DYNAMICS OF PROTONS IN WATER AND AQUEOUS ZnCl2 SOLUTIONS

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DYNAMICS OF PROTONS IN WATER AND AQUEOUS ZnCl2 SOLUTIONS

M.-C. Bellissent-Funel, R. Kahn, A. Dianoux, M. Fontana, G. Maisano, P.

Migliardo, F. Wanderlingh

To cite this version:

M.-C. Bellissent-Funel, R. Kahn, A. Dianoux, M. Fontana, G. Maisano, et al.. DYNAMICS OF

PROTONS IN WATER AND AQUEOUS ZnCl2 SOLUTIONS. Journal de Physique Colloques, 1984,

45 (C7), pp.C7-143-C7-149. �10.1051/jphyscol:1984715�. �jpa-00224280�

DYNAMICS OF PROTONS IN WATER AND AQUEOUS Z n C I Z SOLUTIONS

M.-C. B e l l i s s e n t - F u n e l , R. Kahn, A . J . ~ i a n o u x * , M . P . ~ o n t a n a * * , G . ~ a i s a n o * * * , P . ~ i ~ l i a r d o * * * and F . wanderlingh***

L a b o r a t o i r e Le'on B r i l l o u i n , CEN ~ a c l a ~ ' , 91191 G i f - s u r - Y v e t t e Cedex, France

* I . L . L . ,

**

B.P. 156 X , 38042 Grenoble Cedex, France I s t i t u t o d i F i s i c a and G. N.S.M., P u m a , I t a l y

***

I s t i t u t o d i F i s i c a and G . N.S.M., Messina, I t a l y

Resume - Nous avons & t u d i @ l e s mecanismes de d i f f u s i o n des protons dans

=pure e t l e s s o l u t i o n s aqueuses de ZnC12, par d i f f u s i o n q u a s i - e l a s t i - que incoherente de neutrons e t avons montre q u ' i l e t a i t indispensable de t e n i r compte du mouvement de r o t a t i o n des mol@cules d'eau ; l e temps de r e l a - x a t i o n c a r a c t e r i s t i q u e a s s o c i e passe de 0.8 ps pour l ' e a u pure Z 20 ps pour l a s o l u t i o n s a t u r e e c e que l ' o n i n t e r p r e t e en termes de rotationsg&nees dans l e s s o l u t i o n s concentrees. La p a r t i e t r a n s l a t i o n n e l l e des s p e c t r e s a 6t.S convenablement r e p r e s e n t e e s u r t o u t l e domaine en Q e x p l o r e , Z 1 'a i d e d'un modele de d i f f u s i o n par s a u t s a l e a t o i r e s . La longueur de s a u t obtenue r e s t e pratiquement l a meme quand on passe de l ' e a u l a s o l u t i o n s a t u r e e e t v o i s i n e de l a d i s t a n c e e n t r e protons dans l a mol6cule d ' e a u .

Abstract

-

We s t u d i e d t h e d i f f u s i v e motions of t h e protons i n pure water and ZnCl aqueous s o l u t i o n s , using incoherent q u a s i - e l a s t i c neutron s c a t t e r i n g . We siowed t h a t i t i s e s s e n t i a l t o take i n t o account t h e r o t a t i o n a l motion of t h e water molecules ; t h e a s s o c i a t e d c h a r a c t e r i s t i c r e l a x a t i o n time v a r i e s from 0 . 8 ps f o r H20 t o 20 ps f o r t h e s a t u r a t e d s o l u t i o n which i s i n t e r p r e t e d i n terms of hindered r o t a t i o n s f o r t h e concentrated s o l u t i o n s . The t r a n s l a - t i o n a l linewidth i s conveniently f i t t e d over t h e whole Q-range, using t h e Random Jump Diffusion model f o r which t h e jump length t u r n s out t o be roughly t h e same f o r pure H20 and t h e s a t u r a t e d s o l u t i o n , f a i r l y c l o s e t o t h e d i s - t a n c e between ~ r o t o n s i n t h e water molecule.

The study of microscopic s t r u c t u r e and dynamics i n i o n i c l i q u i d s , and p a r t i c u l a r l y aqueous s o l u t i o n s of s t r o n g e l e c t r o l y t e s (NiCl?, ZnC12, ZnBr2) has received a g r e a t impulse following t h e i n i t i a l neutron d i f f r a c t ~ o n experiments of Enderby e t a1 / I / . The e x i s t e n c e of c o l l e c t i v e v i b r a t i o n a l e x c i t a t i o n s a t s u f f i c i e n t l y high concentra- t i o n s has been e s t a b l i s h e d by Raman spectroscopy /2/ i n many of t h e s e l i q u i d e l e c - t r o l y t e s . Exafs measurements /3/ have provided a d i r e c t proof t h a t i n highly con- c e n t r a t e d ZnBr aqueous s o l u t i o n s , about 80 % of t h e Br atoms a r e found i n t h e f i r s t coordination s 2 e l l around t h e Zn ions t o form complexes. Further o r e t h e Exafs d a t a have shown t h a t t h e l o c a l i o n i c o r d e r extends, a t l e a s t , t o 6-8

!

and t u r n s o u t t o be very s i m i l a r t o t h e c r y s t a l l i n e s t r u c t u r e of t h e corresponding s o l u t e s . Moreover t h e e x i s t e n c e of dynamically c o r r e l a t e d regions has been conjectured f o r ZnC12 solu- t i o n s i n D2O on t h e b a s i s of small angle neutron s c a t t e r i n g / 4 / . The e x i s t e n c e of such regions i n t h e s o l u t i o n s should be r e f l e c t e d by t h e d i f f u s i o n a l dynamics i f studied on t h e a p p r o p r i a t e time and length s c a l e . In t h i s l e t t e r , we p r e s e n t a s t u - dy of t h e d i f f u s i v e motions of t h e protons i n pure water and ZnCl? aqueous solutions a s a f u n c t i o n of t h e s o l u t e c o n c e n t r a t i o n , using incoherent q u a s i - e l a s t i c neutron s c a t t e r i n g . O u r d a t a a r e a c c u r a t e enough t o show t h a t i t i s e s s e n t i a l t o t a k e i n t o account t h e r o t a t i o n a l motion of t h e protons.

The experiments have been performed on t h e IN6 time of f l i g h t spectrometer a t t h e ' ~ a b o r a t o i r e commun C E A , C N R S

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984715

JOURNAL DE PHYSIQUE

ILL, Grenoble. A t a wavelength X = 5.9 A ( i n c i d e n t energy = 2.35 meV), 16 spectra were taken, simultaneously, f o r an angular range v a r y i n g from 12.80 up t o 110.30 degrees. The energy r e s o l u t i o n (FWHM = 50-70 peV) was determined u s i n g a vanadium standard sample. The s o l u t i o n s were placed i n t e f l o n - c o a t e d aluminium p l a n a r c e l l s w i t h 0.15 mm t h i c k w a l l s , and 0.65 mm thickness. Since t h e transmission v a r i e d b e t - ween 0.74 and 0.793 f o r H20 and t h e s a t u r a t e d ZnC12 s o l u t i o n , we have a p p l i e d m u l t i - p l e s c a t t e r i n g c o r r e c t i o n s u s i n g t h e Monte C a r l o program DISCUS / 5 / .

Our experiments have been performed a t (T = 298 K ) , on p u r e water and ZnCl s o l u - t i o n s i n H 0 f o r t h e f o l l o w i n g concentrations : 3M, 6M and 12.6M ( s a t u r a t e 2 s o l u - t i o n ) . I n $ i g u r e l a and l b , we present t h e c o r r e c t e d i n t e n s i t y spectra o f water and o f t h e s a t u r a t e d s o l u t i o n corresponding t o a s c a t t e r i n g angle o f 64.20 degrees.

The main c o n t r i b u t i o n t o t h e s c a t t e r i n g cross s e c t i o n i s t h e incoherent s c a t t e r i n g by protons. I n t h e Born approximation f o r N i d e n t i c a l n u c l e i / 6 / , t h e cross s e c t i o n i s p r o p o r t i o n a l t o t h e incoherent s c a t t e r i n g f u n c t i o n Sinc(Q,w) where

19

and bw denote t h e momentum and energy t r a n s f e r s . Sinc(9,w) i s t h e r o u r i e r transform o f t h e Van Hove /7/ s e l f c o r r e l a t i o n f u n c t i o n G s ( ~ , t ) . The incoherent i n t e r m e d i a t e 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 as :

where L i s t h e p o s i t i o n v e c t o r o f one proton, so t h a t

r=s+fi+i

w i t h : molecular mass c e n t r e p o s i t i o n vector, a : mean p o s i t i o n v e c t o r o f t h e p r o t o n r e l a t i v e t o t h e mass centre. F i n a l l y , u repreyents a1 1 t h e small amp1 i t u d e displacements ( v i b r a t i o n s ) . Assuming no time c o r r e 7 a t i o n between these motions, and as i n t h e q u a s i - e l a s t i c region, t h e v i b r a t i o n s o n l y c o n t r i b u t e t o t h e i n t e n s i t y through a Debye-Waller f a c - t o r , t h e incoherent s c a t t e r i n g law w i l l thus be a c o n v o l u t i o n o f t h e t r a n s l a t i o n a l and r o t a t i o n a l p a r t s . We assume t h a t t h e p r o t o n t r a n s l a t i o n a l motion i s characte- r i z e d by a t r a n s l a t i o n a l d i f f u s i o n broadening AET, and consequently

where AET i s t h e h a l f w i d t h a t h a l f maximum o f t h e q u a s i - e l a s t i c l i n e (HWHM) and D t h e s e l f d i f f u s i o n c o e f f i c i e n t .

For s i m p l i c i t y , we assume t h a t t h e p r o t o n has an i s o t r o p i c r o t a t i o n a l d i f f u s i o n motion around t h e c e n t r e o f mass o f t h e molecule c h a r a c t e r i z e d by a r o t a t i o n a l d i f f u s i o n c o e f f i c i e n t Dr, t h i s m o t i o n being described by t h e Sears model /8/.

Using t h e expression ( 2 ) and t h e Sears model, t h e t h e o r e t i c a l s c a t t e r i n g f u n c t i o n /9/ i s g i v e n by :

n n r n AE,

where j are t h e s p h e r i c a l Bessel f u n c t i o n s and a i s comparable t o t h e 0-H bond l e n g t h t a = 0 . 9 8

8 ) .

T h i s s c a t t e r i n g law i n t h e n convoluted w i t h t h e i n s t r u m e n t a l r e s o l u t i o n f u n c t i o n t o f i t t h e experimental d a t a .

As a f i r s t step i n t h e a n a l y s i s we have t r i e d t o f i t t h e data w i t h t h e s i n g l e l o r e n t z i a n (SL) form which corresponds t o Dr = 0 i n equation ( 3 ) . I n f i g u r e 2, we

Fig. l b

-

Q u a s i - e l a s t i c spe t r a of aqueous ZnC12 s a t u r a t e d s o l u t i o n (T=298K, 0;64.Z0°, Q=l . l 3 k - I ) , o Experimental p o i n t s , - F i t with D r = 0.005 meV.

JOURNAL DE PHYSIQUE

F i g . 2

-

AET versus Q 2 f o r H20 a t T=298K. A f r o m a SL f i t , e From a f i t w i t h D r = 0 . 1 3 meV, x Sakamoto e t a l ' s d a t a (SL) a t T=296K, W h i t e ' s d a t a (SL) a t T=296K, - - Random jump d i f f u s i o n model (SL), -- Random jump d i f f u s i o n model (Dr = 0.13 meV)

,

I T y p i c a l e r r o r b a r .

.3

. ? -

.1

0

p r e s e n t t h e AET v a r i a t i o n w i t h Q[ o b t a i n e d b y t h i s f i t . The r e s u l t s a r e i n good agreement w i t h t h o s e o f Sakamoto e t a1

/ l o /

and a l s o w i t h t h o s e o f White /11/,

However, i t i s a p p a r e n t from a c l o s e e x a m i n a t i o n o f t h e v a r i a t i o n o f (I:,": - I ~ ~ ~ c )

- .

^/

^/c/

/

/ a

,"/

/

- 4

/

_{I Typical error bar}

L I I I I

,

versus w, e s p e c i a l l y i n t h e t a i l r e g i o n , t h a t t h e f i t w i t h a s i n g l e l o r e n i z i a n i s p o o r ( F i g . l a ) .

0 0.5 1.0 1.5 2.0 2.5 Q ' I ~ ~ ~ )

U s i n g t h e e x p r e s s i o n ( 3 ) , we have f i t t e d t h e q u a s i - e l a s t i c p a r t o f t h e measured spectrum f o r a g i v e n a n g l e b y t h e f o l l o w i n g r e l a t i o n : F(Q,w)=A Sinc(Q,w)+B where A r e p r e s e n t s an a m p l i t u d e f a c t o r and B t h e e x p e r i m e n t a l background which can c o n t a i n some i n e l a s t i c c o n t r i b u t i o n . Only t h r e e r o t a t i o n a l l o r e n t z i a n s have been c o n s i d e r e d ( i . e . R 5 3 ) and t h e e x p e r i m e n t a l s p e c t r a have been f i t t e d b y u s i n g 4 parameters,

A and B. We have e v a l u a t e d , i n each case, t h e t r a n s l a t i o n a l d i f f u s i o n AET'

DL'

^.

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

We o b t a i n e d t h e v a l u e o f D r = 0 . 1 3 meV f o r p u r e H20. Dr decreases down t o 0.005 meV as s o l u t e c o n c e n t r a t i o n i s r a i s e d up t o s a t u r a t i o n . C o r r e s p o n d i n g l y , t h e c h a r a c t e - r i s t i c r e l a x a t i o n t i m e -cr=B/6Dr v a r i e s f r o m - c r = 0 . 8 ps f o r H20 t o 20 ps f o r t h e s a t u r a t e d s o l u t i o n . A t low s a l t c o n c e n t r a t i o n s , t h e symmetry o f t h e o c t a h e d r a l c o o r d i n a t i o n i n t h e f i r s t h y d r a t i o n s h e l l (6H20) /3,12/ a l l o w s t h e w a t e r m o l e c u l e s t o r o t a t e v e r y e a s i l y , g i v i n g r i s e t o a v a l u e o f D, s i m i l a r t o t h a t o f water. When t h e s a l t c o n c e n t r a t i o n becomes equal t o 12.6M, t h e w a t e r m o l e c u l e s / z i n c i o n s r a t i o i s a b o u t 2 and so t h e b i n d i n g f o r c e s between t h e e l e m e n t a r y u n i t s , which a l l o w t h e s t r u c t u r e t o be extended o v e r medium range d i s t a n c e a r e v e r y s t r o n g . Thus t h e w a t e r m o l e c u l e r o t a t i o n s become v e r y hard, g i v i n g r i s e t o a v e r y l o w v a l u e o f t h e Dr c p e f f i c i e n t .

I n f i g u r e 3, we present t h e HWHM v a r i a t i o n AET versus QL obtained by f i t t i n g t h e expression ( 3 ) f o r pure Hz0 (Dr = 0.13 meV) and t h e s a t u r a t e d s o l u t i o n (Dr = 0.005 meV) a t 298K. The corresponding r e s u l t s f o r 6M and 3M s o l u t i o n s are a l s o presented. Accor- d i n g t o t h e Random Jump D i f f u s i o n model f o r t r a n s l a t i o n a l d i f f u s i o n /13/ t h e quasi- e l a s t i c h a l f w i d t h should be given by :

II

^Q'Q;

AE, = ( 4 )

o (l+Q2()

Qo i s a c h a r a c t e r i s t i c l e n g t h i n a random d i s t r i b u t i o n o f jump l e n g t h s given by,

and T~ i s t h e residence time o f a molecule i n a q u a s i - e q u i l i b r i u m p o s i t i o n .

We found t h a t eq.(4) could f i t c o n v e n i e n t l y t h e AET vs Q behaviour. For t h e satura- t e d s o l u t i o n of,ZnC12 i n H20, t h e f i t y i e l d s t h e f o l l o w i n g values f o r t h e parameters:

R o = 0 . 5 8 ? 0 . 0 5 A, T = 8 . 1 * 0 . 5 ps (and thus t h e hydrodynamic d i f f u s i o n c o e f f i c i e n t D = Q E / r 0 t u r n s o u t ?o be D = 0.41.10-5 cm2 s e c - I /14/). F o r pure H20, we obtained Q o = 0 . 6 4 * 0 . 0 5 A i n agreement w i t h t h e r e s u l t s o f Chen e t a1 /15/, and . r o = 1 . 7 + 0 . 1

C7-148 JOURNAL DE PHYSIQUE

2 -1

ps, so t h a t D = 2.40. cm sec

,

which i s t h e c o r r e c t value o f t h e macroscopic d i f f u s i o n c o e f f i c ' e n t a t room temperature. From (5), we may deduce t h e mean quadra- t i c jump l e n g t h L3 =

z2

⁼ 6ag i .e. L = &,,ao. we obtained f o r t h e s a t u r a t e d s o l u t i o n and f o r pure water t h e values L = 1.43 A and L =1.58

1

r e s p e c t i e l y which are c l o s e t o t h e d i s t a n c e between protons i n t h e H20 molecule (dH = 1.55

1).

I t i s i n t e r e s t i n g t o note t h a t f o r t h e case o f pure H20 t h e random d i f f u s i o n model o f eq.(4) does n o t seem t o f i t t h e h i g h e r Q data. T h i s discrepancy m i g h t be due t o t e c h n i c a l problems i n t h e f i t t i n g , caused by t h e comparable h a l f - w i d t h s t h a t t h e r o t a t i o n a l and t r a n s l a t i o n a l components have i n the h i g h Q range. However, i t m i g h t a l s o i m p l y a d e f i n i t e tendency o f t h e AET t o bend over a t h i g h Q ' s . I n t h i s case, a more a p p r o p r i a t e model f o r t h e t r a n s l a t i o n a l d i f f u s i o n o f water molecules c o u l d be t h a t proposed by Chudley and E l l i o t t /16/.

C l e a r l y i n order t o d i s t i n g u i s h between these two models f u r t h e r measurements a t h i g h e r Q values a r e needed. A t t h i s time we p r e f e r t o i n t e r p r e t our data on t h e b a s i s o f t h e random jump model s i n c e i t i s more " l i q u i d - l i k e " and i n v o l v e s l e s s r a d i c a l assumptions about t h e microscopic d i f f u s i o n a l motion o f t h e H20 molecules.

I n t h i s paper, we showed t h a t t h e r e e x i s t , a t l e a s t , two components i n t h e quasi- e l a s t i c neutron spectrum from water and h i g h l y concentrated ZnC12 s o l u t i o n s . The broad one i s associated w i t h t h e r o t a t i o n a l m o t i o n o f t h e H20 molecules.

The t r a n s l a t i o n a l p a r t i s described i n t h e whole Q-range i n v e s t i g a t e d by a random jump d i f f u s i o n model f o r both t h e pure H20 and t h e s a t u r a t e d ZnC12 s o l u t i o n .

L e t us n o t e t h a t even i n pure H 0 t h e residence time T t u r n s o u t t o have t h e r e l a - t i v e l y l a r g e value o f 1.7 ps an$ increases up t o 8 ps ?or water i n t h e s a t u r a t e d s o l u t i o n . Such times are o b v i o u s l y long enough t o s u s t a i n c o l l e c t i v e v i b r a t i o n a l e x c i t a t i o n s i n t h e l o c a l l y ordered r e g i o n s and thus c o n f i r m t h e assignment o f low frequency Raman spectra i n these systems as v i b r a t i o n a l d e n s i t y o f s t a t e s /2/.

Another r e s u l t concerns t h e value o f t h e mean jump l e n g t h L which t u r n s o u t t o be r o u g h l y t h e same f o r pure H20 and s a t u r a t e d s o l u t i o n and c l o s e t o t h e value o f t h e d i s t a n c e between protons i n t h e H20 molecule. For t h e i n t e r m e d i a t e case o f t h e more d i l u t e s o l u t i o n s , t h e a n a l y s i s i s more complex and s h a l l be r e p o r t e d i n a f u r t h e r pub1 i c a t i o n .

From t h e present data, on ZnC12 aqueous s o l u t i o n s , we have n o t been a b l e t o separate a c o n t r i b u t i o n from d i f f e r e n t species o f water as i t has been r e p o r t e d by Enderby e t a1 /17/ i n a r e c e n t work on NiC12 s o l u t i o n s . However, we f e e l t h a t , a t l e a s t a t h i g h concentrations, t h e concept o f h y d r a t i o n s h e l l s may l o s e i t s usefulness. I n f a c t our data c o n f i r m t h a t such systems are b e s t described by i n t e r m e d i a t e range ordered patches i n s i d e which e s s e n t i a l l y a l l t h e H20 molecules are more o r l e s s e q u i v a l e n t .

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