STATIC E L E C T R IF IC A T IO N
OF FILAMENTS

b/

R o b e r t Gail Cu n n i n g h a m

AN ABSTRACT

Su b mi t t e d to the School for Adva nc e d G r a d u a t e St udi e s of
Mi c h i g a n Stat e U n i v e r s i t y of A g r i c u l t u r e and
Appl i ed Sc i e nc e in p a r t i a l f u l f i l l me n t of
the r e q u i r e m e n t s f or the d e g r e e of

DOCTOR OF PHI LOSOPHY

D e p a r t m e n t of P h y s i c s and A s t r o n o m y
1957

App r o v e d

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A BS TR ACT
An a p p a r a t u s h a s b e e n c o n s t r u c t e d :o r u b f i l a m e n t s t o g e t h e r
u n d e r c o n t r o l l e d m e c h a n i c a l and a m b i e n t c o n d i t i o n s ,
the c h a r g e r e m a i n i n g a f t e r s e p a r a t i o n .
t hat of He r sh and M o n t g o m e r y ,
t r o l of m e c h a n i c a l v a r i a b l e s ,
ure.

and to m e a s u r e

The a p p a r a t u s i s s i m i l a r to

with r e f i n e m e n t s to obt a i n b e t t e r c o n ­

and to allow v a r i a t i o n of a m b i e n t p r e s s ­

A p h o t o m u l t i p l i e r h a s b e e n adde d n e a r the f i l a m e n t s to d e t e c t

the i n c i d e n c e of e l e c t r i c a l b r e a k d o w n of the a t m o s p h e r e .

Many of

H e r s h ' s fi ndi ngs for 4 5 ° - 4 5 ° r u b s have b e e n c o n f i r m e d ,

specifically

t h o s e on r e p r o d u c i b i l i t y and t r i b o e l e c t r i c s e r i e s .

On the o t h e r h a nd,

s o me f i ndi ngs
have not b e e n s u b s t a n t i a n t e d wh e n the r a n go e of v a r i a b l e s
o
is ext e nde d.

F o r nyl on r u b b e d on p o l y e t h y l e n e , the c h a r g e q s hows

a s q u a r e - r o o t d e p e n d e n c e on the n o r m a l f o r c e F ,

in p l a c e of the

l i n e a r d e p e n d e n c e found by H e r s h ; and the c h a r g e s hows an i n v e r s e
p r o p o r t i o n a l i t y with d i a m e t e r d, in c o n t r a s t wi t h the i n d e p e n d e n c e
not ed by H e r s h .

F o r t a n t a l u m r u b b e d on nylon,

t he c h a r g e is found

to de pe nd on a c o m b i n a t i o n of v e l o c i t y v, c o nd u c t i v i t y a sumably diel e c t r i c constant
jP

€

, and p r e ­

, t o g e t h e r wi t h a c h a r a c t e r i s t i c d i s t a n c e

to be d e t e r m i n e d e m p i r i c a l l y .

If the c h a r g e d e p e n d e n c e on l e n g t h

of r u b L is t a k e n to be the p r o p o r t i o n a l i t y found by H e r s h ,

t he c o m ­

bi ne d r e l a t i o n
i/z ,
q - c ( LF ' /d)

is suggested,

( 1 - e

- 6 v /<rJ0

‘)

w h e r e the si gn and the m a g n i t u d e of c a r e in p r i n c i p l e

d e t e r m i n e d by the d e t a i l s of the band s t r u c t u r e ,
fixed e x p e r i m e n t a l l y .

but in p r a c t i c e a r e

No d e t a i l e d t h e o r e t i c a l p i c t u r e h a s b e e n o b t a i n e d

to j u s t i f y the r e s t of the e x p r e s s i o n ,

and it m u s t be c o n s i d e r e d a t p r e s e n t

a s an e m p i r i c a l r e l a t i o n wh o s e g e n e r a l i t y and b a s i s r e m a i n to be e s t a b l i s h e d

STATIC E L E C T R IF IC A T IO N
OF FILAMENTS

by

R o b e r t Gai l Cu n n i n g h a m

A THESIS

Su b mi t t e d to the School for Adva nc e d G r a d u a t e St udi e s of
Mi c h i g a n St ate U n i v e r s i t y of A g r i c u l t u r e and
Appl i ed S c i e nc e in p a r t i a l f u l f i l l me n t of
the r e q u i r e m e n t s for the d e g r e e of

DOCTOR O F P HI L OSOPHY
D e p a r t m e n t of P h y s i c s and A s t r o n o m y
1957

ACKNOWLEDGMENTS
The a u t h o r w i s h e s to t h a n k P r o f e s s o r D. J

Montgomery

for the s u g g e s t i o n of the p r o b l e m and for hi s e n c o u r a g e m e n t and
a d v i c e d u r i n g the e n t i r e work.
The a u t h o r t ha nk s Dr.

W. G.

H a m m e r l e of the P h y s i c s D e p a r t ­

m e n t o^ Mi c h i g a n State U n i v e r s i t y for s o me d i s c u s s i o n s on the p r o b l e m
of c o nd u c t i o n in d i e l e c t r i c bod i e s .
The a u t h o r is g r a t e f u l for the a s s i s t a n c e e xt e n de d by
Dr.

S. P.

H e r s h of the C a r b i d e and C a r b o n C o r p o r a t i o n ,

Ba l l o u of E.

I.

Dupont De N e m o u r s and Co mp a n y ,

of the F a n s t e e l M e t a l l u r g i c a l C o r p o r a t i o n ,

Dr.

and Mr.

J.

Jack
E.

Brown

in obt ai ni ng the m a t e r i a l

s a m p l e s u s e d in t hi s wor k.
T h a n k s a r e e xt e n de d to Mr

C h a r l e s Ki ng s t o n of the P h y s i c s

D e p a r t m e n t m a c h i n e shop for hi s hel p in de s i g ni ng and bui lding the
final a p p a r a t u s .
The Soci et y of Si g ma Xi and the A l l - C o l l e g e R e s e a r c h Fund
kindly m a d e f unds a v a i l a b l e for s o me of t he l a b o r and m a t e r i a l s .

TABLE OF CONTENTS
CHAPTER
I.

PAGE

I NTRODUCTI ON.
A.
B.
C.

II.

1

History .
Theory . .
Objectives .

1
2
3

APPARATUS .
A.

Rubbi ng A p p a r a t u s . . .
1. B o t t o m Yoke . . . . .
2.
Top Y o k e
3. Dr i v i n g M e c h a n i s m .
4. R o t a r y Sol enoi ds . .
5. N o r m a l F o r c e
. . .
6. N a t u r e of Co n t a c t . .

4
.
.

.

. 4
4
. . 5
5
. 6
. 7
. . 7

B.

Control Apparatus . . . . .
1. Le ng t h of Rub Co n t r o l . .
Z. Ve l o c i t y of Rub C o n t r o l „
3 Rubbi ng Cycl e . . . .
.
4 T i m i n g Co n t r o l . .

8
8
9
9
10

C.

M ea s u r e m en t Apparatus .
1. P h o t o m u l t i p l i e r . . .
2. E l e c t r o m e t e r . . .
3 Recorder .

10
10
11
12

D.

Test Chambers .
1. V a c u u m T a n k ....................................................
2. T e m p e r a t u r e and Humi di t y C o n t r o l
Chamber .
. . .

12
12

.
. .
. .

14

PAGE

CHAPTER
III.

E X P E R I M E N T A L RESULTS.
A.

IV.

.

Reproducibility .
1. R u b - t o - R u b . . . .
2 S a m p l e - t o - Sa mp l e .
3. D a y - t o - D a y . . .

16

.
.

16
16
17
.19

B.

Materials .

. 19

C.

A t m o s p h e r i c B r e a k d o w n .............................................
20
1, De p e n d e n c e of C h a r g e on Amb i e n t P r e s s u r e 20
2. D e t e c t i o n of S p a r k s with P h o t o m u l t i p l i e r .
23

D.

R e s i s t i v i t y , D i e l e c t r i c C o n s t a n t , and Ve l oc i t y
of Rub . . .
.
.
...........................................................
1. T h e o r y
2. E x p e r i m e n t a l P r o c e d u r e .
3. R e s u l t s .
.
.
.

28
.29
31
.33

DISCUSSION ANDCONCLUSIONS

. 37

SUMMARY .

. 43

R E F E R E N C E S CI T E D

46

V.

CHAPTER I
I NTRODUCTI ON

The p h e n o m e n o n of f r i c t i o n a l e l e c t r i f i c a t i o n h a s b e c o m e of
i n c r e a s i n g i m p o r t a n c e in r e c e n t y e a r s with the i nt r o d ac t i on of the
new, p o o r l y c onduc t i ng,
Or i o n ,

and Da c r o n.

s y n t h e t i c m a t e r i a l s s u c h a s nyl on,

Dynel ,

The m a n u f a c t u r e r is pl a g ue d with s uc h p r o b l e m s

a s how to m a k e f i l a m e n t s and f i b e r a s s e m b l i e s p a s s al ong guide s y s ­
t e m s s mo o t h l y , how to fold c h a r g e d f a b r i c s p r o p e r l y into b o x e s ,

and

how to r e d u c e or e l i m i n a t e a t t r a c t i o n or r e p u l s i o n and s p a r k i n g of
charged fabrics.
ments,

The c o n s u m e r is well a c q u a i n t e d wi th c l i ngi ng g a r ­

and the s h o c k e n c o u n t e r e d a f t e r sl i di ng a c r o s s s y n t h e t i c a u t o ­

mo bi l e s e a t c o v e r s .

Moreover,

the p r o b l e m is of m a j o r i m p o r t a n c e

in such p l a c e s a s e x p l o s i v e f a c t o r i e s and f l our m i l l s w h e r e g r e a t
c a r e m u s t be t a k e n to avoid s p a r k s .

For instance,

the w o r k m e n

e ng a ge d in the m a n u f a c t u r e of d y n a m i t e m u s t w e a r s p e c i a l s h o e s wi t h
r u b b e r s o l e s ; e ve n t h e i r shoe l a c e s a r e of a s p e c i a l kind,
m e t a l t i ps,
overalls,

wi t hout

E a c h day t hey m u s t d r a w s u r g i c a l l y c l e a n white c ot t on

underwear,

socks,

and gl o ve s f r o m the p l a n t l au nd r y.

f l o o r s of the b u i l d i n g s a r e m a d e of n o n - s p a r k i n g l e a d ,
ery" m u s t be ma d e of n o n - s p a r k i n g metals'-' t

* R e a d e r ' s Di ge s t ,

O c t o b e r 1956,

p.

129

The

and all m a c h i n ­

Th u s the p r o b l e m is of

2

i n t e r e s t f r o m a p r a c t i c a l s t a n d p o i n t a s well a s f r o m the s t a n d p o i n t
of u n d e r s t a n d i n g che p h y s i c s invol ved.
A.

History
S. P.

H e r s h ( 1 ) h a s s u m m a r i z e d the h i s t o r y of s t a t i c

e l e c t r i f i c a t i o n in hi s t h e s i s p r e s e n t e d for the d o c t o r a t e at P r i n c e t o n
University.

The t r e a t m e n t is b r o k e n into two p a r t s :

1) q u a l i t a t i v e

i n v e s t i g a t i o n s a i m e d at e s t a b l i s h i n g a t r i b o e l e c t r i c s e r i e s ,

and

2) q u a n t i t a t i v e i n v e s t i g a t i o n s a t t e m p t i n g to d e t e r m i n e the f a c t o r s
i nvol ve d and the m a n n e r in which t hey a f f e c t the c h a r g e t r a n s f e r .
B.

Theory
A t h e o r y b a s e d on m o d e r n solid s t a t e t h e o r y Ls o ut l i ne d by

H e r s h and M o n t g o m e r y ( 2 ).

The a s s u m p t i o n s of t hi s t h e o r y a r e :

1) e l e c t r o n s onl y a r e t r a n s f e r r e d f r o m one m a t e r i a l to the ot he r ;
2) the d i r e c t i o n of c h a r g e t r a n s f e r is d e t e r m i n e d oy the r e l a t i v e
p o s i t i o n of the F e r m i l e v e l s in the two c o n t a c t i n g m a t e r i a l s ,

the

t r a n s f e r t aki ng p l a c e so a s to e q u a l i z e the l e v e l s ; 3) the a m o u n t of
c h a r g e t r a n s f e r r e d d u r i n g c o n t a c t i s d e t e r m i n e d by a) the e n e r g y
band s t r u c t u r e of the c o n t a c t i n g m a t e r i a l s ,

and b) the r el a xat i on,

t i m e for e s t a b l i s h m e n t of c h a r g e e q u i l i b r i u m b e t w e e n the m a t e r i a l s ;
4) the a r e a of " t r u e c o n t a c t " , t ha t is,

the a r e a of i n t e r p e n e t r a t i o n

of a t o m i c f i e l d s , d e p e n d s only on the n o r m a l f o r c e b e t w e e n the
m a t e r i a l s r ubbed; 5) a f t e r s e p a r a t i o n the t r a n s f e r r e d c h a r g e is
l o c a l i z e d at t he p l a c e of c o n t a c t in i n s u l a t o r s , but not of c o u r s e in
m e t a l s ; 6) upon s e p a r a t i o n of the m a t e r i a l s a f t e r c o n t a c t , the c h a r g e

3

i n i t i a l l y t r a n s f e r r e d is r e d u c e d by t un ne l i ng t h r o u g h the gap f o r m e d
by the s e p a r a t i n g s u r f a c e s ; 7) the c h a r g e r e m a i n i n g a f t e r s e p a r a t i o n
i s not n e u t r a l i z e d s i g n i f i c a n t l y by ions r e s u l t i n g f r o m a t m o s p h e r i c
breakdown.

The d e g r e e to whi ch 5) in the t h e o r y i s s a t i s f i e d will

o b v i o u s l y de pe nd on the r e s i s t i v i t y and p e r h a p s the d i e l e c t r i c c o n ­
s t a n t of the i n s u l a t i n g m a t e r i a l .

The d e g r e e to whi ch 3b) is s a t i s ­

fied will dep e nd on the l e n g t h of t i m e the m a t e r i a l s a r e in c o n t a c t ,
whi c h in t u r n will de pend on the v e l o c i t y of the r ub.

The a m o u n t of

c h a r g e t u nn e l i ng b a c k t h r o u g h the gap will de pend on 1) the p o t e n t i a l
d i f f e r e n c e a c r o s s the gap,

whi ch in t u r n will de pend on the d e g r e e of

l o c a l i z a t i o n of the charge^ and 2) the t i m e a v a i l a b l e for c h a r g e to
flow b a c k t h r o u g h the gap,

whi ch will depend on the v e l o c i t y of rub.

Th u s the c h a r g e m e a s u r e d in a r u b b i n g e x p e r i m e n t ,

whi ch is a c t u a l l y

the c h a r g e r e t a i n e d upon s e p a r a t i o n ,

should de pend on an i n t e r r e l a ­

t i o n s h i p b e t w e e n ve l o c i t y of r u bb i ng ,

the r e s i s t i v i t y ,

and the d i e l e c t r i c

c o n s t a n t of the m a t e r i a l or m a t e r i a l s r ub be d .
C.

Objectives
The o b j e c t i v e s of t hi s w o r k a r e t h r e e in n u m b e r :

1) to a s s e s s

the va l i d i t y of the c o n c l u s i o n s of H e r s h and M o n t g o m e r y (2,3) by
r e p e a t i n g s e l e c t e d m e a s u r e m e n t s while d i r e c t l y c h e c k i n g f or e l e c t r i c a l
b r e a k d o w n ; 2) to ext end the s t u d i e s of the e f f e c t of ve l o c i t y of r u b ,
wi t h the i d e a of findi ng the i n t e r r e l a t i o n s h i p b e t w e e n the e f f e c t of
velocity,

resistivity,

charge measured;

and d i e l e c t r i c c o n s t a n t of the m a t e r i a l s on the

3) on the b a s i s of t h e s e r e s u l t s ,

to get a m o r e

d e t a i l e d p i c t u r e of the s t a t i c e l e c t r i f i c a t i o n p r o c e s s .

C H A P T E R II
APPARATUS
H e r s h and M o n t g o m e r y { 3 ) found t hat the p r i n c i p a l m e c h a n i ­
cal and a m b i e n t v a r i a b l e s whi ch c o n t r o l the a mo u n t of c h a r g e g e n e r ­
a t e d whe n two m a t e r i a l s a r e r u b b e d t o g e t h e r a r e the following:
1) l e n g t h of r u b ,

2) v e l o c i t y of r u b ,

force between filaments,

3) n a t u r e of c o n t a c t ,

5) t e m p e r a t u r e ,

4} n o r m a l

and 6) r e l a t i v e h u mi d i t y .

The a p p a r a t u s shown in F i g u r e s 1 to 10 is c o n s t r u c t e d in s u c h a
m a n n e r t h a t t h e s e v a r i a b l e s m a y be a d j u s t e d and c o n t r o l l e d .
c o n s i s t s in t h r e e p a r t s apparatus,
A.

1) the r u b b i n g a p p a r a t u s ,

It

2) the c o n t r o l

and 3) the m e a s u r i n g a p p a r a t u s .

Rubbi ng A p p a r a t u s
1.

B o t t o m Yoke
The m a t e r i a l s to be i n v e s t i g a t e d a r e mo u n t e d in the f o r m of

f i l a m e n t s in the y o k e s as shown in F i g u r e 1.
F i g u r e 2,

c o n s i s t s of a c i r c u l a r b r a s s pl at e with an a l u m i n u m c l a m p

mo u n t e d on one s i d e ,
side.

and a s e t of two p u l l e y s m o u n t e d on the o p p o s i t e

The f i l a m e n t is mo u n t e d by c l a m p i n g one end in the c l a m p and

d r a p i n g the o t h e r end o v e r the p u l l e y s .
end,

The b o t t o m yoke,

A l oop is t i ed in the l a t t e r

and we i g h t s a r e a t t a c h e d to p r o v i d e a known t e n s i o n in the

f i l a me n t .

The l e ngt h of f i l a m e n t whi ch m a y be a c c o m m o d a t e d b e ­

t w e e n the c l a m p and p ul l e y is 10. 4 c e n t i m e t e r s .

The b r a s s p l a t e

5

is m a r k e d in d e g r e e s in o r d e r t hat the a z i m u t h a l p o s i t i o n of the
f i l a m e n t m a y be s p e c i f i e d

The yoke i s mo u n t e d on four i n t e r ­

c h a n g e a b l e p o l y s t y r e n e and T e f l o n s t a n d - o f f i n s u l a t o r s ,

whi c h in

t u r n a r e m o u n t e d on a double b r a s s r i n g sl i di ng o v e r t he c y l i n d r i c a l
c a s e a s shown in F i g u r e 1.

The r i n g c a n be m o v e d up or down by

m e a n s of the k n u r l e d s c r e w s t hus c o n t r o l l i n g the he i g h t of the f i l a ­
m e n t above the b a s e pl at e.

Further,

the r i n g c an be r o t a t e d a r o u n d

the c a s e t hus c ha ngi ng the a z i m u t h a l p o s i t i o n of t he f i l a me n t .

A bare

copper wire connected through a glass f e e d-through insulator connects
the b o t t o m yoke to the hi gh t e r m i n a l of a Ke i t h l e y v a c u u m - t u b e e l e c t r o ­
meter,

mo d e l 29, whi ch m e a s u r e s the c h a r g e g e n e r a t e d on the b o t t o m

f i l a me n t .
2

Top Yoke
The top yoke,

shown in F i g u r e 3, is m a d e of a l u m i n u m .

A s p r i n g is c l a m p e d at one end of the yoke,
m e n t to be m o u n t e d is t i ed to the s p r i n g .
o v e r an a l u m i n u m p o s t and f a s t e n e d ,
end to a b r a s s p o s t .

and one end of the f i l a ­

The f i l a m e n t is t he n led

u s u a l l y by gl ui ng,

at the o p p o s i t e

T h i s p o s t is p a r t of a s c r e w whi ch ca n be m o v e d

b a c k and f o r t h by m e a n s of a k n u r l e d nut in o r d e r to c o n t r o l t he t e n s i o n
of the f i l a me n t .

The l e n g t h of f i l a m e n t b e t w e e n p o s t s m a y be a d j u s t e d

up to a m a x i m u m of 5 c e n t i m e t e r s .

The yoke is f a s t e n e d to a s e m i ­

c i r c u l a r b r a s s p l a t e m a r k e d in d e g r e e s for s p e c i f y i n g the p o s i t i o n
of the f i l a me n t .
3.

Dr i v i n g M e c h a n i s m
The p l a t e to whi c h the top yoke is f a s t e n e d is i t s e l f f a s t e n e d

6

to the s u p p o r t i n g a r m a s s hown in F i g u r e 1.

The s u p p o r t i n g a r m

s l i d e s al ong t he gui d e s d r i v e n by a pi n a t t a c h e d to a b i c y c l e c ha i n
The pin r e s t s in a s l ot cut in the a r m s u p p o r t b e t w e e n the g ui de s and
m o v e s the a r m b a c k and f o r t h al ong the gui de s a s the b i c y c l e c h a i n
m o v e s a r o u n d i t s path.
motor,

The b i c y c l e c h a i n is d r i v e n by a s y n c h r o n o u s

c a l l e d the f o l l o w e r ,

and the m o t o r al ong wi t h the g ui d e s i s

f a s t e n e d by m e a n s of m a c h i n e s c r e w s to a s t e e l b a s e pl a t e 3 / 4 i nch
in thick.ne s s .
4.

R o t a r y Sol enoi ds
The a r m s u p p o r t i n g the top yoke is hi nged at the end n e a r e s t

the f ol l o we r ,

in o r d e r t ha t the oppos i t e end m a y mo v e up and down.

The l a t t e r end is s u p p o r t e d by a guide f a s t e n e d to two Z8- v
r o t a r y solenoids,

d-c

Since t h e s e s o l e n o i d s a r e mo u n t e d in o p p o s i t i o n

to e a c h o t h e r , when one is a c t i v a t e d the guide i s in one e x t r e m e
p o s i t i o n and when the o t h e r is a c t i v a t e d t he guide is in the o p p o s i t e
e x t r e m e position.

The t ot al r o t a t i o n f r o m one e x t r e m e to the o t h e r

is a p p r o x i m a t e l y 30°,

c o n s e q u e n t l y the op po s i t e e x t r e m e f r o m t h at

shown in F i g u r e 1 l e a v e s the a r m in a h o r i z o n t a l p o s i t i o n
6- v

Four

E d i s o n s t o r a g e b a t t e r i e s a r e u s e d to o p e r a t e the s o l e n o i d s .

The guide is s p r i n g l oa de d for the p u r p o s e of k e e p i n g the a r m in the
"up" p o s i t i o n wh e n n e i t h e r s ol enoi d is a c t i v a t e d .

The s o l e n o i d s a r e

f a s t e n e d to an a l u m i n u m s u p p o r t and the s u p p o r t is f a s t e n e d to the
b a s e p l a t e by m e a n s of m a c h i n e s c r e w s .

C o n s t r u c t e d in t h i s m a n n e r ,

the f i l a m e n t in the top yoke will c o m e to the s a m e h e i g h t above the
b a s e p l a t e e a c h t i m e it is l o w e r e d

7

5

Normal Force
The n o r m a l f o r c e b e t w e e n the f i l a m e n t s is c o n t r o l l e d s o l e l y

by a d j u s t m e n t s in the b o t t o m yoke.

By ma k i n g the t e n s i o n v e r y hi gh

in the f i l a m e n t mo u n t e d in the top yoke,

and c o n t r o l l i n g the t e n s i o n

and he i ght of the b o t t o m f i l a m e n t a s d e s c r i b e d ,

the e x p r e s s i o n for

the n o r m a l f o r c e ca n be d e r i v e d u n d e r the a s s u m p t i o n t hat the poi nt
of c o n t a c t b e t w e e n f i l a m e n t s is at the c e n t e r of the b o t t o m f i l a me n t .
R e f e r r i n g to F i g u r e 1Z, l et
T = t e n s i o n in b o t t o m f i l a me n t ,
d = d i s p l a c e m e n t of b o t t o m f i l a m e n t ,

JP - l e ngt h of b o t t o m f i l a m e n t b e t w e e n s u p p o r t s ,
& - d i s p l a c e m e n t angle.

and

The n the u p w a r d f o r c e at the poi nt of c o n t a c t will be gi ven by
Normal Force = 4 T d / /
d is s m a l l c o m p a r e d to JP ,

for the c a s e wh e r e
t hi s w o r k

a s is the c a s e in

T h i s r e l a t i o n v e r y n e a r l y gi ves the n o r m a l f o r c e al ong

the whole r u b ,

s i n c e the l e n g t h of r u b is Z. 3 c e n t i m e t e r s ,

10. 4 c e n t i m e t e r s ,

and

J? is

whi ch gi v e s a v a r i a t i o n in n o r m a l f o r c e of Z5%

or l e s s f r o m the e x t r e m e s to the c e n t e r of the r u b b e d p o r t i o n of
the b o t t o m f i l a me n t .
6.

N a t u r e of Co n t a c t
The a z i m u t h a l p o s i t i o n s of the top and b o t t o m yoke d e t e r m i n e

the n a t u r e of the r u b b i n g cont act .

In a p o l a r c o o r d i n a t e s y s t e m in

whi c h the z e r o of t hi s s y s t e m is the d i r e c t i o n in whi ch the top yoke
moves,

the angl e b e t w e e n the l e ngt h of the f i l a m e n t and the d i r e c t i o n

of m o v e m e n t of the top yoke s p e c i f i e s the p o s i t i o n of the f i l a me n t .
The n a t u r e of t he r u b b i n g c o n t a c t is t h e n gi ve n by two a n g l e s .
the f i r s t angl e is the c o o r d i n a t e of t he b o t t o m f i l a m e n t ,
s e c on d is t h at of the top f i l a me n t ,

If

and the

the t h r e e m a j o r f o r m s of r u b b i n g

c o n t a c t r e c o g n i z e d by H e r s h m a y t hen be d e s c r i b e d a s follows:
1) 93- 0,

in wh i c h the l e ngt h of the top f i l a m e n t s a ws into one

spot on the b o t t o m f i l a me nt ;
Z)

0-93,

in which one spot on the top f i l a m e n t s l i d e s al ong

the l e ngt h of the b o t t o m f i l a me nt ;
3)

4 5- 45 ,

in which the l engt h of both f i l a m e n t s a r e r u b b e d

t o g e t h e r ; f r e s h s u r f a c e is a l w a y s c o n t a c t i n g f r e s h s u r f a c e in t h i s r ub.
B.

Control Appar at us
The c o n t r o l a p p a r a t u s ,

synchronous motor,

h e r e a f t e r c a l l e d the d r i v e r ,

a c t i v a t e the r o t a r y s o l e n o i d s ,
d-c motor,
1.

shown in F i g u r e 4, c o n s i s t s of a n o t h e r
m i c r o s w i t c h e s to

a t hy r a t r o n - c o n t r o l l e d c o n s t a n t - spe ed

and a t i m i n g c o n t r ol .

Le n g t h of Rub Co n t r o l
The m i c r o s w i t c h e s a r e o p e r a t e d by m e a n s of c a m s c o n n e c t e d

to the d r i v e r t h r o u g h a g e a r t r a i n whi ch a d j u s t s t he r o t a t i o n of the
c a m s to the r o t a t i o n of t he b i c y c l e c ha i n on the r u b b i n g a p p a r a t u s .
One r e v o l u t i o n of the c a m s c o r r e s p o n d s to one r e v o l u t i o n of the b i c y ­
cl e c h a i n t hus , by a p r o p e r a d j u s t m e n t of the c a m s ,

the a c t i v a t i o n

9

of the r o t a r y s o l e n o i d s c a n be c o n t r o l l e d and the top yoke m a y be
l o w e r e d and r a i s e d at any d e s i r e d t i me d u r i n g the cycl e.
2.

Ve l o c i t y of Rub C o n t r o l
The d r i v e r i s c o n n e c t e d e l e c t r i c a l l y to t he f ol l owe r and is

d r i v e n by the c o n s t a n t s p e e d m o t o r t h r o u g h a l e a t h e r belt.

The s p e e d

of t he l a t t e r m o t o r i s c o n t r o l l e d by m e a n s of a r h e o s t a t whi c h v a r i e s
the a r m a t u r e vol t age of the m o t o r .

Th us the r u b ve l oc i t y and the

l e n g t h of r ub c a n be c o n t r o l l e d a p a r t f r o m the r u b b i n g a p p a r a t u s .
3.

Rubbi ng Cy c l e
B e f o r e e a c h r ub the f i l a m e n t s a r e d i s c h a r g e d with an Iono-

t r on*.

Th u s a c yc l e b e g i n s with the yokes t o g e t h e r but the f i l a m e n t s

not t ou c hi ng, and the I o n o t r o n in p l a c e n e a r the f i l a m e n t s .

The

l o n o t r o n is mo v e d away and about 25 s e c o n d s is a l l owed for t he i ons
to c l e a r .

The c o n s t a n t - s p e e d mo t o r is t hen s t a r t e d ,

yoke m o v e s a way and r e t u r n s .

and the top

As it p a s s e s over the b o t t o m yoke,

one of the m i c r o s w i t c h e s is c l o s e d a c t i v a t i n g t he r o t a r y sol e noi d
whi ch l o w e r s t he top yoke and the f i l a m e n t s m a k e c ont act .

It wa s

found n e c e s s a r y to a t t a c h a b r a s s wi r e to the guide in such a way
t ha t when the top yoke is down the w i r e p r e s s e s a g a i n s t the a r m to
ke e p it f r o m b ou n c i n g when it falls.
Figure 1

The wi r e can be s e e n in

The two f i l a m e n t s a r e t hen r u b b e d t o g e t h e r and when the

d e s i r e d l e n g t h of f i l a m e n t is r u b b e d , the f i r s t m i c r o s w i t c h is ope n e d

* Obt a i n e d f r o m Uni t ed St a t e s R a d i u m C o r p o r a t i o n ,
New Y o r k 7, New Yor k.

535 P e a r l S t r e e t ,

10

and the s e c on d is c l o s e d ,

r a i s i n g the top yoke and b r e a k i n g the c o n ­

t a c t b e t w e e n the f i l a m e n t s .

The top yoke m o v e s awa y and t he n r e t u r n s

to i t s o r i g i n a l p o s i t i o n o v e r the b o t t o m yoke w h e r e it i s stopped.
The I o n o t r o n is t he n mo v e d n e a r the f i l a me n t s .
25 s e c o n d s for c o m p l e t e d i s c h a r g e ,

Af t e r a l l owi ng about

the cyc l e is r e a d y to be r e p e a t e d .

The c o m p l e t e cyc l e t a k e s a bout 1 mi n u t e f r o m b e g i n n i n g to end.
4.

T i m i n g Co n t r o l
The t i m i n g of the c yc l e is m a d e a u t o m a t i c by the u s e of m i c r o ­

s w i t c h e s in the c i r c u i t shown in F i g u r e 6.

The m i c r o s w i t c h wh i c h

s t o ps the c o n s t a n t - s p e e d mo t o r is l o c a t e d n e a r the m i c r o s w i t c h e s
c o n t r o l l i n g the r o t a r y s o l e n o i d s and is o p e r a t e d by a l e v e r a t t a c h e d
to the s a m e axl e a s t h o s e m i c r o s wi t che s .

The o t h e r four m i c r o s w i t c h e s

a r e o p e r a t e d oy c a m s mo u n t e d on a shaf t whi c h is t u r n e d Oy a 1 - r p m
clock motor.
C

M e a s u r e m e n t Apparatus
1.

Photomultiplier
It wa s found d e s i r a b l e to ha ve s o me d i r e c t m e a n s of d e t e c t i n g

the o c c u r r e n c e of e l e c t r i c a l b r e a k d o wn .

Thi s p h e n o m e n o n was s u s ­

p e c t e d by H e r s h and M o n t g o m e r y (2, 3 ) but not v e r i f i e d .
F o r t hi s p u r p o s e ,

an RCA type 5819 e n d - c a t h o d e p h o t o m u l t i ­

p l i e r is mo u n t e d i ns i de the c y l i n d r i c a l b r a s s c a s e d i r e c t l y b e n e a t h
the b o t t o m f i be r .

The c a s e is c l o s e d at the end n e a r e r the f i b e r

by c e m e n t i n g a p i e c e of o r d i n a r y g l a s s with P i c e i n c e m e n t to a c i r ­
c u l a r r i n g of b r a s s a p p r o x i m a t e l y 1 c m . w i d e .

Th i s r i n g is s i l v e r

11

s o l d e r e d to the end of the c y l i n d e r .

The o t h e r end of the c y l i n d e r is

s i l v e r s o l d e r e d to a b r a s s p l a t e which c o n t a i n s a hole of the s a m e
si ze a s the b r a s s c y l i n d e r .
in the s t e e l b a s e p l a t e ,

The c a s e is p l a c e d t h r o u g h a hol e cut

and the pl at e is f a s t e n e d by m e a n s of m a c h i n e

s c r e w s to the u n d e r s i de of the b a s e pl at e.

A rubber O-ring between

the b r a s s p l a t e and s t e e l p l a t e p r o v i d e s an a i r ti ght seal .

A sl ot

about Z c e n t i m e t e r s wide and 5 c e n t i m e t e r s long is cut in the b o t t o m
yoke with t he l o n g e r d i m e n s i o n in the d i r e c t i o n of the b o t t o m f i l a ­
me n t ,

in o r d e r t hat the p h o t o m u l t i p l i e r can " s e e " the f i l a m e n t a s it

is be i ng r u bb e d.

The p h o t o m u l t i p l i e r is e n c a s e d in a m u - m e t a l

shi el d to p r o t e c t it f r o m s t r a y m a g n e t i c fi el ds.

The ope ni ng b e t w e e n

the b a s e of the p h o t o m u l t i p l i e r and the b r a s s c a s e is s e a l e d with
e l e c t r i c a l t a pe in o r d e r to exc l ude s t r a y l ight f r o m bel ow.
p h o t o m u l t i p l i e r c i r c u i t is shown in F i g u r e 5.

The

The b a s e p l a t e is m o u n t e d

on a woode n f r a m e to b r i n g it about 16 i n c h e s off the f l oor and allow
r o o m for a d j u s t m e n t of the p h o t o m u l t i p l i e r and its c a s e .
Z.

Electrometer
The c h a r g e g e n e r a t e d on the b o t t o m f i b e r is d e t e r m i n e d

by o b s e r v i n g the p o t e n t i a l c hange on a s y s t e m of known c a p a c i t a n c e .
A s c h e m a t i c d i a g r a m of the m e a s u r i n g c i r c u i t is shown in F i g u r e 11.
The s y m b o l s C g and C e r e p r e s e n t the c a p a c i t a n c e of the s y s t e m and
electrometer,

respectively.

s u p p o r t i n g the b o t t o m yoke,
electrometer.

R g is the r e s i s t a n c e of t he i n s u l a t o r s
and R g is the l e a k a g e r e s i s t a n c e of the

The c o m b i n a t i o n of R g and R e h a s an e q u i v a l e n t

r e s i s t a n c e n e v e r l e s s t ha n 1 0 ^ o h ms .

The val ue of C g -+■ C e is

m e a s u r e d by o b s e r v i n g the t i m e c o n s t a n t of the s y s t e m when it is

12

c o n n e c t e d to gr ound t h r o u g h a known r e s i s t a n c e .

The val ue l i e s

b e t w e e n 25 and 30 m i c r o m i c r o f a r a d s de p e n d i n g on the d i s t a n c e b e t w e e n
the b o t t o m yoke and t he c a s e h o u s i n g the phot o - m u l t i p l i e r .
3.

Recorder
The s i gna l f r o m the p h o t o m u l t i p l i e r is a m p l i f i e d by m e a n s

of a Ke i t hl e y i s o l a t i o n a m p l i f i e r ,
of a B r u s h t w o - c h a n n e l r e c o r d e r .

and t hen r e c o r d e d on one c h a n n e l
The o t h e r c h a n n e l is u s e d to

r e c o r d the m a g n i t u d e of the c h a r g e g e n e r a t e d as m e a s u r e d by the
electrometer.

It is n e c e s s a r y t hat the r e c o r d e r be r u n n i n g f or only

a s h o r t t i m e d u r i n g the c y c l e ,

so a m i c r o s w i t c h is i n c o r p o r a t e d in

the a u t o m a t i c c o n t r o l a s shown in F i g u r e 6 for s t a r t i n g and st oppi ng
the r e c o r d e r .
D.

Test Chambers
1.

Vacuum Tank
Two t e s t c h a m b e r s a r e u s e d for the c o n t r o l of the a m b i e n t

variables.

The f i r s t c h a m b e r c o n s i s t s of a c y l i n d r i c a l s t e e l s he l l

1/2 i nch t hi ck,

12 1/2 i n c h e s longhand 19 i n c h e s in i ns i de d i a m e t e r

p l a c e d a r o u n d the r u b b i n g a p p a r a t u s ,

with a r u b b e r O - r i n g b e t w e e n

the shel l and the s t e e l b a s e pl a t e p r o v i d i n g an a i r - t i g h t seal .

A

c i r c u l a r s t e e l p l a t e 1/ 2 i nch t h i c k and 25 i n c h e s in d i a m e t e r i s u s e d
to c o v e r the s hel l wi t h a n o t h e r r u b b e r O - r i n g to m a k e a s e a l .
6 inch d i a m e t e r hol e is cut in the top pl a t e ,

A

and a p i e c e of m e t a l

or pl a t e g l a s s c o v e r s the hole d e pe n di n g on w h e t h e r it is d e s i r e d
to w a t c h the o p e r a t i o n of the a p p a r a t u s , o r to m a k e the e n c l o s u r e l i g h t ­
t ight in o r d e r to o b s e r v e e l e c t r i c a l d i s c h a r g e wi th the p h o t o ­

multiplier.

A s t o p c o c k is i n s e r t e d in the wal l t h r o u g h whi c h the

a i r m a y be p u mp e d f r o m the s y s t e m .
a r e m o u n t e d in r e d u c i n g n i p p l e s ,

Two f e e d - t h r o u g h i n s u l a t o r s

and the n i p p l e s a r e f a s t e n e d to

the wal l i n o r d e r t hat the p r o p e r e l e c t r i c a l c o n n e c t i o n s m a y be m a d e .
One of the i n s u l a t o r s i s a s i ngl e f e e d - t h r o u g h for m a k i n g the c o n n e c ­
t i on to the e l e c t r o m e t e r ,

and the o t h e r is a m u l t i p 1e f e e d - t h r o u g h

i n s u l a t o r for ma k i n g the c o n n e c t i o n s b e t w e e n the s y n c h r o n o u s m o t o r s
and for c o n n e c t i n g the r o t a r y s o l e n o i d s to t h e i r p o w e r supply.
F i g u r e 7 s hows the a s s e m b l e d a p p a r a t u s .

F o r t hi s t e s t c h a m b e r ,

s e v e r a l d i f f e r e n t mo u n t i n g s for the l o n o t r o n w e r e a t t e m p t e d , but
no c o m p l e t e l y s a t i s f a c t o r y mou n t i n g wa s found

The b e s t one c o n ­

s i s t s of p l a c i n g the l o n o t r o n in a hollow b r a s s c y l i n d e r wit h a n a r r o w
slot,

and t hen p l a c i n g thi s c y l i n d e r in a sl i ght l y l a r g e r b r a s s c y l i n d e r

wi t h a s i m i l a r slot.

The i n n e r c y l i n d e r is f a s t e n e d to a r o t a r y

sol enoi d in s u c h a m a n n e r t hat when the s ol enoi d is a c t i v a t e d ,
s l o t s a r e in line and the i ons ca n e s c a p e .
l oa de d,

consequently,

the

The s ol e noi d is s p r i n g

when it i s not a c t i v a t e d the s l o t s do not l i ne

up, and m o s t of t he i ons a r e s t opped by the wa l l s of the b r a s s c y l i n d e r
The d e v i c e is t h e n mo u n t e d on the b a s e pl a t e c l o s e to the b o t t o m yoke.
In p r a c t i c e it is found t hat the d e vi c e ca n not be mo u n t e d c l o s e enough
to the b o t t o m f i l a m e n t to d i s c h a r g e it in a r e a s o n a b l e l e ngt h of t i m e
if a p o l o n i u m l o n o t r o n is used.

A r a d i u m l o n o t r o n is a l s o a v a i l a b l e ,

but the a m o u n t of g a m m a r a d i a t i o n not s t oppe d by the b r a s s c y l i n d e r s
is enough to c o n t r i b u t e a l a r g e l e a k a g e c u r r e n t f r o m the b o t t o m yoke.

14

Z,

T e m p e r a t u r e and Humi di t y C o n t r o l C h a m b e r
The s e c on d t e s t c h a m b e r c o n s i s t s of a Ma s o n i t e box

3 feet

s q u a r e and Z f eet deep l i ned on the i n s i d e with c o p p e r s c r e e n to s hi e l d
the a p p a r a t u s e l e c t r o s t a t i c a l l y .
two ways:

E n t r y into the box c a n be m a d e in

1) by r e m o v i n g the c o v e r o v e r a hol e 10 i n c h e s by 6 i n c h e s

cut in the f r o n t of the box, or Z) by r e m o v i n g the e n t i r e f r o n t of the box.
The o p e n i n g s a r e m a d e l i ght - t i ght by gluing s t r i p s of sponge r u b b e r
a r o u n d the e d g e s of the c o v e r s and usi ng snap f a s t e n e r s and t h u mb
s c r e w s to pull the c o v e r s up tight , t h e r e b y c o m p r e s s i n g the sponge
rubber.

Two h e a t e r s and a t h e r m o s t a t a r e mo u n t e d in the box at

the s a m e h ei g h t a s the b a s e p l a t e , to c o n t r o l the t e m p e r a t u r e in the
box.

F i g u r e 8 is a s c h e m a t i c of the h e a t e r and t h e r m o s t a t c i r c u i t .

T r a y s f i l l ed with a s a l t s ol ut i on a r e p l a c e d on the f l oor of the box to
c o n t r o l the h u mi d i t y ,

and a fan is mo u n t e d in the top of the box to

keep a c o n s t a n t s t r e a m of a i r flowing down p a s t the h e a t e r s onto the
trays.

The e l e c t r i c a l c o n n e c t i o n s a r e ma d e t h r o u g h a b a k e l i t e m u l t i ­

ple f e e d - t h r o u g h i n s u l a t o r at the b a c k of the box.
n e c t i o n s a r e s hown in F i g u r e 9.

The v a r i o u s c o n ­

F i g u r e 10 shows the box wi t h the

f r ont c o v e r r e m o v e d and the a p p a r a t u s in p l a c e r e a d y for r ubbi ng.
The d i s c h a r g e of the f i l a m e n t s in t hi s t e s t c h a m b e r is a c c o m p l i s h e d
by mo u n t i n g the p o l o n i u m l o n o t r o n on a b r a s s r o d i n s e r t e d at r i g h t
a n g l e s into a hol e d r i l l e d in an a l u m i n u m r o d of l a r g e r d i a m e t e r
The a l u m i n u m r o d r e s t s in h o l e s d r i l l e d in two p i e c e s of a l u m i n u m
of r e c t a n g u l a r c r o s s s e c t i o n

whi ch a r e t hen bo l t e d to the b a s e pl a t e

15

a s shown in F i g u r e 10.

The l o n o t r o n is c o u n t e r b a l a n c e d by a l e ad

we i ght f a s t e n e d to the o p po s i t e end of the b r a s s r od.
r o d e x t e n d s t h r o u g h a hol e in the box,

The a l u m i n u m

and a c r a n k s e r v e s to r o t a t e

the r o d t hus mo v i n g the l o n o t r o n c l o s e to the f i l a m e n t s o r f a r away
f r o m the f i l a m e n t s .

The openi ng for the a l u m i n u m r o d is m a d e

l i g h t - t i g h t by p a c k i n g the openi ng with cloth.

An e n c l o s u r e m a d e of

a l u m i n u m foil s e r v e s to h o u s e the l o n o t r o n when it i s not b e i n g u s e d
to d i s c h a r g e the f i b e r s ,

t hus p r e v e n t i n g i ons f r o m b e i ng c a r r i e d to

all p a r t s of the box by a i r c u r r e n t s .

A 24-v

d-c motor attached

to a g e a r r e d u c t i o n box r a i s e s and l o w e r s the l o n o t r o n by m e a n s of
a c a m and l e v e r a t t a c h e d to the c r a n k .

The o p e r a t i o n of the l o n o t r o n

is c o n t r o l l e d by two of the m i c r o s w i t che s shown in F i g u r e 6, and by
a t h i r d m i c r o s w i t c h mo u n t e d b e s i d e the c a m c o n n e c t e d to the m o t o r .
The t h i r d m i c r o s w i t c h is u s e d to stop the l o n o t r o n in the b e s t p o s i t i o n
for d i s c h a r g i n g the f i l a m e n t s .

C H A P T E R III
E X P E R I M E N T A L RE S U L T S
A.

Reproducibility
Nyl on y a r n s about 5 m i l s in d i a m e t e r w e r e t a k e n f r o m a p i e c e

of nylon cl ot h not t r e a t e d with a n t i - s t a t i c age nt ,

and p a i r e d with

4 3 / 4 - m i l p o l y e t h y l e n e m o n o f i l a m e n t s t a k e n f r o m the s a m e spool.
The p a i r s w e r e not c l e a n e d in any way b e f o r e mo u n t i n g , but c a r e was
t a k e n to ke e p f r o m c o n t a m i n a t i n g t h e m by t ouc hi ng with the f i n g e r s .
T h e s e p a i r s we r e t he n r u b b e d t o g e t h e r unde r c o n t r o l l e d a m b i e n t
c on di t i on s ,

and the c h a r g e g e n e r a t e d at d i f f e r e n t n o r m a l f o r c e s

wa s m e a s u r e d .
0. 2°C.

The t e m p e r a t u r e wa s kept c o n s t a n t at 30°C to wi t hi n

The r e l a t i v e h u mi d i t y was kept c o n s t a n t at 33% to wi t hi n an

e s t i m a t e d * 5% by p l a c i n g t r a y s c ont a i ni ng a s a t u r a t e d s o l u t i on of
m a g n e s i u m c h l o r i d e on the fl oor of the t e s t c h a m b e r .

The l engt h of

r ub was 2. 3 cm. , and the v e l o c i t y of r u b was 4. 1 c m/ ' s e c .

The

n o r m a l f o r c e wa s c h a ng e d both by c hangi ng the t e n s i o n in the p o l y ­
e t hy l e ne and by c hangi ng the o v e r l a p .
1.

Rub - to - Rub
F i g u r e 13 shows the r e s u l t s for two d i f f e r e n t f i l a m e n t p a i r s ,

with the n o r m a l f o r c e kept c o n s t a n t at 5. 5 g r a m s .
to one p a i r and the c r o s s e s to the o t h e r .

The dot s r e f e r

In g e n e r a l ,

the r e p r o ­

d u c i b i l i t y for s u c c e s s i v e r u b s with d i s c h a r g i n g b e t w e e n r u b s is a s

17

r e p o r t e d by H e r s h : t he c h a r g e m e a s u r e d u s u a l l y l i e s wi t hi n - 5%
of the me a n .

It i s felt t h a t the d i v e r g e n c e of the t h r e e dot s o u t s i d e

t hi s r a n g e was due to a d e f e c t in the m e c h a n i c a l or e l e c t r i c a l p a r t of
the a p p a r a t u s ,

a l t ho ug h t hi s c o n j e c t u r e h a s n e v e r b e e n c o n f i r m e d .

L a t e r m e a s u r e m e n t s wi t h t a n t a l u m r u b b e d a g a i n s t nyl on (see F i g u r e
23) do not have p o i nt s l yi ng out s i de the r a n g e of - 5%, but t hi s
n e i t h e r c o n f i r m s n o r d e n i e s t he e x i s t e n c e of s uch a def ect .
2

Sample-to-Sample
S a m p l e - t o - s a m p l e r e p r o d u c i b i l i t y was not a s good a s

rub-to-rub.

The c h a r g e m e a s u r e d usually l i e s wi t hi n the - 20%

of the m e a n in a g r e e m e n t wit h the f i ndi ngs of H e r s h .

It wa s noted

upon r u b b i n g v a r i o u s p a i r s of f i l a m e n t s t hat two t y p e s of b e h a v i o r
were encountered,

a s p a r k i n g t ype, w h e r e e l e c t r i c a l b r e a k d o w n w a s

d e t e c t e d even at the l o w e s t n o r m a l f o r c e us ed, n a m e l y 1. 60 g r a m s ;
and a n o n - s p a r k i n g t yp e , w h e r e e l e c t r i c a l b r e a k d o w n wa s not
d e t e c t e d until h i g h e r n o r m a l f o r c e s we r e u s e d ,
grams.

on the o r d e r of 3 to 7

F i g u r e 13 shows a p a i r of e a c h t ype, the c r o s s e s r e f e r r i n g

to a s p a r k i n g p a i r ,

and the dot s to a n o n - s p a r k i n g p a i r .

An i n t e r ­

change of nyl on f i l a m e n t s a mo n g v a r i o u s p a i r s s howed the b e h a v i o r
to be c h a r a c t e r i s t i c of the nylon.

In g e n e r a l ,

it wa s found t hat s a m p l e s

t a k e n f r o m d i f f e r e n t y a r n s in the cl ot h s howed this v a r i a t i o n , but
s a m p l e s t a k e n f r o m the s a m e y a r n did not.

If a s a m p l e t a k e n f r o m

one y a r n pul l ed f r o m the cl ot h coul d be c l a s s e d a s a n o n - s p a r k e r ,
t h e n a n o t h e r s a m p l e t a k e n f r o m the s a m e y a r n could a l s o be
c lassed as a n o n - s p a r k e r ,

al t hough the n o r m a l f o r c e which was

18

n e c e s s a r y f or o n s e t of s p a r k i n g would of t en va r y.

Similarly,

s a m p l e t a k e n f r o m one y a r n coul d be c l a s s e d a s a s p a r k e r ,

if a

then

a n o t h e r s a m p l e t a k e n f r o m the s a m e y a r n could a l w a y s be c l a s s e d as
a sparker.

It m a y be s u r m i s e d t hat if e l e c t r i c a l b r e a k d o w n did not

o c c u r for the s p a r k i n g p a i r of F i g u r e 13, t hen the c h a r g e g e n e r a t e d
would be g r e a t e r t han i s shown by the pl ot t ed poi nt s.
v a r i a t i o n in

s a m p l e - t o - sample

v a r i a t i o n ma y be e x pe c t e d.

Th u s a l a r g e r

r e p r o d u c i b i l i t y t ha n the s t a t e d

Ho we v e r ,

the d e c r e a s e in c h a r g e g e n ­

e r a t e d due to e l e c t r i c a l b r e a k d o w n is p r o b a b l y v e r y l i t t l e for the
f i be r p a i r shown in F i g u r e 13,

si nce a few of the m a n y r u b s on t hi s

p a i r gave no e vi de nc e of b r e a k d o w n w h a t s o e v e r ,
r u b s gave onl y one s m a l l s p a r k .

and s o m e of the

The c h a r g e m e a s u r e d for t h e s e

r u b s is not s i gn i f i c a n t l y d i f f e r e n t f r o m the c h a r g e m e a s u r e d for
r u b s w h e r e two or m o r e s p a r k s wer e d e t e c t e d .

Thu s it is f el t t h a t

the b r e a k d o w n whi c h occ ur sy n e u t r a l i z e s v e r y l i t t l e of the c h a r g e
transferred,

and c o n s e q u e n t l y the c h a r g e m e a s u r e d for d i f f e r e n t

s a m p l e s d oe s not v a r y by m o r e t han 20% f r o m the me a n.
p e r h a p s wo r t h whi l e to not e t hat the

rub-to-rub

It is

reproducibility

is b e t t e r for the n o n - s p a r k i n g p a i r t han for the s p a r k i n g p a i r ,
a p a r t f r o m d i v e r g e n c e of the t h r e e po i nt s of w i d e s t v a r i a t i o n whi ch
is b e l i e v e d to be due to i n s t r u m e n t a l ma l f u nc t i o ni ng.

19

3.

Day-to-Day
One -would p e r h a p s e x p e c t the d a y - t o - d a y r e p r o d u c i b i l i t y

of c h a r g e g e n e r a t e d b e t w e e n the s a m e p a i r of f i l a m e n t s to be b e t t e r
t han the s a m p l e - t o - s a m p l e r e p r o d u c i b i l i t y if the m e c h a n i c a l and
a m b i e n t c o n d i t i o n s do not c hange.
however.

Such is u s u a l l y n et the c a s e ,

The b e s t t ha t c a n be sai d is t ha t the d a y - t o - d a y r e p r o ­

d u c i b i l i t y g e n e r a l l y l i e s wi thin -20% of the m e a n ,
He r sh.

a s r e p o r t e d by

V a r i a t i o n s a s l a r g e a s t hi s ha ve b e e n found and in one i s o ­

lated c a s e ,

a s p a r k e r b e c a m e a n o n - s p a r k e r whe n it w a s r e m o u n t e d

and r u b b e d u n d e r the s a m e c on di t i on s as when it wa s f i r s t r u bb e d .
B.

Materials
The m a t e r i a l s u s e d in t hi s wor k a r e the s a m e a s t h os e u s e d

by He r sh and M o n t g o m e r y , wi t h the fol lowing e x c e p t i o n s :
the study of e l e c t r i c a l b r e a k d o w n and n o r m a l f o r c e ,

(1) f or

a pure tungsten

wi r e wa s r u b be d on a p o l y e t h y l e n e mo n o f i l a me n t ; (2) for the st udy
of the i n t e r r e l a t i o n s h i p b e t w e e n r u b b i n g ve l oc i t y,
dielectric constant,

resistivity,

and

a p i e c e of t a n t a l u m wi r e ob t a i ne d f r o m the F a n -

s t e e l M e t a l l u r g i c a l c o r p o r a t i o n was r u bb e d on a nyl on m o n o f i l a me n t ;
(3) for the st udy of d i f f e r e n t ki nds of i n s u l a t o r s ,

w i r e s of v a r i o u s

m a t e r i a l s we r e r u b b e d on c r y s t a l s of v a r i o u s a l k a l i h a l i d e s ,
the c r y s t a l s w e r e r u b b e d a g a i n s t e a c h ot her .

and

20

The r u b b i n g of the m e t a l s and the a l k a l i ha l i de c r y s t a l s
wa s done in the hope of obt a i ni ng e x p e r i m e n t a l v e r i f i c a t i o n of the
t h e o r y wi th s u b s t a n c e s of f a i r l y well known band s t r u c t u r e s { 4

)

The e x p e r i m e n t wa s not f r ui t f ul , h o w e v e r , owi ng to the f a c t t h a t the
ionic c o n d u c t i v i t y of t h e s e m a t e r i a l s is so high t h a t no a p p r e c i a b l e
c h a r g e is left on the c r y s t a l a s it is r u bb e d.

P e r h a p s if h i g h e r r u b ­

bi ng v e l o c i t i e s or l o we r t e m p e r a t u r e s could be a t t a i n e d ,

the e x p e c t e d

r e s u l t s would be obt a i ne d , but such v e l o c i t i e s and t e m p e r a t u r e s w e r e
not a t t a i n a b l e with the d e s c r i b e d a p p a r a t u s .
C.

At mos pher i c Breakdown
1,

De p e n d e n c e of C h a r g e on Amb i e n t P r e s s u r e
He r sh and Mo n t g o me r y found t hat a l i n e a r r e l a t i o n s h i p

e x i s t s b e t w e e n c h a r g e g e n e r a t e d and n o r m a l f o r c e up to a poi nt at
whi ch an i n c r e a s e in n o r m a l f o r c e no l o n g e r r e s u l t s in an i n c r e a s e
in the c h a r g e ( F i g u r e 14).

One c a u s e of t hi s b e h a v i o r m a y be

e l e c t r i c a l b r e a k d o w n of the a t m o s p h e r e s u r r o u n d i n g the c h a r g e d
f i l a me n t s .

The p o t e n t i a l d i f f e r e n c e b e t w e e n two e l e c t r o d e s at a

c o n s t a n t s p a c i n g d e c r e a s e s with d e c r e a s i n g ambien*; p r e s s u r e until
a m i n i m u m is r e a c h e d at whi c h t i me f u r t h e r d e c r e a s e s in a m b i e n t
p r e s s u r e c a u s e an i n c r e a s e in the p o t e n t i a l d i f f e r e n c e .

A t ypi cal

21

curve,

s hown be l o w, i s r e p r o d u c e d f r o m M e e k and C r a g g s (

If the p r o d u c t of p r e s s u r e , p, t i m e s s p a c i n g ,

5

).

d,

10,000

100

01

d (

10

Hg / c in )

e x c e e d s t ha t of the m i n i m u m for the c u r v e shown, and if b r e a k d o w n
is l i mi t i n g the c h a r g e , t h e n the l e v e l i n g off poi nt of the c u r v e of
c h a r g e g e n e r a t e d v e r s u s n o r m a l f o r c e shoul d d e c r e a s e with d e c r e a s i n g
a m b i e n t p r e s s u r e ( F i g u r e 15).
An i n d i r e c t t e s t b a s e d on t h e s e i d e a s wa s m a d e p r i o r to
addi ng the p h o t o m u l t i p l i e r to the a p p a r a t u s .

F o r this purp o s e ,

a b o t t o m yoke s i m i l a r in s i z e and sha pe to the top yoke wa s mo u n t e d
on the b a s e p l a t e , wi t h a l u c i t e i n s u l a t o r s e p a r a t i n g the yoke f r o m the
pl a t e .

The r u b b i n g a p p a r a t u s was t he n p l a c e d in the f i r s t t e s t c h a m ­

b e r w h e r e the a m b i e n t p r e s s u r e coul d be v a r i e d .

F i g u r e 16 s hows

the r e s u l t s of r u b b i n g a p i e c e of 5 - m i l nylon f i l a m e n t a g a i n s t a p i e c e
of 4 3 / 4 - m i l p o l y e t h y l e n e m o n o f i l a m e n t m a n u f a c t u r e d by C o u r t a u l d ' s
Ltd.

E a c h pl ot t e d p oi nt i s the a v e r a g e of t e n s u c c e s s i v e r u b s without

22

discharging,

e x c e p t at the b e g i n n i n g w h e r e it wa s u s u a l l y n e c e s s a r y

to m a k e 50 to 100 r u b s to r e a c h a c o n s t a n t val ue f or the c h a r g e .
The a r r o w s on the c u r v e s show the d i r e c t i o n of v a r i a t i o n of a m b i e n t
pressure.

E a c h c u r v e is a s e p a r a t e s e t of m e a s u r e m e n t s o bt a i n e d

f r o m the s a m e m a t e r i a l s , but on d i f f e r e n t days.

Before each run

the s y s t e m wa s p u m p e d down to a p r e s s u r e of about 4 m m Hg to
r i d the s y s t e m of w a t e r .

The a i r r e e n t e r i n g the t a nk w a s d r i e d by

p a s s i n g it t h r o u g h a d r y i n g c o l u m n c ont a i ni ng D r i e r i t e ,
one co nt a i n i ng Anhydr oue.
wa s about 5. 5 g r a m s ,

and t h r o u g h

The n o r m a l f o r c e b e t w e e n the f i l a m e n t s

and the ve l oc i t y of r ub wa s about 4 1 c m / s e c .

The r e s u l t s a r e q u a l i t a t i v e l y as e x p e c t e d , but the c u r v e s
do not q u a n t i t a t i v e l y follow the shape of the b r e a k d o w n c u r v e shown
on pa ge 21

.

T h i s is not too s e r i o u s , h o w e v e r ,

s i n c e it is p r a c t i c a l l y

i m p o s s i b l e to d e t e r m i n e d, the d i s t a n c e b e t w e e n p o i nt s f r o m whi ch
breakdown occurs.

Furthermore,

the n a t u r e of the m a t e r i a l s and

o t h e r f a c t o r s t end to c hange the s hape of the c u r v e (
the o t h e r hand,

5

).

On

t h e r e is a s e r i o u s di ff i cul t y in the f a c t t h a t n e i t h e r

the two c u r v e s a t low n o r m a l f o r c e n o r those at m e d i u m n o r m a l
f o r c e c oi nc i de .

T h i s d i s p a r i t y is a r e a l e f f ect ,

a s shown by s e t s of

m e a s u r e m e n t s t a k e n wit h the s t a r t i n g poi nt at s o me i n t e r m e d i a t e
p r e s s u r e and con t i n ue d t h r o u g h n e a r l y a c o m p l e t e c yc l e of r a i s i n g
and l o w e r i n g the p r e s s u r e .
b een found*

No e x p l a n a t i o n for t h i s b e h a v i o r h a s

23

2,

De t e c t i o n of S p a r k s ’with P h o t o m u l t i p l i e r
To t e s t the p o s s i b i l i t y of b r e a k d o w n m o r e d i r e c t l y ,

the

p h o t o m u l t i p l i e r 'was m o u l t e d and s p a r k s o c c u r r i n g d u r i n g b r e a k d o w n
w e r e d e t e c t e d on an o s c i l l o s c o p e .

F i g u r e 17 is a s e t of p h o t o g r a p h s

of the a c t u a l o s c i l l o s c o p e t r a c e showi ng e l e c t r i c a l b r e a k d o w n f r o m
the s a m e f i l a m e n t s when r u b b e d at a t m o s p h e r i c p r e s s u r e ,
p r e s s u r e of 1 c m Hg.

It c a r be s e e n t hat s o m e b r e a k d o w n is o c c u r r i n g

e ve n at a t m o s p h e r i c p r e s s u r e s ,
at l o w e r p r e s s u r e s .
larger,

and at a

but the a mo u n t i n c r e a s e s t r e m e n d o u s l y

The a m o u n t of b r e a k d o w n b e c o m e s p r o g r e s s i v e l y

and the s i g n a l s f r o m the s p a r k s get p r o g r e s s i v e l y l a r g e r ,

a s the p r e s s u r e is d e c r e a s e d .
An a t t e m p t wa s m a d e to r e p e a t the m e a s u r e m e n t s for si ngl e
r u b s wit h d i s c h a r g i n g b e t w e e n r u b s but , a s me n t i o n e d p r e v i o u s l y ,
no s a t i s f a c t o r y mo u n t i n g for the s o u r c e of i o n i z a t i o n could be d e v i s e d ,
so t h e s e a t t e m p t s w e r e gi ven up.
An o t h e r e x p e r i m e n t a l v e r i f i c a t i o n wa s a t t e m p t e d by ma k i n g
si ngl e r u b s ,

wi t h d i s c h a r g i n g b e t w e e n r u b s ,

at c o n s t a n t a m b i e n t

p r e s s u r e and u n d e r c o n t r o l l e d condi t i ons of t e m p e r a t u r e and r e l a t i v e
hu mi d i t y .

The c h a r g e g e n e r a t e d wa s m e a s u r e d as a f unct i on of

n o r m a l force.
The r u b b i n g a p p a r a t u s wa s p l a c e d in the s e c on d t e s t c h a m b e r

24

and t r a y s of a s a t u r a t e d s ol u t i o n of m a g n e s i u m c h l o r i d e w e r e p l a c e d
in the c h a m b e r to ke e p the r e l a t i v e h u mi d i t y at 33%.

Th e t e m p e r a t u r e

i n s i d e the c h a m b e r wa s hel d c o n s t a n t to wi t hi n -0. 2°C at 30°C
The v e l o c i t y of r u b wa s 4. 1 c m / s e c .

f or all r u b s .

F i g u r e 18 s hows

the r e s u l t s ob t a i n e d f r o m r u b b i n g an 8 - m i l nyl on m o n o f i l a m e n t a g a i n s t
4 3 / 4 - m i l , 1 0 - mi l , and 1 2 - mi l po l y e t h y l e n e m o n o f i l a m e n t s .

Nyl on and

p o l y e t h y l e n e we r e c h o s e n b e c a u s e t hey g e n e r a t e d high c h a r g e .

The

p l o t t e d po i n t s a r e the a v e r a g e of 5 r u b s m a d e a f t e r th 5 f i l a m e n t s
w e r e r u b b e d 50 o r 60 t i m e s to r e a c h a c o n s t a n t value.

The p o i n t s

wi t h a " s p a r k " b e s i d e t h e m a r e for r u b s w h e r e at l e a s t one s p a r k
wa s d e t e c t e d on s o me of the r u b s ,

and p oi n t s with no " s p a r k s " b e ­

si de t h e m a r e for p o i n t s w h e r e no s p a r k s w e r e d e t e c t e d on any rub.
The c u r v e s a r e to be c o m p a r e d with t h o s e o b t a i n e d by
Hersh (

1 ) who u s e d an 8 - m i l nyl on m o n o f i l a m e n t r u b b e d a g a i n s t

a 1 2 - mi l p o l y e t h y l e n e m o n o f i l a m e n t .

Our c u r v e s for m a t e r i a l s of

t h e s e s a m e d i a m e t e r s a g r e e quite well o v e r the s a m e r a n g e of n o r m a l
forces used,

about 3 to 11. 5 g r a m s ,

out to the h i g h e s t n o r m a l

f o r c e us ed,

and no b r e a k d o w n is o b s e r v e d
11.5 g r a m s .

But the c a r v e s

ob t a i n e d by u s i n g d i f f e r e n t d i a m e t e r p o l y e t h y l e n e f i l a m e n t s a r e
different,

e s p e c i a l l y the one f or the 4 3 / 4 - m i l f i l a m e n t ,

where

b r e a k d o w n b e g i n s to o c c u r at r e l a t i v e l y low n o r m a l f o r c e s .

This

findi ng c o n t r a d i c t s the c o n c l u s i o n of H e r s h , who s t a t e s t ha t the c h a r g e

25

g e n e r a t e d i.s i n d e p e n d e n t of the d i a m e t e r of the f i l a me n t s .
The f o r m of the c u r v e s shown in F i g u r e 18 s u g g e s t s a p o w e r
law* d e p e n d e n c e .
log-log paper.

A c c o r d i n g l y the c u r v e s have b e e n r e p l o t t e d on
The pl ot f or a fixed d i a m e t e r s hows an a p p r o x i m a t e

s q u a r e r o o t d e p e n d e n c e of c h a r g e g e n e r a t e d on n o r m a l f o r c e .
t r e a t the d i a m e t e r e f f e ct at the s a m e t i m e ,

To

t he n o r m a l f o r c e wa s

di vi ded by a d i f f e r e n t f a c t o r f or e a c h c u r v e in o r d e r to a c h i e v e
s u p e r p o s i t i o n of the c u r v e s .
treatment,

F i g u r e 19 shows the r e s u l t s of t hi s

when the f a c t o r wa s n u m e r i c a l l y e qual to the s q u a r e of

the d i a m e t e r f or e a c h f i l a me n t .
t h r o u g h the pl o t t e d poi nt s .

A line of sl ope o n e - h a l f is d r a w n

The fal l i ng of the e x p e r i m e n t a l p o i nt s

bel ow the c u r v e at the top c o i n c i d e s wi th the a p p e a r a n c e of s p a r k s .
The d i v e r g e n c e of the p o i nt s obt a i ne d us i n g the 1 0 - mi l f i l a m e n t at
the l o w e r end c a n be a t t r i b u t e d to the w e a r i n g effect.

Not enough

r u b s w e r e m a d e to r e a c h the fl at p o r t i o n of the c u r v e of c h a r g e vs.
r ub n u m b e r ,

b e f o r e the pl ot t ed dat a w e r e t aken.

T h i s is i l l u s t r a t e d

by the t h r e e s e t s of two po i nt s e a c h t a k e n at the s a m e n o r m a l f o r c e .
The l o w e r - l y i n g p o i n t s w e r e all t a ke n a f t e r o b t a i ni n g a c o m p l e t e
s e t of p o i n t s , b e g i n n i n g wi t h the l o w e s t n o r m a l f o r c e .

Th e d i v e r g e n c e

of the o t h e r p o i n t s is p r o b a b l y due to the f a i l u r e of the me t h o d of
e s t i m a t i n g n o r m a l f o r c e when we i ght s of 5 g r a m s or l e s s a r e hung f r o m
the f i l a me n t .

25

It i s t e m p t i n g to e xpl a i n t hi s d e p e n d e n c e a s p u r e l y a c o n t a c t
a r e a ef fect ,

2 1/2
s i nc e the e m p i r i c a l law c a n be w r i t t e n as q = ( F / d )
,

t h a t i s , the c h a r g e v a r i e s a s the s q u a r e r o o t of s o m e kind of e f f e c t i v e
pressure.
s i mp l e .

Un f o r t u n a t e l y , the r e l a t i o n do s s not a p p e a r to be so

A c c o r d i n g to the w o r k of H e r t z ,

a s gi ven in s a y T i m o s h e n k o (6)

the s u r f a c e of c o n t a c t b e t w e e n two e l a s t i c a l l y d e f o r m e d ,

stiff,

right-

c i r c u l a r c y l i n d e r s with a x e s at r i g h t a n g l e s to e a c h o t h e r h a s the
f o r m of an e l l i p s e wi t h s e m i - a x e s gi ven by
a = Oi ( F m/ ,n ) 1/3

b z j8 ( F m / n ) 1 / 3

and

where

F - n o r m a l force
m - 4 r jr

/ (r j + r 2)

n - 3(1-a 2) / 4 E
The f a c t o r s r ^ and
modulus,

andjjl

r ^ a r e the r a d i i of the

is P o i s s o n ' s r a t i o .

c y l i n d e r s , Eis Yo un g' s

The f a c t o r s

06

and ^ 3

de pe nu

on the r a d i i of the c y l i n d e r s , but t h e i r v a r i a t i o n is qui te e m a i l ,
are

multiplied together,

u s e d in t hi s wor k.

and when t hey

a r e p r a c t i c a l l y c o n s t a n t for the c y l i n d e r s

The c o n t a c t a r e a t h e n b e c o m e s

A - 77" ab = k ^ ( Fr ^ r 2 / r 1 -hr

2 ^^

27

If we a s s u m e q OC F / A ,

_
q

we t h e n obt ai n

1/ 3

I

\ 2/3

(r l + I z |

T h i s gi ve s a o n e - t h i r d p o w e r r e l a t i o n s h i p b e t w e e n c h a r g e and n o r m a l
force,

i n s t e a d of the o n e - h a l f p o w e r o bt a i n e d e x p e r i m e n t a l l y .
E x p e r i m e n t a l l y it is found t hat to obt ai n i d e n t i c a l c h a r g e s

g e n e r a t e d on the 4 3 / 4 - m i l and 1 2 - mi l p o l y e t h y l e n e f i l a m e n t s when
r u b b e d with an 8 - m i l nyl on f i l a m e n t , the n o r m a l f o r c e for the
12 - mi l f i l a m e n t m u s t be 6. 4 t i m e s the n o r m a l f o r c e for the
4 3 / 4 - m i l f i l a me n t .

On the b a s i s of the t h e o r y the f a c t o r t u r n s

out to be 2 . 6 , whi c h i s m u c h too s m a l l to e x pl a i n the o b s e r v e d
results.

L i k e w i s e , the e x p e r i m e n t a l f a c t o r for the 1 0 - mi l and

12 - mi l f i l a m e n t s is 1. 44, w h e r e a s the t h e o r e t i c a l f a c t o r is 1. 17.
Thus t hi s h y p o t h e s i s f ai l s to e xp l a i n d e p e n d e n c e of c h a r g e on
e i t h e r the n o r m a l f o r c e or the d i a m e t e r .
be r e j e c t e d a b s o l u t e l y , h o w e v e r ,

The e x p l a n a t i o n ca nnot

s i nc e it is l i ke l y t hat the m a t e r i a l s

un d e r st udy a r e not p e r f e c t l y e l a s t i c n o r p e r f e c t l y p l a s t i c u n d e r
the c on d i t i o n s of the e x p e r i m e n t , but li e in s o m e i n t e r m e d i a t e r e g i o n
P e r h a p s m o d i f i c a t i o n of the h y p o t h e s i s would p e r m i t t hi s i n t e r p r e ­
t a t i o n to stand.

28

F r o m the r e s u l t s of r u b b i n g nyl on on p o l y e t h y l e n e m o n o f i l a ­
m e n t s of d i f f e r e n t d i a m e t e r s ,
platinum,

and f r o m r e s u l t s of r u b b i n g t u n g s t e n ,

and t i t a n i u m w i r e s on 4 3 / 4 - m i l p o l y e t h y l e n e ,

s o me c o n ­

c l u s i o n s m a y b e r e a c h e d on the va l i di t y of the r e s u l t s of H e r s h and
M o n t g o m e r y a s f a r a s l i m i t a t i o n by a t m o s p h e r i c b r e a k d o w n is c o n ­
cerned.

It m a y be s t a t e d t hat t h e i r m e a s u r e d c h a r g e s a r e not l i m i t e d

by b r e a k d o w n in c a s e s w h e r e the f i l a m e n t d i a m e t e r s a r e l a r g e and
the n o r m a l f o r c e s a r e of m o d e r a t e v a l u e s ; but in al l l i k e l i h oo d t h e i r
m e a s u r e d c h a r g e s a r e l i m i t e d by b r e a k d o w n in s o me of t h e i r r e s u l t s
at high n o r m a l f o r c e s and all t h e i r r e s u l t s wit h s m a l l d i a m e t e r f i l a ­
ments .
D.

Resistivity,

D i e l e c t r i c Co n s t a n t ,

and Ve l o c i t y of Rub

The p h e n o m e n o n of s t a t i c e l e c t r i f i c a t i o n can be b r o k e n into
two p a r t s ;

1)

the gai n of c h a r g e upon ma k i n g c o n t a c t b e t w e e n the

m a t e r i a l s in q u e s t i o n , and
c on t a c t .

2)

the l o s s of c h a r g e upon b r e a k i n g the

Van O s t e n b u r g (7) h a s m a d e s o me t h e o r e t i c a l c a l c u l a t i o n s

of the c h a r g e gai ned upon c o n t a c t , and ha s a t t e m p t e d s o m e i n t e r ­
p r e t a t i o n of the r e s u l t s of H e r s h and M o n t g o m e r y on t hi s b a s i s .
The u t i l i t y of h i s r e s u l t s is d e p e n d e n t on knowl edge of the e n e r g y
l e v e l s in i n s u l a t o r s .

H e r s h and M o n t g o m e r y ha v e a s s i g n e d e n e r g y

l e v e l s to a few m a t e r i a l s b a s e d on the e x p e r i m e n t a l r e s u l t s of r u b b i n g
t h e s e m a t e r i a l s t o g e t h e r , but t h e r e is l i t t l e i n d e p e n d e n t c o n f i r m a t i o n
of the v a l u e s for i n s u l a t o r s .

Th u s the w o r k of Van O s t e n b u r g will

be of r e s t r i c t e d val ue unt i l i n d e p e n d e n t i n f o r m a t i o n is a v a i l a b l e .

29

on the e n e r g y l e v e l s of i n s u l a t o r s .
Only v e r y c r u d e c o n j e c t u r e s on the l o s s of c h a r g e upon b r e a k ­
ing c o n t a c t a r e m a d e by H e r s h and M o n t g o m e r y ( 2

).

One of the

p r i m a r y d i r e c t i o n s of e x t e n s i o n of the wo r k in s t a t i c e l e c t r i f i c a t i o n
is t o w a r d s ga i ni ng m o r e u n d e r s t a n d i n g of the l o s s of c h a r g e upon
b r e a k i n g the c o n t a c t b e t w e e n m a t e r i a l s .
cul t p r o b l e m to a n a l y z e e x a c t l y ,

It is an e x c e e d i n g l y d i f f i ­

and we have a t t e m p t e d to t ake i d e a s

s u g g e s t e d f r o m r e l a t e d p h e n o m e n a of c u r r e n t flow in d i e l e c t r i c s
in o r d e r to a s c e r t a i n the c o n t r o l l i n g f a c t o r s and the r e l a t i o n a mong
t hem.
1.

Theory
In a l i n e a r ,

i s ot r opi c, homogeneous medium,

r e l a t i o n s e x i s t b e t w e e n D,

the following

the e l e c t r i c d i s p l a c e m e n t v e c t o r ; E ,

the e l e c t r i c field v e c t o r ; and J , the c u r r e n t d e n s i t y vect or :
D = £ E ,
J

where

€

z

a~

is t he d i e l e c t r i c c o n s t a n t ,

r e c i p r o c a l of the r e s i s t i v i t y .

and

a~ is the c onduc t i vi t y, or

F r o m t h e s e r e l a t i o n s and M a x w e l l ' s

F i r s t E q u a t i on , we find
V-J =

w h e r e yO

Q— —
.
V- -£~ D -

C
7

is the vol ume c h a r g e de ns i t y.

p
Usi ng t hi s r e l a t i o n ,

e q u a t i o n f or c o n s e r v a t i o n of c h a r g e b e c o m e s

^

p

e

'

+ i£ j t

=

o

the

30

The s o l u t i o n of t h i s e q u a t i o n in t e r m s of the i n i t i a l c h a r g e d e n s i t y ,

Po

- ( r /t) *

■ is

P
Co n s e q u e n t l y ,

" /° o

e

in a m e d i u m of finite r e s i s t i v i t y ,

p e r m a n e n t d i s t r i b u t i o n of f r e e c h a r g e .
z e r o initially,

t h e r e c a n be no

If the c h a r g e d e n s i t y is

it r e m a i n s z e r o for all t i me .

If a c h a r g e is p l a c e d

in the i n t e r i o r of the r e g i o n it d e c a y s e x po n e n t i a l l y with t i m e and,
s i nce it ca n no t r e a p p e a r wi t hi n the v ol u me of the r e g i o n ,

it m u s t

c o me to r e s t on the b o u n d a r y o r o u t e r s u r f a c e of the r e g i o n

The

t i me n e c e s s a r y for the c h a r g e to d e c a y to 1/e of i t s o r i g i n a l val ue,
6

r

= ^

is c a l l e d the r e l a x a t i o n t i me (
o v e r wide r a n g e s ,

8

).

The r e l a x a t i o n t i me c a n ^ar y

f r o m v a l u e s l e s s t han 10 1 2 s e c o n d s for the c a s e

of f a i r l y good c o n d u c t o r s ,

-

up to v a l u e s e x c e e d i n g 10^ s e c o n d s for

good i n s u l a t o r s .
The p r o b l e m of s t a t i c e l e c t r i f i c a t i o n ,

however,

usually

d e a l s wi t h c h a r g e s p l a c e d on the s u r f a c e of an i n s u l a t o r , not in the
interior,

so it i s of i n t e r e s t to know how t h e s e s u r f a c e c h a r g e s d e c a y

in t i me .

The p r o b l e m of what h a p p e n s to a poi nt c h a r g e p l a c e d on

the s u r f a c e of a d i e l e c t r i c s p h e r e is not e x c e s s i v e l y di f f i cul t , but
the r e s u l t is not e a s y to d e s c r i b e s i mpl y.

The c h a r g e d e c a y ca n n o t

be c h a r a c t e r i z e d by a uni que r e l a x a t i o n t i m e , but t h e r e will e x i s t

31

s o m e kind o f a v e r a g e r e l a x a t i o n t i m e not too d i f f e r e n t f r o m t hat
c h a r a c t e r i z i n g the r e l a x a t i o n of c h a r g e in the i n t e r i o r of the d i e l e c t r i c
medium.
In o a r p r o b l e m ,
in s p a c e and t i me .

we have a c o m p l i c a t e d d i s t r i b u t i o n of c h a r g e

We ha ve not b e e n abl e to a t t a c k the p r o b l e m

e x a c t l y , but i n s t e a d ,

we have t r i e d to u n d e r s t a n d the g r o s s e f f e c t s

by c o n s i d e r i n g t h a t the b e h a v i o r can be p a r t i a l l y a n a l y z e d in t e r m s
of the r a t i o of s o me t i m e i n t e r v a l c h a r a c t e r i s t i c of the r u b ,
r e l a x a t i o n t i m e c h a r a c t e r i s t i c of the m a t e r i a l .

to the

The f o r m e r is gi ven

by the t i m e n e c e s s a r y for s o m e c h a r a c t e r i s t i c l e ngt h, £ Q , to be
t r a v e r s e d at a v e l o c i t y,

v, whi ch is
fco

= ^o/v ;

the l a t t e r will be . a ppr oxi ma t e d by the r e l a x a t i o n t i me for a h o m o g e n ­
eous m e d i u m .

He n c e ,

to / ?

the c h a r a c t e r i s t i c p a r a m e t e r is

-

' r j * U 1/

T h ’s s a m e r e s u l t coul d have b e e n r e a c h e d i m m e d i a t e l y by the s t a n d a r d
m e t h o d s of d i m e n s i o n a l a n a l y s i s ,

if the r e l e v a n t v a r i a b l e s a r e

cr

and v ( 9 ) .
2.

Experimental Procedure
A p i e c e of 8 - m i l t a n t a l u m w i r e wa s r u b b e d a g a i n s t an 8 - m i l

nyl on m o n o f i l a m e n t ,

and the t e m p e r a t u r e and the r e l a t i v e h u m i d i t y

we r e v a r i e d so a s to v a r y the r e s i s t i v i t y of the nylon.

F i g u r e 20

?

sh ows t he r e l a t i o n b e t w e e n the r e s i s t i v i t y of nyl o n and the t e m p e r a ­
t u r e f or v a r i o u s r e l a t i v e h u m i d i t i e s ,

and F i g u r e 2 1 s hows the r e l a ­

ti on b e t w e e n the r e s i s t i v i t y and the r e l a t i v e h u mi d i t y for v a r i o u s
temperatures

Bo t h c u r v e s a r e d e r i v e d f r o m H e r s h and M o n t g o m e r y

( 10 ) who m e a s u r e d r e s i s t i v i t y as a f unct i on of r e g a i n .

The m e a s u r

ing c i r c u i t adopt e d by H e r s h and M o n t g o m e r y f or the m e a s u r e m e n t of
the r e s i s t a n c e of v a r i o u s m a t e r i a l s is shown in F i g u r e 22.

The

s a m e c i r c u i t w a s u s e d in t h e s e s t u d i e s to m e a s u r e the r e s i s t i v i t y
of the nyl on s a m p l e b e f o r e and a f t e r r u bbi ng

In t hi s c i r c u i t ,

a

hi gh vol t age suppl y i m p r e s s e s a known vol t age V , a c r o s s the unknow
r e s i s t a n c e of the nyl on, R x .

The vol t a ge ,

V , is a d j u s t e d until the

e l e c t r o m e t e r s hows z e r o po t e n t i a l d i f f e r e n c e a c r o s s its t e r m i n a l s .
The c u r r e n t t h r o u g h R x is t he n e qual to the c u r r e n t t h r o u g h R g»
whi ch is a s t a n d a r d r e s i s t o r of about 10 12 o h m s ,

and Rx is gi ven by

R x = (VX/ V S) RS,
In p r a c t i c e ,

the w i r e f r o m the high vol t age suppl y is c o n n e c t e d s o m e ­

w h e r e n e a r t he c e n t e r of the nyl on f i l a m e n t whi ch is mo u n t e d in
the b o t t o m yoke.

F r o m the knowl e dge of the r e s i s t a n c e of the f i l a ­

ment,

and i t s c r o s s - s e c t i o n a l a r e a ,

i t s l e ng t h,

the s a m p l e c a n t h e n be d e t e r m i n e d .

the r e s i s t i v i t y of

A c ont i nual c h e c k on the

r e s i s t i v i t y of the nyl on c a n be ma d e i n d i r e c t l y by m o n i t o r i n g the
t e m p e r a t u r e and the r e l a t i v e h u mi d i t y in the t e s t c h a m b e r .

The

r e l a t i v e h u m i d i t y is m o n i t o r e d at t h r e e p l a c e s in the c h a m b e r ,
about 6 i n c h e s to the r i g h t and left of the f i l a m e n t and at the top of
the c h a m b e r d i r e c t l y above the f i l a me n t , by the us e of E l - t r o n i c
h u mi d i t y s e n s i n g e l e m e n t s * .
3

Results
F i g u r e s 2 5 and 26 show the r e s u l t s of m e a s u r e m e n t s of c h a r g

g e n e r a t e d on two s e p a r a t e nyl on f i l a me n t s .

The c h a r g e g e n e r a t e d

is p l ot t e d a s a f unct i on of v e l oc i t y for t h r e e d i f f e r e n t t e m p e r a t u r e s ,
wit h the r e l a t i v e h u mi d i t y hel d n e a r l y c o n s t a n t at 75%.

The n o r m a l

f o r c e is kept c o n s t a n t at about 6, 9 g r a m s and t he l engt h of r ub is
2. 3 c m for all r u b s .

The p oi n t s a r e obt a i ned by t aki ng the a v e r a g e

of 5 r u b s a t e a c h ve l oc i t y and n o r m a l i z i n g to r u b n u m b e r 45.

Nor­

m a l i z i n g is n e c e s s a r y a s c a n be s e e n f r o m F i g u r e 2 3, and is a c c o m ­
p l i s h ed in the fol l owi ng m a n n e r :

A s mo o t h c u r v e is d r a w n t h r o u g h

all po i nt s o b t a i ne d at 4. 1 c m / s e c .

The a v e r a g e of the 10 r u b s

b e t w e e n 40 and 50 i s t h e n found, and a h o r i z o n t a l line d r a w n t h r o u g h
the a v e r a g e ( F i g u r e 24).

The c h a r g e at e a c h r u b is t hen mu l t i p l i e d

by the r a t i o of the h e i gh t of the h o r i z o n t a l l ine to the hei ght of the
s mo o t h c u r v e at t h a t poi nt and r e p l o t t e d .
five r u b s at e a c h vel oci t y is found.

* M a n u f a c t u r e d by E l - T r o n i c s ,

The n the a v e r a g e for the

Since the five r u b s at e a c h vel oc

Inc. , Mayf i el d, P e n n s y l v a n i a

34

a r e r e p e a t e d at l e a s t once for e a c h s e t of m e a s u r e m e n t s ,

an a v e r a g e

b e t w e e n t h e s e two s e t s of v a l u e s is t a k e n as the val ue of the c h a r g e
g e n e r a t e d at t h a t ve l oci t y.

The r e s i s t a n c e of the nyl on f i l a m e n t wa s

m e a s u r e d b e f o r e and a f t e r e a c h s e t of m e a s u r e m e n t s .

T a bl e 1

l i s t s the e x p e r i m e n t a l v a l u e s ob t a i n e d for e a c h f i l a m e n t at the
different t e m p e r a t u r e s .

_L :< 1n
^ -cm
(j10 1 0-Q
Te mp .

b e f o r e r ubbi ng

1

25°C

4, 03

5. 38

4 00

30°C

2. 00

1. 97

1. 26

35°C

1. 02

0. 82

1. 00

25°C

4, 00

3. 65

5. 50

U
0
o

m

^ x 10^ 9iT- c m
a f t e r r u bb i ng

Filament no.

3. 35

1. 79

3. 65

35°C

0. 83

0. 87

1. 17

2

Ta bl e 1

With the val ue of 1. 0 x 10 ^ .O . - c m found for f i l a me n t no.
t a k e n a s the c o r r e c t va l ue ,

1 at 35°C

all the o t h e r c u r v e s w e r e n o r m a l i z e d to

t h i s val ue by mu l t i p l y i n g the v e l o c i t y at e a c h poi nt by a n o r m a l i z i n g
factor,

/3

■ The v a l u e s of / 3

a l s o l i s t e d in T a b l e 1.

n e c e s s a r y for n o r m a l i z a t i o n a r e

F i g u r e 27 is a l o g - l o g pl ot of c h a r g e vs.

35

the p r o d u c t of j 3

and ve l o c i t y for the c u r v e s of F i g u r e s 24 and 25.

It i s f el t by t he a u t h o r t h a t the p o i n t s lyi ng off t he c u r v e a r o u n d the
p o i n t s of 7 and 8 /# v

m a y be e x p l a i n e d by the f a c t t hat t h e s e p oi n t s

a r e o b t a i n e d e x p e r i m e n t a l l y at hi gh v e l o c i t i e s f or the rub.

Un de r

t h e s e c i r c u m s t a n c e s the l e n g t h of r u b b e d f i l a m e n t is l e s s owing
to the f a c t t h a t a s m a l l t i m e i n t e r v a l is n e c e s s a r y for l o w e r i n g the
top yoke.

The top yoke a c t u a l l y h a s two c o mp o n e n t s of v e l o c i t y whi l e

it i s b e i n g l o w e r e d ,
d i r e c t i o n of r u b.

one in the d o wn wa r d d i r e c t i o n and one in the

As long a s the d ownwar d c o mp o n e n t of ve l oc i t y

is l a r g e c o m p a r e d wi t h the r ub b i n g ve l oc i t y,

c h a n g e s in the r u b b i n g

v e l o c i t y will a f f e c t the poi nt of c o n t a c t b e t w e e n the top and b o t t o m
f i l ament s v e r y little.

But whe n the r u bb i ng ve l o c i t y b e c o m e s c o m ­

p a r a b l e wi t h t he d o wn wa r d vel oc i t y of the top yoke,

c h a n g e s in the

r u b b i n g ve l o c i t y will c a u s e m e a s u r a b l e c h a n g e s in the c o n t a c t point.
The poi nt at wh i c h the f i l a m e n t s b r e a k c o n t a c t i s v i r t u a l l y u na f f e c t e d
by t h e s e f a c t o r s so it c a n be s e e n t hat the l e n g t h of r u b m a y d e c r e a s e
a t hi gh r u b b i n g v e l o c i t i e s .
The c u r v e h a s b e e n fitted e m p i r i c a l l y wi th the e qu a t i o n
T h e r e a r e only two a d j u s t a b l e p a r a m e t e r s
in the equat i on:

the s a t u r a t i o n val ue of the c h a r g e ,

for the c u r v e shown; and one c o n t r o l l i n g the r a p i d i t y of r i s e ,
for the c u r v e shown.
factor, A

5. 1Z

If it is d e s i r e d to ident ify the n o r m a l i z i n g

wi t h t he p r o d u c t of r e s i s t i v i t y and d i e l e c t r i c c o n s t a n t

36

for the nyl on s a m p l e , the c o n s t a n t c h a r a c t e r i z i n g the r a t e of r i s e of
the c u r v e h a s the d i m e n s i o n s of length.
for the d i e l e c t r i c c o n s t a n t of nyl on,
Z. 9 x 10

_^

cm.

With a val ue of about 6. 5

t hi s l e ngt h t u r n s out to be

T h i s val ue is quite r o u g h ,

s i nc e the d i e l e c t r i c c o n ­

s t a n t is p r o b a b l y not known to b e t t e r t h a n -50%, and the r e s i s t i v i t y
m a y v a r y by a s l a r g e a f a c t o r a s Z or 3 f r o m the m e a s u r e d value
a s will be d i s c u s s e d l a t e r .

Hence the s t a t e d c h a r a c t e r i s t i c l engt h

shoul d p r o b a b l y be c o n s i d e r e d s i g n i f i c a n t only in o r d e r of ma g n i t u d e .
Mo r e w o r k is n e c e s s a r y b e f o r e the value ca n be s t a t e d m o r e p r e ­
c i s e l y and b e f o r e the n a t u r e of t hi s c h a r a c t e r i s t i c l engt h c an be
eluc i dat ed.
The c o m p a r i s o n of j 3
c a n be m a d e f r o m Ta b l e 1.

with the m e a s u r e d v a l u e s of

€ /< r

The c o m p a r i s o n i s di s a ppoi nt i ng.

d i s a g r e e m e n t m a y not be so s e r i o u s , h o w e v e r ,

The

si nce the r e s i s t i v i t y

or d i e l e c t r i c c o n s t a n t or bot h ma y change wi th r ub b i n g

Since the

l engt h of nyl on r u b b e d is Z. 3 c m and the l engt h of nylon u s e d f or the
r e s i s t i v i t y m e a s u r e m e n t is 10. 4 c m,

a f a i r l y l a r g e change in r e s i s ­

ti vit y in the r u b b e d p o r t i o n of the f i l a me n t m a y not m e a s u r a b l y c h a ng e the
r e s i s t i v i t y of the n y l o n ,

A b e t t e r t e chni que for m e a s u r i n g the r e s i s ­

t i vi t y of the r u b b e d p o r t i o n of the nylon is n e c e s s a r y b e f o r e t hi s
p r o b l e m c a n be r e s o l v e d .

C H A P T E R IV
DISCUSSION AND CONCLUSIONS
The t h e o r y put f o r t h by H e r s h and M o n t g o m e r y is b a s e d on
d i v i s i o n of the p r o c e s s of s t a t i c e l e c t r i f i c a t i o n into two s t e p s ,

the

d i r e c t flow of c h a r g e upon ma k i n g c o n t a c t , and the r e v e r s e flow
upon b r e a k i n g cont a c t .

The p o r t i o n of the t h e o r y which t hey gave

the m o s t s p e c i f i c f o r m wa s t hat in whi ch the n a t u r e of the m a t e r i a l s
was t a k e n into a ccount .

De t a i l e d c a l c u l a t i o n s on t hi s poi nt w e r e

c a r r i e d out by Van O s t e n b u r g ,
h a s b e e n shown.

and no c o n t r a d i c t i o n with e x p e r i m e n t

It m u s t be kept in mi n d, h o w e v e r , t hat t h e r e is

l i t t l e i n d e p e n d e n t knowl e dge of the p a r a m e t e r s a p p e a r i n g in the t h e o ­
r e t i c a l e x p r e s s i o n s for c h a r g e t r a n s f e r r e d .

The w o r k of Van O s t e n ­

b u r g p r o c e e d e d f r o m a o n e - d i m e n s i o n a l mo d e l ,
c e r n e d with r e t u r n of c h a r g e upon s e p a r a t i o n .

and was not c o n ­
Co n s e q u e n t l y hi s

wo r k h a s l i t t l e to say about the ef f ect of f i l a m e n t d i a m e t e r o r of
normal force,

and of c o u r s e not hi ng at all on the e f f e ct of ve l oci t y

and r e s i s t i v i t y .
H e r s h and M o n t g o m e r y did not give v e r y def i ni t e f o r m to t h e i r
i d e a s on r e t u r n of c h a r g e .

The r e a s o n s a r e t wo-f ol d,

the e x p e r i ­

m e n t a l w o r k wa s not p r e c i s e enough or e x t e n s i v e enough to e s t a b l i s h
e m p ir ic a l laws,

and the t h e o r e t i c a l i n v e s t i g a t i o n is h a m p e r e d by the

hi gh c o m p l e x i t y of the p h e n o m e n a .

In the p r e s e n t w o r k it h a s b e e n

a t t e m p t e d to find at l e a s t the e m p i r i c a l l a w s d e s c r i b i n g the e f f e ct

38

of f i l a m e n t d i a m e t e r and n o r m a l f o r c e on c h a r g e ga i ne d upon m a k i n g
contact,

and t h o s e d e s c r i b i n g the e f f ect of f i l a m e n t r e s i s t i v i t y and

r u b bi n g v e l o c i t y on c h a r g e l o s t upon b r e a k i n g c ont act .

The hope f or

s u c c e s s in t h i s a t t e m p t wa s founded on the c o n s t r u c t i o n of a b e t t e r
i n s t r u m e n t and on the i m p r o v e d u n d e r s t a n d i n g of the p h e n o m e n a
a c h i e v e d in the e a r l i e r wor k.
The f i r s t p oi nt to be e s t a b l i s h e d in appl yi ng the t h e o r y of H e r s h
and M o n t g o m e r y i s t hat the c h a r g e m e a s u r e d is i ndeed c o n t r o l l e d by
the s o l i d - s t a t e p r o c e s s e s ,
atmosphere.

and not by e l e c t r i c a l b r e a k d o wn , of the

As r e p o r t e d in C h a p t e r III, S e c t i o n C- Z, it a p p e a r s

t hat for the b u l k of the e x p e r i m e n t a l w o r k d e s c r i b e d by H e r s h ,
cal b r e a k d o w n did not o c c u r .

What is a m o r e i m p o r t a n t fact ,

electri­
in the

p r e s e n t w o r k it wa s p o s s i b l e to know when the c h a r g e was l i m i t e d
by b r e a k d o w n .
H e r s h ' s e x p e r i m e n t a l wo r k had shown suf f i c i e nt r e p r o d u c i ­
bil i t y to allow a r a t i o n a l a t t a c k to be ma d e on the p r o b l e m of s t a t i c
electrification.
reproducibility.
disagreement.

The p r e s e n t w o r k shows about the s a m e d e g r e e of
So f ar a s si gn of c h a r g e is c o n c e r n e d ,
So f a r a s m a g n i t u d e is c o n c e r n e d ,

cannot be so c l e a r cut.
c a l l e d f or ,

Ordinarily,

and s o m e a v e r a g i n g .

t h e r e is no

the c o m p a r i s o n

s o me condi t i oni ng o r agi ng is

One would like to be r i d of t h e s e

u n s a t i s f a c t o r y f e a t u r e s , but t hi s is not yet p o s s i b l e .

39

Havi ng a s c e r t a i n e d the a g r e e m e n t in the l a r g e of the p r e s e n t
r e s u l t s with t he e a r l i e r o n e s of H e r s h and M o n t g o m e r y ,
p o s i t i o n to i m p r o v e and ext end the fi ndings.

we a r e in

The e x t e n s i o n t a k e s

p l a c e in two d i r e c t i o n s - the e f f e c t of n o r m a l f o r c e and f i l a me n t
d i a m e t e r on d i r e c t flow of c h a r g e ,

and the e f f e ct of f i l a m e n t r e s i s ­

ti vi t y and r ub bi n g v el oc i t y on r e v e r s e flow of c h a r g e .

Fortunately,

the f o r m of the d e p e n d e n c e of c h a r g e m e a s u r e d on r e s i s t i v i t y and
v e l o c i t y is s uc h t h a t the two e f f e c t s me n t i o n e d can be s e p a r a t e d .

It

will be r e c a l l e d f r o m C h a p t e r III, Sect i on D- 3, t hat the d e p e n d e n c e
of c h a r g e on t h e s e v a r i a b l e s c an be e x p r e s s e d a s

Now if the m a g n i t u d e of the e xpo ne n t is l a r g e enough,
disappears,

its ef f ect

and the p r o p o r t i o n a l i t y f a c t o r m a y be st udi ed by i t sel f.

In p r a c t i c e t h i s end ma y be a c h i e v e d by wo r k i n g at r e l a t i v e l y nigh
v e l o c i t i e s and low c o n d u c t i v i t i e s ,

the l a t t e r obt a i ned by r e d u c i n g

the r e l a t i v e h u mi d i t y or the a m b i e n t t e m p e r a t u r e .
of the p r o p o r t i o n a l i t y f a c t o r on type of m a t e r i a l ,
r u b , d i a m e t e r of f i l a m e n t ,

Th e n the d e p e n d e n c e
type of r u b, l e ng t h of

and n o r m a l f o r c e c an be studied.

It will be r e c a l l e d f r o m C h a p t e r III, Se ct i on C- 2 ,
d e p e n d e n c e of c h a r g e on n o r m a l f o r c e
c a n be e x p r e s s e d as
q cc

F 1 / 2 /d.

t ha t the

F and f i l a m e n t d i a m e t e r d

■:o

In t hi s p a r t of the wo r k the r e l a t i v e h u mi d i t y wa s m a i n t a i n e d low
enough t h a t the r e s u l t a n t losv c o n d uc t i v i t y s u r p r e s s e d the d e p e n d e n c e
of c h a r g e on the f a c t o r s a p p e a r i n g in the e q u a t i o n in the p r e c e d i n g
paragraph

In all l i ke l i hood the p a r a m e t e r

de pe nds on the f i l a m e n t d i a m e t e r .
m e n s t e s t e d , the val ue of
of the r u b b e d f i l a me nt .

in t h a t e qu a t i o n

In f act , for the p a r t i c u l a r s p e c i ­

JPQ is v e r y n e a r l y equal to the d i a m e t e r

Th i s c o i n c i d e n c e is undoubt edl y f o r t u i t o u s ,

but it m a y l end s o me s u p p o r t to the e x i s t e n c e of an addi t i ona l d e p e n ­
den c e on d i a m e t e r .
In the p r e s e n t wo r k ,
r u b was not st udi ed.

the d e p e n d e n c e of c h a r g e on lengt h of

It is di f f i cul t to s e e , h o w e v e r ,

c a n di f f er f r o m the p r o p o r t i o n a l i t y found oy H e r s h ,

t hat the r e l a t i o n
except possibly

under c o n d i t i o n s w h e r e a s t r o n g vel oci t y d e p e n d e n c e o c c u r s .
then

q

OC

We t ake

L-.

The ab ove e q u a t i o n s m a y be c o mb i n e d to give
q - c (L F

1 /?
-€ V /o - J > 0
' / d) { 1 - e

),

w h e r e q is the t o t a l c h a r g e p r o d u c e d on a r u b b e d l e ngt h L of a f i l a ­
m e n t of d i a m e t e r d^ c o nd uc t i v i t y o— , and d i e l e c t r i c c o n s t a n t €
T h i s e x p r e s si on hol d s for 4 5 ° - 4 5 ° r u b s wh e r e f r e s h a r e a s a r e
bei ng r u b b e d on bot h f i l a m e n t s p r e s s e d t o g e t h e r with a n o r m a l f o r c e
F.

The c h a r a c t e r i s t i c d i s t a n c e

Jo

is t a k e n as an a d j u s t a b l e p a r a ­

m e t e r , but it wil l be s u r p r i s i n g if f u r t h e r w o r k c a n not e l u c i d a t e its

41

nature.

The p r o p o r t i o n a l i t y c o n s t a n t c is,

in p r i n c i p l e ,

determined

ay the d e t a i l s of t he ba nd s t r u c t u r e s of the c o n t a c t i n g m a t e r i a l s .
In p r a c t i c e ,

so l i t t l e is known of the band s t r u c t u r e s of the m a t e r i a l s

of i n t e r e s t t h a t c m u s t be fixed e x p e r i m e n t a l l y
The g e n e r a l e q u a t i o n above is an e m p i r i c a l r e l a t i o n c o n n e c t i n g
what m a y be c o n s i d e r e d the m o s t i m p o r t a n t f a c t o r s in s t a t i c e l e c t r i ­
f i c a t i o n,
course,

e x c e p t t h a t r ub type h a s not b e e n incl uded.

It ma y be , of

t hat only the f a c t o r c m a y change with r ub type; but t hi s is

unl i ke l y,

si nce in s o me t y p e s l ocal t e m p e r a t u r e s m u s t b e c o m e v e r y

high and t h e r e b y a l t e r not m e r e l y th«e band s t r u c t u r e but a l s o the
d i s t r i b u t i o n of c h a r g e c a r r i e r s in the b a n d s and the m e c h a n i s m of
charge trapping.

The e l u c i d a t i o n of t h e s e p h e n o m e n a c o n s t i t u t e s a

c h a l l e n g i n g and c o m p l e x p r o b l e m ,
A d i s t u r b i n g f e a t u r e t ha t a p p e a r s f r o m the r e s u l t s of the
p r e s e n t e x p e r i m e n t i s t ha t s o me doubt is t h r o wn on a b a s i c a s s u m p ­
tion of the t h e o r y , n a m e l y , t hat the e q u i l i b r i u m c h a r g e d i s t r i b u t i o n
is a t t a i n e d d u r i n g cont act .

The d e p e nd e n c e of m e a s u r e d c h a r g e on

ve l oc i t y and r e s i s t i v i t y d o e s not s e e m to be i n t e r p r e t a b l e in a
s i m p l e m a n n e r in t e r m s of r e v e r s e flow of c h a r g e .

Rather there

is s o m e s u g g e s t i o n t hat the d i r e c t c h a r g e flow is l i mi t e d by the
i n a b i l i t y of e l e c t r o n s to be f r e e d f r o m t r a p s in the b e t t e r i n s u l a t o r .
The r e s u l t s of H e r s h and M o n t g o m e r y wi th a s y m m e t r i c r u b s ,

in

p a r t i c u l a r w h e r e one spot on an i n s u l a t i n g m a t e r i a l is s a we d into by
a n o t h e r f i l a m e n t of the s a m e m a t e r i a l ,
p h e n o me n o n .

give e vi d e n c e of a s i m i l a r

The hot spot g e n e r a t e d in the s a w e d - i n t o f i l a m e n t s

v i r t u a l l y a l wa y s l o s e s e l e c t r o n s .

On the o t h e r hand, we can equa l l y

wel l s p e c u l a t e t h a t the F e r m i l e ve l r i s e s in an i n s u l a t o r when it is
heated,

a s s u g g e s t e d by H e r s h and Mo n t g o me r y ,

Until f u r t h e r

e x p e r i m e n t a t i o n and a n a l y s i s have b e e n c a r r i e d out,
s i d e r a t i o n s m u s t r e m a i n in the r e a l m of c o n j e c t u r e .

such c o n ­

C HAPTER V
SUMMARY
An a p p a r a t u s h a s b e e n c o n s t r u c t e d to r u b t o g e t h e r f i l a m e n t s
of v a r i o u s m a t e r i a l s and to m e a s u r e the c h a r g e s g e n e r a t e d ,

while

c o n t r o l l i n g the v a r i o u s r e l e v a n t m e c h a n i c a l and a mb i e n t condi t i ons.
The a p p a r a t u s is s i m i l a r in p r i n c i p l e to t ha t u s e d by H e r s h and
M o n t g o m e r y , but it h a s b e e n r e f i n e d in o r d e r to obt ai n b e t t e r c o n t r o l
of the m e c h a n i c a l v a r i a b 1e s ,
pressure.

and to allow v a r i a t i o n of the a mb i e n t

A s p a r k d e t e c t o r h a s b e e n i n c o r p o r a t e d to a s c e r t a i n

the i n c i d e n c e of e l e c t r i c a l b r e a k d o w n of the a t m o s p h e r e .
With t hi s a p p a r a t u s ,
have b e e n r e e x a m i n e d .

s e l e c t e d r e s u l t s of H e r s h and M o n t g o m e r y

These results,

h e r e i n a f t e r r e f e r r e d to as

" e a r l i e r , " a r e a s follows.
1.

R e p r o d u c i b i l i t y - E s s e n t i a l l y the s a m e r e s u l t s as r e p o r t e d
e a r l i e r w e r e obt ai ned.

2.

T r i b o e l e c t r i c s e r i e s - The p o s i t i o n s of the m a t e r i a 1s t e s t e d
w e r e the s a m e a s t h o s e r e p o r t e d e a r l i e r .

3.

E e n g t h d e p e n d e n c e - No v e r i f i c a t i o n of the e a r l i e r r e s u l t s wa s
a t t e mp t e d ; t h e s e r e s u l t s showed a p r o p o r t i o n a l i t y of c h a r g e on
l e ng t h of r u b.

It is u nl i k e l y t ha t t hi s r e l a t i o n would fail to

hold in the p r e s e n t m e a s u r e m e n t s ,

e x c e pt p e r h a p s in the r e g i o n

w h e r e a s t r o n g vel oci t y d e p e n d e n c e e x i s t s

44

4.

Ef f e c t of n a t u r e of r u b - No v e r i f i c a t i o n wa s a t t e m p t e d of the

earlier results.
5.

N o r m a l f o r c e - The n o r m a l f o r c e de pe n d e n c e found e a r l i e r ,

namely,

a l i n e a r d e p e n d e n c e of c h a r g e on n o r m a l f o r c e

of f i l a m e n t d i a m e t e r ,

h a s not b e e n s u b s t a n t i a t e d .

l a r g e n o r m a l f o r c e s and l a r g e d i a m e t e r f i l a m e n t s ,

i n de p e n de n t

For relatively
the d e p e n d e n c e

m a y be a p p r o x i m a t e l y l i n e a r ,

but for s m a l l d i a m e t e r f i l a m e n t s and

r e l a t i v e l y low n o r m a l f o r c e s ,

the d e p e n d e n c e i s def i ni t el y n o n - l i n e a r .

R e s u l t s of nyl on r u b b e d on p ol y e t hy l e ne o v e r the whole r a n g e of
normal forces
us e d,

and for all d i a m e t e r s

of po l y e t h y l e n e f i l a m e n t s

show t h a t
q oc

F 1 / 2 /d

so l ong a s t he c h a r g e is not l i mi t e d by br e a kd own .
6.

T e m p e r a t u r e and r e l a t i v e humi di t y - The t e m p e r a t u r e and

r e l a t i v e h u m i d i t y c o n t r o l the e l e c t r i c a l r e s i s t a n c e of the i n s u l a t i n g
m a t e r i a l s st udi ed.

It is found with t a n t a l u m r ubbe d on nylon t hat

if the r e s i s t i v i t y of the nyl on l i e s in a r a n g e of 10 97 to 10 11 o h m - c m ,
an i n c r e a s e in t he r e s i s t i v i t y will p r o d u c e an i n c r e a s e in the c h a r g e
g e n e r a t e d a s l ong a s m o d e r a t e v e l o c i t i e s of r u b a r e used.
7.

Ve l o c i t y of r u b - When the r e s i s t i v i t y of the nyl on l i e s in the

r a n g e 10^ to 1 0 ^ o h m - c m ,

a ve l oc i t y d e p e n d e n c e for the r a n g e of

velocities available is encountered.

The c h a r g e i n c r e a s e s a s the

45

v e l o c i t y of r u b is i n c r e a s e d up to a poi nt w h e r e a f u r t h e r i n c r e a s e
in v e l o c i t y i n c r e a s e s the c h a r g e v e r y l i t t l e.

The r e g i o n wh e r e t hi s

l e v e l i n g off o c c u r s is d e p e n d e n t on the r e s i s t i v i t y of the b e t t e r i n s u l a ­
tor.

F o r r e s i s t i v i t i e s lyi ng out s i de the r a n g e me n t i o n e d ,

ve l o c i t y d e p e n d e n c e is o b s e r v e d ,

v e r y sl i ght

a s found in m o s t of the e a r l i e r

re suits.
The ef f e ct of v e l o c i t y of r u b and r e s i s t i v i t y ca n be tied t o g e t h e r
by u s e of the e x p e r i m e n t a l l y d e t e r m i n e d r e l a t i o n
q cc
found f r o m t he r e s u l t s of r u bbi ng t a n t a l u m on nyl on of v a r i o u s
r e s i s t i v i t i e s a t d i f f e r e n t v e l o c i t i e s of rub.

The e f f e c t of n o r m a l f o r c e ,
t i vi t y of the b e t t e r i n s u l a t o r ,

d i a m e t e r of r u b be d f i l a me n t ,

l engt h of r ub,

resis­

and vel oci t y of r ub on

the c h a r g e g e n e r a t e d ma y be b r o u g h t t o g e t h e r in one r e l a t i o n ,
namely,
-

/ t

t - i I / 2

q - c(LF

for r u b s of the 4 5 ° - 4 5 ° type.

/ i i

/d)

;

-I

(1 - e

v /<r-J0

)

It m u s t be r e m e m b e r e d , h o w e v e r ,

t h a t the e x p e r i m e n t a l l y d e t e r m i n e d r e l a t i o n for c h a r g e d e p e n d e n c e
on n o r m a l f o r c e and d i a m e t e r

w a s found for a p a i r of m a t e r i a l s

d i f f e r e n t f r o m the p a i r u s e d to obt ai n the e x p e r i m e n t a l d e p e n d e n c e of
c h a r g e on v e l o c i t y and r e s i s t i v i t y .
r e l a t i o n r e m a i n s to be e s t a b l i s h e d .

Th u s the g e n e r a l i t y of the above

46

REFERENCES
1.

Hersh,

2.

H e r s h , S. P. , and M o n t g o m e r y ,
26, 903 (1956).

D. J. , Te x t i l e R e s e a r c h J o u r n a l

3.

H e r s h , S. P. , and M o n t g o m e r y ,
2 5 , 279 (1955).

D. J. , Te x t i l e R e s e a r c h J o u r n a l

4.

Mot t , N. F. , and G u r n e y , R. W. , E l e c t r o n i c P r o c e s s e s in Ionic
C r y s t a l s , C l a r e n d o n P r e s s , Oxf or d (1st ed. , 1940; 2nd ed. , 1948).

5.

Me e k , J. M. , and C r a g g s , J.
Chap. II, Ox f o r d (1953).

6.

T i m o s h e n k o , S. P. , S t r e n g t h of M a t e r i a l s , Chap. VII, D. Van
N o s t r a n d Co. , New Y o r k (1st ed. , 1930;2nd ed. , 1941).

7.

Van O s t e n b u r g , D. O. , and Mo n t g o m e r y ,
Soc. , S e r i e s II, 1, 205 (1956).

8.

S t r a t t o n , J. A. , E l e c t r o m a g n e t i c T h e o r y , p.
New Yo r k (1941).

9.

B r i d g m a n , P. W. , D i m e n s i o n a l A n a l y s i s , Yal e Univ.
(1st ed. , 1922; 2nd ed. , 1931).

10.

S. P. , Ph. D.

T h esis, P rinceton University,

1954.

D. , E l e c t r i c a l B r e a k d o w n of G a s e s ,

D. J. , Bull.

Am.

Phys.

15, M c G r a w - H i l l ,

S h a r m a n , E. P. , H e r s h , S. P. , and M o n t g o m e r y ,
Re s e a r c h J o u r n a l 23, 793 (1953).

Press

D. J. , Te x t i l e

LIST O F FIG U R E S
1.

Rubbi ng a p p a r a t u s

2

B o t t o m yoke

3.

Top yoke

4.

Control apparatus

5.

Photomultiplier circuit

6.

Automatic control d i a g r a m

7.

T e s t c h a m b e r No.

8

T e m p e r a tu r e control circuit

9.

E l e c t r i c a l c o n n e c t i o n s into t e s t c h a m b e r No.

1

10.

T e s t c h a m b e r No

11.

Charge measuring circuit

2

2

12.

D i a g r a m i l l u s t r a t i n g c a l c u l a t i o n of n o r m a l f o r c e

13.

R e p r o d u c i b i l i t y of nyl on r u b b e d on pol y e t hy l e ne

14.

Char ge vs

n o r m a l f o r c e ( after Her s h)

15.

C h a r g e vs.

n o r m a l f o r c e for v a r i o u s a m b i e n t p r e s s u r e s ( t he or e t i c a l )

16

C h a r g e vs.

a m b i e n t p r e s s u r e for v a r i o u s n o r m a l f o r c e s ( e x p e r i me n t a l )

17.

P i c t u r e s of b r e a k d o w n as d e t e c t e d bg p h o t o m u l t i p l i e r

18.

C h a r g e vs n o r m a l f o r c e for nyl on r u bb e d on p o l y e t h y l e n e of
different d i a m e t e r s

19.

L o g - l o g pl ot of c h a r g e vs.

n o r m a l f o r c e x (12. 0 / d i a . )

2

20.

R e s i s t i v i t y of nyl on vs.

t e m p e r a t u r e for v a r i o u s r e l a t i v e

humidities

21.

R e s i s t i v i t y of nyl on vs.

r e l a t i v e h u mi d i t y for v a r i o u s t e m p e r a t u r e s

22.

H ig h -re s is ta n c e m easu rin g circuit

2 3.

Charge

24.

C h a r g e vs. r u b no.
a veraging

for v a r i o u s v e l o c i t i e s i l l u s t r a t i n g m e th od of

25.

Charge

v/'s. v e l o c i t y

for f i l a m e n t no.

1

26.

Charge

vs. v el o ci ty

for f i l a m e n t no

2

27.

vs. ru b no.

for v a r i o u s v e l o c i t i e s

L.og-log plot of c h a r g e vs

t i m e s v elo city

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