H
O

40

 

 

 

 

 

s 32.41111 Ta (-) l
/
/ '
/
— /
.
/ .,
..
/ f,
/ / / / /
- z/ /
0 /
/ (+)
/
/ / o 9.2-mil Ny
.17.0-mil Ny
/ x
/ A 32.0-mil Ny
10 a0 . .50 100 200 ‘500

Weight (g ) N F

Figure 8c. As in Figure 8a, but for 32-mil tantalum wire.

(Short-term. )

9

Voltage V (v)

50

20

10

41

 

S 62-mil Ta (-)

 

   
  
 
 

(+)

0 9.2-mil Ny
X 17.0-mil Ny
A 32.0-mil Ny

 

 

10 _go 50

Weight (g) F

Figure 8d. As in Figure 8a, but for 62-mil tantalum wire.

(Short-term.)

100

200

500

50

20

10

42

 

 

 

 

L 14-mil Ta (-)
17-mil Ny (+)
L .
V/Wknvq/F35
-e¢-—--—-——--—1x-——-———-—- )0————-—---——~
)<
l L l

 

 

5 . 10 20 50 100

‘ WEIGHT w FORCE F
Figure 9. Logarithmic plot of voltage V (propor-
tional to q), and of V/W7 (proportional to q/Fg)
against W (proportional to F) for l4-mil tan-

talum against l7-mil nylon. (Long-term.)

43

 

 

 

 

5.0
L All Ny (+)
i /d
/ '
. ’//
o /
5//’
2 0 - :
/;-
z” a f
2 . z”? 5
r\ i i
7:0 1 0 *— i: / a
\ . °.'~'/
£3 z’U'
4;, .//’. °
<1
>
0.5 -
0.2 _.
0.1 l l l
5 10 20 50 100
dTa Gmils)

Figure 10. Logarithmic plot of V/W3 ( q/Fg)

against dTa’ for nylon filaments of various

diameters in mils, (9.2, 17, 32). (Long-term.)

44

 

 

 

 

5.0
L All dTa (-)
. i
_ 2.0 —' a
L *&
$3 1.
’4 .~
5‘ i a
A“ I? I f
a z» . -
2 1.0 - 1 it.
A .5 T
H\N : z
00 o
\
i3
,3,»
:3
\
;>
0.5 L
0.2 b
1
0.1 rrL ‘
5 10 20 50 100
dNy (mils)

Figure 11. Logarithmic plot of V/W3 ( q/F%)

against dNy , for filaments of various dia-

meters dTa in mils (7, 14, 32, 62). (Long-term.)

45

 

 

 

 

5.0
S A11 Ny (+)
2.0 — . .
0.: z E: O’
E 5
o B o
. :° ;.
. . ,
Afid ; :
\U‘ 1.0 - : ~ : .t
”A
00 at
\
ii
a;
3 0.5 -
0.2 —
0.1 . 1 1 ' I
5 10 20 50 100
dTa Gmils)

Figure 12. Logarithmic plot of V/W3 ( q/Fg)

against d for nylon filaments of various

Ta’
diameters in mils, (9,2,,17, 32). (Short-term.)

46

 

 

 

 

5.0
S All dTa (-)
2.0 .. 5
'- :1
. l
«1: - ~
A“ -.
fl :
U. 1.0 — ?!_
<‘ .
H\N .0
Co 0
\
3
<1
> 0.5 r—
0.2 —
0 . 1 I I l' l l
5 10 20 50 100
dNy (mils)

3v
Figure 13. Logarithmic plot of V/W2 ( q/F%)

against dNy’ for filaments of various dia-

meters dTa in mils (7, 14, 32, 62). (Short-term.)

47

REFERENCES CITED

Park Benjamin, The Aggflp£_Electricity, Charles Scribner's
Sons (1889).

William Gilbert, Qg_M§gnete, London 1600; translated by P.

Fleury Mottelay, New York 1893; reprinted Dover, New York,

1958; translated by Sylvanus P. Thompson, London, 1900; reprinted
Basic Books, New York, 1958.

S.P. Hersh, E.P. Sharman, and D.J. Montgomery, Textile Research
J. 24, 426 (1954).

S.P. Hersh, Ph.D. Thesis, Princeton University 1954;
S.P. Hersh and D.J. Montgomery, Textile Research J. 25, 566 (1955).
S.P. Hersh and D.J. Montgomery, Textile Research J. g9, 903 (1956).

D.0. VanOstenburg, Ph.D. Thesis, Michigan State University, 1956;
O. VanOstenburg and D.J. Montgomery, Textile Research J. 28, (1958)

R.G. Cunningham, Ph.D. Thesis, Michigan State University, 1957;
R.G. Cunningham and D.J. Montgomery, Textile Research J. gg,
971 (1958).

D.J. Montgomery, Solid State Physics 2, 177 (1959).

D.J. Montgomery, A.E. Smith, and E.H. Wintermute, Textile
Research J. 31, 25 (1961).

E.P. Sharman, S.P. Hersh, and D.J. Montgomery, Textile Research J.
23, 793 (1953).

48

10. R. Challande, L. Hantel, and D.J. Montgomery, Comptes rendus
Acad. Sci. Paris, in press (1962).

49
APPENDIX
galgplation of absolute charge per unit length
The charge Q on the system is equal to the voltage V read
by the electrometer, multiplied by the capacitance C of the system.
The charge per unit length is equal to Q/L, where L is the rub length.

Hence

Q/L = CV/L = (25 fl/(farad/S cm) V (volts) = 5 V (volts) ,U/lt/cm.

Calgplatipn of absolute normal force

 

The normal force F between the filaments is equal to twice
the tension T multiplied by the overlap, and divided by half the span.
Moreover, the tension T is equal to the weight W. Hence

F = 2 W (overlap)/%(span) = 4 W (0.46/10.2) = 0.136 W (grams force).

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