1316
M . G R A Z I A G I R I et al.50
t o c o n d u c t i v i t y m a x i m a i n t h e cr((j)) c u r v e s a t Constant O/S r a t i o s ] a n d a w e l l d e f i n e d d r o p l e t d i s p e r s i o n ( a t W/S > 1 1 ) . T h e d i e l e c t r i c s t u d y a t 25 ° C (see T a b l e I ) s h o w s t h e o c c u r r e n c e o f d y n a m i c p e r c o l a t i o n f o r <j> = 0 . 2 -0.46 a n d o f s t a t i c p e r c o l a t i o n a t (f> = 0.5. F r o m t h e cr(<f>) c u r v e s o f [20], a l o n g t h e W/S = 1 1 l i n e , t h e o v a l u e a t 4> = 0.5 is t h e c l o s e s t t o t h e c o n d u c t i v i t y m a x i m u m . I t is w o r t h n o t i n g t h a t s t r u c t u r a l i n v e s t i g a t i o n m u s t b e p e r f o r m e d t o t e s t t h e a b o v e h y p o t h e s i s t h r o u g h o u t t h e t h e r -m a l r a n g e i n w h i c h t h e s y s t e -m is -m o n o p h a s i c . H o w e v e r , t h e i n v e s t i g a t i o n o f t h i s p a p e r h a s c l a r i f i e d t h a t p e r c o -l a t i o n o c c u r s i n P F P E m i c r o e m u -l s i o n s , as d e m o n s t r a t e d b y t h e o c c u r r e n c e o f l a r g e t h e r m a l r a n g e s i n w h i c h p e r -c o l a t i v e l a w s a r e d e t e -c t e d ( t h e r a n g e s o f F i g . 1 e x -c e p t t w o p o i n t s a t t h e l o w e s t t e m p e r a t u r e f o r <j) — 0 . 5 0 1 , one p o i n t a t t h e h i g h e s t t e m p e r a t u r e f o r <f> > 0 . 2 0 5 , a n d o b -v i o u s l y t h e r e g i o n s i n t h e p r o x i m i t y o f t h e t h r e s h o l d ) . O n t h e b a s i s o f t h e a b o v e f ì n d i n g s , d r o p l e t s s e e m t o e x -i s t t h r o u g h o u t l a r g e <f> a n d T r a n g e s -i n t h e c o m p o s -i t -i o n a n d t h e r m a l i n t e r v a l i n w h i c h d y n a m i c p e r c o l a t i o n o c c u r s b o t h b e l o w a n d a b o v e t h r e s h o l d . T h e e x p o n e n t s p r o v i d e s u p p o r t t h a t a t r a n s i t i o n f r o m d y n a m i c t o s t a t i c p e r c o -l a t i o n o c c u r s a t &-lt;f) &-lt; 0-36 a n d cf> > 0.46. A s a m a t t e r o f f a c t , i n t h e r e g i o n a t h i g h s u r f a c t a n t c o n c e n t r a t i o n , a f u r t h e r i n c r e a s e o f d i s p e r s e d p h a s e a t T = 25 ° C l e a d s t o t h e f o r m a t i o n o f a n i s o t r o p i e l i q u i d c r y s t a l s i n e q u i l i b r i u m w i t h m i c r o e m u l s i o n [ 2 8 , 2 9 ] . T h e e v o l u t i o n o f t h e s y s t e m is i n a g r e e m e n t w i t h t h e a n a l y s i s o f [24] i n t e r m s o f N i n -h a m ' s s u r f a c t a n t p a r a m e t e r v/al ( r a t i o b e t w e e n t -h e t a i l v o l u m e a n d h e a d g r o u p a r e a , i n t h e l a m e l l a r p h a s e , m u l -t i p l i e d b y -t h e l e n g -t h ) -t h a -t offers s o m e e x p l a n a -t i o n o f -t h e o c c u r r e n c e o f d r o p l e t s s h a p e d b y P F P E s u r f a c t a n t i n o i l s o f d i f f e r e n t m o l e c u l a r w e i g h t as w e l l as o f t h e r e a s o n w h y h i g h m o l e c u l a r w e i g h t o i l s d o n o t f a v o u r d r o p l e t f o r m a -t i o n . W e feel c o n f i d e n t t h a t t h e r e s u l t s s h o w n i n t h i s p a -p e r offer f u r t h e r s u -p -p o r t t o t h e v i e w t h a t -p e r c o l a t i o n b e l o n g s t o t h e class o f u n i v e r s a l i t y p h e n o m e n a . S D S , A O T , a n d P F P E s u r f a c t a n t s a r e v e r y d i f f e r e n t i n c h e m i c a l c o m p o s i t i o n a n d s t e r i c h i n d r a n c e ( h y d r o g e n a t e d , s i n gle a n d d o u b l é c h a i n S D S a n d A O T , r e s p e c t i v e l y , a n d f l u -o r i n a t e d s i n g l e c h a i n P F P E ) ; h -o w e v e r , w h e n m i x e d w i t h s u i t a b l e n o n c o n d u c t i n g o i l a n d s u i t a b l e d i s p e r s e d l i q u i d , t h e P F P E s u r f a c t a n t g i v e s a d y n a m i c p e r c o l a t i n g s y s t e m l i k e A O T o r S D S a n d a l c o h o l . T h e a u t h o r s a c k n o w l e d g e u s e f u l d i s c u s s i o n s o n p e r c o l a -t i o n -t h e o r y w i -t h R . L i v i a n d -t h a n k D r . P. G a v e z z o -t -t i f o r t h e p r e p a r a t i o n o f s u r f a c t a n t s . T h i s w o r k w a s s u p p o r t e d b y A u s i m o n t S . p . A . a n d b y M U R S T 4 0 % a n d 6 0 % f u n d s . M . G . G i r i t h a n k s A u s i m o n t f o r s u p p o r t d u r i n g t h i s r e -s e a r c h w o r k .[1] M . Lagues, R . Ober, and C . T a u p i n , J . P h y s . (Paris) L e t t . 3 9 , L 4 8 7 (1978).
M . A . van D i j k , P h y s . R e v . L e t t . 5 5 , 1003 (1985). [16 S. B h a t t a c h a r y a , J . P. Stokes, M . W . K i m , and J . S.
Huang, P h y s . R e v . L e t t . 5 5 , 1884 (1985). [17 J . Peyrelasse, M . Moha-Ouchane, and C . Boned, P h y s .
R e v . A 3 8 , 904 (1988). [18 C . C a m e t t i , P. Codastefano, P. Tartaglia, J . R o u c h , and
S. H . C h e n , P h y s . R e v . L e t t . 64, 1461 (1990); P h y s . R e v .
A 4 5 , R 5 3 5 8 (1992). [19 J . Peyrelasse, C . B o n e d , and Z. Saidi, P h y s . R e v . E 4 7 ,
468 (1993); 4 7 , 3412 (1993). [20 M . K o t l a r c h y k , S. H . C h e n , J . S. H u a n g , and M . W . K i m ,
J . P h y s . C h e m . 86, 3273 (1982); P h y s . R e v . L e t t . 5 3 , 941 [21 (1984); P h y s . R e v . A 2 9 , 2054 (1984).
A . D i Biasio, C . C a m e t t i , P. Codastefano, P. Tartaglia, [22 J . R o u c h , and S. H . C h e n , P h y s . R e v . E 4 7 , 4258 (1993). [23 M . K a h l w e i t , G . Busse, and J . W i n k l e r , J . C h e m . P h y s .
9 9 , 5605 (1993). [24 C . B u r g e r - G u e r r i s i and C . Tondre, J . C h i m . P h y s . P h y s .
C h i m . B i o l . 8 6 , 1405 (1989). [25 C . Tondre et al., in Surfactants in Solution, edited by
K . L . M i t t a l and P. Bothorel ( P l e n u m Press, New Y o r k ,
1986), Voi. 6, p. 1345; I . Rico et al., ibid., p. 1397. [26 I. R i c o , and A . L a t t e s , J . Colloid Interface Sci. 1 0 2 , 285
(1984). [27 K . Shinoda, M . Hato, and T . Hayashi, J . P h y s . C h e m .
76, 909 (1972). [28 M . J . Stebe, G . Serratrice, and J . J . Delpuech, J . P h y s .
C h e m . 8 9 , 2837 (1985). [29 Preparation, Properties and Industriai Applications of
Organofluorine Compounds, edited by R . E . B a n k s (Ellis H a r w a r d L t d . , Chichester, 1982).
C . C e c u t t i , A . Novelli, I . Rico and A . L a t t e s , J . Disper-sion Sci. Technol. 11, 115 (1990).
G . Caporiccio, F . B u r z i o , G . Carniselli, and V . B i a n c a r d i , J . Colloid Interface Sci. 9 8 , 202 (1984).
A . Chittofrati, D . L e n t i , A . Sanguineti, M . V i s c a , C . M . C . G a m b i , D . Senatra, and Z. Zhou, Colloids Surf. 4 1 , 45 (1989); Prog. Colloid Polymer Sci. 79, 218 (1989). Recent measurements indicate a molecular weight of 900 instead of 800 as reported in [18,20].
A . Chittofrati, A . Sanguineti, M . V i s c a , and N . K a l l a y , Colloids Surf. 6 3 , 219 (1992).
G . Gebel, S. R i s t o r i , B . Loppinet, and G . M a r t i n i , J . P h y s . C h e m . 9 7 , 8664 (1993).
S. R i s t o r i , P h . D . thesis, University of Florence, 1993. A . Sanguineti, A . Chittofrati, D . L e n t i , and M . V i s c a , J . Colloid Interface Sci. 1 5 5 , 402 (1993).
M . Monduzzi, A . Chittofrati, and M . V i s c a , L a n g m u i r 8, 1278 (1992).
M . G . G i r i , M . C a r l a , C . M . C . G a m b i , D . Senatra, A . Chittofrati, and A . Sanguineti, Meas. Sci. Technol. 5, 627 (1993).
C . Boned, J . Peyrelasse, M . Clausse, B . Lagourette, J . A l -liez, and L . B a b i n , Colloid P o l y m . Sci. 2 5 7 , 1073 (1979). N . K a l l a y and A . Chittofrati, J . P h y s . C h e m . 94, 4755 (1990).
M . Monduzzi, V . Boselli, and A . Chittofrati, J . P h y s . C h e m . (to be published).
A . Chittofrati, V . Boselli, and S. Friberg, J . Dispersion Sci. Tech, (to be published).
