close

Вход

Забыли?

вход по аккаунту

?

THE STRUCTURE OF AMORPHOUS AND STRETCHED RUBBER

код для вставкиСкачать
DOCTORAL DISSERTATION SERIES
?nnf TheShuduTc Offlifiorphous
M
____________________________________________________
ttrekkd hU er
AUTHOR (Im c c M A M I
UNIVERSITY. furheMersihf DATE.M L
DECREE i k l ) .
PUBLICATION NO.. t u
linn i
' 1' ' 1' I I I ' I ' l ' l '
1
I
U M IV E tS IT V
H
ANN ARBOR
i | i i n 11
2
M
IC IO F IL M S
? MICHIGAN
THE STRUCTURE OF AMORPHOUS A n n
STRETCHED RUBBER
C la r e n c e M erton P a r s h a l l - T h e s i s ( P h .D .)
Purdue U n i v e r s i t y , 1941
X - r a y i n v e s t i g a t i o n s o f r u b b e r h ave b ee n c a r r i e d o u t f o r b o th
amorphous and c r y s t a l l i n e m a t e r i a l .
The am orphous m a t e r i a l shows
s
.Q
a p a t t e r n l i k e a l i q u i d w i t h d i f f r a c t i o n r i n g s a t ??j y ? v a l u e s o f
0 .1 0 5 5 , 0 .2 2 2 , 0 .4 1 7 .
T h is p a t t e r n w as o b t a i n e d i n a vacuum camera
o f 8 . 6 cm. d i a m e t e r w i t h molybdenum r a d i a t i o n r e f l e c t e d from a r o c k
s a lt c r y sta l.
The f i l m h o l d e r c a r r i e d c a l i b r a t i o n marks e v e r y 2 0 ░
so a s t o e l i m a t e e r r o r s due t o s h r i n k a g e o f t h e f i l m .
The S c h e m e r e x p r e s s i o n c o r r e l a t i n g h a l f w i d t h and p a r t i c l e
0
s i z e l e a d s t o c r y s t a l l i t e s o f t h e o r d e r o f 80 A .
The p a t t e r n was o b t a i n e d by u s i n g pure l a t e x , p ou red on g l a s s ,
d r i e d and mounted s t r e s s f r e e in t h e c a m e ra .
t h e form o f f l a t
The s a m p le s were i n
s h e e t s 1 . 5 t o 2 . 0 ram. t h i c k .
The m ost i n t e r e s t i n g p roblem i n t h e s t r u c t u r e o f r u b b e r i s t h e
q u e s t i o n o f what h a p p e n s i n th e s t r e t c h i n g p r o c e s s .
To i n v e s t i g a t e
t h i s p roblem t h e maximum e l o n g a t i o n t o w h ic h l a t e x c a n be s t r e t c h e d
a t room te m p e r a t u r e w i t h o u t c r y s t a l l i z i n g was d e t e r m i n e d .
For t h i s
p u r p o s e t h e sam p le was pu t i n a sp e c im e n h o l d e r w h ich a l l o w s t h e
d e t e r m i n a t i o n o f t h e amount o f s t r e t c h and w h ic h can be mounted in
a r e p r o d u c a b l e f a s h i o n i n t h e cam era.
D i f f r a c t i o n p a t t e r n s h av e
b e e n o b t a i n e d a t e l o n g a t i o n s o f 100 p e r c e n t , 200 p e r c e n t , and 250
per c e n t.
At 275 p e r c e n t e l o n g a t i o n t h e sam p le becomes c r y s t a l l i n e
a s i n d i c a t e d by t h e a p p e a r a n c e o f d i f f r a c t i o n
To i n t e r p r e t th e d i f f r a c t i o n p a t t e r n s ,
b een u s e d t o o b t a i n a r a d i a l d i s t r i b u t i o n ,
s p o t s on th e e q u a t o r . N-
f o u r i e r a n a l y s i s has
w it h s u b s t a n c e s su c h a s
r u b b er and o t h e r l i g h t o r g a n i c m a t e r i a l s su c h an a n a l y s i s p r e s e n t s
s e r i o u s e x p e r i m e n t a l d i f f i c u l t i e s due t o t h e f a c t t h a t
(a )
th e
-
2
l a r g e amount o f h y d ro g e n p r e s e n t p r o d u c e s a l a r g e amount o f i n c o h e r e n t
s c a t t e r i n g a t l a r g e a n g l e s and (b ) b e c a u s e t h e s c a t t e r i n g power o f
th e m a te r ia l i s
so s m a l l a s t o become c o m p a r a b le , a t l a r g e a n g l e s ,
w ith th e a c c id e n t a l s c a t t e r in g .
It
is,
th erefo re,
n o t u n iq u e ly
d e t e r m in e d w here one s h o u ld c u t o f f i n t h e e x p e r i m e n t a l c u r v e and
assum e in d e p e n d e n t c o h e r e n t and i n c o h e r e n t s c a t t e r i n g .
several
By t r y i n g
r a n g e s and m a tc h in g th e e x p e r i m e n t a l and t h e o r e t i c a l c u r v e s
i n d i f f e r e n t ways one can o b t a i n q u i t e d i f f e r e n t r e s u l t s .
T h is i s
-
due t o t h e f a c t t h a t t h e c u r v e 3 i ( s ) w h ic h i s t o be a n a l y z e d i n c l u d e s
sin &
3 , i n c r e a s i n g w i t h ?-rj-? . imy s m a l l a r e a i n t h e e x p e r i m e n t a l
s c a t t e r i n g c u r v e a t l a r g e a n g l e s i s th u s made c o m p a r a b le w i t h t h e
l a r g e a r e a due t o w e l l d e f i n e d r i n g s .
In th e c a s e o f r u b b e r where i t
i s known t h a t we a r e d e a l i n g
w i t h a c h a i n - l i k e s t r u c t u r e , t h a t means two f i r s t n e i g h b o r s ,
it
is
p o s s i b l e t o d e t e r m in e e m p i r i c a l l y where t o c u t o f f so a s t o g e t t h e
' c o r r e c t number o f f i r s t n e i g h b o r s .
h a s b e e n u sed th r o u g h o u t t h i s w ork,
In o th e r c a s e s ,
it
-
and t h i s m ethod
i s p o s s i b l e t o match o v e r a
r a n g e by m a tc h in g a r e a s under t h e e x p e r i m e n t a l and t h e o r e t i c a l c u r v e s .
F or t h e a c t u a l a n a l y s i s a scheme o f c a l c u l a t i o n d e v e l o p e d by
D a n i e l s o n and I a n c z o s h a s been u s e d .
V i s u a l c o m p a r is o n o f t h e e x p e r i m e n t a l c u r v e s d o e s n o t show any
str ik in g d iffe r e n c e s .
changed,
The h e i g h t o f t h e f i r s t p eak i s
somewhat
i n c r e a s i n g w i t h i n c r e a s i n g s t r e t c h , and t h e shape and
p o s i t i o n s o f th e o u te r r in g s are s l i g h t l y changed.
Thtree d i f f e r e n t
e x p e r i m e n t s have been c a r r i e d o u t f o r e a ch e l o n g a t i o n and t h e c u r v e s
g iv e n are th e average v a lu e s .
The F o u r i e r a n a l y s e s o f t h e c u r v e s r e v e a l s t h e d e t a i l s o f t h e
a b r u o t (i i r e .
In t h e s t r e s s - f r e e s t a t e we f i n d 1 . 9 n e i g h b o r s a t a
f
o
o
d i s t a n c e o f 1.52 A and 2.36 n e i g h b o r s a t a d i s t a n c e o f 2 . 5 4 A .
-
There i s a s l i g h t
3 -
i n d ic a t io n o f a c o n c e n tr a tio n a t 3 .5
9
0
4 . 2 4 A and a c o n s i d e r a b l e hump a t 5 . 0 6 A .
at 5 A
0
0
a
and a t
The c o n c e n t r a t i o n
i s r e s p o n s i b l e f o r t h e m ain peak i n th e e x p e r i m e n t a l c u r v e
and from o t h e r o r g a n i c s u b s t a n c e s , we know t h a t t h i s must r e p r e s e n t
d i s t a n c e s b e tw e en n e i g h b o r i n g m o l e c u l e s .
The s e c o n d peak i s
b e t t e r r e s o l v e d th a n in t h e a n a l y s i s o f
smoked s h e e t by oim ard and Warren and t h i s c h e c k s w i t h our own
r e su lts
fo r th a t m a te r ia l.
as str e tc h in g in c r e a se s,
t h e se c o n d p eak becom es b e t t e r r e s o l v e d
and a t an e l o n g a t i o n o f 250 p e r c e n t ,
r e so lv e d ,
t h i s peak i s a l m o s t c o m p l e t e l y
a t t h e same tim e t h e c o n c e n t r a t i o n s beyond se c o n d n e i g h b o r s
are q u ite d i s t i n c t .
I t i s a l s o t o be n o t i c e d t h a t t h e number o f
se c o n d n e i g h b o r s d e c r e a s e s and t h a t th e peak i t s e l f a p p e a r s a t a
sh o rter d ista n c e .
To u n d e r s t a n d t h i s ch a n g e we w ant t o r e c a l l t h e s t r u c t u r e o f t h e
r u b b e r c h a in a s a c c e p t e d from c h e m ic a l and o t h e r e v i d e n c e .
T ak in g
o
O
t h e bond a n g l e s a s 109 2 8 ' and 125 16* and s i n g l e and d o u b le c a rb o n
bond d i s t a n c e s a s 1 . 5 4
0
and 1 . 3 S
6
two f i r s t n e i g h b o r s a t 1 .5 1
░
a
r e s p e c t i v e l y , one c a l c u l a t e s
, i n a g r ee m e n t w it h n o s i t i o n and a r e a
o f t h e f i r s t p e a k . T h ere s h o u ld be 2 . 4 n e i g h b o r s a t a d i s t a n c e o f
o
2 . 5 6 A but t h i s number w i l l a lw a y s be l a r g e r b e c a u s e o f th e c o n t r i I
b u tio n o f in t e r p e n e t r a t in g it h ir d n e ig h b o rs.
As t h e s t r e t c h i n g
i n c r e a s e s t h e r u b b e r m o l e c u l e i s no l o n g e r a b l e t o c o i l and u n c o i l
f r e e l y and change i t s
c o n fig u r a tio n .
T h er efo r e, th e c o n t r ib u t io n
o f t h e t h i r d n e i g h b o r s t o t h e s e c o n d peak becomes s m a l l e r and t h e
p o s i t i o n o f t h e t h i r d n e i g h b o r s t h e m s e l v e s becom es more d e f i n i t e l y
fix e d .
The d i s t a n c e o f 3 . 3 3 A
corresp on d s e x a c t l y to th e average
v a l u e between s m a l l e s t and g r e a t e s t d i s t a n c e s o f t h i r d n e ig h b o r ;
- 4 -
3.33 A
o b s e r v e d and 3.32' A
c a lc u la te d .
H e n c e , we c o n c lu d e t h a t t h e r e s u l t s o f t h e i n v e s t i g a t i o n
i n d i c a t e q u i t e d e f i n i t e l y t h a t we do n o t have an e x te n d e d m o l e c u l e
i n t h e u n s t r e t c h e d r u b b e r .b u t have i n s t e a d a f o l d e d m o l e c u l e , w h ic h ,
by r o t a t i o n a b o u t t h e s i n g l e c a rb o n b o n d s,
e lo n g a tio n .
is
i t s e l f c a p a b le o f
In t h e p r o c e s s o f s t r e t c h i n g t h e m o le c u le l o s e s p a r t
o f i t s fr e e d o m t o change c o n f i g u r a t i o n by c o i l i n g and u n c o i l i n g ,
t h e p r o c e s s o f f i x i n g d e f i n i t e p o s i t i o n s b e in g e v id e n c e d by t h e
sh a rp en in g o f th e peaks in th e r a d i a l d i s t r i b u t i o n c u r v e .
I w i s h t o e x p r e s s my d eep a p p r e c i a t i o n and s i n c e r e th a n k s t o
D r. K a r l L a r k - I I o r o v i t z and D r. D. p . M i l l e r f o r t h e i r a s s i s t a n c e
d u rin g th e c o u r se o f t h i s i n v e s t i g a t i o n .
g u i d a n c e and c r i t i c i s m
p o ssib le .
I t has been t h e i r
t h a t h a s made t h e c o m p l e t i o n o f t h e work
A3ST3AGT
X -r a y d i f f r a c t i o n p a t t e r n s o f e v a p o r a te d l a t e x
( s h e e ts , 1 .5 to 2 .0
mn. t h i c k ) a t v a r io u s e l o n g a t i o n s have b e e n o b t a in e d and F o u r ie r a n a l y z e d .
100 p er c e n t , 200 p e r c e n t , and 250 p e r c e n t s t r e t c h i n g produced p a t t e r n s
s i m i l a r i n a p p ea r a n c e to t h e p a t t e r n o f t h e u n s t r e t c h e d m a t e r i a l ; a t 275
p er c e n t e l o n g a t i o n c r y s t a l s t r u c t u r e i s d e f i n i t e l y i n d i c a t e d .
r i n g s have been o b se rv e d i n the amorphous p a t t e r n a t
0 .1 0 4 7 - 0 . 1 0 5 5 ; 0 . 2 1 0 - 0 . 2 2 0 ; 0 . 4 1 1 - 0 . 4 1 8 .
Three
v a lu e s of
The b a l f - b r e a d t h v a lu e o f th e
f i r s t peak rem a in s e s s e n t i a l l y t h e same f o r a l l e l o n g a t i o n s but i t s
h e i g h t and t h e a p p ea r a n c e o f t h e o u ter r i n g s i s ch an g ed .
The d i s t r i b u t i o n c u r v e s from t h e F o u r ie r a n a l y s e s show 1 . 9 f i r s t
0
?
n e ig h b o r s a t 1 .5 2 A ; 2 . 6 t o 2 . 9 se c o n d n e ig h o o r s a t 2 . 4 8 t o 2 .5 4 A , th e
sm aller number and d i s t r n c e c o r r e sp o n d in g t o t h e l a r g e s t e l o n g a t i o n .
T
.7ith
i n c r e a s i n g e l o n g a t i o n the d e f i n i t i o n o f th e second peak i n c r e a s e s and i t
a p p e a r s c o m p le te ly r e s o l v e u a t 250 p e r c e n t .
A c o n c e n t r a t i o n a p p e a r s in
O
a l l d i s t r i b u t i o n curves a t 5 A ; w itn in c r e a s in g e lo n g a tio n c o n c en tr a tio n s
a
o
a t 5 . 5 A and 4 . 2 A , q u i t e weak i n th e d i s t r i b u t i o n curve o f tn e unн
s t r e t c h e d l a t e x , beco:ue s t r o r g l y p ron ou n ced , compjarablq w ith th e peak a t 5
PURDUE UNIVERSITY
T H I S I S T O C E R T IF Y T H A T T H E T H E S I S P R E P A R E D U N D E K MY S U P E R V IS IO N
C la r e n c e W. P a r s h a l l
by
The S t r u e t u r e o f Amor ph ou s and S t r e t c h e d R ubber.
e n t it l e d
C O M P L IE S W IT H T H E U N IV E R S IT Y R E G U L A T IO N S O N G R A D U A T IO N T H E S E S A N D I S A P P H O V E D
BY M E A S F U L F IL L IN G T H I S P A R T O F T H E R E Q U IR E M E N T S F O B T H E D E G B E E O F
D o c t o r o f P h i l o s o phy
P rofessor In Charge of T h e sis
H e a d of School or D epartm ent
X ':
a-
?
T O T H E L IB R A R IA N :?
SEн
T H IS T H E S I S I S N O T T O B E R E G A R D E D AS C O N F ID E N T IA L .
P ro fesso r in Charge
R egistrar F orm 10?2-39? 1M
THE STHJOTUBE OF AMORPHOUS AND
STRETCHED BOBBER
A T h e s is
S u b m itte d t o t h e B h o u lty
of
Purdue U n i v e r s i t y
by
C la r e n c e M erto n P a r s h a l l
in p a r t ia l fu lfillm e n t
of th e
r e q u ir e m e n ts f o r t h e d e g r e e
of
D o c to r o f P h ilo s o p h y
J u n e , 1941
TA31E OF CONTENTS
P age
I.
I n t r o d u c t i o n ....................................................................................................... . . .
1
The S t r u c t u r e o f Rubber
1
A.
....................................................
C hem ical E v i d e n c e .............................................................................................
1
C o m p o sitio n of l a t e x .............................. . . . . . . . . . . .
1
Garb on and H ydrogen R a tio .
.................................. .... ........................
2
D ouble B o n d s ......................................................................................................
2
......................... .... ................................................
2
S t r u c t u r a l Form ula
B.
S t e r e o c h e m ic a l S t r u c t u r e ................................................................ . .
3
M o le c u la r W eight
4
..........................................................
P h y s ic a l P r o p e r t ie s
......................................................................... .....
S t r e s s - S t r a in C h a r a c te r is tic s
4
5
The J o u le E f f e c t
8
D ouble R e f r a c t i o n
D.
. . . . .
H y s t e r e s i s ......................................................................... ..................................
...................................................................................
Van d er W aals F o r c e s
C.
..................................
4
...............................................................................^
. . . . . . . . . . . . . . . . . . .
X -r a y E v i d e n c e ............................
9
8
12
U n s tr e t c h e d Rubber ........................................................................................
12
S t r e t c h e d Rubber . ' ............................................
17
S t r u c t u r e o f C r y s t a l s ..............................................................................
21
E le c t r o n D i f f r a c t i o n
26
..............................................................
M o le c u la r M o d e ls ..................................................................................................
29
The S p i r a l M o d e l.............................................................................................
29
The H ydrogen E v a p o r a tio n -C o n d e n s a tio n Model. . . . . . .
30
The F ran zen M o d e l .......................................................................................
so
The T a n g le d C hain M o d e l .........................................................................
31
The Two P h a se M o d e l ....................................................................................
31
The F l e x i b l e F ib e r M o d e l ..........................................................
31
The ftm am ic T herm al M odel
31
......................................
II.
The P r o b le m ......................................................................................................................
33
III.
The
34
A.
M e t h o d ...............................................................................................................
T h e o r y ...............................................................
3.
54
I n t e n s i t y of S c a t t e r e d B a d i a t i o n ..................................................
34
A tom ic D e n s it y D i s t r i b u t i o n ......................................
36
E x p e r i m e n t a l .............................. I .............................................
36
X -r a y T u b e, I f e d ia t io n and Camera
P r e p a r a tio n and M ounting of Sam ples
...................................
......................................
39
P i c t u r e , M icro p h o to m eter and B la c k e n in g C urves. . . . .
42
C o r r e c t io n s f o r P o l a r i s a t i o n and A b s o r p tio n . . . . . .
44
T h e o r e t i c a l C oheren t a n d In c o h e r e n t S c a t t e r i n g
48
. . . .
....................
M atching Ete.ctor-M eth.ods and D i f f i c u l t i e s
C.
38
48
E v a lu a t io n of S i ( s ) and A n a ly s is fo r Smoked S h e e t . . .
53
B e s u l t s f o r Smoked S h e e t ...........................................
57
. ?
. . .
B e s u lt s f o r E v a p o r a te d l a t e x .................................................................
58
U n s tr e t c h e d E v a p o r a te d l a t e x
..............................
60
E v a p o r a te d l a t e x S t r e t c h e d 100 P er Cent
...................... ?
61
E v a p o r a te d l a t e x S t r e t c h e d 200 P er C e n t ...................................
E v a p o r a te d l a t e x S t r e t c h e d 250 P er C e n t ...................
63
IV.
D is c u s s io n and I n t e r p r e t a t i o n of B e s u lt s
V.
S u m m a r y .......................................
69
A ppendix I .........................
73
B efer e n c es
V it a
.......................... ?
62
. . . . . . . . . . . . .
64
...... .............................. ................................................................... ....
. . . . . . . . . . . . . . .
.......................................... . . .
80
LISTv OF TABIES AND ILMJSTHATIONS
F ig u r e 1 . . . .................................................................
F ig u r e 2 .
. . . . . . . . . . . . . . . .
F ig u r e 3 .
. . . .
......................... . .
.
F ig u r e 4 a . ...........................................................
.....
o
F ig u r e 4 b . . ................................................................
F ig u r e 5 .
F ig u r e
.................... .... ...........................................
.
........................................
F ig u r e 7 .
. . ....................................... ........................
F ig u r e
6
8
.
.............................. .....
F ig u r e 9 . . . ................................................................
F ig u r e 1 0 . . .
....................
. ..............................
F ig u r e 1 1 .............................. ......................................
F ig u r e 1 2 .
.....................................................................
F ig u r e 1 3 . . ............................................
F ig u r e 14 ..........................................................................
F ig u r e 1 5 . . .
..............................
F ig u r e 16 ..........................................................................
F ig u r e 1 7 . . .
....................
. . . . . . . .
F ig u r e 18'
...........................................................
F ig u r e 19 ..........................................................................
F ig u r e 20 ..........................................................................
F ig u r e
..........................................................................
F ig u r e
..........................................................................
F ig u r e г 3 .................... .... ................................................
F ig u r e 2 4 ......................... ................................................
LIST OF TABLES AND ILLUSTRATIONS (C o n t* d .)
Rage
F ig u r e 2 5 ......................................................................................................................
60
F ig u r e 2 6 ......................................................................................................................
61
F ig u r e 2 7 . .............................................................................
62
F ig u r e 2 8 .....................................................................................................................
63
F ig u r e 2 9 ......................................................................................................................
65
................................................................
1
T a b le 1 . . . . . . . . . . . .
T a b le
2
T a b le
.
. . . .
.....................................
...........................................................................................................................
3
23
T a b le 4 .................................................................................................
23
T a b le 5 .
.................................................................................................
47
..........................................................................................................................
49
T a b le 7 ...........................................................................................................................
55
T a b le
6
. .
1
.
INTRODUCTION*
The S t r u c t u r e of- h ib b e r
The d e te r m in a t io n of t h e s t r u c t u r e o f r u b b e r h a s lo n g b e e n a problem
o f e x tr e m e i n t e r e s t ,
is it s
r r o b a b ly th e m ost s t r i k i n g c h a r a c t e r i s t i c o f ru b b er
c a p a c it y t o r e t u r n t o i t s
la r g e e lo n g a t i o n s ,
th is
o r i g i n a l d im e n s io n s a f t e r u n u s u a lly
i s t h e p r i n c i p l e phenomenon t h a t a n y t h e o r y o f
th e s t r u c t u r e o f ru b b er must e x p l a i n .
O ther p r o p e r t i e s c h a r a c t e r i s t i c o f
rubber w i l l be m en tio n ed in t h e c o u r s e o f th e f o l l o w i n g d i s c u s s i o n and
some o f th e t h e o r i e s t h a t h a v e b e e n a d v a n ced t o e x p l a i n t h e s e p r o p e r t i e s
w i l l be d i s c u s s e d .
A.
C o m p o sitio n o f la -ta x .
C hem ical E v id e n c e
A g en era l a n a ly s is o f
?f i r s t l a t e x p l a n t a t i o n
rubber** a s g iv e n by de V ries^- i s shown in T a b le 1 .
T a b le 1 .
(ie n e r a l C hem ical c o m p o s itio n of F i r s t l a t e x H evea P l a n t a t i o n Rubber
M o istu r e
0 .3 -
1.2^&
A c e to n e e x t r a c t
2 .5 -
3 .2
2 .5 -
3 .5
N itr o g e n e o u s s u b s t a n c e s
^ p r o te in s )
A sh
Rubber h y d ro c a r b o n ^ in d ir e c t )
0 .1 5 - 0 . 5
92 - 94
'
The p e r c e n ta g e of r u b b er h y d ro c a r b o n i s o b t a in e d by s u b t r a c t in g
th e t o t a l o b s e r v e d p e r c e n ta g e o f t h e o th e r com ponents from
100
per c e n t.
?C h a p ter i T b y ╗Zhitby and u h a p te r i l l by F i s h e r and u e r k e in D a v is
and B la k e 's " C h em istry and t e c h n o lo g y o f Rubber" (R e in h o la P u b lis h in g
C o ., New Y ork, 1937) have b e e n v e r y h e l p f u l i n w r i t i n g t h i s in t r o d u c t io n
From th e a b o v e t a b l e i t
i s s e e n t h a t th e r u b b er h yd rocarb on c o n s t i t u t e s
th e g r e a t e r p a r t ctf raw r u b b e r ,
i t i s t h i s q u a n tit y i n w hioh we a r e
^ -
m ost i n t e r e s t e d , th o u g h t h e a sh a l s o
I
c o n t a in s some atom s w h ic h can in н
f lu e n c e x - r a y p a t t e r n s o f r u b b e r .
uarbon and H ydrogen R a t i o .
As e a r l y a s 1 8 2 6 , Faraday^ d e te r m in e d th e
r a t i o o f h y d ro g en and carb on in t h e rubber h y d ro ca rb o n g e t t i n g th e f o r н
mula C5 H3 .
l a t e r and more a c c u r a t e w ork h a s c o n fir m e d t h i s v a lu e .
S in c e th e m o le c u la r w e ig h t i s h ig h i t
D ouble B o n d s,
i s u s u a lly w r itte n
(C^Eg)x .
m e ru b b er h y d ro c a r b o n i t s e l f i s u n s a t u r a t e d ,
n o w e v e r,
one can add ozone*1, s u lp h u r ^ , o x y g e n ^ , b rom in e^ , and s e v e r a l o th e r su b н
s t a n c e s t o o b t a in s a t u r a t e d a d d i t i o n p r o d u c t s .
p r o d u c ts show s t h a t t h e r e i s
S t r u c t u r a l F orm u la.
An a n a l y s i s o f t h e s e
one d o u b le carb on bond f o r ea ch
group.
H a r ries* 1, a lm o s t e n t i r e l y by o z o n o l y s i s , h a s
s u c c e e d e d i n g i v i n g th e s k e l e t a l s t r u c t u r e of th e ru b b er h y d ro ca rb o n
and th e p o s i t i o n o f t h e d o u b le carb on bond in e a c h g ro u p ,
he g i v e s t h e
group i n g :
C Hi
H
I
X
I
I
CHj
I
= C ~ C H < ? CH* ? C = C - C
I
H
I
I
+ c H ^-C
1
I
The p o r t io n b etw een th e d o t te d l i n e s i n d i c a t e s th e r e l a t i o n s h i p o f th e
-
ru b b er h y d ro ca rb o n t o is o p r e n e ,
C H,
I
г / г = , C ? C H = c tJ*w h ic h i s c o n s id e r e d t o b e th e most im portant b u ild in g b lo c k of th e
m o le c u le .
sterio f-n em ica .1 s t r u c t u r e .
B ein g u n s a t u r a te d a n d h a v in g u n sy m m e tr ic a l
grou p s a t t a c h e d t o t h e d o u b le bonded carb on a to m s , th e ru b b er h y d r o c a r н
bon m ight w e l l be e x p e c t e d t o p o s s e s s g e o m e tr ic is o m e r is m ,
xhat t h is i s
p o s s i b l e i s m ost e a s i l y s e e n when th e s t r u c t u r e i s w r i t t e n in th e c i s
and t r a n s fo r m s.
HC
H
v
He
7
\
-CH*.
?h
v
c ?
7
,
/
H
\
\
C H ^ - C /-4
c
C M ? CM
,
H3 C
7
The e m p ir ic a l fo rm u la ^0 ^
N
3
c
7
\
x
C ?C
H
c~C
/
N
7
x
-CM.
/гC
7
C= C
C= C
/
H
V
CHл -
C= C7
/
\
H ▒ ? c H*
h
) 3^ i s t h e sane f o r th e p u r i f i e d h y d ro н
carbon o f r u b b e r , b a la t a an d g u t t a - p e r c h a and th e y have th e same g e n e r a l
c h e m ic a l p r o p e r t i e s .
are id e n t ic a l
id e n tic a l8 .
The p u r i f i e d h y d ro c a r b o n s o f g u t t a - p e r c h a and b a la t a
6 7
* ; and h y d r o g u t t a - p e r c h a , h y d ro ru b b er and h y d r o b a la ta a r e
T h is means t h a t th e o n ly d i f f e r e n c e b etw een th e m o le c u le s
o f rubb er and e i t h e r g u t t a - p e r c h a or b a la t a i s i n t h e i r s p a t i a l a r r a n g e н
m ent.
nen.ee th e y axist be s t e r i o i s o m e r s 8
, ^ , ^ <"1?
A c c o r d in g to Meyer an d Mark''-1 , th e s p e c i f i c g r a v i t i e s and m e ltin g
p o in t s o f c i s compounds a r e lo w e r th a n th o s e
of t r a n s com pounds,
we h a v e
th e f o ll o w i n g v a lu e s g iv e n f o r ru b b er and c r y s t a l l i z e d b a la t a *
T ab le 2 .
D e n s ity and M e ltin g P o in t o f Rubber and B a la ta
s p e c i f i c g r a v ity
JUuboer h y d ro ca rb o n
0 .9 2 3 8
1 0 ,1 2
n a la t a
0 .9 5 7 1
1 0 ╗1 4
\2 0 ░ 0 )
M e ltin g p o i n t
15 - 35 w ^
Above 60░ Q
8
T h is w ou ld i n d i c a t e t h a t t h e ru b b er h y d ro ca rb o n i s
in th e a i s form .
s t a u d in g e r 1^ a s s i g n s t h e t r a n s f o m t o i t , a lth o u g h F is h e r and Uerlce b e l i e v e t h a t th e a v a i l a o l e e v id e n c e f a v o r s th e c i s f o rm.
Molecular W eig h t.
The m o le c u la r w e ig h t o f r u b b e r , w h ile known t o be
v e r y h i g i , h a s n o t b e e n d e f i n i t e l y d e te r m in e d ,
i t h a s been shown t h a t
n o t o n ly ru b b er h y d ro ca rb o n a s a w h o le , bu t d i f f u s e d r u b b er a s w e l l , i s
f a r from b e in g hom ogeneous w ith r e s p e c t to m o le c u la r w e ig h t ,
m ethods have b een u se d t o a s c e r t a i n th e m o le c u la r w e i g h t .
are:
la ) d i a l y s i s
o f e t h e r s o l u b l e ru b b er
A ft
p ressu re
sev era l
Among them
; ib ) m easurem ent o f o s m o tic
Q╗7
; (c ) m easurem ent o f v i s c o s i t y * 5'3; id ) th e u l t r a - c e n t r i f u g e and
s e d im e n t a t io n e q u ilib r iu m method"*-о; i e ) a m e th o d ^ in w h ich a s m a ll p r o н
p o r t io n o f s u lp h u r i s com bined w i t h p u re s o l ru b b er in t h e p r e s e n c e o f
te t r s m e t h y lt h iu r a m d i s u l f i d e and z in c s t e a r a t e a f t e r w h ic h t h e v u lc a n i z a t e i s s u b j e c t e d t o r e p e a t e d f r a c t i o n a l s e p a r a t io n u n t i l no f u r t h e r
s e p a r a t io n o c c u r s ,
ay m ethod ie ) t h r e e f r a c t i o n s w it h s u lp h u r o o n t e n ts
o f 0 . 0 5 8 , 0 .1 1 6 an d 0 .1 7 9 p e r c e n t w ere o b t a in e d .
A ssum ing t h a t t h e y
w ere m on o-, d i - and t r i - s u l p h u r d e r i v a t i v e s r e s p e c t i v e l y , a m o le c u la r
w e ig h t o f 5 5 ,0 0 0 was o b t a in e d .
rTom t h e s e v a r io u s m e th o d s, one g e t s v a lu e s o f m o le c u la r w e ig h ts
r a n g in g from 1 0 ,0 0 0 t o 4 5 5 ,0 0 0 .
h.
S tr e s s -s tr a in
r h y s i c a l P r o p e r t ie s
O h a r a c te r i s t i c s .
S t r e s s - s t r a i n c h a r a c t e r i s t i c s f o r commer
c i a l u n v u lc a n iz e d ru b b ers h a v e b e e n ?measured over a w id e ra n g e o f te m p er a tu r e s.
o
й 10
in th e ra n g e from - 1 3 t o - 5 5 u tn e ..n d u lu s in c r e a s e s w ith tem н
p e r a tu r e d e c r e a s e , t h e
in c r e a s e ,
i n i t i a l s t a g e s o f e lo n g a t io n sh ow in g th e s h a r p e s t
in th e range from
o
0
O 17
t o 80 w
t h e m odulus a g a in becom es g r e a t
e r w it h d e c r e a s in g te m p e r a tu r e .
it
co m m ercia l u n v u lc a n iz e d r u b b e r , though,
i s c a p a b le of g r e a t e x t e n s io n and r e t r a c t i o n , shows a c o n s id e r a b le
h y s t e r e s i s e f f e c t and so i s n o t p e r f e c t l y e l a s t i c .
r o r o r d in a r y te m p e r a t u r e s , raw ru b b er h a s an e x t e n s i b i l i t y
comparн
a b le w it h t h a t o f pu re gum v u lc a n i s e d r u b b e r ; i t s u l t i m a t e t e n s i l e
s tr e n g th , how ever, i s
.uzch lo w e r ,
r o r e x a m p le , when a s t r e t c h i n g r a t e
su ch a s i s u s e d fo r co m m ercia l t e s t i n g o f v u lc a n iz e d rubberо^ i s u s e d
on raw r u b b e r , i t s b r e a k in g s t r e n g t h i s a b o u t
10
k ilo g r a m s p e r sq u a re
c e n t im e t e r w h ile t h a t o f v u lc a n i z e d r u b b er i s from 200 t o 300 k ilo g r a m s
p e r sq u a re c e n t im e t e r ,
c r o s s -s e c tio n
30
.
x h e s e s t r e n g t h s a r e c a l c u l a t e d on th e u n s t r a in e d
At low te m p e r a tu r e s th e s t r e n g t h o f raw ru b b er becom es
com parable w it h t h a t of v u lc a n i z e d r u b b e r .
O
At te m p e r a tu r e s o f - 8 0 C
a n d b e lo w i t becom es b r i t t l e , l o s i n g i t s e x t e n s i b i l i t y .
o t r e s s - s t r a i n c u r v e s f o r sm ooth s h e e t a s o b t a in e d by Bosbaud and
.achmid2 о a r e shown i n F ig u r e 1 .
In t h e c a se o f raw r u b b e r , t h e r a t e
e ffe c t
on t h e s t r e s s - s t r a i n c u r v e s ,
of s t r e t c h i n g h a s a marked
jiosbau d and ochm id2о c a r r y in g ou t
t e s t s o f t h i s ty ^ e on smooth, s h e e t , o b t a in e d th e r e s u l t s shown in F ig u r e 2 .
The r a t e o f s t r e t c h and th e tim e d u r in g w h ic h t h e r u b b er i s h e ld in
a s t r a in e d ^ co n d itio n a l s o
i n f lu e n c e th e c o m p le te n e s s o f r e c o v e r y o f raw
ru b b er when e lo n g a t e d ,
a
p i e c e o f raw ru b b er e lo n g a t e d 600 p e r c e n t v e r y
r a p id l y
0 .2
( in from
0 .1
im m e d ia te ly r e l e a s e d .
to
s e c . ; r e c o v e r s a lm o s t c o m p le t e ly i f
is
On t h e o th e r h a n d , i f a p i e c e o f t h e seme ru b b er
i s s t r e t c h e d 500 p e r c e n t s l o w l y
im m e d ia te ly , i t show s a s e t o f
h y s te r e s is .
it
50
i i n a b o u t 3 m in u t e s i and r e l e a s e d
per cen t even a f t e r
10
m in u te s
51
?
r ig u r e 3 i l l u s t r a t e s some m easurem ents made by Hock and
B ostrom о2 on sm ooth s h e e t , w it h an e l o n g a t i o n r a t e of 2 .3 5 p e r c e n t p er
6
2
?c
x> tooo1200 moo m5F
E L O N G A T IO N
F ig u r e 1 .
f t A TE! O F
E L O N G A T IO N
a
E L O N G A T I O N 5-g
F ig u r e 2 .
rnwts nyfcu╗
F ig u r e 3 .
\
second *
A and A^ a r e r e s p e c t i v e l y e x t e n s i o n a n d r e t r a c t i o n c u r v e s * B and
a r e c u r v e s o f a s e c o n d c y c l e o f e x t e n s io n and r e t r a c t i o n ,
i'h e se c u r v e s
w ould i n d i c a t e t h a t -when th e ru b b er i s f i r s t s t r e t c h e d a s t r u c t u r e , w h ic h
w as p r e s e n t i n th e u n s t r e tc x ie d s t a t e , i s b ro k en down,
x h is s t r u c t u r e
change c a u s e s th e la r g e d i f f e r e n c e b e tw e en th e c u r v e s o f th e f i r s t and s e c н
ond c y c l e s ,
xhe la r g e h y s t e r e s i s in th e f i r s t c y c l e i s n o t fo u n d i n v u l н
c a n iz e d r u b b e r .
h o w e v e r , u m s t e i n , Itymers and Wouda
from t h o s e g iv e n a b o v e .
53
h a v e fo u n d r e s u l t s d i f f e r i n g
For b o th high. and low r a t e s o f e l o n g a t i o n , t h e y
fo u n d th a t a r e d u c t io n i n e x t e n s i b i l i t y t a k e s p l a c e a t a b o u t 70 p e r c e n t
e l o n g a t i o n , th e m odulus a ssu m in g a c o n s t a n t and h ig h e r v a lu e a t 70 p e r
c en t e lo n g a tio n .
g h e J o u le S f f f lf t t .
From e x p e r im e n ts c a r r ie d o u t on th e h e a t c h a n g e s
accom panyin g t h e s t r e t c h i n g of r u b b e r , o o u le
18
c o n c lu d e d t h a t a lth o u g h
h e a t was e v o lv e d d u r in g t h e g r e a t e r p a r t of th e e l o n g a t i o n i t w as a c t u a l l y
a b so r b e d c a l o r i m e t r i c a l l y d u r in g th e i n i t i a l e x t e n s i o n ,
e x p e r im e n ts
h ow ever, la t e r
have snown t h a t f o r ru b b er in e q u i l i b r iu m , h e a t i s e v o lv e d
d u rin g s t r e t c h i n g a t low a s w e l l a s a t h ig h e r e l o n g a t i o n s ,
I h is i s a
q u a l i t a t i v e l y r e v e r s i b l e p r o c e s s s i n c e h e a t i s a o s o r b e d d u r in g r e t r a c t i o n .
By u s in g v u lc a n iz e d rubb er in a n e q u ilib r iu m
c o n d it io n
one can demonн
s t r a t e a p r e d i c t i o n o f t h e seco n d la w o f th er m o d y n a m ic s, n a m e ly , t h a t
w it h i n c r e a s i n g te m p er a tu r e t h e m odulus s n o u la i n c r e a s e i f h e a t i s e v o lv e d
d u r in g s t r e t c h i n g and i f th e p r o c e s s i s r e v e r s i b l e ,
w ould n o t be e x p e c t e d t o
e s i s and p l a s t i c f lo w .
show t n i s s i n c e i t
u n v u lc a n iz e d r u b b er
e x h i b i t s c o n s id e r a b le h y s t e r н
Van d e r 't e a ls F o r c e s .
van d er w a a ls f o r c e s p la y an im p o rta n t p a r t in
th e s tu d y o f th e r u b b er m o le c u le ,
?f h e m o le c u la r c o h e s io n o f s e v e r a l
o r g a n ic r a d i c a l s h a s been d eterm in ed
m o le .
bond
OK
, in u n i t s o f c a l o r i e s p e r gram -
The r u s h e r m o le c u le c o n t a in s th e m eth y l group and tn e d o u b le
=CH-, th e c o h e s io n v a lu e s b e in g 1730 and 990 r e s p e c t i v e l y .
On th e
o th e r hand, c e l l u l o s e h a s many h y d r o x y l g ro u p s w it h a c o h e s io n v a lu e o f
7250.
T h is w ou ld i n d i c a t e t h a t th e p h y s i c a l p r o p e r t ie s o f r u b b er and
c e l l u l o s e s h o u ld be c o n s id e r a b ly d i f f e r e n t .
T h is c o n c lu s io n i s borne
o u t by t h e f a c t t h a t rubb er has lo n g -r a n g e e x t e n s i b i l i t y w h ile c e l l u l o s e
d oes n o t .
S u b s ta n c e s w it h p r e o r ie n t e d m o le c u le s show g r e a t e r t e n s i l e
a t l i q u i d a i r te m p e r a tu r e s th a n i s
in an u n o r ie n t e d c o n d i t i o n ,
str en g th s
o b se r v e d when t h e same s u b s ta n c e s a r e
R ubber, g e l a t i n and c e l l u l o s e w ere i n v e s t i v'*'-
g a te d i n t h i s m anner.
F r o z en ru b b er* g i v e s a h ig h e r m odulus th a n l i q u i d ru b b er
TK
, th e
d i f f e r e n c e b e in g a t t r i b u t e d t o t h e e x t e n t o f c o n t a c t o f o r ie n t e d c h a i n s .
In f r o z e n r u b b er t h e r e s h o u ld be a g r e a t e r i n t e r f a c i a l c o n t a c t th a n in
liq u id ru b b er.
L iq u id smoked s h e e t can De v e r y e a s i l y e lo n g a t e d 2 ^ conн
t in u o u s ly by th e a p p l i c a t i o n o f o n ly lig f r t l o a d s .
T h is w ou ld i n d i c a t e
t h a t th e Van d er I h a l s f o r c e s w it h s m a ll i n t e r f a c i a l c o n t a c t a r e n o t
e ffe c tiv e
in p r e v e n tin g s l i p p i n g b etw een th e m o l e c u le s , l e a v i n g a r e s u l t н
a n t perm anent s e t .
D ouble R e f r a c t i o n .
In th e u n s t r e s s e d c o n d i t i o n , ru b b er i s e n t i r e l y
i s o t r o p i c , d i s p l a y i n g th e same o p t i c a l p r o p e r t ie s i n a l l d i r e c t i o n s .
?R ubber w h ic h h a s been a llo w e d t o a g e in th e d a r k or w h ich h a s b e e n h e ld
a t r e d u c e d te m p e r a tu r e s f o r a s u f f i c i e n t l y lo n g tim e t o a llo w c r y s t a l l н
i z a t i o n t o ta k e p la c e i s c a l l e d f r o z e n r u b b e r , xhe p r o c e s s o f rem ovin g
t h e c r y s t a l l i f f i i t i o n e i t h e r by a p p l i c a t i o n o f h e a t or by m e c h a n ic a l
w ork i s known a s th a w in g .
K u n d t^ , S c h e r r - I h o s s ^ , and jru lfrich о ^ f i r s t n o t e d t h a t ru b b er
d o u b le r e f r a c t i o n when i t i s e x te n d e d or c o m p r e sse d .
3 hovs
A lth o u g h Bjerkenо^
c la im e d t h a t s t r e t c h e d raw ru b b er show s n e g a t i v e d o u b le r e f r a c t i o n (th e i n н
dex o f r e f r a c t i o n b e in g la r g e r f o r th e o r d in a r y th a n f o r th e e x tr a o r d in a r y
r a y ) , S c h ille r ^ о and K r o g e r ^ h a v e shown th a t i t
is p o s itiv e .
A c co r d in g t o W iener6 0 , ro d l i k e m i c e l l e s p ro d u ce p o s i t i v e d o u b le r e н
f r a c t i o n , th e n e g a t iv e b e in g p rod u ced b y t h e la m e lla r ty p e o f m i c e l l e .
Subber s t r e t c h e d in o n e d i r e c t i o n shows p o s i t i v e d o u b le r e f r a c t i o n ; s t r e t c h н
in g a f i l m
of it
in a l l d i r e c t i o n s p r o d u c e s n e g a t iv e d o u b le r e f r a c t i o n .
H o w la n d ^ showed t h a t t h e d o u b le r e f r a c t i o n p e r s i s t e d in th e p r e s e n c e
o f an im b ibed l i q u i d o f th e same in d e x o f r e f r a c t i o n .
From h i s e x p e r im e n ts
h e c o n c lu d e d t h a t p o s i t i v e d o u b le r e f r a c t i o n , p o s i t i v e r e s i d u a l d o u b le r e н
f r a c t i o n a n d o p t i c a l l y a c t i v e m i c e l l e s e x i s t in s t r e s s e d r u b b e r .
S in c e d o u b le r e f r a c t i o n i s
p rodu ced a s th e r e s u l t o f d e fo r m a tio n , th e
r e l a t i o n b e tw e e n th e two s h o u ld be q u it e im p o r t a n t.
Van G e el and Eymers
62
in o r d e r t o g e t th e r e l a t i o n b etw een d o u b le r e f r a c t i o n a n d s t r e s s , made
m easurem ents on a n e l a s t i c ru b b er o b t a in e d by e v a p o r a tin g pure l a t e x .
U sin g a new s t r i p f o r e a c h m easurem ent t h e y found a n S -sh a p e d cu rv e up t o
a lo a d o f a b o u t s i x k ilo g r a m s p e r sq u a re c e n tim e te r a t an e l o n g a t i o n o f
70 p e r c e n t .
A f t e r t h i s p o in t t h e r e was a l i n e a r r e l a t i o n b etw een d o u b le
r e f r a c t i o n and t e n s i o n .
The t r a n s i t i o n p o in t o c c u r s a t th e same lo a d a s
in th e c a s e o f th e S -sh a p e d s t r e s s - s t r a i n c u r v e o b t a in e d by O m s t e in .
T h is was a lw a y s a t a b ou t 70 p e r c e n t e l o n g a t i o n .
K atz
27
fou n d t h a t o n ly
a t e lo n g a t i o n ab ove 70 p e r c e n t d o e s one o b t a in x - r a y c r y s t a l i n t e r f e r н
e n c e s w hose i n t e n s i t y in c r e a s e s w it h e l o n g a t i o n .
t h i s in p a r t 0 . , X -r a y E v id e n c e .)
(More w i l l be s a id a b o u t
At h ig h e r te m p e r a tu r e s th e t r a n s i t i o n
p o in t o c c u r s a t lo w er s t r e s s e s but h ig h e r e lo n g a t i o n s when d o u b le r e f r a c -
.
t i o n and e l o n g a t i o n a r e p l o t t e d a s f u n c t i o n s o f s t r e s s *
T h u s, w h ile a
s t r e s s o f s i x k g . p e r s q . cm. and a c o r r e s p o n d in g c r i t i c a l e lo n g a t i o n o f
?
70 p e r c e n t i s fou nd a t a b o u t 20 t o 25
o
0
, t h e s e v a l u e s a r e ohanged t o
o
f i v e k g . p e r s q . am. and 90 p e r c e n t e l o n g a t i o n a t 89 C.
Some of t h e v a lu e s o f th e
in d ex o f r e f r a c t i o n t h a t h a v e b een o b t a in e d
a r e a s f o l l o w s 5 0 * f o r raw r u b b e r , M acallum an d W hitby 1 2 fo u n d
u u r t i s an d M cPherson 6 5 fo u n d th e v a l u e
.
1 .5 2 1 9 .
- 1 .5 1 9 f o r p a le c r e p e , smoked
s h e e t , f i n e p a r a , w ashed p a le c re p e a n d w ash ed sm oked s h e e t ,
x h i s in d i c a t e d
t h a t th e r e f r a c t i v e
M cPherson
in d e x d ep en d s on t h e ru b b er h y d r o c a r b o n .
and oummings6^ c o n c lu d e d t h a t th e n o n -r u b b er com pon en ts do n o t h ave nuoh
e f f e c t on th e r e f r a c t i v e
in d e x s in c e t h e y fo u n d v a lu e s o f
? 1 .5 1 8 8
f o r n e v e a cru de r u b b er a n d w2з ? 1 .5 1 9 0 f o r n e v e a p u r i f i e d r u b b e r .
n . B . ii. T r e lo a r 1ms r e c e n t l y made some i n v e s t i g a t i o n s o f b i r e f r i n н
g e n c e and d e n s i t y ch a n g es i n s t r e t c h e d r u b b e r , u s i n g ru b b er p r e p a r ed from
a v i s c o u s s o l u t i o n o f c r e p e in b e n z e n e .
h e fo u n d t h a t f o r sa m p le s h e ld a t
o
0
u , a h ig h e l o n g a t i o n c a u s e d th e
b ir e f r in g e n c e t o r e a c h a h ig h v a lu e in n ie d ia t e iy a f t e r s t r e t c h i n g ,
howн
e v e r , a t lo w e r e lo n g a t i o n s th e a p p ro a c h t o a s a t u r a t i o n v a lu e was much
s lo w e r .
For sa m p le s h e ld a t 25 G and e lo n g a t e d 360J& o r l e s s he fo u n d t h a t
t h e b ir e f r i n g e n c e te n d e d t o f a l l w ith t i m e .
For e l o n g a t i o n s a b o v e 360J&
th e b ir e f r in g e n c e rem ain ed c o n s ta n t o r showed a s l i g h t i n c r e a s e .
S im ila r
0
r e s u l t s w ere fo u n d a t 50 G w here th e t r a n s i t i o n from th e f a l l i n g t o t h e
r i s i n g ty p e o f c u r v e o c c u r r e d a t an e lo n g a t i o n o f 680^b.
i f one p l o t s t h e r e l a t i v e r e t a r d a t io n p e r mm. o f s t r a in e d t h ic k n e s s
a g a i n s t e l o n g a t i o n , S -sh a p e d c u r v e s a r e o b ta in e d from th e r e s u l t s o f t h e
O
O
e x p e r im e n ts p e r fo r m ed a t 25 C a n d 50 0 w h i l e t h e p o in t s v a r y ab ou t a
s t r a i g h t l i n e f o r t h e work done a t 0 ░ C .
From t h e d e n s i t y m ea su rem en ts a t 0 * u I r e l o a r fo u n d t h a t t h e d e n s i t y
i n c r e a s e was much more r a p i d a t h i g h th a n a t low e l o n g a t i o n s .
At 700%
e l o n g a t i o n a d e n s i t y i n c r e a s e o f s l i g h t l y more th a n 3% was o b s e r v e d a f t e r
a b o u t 15 h o u r s .
At 230% e l o n g a t i o n a n i n c r e a s e of a b o u t 2.5% was o b s e r v e d
a f t e r a b o u t 120 h o u r s .
I f th e p e r c e n t a g e i n c r e a s e i n d e n s i t y i s p l o t t e d
a g a i n s t tim e ,'''S -s h a p e d
c u r v e s a r e fo u n d f o r t h e l o # e r e l o n g a t i o n s w h e r e a s
th e b otto m o f t h e S i s n o t o b s e r v e d f o r
C.
th e h ig h e r e lo n g a t i o n .
X -r a y .E vidence
S i n c e 1 9 2 5 , when K a tz 2 ^ o b s e r v e d t h a t s t r e t c h i n g r u b b e r p r o d u c e d i n
i t a k in d o f c r y s t a l l i z a t i o n or f i b e r i n g , a g r e a t many x - r a y i n v e s t i g a н
t i o n s have b e e n made i n a n a t t e m p t t o g a i n some k n o w led g e w h ic h c o u l d b e
combined w i t h o t h e r e v i d e n c e a n d l e a d to a d e t e r m i n a t i o n o f th e s t r u c t u r e
of rubber.
The g r e a t e r p a r t o f th e w ork h a s b e e n d on e w i t h t h e r u b b e r i n
e i t h e r a s t r e t c h e d o r f r o z e n c o n d i t i o n w here i t
d isp la y s c r y s t a llin e
c h a r a c te r istic s.
U n stretch ed B ib b er.
F n y s i c a l m ea su rem en ts o f h e a t c a p a c i t y , d e n s i t y ,
t e n s i l e p r o p e r t i e s , e t c . h a ve
i n d i c a t e d t h a t t h e r e may b e s e v e r a l m o d i f i н
c a t i o n s o f raw r u b b e r .
X -r a y p a t t e r n s , on t h e o t h e r h a n d , show raw ru b b er
t o be e i t h e r c r y s t a l l i n e
or am orph ous.
The t r a n s i t i o n p o i n t from th e c r y s t a l l i n e t o t h e amorphous s t a t e deн
pen d s on th e p r e s s u r e , t h e l e n g t h o f t i m e d u r i n g w h ic h t h e sample was
f r o z e n a n d , p e r h a p s , up on t h e t e m p e r a t u r e e x i s t i n g
process6 5 .
As i l l u s t r a t i v e
been r e p o r t e d .
from
6
d u r in g t h e f r e e z i n g
o f t h i s d e p e n d en ce th e f o l l o w i n g r e s u l t s h a v e
Bubber f r o z e n f o r s e v e r a l d a y s i n a te m p e r a tu r e r an ge
░U t o -1 0 ░ G had e t r a n s i t i o n p o i n t b e tw e en 5 G and 16 G6 6 .
T h ie sse n
and K ir s c h 6 ^ f o u n d , f o r r u b b er f r o z e n u n d e r . r e s s u r e , a t r a n s i t i o n p o i n t
p
o
b e tw e en 20 C and 2 3 C.
Van Bossem and L o t i c h i u s
13
f o u n d , f o r a sample
f r o z e n f o r f o u r y e a r s , a t r a n s i t i o n p o i n t b e tw e e n 2 1 * 0 and 3 3 ░ u .
An x - r a y i n v e s t i g a t i o n o f t h e s e s a m p le s w h i l e th a w in g showed t h a t t h e
P e b y e - S c h e r r e r r i n g s p r o d u ce d by f r o z e n r u b b er became p r o g r e s s i v e l y weakн
e r a s t h a w in g to o k p l a c e .
J u s t b e f o r e t h e th a w in g was c o m p le te d t h e y w ere
c o m p l e t e l y r e p l a c e d by t h e d i f f r a c t i o n h a l o c h a r a c t e r i s t i c o f amorphus
rubber.
Whitby
30
d e t e r m in e d , by p h y s i c a l m e th o d s , a t r a n s i t i o n te m p e r a tu r e
o f 4 3 . 5 ░ 0 f o r a sam ple o f r u b b er t h a t was b e l i e v e d t o h av e b een f r o z e n f o r
th ir ty y ears.
The x - r a y p a t t e r n s f o r t h e v a r i o u s r u b b e r s m en tio n e d above a r e a l l o f
t h e ty p e known a s a powder p a t t e r n , i . e . t h e y c o n s i s t o f h e b y e - 3 c h e r r e r
r i n g s such a s a r e p ro d u ced by a random arran gem en t of s m a ll c r y s t a l l i t e s .
The o n ly d i f f e r e n c e s i n th e p a t t e r n s a r e s m a ll v a r i a t i o n s o f i n t e n s i t y
and s h a r p n e s s , t h u s i n d i c a t i n g t h a t i n s t e a d o f h a v i n g s e v e r a l m o d i f i c a н
t i o n s o f u n s t r e t c h e d raw r u b b er t h e r e a r e v a r i o u s d e g r e e s o f a p p ro a ch t o
a s ta b le e q u ilib r iu m s t a t e .
In t h e s e powder p a t t e r n s , t h e a n g l e s betv/een
t h e ~ d i r e c t i o n s o f t h e d i f f r a c t e d beams an d th e d i r e c t i o n o f t h e main beam
a r e t h e same a s t h o s e m easured i n th e c a s e of normal s t r e t c h e d r u b b e r .
As compared w i t h o r d in a r y l i q u i d s , t h e m o le c u la r m o b i l i t y i n rubber
a p p e a r s t o be s m a l l .
The optimum te m p e r a tu r e f o r c r y s t a l l i z a t i o n seems t o
be i n t h e la n g e from a b o u t
o
8
0
b e i n g p lu n g e d i n t o l i q u i d a i r ,
to -3 5
й
0
.
I f ru b b er i s f r o z e n s u d d e n ly by
i t d o e s n o t c r y s t a l l i z e w e l l , p r o b a b ly due
t o a l a r g e r e d u c t i o n i n th e v e l o c i t y o f c r y s t a l l i z a t i o n .
There i s a p p a r e n t l y a f a v o r a b l e range o f p r e s s u r e a s .v e il a s o f tem p erн
atu re fo r c r y s t a l l i z a t i o n .
a te m p e r a tu r e o f
0
i)ow5 о found t h a t when cru de rubb er was h e l d a t
░ u a n d a p r e s s u r e o f 3000 k ilo g r a m s p e r sq u are cm. f o r
14 d a y s , no e v i d e n c e o f f r e e z i n g was a p p a r e n t ,
and k i r s c h
67
un t h e o th e r h a n d , i ' h i e s s e n
fo u n d t h a t i n a p r e s s u r e r a n g e o f from 10 t o 25 a t m o s p h e r e s ,
w i t h a f i x e d t e m p e r a t u r e , t h e tim e r e q u i r e d f o r c r y s t a l l i z a t i o n d e c r e a s e d
w i t h h i g h e r p r e s s u r e , an d t h a t a p p l i c a t i o n o f p r e s s u r e p e r m i t t e d c r y s t a l l н
i z a t i o n a t t e m p e r a t u r e s somewhat h i g h e r th a n u s u a l .
i f f r o z e n rubber i s s t r e t c h e d one f i n d s , su p e r im p o se d on t h e ite b y e S c h e r r e r r i n g s , i n t e r f e r e n c e s p o t s w hose i n t e n s i t i e s i n c r e a s e w i t h e l o n g a н
tio n .
T h is na y be due to a l i n i n g Ui. o r o r i e n t i n g o f t h e random ly a r r a n g e d
c r y s t a l l i t e s w h ic h p rod u ce t h e powder p a t t e r n .
h o t a s much work h a s been done on amorphous a s on c r y s t a l l i z e d r u b b e r .
Xhe r i n g s o b t a in e d when raw u n s t r e s s e d r u b b er i s e x p o s e d to x - r a y s a r e
t y p i c a l o f t h o s e f o r i s o t r o p i c l i q u i d s , sh o w in g t h a t in t h i s c o n d i t i o n th e
rubb er m o l e c u l e s a r e i n a random s t a t e .
F ig u r e 4a shows a d i f f r a c t i o n p a t t e r n o f u n s t r e t c h e d l a t e x .
F ig u re
4b i s a p a t t e r n o f an o r d in a r y ru b b er b a n d , th e s p o t t e d r i n g s b e i n g due
to v u lc a n iz in g a g e n ts .
of m o lte n KOI.
For c o m p a r iso n , F ig u r e 5 i s a d i f f r a c t i o n p a t t e r n
T h is p i c t u r e w as ta k e n b y R. P . M i l l e r o f t h i s d e p a r tm e n t,
h e m i c k e and Prins^о f i r s t dedu ced t h e concex^ tion t h a t th e s p a c i n g
c o r r e s p o n d in g to t h i s ty p e o f h a l o d e n o t e s the d i s t a n c e o f n e a r e s t a p p ro a c h
o f n e i g h b o r i n g m o l e c u l e s or a g g r e g a t e s ,
1 4 .7 6 A* and 6.03A*
u lsr k
41
h a s o b t a in e d v a l u e s of
f o r t h e s p a c i n g s i n r u b b e r , t h i s b e i n g i n good a g r e e -
raent 'with t h e v a lu e s o f 14.88A
?
and 6 .05 A
#
found by H auser and Rosbaud
?
rdngs o f s m a l l e r d ia m e t e r c o r r e s p o n d in g t o l a r g e r s p a c i n g s h a v e b e e n r e н
p o r t e d , b u t t h e s e r i n g s may be t h e r e s u l t o f u s i n g r a d i a t i o n w h ic h i s n o t
s t r i c t l y m o n o ch ro m a tic .
In t h e work o f Siraard and iffarren4 4 on smoked
s h e e t and i n t h e work r e p o r t e d i n t h i s t h e s i s on e v a p o r a t e d l a t e x and
smoked s h e e t , m onochrom atic r a d i a t i o n was u s e d ,
ho " in n e r * r i n g was ob-
F ig u r e 4 a .
F ig u r e 4 b .
F ig u r e 5 .
served in th e se e x p e rim en ts.
in n e r r i n g i s o b s e r v e d .
p a s s e d by t h e f i l t e r .
one u s e s f i l t e r e d r a d i a t i o n an
T h i s i s p r o b a b ly cue t o t h e c o n t in u o u s r a d i a t i o n
A p i c t u r e o f l a t e x i n w h ic h th is" s p u r io u s r i n g can
be s e e n i s shown i n F ig u r e
r a d ia tio n .
H ow ever, i f
6
.
T h is p i c t u r e was t a k e n w it n f i l t e r e d C u i^
0
T h is r i n g c o r r e s p o n d s t o a s p a c in g of about 10 A .
F ig u re
6
I f one
.
o
a ssu m es t h a t t n i s r i n g wa s p r o d u ce d by t h e s p a c in g o f 6 . 0 3 A , th e c o r r e s O
pon din g wave l e n g t h m s a v a l u e o f a b o u t 1 A .
T h is i s ^ u s t i n t h e r e g i o n
o f th e maximum o f t h e c o n t in u o u s r a d i a t i o n from t h e t u b e .
й
o
For th e pure ruboer h y d r o c a r o o n , s p a c in g v a l u e s o f 1 1 .1 5 A and 5 . 9 7 A
have been fo u n d .
Trie id e a o f a " c y b o t a c t i c " s t a t e was f i r s t p rop ose.! Dy S te w a r t
92
.
On t h i s id e a t h e r e a r e , a t any i n s t e n t , w e l l - o r d e r e d g r o u p s o f m o le c u le s
or atoms th ro u g h o u t a l i q u i d 'which a r e c a p ab le o f producing- x - r a y d i f f r a c н
tio n e f f e c t s .
I t has a l s o
oeen p r o p o s e d ^ t.oat t h e amorpnous r u n s p roн
duced by u n s t r e s s e d rubber a r e i n d i c a t i v e o f s u c h a s t a t e .
Sircard and iferren^^ h a v e a p p l i e u trie method o f i o u r i e r a n a l y s i s t o unн
s t r e s s e d smomed s h e e t .
In t h i s way, w it h o u t any "a p r i o r i " a ssu m p tio n s
a s t o t h e s t r u c t u r e oi' t h e m o l e c u l e , t h e y h a v e o b t a in e d an a to m ic d e n s i t y
d istr ib u tio n .
( F ig u r e s 7 a n d
8
)
t h e a v e r a g e . 1 . 95 f i r s t n e i g h b o r s
They f i n d t h a t e a c h c a rb o n atom h a s , on
(ca rb o n a t o m s ) a t a d i s t a n c e of 1.52A░ .
neyond t h e s e t h e r e a r e a p p r o x im a t e ly 2 . 4 carbon atom s a t a n a v e r a g e d i s -
9
t a n c e o f 2 .6 8 A .
and 5k .
9
T h ir d and f o u r t h c o n c e n t r a t i o n s are fo u n d a t a b o u t 4A
The r e s u l t s w ere c o n s i d e r e d to
be i n good a g r e e m e n t w i t h th e conн
c e p t o f a lo n g c h a in m o le c u la r s t r u c t u r e , u s i n g th e a c c e p t e d v a l u e s o f
bond l e n g t h s and a n g l e s .
O
The c o n c e n t r a t i o n o b s e r v e d a t a b o u t 5A
s i d e r e d a s d e n o t i n g th e n e a r e s t a p p ro a ch of a c a rb o n atom
m o lecu le,
was conн
in a n eig h b o rin g
x h i s c o n c e n t r a t i o n i s r e s p o n s i b l e f o r t h e s t r o n g e s t p eak i n t h e
observed i n t e n s i t y cu rve.
The r e s u l t s o f " th is worn g i v e no in f o r m a t io n a s t o t h e r e l a t i v e
o r i e n t a t i o n or form o f t h e c h a i n m o l e c u l e s i n r u b b e r .
S t r e t c h e d jftibber.
When one s t r e t c h e s r u b b er beyond a c e r t a i n e l o n g a t i o n
(from 7 5 t o 100 p e r c e n t f o r raw r u b b e r ; from 250 t o 2 75 p e r cen t f o r
e v a p o r a te d l a t e x a t room te m p e r a tu r e
(2 o ░u t o 25 0 ) ) one f i n d s , su p erim н
p o s e d on th e amorphous r i n g s , d i f f r a c t i o n maxima o f th e ty p e fo u n d i n r o t a t
in g c r y s t a l p i c t u r e s ,
f i g u r e 9 shows a p a t t e r n f o r t h e r u b b er band o f
u
0.00
F ig u r e 7 .
0.80
1
I
*
0
2
4
6
Rim k.
F ig u r e
8
.
F ig u r e 9 .
8
F ig u r e 5 when s t r e t c h e d 400 p e r c e n t ,
T hese maxima a r e t y p i c a l o f su b н
s t a n c e s w i t h a f i b e r s t r u c t u r e , i . e . w i t h o r i e n t a t i o n a l o n g one p r e f e r r н
ed d i r e c t i o n .
T h ese p a t t e r n s a r e
i n t e r p r e t e d by a s su m in g t h a t in t h e s t r e t c h e d
rubber t h e r e a r e c r y s t a l l i t e s w h ich a r e a l i g n e d w i t h one ^ue.is a l o n g th e
d ir e c tio n of
a tio n .
s t r e t c h , and w i t h t h e o t h e r two a x e s h a v in g a random o r i e n t н
As m e n tio n e d p r e v i o u s l y , t h e l a t t i c e
sp a cin g s fo r th e hebye-
d c h e r r e r r i n g s o f f r o z e n r u o b e r a g r e e w i t h t h o s e o b t a i n e d from t h e p a t t н
e r n s o f s t r e t c h e d r u b b e r , sh o w in g t h a t t h e .randomly o r i e n t e d c r y s t a l l i t e s
in f r o z e n ru b b er have t h e same s t r u c t u r e a s t h o s e t h a t a r e form ed i n
s t r e t ched r u b b e r .
As s t r e t c h i n g i s
i n c r e a s e d th e
i n t e n s i t y o f t h e sp-ots i n c r e a s e s ,
how ever, t h e i r p o s i t i o n does not ch an ge, in d i c a t i n g a f i x e d i d e n t i t y
p e r io d f o r th e l a t t i c e w h ic h i s c h a r a c t e r i s t i c o f t h e s u b s t a n c e .
erm ore, t n e h a l f - b r e a d t h v a l u e r e g a i n s c o n s t a n t
i n c r e a s e in i n t e n s i t y i s n o t due t o an i n c r e a s e
?
F u rth ?
, sh o w in g t h a t t h e
in s i z e o f th e c r y s t a l s
but i s due t o a l a r g e r number o f c r y s t a l s b e i n g e f f e c t i v e i n t h e d i f f r a c н
tio n p ro cess.
its
w h ile th e p o s i t i o n of th e amorphous r i n g d o e s n o t c h a n g e ,
i n t e n s i t y d e c r e a s e s d u r in g s t r e t c h i n g ,
h e n c e , th e o r d e r e d r e g i o n s
of th e rubb er a x e i n c r e a s i n g a t t n e e x p e n s e o f th e am orphous com pon en t.
Reducing t h e s t r a i n in t n e s t r e t c n e e rubb er by t h e a p p l i c a t i o n o f
h e a t or s w e l l i n g a g e n t s , or by r e l e a s i n g t h e t e n s i o n ,
c a u s e s th e i n t e r н
f e r e n c e maxima t o d i s a p p e a r .
(then raw rubb er i s s t r e t c n e u a lm o s t t o t n e b r e a m in g p o i n t and t h e n
h e a t e d th e i n t e r f e r e n c e s., o t s d i s a p p e a r a t a b o u t 90░ Opо.
..hen l e f t t o
s t a n d in a s t r e t c h e d c o n d i t i o . - o v e r a l o n g p e r i o d of t i m e t h e i n t e r f e r e n c e
maxima d i s a . p e a r g r a d u a l l y .
.irhen v e ry s l o w l y s t r e t c h e d t o 500 p e r c e n t
20
e l o n g a t i o n o n ly an amorphous p a t t e r n i s i o b ta in e d ^ ? , p r o b a b ly b e c a u s e o f
s l i p p a g e or flo .v w h ic h o f f s e t s an y a t t e m p t a t o r i e n t a t i o n .
m a stic a tio n
a l s o d e s t r o y s th e c r y s t a l l i n e c h a r a c t e r of s t r e t c n e d r u b b e r .
xflibber t h a t lias b e e n h i g h l y racked*^ t o th e o r d e r of 9 , 0 0 0 - 1 0 , 0 0 0
p e r c e n t shows v e r y s t r o n g f i b e r p a t t e r n s w i t h o n l y a v e r y f a i n t amorphous
r in g ,
n ere a g a in , i f
t h e t e n s i o n i s r e l e a s e d in some s u i t a b l e manner, th e
in te r fe r e n c e sp o ts d isa p p ea r .
A lth o u g h i t i s u s u a l _ y th o u g h t t h a t th e i n t e r f e r e n c e maxima a p p e a r
im m e d ia te ly u, oil s t r e t c h i n g , A cken, d in g e r a n d J a v e y 0 ^ have snown t h a t a
d e fin ite
i n t e r v a l o f t im e i s
r e q u ir e d f o r t h e p r o c e s s to t a k e p l a c e .
T h is
h a s Deen e x p l a i n e d by a s s u m in g t h a t a f i n i t e tim e i s n e c e s s a r y e i t h e r t o
s q u e e z e o u t m o l e c u l e s t h a t a r e u n f a v o r a b l y o r i e n t e d or t o p u l l o u t th e
t a n g l e d m o l e c u l e s in t o t h e d i r e c t i o n o f s t r e t c h .
Hark and von S u s i c h
fo u n d t h a t when th e x - r a y beam was p e r p e n d ic u н
l a r to th e s u r fa c e of a s t r e t c h e d f i l m of rubb er, th e i n t e n s i t y of th e
d i f f r a c t i o n s ^ o t s was d i f f e r e n t from t h a t o b s e r v e d wn^n th e d i r e c t i o n o f
t h e beam was p a r a l l e l t o the s u r f a c e .
Tne f i r s t e q u a t o r i a l s p o t , Ax ,
was p r a c t i c a l l y a b s e n t when th e beam w as p a r a l l e l to t h e f i l m and t h e
s e c o n d e q u a t o r i a l s p o t , ko , was a b s e n t when th e beam was p e r p e n d i c u l a r
t o th e f i l m .
I f t h e f i l m was r o t a t e d t h e y o b t a in e d th e norm al d ia g r a m .
They c o n c lu d e d t h a t t h e c r y s t a l l i t e s
in th e f i l m had a l l t h r e e a x e s a l i g n e d
and g a v e th e e f f e c t o f a s i n g l e c r y s t a l .
o r ie n ta tio n " .
T h is phenomenon i s c a l l e d " h ig h e r
Gehnan and F i e l d * ^ s t u d i e d th e c o n d i t i o n s u n d er -which
" h ig h e r o r i e n t a t i o n " o c c u r s and fo u n d t h a t
i t can b e produ ced when the p e r
c e n t c o n t r a c t i o n i n gauge e x c e e d s t h a t i n -w idth.
c o n d i t i o n by u s i n g s h o r t , w id e s h e e t s o f r u o b e r .
One can s a t i s f y t h i s
S tru ctu re of c r y s t a l s ,
Mirk and von S u s i c h assum ed t h a t th e f i r s t two
e q u a t o r i a l s p o t s , d e s i g n a t e d a s Aq and kg a b o v e , w ere due t o two f a m i l i e s
of p la n es p j r a c tic a ily p e r p en d icu la r to each o th e r ,
hom'oic l a t t i c e and in d e x e d Aq a s
(200) and A2 a s
They assum ed an o r t h o r -
(0 2 0 ).
They c o n c e i v e d
f o u r l o n g - c h a i n m o l e c u l e s t r a v e r s i n g t h e c e l l i n th e d i r e c t i o n o f t h e f i b e r
a x is.
No d i f f r a c t i o n from t h e p l a n e s
was o b s e r v e d , a s a r e s u l t
(1 0 0 ),
( 0 1 0 ) , and (00 1) i n odd o r d e r s
of w h ic h t h e y c o n c lu d e d t h a t tv/of o l d scr e w a x e s
p a s s e d th r o u g h t h e c r y s t a l l i t e s
in
a l l t h r e e d i r e c t i o n s . T h is
t h e space group Y4 . The t w o f o l d screw a x i s
form o f t h e h y d ro c a r b o n c h a i n .
was a t t r i b u t e d
w ould g i v e
t o th e c i s
They c o n c lu d e d t h a t t h e r e were e i g h t i s o -
p ren e u n i t s p e r u n i t c e l l .
I f one knows t h e u n i t c e l l , th e d e n s i t y can oe c a l c u l a t e d from t h e
fo r m u la 6^
d *
where
1 . 6 5 HZ
T
,
d - d e n s i t y i n gm. p e r c c .
M - m o le c u la r w e ig h t of t h e r e p e a t i n g u n i t
V - volum e o f
c e l l in c u b ic a n g str o m s
Z - number o f r e p e a t i n g u n i t s p e r c e l l .
o
й
iлark a n d von S u s i c h found th e v a l u e s a * 12.3A t b = 8.3A and c m
8.1A
o
f o r t h e d im e n s io n s o f t h e u n i t c e l l .
c u l a t e d from t h e i r r e s u l t s i s
is 0 .9 6 5 .
The d e n s i t y o f ru b b er a s c a l н
1 . 0 8 gm. p e r c c .
Tne h i g h e s t measured v a l u e
F u r t h e r , t h e f i b e r i d e n t i t y p e r i o d was t o o s m a ll f o r two i s o -
p ren e g ro u p s of t h e z i g z a g p la n a r h y u ro c a r b o n m o le c u le w h ic h t h e y a ssu m ed ,
and t h e A4 e q u a t o r i a l r e f l e c t i o n w h ic h t h e y h a d in d e x e d a s
(040) d id n ot
conform t o th e l a t t i c e .
Lotmar and L ie y e r ^ made a d e t e r m i n a t i o n o f th e s t r u c t u r e from a g r a p h i н
c a l e v a lu a tio n of th e d if f r a c t io n p a tte r n .
They in d e x e d th e A4 e q u a t o r i a l
22
spot a s
c e ll.
(3 0 4 ) w h ic h s e r v e d t o d e te r m in e t h e a x i a l a n g l e o f a m o n o c lin io
The co m p ariso n Detween t h e m easured s p a c i n g s s n d t h o s e c a l c u l a t e d
from t h e c e l l i s g i v e n i n T able 3
65
?
From t h e u n i t c e l l o f Lotmar and Meyer one o b t a i n s a d e n s i t y of 1 .0 2
gm. p e r c c . , a b e t t e r v a l u e th a n was fou nd b y Hark and von S u s i c h , but
s t i l l to o h ig h .
They assum ed a t h r e e - d i i a e n s i o n a l c h a i n form whose e x a c t
rhape was n o t d e f i n i t e l y
th ro u g h t h e u n i t c e l l ,
e sta b lish e d .
Four prim a ry v a l e n c e c h a i n s p a s s e d
th e c h a i n s b e in g s p i r a l s w i t h d e f i n i t e d i r e c t i o n s
of r o t a t i o n b e c a u s e o f t h e p o s i t i o n of th e i s o p r e n e r e s i d u e s .
The c h a in s
were c o n s i d e r e d a s b e i n g a l t e r n a t e l y s t e r i o i s o m e r i c r ig h t - h a n d e d a n d l e f t han ded.
From t h e o b s e r v e d r e f l e c t i o n s sn d e x t i n c t i o n s t h e y d edu ced th e
sp a ce group
0^
.
Working w i t h r a ck ed sam ples show ing h i g h e r o r i e n t a t i o n , S a u t e r
70
c la im e d t h a t th e u n i t c e l l a d v a n c e d by notmar and Meyer was i m p o s s i b l e .
lie p r o p o se d an o r th o r h o m b ic u n i t c e l l c o n s i d e r i n g t h a t t h e s t r o n g A%
e q u a t o r i a l s p o t was a d o u b le s p o t .
He in d e x e d th e:; a s
(0 0 2 ) a n d 1300) .
T h is g i v e s th e u n i t c e l l a g r e a t e r volum e and l e a d s t o a d e n s i t y o f 0 .9 7 4
gm. p e r c c .
However, hotmar and Meyer h a v e d i s p u t e d h i s c l a i m s .
juOrss 71 , u s i n g a c y l i n d r i c a l cam era, h a s m easured a b o u t f o r t y l a t t i c e
s p a c in g s and h a s e x p r e s s e d th e r e s u l t s i n r e c i p r o c a l l a t t i c e c o o r d i n a t e s .
He p r o p o s e d a m o n o c l i n i c c e l l u s i n g th e data o f Lotmar and - e y e r t o o b t a in
a u s o lu te l a t t i c e sp a c in g v a l u e s ,
gm. p e r c c .
- i s u n it
c e l l g i v e s a d e n s ity o f 0 .9 6 5
He d id n o t b e l i e v e t h a t th e wor-c o f -mark and von S u s ic h
n e c e s s i t a t e d t h a t the Ap a n d Ag e q u a t o r i a l s p o t s w ere d i f f r a c t i o n s from
p e r p e n d ic u l a r s e t s o f p l a n e s .
T ab le
4
compares t h e s e v a r i o u s p r o p o s e d u n i t c e l l s о о .
Zable 3 .
X -r a y I n t e r f e r e n c e s o f S t r e t c h e d Blabber (Lotmar and Meyer)
Designaн
t i o n of
Spot
sin 0
Indices hkl
Spacing
A*
Inten
sity
s
YS
W
vw
vw
s
fa
w
vw
w
m
w
m
w
w
vw
vw
vw
w
vw
vw
vw
vw
(002)
6.29
(200)
4 .2 4
3 .14
(004)
(304)
2 .2 3
5.50
(111)
(012)
5.00
(2 1 0 ), (0 1 3 ),(2 1 1 ) 3 .7 6
( 2 l l ) , (212)
3 .4 5
(114)
2. 86
(3 1 2 ), (3 1 1 ), (2 14 )2 .58
(020)
4 .1 0
(120), (121)
3 .70
(121), (022)
3 .4 5
(2 2 0 ), _ ( 0 2 3 ) ,(2 2 1 ) 3 .0 1
(221), (222)
2 .7 8
(222)
2 .56
(124)
2.39
2.20
(224)
(224)
2 .0 8
(4 2 1), (420)
1.92
(1 3 0), (131)
2 .5 8
(2 3 0 ), (231)
2.29
(034)
2 .06
Al
A2
A4
II
12
J3
*4
15
16
no
Hi
? 2
US
114
115
US
II7
US
119
IIIl
III2
III3
(Measured)
0.079
0 .11 8
0.159
0 .22 4
0.091
0.100
0 .13 3
0 .1 4 5
0 .1 7 5
0 .19 4
0.122
0 .135
0 .145
0.166
0.180
0 .1 9 5
0 .209
0.227
0.240
0.260
0 .194
0.218
0 .243
sin 0
(Calculated)
0.079
0 .11 8
0.159
0 .22 4
0.090
0.100
0 .1 3 3 , 0 .1 3 4 , 0.134
0 .1 4 2 , 0.147
0 .17 4
0 .1 9 5 , 0 .1 9 5 , 0 .19 6
0.122
0 .1 3 5 , 0.139
0 .1 4 3 , 0 .145
0 .1 7 0 , 0 .1 7 0 , 0 .171
0 .1 7 7 , 0.181
0.193
0 .209
0 .22 3
0 .24 2
0 .2 6 4 , 0.265
0 .1 9 2 , 0.195
0 .2 1 7 , 0 .219
0 .2 4 2
Z a b le 4 .
Comparison o f v a r i o u s u n i t
Sp onsor
Mark and v . S u s i c h
Lotmar and Meyer
S au ter
Morss
C la s s
c e l l s p r o p o s e d f o r s t r e t c h e d r u b b er
a
D im e n sio n s
b
c
A
A
8 .3
Orthorhom bic 1 2 . 3
8 .5 4 8 . 2 0
M o n o c lin ic
Orthorhom bic 8 . 9 1 8 . 2 0
2 6 .3 8 .1 5
M o n o c lin ic
Monoc lin ic
A ngle
A
8. 1 (f.p .)
#
83 2 0 ?
( f . p . ) 1 2 .6 5
( i . p . ) 1 2 .6 0
8 .9
109* 3 0 '
(f.p .)
C alcuн
la te d
Denн
sity
1 .0 8
1 .0 2
0 .9 7 4
0 .9 6 5
The v a lu e o f th e f i b e r p e r i o d h a s l e f t l i t t l e
d o u o t t h a t t h e c h a in
m o l e c u l e s i n s t r e t c h e d ru b b er c r y s t a l l i t e s a r e n o t p l a n a r .
S a u ter^0 has
d i s c u s s e d the p o s s i b i l i t y t h a t t h e symmetry of t h e t w o f o l d s p i r a l a x e s
does not
e x i s t i n th e p rim a ry v a l e n c e c h a i n s bu t i s r a t h e r due t o th e
c h a in s b e i n g d i s p l a c e d by n a i f a l i b e r p e r i o d w i t h r e s p e c t t o e a ch o t h e r
so a s t o g i v e t h e most d e n s e
a c h in g .
Lotmar and iie y e r showed t h a t b e н
c a u s e t h e r e -.x-y be r o t a t i o n a bou t s i n g l e b a n d s , x - r a y d a ta d oes n o t d eн
f i n i t e l y e s t a b l i s h th e
c h a in s t r u c t u r e ev en th ou gh one r e t a i n s r e c o g n i z e d
a t o n i c d i s t a n c e s and v a l e n c e a n g l e s .
Prom m easurem ents of th e h a l f - b r e a d t h of t h e i n t e r f e r e n c e maxima and
th e u s e o f th e S c h e r r e r e q u a t i o n , iie y e r and ╗ r r k a r r i v e a t th e f o l l o w i n g
f i g u r e s f o r th e s i z e of a r u b b er ?e r y s t a l l i t e :
f i b e r a x i s , from 500 A
0
200 A .
l e n g t h of l a t t i c e
in th e
t o 600 A ; w id th a n d t h i c k n e s s , from 100 A
T h is w ould i n d i c a t e t h a t a c r y s t a l l i t e
to
c o n t a i n s from 1 0 ,0 0 0 t o
2 0 ,0 0 0 u n i t
c e l l s o r from 8 0 ,0 0 0 t o 1 5 0 ,0 0 0 i s o p r e n e u n i t s . H e n g ste n b e r g * ^
?
o
й
g i v e s v a l u e s o f 600 A , 500 A and 150 A r e s p e c t i v e l y f o r l e n g t h , w id t h
and t h i c k n e s s r e s p e c t i v e l y .
I t a p p e a r s t h a t th e u n i t
c e l l i s a v e r y s m a ll f r a c t i o n of t h e l e n g t h
o f the c h a in s a s ded u ced f o r r u b b er by o th ^ r m e th o u s .
Even th e c r y s t a l
l e n g t h i s e v i d e n t l y o n ly a am all p a r t of t h e m o le c u la r l e n g t h .
Assuming
a m o le c u la r w e ig h t o f 1 0 0 , 0 0 0 , th e e q u i v a l e n t o f 1500 i s o p r e n e u n i t s , a
c h a in l e n g t h o f a b o u t 7000 A* w ould be o b t a i n e d .
o
i s g i v e n a s 600 A .
hence i t
The l e n g t h o f t h e c r y s t a l
i s q u i t e p o s s i o l e t h a t one c h a in may p l a y a
p a r t i n s e v e r a l o f t h e c r y s t a l s t h a t a r e form ed d u r in g th e s t r e t c h i n g
process.
T h is means t h e t t h e whole m o le c u le i s n o t n e c e s s a r i l y o r i e n t e d
a lo n g i t s
e n t i r e l e n g t h , but r e q u i r e s o r i e n t a t i o n o f
i t to s a t i s f y th e s e c o n d it io n s .
o n ly s m a ll ^ a r t s o f
25
T here h a s been c o n s i d e r a b l e
c r y s ta ls in s tr e tc h e d rubber,
d i s c u s s i o n c o n c e r n in g th e f o r m a t i o n o f
dehman a n d F i e l d ^ fou n d i n t e n s e f i b e r
d iagram s when, raw r u b b e r was s t r e t c h e d t o m o d era te e l o n g a t i o n s and t h e n
frozen .
T h is w ould i n d i c a t e t h a t t h e c r y s t a l l i z a t i o n i n t h e f r o z e n
r u b b er p r o c e e d s from n u c l e i s e t up by t h e s t r e t c h i n g .
n a t z c o n te n d e d t h a t t h e c r y s t a l s a r e fo rm ed d u r in g s t r e t c h i n g , t h u s
g i v i n g i n t e r f e r e n c e s p o t s w i t h o u t t h e a p p e a r a n c e o f it e b y e - o c h e r r e r r i n g s .
The a s s u m p t i o n s o f h a u s e r en d i& rk
t h e i r '?s w e l l i n g ** t h e o i y .
, on th e o th e r h a n d , a r e embodied i n
l ?h ey assume t h a t t h e c r y s t a l l i t e s a r e p refo rm ed
in th e u n s t r e t c h e d c o n d i t i o n but a r e s w o l l e n by th e n o n - c r y s t a l l i n e comн
p o n e n ts o f t h e r u b b e r h y d r o c a r b o n .
mhen s t r e t c h e d t h e l a t t e r a r e e j e c t e d
from th e c r y s t a l l i t e s snd a n i n t e r f e r e n c e p a t t e r n i s o b t a i n e d ,
The i n н
c r e a s e i n i n t e n s i t y of th e s p o t s i s a t t r i b u t e d t o t h e p r o g r e s s i v e d e - s w e l l н
in g of c r y s t a l l i t e s
o f the same s i z e .
The c o n s t a n c y of s i z e
of t h e c r y s t a l l н
i t e s must be assu m ed b e c a u s e of t h e c o n s t a n t h a l f - o r e a d t h v a l u e s o f t h e
x - r a y i n t e r f e r e n c e maxima.
When th e t e n s i o n i s r e l e a s e d , s w e l l i n g a g a i n
t a k e s p l a c e and th e p a t t e r n d i s a p p e a r s .
in th e s w o l l e n c o n d i t i o n th e
a m p litu d e o f m o tio n o f t h e m o l e c u l e s i s c o n s i d e r e d t o o g r e a t f o r c l e a r
in te r fe r e n c e s to
oe fo r m e d .
The j j e b y e -S c h e r r e r r i n g s of f r o z e n rubber a r e e x p l a i n e d by t h i s t h e o r y
on th e a s s u m p tio n t h a t d i r i n g the a g i n g p e r i o d t h e r e have been s t r u c t u r a l
ch a n g es w hich h a v e r e s u l t e d i n a c o n t r a c t i o n or r i g i d i t y o f th e c r y s t a l l н
ite s.
T h e se b e in g random ly o r i e n t e d th en g i v e th e t y p i c a l powder p a t t e r n .
hock * ^ c o n s i a e r s i t l i k e l y t h a t
lo n g c h e i n - l i k e m o l e c u l e s p r e e x i s t
in u n s t r e t c h e d rubb er and a r e t h e n a l i g n c c c u r i n g t h e s t r e t c h i n g p r o c e s s .
T h is d o e s n o t n e c e s s i t a t e t h a t t h e a c t u a l c r y s t a l l i n e s t r u c t u r e s h o u ld be
p r e fo r m e d .
2*
G-ehman░о r e p o r t s some r e c e n t work w h io o i s o f i n t e r e s t w ith, r e g a r d
t o t h e f o r m a t i o n o f c r y s t a l s when rubber i s s t r e t c h e d .
i n h i s f i r s t work
w it h s t r e t c h e d r u b b e r , k a t z had fo u n d t h a t c r y s t a l l i t e s w ere fo r m e d , o r \ t
l e a s t th e d i f f r a c t i o n s p o t s were o b t a i n e d , o n ly i f a minimum e l o n g a t i o n
was e x c e e d e d .
l ?h i s minimum e l o n g a t i o n was a b o u t 30 p e r c e n t , a v a lu e w h ich
'was l a t e r s u b s t a n t i a t e d by n a u s e r and y a r k .
h o w e v e r , t h i s minimum depends
on th e rubb er and on the te m p e r a tu r e . ^As h a s been p r e v i o u s l y m e n t io n e d ,
O
0
f o r e v a p o r a t e d l a t e x a t 20 0 t o 25 o th e minimum e l o n g a t i o n i s fou nd t o be
betw een 150 p e r c en t and 300 p e r c e n t ,
i n t h e work t o be r e p o r t e d h e r e
i t was from 2 5 0 -2 7 5 p e r c e n t .
Above t h i s minimum e l o n g a t i o n t h e above m e n tio n e d i n v e s t i g a t o r s found
th e i n t e n s i t y
tio n .
of t h e s p o t s t o i n c r e a s e a p p r o x im a t e ly l i n e a r l y w i t h e l o n g a н
iiehman c la im s t h a t t h e s e r e s u l t s a r e due t o an e x p e r i m e n t a l e r r o r ,
t h e e r r o r l y i n g i n the f a c t t h a t no c o r r e c t i o n was a p p l i e d f o r t h e d im in i s h i n g t h i c k n e s s o f rubb er u s e d ,
using' s a m p le s of th e same f i n a l t h i c k n e s s
he f i n d s th e i n t e n s i t y o f th e s p o t s t o be r e l a t e d to t h e e l o n g a t i o n by an
3 -s h a p e d c u r v e a s shown i n F ig u r e 10 65 ?
The s h a p e o f t h i s c u r v e i m p l i e s t h a t t h e c r y s t a l l i t e s
a s soon as s t r e t c h in g b e g in s ,
s t a r t t o form
h o w e v e r , t h e r e way b e a more or l e s s c r i t i c a l
e l o n g a t i o n n e c e s s a r y b e f o r e t h e d i f f r a c t i o n p ro d u ced b y them i s
enough to be o b s e r v a b l e ,
in te n se
u-ehman? s i n v e s t i g a t i o n g i v e s a b e t t e r c o r r e l a t i o n
betw een t h e form of t h e i n t e n s i t y - e l o n g a t i o n curve and t h e s t r e s s - s t r a i n
curve th an h a s been o b t a i n e d h e r e t o f o r e .
E le ctr o n D if f r a c t io n .
K r u ilo v ^ 6 h a s u s e d an e l e c t r o n beam t o s tu d y t h e
c r y s t a l s t r u c t u r e of r u b b e r .
T hin f i l m s n e c e s s a i y
f o r t h e method may be
o b t a in e d b y a l l o w i n g dro ^ s o f a d i l u t e s o l u t i o n in b en zen e t o f a l l on
w a ter.
The s o l v e n t e v a p o r a t e s and t n e f i l m s a r e t h e n s u p p o r t e d by any one
V
v
&
z
g
u
r
%
TEM PERATU RE - 2S*C.
"5(55-----1---- " iAfl _
E L O N G A T IO N
%
F ig u r e 1 0 .
o f t h e s p e c i a l t e c h n i q u e s t h a t h a v e b e e n d e v e lo p e d in e l e c t r o n d i f f r a c t i o n
-5
F ilm s a b o u t 10
cm. t h i c k w ere e x p o s e d t o oeams of wave l e n g t h
?
o
0 .0 6 5 5 A - 0 .0 6 5 0 A t and r i n g s , i n d i c a t i n g a n amorphous s t r u c t u r e , w ere
work;.
fo u n d ,
i ' r i l l o t a n d iiiotz3 о showed t h a t a f i b e r d iagram c o u ld be o b t a in e d
im m e d ia te ly a f t e r s t r e t c h i n g t h e f i l m s bu t t h e s p o t s d i s a p p e a r e d w i t h i n
?
a s h o r t t i m e , prom t n e i r p i c t u r e s h r u i l o v o b t a i n e d l e n g t h s of 1 2 . 3A,
?
?
3 .3A and 8.1A f o r t h e a , b and c a x e s r e s p e c t i v e l y .
T h is a g r e e s e x a c t l y
w i t h t h e v a l u e s o b t a i n e d by iaark and von S u s i c h from t h e i r x - r a y i n v e s t i н
g a tio n s.
Stork J
-has o b t a in e d e l e c t r o n d i f f r a c t i o n p a t t e r n s of s t r e t c h e d and
╗
u n s t r e t c h e d g u t t a - p e r c h a . The f i l m s u s e a a s sp e cim en s w ere a b o u t 200A
th ic k .
From t h e d i f f r a c t i o n p a t t e r n s of s t r e t c h e d p u r e - w h i t e g u t t a - p e r c h a
г
( ^ m o d i f i c a t i o n ) he f i n d s a f i b e r p e r io d of 9.46A , i n g o o d a g r e e m e n t w it h
th e v a l u e 9 .5 4 A
O
o b t a in e d by F u l l e r a n d n r i c k s o n
S t o r k fo u n d th a t t h e c r y s t a l l i t e s
Q/
from x - r a y d a t a .
in u n s t r e t c h e d .f ilm s of g u tta -p e r c h a
w ere o r i e n t e d w i t h t h e i r f i b e r a x e s a p p r o x im a t e ly norma 1 t o the s u r f a c e o f
th e f i l m .
For t h e ?pure?w h i t e " g u t t a - p e r c h a he fo u n d t h a t the l a r g e s t
a n g l e b e tw e en th e norm al t o th e f i l m s u r f a c e and an a p p r e c i a b l e number o f
f i b e r a x e s d id n o t e x c e e d
6
; f o r a f i l m o f *╗3r-4rt g r a d e g u t t a - p e r c h a t h i s
O
a n g le does n o t exceed 4 ?
S i n c e th e t h i c k n e s s o f t h e f i l m s i s much l e s s th a n th e l e n g t h o f a
g u t t a - p e r c h a m a c r o m o le c u le , t h e a lm o s t p e r f e c t o r i e n t a t i o n of th e c r y s t a l l н
i t e s i n d i c a t e s t h a t , h e r e , th e m a c r o m o le c u la r c o n f i g u r a t i o n of g u t t a - p e r c h a
i s not g e n e r a lly lin e a r .
r o ta tio n about i t s
The m a c r o m o le cu le may f o l d by a mechanism o f
s i n g l e b a n d s , r e l a t i v e l y few f o l d s p e r m a cr o m o le cu le
b e in g r e q u i r e d s i n c e t h e
c h e m ic a l r e p e a t i n g u n i t
is
sh ort,
s to r k c o n ceiv es
t h a t such a f o ld in g - can ta^-ce p l a c e w ith o u t a f f e c t i n g t h e c r y s t a l s t r u c t u r e .
29
D.
M o le c u la r M odels
S e v e r a l m odels h a v e b e e n p r o p o se d to r e - r e s e n t t h e m o le c u la r s t r u c t u r e o f r u b b er 15 ╗
1?h.ese
m odels
a r e g e n e r a l l y c l a s s i f i e d i n t o two g r o u p s :
t h o s e in w h ic h t h e m o le c u le i t s e l f
is
c a p ab le o f e l o n g a t i o n ,
c a lle d fo ld н
ed c h a i n s ; a n d , t h o s e in w h ic h t h e m o le c u le i s n o t cap,able of e l o n g a t i o n ,
c a lle d extended c h a in s,
i h u s f a r , n e i t h e r t h e o r e t i c a l n o r e x p e r im e n t a l
work h a s b e e n a b le t o d e c i d e c o n c l u s i v e l y w h ic h t y p e of s t r u c t u r e a c t u a l l y
e x ists..
F i s h e r a n d u-erke
Q}he S p i r a l M o d el.
d is c u s s th e fo llo w in g ty p e s s
In t h i s model t h e r e a r e i s o p e n t e n e g r o u p s l i n k e d t o н
g e t h e r a t t h e d o u b le bo n d , th e e t . i y l e n e c n a i n s b e in g i n a c i s ' c o n f i g u r a t i o n .
In th e u n s t r e t c h e d s t a t e , t h e m o l e c u l e s a r e
in a s p i r a l or c o i l e d s p r in g
form , th e d o u b le oonas o e i n g a t o p p o s i t e ends of th e d ia m e te r o f t h e s p i r a l
and form in g a row on b o t h s i d e s of the
sp ir a l.
tfhen e l o n g a t i o n t a k e s p l a c e t h e r e i s a n i n i t i a l s t i f f n e s s due
s e p a r a t i n g o f the d o u b le b o n d s ,
t o th e
?i h i s would a c c o u n t f o r t h e i n i t i a l
c h a r s c t e r i s t i c s of the s t r e s s - s t r a i n c u r v e s b a s e d on o r i g i n a l c r o s s - s e c t i o n .
For t h i s m o d e l, h e a t w o u ld be a b s o r b e d d u r in g th e i n i t i a l p r o c e s s of e l o n g a н
tio n .
F u r th e r e l o n g a t i o n would e v o l v e h e a t , t n e e v o l u t i o n b e in g due t o
c r y s t a l l i s a t i o n or o r i e n t a t i o n of th e m o l e c u l e s .
I f te n s io n is a p p lie d
a f t e r c o m p le te o r i e n t a t i o n h a s b e e n o b t a in e d r u p tu r e r e s u l t s .
The a b o v e c o n s i d e r a t i o n s a p p ly f o r a s i n g l e m o l e c u l e .
d e s c r i p t i o n s h o u ld be v ie w e d in
a s ta tistic a l
o r i e n t a t i o n o f th e m o l e c u l e s in
th e u n s t r e t c h e d r u b b e r .
A c t u a l l y th e
s e n s e , b e c a u s e o f t h e random
The o b j e c t i o n s to t h i s model a r e ; th e s p i r a l i t s e l f d o e s n o t p o s s e s s
th e n e c e s s a r y l o n g - r a n g e e l o n g a t i o n 4 6 ; th e d o u o le bonds a r e sp a c e d t o o
fa r apart fo r
Van d e r w aals f o r c e s t o o p e r a t e 4 6 ; on the i n i t i a l e l o n g a t i o n
00
h e a t i s e v o lv e d i n s t e a d o f b e in g a b s o r b e d
IQ
?
l ?he Hydrogen Evas ora t io n - G o n d e n s a tio n M o d e l.
e la stic ity
lik e
T h is m o d e l ^ a t t r i b u t e s t h e
o f ru b b er t o t h e s i n g l e m o l e c u l e s , c o n s i d e r i n g them t o behave
sp r in g s,
i t p o stu la te s th a t,
due t o van d e r w a ais f o r c e s , t h e r e a r e
no c l a s s i c a l l y f r e e r o t a t i o n s a b o u t t h e s i n g l e carb on b o n d s .
The Van der
,fa a ls f o r c e s a r e a t t r a c t i v e f o r c e s e x i s t i n g b e tw e en th e h y d ro g en atom s on
a d j a c e n t s i n g l e bonded ca rb o n a to m s .
The s i n g l e bonds a d j a c e n t to th e
d o u b le bonded carb on atom s may r o t a t e o n ly under m e c h a n ic a l s t r e s s - , v/hi l e
t h o s e b e tw e e n th e UEg g r o u p s ,
i.e .
r o t a t e u n d er m e c h a n ic a l s t r e s s ,
t h o s e a d j a c e n t to t h e bonds t h a t can
cannot r o t a t e e v e n under s t r e s s .
Jslonga-
t i o n w ould c a u s e an u n l i n k i n g of t h e c h a in s by a. r o t a t i o n o f t h e bon d s
not r ig id ly f ix e d .
T h is w ould produce a s e p a r a t i o n o f t h e h y d ro g e n a to m s ,
th e s e p a r a t i o n b e i n g c a l l e d e v a p o r a t i o n .
The r e v e r s e p r o c e s s w ould be
c a l l e d c o n d e n sa tio n .
h o w e v e r , from c o n s i d e r a t i o n s o f t h e f i r s t
th e f a c t t h a t th e J o u l e e f f e c t
Isw of therm odynam ics and
i s a c t u a l l y o p p o s i t e in s i g n t o t h a t r e н
q u i r e d , th e model d o e s n o t a p p ea r t o be v e r y s a t i s f a c t o r y .
The i r a n z e n M odel.
T h is m odei^?'? p o s t u l a t e s g r o u p s or b u n d le s o f e x te n d e d
m o le c u le s w it h f r i n g e d e n d s , t h e
e c t e d w it h t h o s e
end gro u p s ox one b u n d le b e i n g i n t e r c o n n н
of o t h e r b u n d l e s .
Thus we w ould have g r o u p in g s or c r y s t a l l н
i t e s even, i n t h e u n s t r e s s e d raw r u b b e r .
p a ttern s.
The... s h o u ld g i v e x - r a y d i f f r a c t i o n
The o n ly c a s e s where t h i s h a s b e e n o b s e r v e d a r e f o r sa m p le s t h a t
h av e a g e d o v e r l o n g periods o f t i m e .
T h ese f r o z e n sa m p le s show th e d e o y e -
bcherrer p a t te r n .
H ow ever, a s h a s b e e n m en tio n ed p r e v i o u s l y , t h i s p a t t e r n
d oes n o t a p p e a r i f
th e sam ples a r e wa.rmed or h a v e oeen r e p e a t e d l y s t r e t c h e d
and r e l a x e d .
i f th e p a t t e r n p e r s i s t e d a f t e r r e p e a t e d s t r e t c h i n g , and ga ve
a u n i t c e i l o f t h e same s i z e a s t h a t d e te r m in e d from tn e d i f f r a c t i o n
p a t t e r n o f s t r e t c h e d r u b b e r , o r e would h a v e a d i r e c t i n d i c a t i o n o f p r e н
formed c r y s t a l l i r i t y
in the u n s t r e s s e d r u b b e r .
A n o tn er o b j e c t i o n t o t h i s
model i s t h a t i t g i v e s no mechanism t o e x p l a i n lo n g - r a n g e e x t e n s i b i l i t y .
?i h e Wangled Ohain M odel.
i'h is m o d e l ^ p r o p o s e s lon g f l e x i b l e c h a in s in
w h ich one n a y h a v e , at some p o i n t s , p a r t i a l s l i p p i n g a n d , a t o th e r p o i n t s ,
\
l i n k i n g s or b i n d i n g s b etw een c h a i n s . .c J o n g a tio n w ould produce a jamming
i n th e c n a i n s .
hue t o random o r i e n t a t i o n and th e r m a l a g i t a t i o n th e m oleн
c u l e i s assum ed t o be, p a r t i a l l y f o l d e d ,
rhe mechanism o f e l a s t i c i t y f o r
t h i s model )ia s n o t b e e n f u l ^ y d e v e l o p e d .
The Two Phas e M o d el.
T h is moo e l w as d i s c u s s e d i n t h e p r e v io u s s e c t i o n
on x - r a y d i f f r a c t i o n p a t t e r n s of s t r e t c h e d rubber where t h e ?s w e l l i n g "
t h e o r y o f n a u s e r and n a ru was c o n s i d e r e d .
At t h e p r e s e n t i t
i s not v e r y
h ig h ly fa v o r e d .
The F l e x i b l e ffib e r l l o d e l .
AQ
h e r e ░ th e m o l e c u l e s a r e assumed t o be c h a in s
w i t h a l e n g t h v e r y g r e a t a s compared w i t h t . i e i r c r o s s - s e c t i o n ; th e y a r e
a r r a n g e d i n a random f a s h i o n and l i n k w henever t h e y m e e t .
c i t y i s ta k e n t o be due t o a change i n fo r m .
T h e ir e l a s t i н
During t h e i n i t i a l e x t e n s i o n
some o f tn e f i b e r s a r e com p ressed w i t h tne c o n s e q u e n t s t o r i n g o f e n e r g y .
As e x t e n s i o n c o n t i n u e s , t h e s e com p ressed f i b r e s p a s s th ro u g h s c r i t i c a l
a n g l e a f t e r which t n e y a r e e x t e n d e d ,
ho e n e rg y i s r e q u i r e d t o e x te n d
?
them, t n e p o t e n t i a l e n e r g y s t o r e d d u r in g c o m p r e ssio n a c t u a l l y a s s i s t i n g
the e l o n g a t i o n .
Tne t h e o r y d o e s n o t tak e i n t o c o n s i d e r a t i o n th e J o u le
e f f e c t a n d h a s n o t b e e n s u f f i c i e n t l y d e v e lo p e d t o a l i a ? q u a n t i t a t i v e t e s t н
in g .
The Dynamic Thermal T.lmlel.
t o th e r e s t r a i n e d
3 row n ia n
3y a t t r i b u t i n g the e l a s t i c i t y o f th e m o le c u le s
m otion of t h e f r e e l i n k a g e s oetw een s i n g l e
One g e t s n o t a n e x te n d e d m o le c u le but one kinxeu. i n t o i r r e g u l a r l o o p s .
bonds
49
╗
82
For a c h a in l e n g t h o f 1 0 ,0 0 0 carb on a t o m s , t h e a v e r a g e a n g u l a r i t y of t h e
й
a r c s i s 163 .
T h is m od el b r in g s o u t th e
q u e s t i o n a s t o w hether th e s o u r c e
o f e l a s t i c i t y i s e n e r g y s t o r e d by t h e s t r a i n i n an a s s e m b la g e o f m o l e c u l e s
w h icn a r e c r o o k e d b e c a u s e o f th e r m a l a g i t a t i o n p e r p e n d i c u l a r t o the l e n g t h
o f th e m o le c u le or w h e th e r i t
th em se lv e s.
i s due to s t a t i c s t r a i n i n th e m o l e c u l e s
The f i r s t c a s e would be com p a ra b le w i t h t h a t o f a monatomic
g a s w h i l e th e seco n d w ou ld be s i m i l a r t o t h e e l a s t i c i t y in a s p r i n g .
So f a r a s the p h y s i c a l p r o p e r t i e s o f r u b b e r a r e c o n c e r n e d e l a s t i c i t y
can be v e r y w e l l e x p l a i n e d by th e r m a l a g i t a t i o n , p r o v id e d th e Van d e r
\f a a i s f o r c e s a r e g iv e n p r o p e r c o n s i d e r a t i o n .
The i n c r e a s i n g r e s i s t a n c e t o
s t r e t c h i n g a t g r e a t e x t e n s i o n s nay be a t t r i b u t e d t o b e t t e r c o n t a c t b e tw e e n
m o l e c u l e s w i t h c o n s e q u e n t i n c r e a s e o f Van der Vfeals f o r c e s .
T h is model i s q u i t e s im p le and i s
observed p r o p e r tie s of rubber.
c a p a b le o f e x p l a i n i n g many o f t h e
The m o d i f i c a t i o n s n e e d e d w i l l depend upon
t h e r e s u l t s of f u r t h e r i n v e s t i g a t i o n s .
H. M. James o f t h i s d ep a rtm en t h a s u s e d a s t a t i s t i c a l method t o e x н
p l a i n th e b e h a v io r of r u b b e r ,
work o f f l e x i b l e
h e a ssu m es a l o o s e t h r e e d im e n s io n a l n e t н
c h a in s i n an i n c o m p r e s s i b l e f l u i d ,
jfrom s u c h a model he
e x p l a i n s th e s h a p e of t h e s t r e s s - s t r ? i n c u r v e a s f o l l o w s :
a t the b e g in n in g o f th e curve i s
th e r a p id r i s e
due t o a d e c r e a s e o f i n t e r n a l г .r e s s u r e ;
t h e n e x t , more s l o w l y r i s i n g p o r t i o n ,
th e f i n a l p a r t , w here a sudden r i s e
i s due to i n t e r n a l f o r c e s o f t h e n e t ;
in s t r e s s o c c u r s w i t h e l o n g a t i o n ,
is
a t t r i b u t e d t o th e f a c t t h a t th e c n a i n s a r e r e s c u i n g t h e i r maximum e x t e n s i o n .
James p o i n t s out t h a t ,
but l e t
i f we do n o t c o n s i d e r th e volume t o be c o n s t a n t
i t depend on t h e t e m p e r a t u r e , t h e t h e o r y may oe e x t e n d e d t o a c c o u n t
fo r th e observed s tr e s s - te n p e r a tu r e c u r v es.
T h is work lia s not b e e n p u b l i s h e d t o d a t e .
II.
THE FHOBII4I
As was p o i n t e d out in t h e i n t r o d u c t i o n , v e r y l i t t l e x - r a y work has
b e e n done on t h e s t r u c t u r e o f amorphous r u b b e r .
The work o f Simard and
Vferren on u n s t r e s s e d smoked s h e e t showed t h a t , by vising a f o u r i e r a n a l н
y s i s method s u c h a s h a s b een a p p l i e d i n t h e c a s e o f l i q u i d s , one c o u ld
o b t a i n q u a n t i t a t i v e r e s u l t s a s r e g a r d s th e number and p o s i t i o n o f n e i g h н
b o r in g atom s about any one atom in th e m o l e c u l e .
Ur. I a r k - h o r o v i t z s u g g e s t e d t h a t , by u s i n g t h i s same m eth od, i t
s h o u ld
be p o s s i b l e t o d e te r m in e what changes o c c u r in t h e a t o m ic d i s t r i b u t i o n
when rubb er i s
stretch ed .
In s u c h i n v e s t i g a t i o n s ,
of c o u r s e , s t r e t c h i n g must be l i m i t e d t o a
c e r t a i n maximum e l o n g a t i o n , n a m e ly , t h a t a t w h ic h t h e d i f f r a c t i o n p a t t e r n
shows e v i d e n c e s o f c r y s t a l l i z a t i o n .
For th e l a t e x u s e d t h i s l i m i t s one
o
e
t o an e l o n g a t i o n o f 2 5 0 -2 7 5 p e r c e n t a t te m p e r a tu r e s o f 20 C t o 25 C.
S in c e t n e a n a l y s i s g i v e s u s th e d i s t r i b u t i o n o f atom s a b ou t a n y one
atom in t h e m o l e c u l e ,
one w ould e x p e c t s t r e t c h i n g to produ ce l i t t l e
no change in th e d e n s i t y d i s t r i b u t i o n ,
if it
or
i s assum ed t h a t i n th e unн
s t r e s s e d r u b b er t h e m o le c u le i s a l r e a d y f u l l y e x t e n d e d .
On t h e o t h e r
ha n d , i f th e m o le c u le i n u n s t r e s s e d ru b b er i s n o t e x t e n d e d , but i s c o i l н
e d or k in k e d i n some f a s h i o n w h ich xierm its r o t a t i o n a b o u t th e s i n g l e b o n d s ,
t h e n one s h o u ld be a b l e t o d e t e c t a change i n t h e d e n s i t y d i s t r i b u t i o n o f
n e ig h b o r i n g ato m s a s th e s t r e s s i n c r e a s e s .
c o n s e q u e n t l y , th e problem r e s o l v e s i t s e l f
i n t o a n a tt e m p t t o a s c e r н
t a i n , f i r s t o f a l l , w hether or n o t any ch a n g es i n t h e d i s t r i b u t i o n o f t h e
atoms su r ro u n d in g an y one atom can be o b s e r v e d a s t h e rubber i s s t r e t c h e d ;
s e c o n d l y , i f su c h ch a n g es do o c c u r , t o see i f t h e y c a n a s s i s t i n g i v i n g a
c le a r e r p ic tu r e
of t h e s t r u c t u r e o f th e rubb er m o l e c u l e .
III.
THE METHOD
We s h a l l c o n s i d e r two a s p e c t s o f t h e method u s e d in a t t a c k i n g t h e
p ro b lem , n a m e ly , t h e t h e o r e t i c a l arkL th e e x p e r i m e n t a l .
We s h a l l f i r s t
c o n s id e r th e t h e o r e t i c a l c a l c u l a t i o n s o f i n t e n s i t y and f o l l o w i n g t h i s
s h a l l s e e how, from t h e i n t e n s i t y d i s t r i b u t i o n , one can d e r i v e an e x p r e s s н
io n f o r t h e a to m ic d e n s i t y d i s t r i b u t i o n .
Then we s h a l l c o n s i d e r t h e e x н
p e r im e n t a l equipm ent and t e c h n iq u e w h ich is n e c e s s a r y i n o r d e r to make
p r a c t ic a l use o f t h i s t h e o r e t i c a l l y d e r iv ed e x p r e s s io n .
A.
T heory
As was s h a m by F i g u r e s 4a and 5 , th e d i f f r a c t i o n x a t t e r n o f rubber
d o e s n o t d i f f e r g r e a t l y from t h a t of a l i q u i d .
I t was m e n tio n e d e a r l i e r
t h a t t h e c o n c e p t o f th e ,* o y b o t a c t i c ,, s t a t e h a s been a d v a n ced f o r rubber
as w e ll as fo r l i q u i d s .
There a p p e a r s t o be no r e a s o n why an a n a l y s i s o f
th e d i f f r a c t i o n p a t t e r n o f r u b b er c o u ld n o t be c a r r i e d out i n j u s t th e
same way a s i s done in t h e c a s e o f a l i q u i d .
The r e s u l t s o f Sim ard and
V fe r r e n ,o b ta in e d from t h e i r a n a l y s i s o f smoked s h e e t , h a v e a l r e a d y been
m entioned and have shown t h e method to be p r a c t i c a b l e .
I n t e n s i t y o f S c a t t e r e d > te.d ia tion .
A d e t a ile d c o n s id e r a tio n of th e
s c a t t e r i n g due t o t h e a to m s and m o l e c u l e s in a l i q u i d h a s been g i v e n i n th e
t h e s i s o f E. P . M i l l e r .
72
w ith o u t g o in g i n t o d e t a i l we s h a l l o u t l i n e
b r i e f l y a d e r i v a t i o n o f th e e x p r e s s i o n f o r t h e i n t e n s i t y o f t h e s c a t t e r e d
r a d ia t io n .
The s c a t t e r i n g from a s i n g l e atom h a s been c a l c u l a t e d by ff e n tz e l
a n d , l a t e r , by V fe lle r 7 ^ u s i n g wave m e c h a n ic s .
t e n s i t y can b e w r i t t e n a s
75
The e x p r e s s i o n f o r t h e i n н
35
T c
+ Z
l
( 3 .1 )
?
where
-2"e =
-J-e.
^ z
Fa. )
(3 .2 )
i s th e c o h e r e n t or unm odified, s c a t t e r i n g and
T i
(3 .3 )
~ T e . C z - I f: )
i s t h e in c o h e r e n t or m o d i f i e d s c a t t e r i n g .
s c a t t e r i n g from a s i n g l e
The f a c t o r I e i s th e Thompson
e l e c t r o n a s d e r i v e ^ from c l a s s i c a l e l e c t r o d y n a н
m i c s , n a m ely ,
X mIn e q u a t i o n
e *
t
... f / +
*?
0
^
- I
(3 .4 )
(3 .4 )
I 0= i n t e n s i t y of i n c i d e n t r a d i a t i o n
e s e l e c t r o n i c cnarge
m = e l e c t r o n i c m ass
c = v e l o c i t y of l i g h t
r = d i s t a n c e from e l e c t r o n t o p o in t of o b s e r v a t i o n
<p = a n g l e betw een t h e d i r e c t i o n s o f th e i n c i d e n t and s c a t t e r e d
r a d ia tio n .
In e q u a t i o n s
( 3 . 2 ) and ( 3 . 3 ) th e q u a n t i t y ^ ^
i s th e a t o m ic s t r u c t u r e
f a c t o r F, where f-n i s th e e l e c t r o n s t r u c t u r e f a c t o r o f t h e n t h e l e c t r o n .
The s t a n f a c t o r s f o r h e a v y e le m e n t s
and Fermi^о.
They c o n s i d e r th e atom
77
( 2 >20) have been c a l c u l a t e d by Thomas
t o be made up o f a n u c l e u s surrou nded
by an e l e c t r o n g a s whose d e n s i t y i s a f u n c t i o n o n ly of t h e r a d i u s .
l i g h t e le m e n t s
For
H artree^о h a s u s e d t h e method o f " s e l f - c o n s i s t e n t
f i e l d s ' * and h a s o b t a i n e d q u i t e good r e s u l t s .
J a n e s and d r i n d l e y
90
by
a p p l y i n g b o t h m ethods h av e e v a l u a t e d F?f a c t o r s f o r most o f t h e e l e m e n t s .
H e i s e n b e r g 3^
dewiloguaо*^ , by a method s i m i l a r t o F e r m i ' s , nave c a l c u l ?
36
* c
a t e d th e term dLrn
w h ich a p p e a r s in th e in c o h e r e n t p a r t of t h e s c a t t e r i n g ,
83
84or
E h r e n f e s t 0 , Debye , and Z er n ick e and F r i n s
have c a l c u l a t e d t h e
s c a t t e r i n g from a s i n g l e m o l e c u l e , th e r e s u l t b e in g th e E h r e n f e s t forrxula
__
wiiere 3 = *4JT
^
d
& bein g h a l f th e a n g l e betw een th e d i r e c t i o n o f
th e s c a t t e r e d r a d i a t i o n s n d the- main beam and y) b e in g t h e waveн
le n g th u s e d .
= d i s t a n c e from atom i to atom j .
Ft
s a t o m ic s t r u c t u r e f a c t o r f o r atom i .
Fj
s a to m ic s t r u c t u r e f a c t o r f o r atom j .
For a monatomic l i q u i d th e above e x p r e s s i o n r e d u c e s t o
i
r?
X ( 5 ) =X e N F t/F.
*л i/
Atomio D e n s i t y D i s t r i b u t i o n .
C
t)
?SSV:
(3 .6 )
<svt
In a l i q u i d , and i n rubb er a s w e l l , t h e r e
a r e s t a t i s t i c a l f l u c t u a t i o n s i n t h e a to m ic d e n s i t y i n th e n e ig h b o r h o o d
o f an y g i v e n atom.
At g r e a t e r d i s t a n c e s from th e atom th e f l u c t u a t i o n s
become s m a lle r an d , e v e n t u a l l y , th e a to m ic d e n s i t y d i s t r i b u t i o n w i l l be
g i v e n b y t h e a v e r a g e a to m ic d e n s i t y d i s t r i b u t i o n 4 7 r X f a) pa b e i n g th e
a v e r a g e a to m ic d e n s i t y .
may be c a l c u l a t e d from the e x p r e s s i o n
N nd
f .*
^
wnere N - A v o ga d ro ? s number
d - d e n s i t y i n gm. p e r c . c .
n - number o f atom s p e r m o le c u le
?<7 - m o le c u la r w e i g h t .
( S . 7)
S e m ic & e and P r i n s Q6 f i r s t u s e d the c o n c e p t o f a d e n s i t y d i s t r i b u t i o n
f u n c t i o n t o e x p r e s s t h e s c a t t e r i n g i r o n monatomic l i q u i d s .
fu n c tio n g (r )
is u e fin ed
A d istr ib u tio n
such t h a t V T T V t - ^ ^ r e p r e s e n t s th e number o f
a t o m s , a b o u t a ry one atom , b e tw e e n r and r + a r .
E q u a t io n ( 3 . 6 ) can t h e n
be w r i t t e n i n t n e i n t e g r a l form .
T ts)~ N l-l^
I I
^
T h is i s a d i v e r g e n t i n t e g r a l a s i t
i
now s t a n d s .
(░ * 8)
Haw e v e r , f o r a homogeneous
c o n t in u o u s d i s t r i b u t i o n o f s c a t t e r i n g m a t e r i a l o f d e n s i t y ^ t h e m utual i n н
t e r f e r e n c e s w i l l le a d to c a n c e l l a t i o n
o f th e s c a t t e r e d r a d i a t i o n .
H ence,
one can a d d s u c h a c o n t i n u o u s d i s t r i b u t i o n o f s c a t t e r i n g m a t e r i a l .
means in tz 'o d u c in g t h e f u n c t i o n
f(~) =
E q u a t io n ( 3 . 8 )
l s - 91
can t h e n be e x p r e s s e d a s
T < s J> -= A / F X e f t + )(p j r j C ' t f < * > - г )
w here I ( s )
(
?
i s th e e x p e r i m e n t a l l y o b s e r v a b l e i n t e n s i t y .
V7e a r e i n t e r e s t e d in fetezmining th e a t o m ic d i s t r i b u t i o n from th e
observed i n t e n s i t y cu rv e.
_ZT <X>
LCs ) = A/ F %
To do t h i s one d e f i n e s
~~-E"t
^
_/
=
jF
t
(3 .1 1 )
/
w here
- e x p e r im e n ta lly observed s c a t t e r in g
Ii
- t h e o r e t i c a l in c o h e r e n t s c a t t e r i n g
Ic
- t h e o r e t i c a l com erent s c a t t e r i n g
Then we c a n w r i t e
/^a<>
i a ) = r^ /T sc'C P C '*-)
So
lr7 l p \
<Tsr,
^
T h is
58
Lii.lt ip l y i n g th r o u g h by
OO
3
we g e t
shcs) = ^ n j l ^ C f c A d - s i ) J - * .
(5.13)
T h is i s an i n t e g r a l e q u a t i o n t o w h ic h th e F o u r i e r r e c i p r o c i t y th eo rem ran
be a p p l i e d .
T h is g i v e s t h e e x p r e s s i o n
oD
s
d
i
f
c
^
-
f
0 s its) ^ ^ C s -A .) J s
,
-
( 2 - 1 4 )
or f i n a l l y ,
oO
J_
J,
P ( /t )
SX.
+~7T~Jso S i C s )
v
(-**0 J S
(o .l5 )
As we s e e from e q u a t i o n ( 3 . 1 1 ) we can d eterm in e i ( s ) ,
s i n c e we can
f i n d 1 ^ e x p e r i m e n t a l l y a n d have I i and I c i n t a b u l a t e d formо^.
Then we
can a l s o d e te r m in e s i ( s ) a n d , a s a r e s u l t , th e e v a l u a t i o n o f t h e i n t e g r a l
in e q u a t i o n ( 3 . 1 5 ) w i l l g i v e u s t h e d i s t r i b u t i o n o f atom s about any one
atom .
T h is d i s t r i b u t i o n i s c a l c u l a t e d from th e o b s e r v e d i n t e n s i t y c u r v e
and i n v o l v e s no "a p rio r i* * a s s u m p t io n s r e g a r d in g s t r u c t u r e
(sp a tia l
a rran gem en t of a t o m s ) .
A d e t a i l e d a c c o u n t o f th e method o f e v a l u a t i n g t h e i n t e g r a l i n ( 3 . 1 5 )
QQ
i s g i v e n in th e t h e s i s o f G. 0 . D a n ie ls o n
and so w i l l n o t be d i s c u s s e d
here.
How ever, an a n a l y s i s w i l l be c a r r i e d th r o u g h s c t h a t t h e m e c h a n io s
o f t h e method w i l l be u n d e r s t o o d .
3.
E x p e r im e n ta l
X -ra y Tube. E a d i a t i o n and Camera.
of th e ty p e d e s i g n e d by E. F. H i l l e r
The x - r a y tu b e u s e d i n t h i s work; was39
.
T his i s a s e l f - r e c t i f y i n g deн
m ountable tu b e w it h i n t e r c h a n g e a o l e t a r g e t s .
f la t target fa c e .
The f il a m e n t was grou n d ed ; t h e t a r g e t b e i n g a t an
e f f e c t iv e p o t e n t ia l of 1 0 .4 k i l o v o l t s .
in a l l c a s e s .
A l i n e f o c u s was u s e d on a
A tu b e c u r r e n t o f 40 ma. was u s e d
The n e c e s s a r y e x p o s u r e depended on th e t h i c k n e s s o f th e
sa m p le , t h e a v e r a g e b e in g a b o u t 50 h o u r s .
A molybdenum t a r g e t w as u s e d , ISo
f l e c t i o n from a roc<c s a l t c r y s t a l .
r a d i a t i o n b ein g o b t a in e d b y r e н
I k e u s e o f a monochromator r e s u l t s i n
a g r e a t r e d u c t i o n i n i n t e n s i t y but i t was fo u n d to be n e c e s s a r y i n order
t o a v o i d e x c e s s s c a t t e r i n g a n d a l s o to a v o i d s p u r io u s e f f e c t s w h ic h may
be o b ta in ed w ith f i l t e r e d r a d i a t i o n .
I h e e x p e r i m e n t a l s e t - u p i s shown i n F i g u r e s 11 and 1 2 .
The c y l i n d н
r i c a l camera h a s a r a d i u s o f 4 3 . 0 3 mm., a s d e te r m in e d by c a l i b r a t i n g i t
w ith tu n g ste n w ir e .
The f i l m t r a c k c a r r i e s in d e x marks e v e r y 20 d e g r e e s ,
t h e s e i n d i c e s b e i n g r e g i s t e r e d on t h e f i l m d u r in g e x p o s u r e .- T h i s r u l e s
o u t any e r r o r due t o s h r in k a g e t h a t may t a k e p l a c e i n t h e f i l m d u r in g t h e
d e v e lo p in g p r o c e s s .
D u rin g e x p o s u r e , th e e n t i r e camera was p l a c e d i n a n
e v a c u a t e d chamber t o a v o i d a i r s c a t t e r i n g .
P r e p a r a t i o n a n d M o u n tin g o f S a m p le s .
Pure m u l t i - c e n t r i f u g e d l a t e x , o b t a in e d
from Dr. E. Guth o f N o tr e Dame, was p o u re d o u t o n t o g l a s s p l a t e s and a l l o w н
ed t o dry in s h e e t s 1 . 5 t o 2 . 0 mm. t h i c k .
from t h e s e s n e e t s ,
I h e s p e c im e n s u s e d w ere t h e n c u t
c a r e b e in g t a k e n t o a s s u r e t h a t no a i r b u b b le s were in н
c lu d e d in t h e p a r t u s e d a s a s a m p le .
target
CRYSTAL
F ig u r e 11
40
F ig u r e 1 2 .
41
The sp ecim en h o l d e r u s e d in th e cam era, t o g e t h e r w i t h th e s t r e t c h i n g "
d e v i c e , i s shown in F ig u r e 1 3 .
' ^a/.
ISIS
In m o u n tin g a sample i t
is f i r s t fa sten ed
VW
?
-
_ ------ ?
....
?
F ig u r e 1 3 .
t o t h e jaw s o f th e s t r e t c h e r "by t h e clam ps A
a f t e r w h io h i t s l e n g t h i n
t n e u n s t r e t c h e d c o n d i t i o n c a n ue d e t e r m in e d .
The a d j u s t a g l e
stop S
can
t h e n be s e t i n p o s i t i o n so t h a t t h e d e s i r e d e i o n g a t i o n w i l l be o b t a in e d
when t h e m ovable jaw J
i s b r o u g h t i n t o c o n t a c t w it h 3 . J ca n t h e n be
clam ped i n t h i s p o s i t i o n .
The c e n t r a l p o r t i o n of t h e s t r e t c h e d sam ple i s n e x t f a s t e n e d t o t h e
rem ovable p l a t e F o f t h e camera s p e cim en h o l d e r .
T his p l a t e s e t s
in to
t h e c y l i n d r i c a l b a s e o f th e h o l d e r , t h e b a s e t h e n b e in g i n s e r t e d i n a c e n н
t e r e d h o le
i n t h e f l o o r o f t h e cam era,
i h e c e n t e r o f th e h o l e i n th e
p l a t e P , th r o u g h w n ich th e i n c i d e n t beam p a s s e s , i s
sy ste m o f t h e camera.
in l i n e w i t h th e s l i t
The f l a t s p e cim en may be s e t e i t h e r norm al t o t h e
i n c i d e n t beam or a t an a n g le
to i t .
In t h i s worx th e norm al t o t n e sample
made an a n g l e o f 3 0 ░ w i t h th e m ain beam.
T h is was done i n o r d e r t h a t one
m ight o b t a i n more d e t a i l i n t h e p a t t e r n a t l a r g e s c a t t e r i n g a n g l e s .
42
We w i l l now g o th.rou.gh t h e p r o c e d u r e f o l l o w e d i n o b t a i n i n g th e a to m ic
d e n s i t y d i s t r i b u t i o n f o r a sample o f smoked s h e e t , s t a r t i n g w it h th e o r i н
g i n a l d i f f r a c t i o n p a t t e r n a n d f o l l o w i n g th r o u g h t o th e f i n a l a n a l y s i s .
P i c t u r e , Minro p h o to m e te r and B la c k e n in g C urves.
o f smoked s h e e t i s
shown i n F ig u r e 1 4 .
For t h i s p i c t u r e a sam p le 2 . 0 mm.
t h i c k was u s e d , t h e e x p o s u r e tim e b e i n g 30 h o u r s .
p a t t e r n we roust o b t a i n fro m i t an i n t e n s i t y c u r v e .
m ic r o p h o to m e te r th e p a t t e r n .
The d i f f r a c t i o n p a t t e r n
To make u s e of t h i s
The f i r s t s t e p i s t o
T h is w as done on a r e c o r d in g m ic r o p h o to m e te r
of th e th er m o c o u p le ty p e w h ic h was b u i l t by H. J . Y e a r ia n of t h i s d e p a r t н
m ent.
To c a l i b r a t e t h e t r a c e , l i n e s w ere s c r a t c h e d on th e f i l m a t tw o o f
th e in d e x marks p r e v i o u s l y m e n t io n e d .
tr a c e p e r m ittin g i t s c a lib r a t io n .
T hese were th e n r e c o r d e d on t h e
The m ic r o p h o to m e ter t r a c e of th e
p a t t e r n shown i n F ig u r e 14 i s g i v e n
in F ig u r e 1 5 .
To o b t a i n a b l a c k e n i n g cu rv e from th e m ic r o p h o to m e ter t r a c e , one u s e s
th e r e l a t i o n
where
i c = i n t e n s i t y o f l i g h t t r a n s m i t t e d th rou gn th e c l e a r f i l m .
i
s i n t e n s i t y o f l i g h t t r a n s m i t t e d th r o u g h th e f i l m a t t h e
a n g l e 29 i n q u e s t i o n
B
= b la c k e n i n g
We h a v e made t e s t s w h ic h snowed t h a t f o r Eastman N o -S c r e e n x - r a y
f i l m one o b t a i n s a l i n e a r b la c k e n i n g c h a r a c t e r i s t i c up t o a v a lu e o f a t
le a st
1 .5
and p o s s i b l y
2
.
In tn e p i c t u r e s u sed in t n i s work th e b la c k e n н
in g was n e v e r much g r e a t e r t n a n
1
.
lie n e e , i t c a n oe assu m ed t h a t th e
b la c k e n i n g i s p r o p o r t i o n a l t o th e i n t e n s i t y
th e f i l m .
of t h e r a d i a t i o n s t r i k i n g
43
--------------
O
-L-___________ I____________ I____________ I_______
20
40
60
F ig u r e 15.
80
20
The m ic r o p h o to m e ter c u r v e was r e.-u ced t o a b la c k e n i n g cu r v e by th e u s e
o f t h e l o g a r i t h m i c p r o t r a c t o r d e s i g n e d by Y earian ^ 0 *
By th e u se o f t h i s
in s t r u m e n t , one can t r a c e t h e m ic r o p h o to m e te r curve and o b t a i n , a u t o m a t iн
c a l l y , a c o n t in u o u s t r a c e o f t h e b la c k e n i n g c u r v e .
T his e l i m i n a t e s th e
n e c e s s i t y o f c a l c u l a t i n g t h e b la c k e n i n g from p o i n t to p o i n t on th e c u r v e .
The b la c k e n i n g cu r v e o b t a i n e d from th e curve o f F ig u r e 15 i s
shown i n
F ig u r e 1 6.
1
r
- . ~ - . T
-
F ig u r e 1 6 .
C o r r e c t i o n f o r p o l a r i z a t i o n and A b s o r p t io n .
Having o o t a i n e u a r e l a t i v e
i n t e n s i t y c u r v e in t h e manner j u s t d e s c r i b e d , th e n e x t s t e p i s to make t h e
n e c e s s a r y c o r r e c t i o n s f o r th e p o l a r i z a t i o n
of th e r a d i a t i o n and f o r t h e
a D s o r p t io n w h ic h t o o k p l a c e i n t h e s a m p le .
The q u a n t i t y I e , w h ich r e p r e s e n t s t h e
i n t e n s i t y s c a t t e r e d by a
sin g le
e l e c t r o n and w h ie u a p p e a r s i n t h e e x p r e s s i o n f o r b o t h th e t h e o r e t i c a l c o н
ne r e n t a n d i n c o h e r e n t s c a t t e r i n g , c o n t a i n s th e p o l a r i z a t i o n f a c t o r 0
w h ich i s due t o s c a t t e r i n g o f tn e beam from t h e s a m p le .
3 rag g a n g l e .
H ere,
Q i s th e
To ta k e i n t o a c c o u n t t h e p o l a r i z a t i o n w h ich o c c u r s when t h e
beam i s r e f l e c t e d from t h e m onochrom ating c r y s t a l we m u l t i p l y th e term
*
cos 2 0
*
by c o s ZGg, S j Deing th e glancing a n g l e f o r t h e p a r t i c u l a r c r y s t a l
and r a d i a t i o n b e in g u s e d .
F o r th e r e f l e c t i o n o f t h e Mo
(200) p la n e o f r o c k s a l t t h i s a n g le i s 7
o
1 5 .5 ? .
l i n e from t h e
H e n c e, our p o l a r i z a t i o n
f a c t o r becomes
/+
&
P=
Z
/+0. ? 37 г
~
G
^
( S . 17)
To make t h e p o l a r i z a t i o n c o r r e c t i o n we may e i t h e r m u l t i p l y the
t h e o r e t i c a l c o h e r e n t a n d i n c o h e r e n t s c a t t e r i n g by t h e a o o v e q u a n t i t y o r ,
a s w as done i n t h i s 'work, d i v i d e th e o b s e r v e d e x p e r im e n t a l s c a t t e r i n g
by i t .
To c o r r e c t t h e i n t e n s i t y cu r v e f o r a b s o r p t i o n one n e e d s t o c o n s i d e r
th e g e o m e try o f t h e e x p e r im e n t a l s e t - u p .
For th e c a s e where we h a v e i n н
c i d e n t r a d i a t i o n o f i n t e n s i t y I 0 s t r i k i n g a f l a t sample o f t h i c k n e s s d
s e t s o t h a t i t s normal makes a n a n g le f t w i t h t h e main beam, one can show
t h a t th e i n t e n s i t y o f r a d i a t i o n I * s c a t t e r e d a t a n a n g le (f> t o th e d i r e c t i o n
o f the main beam w i l l be r e l a t e d t o I 0 b y t h e e x p r e s s i o n
r
_
x
f
L
- / < d ?VLe.C<*-&
- S tJ '* * * '/3
1
__________________ n г -----------------------/
p
&
J
(2 . i 8 )
H e r e , J~( - l i n e a r a b s o r p t i o n c o e f f i c i e n t o f t h e sam ple f o r t h e r a d i a t i o n
used.
f t - th e a n g le b e tw e en t h e normal t o t h e f l a t sa m p le and th e d i r e c t н
io n of t h e main beam.
46
K - \a _ c o n s t a n t d e fe n d in g upon the s c a t t e r i n g power o f th e s a m p le ,
a - area ir r a d ia te d .
For t h e c a s e of 0
=? 0 t h e above e x p r e s s i o n oecomes in d e t e r m i n a t e .
Upon d i f f e r e n t i a t i n g b o th num erator and denom inator to remove t h e i n d e t e r н
m in a c y , one o b t a i n s th e e x p r e s s i o n
?o
The c o r r e c t i o n c a n b e s i m p l i f i e d i f one n o r m a li z e s t o t h e i n t e n s i t y
s c a t t e r e d a lo n g t h e norm al t o th e f l a t s a m p le , i . e . t o th e i n t e n s i t y
s c a t t e r e d a t t^ e a n g le
.
By d o in g s o one can o b t a i n , from e q u a t i o n
( 3 . 1 8 ) , an a b s o r p t i o n m u l t i p l y i n g f a c t o r A*
I f one c a l l s
/C╗╗ C0 ?/ O
^ =
/
* -
/ _
e
^ m' 13
Si?c/ CI ~
Ctp-
c &?
/3)
e
/ - xunu / 3
Ci -
-
s + J ___
/3) e,
c
th en
F~ EC
B г - г >
f o r g e n e r a l <t> and f o r
A ^ o
0
=
~
0
'
(3*19)
,
/Z
s&O-Xs- f t
o
s*d
F o r th e sample o f smoked s h e e t vie a r e c o n s i d e r i n g , / < = 0 . 5 5 6 f o r
o
Mo K,* r a d i a t i o n , d = 0 . 2 0 cm. a n d ^ ╗ 30 .
29m 0░ t o 26m 80░ a r e g i v e n i n Table 5 .
of th e o r d i n a t e ,
The r e l a t i v e
i n t e n s i t i e s from
In t h i s t a b l e i ob
i s the v a lu e
i n a r b i t r a r y s c a l e u n i t s , a s o u t 3 in e a from t h e b la c k e n i n g
c u r v e ; F i s th e p o l a r i z a t i o n f a c t o r and A i s th e m u l t i p l y i n g f a c t o r f o r
th e a b so r p tio n c o r r e c t io n ,
curve i n s r o i t r a r .
u n its.
loo*.*,. i s t h e c o r r e c t e d r e l a t i v e i n t e n s i t y
The n e tn o d by w hicn t h i s c u r v e can be p u t on a n
S a b le 5 .
C o r r e c t e d I n t e n s i t y Curve f o r Smoked S h e e t
sin й
20
0 ░
2 .5
5
7 .5
10
1 2 .5
15
1 7 .5
20
2 2 .5
25
2 7 .5
30
3 2 .5
35
3 7 .5
40
4 2 .5
45
4 7 .5
50
5 2 .5
55
5 7 .5
60
6 2 .5
65
6 7 .5
70
7 2 .5
75
7 7 .5
80
F i r s t Peak
8 ░ \2 5 *
]
^ob
P
k
0
.0 3 0 8
.0 6 1 6
.0 9 2 4
.1 2 3 1
.1 5 3 8
.1 8 4 4
.2 1 4 9
.2 4 5 3
.2 7 5 6
.3 0 5 8
.3 3 5 8
.3 6 5 7
.3 9 5 4
.4 2 4 9
.4 5 4 1
.4 8 3 2
.5 1 2 1
.5 4 0 7
.5 6 9 0
.5 9 7 1
.6 2 4 9
.6 5 2 4
.6 7 9 6
.7 0 6 4
.7 3 2 9
.7 5 9 1
.7 8 4 9
.8 1 0 4
.8 3 5 4
.8 6 0 1
.8 8 4 3
.9 0 8 2
0
5 .2 7
1 4 .1 7
3 4 .9 4
2 8 .9 4
1 4 .9 0
9 .5 2
9 .0 5
8 .3 3
9 .7 9
5 .9 7
5 .5 5
5 .5 0
5 .6 2
5 .5 8
5 .2 0
4 .7 0
4 .3 4
4 .0 5
3 .8 9
3 .3 4
3 .8 2
3 .8 0
3 .7 3
3 .6 1
3 .4 8
3 .3 5
3 .2 2
3 .1 0
2 .9 9
2 .8 7
2 .7 9
2 .6 8
.9 6 9
.9 6 6
.9 6 2
.9 5 6
.9 4 8
.9 3 9
.9 2 8
.9 1 5
.9 0 1
.8 8 6
.8 7 0
.8 5 8
.8 3 4
.8 1 6
.7 9 6
.7 7 6
.7 5 5
.7 3 5
.7 1 5
.6 9 4
.6 7 4
.6 5 5
.6 3 6
.6 1 8
- .6 0 0
.584
.5 6 9
.555
.5 4 3
.5 3 2
.5 2 2
.5 1 6
1 .0 0 5 0
1 .0 0 4 0
1 .0 0 3 1
1 .0 0 2 4
1 .0 0 1 8
1 .0 0 1 3
1 .0 0 0 9
1 .0 0 0 6
1 .0 0 0 3
1 .0 0 0 2
1 .0 0 0 1
1 .0 0 0 0
1 .0 0 0 1
1 .0 0 0 2
1 .0 0 0 3
1 .0 0 0 6
1.00 09 1 .0 0 1 3
1 .0 0 1 8
1 .0 0 2 4
1 .0 0 3 1
1 .0 0 4 0
1 .0 0 5 0
1 .0 0 6 1
1 .0 0 7 6
1 .0 0 9 4
1 .0 1 1 5
1 .0 1 4 1
1 .0 1 7 1
1 .0 2 0 5
1 .0 2 4 5
1 .0 2 9 2
*oorr
0
5 .4 7
1 4 .7 3
3 6 .4 3
3 0 .3 4
1 5 .7 5
1 0 .1 5
9 .7 6
9 .1 1
7 .5 4
6 .7 4
6 .3 8
6 .4 1
6 .7 4
6 .8 4
6 .5 3
6 .0 6
5 .7 6
5 .5 2
5 .4 5
5 .5 4
5 .6 9
5 .8 2
5 .8 9
5 .8 8
5 .8 4
5 .7 9
5 .7 3
5 .6 7
5 .6 0
5 .5 0
5 .4 7
5 .3 4
.1 0 4 1
3 8 .5 0
.9 6 0
1 .0 0 2 8
4 0 .2 1
49
a b s o l u t e b a s i s by m a tch in g i t
t o th e t h e o r e t i c a l c o h e r e n t and in c o h e r e n t
s c a t t e r i n g c u r v e s w i l l be t a k e n up i n a l a t e r s e c t i o n .
T h e o r e t i c a l C oherent a n d I n c o h e r e n t S c a t t e r i n g .
E q u a tio n (. 3 . 2 ) g i v e s th e
e x p r e s s i o n l o r th e c o n e r e n t s c a t t e r i n g and e q u a t io n ( 5 . 3 ) e x p r e s s e s th e i n н
coherent s c a t t e r in g .
S i n c e we a r e c o n s i d e r i n g o n ly r e l a t i v e i n t e n s i t i e s
we may u s e s im p ly th e e x p r e s s i o n
X
= ( f
X -=
l3 -2 0 )
(2-21'
(Z-г-fC )
and w r i t e f o r th e e x p e r im e n t a l i n t e n s i t y
r r ? T aoht.
(3 . 2 2 )
where m i s th e ??matching f a c t o r H w h icn we u s e t o put t h e c o r r e c t e d o b s e r v e d
i n t e n s i t y curve on the same s c a l e a s th e c o h e r e n t and in c o h e r e n t s c a t t e r i n g .
The v a l u e s o f ^ pn and
w ere ta x e n from Compton and A l l i s o n ,
??X-rays i n T heory and E x p e r im e n t?*, p a g e s 781 and 7 8 2 .
F o r t h e s c a t t e r i n g from r u b b e r , CgHg, th e c o h e r e n t s c a t t e r i n g of t h e
hyd rogen may be n e g l e c t e d a s compared w it n t h a t o f c a rb o n .
t h e in c o h e r e n t s c a t t e r i n g t h i s cannot be d o n e .
However, f o r
In o r d e r t o g e t e q u i v a l e n t
s c a t t e r i n g ' p e r a to m , th e t o t a l in c o h e r e n t s c a t t e r i n g was ta k e n a s t h a t due
t o t h e carb on p l u s e i g h t - f i f t h s
sc a tte r in g i s
of t h a t due t o t h e n y d ro g en .
th en th e sum o f t h e s e tw o, n a m ely , I c
+
1
^
The t o t a l
.
The v a l u e s o f tne t h e o r e t i c a l c o h e r e n t and i n c o h e r e n t s c a t t e r i n g f o r
C5 H8 a r e g i v e n in T able
6
.
Ajatchinr: P h c to r -H e th o d s ana D i f f i c u l t i e s .
P ro b ab ly th e g r e a t e s t e r r o r
in the d e t e r m i n a t i o n o f d e n s i t y d i s t r i b u t i o n s i s in t r o a u c e d when one
a t t e m p t s t o p l a c e th e c o r r e c t e d e x p e r im e n ta l i n t e n s i t y curve on an a b s o l u t e
b a s i s by m a tch in g i t t o t h e t h e o r e t i c a l s c a t t e r i n g .
T his i s e s p e c i a l l y
49
T a b le 6 .
C oherent and I n c o h e r e n t S c a t t e r i n g For Btibber, C5 H8
sinй
a
A
г
0
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1 .0
6 .0
4 .6
3 .0
2 .2
1 .9
1 .7
1 .6
1 .4
1 .3
1 .2
1 .0
/f
4.
-T.
3 6 .0 0 3 6 .0 0
2 1 .1 6 2 1 .1 6
9 .0 0 9 .0 0
4 .8 4 4 .8 4
3 .6 1 3 .6 1
2 .8 9 2 .8 9
2 .5 6 2 .5 6
1 .9 6 1 .9 6
1 .6 9 1 .6 9
1 .4 4 1 .4 4
1 .0 0 1 .0 0
6 .0
4 .0
2 .7
1 .8
1 .5
1 .3
1 .0
0 .8
0 .7
0 .6
0 .5
1 .0 0
0 .6 6
0 .2 3
0 .0 6
0 .0 2
0
0
0
0
0
0
0 .0
2 .0
3 .3
4 .2
4 .5
4 .7
5 .0
5 .2
5 .3
5 .4
5 .5
0 .0 0
0 .3 4
0 .7 7
0 .9 4
0 .9 8
1 .0 0
1 .0 0
1 .0 0
1 .0 0
1 .0 0
1 .0 0
0 .0 0
0 .5 4
1 .2 3
1 .5 0
1 .5 7
1 .6 0
1 .6 0
1 .6 0
1 .6 0
1 .6 0
1 .6 0
0 .0 0
2 .5 4
4 .5 3
5 .7 0
6 .0 7
6 .3 0
6 .6 0
6 . 80
6 .9 0
7 .0 0
7 .1 0
0 .0 0
2 .5 4
4 .5 3
5 .7 0
6 .0 7
6 .3 0
6 .6 0
6 .8 0
6 .9 0
7 .0 0
7 .1 0
3 6 .0 0
2 3 .7 0
1 3 .5 3
1 0 .5 4
9 .6 8
9 .1 9
9 .1 6
8 .7 6
8 .5 9
8 .4 4
8 .1 0
50
t r u e when t h e s c a t t e r i n g x a a t e r ia l i s composed ox atom s w it h s m a ll a to m io
number s i n c e f o r t h e s e s t o m s t h e c o h e r e n t s c a t t e r i n g a t l a r g e s c a t t e r i n g
a n g le s i s
s m a ll compared to t h e i n c o h e r e n t s c a t t e r i n g .
I t is neoesaary?
t h a t t h i s m a tc h in g be done i n o r d e r t o e x p r e s s th e e x p e r i m e n t a l l y o b se r v e d
i n t e n s i t y i n th e same u n i t s w h ic h a r e u s e d f o r t h e c o h e r e n t a n d in c o h e r e n t
sc a tte r in g , i . e .
i n e l e c t r o n u n i t s p e r a to m .
c ie n t ly la r g e v a lu e s o f
in d e p e n d e n t o f e a c h o t h e r .
I t i s assum ed t h a t a t s u f f i н
| & t h e c o h e r e n t a n d in c o h e r e n t s c a t t e r i n g a r e
C o n s e q u e n t ly , t h e i r sum s h o u ld De e q u a l t o th e
t o t a l o b s e r v e d s c a t t e r i n g . in t n i s r e g i o n .
T h is would i n d i c a t e a method o f
m atch in g ? make th e e x p e r i m e n t a l l y o b s e r v e d i n t e n s i t y e q u a l t o th e sum o f
trie c o h e r e n t en d in c o h e r e n t s c a t t e r i n g a t l a r g e v a l u e s o f S1^ '
-f-Q OI-I- ~ Z ,
i.e .
le t
^L
T h is ap p ea l's t o oe a p e r f e c t 1;.- s t r a i g h t f o r w a r d p r o c ed u r e l i m i t e d o n ly
by th e a c c u r a c y o f t h e a b o v e a s s u m p t i o n .
o f u n ce r ta in ty .
A c tu a lly i t e n t a i l s a g rea t deal
One can n e v ^ r be s u r e J u s t how l a r g e th e v a lu e o f
?
must be in o r d e r t h a t th e a b o v e a s s u m p tio n s h a l l be v a l i d , nor d o es one
know how mu Oil o f the o b s e r v e d s c a t t e r i n g i s a c c i d e n t a l s c a t t e r i n g ,
how much of i t
i.e .
i s due to s c a t t e r i n g from a i r and from p a r t s of t h e camera
and s p e cim en h o l d e r .
A c c i d e n t a l s c a t t e r i n g a n d r e s u l t a n t background can oe retraced t o a comн
p a r a t i v e l y i n a p p r e c i a b l e q u a n t i t y by the c o r r e c t e x p e r im e n t a l p r o c e d u r e .
The
u s e o f a n e v a c u a t e d camera w it ., a s m a l l , w e ir c o l l i m a t e d , bean of monochromн
a t i c r a d ia tio n w ill u s u a lly elim in a te t h is d i f f i c u l t y .
When a f l a t sam ple i s u se u t h e r e i s
a maximum v a lu e o f
o b se rv a b le,
t h i s v a l u e b e i n g d e te r m in e d by th e p o i n t a t w hich t h e f l a t sam ple and h o ld e r
p ro d u ces a c u t - o f f in th e s c a t t e r e d r a d i a t i o n .
T nis maximum v a lu e can be i n н
c r e a s e d by s e t t i n g th e sam p le a t an a n g l e t o th e i n c i d e n t o ea u .
However,
51
e v e n though i t
i s g e o m e trica ily p o ssib le
t h e s e l a r g e r S.^~S. г
it
to o b s e r v e th e s c a t t e r i n g a t
v a l u e s , t h e i n t e n s i t y i n t h i s r e g i o n i s so weak t h a t
i s d i f f i c u l t t o d e c i d e ^ u st how f a r ones o b s e r v a t i o n s a r e t r u s t w o r t h y .
The c h o i c e o f a m atch ing f a c t o r w i l l h av e a n a r k e d e f f e c t on t h e r e н
s u l t s o f th e a n a l y s i s .
T h is comes a b o u t i n th e f o l l o w i n g w a y.
In t h e
d e t e r m i n a t i o n o f J*(r) we h a v e to e v a l u a t e th e i n t e g r a l
/fe i(s)
sin (sr )d s, ,
s in o
where s *
i(s)
conies d i r e c t l y from the r a t i o
of e x p e r im e n t a l to c o h e r e n t
sc a tte r in g .
T h u s, b e c a u s e of th e i n c r e a s e i n s w i t h a n g l e , any s m a ll i r r e g u l a r itie s
s in d
i n t h e e x p e r i m e n t a l s c a t t e r i n g cu rve a t l a r g e v a l u e s o f ?
gi ve
/J
c o n t r i b u t i o n s t o th e s i ( s )
c u r v e , and th u s to th e v a l u e of th e a b o v e i n н
t e g r a l , w h ic h a r e com parable w itn th e a r e a s due to w e l l d e f i n e d r i n g s .
In th e c a s e o f r u o o e r w here we a r e d e a lin g w i t h c h a i n - l i k e m o l e c u l e s
we knew t h a t we w i l l h a v e two f i r s t n e ig h b o r s a o o u t any one atom .
Hence
we c o u ld u s e t h i s c r i t e r i o n t o a s c e r t a i n w h eth er or not the f i n a l a n a l y s i s
is co rrect.
e ssita te
The o b j e c t i o n t o t h i s method i s t h a t i t would p r o b a b ly n e c н
s e v e r a l t r i a l a n a l y s e s o e f o r e t h e c o r r e c t one was o b t a i n e d .
liven
th o u gh th e tim e and la b o r i n v o l v e d i n m skin g an a n a l y s i s have b e e n g r e a t l y
s n o r t e n e d by th e d e v e lo p m e n ts o f D a n ie ls o n and L a n c z o s , t h e y a r e s t i l l t o o
g r e a t t o maxe su c h a ruetnod of n o t c h in g V er y p r a c t i c a b l e .
E U rth er, one i s
n o t a lw a y s d e a l i n g w ith c n a in m o l e c u l e s and. so a more r i g o r o u s u e tn o d o f
m a tch in g i s t o be d e s i r e d .
D a n i e l s o n 93 h a s u s e a the method of l e a s t s q u a r e s i n th e range o f l a r g e
v a l u e s of
t o o b t a i n a .o a tc n in g f a c t o r .
?7
q u ite s a tis fa c to r y r e s u l t s .
The method a p p e a r s t o g i v e
52
One s h o u ld be s o l e
t o assume t h a t t h e t o t a i r a d i a t i o n s c a t t e r e d i s
e q u a l to the sum o f th e t o t s x c o h e r e n t a n d in c o h e r e n t s c a t t e r i n g .
would mean t h a t th e t o t a l area u n d er the i ( s )
T h is
curve s h o u ld oe z e r o .
Howн
e v e r , we do n o t know ^ust what s c a t t e r i n g we have in the forw ard d i r e c t i o n
and a s a r e s u l t t h i s i d e a oannot be r i g o r o u s l y a p p l i e d .
T. E. Ifeyer h a s s u g g e s t e d t h a t a t r ? 0 , j-* (r ) s h o u ld be z e r o .
le a d s to th e e x p r essio n
T h is
-00
= -*77'*^ S'
w h ich c o u ld be u s e d a s a m a tch in g c r i t e r i o n .
sist
o f a t r i a l and e r r o r p r o c e d u r e .
seems to
T h is method w ould a l s o conн
The f a c t o r o b t a in e d by t h i s method
oe c o m p a t ib le w it h t h a t o b t a in e d by the methods a l r e a d y m e n tio n e d .
I t s c h i e f d i s a d v a n t a g e a r i s e s from th e f a c t t h a t t h e v a lu e o f f*
is very
s m a ll ( a p p . - .Ofi-) and h e n c e t h e i n t e g r a l must be p e r f e c t l y a c c u r a t e b e f o r e
r
a r e l i a o l e m a tc h in g can oe made.
A match o f t n e c u r v e s iuay g i v e p l a u s i b l e
r e s u l t s i n an a n a l y s i s and s t i l l have the a b o v e c o n d i t i o n f a r from s a t i s н
fie d .
i a n c z o s h as s u g g e s t e d t h e f a l l o w i n g method o f Hatching.
7/e w r i t e ,
as u su a l,
S in c e I
is g iv e n
St-(s) =
An a n a l y s i s
, we c a n a l s o w r i t e t h i s a s
oy
/ \ ? , ^ 3- C.ot-y- 7 ? hrS
5
i s made fo r
5
?
a \K*? * 3r
7 - '
~/ J
n i n su c h a .ray t h a t tn e l a s t few f o u r i e r c o e f f i c i e n t s
12) a r e made a s s m a ll a s p o s s i o l e .
squares.
?
^CLe th e n c h o o s e s
(sa y th e l a s t 10 or
T h is .ray be done by the method o f l e a s t
The j u s t i f i c a t i o n f o r doin g t n i s l i e s i n th e f a c t t h a t th e v a l u e s
o f r c o r r e s p o n d in g t o t h e l a s t few c o e f f i c i e n t s a r e o f su ch m agnitude
t h a t th e d e n s i t y d i s t r i b u t i o n
s h o u ld be a p p r o a c h in g th e a v e r a g e
d e n s i t y d i s t r i b u t i o n tJTT/i. f%
and, h ence,
the d e v i a t i o n s from a v e r a g e
d e n s i t y s h o u ld be s m a l l .
The a p p l i c a t i o n of t h i s method to t h e a n a l y s i s o f smoixed s h e e t d id not
biv e s a t is f a c t o r y r e s u l t s .
E. P . M i l l e r h a s p o i n t e d out t h a t one s h o u ld a t t e m p t t o m in im ize th e
?
?
o
J.
c o e x f x c i e n t s m t h e range o f r from 0 A
o
to 1 A
n o t e x p e c t a n y n e ig h b o r s w i t h i n t h i s d i s t a n c e .
s i n c e we w ould c e r t a i n l y
Doing t h i s
fo r th e a n a l y s i s
m en tion ed a b o v e g a v e r e s u l t s w hich were i n good agreem ent w i t h t n o s e obн
t a i n e d 7/hen th e m atch in g f a c t o r was d e te r m in e d by m a tc h in g a t l a r g e v a l u e s
, sin &
01
?
?
For t h e a n a l y s e s r e p o r t e d i n t h i s worm t h e m atch in g f e e t or was d e t e r н
mined by is. t e llin g a r e a s under th e e x p e r im e n ta l curve and th e c u r v e r e p r e s ,.
e n t i n g tn e
,
sum 1 c +
Ip
. . .
sin Q
~
,
sin Q
m t n e r a n g e xrom ? ? - 0 . 2 0 t o ?^----- = 0 . 6 5 .
T h is gav e q u i t e r e a s o n a b l e r e s u l t s and i n a d d i t i o n was a m ethod w h ic h was
c o n s i s t e n t from p i c t u r e t o p i c t u r e .
D e s p i t e th e f a c t t h a t a l l t h e methods m en tio n e d above sound r e a s o n н
a b le and c a n be a p p l i e d , one i s
s t i l l u n a b le t o g i v e a d e f i n i t e s ta te m e n t
a s t o "the** c o r r e c t p r o c e d u r e t o be f o l l o w e d i n o b t a i n i n g a m a tch in g f a c t o r .
E v a lu a t i o n o f s i t s ) and A n a l y s i s fo r Smoxed S h e e t .
Curve A i n F ig u r e 17
shows t h e e x p e r im e n ta l i n t e n s i t y cuz-ve, c o r r e c t e d f o r p o l a r i z a t i o n a n d a b s in d
s o r p t i o n ^ p l o t t e d a s a f u n c t i o n of ? ? .
In th e same f i g u r e , cu rve 3 i s
th e c o h e r e n t s c a t t e r i n g , curve C i s t h e in c o h e r e n t s c a t t e r i n g , and curve D
r e p r e s e n t s t h e sum o f c u r v e s 3 and C.
From a com parison o f a r e a s under
c u r v e s A and D i n the r e g i o n from ?
??*г- - - 0 . 2 t o
/I
fa cto r is
found t o be 1 . 5 0 .
f
0 . 6 5 th e m atch in g
n
U sin g t h i s v a l u e tn e matcheu e x p e r im e n t a l
54
I
\_
F ig u r e 1 7 .
curve E i s
at
o b ta in e d .
s 0 .1 0 4 0 .
From t n i s
curve we s e e t h a t t h e f i r s t maximum o c c u r s
The seco n d and t h i r d maxima come a t 0 .2 1 6 0 and 0 .4 2 2 0
r e sp e c tiv e ly .
In t h i s
case i t i s
assumeu t h a t the c u r v e s raatca e x a c t l y from t h e
p o i n t 5 ^ t ^ ? 0 .6 6 5 0 t o i n f i n i t y , s i n c e the e x p e r im e n t a l c u r v e cannot a c c u r a t e l y be o b s e r v e d beyond t h i s p o i n t .
must b e made i f th e s i ( s )
The
T h is a s s u m p tio n c o n c e r n in g the c u r v e s
curve i s t o h a v e a f i n i t e r a n g e .
curve i ( s ) i s o b t a i n e d from c u r v e s E, B, and 0 by
=
7? R
~G' ? - 1 .
eq u a tio n
i(s)
w hich i s
tn e cu rv e t o be a n a l y z e d .
M u l t i p l i c a t i o n by s t h e n g i v e s u s th e cu rv e
The e v a l u a t i o n o f s i ( s )
T able 7 and th e c u r v e i t s e l f i s shown in F ig u r e 1 8 .
i n o b t a in in g 1 the a n a l y s i s a r e g i v e n i n th e a p p e n d ix .
i
t h e u s e o f th e
is g iv e n
s i(s)
in
Tne form s h e e t s u s e d
55
T a b le 7 .
E v a l u a t i o n o f S i ( s ) For Smoked S h e e t
sin &
K
a
*ex
Ii
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
25
24
25
26
27
28
29
30
31
32
55
54
55
36
.0 2
.0 4
.0 6
.0 8
.1 0
.1 2
.1 4
.1 6
.1 8
.2 0
.2 2
.2 4
.2 6
.2 8
.3 0
. 32
.3 4
.3 6
.3 8
.4 0
.4 2
.4 4
.4 6
.4 8
.5 0
.5 2
.5 4
.5 6
.5 8
.6 0
.6 2
.6 4
? 66
.6 8
.7 0
.7 2
4 .2 5
1 2 .1 0
2 1 .3 5
3 5 .8 0
6 0 .2 0
4 3 .4 5
2 9 .1 0
2 2 .2 5
1 5 .8 8
1 4 .5 3
1 4 .6 1
1 4 .0 0
1 2 .5 0
1 1 .1 0
1 0 .3 1
9 .7 9
9 .5 6
9 .5 8
9 .8 7
1 0 .1 9
1 0 .2 8
1 0 .0 9
9 .6 5
9 .1 6
8 .8 0
8 .5 2
S . 29
8 .1 7
8 .2 0
8 .3 2
8 .5 0
8 .6 8
8 .7 9
8 .8 4
.5 3
1 .0 5
1 .5 5
2 .0 3
2 .5 4
3 .0 0
3 .4 5
3 .8 4
4 .2 1
4 .5 3
4 .8 6
5 .1 2
5 .3 7
5 .5 5
5 .7 0
5 .8 1
5 .9 0
5 .9 8
6 .0 1
6 .0 7
6 .1 1
6 .1 6
6 .2 0
6 .2 5
6 .3 0
6 .3 7
6 .4 1
6 .4 8
6 .5 3
6 . 60
6 .6 4
6 .6 8
6 .7 2
6 .7 6
6 .8 0
6 .8 2
i (s )
3 5 .0 0
3 3 .0 9
2 9 .1 2
2 4 .7 5
2 1 .1 6
1 8 .0 7
1 5 .1 5
1 2 .6 8
1 0 .6 3
9 .0 0
7 .7 6
6 .7 1
5 .9 0
5 .2 9
4 .8 4
4 .5 0
4 .2 1
3 .9 6
3 .7 6
5 .6 1
3 .4 5
3 .3 1
3 .1 8
3 .0 3
2 .8 9
2 .7 5
2 .6 4
2 .5 3
2 .4 3
2 .3 3
2 .2 4
2 .1 6
2 .0 9
2 .0 0
1 .9 6
1 .8 8
-.8 9 3 7
-.6 6 6 1
-.3 2 0 1
.3 6 4 4
1 .7 2 5 0
1 .5 1 5 2
.6 9 3 1
.4 5 1 9
.0 9 7 8
.1 1 1 1
? 2564
.3 2 3 4
.2 0 8 5
.0 4 9 1
-.0 4 7 5
-.1 1 5 6
-.1 3 0 6
-.0 9 0 9
.0 2 6 6
.1 4 1 3
.2 0 8 7
.1 8 7 3
.0 8 4 9
-.0 3 9 6
-.1 3 4 9
-.2 1 8 2
-.2 8 7 9
-.3 3 2 0
-.3 1 2 8
-.2 6 1 8
-.1 6 9 6
-.0 7 4 1
-.0 0 9 6
0
0
0
s
.2 5 1 3
.5 0 2 7
.7 5 4 0
1 .0 0 5 3
1 .2 5 6 6
1 .5 0 8 0
1 .7 5 9 3
2 .0 1 0 6
2 .2 6 2 0
2 .5 1 3 3
2 .7 6 4 6
3 .0 1 5 9
3 .2 6 7 3
3 .5 1 8 6
3 .7 6 9 9
4 .0 2 1 2
4 .2 7 2 6
4 .5 2 3 9
4 .7 7 5 2
5 .0 2 6 6
5 .2 7 7 9
5 .5 2 9 2
5 .7 8 0 5
6 .0 3 1 9
6 .2 8 3 2
6 .5 3 4 5
6 .7 8 5 9
7 .0 3 7 2
7 .2 8 8 5
7 ,5 3 9 8
7 .7 9 1 2
8 .0 4 2 5
8 .2 9 3 8
8 .5 4 5 2
8 .7 9 6 5
9 .0 4 7 8
si(s)
-.2 2 5
?.o 3 5
-.2 4 1
.3 6 6
2 .1 6 8
2 .2 8 5
1 .2 1 9
.9 0 9
.2 2 1
.2 7 9
.7 0 9
.9 7 5
.6 8 1
.1 7 3
-.1 7 9
-.4 6 5
-.5 5 8
-.4 1 1
.1 2 7
.7 1 0
1 .1 0 1
1 .0 3 6
.4 9 1
-.2 3 9
-.8 4 8
-1 .4 2 6
-1 .9 5 4
-2 .3 3 6
-2 .2 8 0
-1 .9 7 4
-1 .3 2 1
- .5 9 6
- .0 8 0
0
0
0
F ig u r e 1 8 .
F ig u r e 19
R e s u l t s f o r Smoked S h e e t .
age d e n s ity curve
I f one p l o t s
HIT A,
th e d e n s i t y
i n t e g r a l on t h e a v e r н
( u s i n g a d e n s i t y o f 0 . 9 4 gram s p e r c c .
sn o k e d s h e e t g i v e s a v a l u e o f 0 . 0 4 2 c a r b o n atojas p e r :/*. f o r
fo rm c u r v e ( d e n s i t y d i s t r i b u t i o n )
o f F i g u r e 19 i s o b t a i n e d .
for
) th e t r a n s н
From t h i s
O
d i s t r i b u t i o n we f i n d 1 . 9 6 c a r b o n a to m s a t 1 . 5 5 A ; 2 . 8 0 c a r b o n a to m s a t
o
e
o
2 .5 0 A ; and f u r t h e r c o n c e n t r a t io n s a t about 3 . 4 A , 4 . 1 A
o
and 5 A .
An i n s p e c t i o n o f F i g u r e 20 show s t h a t t h e s e r e s u l t s a r e i n g o o d a g r e e m e n t
w ith th e c o n c e p t o f a lo n g a h a in m o le c u le .
From t h i s m o d el we w o u ld o b -
й
o
t a i n 2 . 0 f i r s t n e i g h b o r s a t 1 . 5 1 A an d 2 . 4 s e c o n d n e i g h b o r s a t 2 . 5 6 A ?
'3
ChW *
w' ^ H
n /r
c
H
> - l3 0
c-.
C
H,
H
-H
C'
H
H
-C
H\
H
=C
c
H
H
CH,
F ig u re 2 0 .
From F i g u r e 19 we s e e t h a t th e s e c o n d p e a k i s n o t c o m p l e t e l y r e s o l v e d .
H ence i t
i n c l u d e s some o f th e n e a r e r t h i r d n e i g h b o r s a s w e l l a s t h e 2 . 4
second n e ig h b o r s.
The t h i r d n e i g h b o r s d i s t a n c e s depend u p o n r o t a t i o n
*
a b o u t t h e s i n g l e b o n d s and v a r y from a minimum o f 2 . 5 6 A t o a maximum o f
4 .0 4 A ░.
T h e s e n e i g n b o r s p r o b a b l y a c c o u n t f o r th e o b s e r v e d c o n c e n t r a t i o n s
a t 5 . 4 A░ an d 4 . 1 A░ ?
The c o n c e n t r a t i o n a t 5 A
i s a t t r i b u t e d t o th e
n e a r e s t c a rb o n atom s in o t h e r c h a i n s .
I t i s t h i s c o n c e n t r a t i o n w h ic h i s
r e s p o n s ib le fo r th e str o n g peak a t
^ ? 0 .1 0 4 0 i n t h e e x p e r im e n t a l i n ?
n
te n s ity cu rve.
A lth o u g h t h e r e s u l t s oi' t h i s a n a l y s i s a g r e e w i t h t h e a c c e p t e d p i c t u r e
fo r th e
str u c tu r e
o f th e r u b b e r m o le c u le t h e y do n o t t e l l u s a n y t h in g a b o u t
th e o r i e n t a t i o n of th e :o o le c u le n o r d o t h e y t e l l u s w h e th e r th e m o le c u le i s
e x te n d e d or f o l d e d .
C.
R e s u l t s f o r E v a p o r a te d l a t e x
P i c t u r e s w e r e t a k e n o f f l a t s a m p le s o f e v a p o r a te d l a t e x u n d er fo u r
c o n d i t i o n s o f s t r e s s , n a m e ly ,
(3 )
( l) u n str e tc h e d ;
(2 ) e lo n g a t e d 100 p e r c e n t ;
e l o n g a t e d 200 p e r c e n t ; an d (4 ) e l o n g a t e d 2 50 p e r c e n t .
D iffr a c tio n
p a t t e r n s o f e v a p o r a te d l a t e x , u n s t r e t c h e d and s t r e t c h e d 100 p e r c e n t ,
200 p e r c e n t , and 250 p e r c e n t a r e show n i n F ig u r e s 2 1 , 2 2 , 2 3 and 24
r e s p e c tiv e ly .
In o r d e r t o r e d u c e t h e e f f e c t o f random e x p e r im e n t a l
e r r o r s a s much a s p o s s i b l e , t h r e e p i c t u r e s w e re t a k e n f o r e a c h o f t h e
above c o n d itio n s .
The t h r e e r e l a t i v e
p e n d e n t ly a-nri th a n a v e r a g e d .
i n t e n s i t y c u r v e s w ere m atched in d e н
T h is g a v e a n a v e r a g e d m atch ed e x p e r im e n ta l
c u r v e w h ic h w as u s e d i n d e te r m in in g th e s i ( s )
The m easu red v a lu e
0 . 9 3 gm. p e r c . c .
c u r v e t o b e a n a ly z e d .
o f d e n s i t y f o r u n s t r e t c h e d e v a p o r a te d l a t e x was
T h is g i v e s a n a to m ic d e n s i t y o f
O3
- 0 .0 4 1 a to m s p e r A
F ig u re 21.
F ig u r e 2 o .
F igu r e 2 4 .
U n s tr e t c h e d E v a p o r a te d l a t e x .
F ig u r e 25A show s t h e a v e r a g e d m atched e x - .
p e r i m e n ta l c u r v e E o f u n s t r e t c h e d e v a p o r a te d l a t e x .
s i(s )
F ig u r e 25 B show s t h e
c u r v e o b t a in e d and F ig u r e 2 5 0 g i v e s th e r e s u l t a n t a n a l y s i s .
From F ig u r e 25A we s e e th a t th e f i r s t peak; com es
0 .1 0 5 5 .
at a
v a lu e o f
The s e c o n d a n d t h i r d p e a k s come a t v a lu e s o f 0 .2 2 2 and 0 .4 1 7 r e s н
p e c tiv e ly .
From t h e a n a l y s i s g i v e n in F ig u r e 250 we f i n d 1 .9 0 f i r s t n e ig h b o r s a t
an a v e r a g e d is t a n c e o f 1 .5 2 A* a n d 2 .8 6 n e ig h b o r s a t a n a v e r a g e d is t a n c e
O
o f 2 .5 4 A , t h e s e o o n d p eak n o t being' c o m p le t e ly r e s o l v e d . R e l a t i v e l y
O
weak i n d i c a t i o n s o f c o n c e n t r a t io n s a t 3 .5 0 A
5 .0 6 A
t h e r e i s a q u it e
fo r e , th is is
O
and 4 .2 5 A c a n be s e e n .
s tr o n g i n d i c a t i o n o f a n s t o m ic g r o u p in g .
As b e н
in t e r p r e t e d a s b e in g due t o a g g r e g a t e s o f ca rb o n atom s i n
n e ig h b o r in g c h a i n s .
r\A P O R A l! (
F ig u re 2 5 .
At
E v a p o r a te d l a t e x S t r e t c h e d 100 P e r G en t.
m atch ed e x p e r im e n t a l c u r v e , t h e s i ( s )
In. F ig u r e г 6 th e a v e r a g e d
c u r v e o b t a in e d from i t , and th e
r e s u l t a n t a n a l y s i s a r e show n f o r e v a p o r a te d l a t e x s t r e t c h e d 100 p e r c e n t*
From F ig u r e 26A one f i n d s s ^ | 9
f o r t h e p o s i t i o n o f th e t h r e e p ea k s
The a n a l y s i s
v a lu e s of 0 .1 0 4 7 , 0 .2 2 0 and 0 .4 1 8
in t h e i n t e n s i t y c u r v e .
(F ig u r e 26C) show s t h a t we h a v e 1 .8 7 f i r s t n e ig h b o r s
a t a n a v e r a g e d i s t a n c e _of 1 .5 г A ░and 2 .7 1 n e ig h b o r s a t s n a v e r a g e d i s й
ta n o e o f 2 .5 4 A ?
T h ird * f o u r t h and f i f t h
c o n c e n t r a t io n s a r e i n d i c a t e d
O
o
6
a t 3 .5 0 A , 4 .2 5 A , a n d 5 .0 4 A r e s p e c t i v e l y .
E V APO R A T E D
S IR
1CHI D
LATEX
D O */?
\.
V
l-X.'N
F ig u r e 2 6 .
E v a p o ra ted . l a t e x S t r e t c h e d 200 P e r P e n t .
In F ig u r e 27 i s sh ow n t h e a v e r н
a g e d nB.toh.ed e x p e r im e n t a l c u r v e , th e s i ( s )
curve a id th e a n a ly s is
p o r a te d l a t e x
s t r e t c h e d 200 p e r c e n t .
An i n s p e c t i o n
to
o c c u r a t -s-
of evaн
o f t h e e x p e r im e n t a l c u r v e i n F ig u r e 2 7A show s t h e p e a k s
& v a l u e s o f 0 . 1 0 4 8 , 0 .2 1 0 a n d 0 . 4 1 1 .
From t h e a n a l y s i s
(F ig u r e 2 7 0 ) , one f i n d s 1 .8 8 f i r s t n e ig h b o r s a t a n
a v e r a g e d i s t a n c e o f 1 .5 3 A░ w i t h 2 .6 9 n e ig h b o r s a t a n a v e r a g e d i s t a n c e
O
o f 2 .5 3 A ? A g a in th e s e c o n d p ea k i s n o t c o m p le t e ly r e s o l v e d a lt h o u g h
th e r e s o lu t io n
i s b e t t e r th a n in t h e two p r e v io u s c a s e s .
й
O
t r a t i o n s a p p e a r a t 3 .4 0 A , 4 . 2 2 A
O
a n d 5 .0 4 A .
F ig u r e 2 7 .
'
F u r th e r c o n c e n -
Evapora t e d l a t e x S tr e tc h e d 250 P er C ent.
The r e s u l t s f o r eva p o ra ted
l a t e x s t r e t c h e d 250 p e r c e n t a r e shown i n F ig u r e 2 8 .
T h is was t h e m axiн
mum e lo n g a t i o n u s e d .
I n F ig u r e 28A th e
^
v a lu e s of th e p ea k s a r e fo u n d to b e 0 .1 0 5 0 ,
0 .2 1 6 and 0 . 4 1 5 .
From F ig u r e 2 8 0 we f i n d 1 .9 0 f i r s t n e ig h b o r s a t an a v e r a g e d i s t a n c e
O
O
o f 1 .5 2 A and 2 .6 2 n e ig h b o r s a t a n a v e r a g e d i s t a n c e o f 2 .4 8 A .
It is
t o b e n o te d t h a t t h e s e c o n d p eak i s now a lm o s t c o m p le te ly r e s o l v e d .
F u r th e r c o n c e n t r a t io n s a r e fo u n d a t 5 .3 3 A░ , 4 .2 2 A░ , and 4 .9 5 A ░.
I
EV A PO RA TED LATEX
STRETCHED
2 S O /-
(B)
s in
e
P.
F ig u re 2 8 .
17.
DISCUSSION AND INTEBPHKEATION OP HESUIffiS
From a v i s u a l in s p e c t io n o f F ig u r e s 21 to 24 one cannot d e t e c t a n y
c h a n g e s i n th e d i f f r a c t i o n j n t t e r n s .
e n c e s in th e r e l a t i v e i n t e n s i t y
H ow ever, one can n o t i c e s l i g h t d i f f e r н
c u r v e s shown i n F ig u r e s 25 t o 2 8 .
c u r v e s r i s e a t s n a i l v a lu e s o f
^
She
(0 t o O .S) and f a l l a t la r g e r v a lu e s
( 0 . 4 t o 0 . 6 5 ) , w it h th e sh a p e s o f t h e o u te r p e a k s ch a n g in g s l i g h t l y a s
s tr e tc h in g in c r e a s e s .
T here i s no la r g e ,
v a r i a t i o n in t h e ?j
o f th e v a r io u s p ea k s a s we go from one e lo n g a t i o n t o a n o t h e r .
? ~ v a lu e s
The v a lu e
o f t h e h a l f w id th o f th e f i r s t peak rem a in s th e same a t t h e v a r io u s e lo n g н
a tio n s .
I t i s g e n e r a ll y c o n s id e r e d t i n t th e b r e a d th , a t h a l f m aximum, o f a
d i f f r a c t i o n r in g can be u s e d a s an i n d i c a t i o n o f t h e s i z e o f th e d i f f r a c t н
in g e le m e n t s .
The e x p r e s s io n c o r r e l a t i n g p a r t i c l e s i z e and l i n e w id t h , a s
d e r iv e d by S c h e r r e r i s ,
B =
' i9 J P г -c-*-*- &
-where B = h a lf - b r e a d t h o f l i n e
+ 6
( in r a d ia n s )
t - p a r tic le s iz e
- wave le n g t h o f in c id e n t r a d i a t i o n
?> s h a l f t h e a n g le b etw een t h e d i r e c t i o n o f th e m ain beam and th e
s c a t t e r e d r a d ia t i o n
fa = g e o m e tr ic b r e a d th o f l i n e , d e fe n d in g on s l i t sy ste m and t h e
g eo m e try o f t h e cam era.
I f one assu m es th a t t h i s e x p r e s s io n can be a p p l i e d t o p i c t u r e s o f th e
ty p e b e in g c o n s id e r e d h e r e , t h i s e x p r e s s io n g i v e s a v a lu e o f 80 A
s i z e o f t h e " c r y s t a l l i t e 1*.
f o r th e
In F ig u r e 29 t h e a n a ly s e s w h ich w ere g iv e n in F ig u r e s 25 t o 28 a r e
evaporated
latex
u nstretched
S'Rt TCr-гD >907.
>6
F ig u r e 2 9 .
g ro u p ed t o g e t h e r to f a c i l i t a t e
c o m p a r iso n .
From a n e x a m in a tio n o f t h e s e
a n a ly s e s we s e e th : t a s th e e lo n g a t i o n i s in c r e a s e d ,
(1 ) th e s e c o n d p ea k
becom es more n e a r ly r e s o lv e d w h ile th e a r e a u n d er i t d e c r e a s e s ; a t 250 p e r
c e n t e l o n g a t i o n r e s o l u t i o n i s p r a c t i c a l l y c o m p le te ;
(2 ) th e t h ir d a n d fo u r н
th c o n c e n t r a t io n s become more s h a r p ly d e f in e d and a t 250 p e r c e n t e lo n g a -
O
t i o n a r e co m p arab le w it h t h e c o n c e n t r a t io n a t 5 A ; (3 ) th e p o s i t i o n o f
th e f i r s t p ea k a n d t h e a r e a u n d er i t rem ain th e same f o r a l l e lo n g a t i o n s ;
(4) t h e r e i s no a p p r e c ia b le ch an ge in t h e p o s i t i o n and s h a r p n e ss o f th e
o
c o n c e n t r a t io n a t 5 A .
One o f th e d i f f i c u l t i e s e n c o u n te r e d in th e a n a l y s i s o f s t r e t c h e d
ru b b er i s t h e c h o ic e of t h e c o r r e c t v a lu e o f th e d e n s i t y .
A l l th e c r y s t a l
66
\
a n a l y s i s v a l u e s g i v e a d e n s i t y o f 1 .0 and higher*
_
T he h i g h e s t m easured
v a lu e ( f o r ru b b er s t r e t c h e d a lm o s t to t h e b r e a k in g p o in t anrt th e n f r o z e n )
i s 0 .9 6 5 .
The f a c t t h a t th e d e n s i t y of th e m a t e r ia l in c r e a s e s w it h e lo n g a н
t i o n - i n d i c a t e s d e f i n i t e l y t h a t t h e m o b ilit y o f th e atom s i s d e c r e a s e d .
T h is i s i n agreem en t w i t h th e r e s u l t s r e p o r t e d h e r e .
I t d o e s r a i s e th e
q u e s t io n o f m a t v a lu e o f th e d e n s i t y s h o u ld b e u s e d i n th e a n a l y s e s .
We
jo b ta in th e d e v i a t i o n from th e a v e r a g e d e n s i t y d i r e c t l y fro m t h e a n a l y s i s
o f th e s i ( s )
curve.
T h e se d e v i a t i o n s a r e p l o t t e d on th e p a r a b o la r e p r e s н
e n t in g t h e a v e r a g e d e n s it y an d g i v e p eak s w h ose a r e a s c o r r e sp o n d t o t h e
number o f n e a r e s t n e ig h b o r s .
An a n a l y s i s o f e v a p o r a te d l a t e x s t r e t c h e d
250 p e r c e n t was m ade, u s i n g a d e n s i t y o f 0 .9 6 5 gm. p e r c c . t o c a l c u l a t e
t h e a v e r a g e a to m ic d e n s i t y
.
The a n a l y s i s g a v e t h e same number o f f i r s t
n e ig h b o r s a s w ere o b ta in e d when th e d e n s i t y 0 .9 3 gm. p e r c c . w as u s e d ,
w h ile 2 .6 6 se c o n d n e ig h b o r s w ere fo u n d a s com pared t o 2 .6 2 in t h e p r e v io u s
ca se.
Both f i r s t an d s e c o n d n e ig h b o r s came a t th e same d i s t a n c e s a s b e н
fo r e .
S in c e t h e d i f f e r e n c e s w ere so s l i g h t , th e d e n s i t y v a lu e m easured
f o r t h e u n s t r e t c h e d e v a p o r a te d l a t e x , 0 .9 3 gm. p e r o c . , was u s e d th ro u g h н
out th e w o rk .
A c t u a l l y , an y d i f f e r e n c e s w ould h ave b een s m a lle r th a n i n н
d ic a t e d a b ove s i n c e a t 250 p e r c e n t e l o n g a t i o n we w ould n o t e x p e c t th e
d e n s i t y t o h a v e r e a c h e d th e v a lu e 0 .9 6 5 gm. p e r c c .
The la c k o f r e s o l u t i o n o f th e se c o n d peak in th e e a r ly s t a g e s o f
e l o n g a t i o n w o u ld i n d i c a t e t h a t th e a r ea u n d er i t r e p r e s e n t s n o t o n ly th e
s e c o n d n e ig h b o r s b u t a l s o th e n e a r e r o f t h e t h i r d n e ig h b o r s .
r o t a t i o n a b o u t th e s i n g l e carb on bon ds i t
B eca u se o f
i s p o s s i b l e aor t h e n e a r e r o f
t h e s e t h i r d n e ig h b o r s to be a t a d is t a n c e w h ich i s a p p r o x im a te ly th e same
a s t h e a v e r a g e d is t a n c e o f t h e s e c o n d n e ig h b o r s .
Prom t h e m odel o f F ig u r e
20 we ca n s e e th a t t h e s e t h ir d n e ig h b o r d is t a n c e s w i l l v a iy .f r o m a m in ia im
67
й
o f г .5 6 A
0
t o a maximum o f 4 .0 4 A .
The b e t t e r r e s o l u t i o n and d e c r e a s e of a r e a o f th e sec o n d p ea k w it h i n н
c r e a s in g e l o n g a t i o n roust mean t h a t th e n e a r e r t h i r d n e ig h b o r s a r e n o t
a p p r o a c h in g a s c l o s e l y a s th e y d id when th e ru b b er w as u n e x te n d e d .
T h is
c o n c lu s io n i s b orn e out b y t h e f a c t t h a t t h e t h i r d n e ig h b o r s th e m s e lv e s
a r e becom ing o e t t e r d e f in e d a s e v id e n c e d b y t h e s h a r p e n in g o f th e t h i r d
c o n c e n t r a t io n i n th e a n a l y s e s .
The d i s t a n c e 5 .3 3 A░ o b ta in e d f o r t h e p o s н
i t i o n o f th e t h i r d p e a k w hen th e e l o n g a t i o n was 250 p e r c e n t a g r e e s v e r y
o
w e l l w it h 3 .3 0 A , th e a v e r a g e v a lu e b etw een th e g r e a t e s t and s m a lle s t
d i s t a n c e o f t h i r d n e ig h b o r s .
The f o u r t h c o n c e n t r a t io n b eco m es s h a r p e r a s e l o n g a t i o n i n c r e a s e s ,
th o u g h th e c h a n g e i s n o t a s marked a s i t i s f o r t h e t h i r d g r o u p in g .
T h is
f o u r t h g r o u p in g p r o b a b ly c o m p r is e s t h e f a r t h e r t h i r d n e ig h b o r s a n d , p e r н
h a p s , som e atom s w h ic h we m ight c a l l f o u r t h n e ig h b o r s .
The in a p p r e c ia b le change i n p o s i t i o n and s h a r p n e s s o f t h e f i f t h p ea k
o f t h e a n a l y s e s h a s a lr e a d y b e e n m e n tio n e d .
I f we a r e c o r r e c t i n a t t r i н
b u t in g t h i s peak t o th e n e a r e s t c a r b o n atom s i n n e ig h b o r in g c h a i n s , th e n
th e d i s t a n c e b e tw e e n c h a in s must b e q u it e c o n s ta n t a s t h e e x t e n s i o n i n н
c r e a s e s , a t l e a s t up t o e l o n g a t i o n s o f 250 p e r c e n t .
From a c o n s i d e r a t i o n o f th e a b o v e r e s u l t s i t i s
e v id e n t t h a t t h e
a s s u m p tio n o f an e x te n d e d m o le c u le i n u n s t r e t c h e d ru b b er i s n o t v e r y s a t н
is fa c to r y .
I t w o u ld n o t e x p la i n t h e sh a r p e n in g of th e t h i r d a n d f o u r t h
p e a k s n o r w ould i t
o f t h e se c o n d p e a k .
accou nt f o r th e b e t t e r r e s o lu t io n and d e c re a se in a rea
On th e o th e r h an d , i f we assum e a m o le c u le
(illu s tr a te d
s c h e m a t ic a lly in F ig u r e 20) in w h ic h v.e c a n have r o t a t i o n a b o u t th e s i n g l e
ca rb o n bonds a n d , f u r t h e r , a ssu m e t h a t b eca u se o f t h i s p o s s i b i l i t y o f r o t a н
t i o n we can h ave a ?? fo ld e d 1* m o le c u le when t h e r u b b e r i s
in a n u n e x te n d e d
c o n d i t i o n , t h e e f f e c t s p o in t e d out a b o v e ca n b e a c c o u n te d f o r .
T h is w o u ld
mean t h a t p a r t o f th e e x t e n s i b i l i t y o f ru b b er i s due t o e x t e n s i o n s a n d c o n н
t r a c t i o n s i n t h e i n d i v i d u a l c h a in s ? e x t e n s i o n s i n t h e d i r e c t i o n o f s t r e t c h
and c o n tr a c tio n s n o rn a l t o t h i s d ir e c t io n .
T h is d o e s n o t n e c e s s i t a t e t h a t
a l l t h e e x t e n s i b i l i t y s h o u ld be a t t r i b u t e d t o
i n d i v i d u a l c h a in s o r m o le c u le s .
At l a r g e e l o n g a t i o n s we may h ave s l i p p i n g o f some s o r t b e tw e e n c h a i n s .
T h is c o u ld a c c o u n t f o r t h e sh a r p r i s e
s tr a in s .
in t h e s t r e s s - s t r a i n c u r v e a t la r g e
The i n c r e a s e i n Van d e r I fe a ls f o r c e s , due t o b e t t e r i n t e r f a c i a l
c o n t a c t b e tw e e n t h e m o le c u le s a t la r g e e l o n g a t i o n s , i s
i n a g reem en t w it h
su c h a c o n c e p t io n o f th e m o le c u le .
H e n c e , we c o n c lu d e t h a t t h e r e s u l t s o f th e i n v e s t i g a t i o n i n d i c a t e
q u it e d e f i n i t e l y t h a t one d o e s n o t h a v e a n e x te n d e d m o le c u le i n t h e unн
s t r e t c h e d r u b b er b u t h a s i n s t e a d a f o ld e d m o le c u le w h ic h , by r o t a t i o n
a b o u t t h e s i n g l e c a rb o n b o n d s , i s i t s e l f c a p a b le o f e l o n g a t i o n .
p r o c e s s o f s t r e t c h i n g th e
In t h e
m o le c u le l o s e s p a r t o f i t s fr e ed o m to ch a n g e con н
f i g u r a t i o n b y c o i l i n g and u n c o i l i n g ,
th e l o s s o f t h i s a b i l i t y and t h e f i x н
in g o f d e f i n i t e p o s i t i o n s b e in g e v id e n c e d by t h e sh a r p e n in g o f t h e p e a k s
in th e r a d ia l d is t r ib u t io n cu rv e.
|g
ft
69
V.
SUMMARY
X -r a y i n v e s t i g a t i o n s o f ru b b er h a v e been c a r r ie d out f o r b o th amorphous
an d c r y s t a l l i n e m a t e r ia l.
The amorphous m a t e r ia l snow s a p a t t e r n l i k e a
l i q u i d w it n d i f f r a c t i o n r in g s a t 5-^ - - v a lu e s o f 0 .1 0 5 5 , 0 .2 2 2 , 0 .4 1 7 .
T h is p a t t e r n was o b ta in e d in a vacuum camera o f 8 .6 cm. d ia m e te r w it h m olybн
denum r a d i a t i o n r e f l e c t e d from
c a l i b r a t i o n m arxs e v e r y 20
a r o c k s a l t c r y s t a l . The
f i l m h o ld e r c a r r ie d
so a s t o e lim a t e e r r o r s due t o s h r in k a g e o f th e
film .
The S c h e r r e r e x p r e s s io n c o r r e l a t in g h a l f w id th and p a r t i c l e
e
t o c r y s t a l l i t e s o f th e o r d e r o f 80 A .
s i z e le a d s
The p a t t e r n was o b ta in e d b y u s in g pu re l a t e x , p ou red on g l a s s , d r ie d
and m ounted s t r e s s f r e e in
th e cam era.
The sam ples w ere
i n th e form o f
f l a t s h e e t s 1 .5 t o 2 .0 mm.t h i c k .
The m ost i n t e r e s t i n g p rob lem in t h e s t r u c t u r e o f ru b b er i s t h e q u e s t io n
o f w hat h ap p en s in th e s t r e t c h i n g p r o c e s s .
To i n v e s t i g a t e t h i s p rob lem
th e rm.yimum e lo n g a t i o n t o w h ic h l a t e x ca n be s t r e t c h e d a t room te m p er a tu r e
w ith o u t c r y s t a l l i z i n g was d e te r m in e d .
For t h i s p u r p o se t h e sam ple was put
i n a sp e c im e n h o ld e r vdiich a llo w s th e d e te r m in a tio n o f t h e amount o f
s t r e t c h and w h ich can be m ounted in a r e p r o d u c a b le f a s h io n i n th e cam era.
D i f f r a c t i o n p a t t e r n s h a v e b e e n o b ta in e d a t e l o n g a t i o n s of 100 p e r c e n t , 200
p e r c e n t , and 250 p e r c e n t .
At 275 p er c e n t e lo n g a t i o n t h e sa m p le becom es
c r y s t a l l i n e a s in d ic a t e d by t h e a p p ea ra n ce o f d i f f r a c t i o n s p o t s on the
eq u a to r.
To i n t e r p r e t th e d i f f r a c t i o n p a t t e r n s , f o u r i e r a n a l y s i s h a s b een u s e d
t o o b t a in a r a d i a l d i s t r i b u t i o n ,
vtfith s u b s ta n c e s such a s ru b b er and o th e r
l i g h t o r g a n ic m a t e r ia ls such a n a n a l y s i s p r e s e n t s s e r i o u s e x p e r im e n ta l
69
V.
SULEJABY
X -r a y i n v e s t i g a t i o n s o f ru b b er h ave been c a r r ie d out f o r b o th amorphous
and c r y s t a l l i n e m a t e r ia l.
The amorphous m a t e r ia l snow s a p a t t e r n l i k e a
l i q u i d w ith d i f f r a c t i o n r in g s a t
? v a lu e s o f 0 .1 0 5 5 , 0 .2 2 2 , 0 .4 1 7 .
T h is p a t t e r n was o b ta in e d in a vacuum camera o f 8 .6 cm. d ia m e te r w it h m olybн
denum r a d i a t i o n r e f l e c t e d from
a r o c k s a l t c r y s t a l . The
f i l m h o ld e r c a r r ie d
c a l i b r a t i o n a a r i s e v e r y 2 0 ░ so
a s t o e lim a t e e r r o r s due t o s h r in k a g e o f th e
film .
The S c h e r r e r e x p r e s s io n c o r r e la tin g - h a l f w id th and p a r t i c l e
s i z e le a d s
to c r y s t a l l i t e s o f th e o r d e r o f 30 A .
The p a t t e r n was o b ta in e d by u s in g pure l a t e x , p ou red on g l a s s , d r ie d
and mounted s t r e s s f r e e i n th e
cam era.
The sam ples w ere i n th e form o f
f l a t s h e e t s 1 .5 to 2 .0 mm. t h i c k .
The most i n t e r e s t i n g prob lem in t h e s t r u c t u r e o f rubb er i s t h e q u e s t io n
o f w hat h ap p en s in th e s t r e t c h i n g p r o c e s s .
To i n v e s t i g a t e t h i s p roblem
th e maximum e lo n g a t i o n t o w h ic h l a t e x can be s t r e t c h e d a t room te m p er a tu r e
w ith o u t c r y s t a l l i z i n g was d e te r m in e d .
For t h i s p u r p o se t be sam ple w as put
i n a sp e c im e n h o ld e r w h ich a llo w s th e d e te r m in a tio n o f t h e amount o f
s t r e t c h and w h ich can be mounted in a r e p r o d u c a b le f a s h i o n i n th e ca m era .
D i f f r a c t i o n p a t t e r n s h a v e b e e n o b ta in e d a t e lo n g a t i o n s of 100 pier c e n t , 200
p e r c e n t , and 250 p e r c e n t .
At 275 p e r c e n t e l o x g a t io n t h e sa m p le becom es
c r y s t a l l i n e a s in d ic a t e d by th e a p p ea ra n ce o f d i f f r a c t i o n s p o t s on th e
e q u a to r.
To i n t e r p r e t th e d i f f r a c t i o n p a t t e r n s , f o u r i e r a n a l y s i s h a s b een u s e d
t o o b t a in a r a d i a l d i s t r i o u t i on.
,еith s u b s ta n c e s such a s r u o o e r and o th e r
l i g h t o r g a n ic m a t e r ia ls such a n a n a l y s i s p r e s e n t s s e r i o u s e x p e r im e n ta l
d i f f i c u l t i e s due t o t h e f a c t t h a t
(a ) t h e la r g e amount o f h y d ro g e n p r e s e n t
p r o d u c e s a la r g e am ount o f in c o h e r e n t s c a t t e r i n g a t la r g e a n g le s and (b)
b e c a u s e t h e s c a t t e r i n g pov/er o f t h e m t e r i a l i s
so s n a i l a s t o becom e com н
p a r a b le , a t l a r g e a n g l e s , w ith th e a c c i d e n t a l s c a t t e r i n g .
I t i s , th e r e н
f o r e , n o t u n iq u e ly d e te r m in e d w here one s h o u ld c u t o f f i n t h e e x p e r im e n ta l
c u r v e and assu m e in d e p e n d e n t c o h e r e n t and in c o h e r e n t s c a t t e r i n g .
By t r y i n g
s e v e r a l r a n g e s and n n tc h in g t h e e x p e r im e n ta l and t h e o r e t i c a l c u r v e s i n
d i f f e r e n t w ays one can o b t a in q u it e d i f f e r e n t r e s u l t s .
T h is i s due t o t h e
f a c t t h a t th e c u r v e S i ( s ) w h ich i s t o be a n a ly z e d in c lu d e s S , in c r e a s in g
w it h
.
Any s m a ll a r e a in th e e x p e r im e n ta l s c a t t e r i n g c u r v e a t l a r g e
a n g le s i s t h u s made com parable w it h t h e la r g e a r e a due to w e l l d e f in e d r i n g s .
In t h e c a s e o f ru b b er w here i t i s
known th a t we a r e d e a lin g w i t h a
c h a i n - l i k e s t r u c t u r e , t h a t means two f i r s t n e ig h b o r s , i t i s p o s s i b l e t o d e н
te r m in e e m p i r i c a l l y w here t o c u t o f f so a s t o g e t t h e c o r r e c t nunfcer o f
f i r s t n e ig h b o r s .
t h i s w ork, i t
In o t h e r c a s e s , and t h i s m ethod h a s b e e n u s e d th ro u g h o u t
i s p o s s i b l e to m atch over a r a n g e by m a tch in g a r e a s un d er t h e
e x p e r im e n ta l and t h e o r e t i c a l c u r v e s .
For th e a c t u a l a n a l y s i s a schem e of
c a l c u l a t i o n d e v e lo p e d by D a n ie ls o n an d I a n c z o s h a s b een u s e d .
V is u a l c o m p a r iso n o f th e e x p e r im e n ta l c u r v e s d o e s n o t show an y s t r i k н
in g d i f f e r e n c e s .
The h e ig h t o f th e f i r s t
peak i s somewhat c h a n g e d , i n c r e a s н
in g w it h in c r e a s in g s t r e t c h , and th e sh ap e and p o s i t i o n s o f th e o u te r r in g s
a re s l i g h t l y changed.
T hree d i f f e r e n t e x p e r im e n ts h a v e b e e n c a r r i e d out
f o r e a c h e lo n g a t i o n and th e c u r v e s g iv e n a r e th e a v e r a g e v a l u e s .
The F o u r ie r a n a ly s e s o f th e c u r v e s r e v e a l s t h e d e t a i l s o f t h e s t r u c н
tu r e .
In t h e
s t r e s s - f r e e s t a t e we f in d 1 .9 n e ig h b o r s a t a d i s t a n c e o f
1 .5 2 A░ and 2 .8 6 n e ig h b o r s a t a d is t a n c e of 2 .5 4 A .
T here i s a s l i g h t
i n d i c a t i o n o f a c o n c e n t r a t io n a t 8 . 5 A░ and a t 4 .2 4 A* and a c o n s id e r a b le
░
kump a t 5 .0 6 A ?
The o o n .c e n tla tio n a t 5 A
0
is
r e s p o n s ib le f o r t h e m ain
p eak i n t h e e x p e r im e n ta l c u iv e a n d from o th e r o r g a n ic s u b s t a n c e s , we know
t h ? t t h i s m ust r e p r e s e n t d i s t a n c e s b etw een n e ig h b o r in g m o le c u le s *
The s e c o n d p ea k i s b e t t e r r e s o lv e d th a n in t h e a n a l y s i s o f smoked
s h e e t b y Sim ard and ife r r e n and t h i s c h e ck s w it h our own r e s u l t s f o r t h a t
m a te r ia l.
As s t r e t c h i n g i n c r e a s e s ,
th e se c o n d peak becom es b e t t e r r e s o lv e d a n d
a t an e l o n g a t i o n o f 250 p e r c e n t , t h i s peaK i s a lm o s t c o m p le t e ly r e s o l v e d .
A t t h e same t ime th e c o n c e n t r a t io n s b eyon d s e c o n d n e ig h b o r s a r e q u i t e
d is tin c t.
I t i s a l s o t o be n o t ic e d th a t th e nunfrer o f s e c o n d n e ig h b o r s
d e c r e a s e s a n d t h a t th e peak i t s e l f a p p e a r s a t a s h o r t e r d i s t a n o e .
To u n d e r sta n d t h i s change we want to r e c a l l th e s t r u c t u r e o f th e
ru b b er c h a in a s a c c e p t e d from c h e m ic a l and o th e r e v i d e n c e .
T a k in g th e
0
0
and 1*38 A
r e s p e c t i v e l y , one c a l c u l a t e s tw o f i r s t
bond a n g l e s a s 109 28* and 125 1 6 ' and s i n g l e and d o u b le ca rb o n bond d i s ta n c e s a s 1 .5 4 A
o
n e ig h b o r s a t 1 .5 1 A , in agreem ent w it h p o s i t i o n and a r e a of t h e f i r s t
peak.
P
T here sh o u ld be 2 .4 n e ig h b o r s a t a d i s t a n c e o f 2 .5 6 A but t h i s
number w i l l a lw a y s b e l a r g e r b e c a u s e o f t h e c o n t r i b u t i o n o f i n t e r p e n e t r a t н
in g t h i r d n e ig h b o r s .
As th e s t r e t c n i n g
i n c r e a s e s th e rubb er m o le c u le i s
no lo n g e r a b le to c o i l a n d u n c o i l f r e e l y a n d change i t s c o n f i g u r a t i o n .
T h e r e f o r e , t h e c o n t r i b u t i o n of th e t h i r d n e ig h b o r s t o th e s e c o n d p eak
becom es s m a lle r and th e p o s i t i o n o f th e t h i r d n e ig h o o r s t h e m s e lv e s b e н
comes more d e f i n i t e l y f i x e d .
The d is t a n c e o f 3 .3 3 A* c o r r e sp o n d s e x н
a c t l y t o t h e a v e r a g e v a lu e b etw een s m a lle s t and g r e a t e s t d i s t a n c e s o f
?
?
t h i r d n e ig h b o r ; 3 .3 3 A o b se r v e d a n d 3 .3 2 A
c a lc u la te d .
H e n c e, we c o n c lu d e t h a t t h e r e s u l t s o f th e i n v e s t i g a t i o n i n d i c a t e
q u it e d e f i n i t e l y t h a t -,ve do n o t h a v e a n e x te n d e d m o le c u le i n t h e u n s t r e t c h -
72
ed ru b b er b u t h a v e i n s t e a d a f o ld e d m o le c u le , w h ic h , by r o t a t i o n a b o u t t h e
s i n g l e carb on b o n d s , i s
i t s e l f c a ..a b le o f e l o n g a t i o n .
In th e p r o c e s s o f
s t r e t c h i n g tn e m o le c u le l o s e s p a r t o f i t s freed o m to ch an ge c o n f ig u r a t io n
by c o i l i n g a n d u n c o i l i n g , t h e p r o c e s s o f f i x i n g d e f i n i t e p o s i t i o n s b e in g
e v id e n c e d by th e sh a r p e n in g o f th e p e a t s i n th e r a d i a l d i s t r i b u t i o n c u r v e .
I w ish to e x p r e s s ray deep a p p r e c i a t i o n and s i n c e r e th a n k s t o Hr. K arl
X a r k -H o r o v itz and Hr. E. P . H i l l e r f o r t h e i r a s s i s t a n c e during' t h e c o u r s e
of t h i s in v e s t ig a t io n .
I t h a s b e e n t h e i r g u id a n c e and c r i t i c i s m t h a t h a s
made th e c o m p le tio n o f th e w o rt p o s s i b l e .
73
(/)
APEENDIX I
c o u r ie r /a n a ly s is f o r 36 C o e f f i c i e n t s by Two A n a ly s e s f o r 18
^
2yK ' ZK+1*
Z /g
░'
c ╗ El +-?
K
(C
= / 3 / ?
'
*
=Bi
K ~ ^
36-K
(K Odd) Ak
SiK +StoK? A18_K" S1K~ S2K F o u r i e r C o e f f . uK = 0 ( K ) = ZcK * c;г
lb
(K even)AK = S & ' + S ^ , * 1 8 _K =
D e n s i t y I n t e g r a l л I(K ) = K cK
(K odd)
╗ S5K ? s 6K, Dl b _K = S ^ - S g ^ D i s t a n c e fro:' a t o r rK = K fT /a
(K <
- ->7K
= S?K-S
&f- = hT, c o s f T /3 6 K ? 22. s in * / 3 6
-
--
A
1
- 3 3vS17
fc
16
15
-d~7S
~/?7е
tJk(sum) ~ 3 3 S-
- 2 .3 a
3 U
Vjr( 6.1 f f ) - J 3 vT
_l----.
? г2.
O
?o 9
е 25-9
* ? ..7 .1
14
-2.33U
13
'/ V
z
-
.
1 8
--------- IX&L 1............ . ur fllHa t fa
A
3
5
3 Id(, 2 2 . 2 S<S
0 *4 7 $ .
л teoZ?S-'A 0 .8 6 6 = 9 7 е W
Check; y*
2
.... - ...
y>:
where th e range a = ?.
L
~/*42? - f / е 7
3 2 i/vS"
/7o*s-
7
77& 6
/7 3
12
-23 9
/ 0 3 1,
7/t
7 * !>
/2 0 ?
2еsr
/2 /е
~S&>3
-//7 b '
- е6'S-& -
11
v / / _ 9
10
- v / /
S h i f t i n g Odd O r d in a t e s
0
K
8
yK
-22sy
2yK
-
- a *7
~3o S S
10
7
11
//л/
.
7S2
~ / 3 3*3
- S6S
-/
/JJе
St
7jk
1
- 3 0 SS
17
O
^K(sum)
-vS^'vT? S '
*4 е 2
/ .* / / г
/ 3 1*2
- 33~ г
-///& >
-70S
2 It Id
?/ I S *
32. 2
3&>
2 Id O (d
/7SQ
70S
- 2 . Id (d
JAfJL
-Z-2.2.
12
13
14
15
-//* ? />
-3 Jo X
- / / е
/S /o
2
1 s&>г
/ / е
o f S
~ /S/o
-
a ?+S2.
-209 S
2 .(* < 3 2
7372. ~/3 7 0
2 7 i, S
*/2 J 2
2
SO s
16
17
- 2 <4S2
- 2 0 7 6>
/ I l l
/* - < / < /
/* ~ -7 t
J 0 SO
to
- 3
18
- <T<7
- / 6> 0
0
/г o
Odd O r d in a t e s ( s h i f t e d )
p
6
4
5
/
i╗
S
*4
2
/*
(fi
7╗ S
2 S 0 le / 7 3 t
13
12
14
15
16
- / S t -2ег2 - a o r s . - / s / o . . / / *
- 3 0 SZ
VK ( d i f f ) - Z o S S
~/3 2 /
-/7 v r y
z y 7 /
2 2 02
0
~ / 7 ?
- 2 . Lo{t>
2.1*3 f
/a
4tsi_
/ z j ?
<-/3 2 L> 2 .1 4 3 E
?X+l
Zv
7 Q ?
a ?/ L г
0
~ /S 0
7
8
- 3 L>
* 7 -2 .^
11
10
/77V
S 6 S
0>
- //? o
/ 2 ?S
-/3 7 a
9
-/o S o
x- .172-6 = s in
t-^
o
0
to
1
%
.3 0 0 0 -- s i n
p.- . 34F0 = s i n
P0░
4-
. 64 OH - s i n 4 0 ? 6 - .8 6 0 0 - s in
i ^?(#n O r d in a t e s
fr
TJl
Uo,
- 3 3 s-
3 //
r?
/?& г
9
? /h г
J //
'K-'r
A ^*2f
/ <A~г
-a.'sr?
_-2
7
- J /v T
-/3 ~ ie
-9
9
- 3 3sT ?3 / /
71
- 3 3 S'
O
L.
U7
U8
- / / * / ? / ? i fl 7
3
7
//3 b
: J7?
nJ
??i_
-< s ~ 7 J - / , o s
_7
-1
-_ z ./o
-1
/ f /
9
-9
-/W 7
/j
?JJ.'Sr?
6
36>Sf
6
3hTS
0
- / at
4
- .2 /vS~
6
3
-=2 f *
8
-6
- J30
?3 (oS S
V_
/
V5
/ 7 o s/L 7 ?
r-<S~-г3
-6
4
? \S? 'SVS*
-8
30c
?~s- .7 6 6 0 = s:' n 5 0 ░
suir.
U9
-V //
- V //
-9
V //
9
- V //
-y
v //
9
- y //
?
?
S1 K
"2 j a
<r
- d~ Le
-7 ?
6
- г - 2.* / - / r r
8
3 <S~^
-2 2 7
4
/ Oh'S" - / V < F
.9 8 9 7 = s i n
8-
.9 8 4 8 = s i n 8 0 ░
U4
-/y -z 7
A.
- 7 /7
6
-/~г 3 (p
- rr,
V / /
-8
/y z> ir-
U6
73 &
6
2 t^ 7
0
U8
-Z VvS~
8
2*-//
-6
sum
S2 K
-//F
- -Z. /- 2
4
/3 ~ 7
~ / 6 c/ 7
г 3 ,7
- 7V
77/0
V.
6
V
ta
sun:
0
-6
-C .3 7
6
-2 ./?
- 3 <7/3
sum
V
2
3K.
y iJ 7 7 -
/*/г/
8
7 ^ 7
6
--z< r> v
A
6
-7 7 7
f.
/<? 7 г
^ 7 v i"
--2 г -2-7
-/V 7 7
U?
60░
70░ 9 - / c
7-
t V4
2 2 l/iS?
8
3/76,
r///o
-6
7 d >o >
-2 o / i
7 -2 /y
6
/o * s r /
-6
-/o io r /
0
o
6
/O S -/
- / / P'S"
0ti
o
-4
7vdT 7 7 6 7
6 .___
-/o /2 - 2 / / S
-8
/S 'S -7
0 d d 0 rd i m-1 e s ( s h i f t e d )
K
U1
- 3 0 XZ
1
u.
7 vT -2
3
7 7 г
?
a
л/
5
- 2 2 г*S?
7
-/nr?o
-3
7г
-3
-i
-3 /г
3 ho
g
9
-9
-& o S t - 7 vT-2 - 2 o 7 ( *
7
T
?1
v?
7. 3* l г 7 ^ / 2
2
6
- / o s b 2i><-fг
A ?
?x
6
-t? s* 3 W ?
6
0
o
-2 6 7*
8
-6
r*oH / -3b43
i
-2.C 7&
-/O 3 f
_v
/ / s /
-/?$?*/е
ia ,
U-,iZ
- 2 .7 3
-1
3
<4/ г
-S4L
V--
V7
/sT V * /
~//?o
'i
-7 b s-8
H
-vT - 2- J
//7 -i
6
-6
-Z 337 -/a 3 /
fi
.*
U9
-/<? 7 o
9
- / u 3 "(3
- :J
/<* <To
9
- / o 7<I
r-j
/<> <r<*
j
/ л J ~0
SUB;
S r,K
--2 ^ / 7
-------
-7 V
*237.
6
U.
n
- / 3 70
4
-F?3
6
U6
/7 7 7
6
/'3 s 7
0
o
-2. 3 ^ / / F ._. - /^ < ? /
-6
8
- 7 - 2 / ^ 2 * 0 ? V / v S ? -/u 'v r 7
6
-8 - / V -2 0 W ' 7 ^ / 3 ip? / iTm ~ 7
---------------A r *7
Vrit
SUBS
V6
?"7K
-------
r
2 . 7^^.
4
^ : 7 _ o ._
6
8
33 <- / г / 7 7 F . Z . 7 & 3 / 3 /, 0
f-'
-6
8
?
?
6
.0
~/3/>0
7 3░7 77^ ^
0
6
6
0
-2Y30
6
**4r
г
' / 3 /pO
\-'г '2 ? a i 7 y ^
UB
sum
/ 2 / r
8
*^6 K
A Z 7^
2 7 7 /
-6
- / / 2 V --2 /0
-------??8
~/3 7 O
sum
S8 K
_y г 7
7 7 /
e
'//7 г
-8
/3 V >
3- 2 0<S~
" /2 2 /
/ S ^ r/
vft
*
to
to
5
s
u
$
54
=4
л
\
V
3
Os
<s╗
,v>
X
s3
*>
X
X
>
X
>
X
*7
>
X
u
**
%
>
Os
>a
*
X
va
%
?
\
X
?
<0
X
X
*s/
3
R
(K
"n
Os
W
X
X
>
cx
X
X
л
>
X
N
X
X
^1
X
?y
X
X
i
X
г
?
'D
<b
--------
ta
X
/*
X |
X
S
<y
N3
1 *
<o
CO
0
N
X.
**r
5л
1
0
%
c
H
to <
CO .
^
O'
?
rH
O'
CD
CC
cc
?
rH
CO
CO
CO
UO
л
rH
CO
H
tO
lO
in
o
?
pH
H
r?
4
H
?
ta
ti>
<-*
?
Os
*
<*
N
I
X
N
>
X
w?
o
CO
o*
>
< -a
░
*
*X?
X
X.M
1
H
"7
5t
CVJ
t
X
X
X
J*
a
*
\
r
o
^3
X
X
X
<J
1
N
<v
1
s?o
X
<5
*
c,
>3
X
Ki
*<3
%
I
X
(*7
>3
h?
>S
X
>
X
Ol
no
<>/
X
GO
b
*
(X
X
X
<a
*0
>
г
X
<M
tO
o╗
O'
?
cc
3
o>
?
*
N
o?H
O
&
CO
л
tr.
M
X
CO
s╗
4
CD
CO
CO
?
CO
O
t>
CO
?
\
N
*
CO
w
CO
<N2
pH
>
(X
5
c--
u:
\r.
ID
ts
to
to
to
4
tH
o
o r1
v3
pH
rH
?H
t-0
rH
CO
CO
CO
t>
л
*H
з
11
-
?
?V
3
a
no
X
t
O'
to
to
O'
t
X
>
C'o
0
O'
to
CT>
?
CO
to
c
O'
?
&
o
CD
CD
CO
CO
<*
CO
╗
vr^
?
co
CO
tjt
lO
?
?
X
<Q
CM
CM
O
to
to
CO
?
?O
X>
X
o
o
to
o
?
to
╗
a
?tj-
pH
?S?)
^f*
?r
?
<-H
8?
O
O
O
to
л
in
m
╗o
in
?
rH
/H
pH
л
ti
X
'a
X
X
1
1
0
0
>
1
^3
X
X
*N
1
v3
btj
X
>
cr:
<?4
<*>
>3
CO
O'
r~i
CD
*
е
?
NS
CO
CO
CO
CN
?
sO
0
0
?
CO
л
rH
%
CO
co
CJ
CO
?
X
%
X
X
to
X
X
?
"*3
?
X
rH
tO
in
in
0
?
H
rH
?
rH
pH
rH
rH
H
?
pH
CO
c^>
c^<s
?
CO
CO
to
CD
?
C*
CD
CO
CO
?
tp
sf
si*
cn
?
*
X
to
h
V
X
I
X
0
0
8
?
rH
0
л
1
0
0
1*1
0
>
>
л
kX
3
>
%
f\
1
>
X
*
0
H
cc
tO
to
X
'N
l
r?
CO
O'
л
X,
Cxj
?
1?1
гN
O
cs
0
?o
X
?
00
CO
<?
to
1
to
CO
tл
X
X
b
co
C'
in
O
Q
t
'O
>
1
>
1
*
SJ
X
SS
X
1
\
N
X
'VJ
1
O
л
0
r?i
X
>
in
CO
O'
r-i
>X)
X
>
X
X
X
>
X
X
1
i
1
0
CD
to
m
CM
?
n
Cs
1?I
?
w
oCD
O
?
>
X
X
X
X
CO
?V
>>
b
OS
CO
Sp
to
л
X
X
X
\
01
CO
╗
CD
rH
CM
rH
?
w
0
O'
?
tn
pH
E'н
en
tO
O'
*
vf
r -1
Q
X
X
X
to
X
X
X
0
h
\
л
i
0
X
X
X
X
X
~n
X
to
0
H
X
?O'
?
0
tO
'V
X
X
╗
?
to
CD
?
-o
X
>s
^9
<v
tO
CO
0
0
0
X
X
X
X
X
X
X
X
X
X
tO
to
0
\
X
>
IX
'N
b t,
1
X
*
CN
0
h
1
>
to
CO
C'
in
cc
>
1
b>0
X
CO
CO
CO'
л
pH
to
"i
X
>
%
f
01
S9
>
>л
bq
'4
X
X
1
x
cx
>
л
>
i
ro
vS
cS
X
I
tx
\
O
<V
i
to
CO
orH
CO
0
Ua
h
in
<
f-J
X
>>
(X
<0
N
i
<a
>
X
X
si
X
"i
>
h
>
<3
^S)
X
&Q
L-W
>
V$ )
n
o
c
a
c~
C'
c?
*
*>
?
X
sS
X
2
?y
X
N
N
X
>
IS
o
лt
*
O'
CO
?
CO
<T╗
?
in
tO
O'
in
rH
<0
rH
CD
to
o>
cn
?
t>
rH
0
c
0
?
rH
CD
rH
76
REFERENCES
1╗
Eо V r i e s , " E s ta te R ubber, i t s P r e p a r a tio n , P r o p e r t ie s and T e stin g '* ,
3 a ta v ia , 1920, p . 601.
2.
I h r a d a y , Q u a r t. J . S c i . , 2 1 , 1 9 ,
(1 8 2 6 ).
3.
H a r r i e s , U n tersu ch u n g en u b er d ie n a t u r lic h e n und K u n stlic h e n
K a u tsc h u k a r te n , B e r l i n , 1 9 1 9 .
4.
W eber, C. 0 . ,
"The C h em istry o f In d ia Rubber", London,
5.
Pummererand 3 u r k a r d , B e r ., 5 5 , 3 4 5 8 ,
6.
H o p ff and von S u s ic h , K au tsch u k , 6 , 2 5 4 ,
4, 75,
1909.
(1 9 2 2 ).
(1 9 3 0 ); Rubber Chem. T e c h .,
(1 9 3 1 ).
7.
S t i l l v / e i l an d Clark;, In d .
Eng. Chem., 2 5 , 7 0 6 ,
(1 9 5 1 ).
8.
S t a u d in g e r , K au tsch u k , 1 ,
9,
9.
S t a u d in g e r , K au tsch u k , 5 ,
129,
10.
S t a u d in g e r , B e r ., 6 3 , 9 2 1 ,
11.
Lfeyer and I h r k , "Per Aufban der H ochpolym eren O rgan isch en N a t u r s t o f f e " ,
(1 9 2 5 ) .
(1 9 2 9 ) .
(1 9 3 0 ); B ib b er
Chem. T e c h ., 2 , 5 8 6 ,
(1 9 3 0 ) .
L e i p z ig , 1 9 3 0 .
12.
U cCallum and W hitby, T r a n s. R oy. S o c . C a n ., 1 8 , 1 9 1 ,
13.
Von B ossem and L o t ic h iu s , K au tsch u k , 5 , 2 ,
T e c h ., 2 , 3 7 8 ,
(1 9 2 4 ) .
-
(1 9 2 9 ); Bubber Chem.
(1 9 2 9 ) .
14.
K ir c h o f f , K au tsch u k , 5 , 1 7 5 ,
(1 9 2 9 ) .
15.
P is h e r and G e rk e, in D a v is and B la k e , '?C hem istry and T ech n o lo g y of
Rubber'*, New Y ork, 1 9 5 7 , C hapter I I I .
16.
L e31anc ard K ro g er,
K o llo id ?2 . , 3 7 , 2 0 5 ,
17.
H a u se r - and R osbaud, K au tsch u k , 4 , 1 2 ,
18.
J o u l e , P r o c . R oy. S o c . , 8 , 5 5 5 ,
19.
W iegand and S n y d e r,
20.
G erk e, In d . E ng. Chem., 2 2 , 7 3 ,
(1 9 2 5 ) .
(1 9 2 8 ) .
(1 8 5 7 ) .
T ra n s. I n s t . Rubber I n d ., 1 0 , 2 3 4 ,
(1 9 3 0 ) .
(1 9 5 5 ).
77
21.
Pummerer, K au tsch u k , 5 , 2 3 5 ,
22.
G a s p a r i, J . Chem. S o o ., 1 0 5 , 2 1 3 9 ,
23.
S ta u d in g e r and B ondy, A n n ., 4 6 8 , 1 2 7 ,
24.
m id g le y , H enne, Shepard and R e n o ll, J . Am. Chem. S o c . , 5 6 , 1 5 2 5 ,
25.
R in k e l, Z e i t . F h y s ik . Chem., 1 5 8 , 4 5 ,
26.
R osbaud a n d Schm id, Z. t e c h . P h y s ik , 9 , 9 8 ,
27.
K a tz , N a t u r w is s e n s c la f t e n , 1 3 , 4 1 0 ,
28.
H auser and Mark, K o llo id chem. B e i h e f t e , 2 2 , 6 5 ,
(1 9 2 6 ) .
29.
H auser a n d Mark, K o llo id chem. B e i h e f t e , 2 3 , 6 4 ,
(1 9 2 7 ) .
30.
YThitby, in D a v is and B la k e , ??C hem istry and T ech n o lo g y of Rubber",
New Y ork, 1 9 3 7 .
(1 9 2 7 ).
(1 9 1 4 ).
(1 9 3 1 ) .
(1 9 3 4 ) .
(1 9 2 8 ) .
(1 9 2 8 ) .
(1 9 2 5 ) .
C hapter I I I .
31.
F e u c h t e r , K au tsch u k , 2 , 2 6 0 , 2 8 2 ,
(1 9 2 6 ) .
52.
A oken, S in g e r and D&vey, In d . E ng. Chem., 2 4 , 5 4 ,
33.
Mark and v o n S u s ic h , K o llo id
Z ., 4 6 ,
34.
H e r g s tc n b e r g , Z. K r i s t . , 6 9 ,
271,
35.
Gehman and F i e l d , J o u r . App.
P h y s ., 1 0 , 5 6 4 ,
36.
W hitby an d B a r n e s , i n D a v is and B la k e , "C hem istry and T ec h n o lo g y o f
11,
(1 9 2 8 ) .
(1 9 2 8 ) .
B ib b e r " , New Y ork, 1 9 3 7 .
(1 9 3 9 ) .
F o o tn o te , p . 3 1 .
37.
H ock, K o llo id Z . , 3 5 , 4 0 ,
38.
K r u ilo v , P h y s. Z. S o w je tu n io n , 8 , 1 3 6 ,
39.
T r i l l o t and, M otz, Compt. R e u d ., 1 9 8 , 2 1 4 7 ,
40.
(1 9 5 2 ) .
(1 9 2 4 ).
Z e r n ic k e and P r i n s , Z. P h y s ik , 4 1 , 1 8 4 ,
(1 9 3 5 ) .
(1 9 3 4 ) .
(1 9 2 7 ) .
41.
C la r k e , N a tu r e , 1 2 0 , 1 1 9 ,
(1 9 2 7 ).
42.
H au ser and R osbaud, K au tsch u k , 5 , 1 7 ,
45.
K a tz , T r a n s. F araday S o c . , 2 9 , 2 0 8 ,
44.
Sim ard and W arren, J . Am. Ghem. S o c . , 5 8 , 5 0 7 ,
45.
B u s s e , J . P h y s. Chem ., 3 6 , 2 8 6 2 ,
(1 9 2 7 ) .
(1 9 5 3 ) .
(193H ).
(1 9 o o ).
78
46.
Hook, J . Am. Chem. 3 o c . , 5 6 , 2 7 5 7 ,
(1 9 5 4 ) .
47.
Hermann and G e r n g r o s s , K a u tsch u k , 8 , 1 8 1 ,
48.
S h e c k lo c k , T r a n s. I n s t . Rubber I n d ., 3 , 558 and 5 8 0 ,
(1 9 5 2 ).
9 , 94,
(1935)
(1 9 5 5 ) .
49.
H a l l e r , K o llo id Z . , 5 6 , 2 5 7 ,
50.
Am. S o c . T e s t in g M a t e r ia ls , S ta n d a rd s on Rubber P r o d u c ts , O c t ., 1 9 3 5 .
51.
F e u c h t e r , K a u tsch u k , 5 , 1 4 9 ,
52.
Hock and B ostrom , K au tsch u k , 2 , 1 3 0 ,
53.
(1 9 3 1 ) .
(1 9 2 7 ) .
(1 9 2 6 ) .
O r n s t e in , Pym ers and Vouda, P r o c . Hoy. A cad. Amsterdam, 5 2 , 1 2 3 5 ,
( 1 9 2 9 ) ; O r n s te in , Wouda and ly m e r s , Idem.
54.
K undt, Ann. P h y s ik , 1 5 1 , 1 2 5 ,
(1 9 5 0 ) .
(1 8 7 4 ) .
55.
Von S c h e r r - T h o s s , Ann. P h y s ik , 6 , 2 7 0 , (1 8 7 9 )
56.
P u lx r ic h , Ann. P h y s ik , 1 4 , 1 7 7 ,
57.
33, 273,
B je r k e n , Ann. P h y s ik , 4 5 , 3 1 7 ,
(1 8 8 2 ) .
(1 8 9 1 ).
58.
S c h i l l e r , D is s e r t a t io n , L e ip z ig , 1911.
59.
K r o g er , K o llo id Z ., 4 5 , 5 2 ,
(1 9 2 8 ) .
60.
W ien er, P h y s. Z ., 5 , 5 3 2 ,
(1 9 0 4 ) .
61.
H owland, In d . E ng. Chem., 2 2 , 1 1 8 2 ,
62.
Van Gee 1 and I^ m e r s, Z. P h y s. Chem., 3 , 2 4 0 ,
63.
C u r t is and M cPherson, B ur. S ta n d a r d s , T ech . Paper no 2 9 9 , 6 9 8 ,
64.
M cPherson and C u n n in gs, B ur. S ta n d a rd s
65.
Gehman, Chem. R e v ., 2 6 , 2 0 4 ,
(1 9 3 0 ) .
(1 9 2 9 ) .
J . R esea rch , 14, 5 5 3 ,
(1 9 4 0 ) .
66.
B e k k e d a h l, J . R e se a r c h H a t. B ur. S ta n d a r d s , 1 5 , 4 1 1 ,
67.
T h i e s s e n an d K ir s c h ,
68.
Dow, J . Chem. P h y s ., 7 , 2 0 1 ,
69.
Lotmar and M eyer, M onatsh, 6 9 , 1 1 5 ,
70.
S a u t e r , Z. P h y s ik . Chem., 3 3 6 , 4 0 5 ,
H a tu r v v iss e n sc h a fte n , 2 6 , 5 8 7 ,
(1 9 3 9 ).
(1 9 3 6 ) .
(1 9 3 7 ).
(1 9 3 4 ).
(1 9 5 3 ) .
(1 9 2 5 ).
(1 9 3 5 ) .
71.
M orss, J . A.m. Chem. S o c . , 6 0 , 2 3 7 ,
(1 9 3 3 ) .
72.
E . P . H i l l e r , D i s s e r t a t i o n , P urdue,
73.
Woo, P h y s. R e v ., 4 1 , 2 1 ,
74.
J a u n c e y , x h y s . R e v ., 3 7 , 1 1 9 5 ,
75.
W e n tz e l, Z e i t s . f . P h y s ., 4 3 , 1 and 7 7 9 ,
76.
W a lle r , P h io . Mag,**. 5 0 , 2 8 9 ,
77.
Thomas, P r o c . Camb. P h i l . S o c . , 2 3 , 5 4 2 ,
78.
F erm i, Z e i t . f . P h y s ., 4 8 , 7 3 ,
79.
H a r t r e e , P r o c . Camb. P h i l . S o c . , 2 4 , 89 and 1 1 1 ,
80.
James a n d 3 r i n d l e y , P h i l . Mag. 1 2 , 1 0 4 ,
(1 9 3 6 ) .
(1 9 5 2 ).
(1 9 5 1 ) .
(1 9 2 7 ).
(1 9 2 5 ) .
(1 9 2 7 ) .
(1 9 2 8 ) .
Z e it. f . K r is t ., 78, 470,
(1 9 3 1 ) .
(1 9 3 1 ) .
81.
H e is e n b e r g , P h y s. Z e i t s . , 5 2 , 7 3 7 , ( 1 9 3 1 ) .
82.
3 e w ilo g u a , P h y s. Z e i t s . , 3 2 , 7 4 0 ,
83.
E h r e n f e s t , P r o c . Amsterdam A c a d ., 1 7 , 1 1 8 4 ,
84.
D eb ye, P h y s. Z e i t s . , 4 6 , 8 0 9 ,
85.
Z e m ic k e and
P r in s ,
Z e it. f .
86.
Z e m ic k e and
P r in s ,
Z e i t . f . P h y s .,
(1 9 3 1 ) .
See R e fe r e n c e 8 0 .
(1 9 2 5 ) .
(1 9 1 5 ).
P h y s .,
4 1 , 1 8 4 , (1 9 2 7 ) .
4 1 , 1 8 4 , (1927)
Z e i t . f . P h y s .,
87.
(1 9 2 8 ) .
56, 617,
(1929)
A ppendix IV, Comptonand A l l i s o n , "X -rays in
T heory and E x p erim en t" , New York, 1 9 5 5 .
88.
G. G. D a n ie ls o n , D i s s e r t a t i o n , P urdue, 1 9 4 0 .
89.
E . P . H i l l e r , R ev. 3 c i .
90.
H. J . Y e a r ia n , R ev. S c i . I n s t . , 4 , 4 0 7 ,
91.
T r e lo a r , T r a n s. Ifer. S o c . , 8 4 , 3 7 ,
92.
S t e w a r t , R ev. Mod. P h y s .,
93.
S t o r k , J . Am. Chem. S o c . , 6 0 , 1 7 5 3 ,
94.
F u l l e r and E r ic k s o n , J . Am. Chem. S o c . , 5 9 , 3 4 4 ,
I n s t ., 4 , 379,
116,
(1 9 3 3 ) .
(1 9 3 5 ) .
(1 9 4 1 ) .
(1 9 5 0 ) .
(1 9 5 8 ) .
(1 9 3 7 ) .
VITA
C la r e n c e M erton P a r s h a l l , born A p r il 1 9 , 1 9 1 4 , a t W ash in gton , Pennн
s y lv a n ia ; e a r l y s c h o o lin g a t C l a y s v i l l e , P e n n sy lv a n ia ; g r a d u a te d from
C l a y s v i l l e H igh S c h o o l in 1931; m a t r ic u la t e d a t M kshington and J e f f e r s o n
C o lle g e in 1931 and r e c e iv e d B .S . d eg ree in 1935; r e c e iv e d M .S. d e g r ee
i n 1937 from W ashihgt on and J e f f e r s o n ; a s s i s t a n t in P h y s ic s a t Purdue
U n i v e r s i t y from Septem ber 1937 up t o the p r e se n t tim e
(June 1 9 4 1 ) .
rom
In t h i s t a b l e i ob
i s the v a lu e
i n a r b i t r a r y s c a l e u n i t s , a s o u t 3 in e a from t h e b la c k e n i n g
c u r v e ; F i s th e p o l a r i z a t i o n f a c t o r and A i s th e m u l t i p l y i n g f a c t o r f o r
th e a b so r p tio n c o r r e c t io n ,
curve i n s r o i t r a r .
u n its.
loo*.*,. i s t h e c o r r e c t e d r e l a t i v e i n t e n s i t y
The n e tn o d by w hicn t h i s c u r v e can be p u t on a n
S a b le 5 .
C o r r e c t e d I n t e n s i t y Curve f o r Smoked S h e e t
sin й
20
0 ░
2 .5
5
7 .5
10
1 2 .5
15
1 7 .5
20
2 2 .5
25
2 7 .5
30
3 2 .5
35
3 7 .5
40
4 2 .5
45
4 7 .5
50
5 2 .5
55
5 7 .5
60
6 2 .5
65
6 7 .5
70
7 2 .5
75
7 7 .5
80
F i r s t Peak
8 ░ \2 5 *
]
^ob
P
k
0
.0 3 0 8
.0 6 1 6
.0 9 2 4
.1 2 3 1
.1 5 3 8
.1 8 4 4
.2 1 4 9
.2 4 5 3
.2 7 5 6
.3 0 5 8
.3 3 5 8
.3 6 5 7
.3 9 5 4
.4 2 4 9
.4 5 4 1
.4 8 3 2
.5 1 2 1
.5 4 0 7
.5 6 9 0
.5 9 7 1
.6 2 4 9
.6 5 2 4
.6 7 9 6
.7 0 6 4
.7 3 2 9
.7 5 9 1
.7 8 4 9
.8 1 0 4
.8 3 5 4
.8 6 0 1
.8 8 4 3
.9 0 8 2
0
5 .2 7
1 4 .1 7
3 4 .9 4
2 8 .9 4
1 4 .9 0
9 .5 2
9 .0 5
8 .3 3
9 .7 9
5 .9 7
5 .5 5
5 .5 0
5 .6 2
5 .5 8
5 .2 0
4 .7 0
4 .3 4
4 .0 5
3 .8 9
3 .3 4
3 .8 2
3 .8 0
3 .7 3
3 .6 1
3 .4 8
3 .3 5
3 .2 2
3 .1 0
2 .9 9
2 .8 7
2 .7 9
2 .6 8
.9 6 9
.9 6 6
.9 6 2
.9 5 6
.9 4 8
.9 3 9
.9 2 8
.9 1 5
.9 0 1
.8 8 6
.8 7 0
.8 5 8
.8 3 4
.8 1 6
.7 9 6
.7 7 6
.7 5 5
.7 3 5
.7 1 5
.6 9 4
.6 7 4
.6 5 5
.6 3 6
.6 1 8
- .6 0 0
.584
.5 6 9
.555
.5 4 3
.5 3 2
.5 2 2
.5 1 6
1 .0 0 5 0
1 .0 0 4 0
1 .0 0 3 1
1 .0 0 2 4
1 .0 0 1 8
1 .0 0 1 3
1 .0 0 0 9
1 .0 0 0 6
1 .0 0 0 3
1 .0 0 0 2
1 .0 0 0 1
1 .0 0 0 0
1 .0 0 0 1
1 .0 0 0 2
1 .0 0 0 3
1 .0 0 0 6
1.00 09 1 .0 0 1 3
1 .0 0 1 8
1 .0 0 2 4
1 .0 0 3 1
1 .0 0 4 0
1 .0 0 5 0
1 .0 0 6 1
1 .0 0 7 6
1 .0 0 9 4
1 .0 1 1 5
1 .0 1 4 1
1 .0 1 7 1
1 .0 2 0 5
1 .0 2 4 5
1 .0 2 9 2
*oorr
0
5 .4 7
1 4 .7 3
3 6 .4 3
3 0 .3 4
1 5 .7 5
1 0 .1 5
9 .7 6
9 .1 1
7 .5 4
6 .7 4
6 .3 8
6 .4 1
6 .7 4
6 .8 4
6 .5 3
6 .0 6
5 .7 6
5 .5 2
5 .4 5
5 .5 4
5 .6 9
5 .8 2
5 .8 9
5 .8 8
5 .8 4
5 .7 9
5 .7 3
5 .6 7
5 .6 0
5 .5 0
5 .4 7
5 .3 4
.1 0 4 1
3 8 .5 0
.9 6 0
1 .0 0 2 8
4 0 .2 1
49
a b s o l u t e b a s i s by m a tch in g i t
t o th e t h e o r e t i c a l c o h e r e n t and in c o h e r e n t
s c a t t e r i n g c u r v e s w i l l be t a k e n up i n a l a t e r s e c t i o n .
T h e o r e t i c a l C oherent a n d I n c o h e r e n t S c a t t e r i n g .
E q u a tio n (. 3 . 2 ) g i v e s th e
e x p r e s s i o n l o r th e c o n e r e n t s c a t t e r i n g and e q u a t io n ( 5 . 3 ) e x p r e s s e s th e i n н
coherent s c a t t e r in g .
S i n c e we a r e c o n s i d e r i n g o n ly r e l a t i v e i n t e n s i t i e s
we may u s e s im p ly th e e x p r e s s i o n
X
= ( f
X -=
l3 -2 0 )
(2-21'
(Z-г-fC )
and w r i t e f o r th e e x p e r im e n t a l i n t e n s i t y
r r ? T aoht.
(3 . 2 2 )
where m i s th e ??matching f a c t o r H w h icn we u s e t o put t h e c o r r e c t e d o b s e r v e d
i n t e n s i t y curve on the same s c a l e a s th e c o h e r e n t and in c o h e r e n t s c a t t e r i n g .
The v a l u e s o f ^ pn and
w ere ta x e n from Compton and A l l i s o n ,
??X-rays i n T heory and E x p e r im e n t?*, p a g e s 781 and 7 8 2 .
F o r t h e s c a t t e r i n g from r u b b e r , CgHg, th e c o h e r e n t s c a t t e r i n g of t h e
hyd rogen may be n e g l e c t e d a s compared w it n t h a t o f c a rb o n .
t h e in c o h e r e n t s c a t t e r i n g t h i s cannot be d o n e .
However, f o r
In o r d e r t o g e t e q u i v a l e n t
s c a t t e r i n g ' p e r a to m , th e t o t a l in c o h e r e n t s c a t t e r i n g was ta k e n a s t h a t due
t o t h e carb on p l u s e i g h t - f i f t h s
sc a tte r in g i s
of t h a t due t o t h e n y d ro g en .
th en th e sum o f t h e s e tw o, n a m ely , I c
+
1
^
The t o t a l
.
The v a l u e s o f tne t h e o r e t i c a l c o h e r e n t and i n c o h e r e n t s c a t t e r i n g f o r
C5 H8 a r e g i v e n in T able
6
.
Ajatchinr: P h c to r -H e th o d s ana D i f f i c u l t i e s .
P ro b ab ly th e g r e a t e s t e r r o r
in the d e t e r m i n a t i o n o f d e n s i t y d i s t r i b u t i o n s i s in t r o a u c e d when one
a t t e m p t s t o p l a c e th e c o r r e c t e d e x p e r im e n ta l i n t e n s i t y curve on an a b s o l u t e
b a s i s by m a tch in g i t t o t h e t h e o r e t i c a l s c a t t e r i n g .
T his i s e s p e c i a l l y
49
T a b le 6 .
C oherent and I n c o h e r e n t S c a t t e r i n g For Btibber, C5 H8
sinй
a
A
г
0
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1 .0
6 .0
4 .6
3 .0
2 .2
1 .9
1 .7
1 .6
1 .4
1 .3
1 .2
1 .0
/f
4.
-T.
3 6 .0 0 3 6 .0 0
2 1 .1 6 2 1 .1 6
9 .0 0 9 .0 0
4 .8 4 4 .8 4
3 .6 1 3 .6 1
2 .8 9 2 .8 9
2 .5 6 2 .5 6
1 .9 6 1 .9 6
1 .6 9 1 .6 9
1 .4 4 1 .4 4
1 .0 0 1 .0 0
6 .0
4 .0
2 .7
1 .8
1 .5
1 .3
1 .0
0 .8
0 .7
0 .6
0 .5
1 .0 0
0 .6 6
0 .2 3
0 .0 6
0 .0 2
0
0
0
0
0
0
0 .0
2 .0
3 .3
4 .2
4 .5
4 .7
5 .0
5 .2
5 .3
5 .4
5 .5
0 .0 0
0 .3 4
0 .7 7
0 .9 4
0 .9 8
1 .0 0
1 .0 0
1 .0 0
1 .0 0
1 .0 0
1 .0 0
0 .0 0
0 .5 4
1 .2 3
1 .5 0
1 .5 7
1 .6 0
1 .6 0
1 .6 0
1 .6 0
1 .6 0
1 .6 0
0 .0 0
2 .5 4
4 .5 3
5 .7 0
6 .0 7
6 .3 0
6 .6 0
6 . 80
6 .9 0
7 .0 0
7 .1 0
0 .0 0
2 .5 4
4 .5 3
5 .7 0
6 .0 7
6 .3 0
6 .6 0
6 .8 0
6 .9 0
7 .0 0
7 .1 0
3 6 .0 0
2 3 .7 0
1 3 .5 3
1 0 .5 4
9 .6 8
9 .1 9
9 .1 6
8 .7 6
8 .5 9
8 .4 4
8 .1 0
50
t r u e when t h e s c a t t e r i n g x a a t e r ia l i s composed ox atom s w it h s m a ll a to m io
number s i n c e f o r t h e s e s t o m s t h e c o h e r e n t s c a t t e r i n g a t l a r g e s c a t t e r i n g
a n g le s i s
s m a ll compared to t h e i n c o h e r e n t s c a t t e r i n g .
I t is neoesaary?
t h a t t h i s m a tc h in g be done i n o r d e r t o e x p r e s s th e e x p e r i m e n t a l l y o b se r v e d
i n t e n s i t y i n th e same u n i t s w h ic h a r e u s e d f o r t h e c o h e r e n t a n d in c o h e r e n t
sc a tte r in g , i . e .
i n e l e c t r o n u n i t s p e r a to m .
c ie n t ly la r g e v a lu e s o f
in d e p e n d e n t o f e a c h o t h e r .
I t i s assum ed t h a t a t s u f f i н
| & t h e c o h e r e n t a n d in c o h e r e n t s c a t t e r i n g a r e
C o n s e q u e n t ly , t h e i r sum s h o u ld De e q u a l t o th e
t o t a l o b s e r v e d s c a t t e r i n g . in t n i s r e g i o n .
T h is would i n d i c a t e a method o f
m atch in g ? make th e e x p e r i m e n t a l l y o b s e r v e d i n t e n s i t y e q u a l t o th e sum o f
trie c o h e r e n t en d in c o h e r e n t s c a t t e r i n g a t l a r g e v a l u e s o f S1^ '
-f-Q OI-I- ~ Z ,
i.e .
le t
^L
T h is ap p ea l's t o oe a p e r f e c t 1;.- s t r a i g h t f o r w a r d p r o c ed u r e l i m i t e d o n ly
by th e a c c u r a c y o f t h e a b o v e a s s u m p t i o n .
o f u n ce r ta in ty .
A c tu a lly i t e n t a i l s a g rea t deal
One can n e v ^ r be s u r e J u s t how l a r g e th e v a lu e o f
?
must be in o r d e r t h a t th e a b o v e a s s u m p tio n s h a l l be v a l i d , nor d o es one
know how mu Oil o f the o b s e r v e d s c a t t e r i n g i s a c c i d e n t a l s c a t t e r i n g ,
how much of i t
i.e .
i s due to s c a t t e r i n g from a i r and from p a r t s of t h e camera
and s p e cim en h o l d e r .
A c c i d e n t a l s c a t t e r i n g a n d r e s u l t a n t background can oe retraced t o a comн
p a r a t i v e l y i n a p p r e c i a b l e q u a n t i t y by the c o r r e c t e x p e r im e n t a l p r o c e d u r e .
The
u s e o f a n e v a c u a t e d camera w it ., a s m a l l , w e ir c o l l i m a t e d , bean of monochromн
a t i c r a d ia tio n w ill u s u a lly elim in a te t h is d i f f i c u l t y .
When a f l a t sam ple i s u se u t h e r e i s
a maximum v a lu e o f
o b se rv a b le,
t h i s v a l u e b e i n g d e te r m in e d by th e p o i n t a t w hich t h e f l a t sam ple and h o ld e r
p ro d u ces a c u t - o f f in th e s c a t t e r e d r a d i a t i o n .
T nis maximum v a lu e can be i n н
c r e a s e d by s e t t i n g th e sam p le a t an a n g l e t o th e i n c i d e n t o ea u .
However,
51
e v e n though i t
i s g e o m e trica ily p o ssib le
t h e s e l a r g e r S.^~S. г
it
to o b s e r v e th e s c a t t e r i n g a t
v a l u e s , t h e i n t e n s i t y i n t h i s r e g i o n i s so weak t h a t
i s d i f f i c u l t t o d e c i d e ^ u st how f a r ones o b s e r v a t i o n s a r e t r u s t w o r t h y .
The c h o i c e o f a m atch ing f a c t o r w i l l h av e a n a r k e d e f f e c t on t h e r e н
s u l t s o f th e a n a l y s i s .
T h is comes a b o u t i n th e f o l l o w i n g w a y.
In t h e
d e t e r m i n a t i o n o f J*(r) we h a v e to e v a l u a t e th e i n t e g r a l
/fe i(s)
sin (sr )d s, ,
s in o
where s *
i(s)
conies d i r e c t l y from the r a t i o
of e x p e r im e n t a l to c o h e r e n t
sc a tte r in g .
T h u s, b e c a u s e of th e i n c r e a s e i n s w i t h a n g l e , any s m a ll i r r e g u l a r itie s
s in d
i n t h e e x p e r i m e n t a l s c a t t e r i n g cu rve a t l a r g e v a l u e s o f ?
gi ve
/J
c o n t r i b u t i o n s t o th e s i ( s )
c u r v e , and th u s to th e v a l u e of th e a b o v e i n н
t e g r a l , w h ic h a r e com parable w itn th e a r e a s due to w e l l d e f i n e d r i n g s .
In th e c a s e o f r u o o e r w here we a r e d e a lin g w i t h c h a i n - l i k e m o l e c u l e s
we knew t h a t we w i l l h a v e two f i r s t n e ig h b o r s a o o u t any one atom .
Hence
we c o u ld u s e t h i s c r i t e r i o n t o a s c e r t a i n w h eth er or not the f i n a l a n a l y s i s
is co rrect.
e ssita te
The o b j e c t i o n t o t h i s method i s t h a t i t would p r o b a b ly n e c н
s e v e r a l t r i a l a n a l y s e s o e f o r e t h e c o r r e c t one was o b t a i n e d .
liven
th o u gh th e tim e and la b o r i n v o l v e d i n m skin g an a n a l y s i s have b e e n g r e a t l y
s n o r t e n e d by th e d e v e lo p m e n ts o f D a n ie ls o n and L a n c z o s , t h e y a r e s t i l l t o o
g r e a t t o maxe su c h a ruetnod of n o t c h in g V er y p r a c t i c a b l e .
E U rth er, one i s
n o t a lw a y s d e a l i n g w ith c n a in m o l e c u l e s and. so a more r i g o r o u s u e tn o d o f
m a tch in g i s t o be d e s i r e d .
D a n i e l s o n 93 h a s u s e a the method of l e a s t s q u a r e s i n th e range o f l a r g e
v a l u e s of
t o o b t a i n a .o a tc n in g f a c t o r .
?7
q u ite s a tis fa c to r y r e s u l t s .
The method a p p e a r s t o g i v e
52
One s h o u ld be s o l e
t o assume t h a t t h e t o t a i r a d i a t i o n s c a t t e r e d i s
e q u a l to the sum o f th e t o t s x c o h e r e n t a n d in c o h e r e n t s c a t t e r i n g .
would mean t h a t th e t o t a l area u n d er the i ( s )
T h is
curve s h o u ld oe z e r o .
Howн
e v e r , we do n o t know ^ust what s c a t t e r i n g we have in the forw ard d i r e c t i o n
and a s a r e s u l t t h i s i d e a oannot be r i g o r o u s l y a p p l i e d .
T. E. Ifeyer h a s s u g g e s t e d t h a t a t r ? 0 , j-* (r ) s h o u ld be z e r o .
le a d s to th e e x p r essio n
T h is
-00
= -*77'*^ S'
w h ich c o u ld be u s e d a s a m a tch in g c r i t e r i o n .
sist
o f a t r i a l and e r r o r p r o c e d u r e .
seems to
T h is method w ould a l s o conн
The f a c t o r o b t a in e d by t h i s method
oe c o m p a t ib le w it h t h a t o b t a in e d by the methods a l r e a d y m e n tio n e d .
I t s c h i e f d i s a d v a n t a g e a r i s e s from th e f a c t t h a t t h e v a lu e o f f*
is very
s m a ll ( a p p . - .Ofi-) and h e n c e t h e i n t e g r a l must be p e r f e c t l y a c c u r a t e b e f o r e
r
a r e l i a o l e m a tc h in g can oe made.
A match o f t n e c u r v e s iuay g i v e p l a u s i b l e
r e s u l t s i n an a n a l y s i s and s t i l l have the a b o v e c o n d i t i o n f a r from s a t i s н
fie d .
i a n c z o s h as s u g g e s t e d t h e f a l l o w i n g method o f Hatching.
7/e w r i t e ,
as u su a l,
S in c e I
is g iv e n
St-(s) =
An a n a l y s i s
, we c a n a l s o w r i t e t h i s a s
oy
/ \ ? , ^ 3- C.ot-y- 7 ? hrS
5
i s made fo r
5
?
a \K*? * 3r
7 - '
~/ J
n i n su c h a .ray t h a t tn e l a s t few f o u r i e r c o e f f i c i e n t s
12) a r e made a s s m a ll a s p o s s i o l e .
squares.
?
^CLe th e n c h o o s e s
(sa y th e l a s t 10 or
T h is .ray be done by the method o f l e a s t
The j u s t i f i c a t i o n f o r doin g t n i s l i e s i n th e f a c t t h a t th e v a l u e s
o f r c o r r e s p o n d in g t o t h e l a s t few c o e f f i c i e n t s a r e o f su ch m agnitude
t h a t th e d e n s i t y d i s t r i b u t i o n
s h o u ld be a p p r o a c h in g th e a v e r a g e
d e n s i t y d i s t r i b u t i o n tJTT/i. f%
and, h ence,
the d e v i a t i o n s from a v e r a g e
d e n s i t y s h o u ld be s m a l l .
The a p p l i c a t i o n of t h i s method to t h e a n a l y s i s o f smoixed s h e e t d id not
biv e s a t is f a c t o r y r e s u l t s .
E. P . M i l l e r h a s p o i n t e d out t h a t one s h o u ld a t t e m p t t o m in im ize th e
?
?
o
J.
c o e x f x c i e n t s m t h e range o f r from 0 A
o
to 1 A
n o t e x p e c t a n y n e ig h b o r s w i t h i n t h i s d i s t a n c e .
s i n c e we w ould c e r t a i n l y
Doing t h i s
fo r th e a n a l y s i s
m en tion ed a b o v e g a v e r e s u l t s w hich were i n good agreem ent w i t h t n o s e obн
t a i n e d 7/hen th e m atch in g f a c t o r was d e te r m in e d by m a tc h in g a t l a r g e v a l u e s
, sin &
01
?
?
For t h e a n a l y s e s r e p o r t e d i n t h i s worm t h e m atch in g f e e t or was d e t e r н
mined by is. t e llin g a r e a s under th e e x p e r im e n ta l curve and th e c u r v e r e p r e s ,.
e n t i n g tn e
,
sum 1 c +
Ip
. . .
sin Q
~
,
sin Q
m t n e r a n g e xrom ? ? - 0 . 2 0 t o ?^----- = 0 . 6 5 .
T h is gav e q u i t e r e a s o n a b l e r e s u l t s and i n a d d i t i o n was a m ethod w h ic h was
c o n s i s t e n t from p i c t u r e t o p i c t u r e .
D e s p i t e th e f a c t t h a t a l l t h e methods m en tio n e d above sound r e a s o n н
a b le and c a n be a p p l i e d , one i s
s t i l l u n a b le t o g i v e a d e f i n i t e s ta te m e n t
a s t o "the** c o r r e c t p r o c e d u r e t o be f o l l o w e d i n o b t a i n i n g a m a tch in g f a c t o r .
E v a lu a t i o n o f s i t s ) and A n a l y s i s fo r Smoxed S h e e t .
Curve A i n F ig u r e 17
shows t h e e x p e r im e n ta l i n t e n s i t y cuz-ve, c o r r e c t e d f o r p o l a r i z a t i o n a n d a b s in d
s o r p t i o n ^ p l o t t e d a s a f u n c t i o n of ? ? .
In th e same f i g u r e , cu rve 3 i s
th e c o h e r e n t s c a t t e r i n g , curve C i s t h e in c o h e r e n t s c a t t e r i n g , and curve D
r e p r e s e n t s t h e sum o f c u r v e s 3 and C.
From a com parison o f a r e a s under
c u r v e s A and D i n the r e g i o n from ?
??*г- - - 0 . 2 t o
/I
fa cto r is
found t o be 1 . 5 0 .
f
0 . 6 5 th e m atch in g
n
U sin g t h i s v a l u e tn e matcheu e x p e r im e n t a l
54
I
\_
F ig u r e 1 7 .
curve E i s
at
o b ta in e d .
s 0 .1 0 4 0 .
From t n i s
curve we s e e t h a t t h e f i r s t maximum o c c u r s
The seco n d and t h i r d maxima come a t 0 .2 1 6 0 and 0 .4 2 2 0
r e sp e c tiv e ly .
In t h i s
case i t i s
assumeu t h a t the c u r v e s raatca e x a c t l y from t h e
p o i n t 5 ^ t ^ ? 0 .6 6 5 0 t o i n f i n i t y , s i n c e the e x p e r im e n t a l c u r v e cannot a c c u r a t e l y be o b s e r v e d beyond t h i s p o i n t .
must b e made i f th e s i ( s )
The
T h is a s s u m p tio n c o n c e r n in g the c u r v e s
curve i s t o h a v e a f i n i t e r a n g e .
curve i ( s ) i s o b t a i n e d from c u r v e s E, B, and 0 by
=
7? R
~G' ? - 1 .
eq u a tio n
i(s)
w hich i s
tn e cu rv e t o be a n a l y z e d .
M u l t i p l i c a t i
Документ
Категория
Без категории
Просмотров
2
Размер файла
3 834 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа