DYNAMICS OF SUPERCOOLED WATER STUDIED BY NEUTRON SCATTERING

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DYNAMICS OF SUPERCOOLED WATER STUDIED BY NEUTRON SCATTERING

J. Teixeira, M.-C. Bellissent-Funel, S.-H. Chen, A. Dianoux

To cite this version:

J. Teixeira, M.-C. Bellissent-Funel, S.-H. Chen, A. Dianoux. DYNAMICS OF SUPERCOOLED

WATER STUDIED BY NEUTRON SCATTERING. Journal de Physique Colloques, 1984, 45 (C7),

pp.C7-65-C7-71. �10.1051/jphyscol:1984706�. �jpa-00224267�

DYNAMICS OF SUPERCOOLED WATER STUDIED BY NEUTRON SCATTERING

J .

T e i x e i r a ,

Bellissent-Funel,

chen* and

~ianoux**

Laboratoire Lion BriZZouin, CEN ~ a c ~ a ~ + , 91191 Gif-sur-Yvette Cedex, Fronce

* ~ u c Z e a r Engineering Department, Massachusetts I n s t i t u t e o f TechnoZogy, Cambridge, Ma 02139, U.S.A.

** I n s t i t u t Laue-Langevin,

GrenobZe Cedex, France

Résumé - Nous présentons des r é s u l t a t s d'expériences de d i f f u s i o n incohé- r e n t e de neutrons, q u a s i - é l a s t i q u e e t i n é l a s t i q u e , par de l ' e a u en phase surfondue. L ' a n a l y s e du s p e c t r e q u a s i - é l a s t i q u e permet de déterminer deux temps c a r a c t é r i s t i q u e s e t l e u r dépendance en température. La d i f f u s i o n e s t expliquée par l e modèle de saut e t un mécanisme de r u p t u r e de l a l i a i s o n hydrogène e s t proposé. Le s p e c t r e i n é l a s t i q u e e s t étendu j u s q u ' à 600 meV montrant, pour l a première f o i s , l a r a i e due aux v i b r a t i o n s intramoléculaires de s t r e t c h i n g .

A b s t r a c t - Incoherent q u a s i - e l a s t i c and i n e l a s t i c neutron s c a t t e r i n g by water was performed i n a temperature range extending t o t h e supercooled s t a t e . The a n a l y s i s o f t h e q u a s i - e l a s t i c snectrum separates two main compo- nents and gives two c h a r a c t e r i s t i c times. T h e i r temperature a n a l y s i s j u s t i - f i e s t h e use o f t h e Jump D i f f u s i o n mode1 and suggests a mechanism f o r t h e hydrogen bond breaking. The i n e l a s t i c s p e c t r a extend u n t i l 600 meV, i .e.

covering t h e i n t r a m o l e c u l a r v i b r a t i o n r e g i o n showing, f o r t h e f i r s t time, t h e s t r e t c h i n g band.

As many o t h e r l i q u i d s , water molecules form between them hydrogen bonds. However, some pecul i a r i t i e s make i t s behaviour very s p e c i f i c . F i r s t l y , t h e hydrogen bond framework i s v e r y dense. A c t u a l l y , even a t room temperature, as much as 80 % o f t h e p o s s i b l e bondsare formed /1/. Secondly, t h e hydrogen bonds a r e f r a g i l e , i . e . , extremely temperature and pressure dependent, because o f t h e i r energy and d i r e c - t i o n a l character. F i n a l l y , t h e bonds form l o c a l l y a t e t r a h e d r a l l a t t i c e , i .e., a very open s t r u c t u r e where each molecule i s surrounded by about f o u r n e x t neighbours.

When t h e temperature i s decreased, t h e number o f bonds increases /1/, t h e angular c o r r e l a t i o n s a i s o i n c r e a s e / 2 / and consequently t h e observed anomalies i n t h e beha- v i o u r o f water a r e more pronounced. A t low temperatures, Say below room temperature and i n t h e su ercooled s t a t e , t h e s t r u c t u r a l aspects dominate and t h e p r o p e r t i e s o f water can l e explained from geometrical c o n s i d e r a t i o n s / 3 / . L t f o l l o w s , as a consequence, t h a t i n t h i s low temperature range, t h e n a t u r e of t h e p o t e n t i a l used, f o r instance i n numerical s i m u l a t i o n s i s n o t very c r u c i a l and d i f f e r e n t choices can g i v e good r e s u l t s , as f a r as t h e t e t r a h e d r a l s t r u c t u r e i s reproduced.

Because o f t h e importance o f hydrogen bonding, one can ask t h e f o l l o w i n g question : what i s t h e dyhamical behaviour o f an hydrogen bond and how i s i t r e l a t e d w i t h t h e t r a n s p o r t p r o p k r t i e s o f l i q u i d water ?

C l e a r l y , t h e r e i s no simple way t o i s o l a t e t h e hydrogen bond from t h e molecular dynamics. A c t u a l l y , most o f the techniques are m a i n l y s e n s i t i v e t o the molecule as a whole and t h e s e p a r a t i o n o f t h e hydrogen bond behaviour i s hazardous.

However, incoherent q u a s i - e l a s t i c and i n e l a s t i c neutron s c a t t e r i n g appears t o be

abor oratoire ^commun

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984706

C7-66 JOURNAL DE PHYSIQUE

r a t h e r a p p r o p r i a t e because one i s t h e r e s e n s i t i v e t o t h e p r o t o n dynamics, then t o the hydrogen bond.

I n a t y p i c a l neutron s c a t t e r i n g experiment, a beam of monoenergetic neutrons i s s c a t t e r e d by t h e sample. Angular and energy a n a l y s i s o f t h e s c a t t e r e d neutrons p r o v i d e i n f o r m a t i o n on both s t r u c t u r e and dynamics a t a molecular and atomic l e v e l . Incoherent neutron s c a t t e r i n g , i n p a r t i c u l a r , i s r e l a t e d w i t h t h e dynamic s t r u c - t u r e f a c t o r , Ss(Q,E), and can be expressed i n terms o f t h e atomic i n d i v i d u a l move- ments. Because o f t h e v e r y h i g h incoherent cross s e c t i o n o f hydrogen atoms, t h e s c a t t e r i n g by Hz0 molecules can be assumed t o be o r i g i n a t e d by hydrogen atoms and the observed energy spectrum measures t h e p r o t o n dynamics.

The experimental d e t e r m i n a t i o n o f t h e incoherent i n e l a s t i c spectrum i s a compromise between t h e amplitude of t h e energy t r a n s f e r range and t h e energy r e s o l u t i o n . ide present here two s e t s of experiments q u i t e d i f f e r e n t from t h i s p o i n t o f view.

One s e t o f experiments used t h e Intense Pulsed Neutron Source a t Argonne (U.S.A.).

The i n c i d e n t neutron energy was 800 meV which a l l o w s one,t equal t o 600 meV a t reasonable Q values ( s m a l l e r than 8 A- P ) . reach energy t r a n s f e r s

F i g 1 - G(Q, E) defined by Eq.(l), obtained a t - 15OC. The energy o f t h e i n c i d e n t neutrons was 800 meV.

I n F i g . 1 we show t h e f u n c t i o n

G(Q,E)

-7 ~2 Ss(Q,E)

Q ⁽¹⁾

(where E i s t h e energy t r a n s f e r and Q the wave v e c t o r ) obtained a t -15"C, i .e. w i t h a supercooled sample. For t h i s purpose we used a s e t o f 150 P i r e x c a p i l l a r i e s 0.8 mm i . d .

From t h e f i g u r e we i d e n t i f y c l e a r l y t h r e e main bands : the l i b r a t i o n a l band a t 96

meV, t h e i ntramol e c u l a r v i b r a t i o n a l bendi ng band a t 207 meV and t h e i n t r a m o l e c u l a r

1 ) the l i b r a t i o n a l band s h i f t s towards high frequencies when temperature decreases.

2) the bending l i n e i s almost temperature independent.

3 ) t h e stretching l i n e s h i f t s towards low frequencies with decreasing temperature.

In contrast with the equivalent peak i n the Raman spectrum, i t cannot be separated in d i f f e r e n t components. Al1 these r e s u l t s indicate t h a t the proton motion i n water molecules i s strongly affected by the formation of hydrogen bonds. In p a r t i c u l a r

i t i s the origin of the l i b r a t i o n a l band which i s not present i n gas phase. The temperature variation of the l i b r a t i o n a l band can a l s o be explained noting t h a t the hydrogen bond network i s more d i s t o r t e d when temperature increases and will be b e t t e r understood wi t h the quasi-el astic spectrunl analysis we present below.

A more detailed analysis of t h i s s e t of r e s u l t s will be presented elsewhere /4/

Another s e t of experiments was performed a t the I n s t i t u t Laue-Langevin (Grenoble).

The incident neutron energy was 3.14 meV, in order t o obtain a resolution high enough t o study the quasi-elastic component of the incoherent spectrum, even a t low temperatures. The sample was composed of about 80 Pyrex c a p i l l a r i e s ( i . d .

0.3 mm) i n order t o decrease the temperature down t o -20°C. Spectra were recorded a t ni ne d i f f e r e n t temperatures below room temperature, and f o r 19,d'fferent angles corresponding t o e l a s t i c wave-vectors 4 extending from 0.25 t o 2 A-1. A n example of t h e obtained spectra i s given i n Fig.2.

Fig 2 - Typical quasi-elastic spectra, obtained a t - 5OC. The energy of the incident neutrons was 3.14 meV. Points represent the experimental data. The solid l i n e s are the best f i t . The dashed l i n e s represent the resolution function.

The f i t was done assuming two dynamic processus each of them described by lorent- zians

The f i r s t term i s the Debye-Waller f a c t o r , < u 2 > i s the vibrational amplitude and

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* means c o n v o l u t i o n . The mathematical form o f t h e o t h e r terms a r e :

I n t h i s expressions t h e energy t r a n s f e r i s now represented by w,

(Qa) a r e s p h e r i - c a l Bessel f u n c t i o n s and a

0.98 A ( t h e O-H d i s t a n c e ) i s a r a d i u s %f g y r a t i o n f o r t h e r o t a t i o n .

T(Q,w) i s a l o r e n t z i a n w i t h HWHM

T(Q) and,in a c l a s s i c a l p i c t u r e , i s associated w i t h d i f f u s i o n processes. We analysed t h e w i d t h r ( Q ) w i t h i n t h e Jump D i f f u s i o n mode1 /5/:

where D i s 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 and

represents a residence time. Fig.3 shows t h e r e s u l t o f t h i s f i t a t d i f f e r e n t temperatures between 20°C and -20°C.

Fig.3 - HWHM o f t h e t r a n s l a t i o n a l l o r e n t z i a n a t d i f f e r e n t temperatures. The s o l i d l i n e s reoresent t h e b e s t f i t . For T=20°C t h e s e l f - d i f f u s i o n l i n e i s shown.

The broad components R(Q,w) are normally associated w i t h r o t a t i o n a l r e l a x a t i o n . They a r e Q independent. If we d e f i n e a c h a r a c t e r i s t i c t i m e

given by

=q

( 6 )

we o b t a i n an Arrhentus behaviour f o r i t s temperature dependence ( F i g . 4 ) .

F i n a l l y , we determined t h e Debye-Waller parameter. I t i s , w i t h i n the experimental

and ~ e r c o l a t i o n madel l Bertoliniet al.)

Fig.4 - Arrhenius p l o t of

and

determined i n Our experiment. D i f f e r e n t t r a n s - p o r t p r o p e r t i e s and r e l a x a t i o n times a r e shown t o g e t h e r .

e r r o r temperature independent. The value of t h e v i b r a t i o n a l ampli tude i s

<u2>1I2

0.484 1. We must emphasize t h a t al1 t h e d a t a a r e f i t t e d with a t y p i c a l e r r o r of 1 % with t h r e e f r e e parameters : <u2>, r(Q) and D r . In Fig.2 t h e s o l i d l i n e s r e p r e s e n t t h e f i n a l f i t .

From t h i s f e a t u r e s , i t i s p o s s i b l e t o j u s t i f y a mechanism f o r t h e proton motion.

As we pointed o u t above, water molecules a r e i n s t a n t a n e o u s l y connected with most o f t h e i r neighbours through hydrogen bonds. However, each hydrogen bond i s very d i r e c - t i o n a l and t h e 1 i b r a t i o n amplitude i s very l a r g e . Molecular dynamics computer simulations of Impey e t al / 6 / i n d i c a t e t h a t , when t h e amplitude of l i b r a t i o n i s above 25" t h bond i s broken. This e s t i m a t i o n i s i n very good agreement with t h e value < u 2 > l / ?

0.484 8. we deduced from t h e Debye-Waller f a c t o r .

When a bond i s broken, t h e molecule can form a bond with another neighbour. Then, t h e time TI i s a measure of t h i s c h a r a c t e r i s t i c time, and we j u s t i f y t h e use of Eq. ( 4 ) i n t h e f i t t i n g procedure, noting t h a t t h i s processus corresponds t o a r o t a t i o n a l movement. Independent determi nations of t h e hydrogen bond 1 i fe-time / 7 / lead t o values with t h e same o r d e r of magnitude ( F i g . 4 ) , but what must be emphasized i s t h a t i n both cases one f i n d s an Arrhenius temperature dependence. This normal behaviour i s d i f f e r e n t from those of a l 1 o t h e r p r o p e r t i e s of water and i t i s c e r - t a i n l y a m a n i f e s t a t i o n of t h e hydrogen bond dynamics.

On t h e o t h e r hand, t h e d i f f u s i o n of t h e molecule i s p o s s i b l e only when a s u f f i c i e n t

number of bonds i s broken simultaneously. With decreasing temperature, t h e f r a c t i o n

of mobile molecules becomes extremely small and consequently the.temperature depen-

dence of a l 1 t h e t r a n s p o r t p r o p e r t i e s i s s t r o n g l y non-Arrhenius. A simple p i c t u r e

based on t h e geometrical p r o p e r t i e s of t h e hydrogen bond framework has been propo-

sed /3/ t o r e l a t e t h e hydrogen bond l i f e t i m e and t h e t r a n s p o r t p r o p e r t i e s and used

with success i n t h e i n t e r p r e t a t i o n of t h e d i e l e c t r i c r e l a x a t i o n time / 8 / . In

C7-70 JOURNAL DE PHYSIQUE

experiments, t h e anomalous temperature behaviour i s followed by t h e residence time

T~

( F i g . 4 ) .

I t i s worth noting moreover t h a t a c h a r a c t e r i s t i c jump length L can be defined i n t h e c l a s s i c a l way from Eq.15) by

L

(6 D -ro) 1 / 2 _{( 7 )}

The temperature dependence we o b t a i n f o r L i s given i n Fig . 5 . I t s value i s i n average

Fig.5 - Temperature dependence,of t h e jump length L defined by Eq.(7). Note t h a t i t i s i n average c l o s e t o 1 . 6 A , t h e d i s t a n c e between t h e two protons i n water molecule.

equal t o 1.6 1\, which suggests t h a t t h e d i f f u s i o n i s made by r o t a t i o n a l jumps.

Actually t h i s d i s t a n c e corresponds t o t h e d i s t a n c e between two protons, then t o two p o s s i b l e bonds of t h e water molecule. The small temperature dependence can be understood i f we remember t h a t a t high temperatures t h e hydrogen bond frarnework is more deformed and t h e d i s t a n c e L i s reduced.

Fig.4 shows p l o t t e d t o g e t h e r d i f f e r e n t r e l a x a t i o n times and dynamic p r o p e r t i e s of l i q u i d water. While t r a n s p o r t p r o p e r t i e s and molecular r e l a x a t i o n times a r e not Arrhenius temperature dependent, a s h o r t e r time i s observed i n depolarized l i g h t Rayleigh s c a t t e r i n g /7/ and i n O u r experiment. The temperature dependence of t h e hydrogen bond 1 ifetirne deduced by Bert01 i n i e t a l /8/ has a l s o a small temperature dependence w i t h an a s s o c i a t e d a c t i v a t i o n energy c l o s e t o t h a t of

The a c t i v a t i o n energy deduced from Rayleigh s c a t t e r i n g is s l i g h t l y h i g h e r perhaps because i t i s t k r e a s s o c i a t e d with t h e iholecular p o l a r i z a b i l i t y .

Ne described above a mechanism t o r e l a t e t h e two d i f f e r e n t behaviours i n temperature

of t h e c h a r a c t e r i s t i c times .ro and

. However,

approach i s c e r t a i n l y t o o crude,

i n p a r t i c u l a r , w r i t i n g Eq.(2). ~ c t u a i l ~ , t h e mode1 we propose i s not compatible with

t h e convolution of t h e d i f f u s i o n and r o t a t i o n components which supposes t h a t t h e

temperature dependent. With such a s p e c i f i c model , i t w i l l be p o s s i b l e t o p r e c i s e more q u a n t i t a t i v e l y t h e molecular dynamics o f water. Our a n a l y s i s represents i n t h i s sense a f i r s t order approximation.

REFERENCES

/1/ G.E.Walrafen i n Water : A Comprehensive T r e a t i s e , e d i t e d by F.Franks (Plenum N.Y.,1972) v o l . 1 ; G. d l A r r i g o , G. Maisano, F. Mallamace, P. M i g l i a r d o and F. Wanderlingh, J.Chem.Phys. 75, 4264 (1981) ; W.A.P. Luck and W. D i t t e r , J .Phys.Chem. - 74, 3687 (1970) .-

/2/ L. Bosio, J. T e i x e i r a , J.C. Dore, D. S t e y t l e r and P. Chieux, Mol.Phys. 50, 733 (1983)

L. Bosio, S.-H. Chen and 3 . T e i x e i r a , Phys.Rev. Ac, ^{1468 -}

(1983).

/3/ H.E. Stanley and J . T e i x e i r a , J.Chem.Phys. 2, 3404 (1980).

/4/ S.-H. Chen, K. Toukan, C. Loong, D. P r i c e and J . T e i x e i r a ( t o be published).

/5/ P.A. E g e l s t a f f , An I n t r o d u c t i o n t o t h e L i q u i d S t a t e (Academic, London, 1967)

/ 6 / R.W. Impey, P.A. Madden and I.R. McDonald, Mol.Phys. 5, 513 (1982).

/7/ C.J. Montrose, J.A. Bucaro, J. Marshall-Coakley and T.A. L i t o w i t z , J-Chem.

Phys. 60, 5025 (1974) ; O. Co.nde and J. T e i x e i r a , J .Phys. ( P a r i s ) 5, 525 (1983):

/8/ D. B e r t o l i n i , M. C a s s e t t a r i and G. S a l v e t t i , 3.Chem.Phys. c, 3285 (1982).