12
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Neutron Studies of Perfluorosulfonated Polymer Structures
1
M. PINERI, R. DUPLESSIX, and F. VOLINO Equipe Physico-ChimieMoléculaire,Section de Physique du Solide, Département de Recherche Fondamentale, Centre d'EtudesNucléairesde Grenoble, 85 X, 38041 Grenoble Cedex, France X-ray and e l e c t r o n microscopy have been widely used to provide d i r e c t i n f o r m a t i o n on the s t r u c t u r e of polymers. The necess a r y c o n t r a s t i s given by d i f f e r e n c e s i n e l e c t r o n i c a l d e n s i t y . X-ray diffraction i s the necessary technique f o r small molecule c r y s t a l l o g r a p h y and the s c a t t e r i n g by an object i n s o l u t i o n i s a l s o used as a source of s t r u c t u r a l i n f o r m a t i o n . The small angle s c a t t e r i n g o r i g i n a t e s from the existence i n s i d e the m a t e r i a l of domains whose s i z e i s g e n e r a l l y the r a d i a t i o n wavelength (1 - 5). A model of s t r u c t u r e has been developped from e l e c t r o n microscopy and X-ray studies i n Nafions (6). No b a s i c d i f f e r e n c e e x i s t s between X-ray and neutron techniques. Nuclear i n t e r a c t i o n s of neutrons with matter are c h a r a c t e r i z e d by the coherent s c a t t e r i n g length and the corresponding values f o r H and D are very d i f f e r e n t Because of the d i f f e r e n t o r i g i n s of the c o n t r a s t , X-ray and neutron small angle s c a t t e r i n g techniques are complementary.
I n t e r a c t i o n s of neutrons w i t h matter P r o p e r t i e s of the n e u t r o n . The f r e e neutron i s an e l e mentary p a r t i c l e w i t h z e r o charge and s p i n 1/2, l i b e r a t e d f o r example d u r i n g the process of f i s s i o n of a heavy n u c l e u s . In a n u c l e a r r e a c t o r , the neutrons are t h e r m a l i z e d by the atoms of the moderator y i e l d i n g a M a x w e l l i a n d i s t r i b u t i o n of v e l o c i t i e s v peaked at some v such t h a t the average ( k i n e t i c ) energy E i s
E
1
1 - - r
- 2
\
v
3 - - r
V
Current address: C.R.M., 6 rue de Boussingault, 67083 Strasbourg, France
0097-6156/82/0180-0249$08.50/ 0 ©
1982 American Chemical Society
250
PERFLUORINATED IONOMER
MEMBRANES
where m i s the mass of the neutron. Neutrons can a l s o be considered as plane waves of wave number lc or wavelength X = 2Tr/k. The r e l a t i o n s h i p s between p a r t i c l e and wave aspects are : 0
0
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2m n and -K k V = For thermal neutrons (T = 300K), we have E = 26 meV and X = 1.8 A. I t i s important t o note that these v a l u e s are of the same order of magnitude as the i n t e r m o l e c u l a r energies and molecular dimensions, r e s p e c t i v e l y . Neutron-nucleus i n t e r a c t i o n . A neutron i n t e r a c t s w i t h a nucleus v i a n u c l e a r and magnetic f o r c e s . For the n u c l e a r p a r t , s i n c e n u c l e a r i n t e r a c t i o n s are very short range compared t o the(thermal) neutron wavelength, i t can be shown that the i n t e r a c t i o n p o t e n t i a l between a neutron l o c a t e d at r and a nucleus i l o c a t e d at r . can be w r i t t e n as V (
H
) =
-IT—
b
6(
i H
" *i>
n In t h i s e x p r e s s i o n (the s o - c a l l e d Fermi p s e u d o - p o t e n t i a l ) , the s c a t t e r i n g l e n g t h b. c h a r a c t e r i z e s the i n t e r a c t i o n and i s i n d e pendent of neutron energy, b. can be p o s i t i v e or n e g a t i v e according to the a t t r a c t i v e or r e p u l s i v e nature of the i n t e r a c t i o n The t h e o r i c a l c a l c u l a t i o n of b. i s very d i f f i c u l t and i n p r a c t i c e i t i s determined e x p e r i m e n t a l l y . Concerning the magnetic i n t e r a c t i o n , the neutron i n t e r a c t s w i t h the spins v i a the d i p o l e d i p o l e c o u p l i n g . For diamagnetic systems, i t i s always n e g l i g i b l e compared to the n u c l e a r i n t e r a c t i o n and w i l l be considered i n the following. Coherent and incoherent s c a t t e r i n g lengths and c r o s s - s e c t i o n s . Consider an assembly of a given atomic species i , w i t h many i s o t o p e s possessing a n u c l e a r s p i n . The s c a t t e r i n g l e n g t h b. w i l l change from one atom to another, s i n c e the i n t e r a c t i o n depends on the nature of the nucleus and on the t o t a l s p i n s t a t e of the nucleus neutron system. The average < b.> of b. over a l l the i s o t o p e s and s p i n s t a t e s i s c a l l e d the coherent s c a t t e r i n g l e n g t h . We thus have =
< b.> l
12.
Neutron Studies
PINERI E T A L .
b.
i n c o h
1
= [< b .
2
>-
]
1 / 2
00
1
l n c o
From these d e f i n i t i o n s , i t i s c l e a r that b * and b ^ b changed merely by modifying the r e l a t i v e concentration of the v a r i o u s isotopes. This f a c t i s of great p r a c t i c a l importance i n neutron experiments ( i s o t o p i c s u b s t i t u t i o n ) . The coherent and incoherent s c a t t e r i n g c r o s s - s e c t i o n are defined by
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c a n
a. l
coh
. coh 2 = 47T(b^ )
incoh
, incotu2 = 4iTCb. ) l
e
N
In the f o l l o w i n g t a b l e ^ ^ r e J i s t e d the values of these q u a n t i t i e s i n barns (1 barn = 1 0 cm ) f o r a few common atoms. Table I
atoms
spin
incoh
coh a
a
0
4.2
-
0
5.5
-
1
11.6
D
1
5.6
H
1 2
1 .76
1 6
o
I 2
c
Small angle neutron
^
0.3 2.0 79.7
s c a t t e r i n g experiment.
Information about the s t r u c t u r e of a m a t e r i a l i s obtained from small angle s c a t t e r i n g by analyzing the coherent scattered i n t e n s i t y which i s given by
252
PERFLUORINATED IONOMER M E M B R A N E S
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I (Q) =
< E E d d i j i j
exp [-iQ.(r - r ) ] > 1 1
where Q i s the s c a t t e r i n g v e c t o r whose magniture i s given by 4Trsin ~ 0/A, where 9 i s h a l f the s c a t t e r i n g angle^and X i s the wavelength of the i n c i d e n t r a d i a t i o n . The v e c t o r r . i s drawn from an a r b i t r a r y o r i g i n to a p o i n t which possesses a coherent s c a t t e r i n g f a c t o r d.. For a system w i t h two s c a t t e r i n g components the previous equation can be s i m p l i f i e d t o g i v e HQ) - C(dj - d ) S(Q) 2
2
where S(Q) = < £
I
exp [ i Q . ( r
i
- r.)]>
where dj and d^ denote the s c a t t e r i n g f a c t o r s of r e g i o n 1 and 2, C i s a constant, and < > denotes an e q u i l i b r i u m average. For small-angle neutron s c a t t e r i n g (SANS), the s c a t t e r i n g f a c t o r i s p r o p o r t i o n a l to the coherent neutron s c a t t e r i n g - l e n g t h d e n s i t y 6 , g i v i n g the r e s u l t that TABLE I I
S c a t t e r i n g parameters of Nafion-Water system
i
Group
(10
/
b
e
o o
cm A
)
3
(mole el/cm )
d
3
(g/cm )
3.84
0.91
1.9
4.45
1.05
2.2
RS0 H
2.5-3.7
0.5-0.75
1-1 .5
RS0 Na
2.7-3.9
0.53-0.8
1.1-1 .6
CF^ amorphous CF^ c r y s t a l l i n e 3
3
H0
-0.56
0.55
1
D0
6.46
0.55
1.1
2
2
12.
Neutron
PINERI E T A L .
(dj - d )
253
Studies
= (Bj - e ) coh coh
2
2
2
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The coherent s c a t t e r i n g length d e n s i t y i s defined by
6
coh
P
-
Z
V K
7
Z
Y K
K
K
where P i s the mass d e n s i t y , and n i s the number of atoms w i t h coherent s c a t t e r i n g length b and mass m. For SAXS the c o n t r a s t i s determined by the d i f f e r e n c e i n e l e c t r o n d e n s i t y
2
(d, - d ) = ( a j - a* )
2
2
Values of coherent neutron s c a t t e r i n g length d e n s i t i e s and e l e c t r o n d e n s i t i e s r e l e v a n t t o the Nafion-water system are given i n Table I I . Values f o r CF^ ar^e given corresponding t o mass d e n s i t i e s of 2.2 and 1.9 g/cm f o r c r y s t a l l i n e and amorphous m a t e r i a l s , r e s p e c t i v e l y . An e x c e l l e n t SANS c o n t r a s t e x i s t s between e i t h e r amorphous or c r y s t a l l i n e C F and l^O. A d i f f e r e n c e of 4 10~14cm.X~3 i s g e n e r a l l y considered good enough t o g i v e a reasonable s i g n a l . The d i f f e r e n c e between the s i d e groups and the CF^ backbone i s l e s s w e l l defined owing t o u n c e r t a i n t i e s i n the mass d e n s i t i e s but i s c e r t a i n l y much s m a l l . Thus the SANS technique i s much l e s s s e n s i t i v e t o aggregation of the i o n i c groups than i t i s t o aggregation of water molecules. A s i m i l a r s i t u a t i o n e x i s t s f o r SAXS w i t h r e l a t i v e l y l a r g e e l e c t r o n d e n s i t y d i f f e r e n c e between C F and water and a smaller c o n t r a s t between CF^ and the i o n i c side groups. Information about both the s i z e and the geometry of the s c a t t e r i n g p a r t i c l e s can be obtained from d i f f e r e n t s c a t t e r i n g domains. In the G u i n i e r range w i t h QR < < 1 the s c a t t e r i n g f u n c t i o n can be w r i t t e n 2
2
2 2 S(Q)
^ 1 -
where R i s the r a d i u s of g y r a t i o n of the d i f f u s i n g o b j e c t . I n the intermediate range the s c a t t e r i n g f u n c t i o n can be w r i t t e n
S(Q)
