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STUDIES OF THE STRUCTURE AND DYNAMICS OF AQUEOUS SOLUTIONS
G. Neilson
To cite this version:
G. Neilson. STUDIES OF THE STRUCTURE AND DYNAMICS OF AQUEOUS SOLUTIONS.
Journal de Physique Colloques, 1984, 45 (C7), pp.C7-119-C7-129. �10.1051/jphyscol:1984712�. �jpa-
00224273�
JOURNAL DE PHYSIQUE
Colloque C7, suppl6ment au n09, Tome 45, s e p t e m b r e 1984 page C7-119
STUDIES
OFTHE STRUCTURE AND DYNAMICS
OFAQUEOUS SOLUTIONS
G.W. N e i l s o n
H. H. WiZZs Physics Laboratory, Unive5sity of BristoZ, BristoZ BS8 ITL, U.K.
Rdsumd
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Cet a r t i c l e rdsume q u e l q u e s r 6 s u l t a t s r d c e n t s o b t e n u s p a r d i f f u s i o n de n e u t r o n s dans l ' d t u d e de s o l u t i o n s a q u e u s e s . Ces r d s u l t a t s o n t 6 t 6 a t t e i n t s gr'lce B deux mdthodes e x p d r i m e n t a l e s n o u v e l l e s : l e s mdthodes d e d i f f r a c t i o n du p r e m i e r e t du second o r d r e , q u i s o n t b a s d e s s u r l e s t e c h n i q u e s d e s u b s t i - t u t i o n s i s o t o p i q u e s f o u r n i s s e n t l e s i n f o r m a t i o n s d d t a i l l s e s c o n c e r n a n t l ' h y d r a - t a t i o n i o n i q u e e t l e s c o r r d l a t i o n s i o n - i o n ; l a d i f f u s i o n q u a s i d l a s t i q u e d e s n e u t r o n s du t y p e d e c e l l e r d a l i s d e s u r l e s p e c t r o m S t r e IN10 de 1 ' I L L f o u r n i t d e s i n f o r m a t i o n s s u r l e comportement dynamique d e s p r o t o n s e n s o l u t i o n . Les r d s u l t a t s d e c e s deux t y p e s d ' d t u d e s o n t u t i l i s d s p o u r d i s c u t e r l a v a l i - d i t d d e modeles t h d o r i q u e s e t l e s r d s u l t a t s d e s i m u l a t i o n s u r o r d i n a t e u r . A b s t r a c t-
The f o l l o w i n g a r t i c l e summarises r e c e n t r e s u l t s o b t a i n e d from n e u t r o n s c a t t e r i n g s t u d i e s o f aqueous s o l u t i o n s . The r e s u l t s have been d e r i v e d from two r e c e n t l y d e v e l o p e d e x p e r i m e n t a l p r o c e d u r e s : t h e f i r s t and second o r d e r d i f f e r e n c e methods o f n e u t r o n d i f f r a c t i o n , which a r e b a s e d on t h e t e c h n i q u e of i s o t o p i c s u b s t i t u t i o n , p r o v i d e d e t a i l e d s t r u c t u r a l i n f o r - m a t i o n r e g a r d i n g i o n i c h y d r a t i o n and i o n - i o n c o r r e l a t i o n s , and q u a s i e l a s t i c n e u t r o n s c a t t e r i n g of t h e t y p e c a r r i e d o u t on t h e IN10 s p e c t r o m e t e r of t h e I . L . L . p r o v i d e s i n f o r m a t i o n r e g a r d i n g t h e dynamical b e h a v i o u r of p r o t o n s i n s o l u t i o n .The r e s u l t s from b o t h t y p e s o f s t u d y a r e u s e d t o comment on t h e s u c c e s s e s of t h e v a l i d i t y o f t h e o r e t i c a l models and r e s u l t s of computer s i m u l a t i o n .
INTRODUCTION
Over t h e p a s t d e c a d e , o u r u n d e r s t a n d i n g of aqueous e l e c t r o l y t e s o l u t i o n s h a s i n c r e a s e d s i g n i f i c a n t l y . ( l ) The i n t r o d u c t i o n o f new e x p e r i m e n t a l methods on t h e one hand, e s p e c i a l l y t h o s e a s s o c i a t e d w i t h n e u t r o n s c a t t e r i n g and n e u t r o n and x-ray d i f f r a c t i o n , and t h e improvement o f t h e o r e t i c 1 c a l c u l a t i o n s b r o u g h t a b o u t by t h e i n t r o d u c t i o n of l a r g e h i g h s p e e d computers,(38 on t h e o t h e r , have p r o v i d e d a d e e p e r i n s i g h t i n t o t h e b e h a v i o u r o f i o n s i n s o l u t i o n .
The o b j e c t of t h i s a r t i c l e i s t o r e v i e w and comment on t h e c o n t r i b u t i o n s which n e u t r o n d i f f r a c t i o n and n e u t r o n q u a s i e l a s t i c s c a t t e r i n g (NQS) have made t o o u r knowledge of t h e d e t a i l e d s t r u c t u r e around i o n s , and t h e dynamics of p r o t o n s a s s o c i a t e d w i t h t h e w a t e r m o l e c u l e s i n e l e c t r o l y t e s o l u t i o n s . Because many r e v i e w s have a l r e a d y been p u b l i s h e d on t h i s t o p i c ( s e e f o r example r e f . 2 ) , t h e d e t a i l e d m a t h e m a t i c a l background of n e u t r o n d i f f r a c t i o n and NQS, and d e s c r i p t i o n s of t h e e x p e r i m e n t a l t e c h n i q u e and d a t a a n a l y s i s w i l l b e o m i t t e d . Emphasis i n s t e a d w i l l be c o n c e n t r a t e d on t h e r e s u l t s t h e m s e l v e s and t h e i r u s e f u l n e s s i n p r o v i d i n g a c l e a r e r u n d e r s t a n d i n g of t h e b e h a v i o u r of i o n s i n w a t e r .
I n g e n e r a l , t h e s y s t e m s u n d e r c o n s i d e r a t i o n a r e i n t h e form of a s a l t , MXn, i n heavy w a t e r ( F i g . 1) (heavy w a t e r i s u s e d i n p r e f e r e n c e t o water, b e c a u s e of i t s more c o n v e n i e n t n e u t r o n s c a t t e r i n g p r o p e r t i e s and t h e r e l a t i v e e a s e w i t h which t h e d a t a can b e A a n a l y s e d ) . The s p a t i a l d i s t r i b u t i o n o f s u c h a s y s t e m i s c o n v e n i e n t l y d e s c r i b e d i n t e r m s of p a i r r a d i a l d i s t r i b u t i o n f u n c t i o n s , g ( r ) , where r i s an i n t e r p a r t i c l e s e p a r a t i o n . I n t h e p r e s e n t c a s e t h e r e a r e t e n s u c h f u n c t i o n s : t h o s e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984712
C7-120 JOURNAL DE PHYSIQUE
which r e l a t e t o t h e heavy water molecules a r e ~ D D , go^, go0, t h o s e which d e f i n e i o n i c h y d r a t i o n a r e ~ M O , gMD, gXO, gXD, and t h o s e which d e s c r i b e ion-ion c o r r e l a - t i o n s a r e gm, gMX and gXX. The d i f f e r e n c e methods of neutron d i f f r a c t i o n , which a r e based on i s o t o p i c s u b s t i t u t i o n of i o n s can be used t o g i v e q u a n t i t a t i v e i n f o r m a t i o n r e g a r d i n g t h e l a t t e r two groups of g ( r ) ' ~ . ( ~ )
F i g . 1
-
A microscopic p i c t u r e of an aqueous s o l u t i o n c o n t a i n i n g c a t i o n s M+, anions 0 , ~ - and water molecules.From t h e f i r s t o r d e r d i f f e r e n c e method (5) i t is p o s s i b l e t o determine t h e l o c a l c o o r d i n a t i o n around t h e i s o t o p i c a l l y s u b s t i t u t e d i o n , I , i n terms of a l i n e a r combination, G I ( r ) , of t h e f o u r s p e c i f i c i o n - o t h e r p a r t i c l e i n t e r a c t i o n s . For example, by c a r r y i n g o u t two d i f f r a c t i o n experiments on two chemically i d e n t i c a l samples which d i f f e r only i n t h e i s o t o p i c s t a t e of i o n I t h e n one can show t h a t : ( 5 )
where E =
-
(A+
B+
C+
D), A = 2 c I c o ( f I - f ; ) f o , B = 2c c ( f - f ; ) f D , I D IC = 2 c c (f - f ' ) f 2 2 2
I I I J , D = c ( f - f ' I I I ) and c
-
atomic c o n c e n t r a t i o n of s p e c i e s ' a 'f a
-
neutron s c a t t e r i n g l e n g t h of s p e c i e s ' a 'f and f; a r e t h e d i f f e r e n t s c a t t e r i n g l e n g t h s of ion I i n t h e two s o l u t i o n s . I
R e c a l l t h a t from knowledge of i n d i v i d u a l g ( r ) ' s i t i s p o s s i b l e t o d e f i n e most probable i n t e r p a r t i c l e s e p a r a t i o n s and c o o r d i n a t i o n numbers. For example, t h e number of s p e c i e s a around B i n t h e element of volume 6 r a t r i s given by
c p41rr 6 r gag(') 2 where P ( = ~ / ~ ) i s t h e t o t a l number d e n s i t y f o r t h e N p a r t i c l e s of t g e system I n volume V .
The second o r d e r d i f f e r e n c e method(4) i s based on a second s u b s t i t u t i o n of t h e i o n I , o r a double s u b s t i t u t i o n of i o n s I and J . The former s e t of t h r e e experiments e n a b l e s one t o determine g I I ( r ) , and t h e l a t t e r s e t of f o u r experiments t o
d e t e r m i n e g I J ( ~ )
G
(I) and t h e i n d i v i d u a l g ( r ) o r g ( r ) p r o v i d e a c r i t i c a l q u a n t i t a t i v e t e s t o f t i e o r e t i c a l models of s o l u $ l o n s , a 3 I r e s u l t s from computer s i m u l a t i o n . F o r example, t h e p r i m i t i v e model o f s o l u t i o n s which r e p r e s e n t s t h e s y s t e m a s i o n s i n ad i e l e c t r i c continuum c a n b e examined a t a d e t a i l e d l e v e l and comments c a n b e made c o n c e r n i n g i t s r a n g e o f v a l i d i t y .
Neutron q u a s i e l a s t i c s c a t t e r i n g p r o v i d e s a means by which t r a n s l a t i o n a l motion of p r o t o n s o f a s y s t e m c a n be i n v e s t i g a t e d . I f t h e IN 1 0 h i g h r e s o l u t i o n back s c a t t e r i n g s p e c t r o m e t e r of t h e I . L . L . i s u s e d one c a n s t u d y t h i s i n a f o r m a l l y e x a c t manner i n terms of f i t t i n g L o r e n t z i a n f u n c t i o n s t o t h e d a t a . The u p s h o t o f t h i s p r o c e d u r e i s t h a t when t h e r e s u l t s a r e combined w i t h r e s u l t s from t h e k i n d of d i f f r a c t i o n s t u d i e s d e s c r i b e d above, one c a n o b t a i n u s e f u l i n f o r m a t i o n r e g a r d i n g t h e dynamics o f w a t e r around i o n s and i n t h e b u l k of t h e s o l u t i o n ( 6 ) . Such r e s u l t s g i v e t h e i n s i g h t n e c e s s a r y t o examine t h e v a l i d i t y of ynamical models o f s o l u t i o n s . F o r example, t h e model p r o p o s e d by Frank and Wen(7' s e e k s t o r e p r e s e n t t h e i o n - w a t e r s u b s y s t e m a s b e i n g made up o f a number o f h y d r a t i o n zones e a c h w i t h i t s u n i q u e dynamical and s t r u c t u r a l p r o p e r t i e s .
RESULTS
1. Ion-water c o o r d i n a t i o n .
The f i r s t o r d e r d i f f e r e n c e method o f n e u t r p n d i f f r a c t i o n (5) a l l o w s f o r a d i r e c t d e t e r m i n a t i o n of i o n - w a t e r c o o r d i n a t i o n i n t e r m s of a w e i g h t e d sum o v e r p a i r d i s - t r i b u t i o n f u n c t i o n s Equ. ( 1 ) . T y p i c a l forms of c I ( r ) f o r c a t i o n s and a s i m p l e a n i o n a r e shown i n F i g u r e s 2 and 3 r e s p e c t i v e l y . I n g e n e r a l , p o s i t i v e i o n s
c o o r d i n a t e w a t e r m o l e c u l e s w i t h t h e oxygen atoms n e a r e s t t h e i o n ( s e e i n s e t F i g . 2 ) , whereas a n i o n s c o o r d i n a t e w a t e r m o l e c u l e s w i t h t h e hydrogen atom n e a r e s t , ( s e e i n s e t F i g . 3 ) . There a r e , however, s i g n i f i c a n t d i f f e r e n c e s i n t h e d e t a i l s of l o c a l c o n f o r m a t i o n ( i . e . i o n - w a t e r s e p a r a t i o n s , t i l t a n g l e , c o o r d i n a t i o n numbers) f o r i n d i v i d u a l c a t i o n s ( T a b l e 1 ) .
S e v e r a l d e t a i l e d s t u d i e s have now been c a r r i e d o u t ( 4 ) and g e n e r a l p i c t u r e s a r e b e g i n n i n g t o emerge. The most comprehensive of t h e s e , n o t s u r p r i s i n g l y , was c a r r i e d o u t on s e v e r a l n i c k e l c h l o r i d e 6 ~ o l u t i o n s , (I1) where t h e l a r g e d i f f e r e n c e i n s c a t t e r i n g l e n g t h between 5 8 ~ i and N i , and p r e v i o u s knowledge of n i c k e l h y d r a t i o n from X-ray d i f f r a c t i o n , makes i t a p a r t i c u l a r l y s u l t a b l e s y s t e m f o r t h e
i s o t o p i c s u b s t i t u t i o n method. F i g u r e 2 shows t h e f i r s t o r d e r d i f f e r e n c e f u n c t i o n G ( r ) , f o r a 4.35m NiC12.D20 s o l u t i o n . The f i r s t two peaks r e p r e s e n t Ni-0 and Ni-D c o r r e l a t i o n s r e s p e c t i v e l y and b e i n g i n t h e n u m e r i c a l r a t i o o f 6:12 ( e q u a t i o n 1 ) i t i s i n f e r r e d t h a t t h e r e a r e a b o u t 6 w a t e r m o l e c u l e s around a ~ ii o n . ~ +From t h e n e a r n e i g h b o u r d i s t a n c e s rNiWo and r ~and assuming ~ - ~rOD =
12
and< DOD = 104.5O i t i s c a l c u l a t e d t h a t t h e a n g l e between t h e Ni-0 a x i s and t h e p l a n e o f t h e w a t e r molecule ( a n g l e o f t i l t ) i s a42O ( F i g u r e 2 i n s e t ) . T h i s a n g l e i s i n t e r m e d i a t e between t h e l o n e p a i r c o n f i g u r a t i o n ~ 5 and t h e d i p o l e c o n f i g u r a t i o n 5 ~
o0
and i s a s t r o n g f u n c t i o n o f c o n c e n t r a t i o n . (I1) T h i s e f f e c t i s , we b e l i e v e , a consequence of d i s t o r t i o n s of t h e h y d r a t i o n s p h e r e s a s t h e p a c k i n g f r a c t i o n i s i n c r e a s e d . T h e r e have been no t h e o r e t i c a l s t u d i e s aimed a t understanding t h i s o b s e r v a t i o n . I n o r d e r t o d e t e r m i n e w h e t h e r it was a consequence o f C1 i o n p e r - t u r b a t i o n o f t h e ~ ii o n s , an experiment was u n d e r t a k e n on an 3.8m N i 0 .D 0 ~ + s o l u t i o n where i t i s known t h a t i o n p a i r i n g is u n l i k e l y . N e w s o m e e t a 1 (1% 4 2 showed t h a tG
( r ) i s e s s e n t i a l l y i n d e p e n d e n t o f t h e a n i o n ( T a b l e 1 ) .N i
s i m i l a r s c t u r a l p a t t e r n s t o F i g u r e 2 have been o b s e r v e d f o r t h e i o n s of L i + ( 8 ) and c a 2 +
t4Y,
i n d i c a t i n g an a l m o s t i d e n t i c a l i o n - w a t e r c o n f o r m a t i o n ( i n s e t F i g u r e 2 ) . However, i n b o t h c a s e s t h e r e i s an a p p r e c i a b l e change i n c o o r d i n a t i o n number upon d i l u t i o h ( T a b l e 1 ) . T h e r e have been s e v e r a l a b i n i t i o c l u s t e r c a l c u l a t i o n s(15)and computer s i m u l a t i o n s s t u d i e s (16) of t h e c o o r d i n a t i o n of ~ i + t o w a t e r .
C7-122 JOURNAL
DE
PHYSIQUEG e n e r a l l y i t i s found t h a t t h e ion-oxygen d i s t a n c e s a r e b e t t e r r e p r e s e n t e d by i n i t i o quantum c h e m i s t r y whereas t h e computer s i m u l a t i o n t e n d s t o g i v e a b e t t e r agreement w i t h c o o r d i n a t i o n numbers. A r e c e n t s t u d y h a s been u n d e r t a k e n on K+ i o n s i n c o n c e n t r a t e d KC1 s o l u t i o n , t h e o b j e c t b e i n g t o examine t h e d i f f e r e n c e s , i f any, between t h e h y d r a t i o n p r o p e r t i e s o f t h e a l k a l i s e r i e s of i o n s . The d a t a , o b t a i n e d on D4B, a r e p r e s e n t l y b e i n g a n a l y s e d .
Table 1. Cation hydration determined by neutron d i f f r a c t i o n
-- -
Ion Solute Molality Ion-Oxygen I o n - d e u t e r i y
ea
Coordination Ref.d i s t a n c e ( & d i s t a n c e
(2)
numbera~ornputed on t h e b a s i s of rOD =
12
and DOD = 1 0 4 . 5 ~ (see i n s e t t o F i g . 2 ) .Two o t h e r c a t i o n s t u d i e s have been c o m p l e t e d , ND; i n 8 m o l a l ND4C1-D20 where t h e i s o t o p e s 1 4 N and 1 5 ~ were u s e d ( 9 ) and cu2+ i n 4 . 3 5 m o l a l CuC12.D20 u s i n g t h e i s o t o p e s
e3cu
a n d e 5 c u ( I 3 ) . I n t h e former c a s e a b r o a d u n r e s o l v e d f e a t u r e i s o b s e r v e d i n G N ( r ) T h i s r e s u l t i s i n b r o a d agreement w i t h a m o l e c u l a r dynamics s i m u l a t i o n s t u d y { l 7 ) , b o t h r e s u l t s g i v i n g a c o o r d i n a t i o n number o f between 10-11 w a t e r m o l e c u l e s around t h e N D ~ i o n . There i s , however, a l a r g e d i s c r e p a n c y a r i s i n g from t h e o v e r a l l s h a p e o f c N ( r ) . The s i m u l a t e d G N ( r ) i s much s h a r p e r and a p p e a r s t o o v e r - e s t i m a t e e i t h e r t h e h y d r a t i n g s t r e n g t h of t h e N D ~ i o n , o r t h e s p h e r i c a l n a t u r e o f i t s e f f e c t i v e p o t e n t i a l .A much more c o m p l i c a t e d GCu!r) i s d e t e r m i n e d f o r t h e c o o r d i n a t i o n of cu2+ i n s o l u t i o n ( I 3 ) . A 2+4 c o o r d ~ n a t i o n around t h e cu2' i o n i s c l e a r l y e v i d e n t con- f i r m i n g t h e view t h a t l o c a l c h e m i c a l e f f e c t s dominate t h e c o n f o r m a t i o n of t h e i o n - w a t e r sub-system. E f f e c t i v e i o n - w a t e r p o t e n t i a l s u s e d i n s i m u l a t i o n s t u d i e s must b e s u f f i c i e n t l y r e a l i s t i c t o r e f l e c t t h i s f a c t .
F i g . 2
-
N i 2+ d i s t r i b u t i o n f u n c t i o n , GNi(r) f o r a 4.35 m o l a l NiC12 heavy w a t e r s o l u t i o n . The i n s e t a t t o p l e f t r e p r e s e n t s t h e l o c a l N i 2 + w a t e r m o l e c u l e c o n f o r - m a t i o n i n f e r r e d from t h e r e s u l t s .A r e c e n t s t u d y ( I 4 ) o f a 2.85 NdC13 s o l u t i o n shows t h a t t h e Nd3+ - w a t e r c o n f o r m a t i o n i s s i m i l a r t o t h a t f o r N i 2 + .
F o r a n i o n s , t h e most e x t e n s i v e i n v e s t i g a t i o n s have been w i t h ~ 1 - where i s o t o p e s of 3 5 ~ 1 and 3 7 ~ 1 e n a b l e d many s u c c e s s f u l a p p l i c a t i o n s o f t h e f i r s t and s e c o n d o r d e r d i f f e r e n c e methods. T h e r e a p p e a r s t o be a u n i v e r s a l i t y of s t r u c t u r e of C1 i n s o l u t i o n ( I 8 ) a s e v i d e n c e from t y p i c a l GCl(r)s d e m o n s t r a t e s , F i g u r e 3 and T a b l e 2 . These r e s u l t s have a g a i n been c o n f i r m e d i n s i m i l a r s t u d i e s of ZnC12 s o l u t i o n s a t v e r y h i g h c o n c e n t r a t i o n s . ( 2 0 )
The d i s t a n c e s
rclo
and r c l ~ a r e i n e x c e l l e n t agreement w i t h t h o s e o b t a i n e d from quantum m e c h a n i c a l c a l c u l a t i o n s . I n g e n e r a l ,rclo
i s g r e a t e r t h a n t h a t o b t a i n e d from X-ray d i f f r a c t i o n , a c o n s e q u e n c e , we b e l i e v e of t h e i n h e r e n t l y low d i s - c r i m i n a t i o n of t o t a l X-ray p a t t e r n s of s o l u t i o n s ('1.Computer s i m u l a t i o n s b a s e d on t h e ST2 p o t e n t i a l p r e d i c t s i g n i f i c a n t c o u n t e r i o n e f f e c t s which a r e c l e a r l y a t v a r i a n c e w i t h t h e o b s e r v a t i o n s h e r e . I t w i l l be i n t e r e s t i n g t o s e e i f o t h e r t y p e s o f p o t e n t i a l s , e . g . t h e ' c e n t r a l f o r c e ' model, d e m o n s t r a t e t h a t GCl(r) i s i n d e e d i n d e p e n d e n t of c o u n t e r i o n and c o n c e n t r a t i o n ( 1 7 ) .
JOURNAL
DE
PHYSIQUEF i g . 3 - GCl(r) f o r t w o a l k a l i c h l o r i d e h e a v y w a t e r s o l u t i o n s : F u l l c u r v e
-
9 m o l a l L i C l i n D20, c r o s s e d c u r v e - 5 . 3 2 m o l a l NaCl i n D20 a f t e r s c a l i n g f o r c o n c e n t r a t i o n f a c t o r o f 1 . 8 7 .Table 2. Anion h y d r a t i o n determined by n e u t r o n d i f f r a c t i o n
-- - -
Ion S o l u t e M o l a l i t y X-D(1) X-0 X-D(2) a C o o r d i n a t i o n Ref.
(2) (2)
( 8 ) $ number~ 1 - L i c l LiCl
NaCl RbCl CaC12 NiC12
NO; NaNO 7 . 9 2 . 0 5 f l . 0 2 ~ 2.65+0.10b
-
2 0 ~ 5 1 0 ~ 1.350.2 (22 )a . Computed on t h e b a s i s of r =
18
( s e e i n s e t t o F i g . 3 ) ODb. D i s t a n c e s from n i t r o g e n n u c l e u s
A r e c e n t s t u d y h a s been c a r r i e d o u t on t h e a n i o n 0- i n a 7.8m s o l u t i o n of NaN03 i n heavy w a t e r ( 2 2 ) . N i t r o g e n i s o t o p e s 1 4 ~ and lgN3were u s e d and t h e d i f f e r e n c e method was a p p l i e d . The r e s u l t s show t h a t t h e N O h a s a u n i q u e l o c a l c o n f o r m a t i o n . There a r e between one and two n e a r e s t n e i g h b o u r D20 m o l e c u l e s and about 3 D-
bonded n e x t n e a r e s t n e i g h b o u r D20 m o l e c u l e s i n t h e immediate environment of t h e NO3. R e s u l t s from X-ray d i f f r a c t i o n C a 3 ) were u n a b l e t o d i s c e r n t h i s s t r u c t u r e b e c a u s e of t h e lower d i s c r i m i n a t i o n of t h e r e s u l t s t o g e t h e r w i t h t h e o v e r l a p p i n g c o r r e l a t i o n s from N and 0 atoms.
2. Ion-Ion S t r u c t u r e
F i g . 4 - The p a i r c o r r e l a t i o n f u n c t i o n s gNiNi(r), gCIC1(r) and gNiC ( r ) f o r 4.35 m o l a l n i c k e l c h l o r i d e i n heavy w a t e r . The d o t t e d c u r v e c e n t r e d a t i . 4 2 i n d i c a t e s t h e magnitude of gNiCl(r) e x p e c t e d i f i n n e r s p h e r e complexing proposed by Wein- g a r t n e r e t a1(28) a c t u a l l y o c c u r s .
The f i r s t and b e s t s y s t e m on which t o u s e t h e s e c o n d o r d e r d i f f e r e n c e s method i s n i c k e l c h l o r i d e i n heavy w a t e r . I n a s e r i e s o f s i x e x p e r i m e n t s on a 4.35 m o l a l NiC12 heavy w a t e r s o l u t i o n it was p o s s i b l e t o o b t a i n t h e t h r e e i o n - i o n p a r t i a l d i s t r i b u t i o n f u n c t i o n s ( 2 4 ) . The g ( r ) f o r N i - N i c o r r e l a t i o n s i s n o t w e l l d e f i n e d
( F i g . 4) a l t h o u g h t h e c u t - o f f d i s t a n c e a t r = 4 . 1 2 i s remarkably i n s e n s i t i v e t o t h e l a r g e e r r o r s i n t h e raw d a t a . A d i s t a n c e corn r a b l e t o t h i s h a s been c a l c u - l a t e d t h e o r e t i c a l l y i n i r o n c h l o r i d e s o l u t i o n s (2QB. F u r t h e r m o r e , model
C7-126 JOURNAL DE PHYSIQUE
c a l c u l a t i o n s by Friedman and Dudowicx (26) d e m o n s t r a t e t h a t t h e g r o s s f e a t u r e s o f gNiNi c a n b e w e l l u n d e r s t o o d i n t e r m s of s o f t c o r e r e p u l s i o n s and Coulomb i n t e r - a c t i o n s w i t h i n t h e framework of t h e p r i m i t i v e model. There a p p e a r s t o b e no need t o i n v o k e s p e c i f i c o r d i r e c t i o n a l i n t e r a c t i o n s s o f a r a s N i 2 + i s c o n c e r n e d . We c o n c l u d e t h a t t h e h y d r a t e d s p e c i e s come i n t o c o n t a c t i n a s t a g g e r e d way, a w a t e r m o l e c u l e o f one h y d r a t i o n s p h e r e f i t t i n g i n t o t h e i n t e r s t i c i e s o f t h e o t h e r .
TABLE 3
-
Solute Molality Pair correlation Cut-off distance Position of Position of Coordination function (rc)/X first maximua/x first mimimum/8 numbert
(TM) (I-)
NiCI 4.35 Ni-NI 4.120.1 4.720.2 5.6c0.2
NI-C1 3.920.1 4,620.2 6.120.2
5.8+0.3(~1- around ~i'+)
C1-C1 5.0+0.1 6.lr0.2 7.5+0.2
8.5~0.3
LiCl 14.9 C1-Cl 2.95c0.05 3.75+0.05 4.8+0.1 2.320.3
'obtained by integrarlng 4n(N/V)cu &(r)r2 between the limits r < r c r
The r e s u l t s f o r gNiCl(r) on t h e same system shows some i n t e r e s t i n g f e a t u r e s which c a n be summarised a s f o l l o w s : -
( i ) T h e r e i s no e v i d e n c e f o r s u b s t a n t i a l i n n e r s p h e r e complexing of ~ 1 - by I4i2+. The rc v a l u e o f 3.92 ( T a b l e 3) s u g g e s t s t h a t ~ 1 - i s e f f e c t i v e l y e x c l u d e d from t h e i n n e r - s p h e r e , a c o n c l u s i o n s u p p o r t e d by t h e r e c e n t n . m . r . work of Hunt ( 2 7 ) . On t h e o t h e r h a n d , W e i n g a r t n e r and H e r t z (28) p r e v i o u s l y s u g g e s t e d t h a t t h e c o n c e n t r a t i o n of t h e i n n e r s p h e r e complex Ni(H20)5C1+ i s a b o u t 2 . 5 m o l a l b u t t h i s i s n o t c o n s i s t e n t w i t h t h e e x p e r i m e n t a l r e s u l t s ( s e e f i g u r e 4 ) .
( i i ) There i s s t r o n g p a i r i n g between N i 2 + and ~ 1 - a s shown by t h e peak c e n t r e d around 4.68. The c o o r d i n a t i o n number f o r ~ 1 - around ~ iof 5.8: ~ +0 . 3 s u g g e s t s t h a t 2/3 of t h e a v a i l a b l e s i t e s a s s o c i a t e d w i t h t h e w a t e r i n t h e Ni(H20)6 2+
complex a r e o c c u p i e d .
( i i i ) The i o n - p a i r i n g i s m e d i a t e d by t h e i n c e r s p h e r e w a t e r and w i l l t h e r e f o r e have a l i f e t i m e of 5 x 10-12s o r l e s s ( i . e . t h e l i f e t i m e o f c ~ - - D ~ o ) . T h i s t i m e i s comparable w i t h t h e b i n d i n g t i m e between w a t e r m o l e c u l e s t h e m s e l v e s s o t h a t i n s p i t e of t h e w e l l d e f i n e d peak i n gNicl(r) t h e i o n - p a i r must n o t b e t h o u g h t of a s a s t a b l e e n t i t y . C h l o r i d e i o n s exchange r a p i d l y w i t h t h e h y d r a t e d n i c k e l i o n a l t h o u g h t h e i n t e r a c t i o n i s b o t h d i r e c t i o n a l and s p e c i f i c . The form o f g ~ i c l ( r ) r u l s o u t s t r u c t u r a l models p r o p o s e d by March & T o s i (29) and S o r e n s e n and S c o t t (305, which p r e d i c t a peak around 2.48. The a b s e n c e o f c l o s e c o r r e l a t i o n between N i 2 + and C1-, a f a c t e s t a b l i s h e d by t h e s e l f - d i f f u s i o n s t u d i e s of M i l l s e t a 1 ( 2 8 ) , i s c l e a r l y confirmed by t h e p r e s e n t s t u d y .
R e s u l t s f o r g ( r ) a r e shown i n f i g u r e 4. We n o t e t h a t t h e rc v a l u e of 5 . 0 8 i s g r e a t e r t h a n F E 1 s e p a r a t i o n of c h l o r i d e i o n s hydrogen bonded t o t h e same w a t e r m o l e c u l e . Moreover, t h e o c c u p a t i o n of a l l f o u r s i t e s on a d j a c e n t w a t e r m o l e c u l e s c a n n o t o c c u r b e c a u s e of an e x c l u d e d volume e f f e c t and we c o n c l u d e t h a t c h l o r i d e i o n s a r e bonded t o a d j a c e n t w a t e r m o l e c u l e s . Such c o n f i g u r a t i o n s w i l l g i v e r i s e t o a maximum i n gCIC1(r) a t r
-
5 . 9 2 which i s i n good agreement w i t h t h e e x p e n m e n t a l r e s u l t s ( f i g u r e 4 , t a b l e 3 ) . T h i s scheme g i v e s a n a t u r a l e x p l a n a t i o n o f t h e o b s e r v e d N i 2 + - ~ 1 - c o o r d i n a t i o n number.The c r u c i a l p o i n t t o emphasize i s t h a t t h e form of g c l c l ( r ) i s a n i n d i r e c t consequence of t h e g e o m e t r i c a l s t a b l i l i t y of t h e ~ i ( ~ ~ ~ ) ~ + c o m ~ l e x . A t t h e s e c o n c e n t r a t i o n s a s u b s t a n t i a l f r a c t i o n of t h e c h l o r i d e i o n s hydrogen-bond t o t h e complex and t h i s f a c t w i l l dominate t h e s h o r t - r a n g e c h a r a c t e r of gCICl(r). T h i s i n t u r n w i l l l e a d t o a m a j o r d e p a r t u r e from t h e b e h a v i o u r p r e d i c t e d by p r i m i t i v e models f o r which t h e i o n - i o n p o t e n t i a l is s p h e r i c a l and n o n - s p e c i f i c . I t f o l l o w s t h a t c h l o r i d e i o n s i n s o l u t i o n s w i t h weakly c o o r d i n a t i n g c a t i o n s ( e . g . ~ a + o r KC) w i l l have a much s i m p l e r s t r u c t u r e .
SCIC-.!k)
h a s been o b t a i n e d i n two o t h e r s o l u t i o n s ( 4 ) . I n a 5 . 3 2 m o l a l NaCl s o l u i o n t h e res were shown t o b e c o n s i s t e n t w i t h t h e USA v e r s i o n o f t h e p r i m i t i v e model'"'.
A much more s e n s i t i v e t e s t of t h e t h e o r y h a s been c a r r i e d o u t by Copestake and N e i l s o n who d e t e r m i n e d SC Cl(k) f o r a 14.9 m o l a l L i C l s o l u t i o n . A t h e o r e t i c a l c a l c u l a t i o n b a s e d on t h e MSA w i t B a p r i m i t i v e model i n which t h e b u l k d i e l e c t r i c c o n s t a n t of t h e s o l u t i o n i s 2 5 , t h e ~ i + and C1- d i a m e t e r s a r e 5 2 and 32 r e s p e c t i v e l y shows t h a t SCIC1(k) i s i n good q u a l i t a t i v e agreement w i t h t h e e x p e r i m e n t a l r e s u l t ( 2 ) .I t w i l l b e n e c e s s a r y t o c a r r y o u t more e x p e r i m e n t s u s i n g t h e s e c o n d o r d e r d i f f e r e n c e t e c h n i q u e s o t h a t one c a n e s t a b l i s h t h e e x t e n t t o which p r i m i t i v e models a r e a p p l i c a b l e t o i o n i c s o l u t i o n s .
3. P r o t o n dynamics.
Hewish e t a 1 ( 6 ) c a r r i e d o u t a s e r i e s o f e x p e r i m e n t s on a v a r i e t y of aqueous s o l u t i o n s . The r e s u l t s were d e r i v e d from IN10 d a t a and were a r r i v e d a t a f t e r c a r e - f u l c o r r e c t i o n s f o r m u l t i p l e s c a t t e r i n g . From t h e i r r e s u l t s t h e y were a b l e t o i d e n t i f y ( @ two l i m i t i n g c a s e s known t o o c c u r f o r p r o t o n r a t e p r o c e s s e s i n s o l u t i o n
.
I n t h e f i r s t c a s e , f a s t exchange, t h e r e s u l t s c a n b e a n a l y s e d a s a s i n g l e L o r e n t z i a n which g i v e s an a v e r a g e p r o t o n d i f f u s i o n c o e f f i c i e n t i n s o l u t i o n . T h i s t y p e o f b e h a v i o u r i s o b s e r v e d i n weakly h y d r a t i n g s y s t e m s s u c h a s CsC1. I n t h e second c a s e , t h e s l o w exchange, i t was p o s s i b l e t o i d e n t i f y two t y p e s of p r o t o n b e h a v i o u r . T h i s o b s e r v a t i o n was b a s e d on t h e n e c e s s i t y o f a two L o r e n t z i a n f i t t o t h e e x p e r i m e n t a l r e s u l t s . Two d i f f u s i o n c o e f f i c i e n t s were i d e n t i f i e d , Dl = Dion, t h a t c h a r a c t e r i s t i c of t h e s t r o n g l y h y d r a t i n g i o n , andD2
which i s an a v e r a g e o f p r o t o n s i n a l l o t h e r e n v i r o n m e n t s . Systems whose i o n s e x h i b i t s l o w exchange a r e s o l u t i o n s of NiC12 and YgC12. The n i c k e l c h l o r i d e r e s u l t s were a n a l y s e d u s i n g t h e v a l u e of Dion known from t r a c e r measurements and t h e d i f f r a c t i o n r e s u l t s d e r i v e d from d i f f e r e n c e methods were u s e d t o w e i g h t c o r r e c t l y t h e two L o r e n t z i a n s . I t was t h e r e b y p o s s i b l e t o e x t r a c t t h e d i f f u s i o n c o e f f i c i e n t (Dsec) of a second zone of h y d r a t e w a t e r . T h i s r e s u l t a d d s c r e d e n c e t o a model p r o p o s e d by Frank and which p r e d i c t s t h a t , i n g e n e r a l , s e v e r a l z o n e s o f h y d r a t i o n , e a c h w i t h a c h a r a c t e r i s t i c m o b i l i t y , w i l l e x i s t .These t y p e s of s t u d i e s a r e c o n u i n g on o t h e r s y s t e m s w i t h a view t o v a r y i n g c o u n t e r i o n and t e m p e r a t u r e
(9bi
and t h e f u l l i m p l i c a t i o n s a r e c u r r e n t l y b e i n g a s s e s s e d .CONCLUSIONS AND FUTURE STUDIES
The one g e n e r a l c o n c l u s i o n which c a n be drawn from t h e r e s u l t s l i s t e d above i s t h a t t h e t e c h n i q u e s of q u a s i e l a s t i c n e u t r o n s c a t t e r i n g and n e u t r o n d i f f r a c t i o n w i t h i s o t o p i c s u b s t i t u t i o n o f f e r a u n i q u e means by which new and u s e f u l i n f o r m a t i o n can b e g a t h e r e d on aqueous s y s t e m s . F u r t h e r m o r e , t h e q u a n t i t a t i v e n a t u r e o f t h e r e s u l t s p r o v i d e a s e n s i t i v e t e s t o f t h e o r e t i c a l models of s o l u t i o n and t h e r e b y deepens o u r u n d e r s t a n d i n g o f t h e s e u n i v e r s a l l y common s y s t e m s .
With t h e r e c o n s t r u c t i o n of D4 a t t h e I.L.L. and t h e s o o n t o b e commissioned l k q u i d s i n s t r u m e n t s on t h e s p a l l a t i o n n e u t r o n s o u r c e a t t h e R u t h e r f o r d Appleton L a b o r a t o r y p r o s p e c t s a r e good f o r many new and e x c i t i n g e x p e r i m e n t s . The
f o l l o w i n g t h r e e examples s e r v e t o i l l u s t r a t e t h e s c o p e of d i f f r a c t i o n t y p e s t u d i e s :
C7-128 JOURNAL
DE
PHYSIQUE( i ) I n v e s t i g a t i o n of t h e s t r u c t u r e around i o n s whose i s o t o p e s show o n l y s m a l l d i f f e r e n c e s i n s c a t t e r i n g l e n g t h s e.g. K+.
( i i ) S t u d i e s of i o n i c s t r u c t u r e i n more d i l u t e s y s t e m s , moving i n t o a r e g i o n where t h e Debye-Hiickel t h e o r y i s e x p e c t e d t o a p p l y .
( i i i ) I n v e s t i g a t i o n s of i o n i c h y d r a t i o n a s a f u n c t i o n of p r e s s u r e and t e m p e r a t u r e , e s p e c i a l l y i n t o t h e s u p e r c r i t i c a l r e g i o n where many i n t e r e s t i n g r e s u l t s might be a n t i c i p a t e d from b u l k p r o p e r t y measurements.
Our u n d e r s t a n d i n g of t h e dynamical behaviour of aqueous s o l u t i o n s w i l l c o n t i n u e t o grow as n e u t r o n s c a t t e r i n g e x p e r i m e n t s c o n t i n u e t o be a p p l i e d t o a w i d e r r a n g e of systems. Furthermore a s o u r i n s i g h t deepens, i t i s a n t i c i p a t e d t h a t o u r i n v e s t i - g a t i o n s w i l l widen t o i n c l u d e r o t a t i o n a l and v i b r a t i o n a l s t u d i e s of w a t e r m o l e c u l e s . A s w i t h t h e work on d i f f r a c t i o n i t w i l l b e v e r y worthwhile t o i n t r o d u c e t h e
t e m p e r a t u r e v a r i a b l e i n o r d e r t o move i o n s i n t o and o u t of t h e slow exchange regime and t h e r e b y deepen o u r u n d e r s t a n d i n g of t h e mechanics of t h e c o u p l i n g between i o n s and w a t e r .
REFERENCES
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