DYNAMICS OF PRESSURIZED AND SUPERCOOLED WATER AND AQUEOUS SOLUTIONS STUDIED BY NMR

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DYNAMICS OF PRESSURIZED AND SUPERCOOLED WATER AND AQUEOUS

SOLUTIONS STUDIED BY NMR

H.-D. Lüdemann, E. Lang

To cite this version:

H.-D. Lüdemann, E. Lang. DYNAMICS OF PRESSURIZED AND SUPERCOOLED WATER AND

AQUEOUS SOLUTIONS STUDIED BY NMR. Journal de Physique Colloques, 1984, 45 (C7), pp.C7-

41-C7-48. �10.1051/jphyscol:1984704�. �jpa-00224265�

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J O U R N A L DE PHYSIQUE

Colloque C7, supplément au n09, Tome 45, septembre 1984 page C7-41

DYNAMICS OF PRESSURIZED AND SUPERCOOLED WATER AND AQUEOUS SOLUTIONS STUDIED BY NMR

H.-D. ~ ü d e m a n n and E. W. Lang

I n s t i t u t für Biophysik und PhysikaZische Biochernie, Universitat Regensburg, Postfach 397, 0-8400 Regensburg, F.R. G.

1 2

Résumé

-

Les temps de r e l a x a t i o n ( T l ) pour lH, 1H e t 170 de 1 'eau l é g è r e e t -au l o u r d e o n t é t é é t u d i é s dans l a r é g i o n s u r f o n i u e j u s q u ' à 185 K. Les mesures couvrent une gamme de p r e s s i o n e n t r e 0 , l e t 300 MPa. Près de l a l i m i t e de s u r f u s i o n vers 195 K, l e s Tl présentent un minimum e t deviennent dépendants de l a fréquence.

On montre que l a dynamique des molécules d'eau peut ê t r e d é c r i t e p a r l e modèle de d i f f u s i o n r o t a t i o n n e l l e i s o t r o p e . Dans l a r é g i o n surfondue l e temps de c o r r é l a t i o n 7, e s t p l u s l o n g d'un f a c t e u r 103 q u ' à température ambiante.

&

1 2 17

A b s t r a c t - The s p i n l a t t i c e r e l a x a t i o n times ( T l ) f o r lH, 1H and 80 o f l i g h t and heavy water have been s t u d i e d i n t h e supercooled range down t o

185 K. The measurements cover t h e pressure range between 0 . 1 and 300 MPa. I n the extreme o f supercooling around

-

195 K t h e T l show a minimum and becone frequency dependent.

I t i s shown, t h a t the s i n g l e molecule dynamics o f water can be described by 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 . I n the supercooled range t h e c o r r e l a t i o n time T2 i s compared t o ambient t e ~ p e r a t u r e s longer by more than a f a c t o r o f 103.

I N T R O D U C T I O N

A11 unusual p r o p e r t i e s o f l i q u i d water become more pronounced i n the supercooled range. A t ambient pressure water can be k e p t l i q u i d down t o

-

239 K, where i t c r y s t a l l i z e s homogeneously. Cooling b u l k samples t o t h i s temperature range f o r an extended p e r i o d o f time appears t o be extremely d i f f i c u l t and hampered by l a c k o f reproduci b i l i t y . Microscopic samples, i .e. dropl e t s o f pure water wi t h a diaineter of a few I.im suspended i n a c l o u d chamber o r i n an organic l i q u i d can very r e l i a b l e be supercooled t o t h i s temperature /1,2,3/. Emulsions o f water i n a m i x t u r e o f a l kanes can be s t a b i l i z e d by a d d i t i o n o f a water i n s o l u b l e emulqator l i k e s o r b i t a n t r i s t e a - r a t . I n such emulsions most o f the water d r o p i e t s remain l i q u i d i n t h e metastable

range between 273 K and 239 K f o r p e r i ods o f months /4/.

Kanno e t a l . /5,6/ s t u d i e d i n such emulsions the pressure dependence o f the homogeneous n u c l e a t i o n tempe- r a t u r e (TH) o f l i g h t and heavy water t o a maximal pressure o f 300 MPa.

F i g . 1 compiles t h e r e s u l t s . These emulsions are due t o the mu1 t i p l e phase boundaries opaque white, and thus most spectroscopic methods cannot be applied.

F i g u r e 1

-

p - T - p r o j e c t i o n o f the phase

L - - - diagram o f H20 and D20. TM=mel ti n g tempe-

180 r a t u r e , TH=homogeneous n u c l e a t i o n tempe-

r a t u r e /5,6/.

0 50 100 150 200

-

250 ^piMPa)300

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984704

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C7-42 J O U R N A L DE PHYSIQUE

E l e c t r o m a g n e t i c r a d i a t i o n i n t h e f r e q u e n c y range o f 10-400 MHz, as used i n NMR spectroscopy, r e a d i l y p e n e t r a t e s t h e m u l t i p l e phase boundaries o f t h e s e emulsions, and Hindman e t a l . /7,8/ c o u l d t h u s e x t e n d s p i n l a t t i c e r e l a x a t i o n t i m e ( T l ) measurements o f t h e deuterons i n heavy w a t e r and o f oxygen-17 n u c l e i i n e n r i c h e d l i g h t water t o s 240 K. Our group has a p p l i e d t h e s e emulsions i n s t u d i e s o f t h e p r e s s u r e dependence o f T l a t p r e s s u r e s up t o 300 MPa. We succeeded i n s u p e r c o o l i n g a t p > 200 MPa D20 t o 188 K and Hz0 t o 185 K, and were a b l e t o measure T l o f t h e deuterons /9/ and p r o t o n s / I O / under these c o n d i t i o n s . Unsurmountable e x p e r i m e n t a l d i f f i c u l t i e s l i m i t e d t h e t e m p e r a t u r e range f o r oxygen-17-Tl s t u d i e s i n l i g h t and heavy w a t e r t o T

2

240 K /Il/. I n t h e s e experiments a h i g h pressure-NMR-ce11 o f t h e s t r e n g t h e n e d g l a s s ce11 d e s i g n i n t r o d u c e by Yamada /12/ was a p p l i e d .

E X P E R I M E N T A L

The oxygen f r e e emulsions were p r e p a r e d by s l a s h i n a a t h o r o u g h l y degassed m i x t u r e o f water, m e t h y l c y c l o p e n t a n e and methylcyclohexane i n a s e a l e d ampoule t h r o u g h a s t a i n - l e s s s t e e l n e t . The emulsions a r e s t a b i l i z e d b y t h e a d d i t i o n o f 4 % W/W s o r b i t a n - t r i s t e a r a t (Span 65) t o t h e o r g a n i c phase. D e t a i l s o f t h e procedure have been p u b l i s h e d /Il/. The m o d i f i c a t i o n o f t h e s t r e n g t h e n e d g l a s s ce11 used i n t h e s e ex- p e r i m e n t s i s d e s c r i b e d i n t h e li t e r a t u r e /13/.

The s p i n l a t t i c e r e l a x a t i o n t i m e s T l o f t h e t h r e e n u c l e i were o b t a i n e d w i t h t h e usual

-

T

-

^IT

-

T

- -

p u l s e sequence on a V a r i a n XL-100-15 FT NMR s p e c t r o m e t e r .

2 2

O p e r a t i n c a t 13.56 MHz f o r t h e oxygen-17, a t 15.35 f o r t h e deuterons and a t 100.1 MHz f o r t h e p r o t o n s . R e c e n t l y L. P i c u l e l l and E.W. Lang /14/ o b t a i n e d t h e d e u t e r o n - T l i n heavy w a t e r emulsions a t 39.14 MHz and a t 55.54 PIHz.

T H E O R E T I C A L

I n n u c l e a r magnetic r e l a x a t i o n experiments t h e c o u p l i n g o f n u c l e a r s p i n s w i t h t h e s u r r o u n d i n g l a t t i c e i s used t o o b t a i n i n f o r m a t i o n a b o u t m o l e c u l a r m o t i o n s /14,15/.

The r e l e v a n t i n t e r a c t i o n H a m i l t o n i a n f o r d i f f e r e n t c o u p l i n g s X i s g e n e r a l l y g i v e n i n a l a b o r a t o r v - f i x e d frame bv: ^O ,

w i t h S: d e n o t i n g i r r e d u c i b l e t e n s o r o p e r a t o r s o f rank 1 a c t i n g on s p i n v a r i a b l e s o n l y an8 t h e L?, a r e i r r e d u c i b l e t e n s o r o p e r a t o r s o f r a n k 1 a c t i n g on l a t t i c e degrees o f freedom. We w i l l be concerned w i t h magnetic d i p o l e - d i p o l e and e l e c t r i c quadrupole c o u p l i n g s w h i c h a r e g i v e n by second r a n k t e n s o r s and a r e most c o n v e n i e n t - l y expressed i n a m o l e c u l e f i x e d p r i n c i p a l a x i s system. The frame t r a n s f o r m a t i o n f r o w t h e m o l e c u l e f i x e d t o t h e l a b o r a t o r y f i x e d a x i s system becomes t i m e dependent due t o m o l e c u l a r motions. I t i s t h i s t i m e dependence w h i c h c o n t a i n s i n f o r m a t i o n a b o u t m o l e c u l a r dynamics i n 1 iq u i d s . I n n u c l e a r magnetic r e l a x a t i o n experirnents one can observe two d i s t i n c t l y d i f f e r e n t r e l a x a t i o n r a t e s . I n thermal e q u i l i b r i um t h e n u c l e a r s p i n s a r e p o l a r i z e d para1 l e 1 t o t h e appl i e d s t a t i c magnetic i n d u c t i o n Bo, A p p l i c a t i o n o f a t i m e dependent magnetic i n d u c t i o n Bl(t) a t t h e f r e q u e n c y wg/2.rr i n - duces a n o n - e q u i l i b r i u m m a y e t i s a t i o n where components p a r a l l e l and p e r p e n d i c u l a r t o Bo r e l a x w i t h d i f f e r e n t r a t e s t o e q u i l i b r i u m . The f o r m e r i s c a l l e d t h e s p i n - l a t t i c e r e l a x a t i o n r a t e - a n d 1 i s due t o an energy exchange between t h e s p i n system

T l . 1

and t h e l a t t i c e . The l a t t e r 1s c a l l e d t h e s p i n - s p i n r e l a x a t i o n r a t e - and i s due t o

a l o s s o f phase coherence o f t h e s p i n s . T2

The e x p e r i m e n t a l l y o b s e r v a b l e r e l a x a t i o n r a t e s a r e p r o p o r t i o n a l t o c e r t a i n com- b i n a t i o n s o f s p e c t r a l d e n s i t y f u n c t i o n s JI, w h i c h i n t u r n a r e t h e F o u r i e r - L a p l a c e - t r a n s f o r m s o f t i m e a u t o c o r r e l a t i o n f u n c t i o n s o f t h e l a t t i c e o p e r a t o r s L,: f o r d i f f e r e n t c o u p l i n g s e v a l u a t e d a t t h e o b s e r v i n g frequency wo/2n:

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I n the case o f e l e c t r i c quadrupole i n t e r a c t i o n s ( A = Q) the l a t t i c e f u n c t i o n s L i m depend o n l y on o r i e n t a t i o n a l v a r i a b l e s , namely t h e E u l e r angles s p e c i f y i n g t h e o r i e n t a t i o n of the molecule f i x e d frame w i t h r e s p e c t t o the l a b o r a t o r y a x i s system.

Thus t h i s i n t e r a c t i o n moni t o r s s i n g l e molecule r e o r i e n t a t i o n a l motions only. This i s the dominant r e l a x a t i o n mechanism f o r deuterons and oxygen-17-nuclei . For i s o t r o p i c r e o r i e n t a t i o n a l motions the a u t o c o r r e l a t i o n f u n c t i o n i s i n most cases exponential a t l o n g times w i t h a s i n g l e time constant, t h e c o r r e l a t i o n t i m e 72. The r e l a x a t i o n r a t e s are then given by

1 denotes t h e s p i n quantum number which i s 1=1 f o r deuterons and 1 = - fo r 0-17- 5 2

e2q

Q

n u c l e i .

(*)

t h e quadrupole c o u p l i n g constant i n frequency u n i t s and

n

the

Q

asymmetry parameter o f the trace1 ess diagonal e l e c t r i c f i e l d g r a d i e n t tensor a t the nucleus i n question.

I t must be noted t h a t f o r a t o t a l s p i n I > 1 a s i n g l e r e l a x a t i o n time T i (i=1,2) i s obtained i n the motional narrowing l i m i t ( ~ 5 ~ 6 << 1 ) only. This i s g e n e r a l l y the case i n low molecular weight, low v i s c o s i t y liqu'ids. I n l i q u i d water t e c h n i c a l d i f f i c u l t i e s do n o t p e r m i t measurements o f oxygen-17-relaxation times o u t s i d e the motional narrowing 1 im i t , i .e. i n t h e deeply supercooled region.

I n the case o f magnetic di pole-dipole i n t e r a c t i o n s (h=D) the 1 a t t i c e functions Llm depend on o r i e n t a t i o n a l v a r i a b l e s as w e l l as on t h e d i s t a n c e r i between two i n t e r a c t i n ~ n u c l e i . Only i f the i n t e r a c t i n g p a i r o f n u c l e i belongs

20

^{the same}

r i ç i d molecule i s t h e i r d i s t a n c e r i j independent o f time. I n t h i s case the i n t r a - molecular d i p o l a r i n t e r a c t i o n a l s o monitors s i n g l e molecule r e o r i e n t a t i o n a l motions o n l y and the i n t r a m o l e c u l a r r e l a x a t i o n r a t e s f o r l i k e spins a r e given by t h e same expressions as f o r t h e quadrupolar i n t e r a c t i o n . The mu1 t i p l y i n g f a c t o r i n f r o n t o f t h e brackets i n equ. (3) i s now given by

I f the two i n t e r a c t i n g n u c l e i belong t o d i f f e r e n t molecules, t h e i n t e r m o l e c u l a r d i - p o l a r i n t e r a c t i o n i s modulated by t r a n s l a t i o n a l and r o t a t i o n a l motions. The corresponding s p e c t r a l densi ty f u n c t i o n s are d i f f i c u l t t o o b t a i n and depend s t r o n g l y on the motional model. I n the present discussion we w i l l n o t consider t h i s c o n t r i b u t i o n i n d e t a i l , b u t i t w i l l be assumed t h a t the t o t a l d i p o l a r r e l a x a t i o n r a t e i s given by

1 - /l

- -

+ -

1

\

T? (?)i n t r a (Tlli n t e r

where

(k)

i s the i n t r a m o l e c u l a r r e l a x a t i o n r a t e i n the r i g i d molecule approxi- Tl i n t r a

mation. I t has been shown, t h a t a t temperatures below

-

³⁵⁰K t h e p r o t o n r e l a x a t i o n i n l i q u i d l i g h t water i s completely described by t h e dipole-di pole-interaction /17,13/.

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C7-44 JOURNAL DE PHYSIQUE

R E S U L T S

55.54 MHz 39.14MHz

15.35MHz

F i q u r e 2

-

Isotherms o f t h e deuteron

1

s p i n l a t t i c e r e l a x a t i o n times Tl i n D,O. r /23,24/. O /9/

F i g u r e 3

-

Isobars o f the deuteron s p i n 1 a t t i c e r e l a x a t i o n times T l i n supercooled D20 a t t h r e e NMK-frequencies /9,13/.

I n F i g . 2 the deuteron s p i n l a t t i c e r e l a x a t i o n times T l o f heavy water are presented. I n a l 1 o t h e r l i q u i d s s t u d i e d h i t h e r t o , a p p l i c a t i o n o f pressure a t constant temperature reduces t h e m o b i l i t y o f t h e molecules and thus shortens Tl. This behaviour i s observed i n l i q u i d water a t temperatures above

-

350 K and below

-

^{200 K.}

I n the i n t e r m e d i a t e temperature range the i n i t i a l a p p l i c a t i o n o f pressure leads t o a d r a s t i c increase o f T l . The various isotherms do show maxima a t pressures between 150 and 250 MPa. These maxima become most pronounced i n t h e supercooled range, where f o r i n s t a n c e the 249 K-isotherm increases by approximately 4,5 times.

The data given i n F i g . 2 were obtained a t 15.35 MHz. F u r t h e r l o w e r i n g o f the temperature, which i n o r d e r t o a v o i d homogeneous n u c l e a t i o n must be done a t p >

225 MPa, leads t o a minimum i n T l , shown i n F i ç . 3. This minimum i s p r e d i c t e d by theory (equ. 3) t o occur f o r any l i q u i d o f s u f f i c i e n t l y low molecular m o b i l i t y . The theory demands, t h a t i n t h i s range the T become frequency dependent. The data obtained very r e c e n t l y by Lang and P i c u l e l l )13/ a t 39.14 MHz and 55.54 MHz ( F i g . 3) show t h i s expected behaviour.

The oxygen-17-Tl o f D 170 /Il/ show between 243 K and 450 K w i t h i n experimental e r r o r the rame pressure an$ d e n s i t y dependence as the deuteron Tl o f 02160. However, comparison o f the oxygen-17-Tl l i g h t and heavy water r e v e a l , t h a t the r a t i o

17

-

tT1(D2 O).T1 ' ( ~ ~ ' ~ 0 ) lp,T i s a f u n c t i o n o f temperature and pressure. F i ç . 4 pre- sents t h i s r a t i o a t two pressures.

These data a r e o f immediate relevance t o t h e usual a n a l y s i s o f biopolymer hydration, where t h e deuteron-Tl i n heavy water s o l u t i o n s a r e used t o o b t a i n t h e

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i n t r a n o l e c u l e r c o n t r i butions t o proton r e l a x a t i o n i n l i g h t water. I t can be seen from t h e d a t a given in Fig. 4 , t h a t

250MPa t h e a p p r o p r i a t e s c a l i n g f o r t h e isotope e f f e c t of the c o r r e l a t i o n times, when

t

^•^• comparing l i g h t and heavy water, i s by

* * O . . .

i

no means s t r a i g h t - f o r w a r d and prone t o s i g n i f i c a n t e r r o r s . Fig. 5 gives t h e 225 MPa-isobar f o r t h e proton-Tl i n l i g h t water a t 100.1 MHz.

2 0-

15- -

10

O Again one observes t h e minimum o f Tl. In

o r d e r t o s e p a r a t e t h e intramolecular c o n t r i b u t i o n t o t h i s experimental r a t e ,

SMPa one can use t h e oxygen-17-Tl obtained i n

a

0. l i g h t water enriched with oxygen-17 / I l / .

* m .

* O • However, technical d i f f i c u l t i e s 1 imi t

..

t h e s e measurements t o temperatures T >

0 240 K . For t h e extremely supercooled

$56 ' ' ' 3 6 0 ' ' '350' ' ' ' 4 b 0 ' ' '460' range a d i f f e r e n t approach has t o be

- T ( K ) used f o r t h e c h a r a c t e r i z a t i o n of t h e r o t a t i o n a l motion of t h e H20 molecule:

Figure 4

-

Dynamic i s o t o p e e f f e c t a t The.only way found h i t h e r t o i s t o study 5 MPa and 250 MPa a s obtained from t h e t h e proton-relaxation r a t e s of l i g h t r a t i o of t h e oxygen-17-Tl i n l i g h t and water enriched with oxygen-17. The geo- heavy water a s function of temperature. metric c o n s t r a i n t s of t h e water s t r u c -

t u r e , t h e small s i z e of t h e di pole

-6 moment of t h e oxygen-17 nucleus, and the

r dependence make t h e c o n t r i b u t i o n of t h e oxygen-17 t o proton r e l a x a t i o n p r a c t i - c a l l y an i n t r a m o l e c u l a r c o n t r i b u t i o n . Equ. (7) has i n t h i s case t o be w r i t t e n a s :

i n t r a i n t r a i n t e r

=

(:lHH

⁺^(k)170-H¹ ⁺

(\XH

⁽⁸⁾

X = mole f r a c t i o n 0-17.

The term ( x / ( T ~ ) ; ~ ~ ~ ~ i s derived by s u b s t r a c t i n g e r e l a x a t i o n r a t e s

il

^obtained

OH i n H21p0 from t h e corresponding d a t a

determined i n ~ 2 1 7 0 . Provided, t h e O-H

10; bond length and t h e H-H d i s t a n c e i n

5- l i q u i d water i s known and t h e isotropie

TI - r e o r i e n t a t i o n a l mode1 (equ. 3) can be

IS)

-

a p p l i e d i t i s s t r a i g h t - f o r w a r d t o c a l -

,-

c u l a t e t h e intermolecular c o n t r i b u t i o n

t o t h e proton r e l a x a t i o n i n l i g h t water.

The r e s u l t s of t h i s s e p a r a t i o n a r e given

0 5 -

i n Fig. 6 . I t can be seen, t h a t t h e ano- malies of t h e dynamics of t h e water mole- c u l e s manifest themsel ve i n t h e i s o b a r s

01, f o r t h e i n t r a m o l e c u l a r c o n t r i bution as

well a s i n t h e i n t e r m o l e c u l a r terrns.

005- Contrary t o t h e behaviour observed i n

normal l i q u i d s , where pressure produces a l a r g e r change of t h e intermolecular r a t e s /18,19/ one observes, t h a t i n

Oo1-i5 jo j5 ' 5

--

5'0 1 0 0 0 i ~ - l ) 5'5 supercooled water t h e intramolecular c o n t r i b u t i o n has a s i g n ~ f i c a n t l y more

T pronounced pressure and temperature de- Figure 5 - 225 MPa-isobar of t h e proton pendence.

s p i n l a t t i c e r e l a x a t i o n times (Tl) i n supercooled H20 a t 100.1 MHz. /10,25/.

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JOURNAL DE PHYSIQUE

D I S C U S S I O N

The frequency d i s p e r s i o n o f the deute-

' n - 2 1 3 K ron-Tl around 200 K ( F i g . 3) o f f e r s the

223K unique p o s s i b i l i t y t o t e s t the appl i-

c a b i l i t y o f t h e motional model proposed i n the t h e o r e t i c a l s e c t i o n . From the

ZL3K

minimum c o n d i t i o n f o r the t h r e e curves

::::

one can d e r i v e the quadrupole c o u p l i n g

283K 2B3K constant and wi t h the c o n s t a n t d e r i v e d

one can f i t equ. ( 3 ) and ( 4 ) t o t h e

3 2 3 ~ experimental r e s u l t s . The 1 ines drawn

through the experimental p o i n t s are d e r i v e d from such a procedure. They i n - d i c a t e , t h a t t h e model o f i s o t r o p i c r e -

0 0 1

- o so ioo

-

i s o ^pIMPalZOO h r r

-

Ï P I M P ~ I r & wi t h i n experimental e r r o r . F u r t h e r o r i e n t a t i o n a l motions f i t s the data support f o r t h i s conclusion i s drawn F i g u r e 6

-

Isotherms o f the

( )

^and from the f i n d i n g t h a t i n t h e r e g i o n o f

1 i n t r a overlap the experimental deuteron- and

( )

c o n t r i b u t i o n s t o t h e p r o t o n oxygen-17-Tl do possess an i d e n t i c a l

1 i n t e r temperature and pressure dependence.

r e l a x a t i o n i n supercooled water. I n equ. ( 5 ) the quadrupole coup- l i n g constant (qcc) i s defined. I t i s a measure f o r t h e g r a d i e n t o f the e l e c t r i c f i e l d a t the quadrupolar nucleus. I n hydrogen bond forming systems the degree o f bond formation must i n f l u e n c e t h i s q u a n t i t y . Table 1 contains t h e qcc i n various phases of D20. I n the gas phase and i n s o l i d s the qcc can be determined e x p e r i m e n t a l l y . The data d e r i v e d from the minimum c o n d i t i o n o f the deuteron-Tl curve /13/ a r e a l s o i n - c l uded. V a r i a t i o n o f temperature and pressure i n 1 i q u i d water i n f l uences hydrogen bonding and o b v i o u s l y the qcc must be a f u n c t i o n o f temperature and pressure.

Table 1: Deuteron quadrupole c o u p l i n g constant o f D20

3

2 (kHz) i1 Ref.

h

I c e I h 213.4

+

0.3 0.112

+

0.005 20

~HDO vapour 318.6

+

2.4 0.06

+

0.16 21

1

supercool ed

1 iq u i d 201 2 5

However, r e l i a b l e estimates o f t h i s e f f e c t c o v e r i n g the whole l i q u i d range are l a c k i n g , and the c a l c u l a t i o n presented i n t h e f o l l o w i n g were performed w i t h the con- s t a n t qcc given i n Table 1.

From the Tl- and T2-data c o l l e c t e d one c a l c u l a t e s t h e o r i e n t a t i o n a l c o r r e l a t i o n time as f u n c t i o n o f temperature and pressure. I n simple l i q u i d s t h e i s o b a r i c and i s o c h o r i c temperature dependence o f T2 can o f t e n be represented by a simple

Arrhenius equation. I t i s w e l l known t h a t the dynamics o f water cannot be described by t h i s simple approach. The slope o f the i s o b a r s increases w i t h f a l l i n g temperature.

For normal viscous l i q u i d s t h e i s o b a r i c temperature dependence o f t h e dynamic p r o - p e r t i e s i s o f t e n w e l l represented by the VTF-equation:

where To i s the i d e a l glass temperature. The ï d e r i v e d f o r p > 150 MPa a r e w e l l represented by equation ( 9 ) /Il/. Least square$ f i t t i n g o f the-ï2 l e a d t o the i d e a l glass t r a n s i t i o n temperatures given i n Fig. 7. The To do show a pronounced i s o t o p e

(8)

Figure 7

-

p-T-projection of the phase Figure 8

-

Representation of some r2- aiagramof i-i20 and D20, including: TS= isobars as function O-f the reduced tempe-

temperature of s i n g u l a r i t y , T,=ideal ratures / I l / ('2: orientational corre- glass t r a n s i t i o n temperature. TS was l a t i o n time, TS s i n u l a r i t y tem e r a t u r e ) .

1

S

obtained by f i t t i n g the r2 data to the 0 Calculated from 1g0-T~ in H 2 O ;

Speedy-Ançell equation. @ calculated from ~ : O - T ~ in ~ ~ ' ~ 0 ;

A

calculated from : H - T ~ in 020 / 9 / ; i c a l c u l a t e d from :H-T~ in D20 /23,24/.

e f f e c t , and a small increase of To with pressure. A t lower pressures the T2 change in the supercooled range much f a s t e r with f a l l i n g temperature, than predicted by the VTF-equation. This i s most evident, i f the l e a s t squares f i t t i n g i s r e s t r i c t e d t o the range of To-values commonly accepted in the l i t e r a t u r e .

Speedy and Ange11 /22/ proposed t o describe the temperature dependence of a variety of s t a t i c and dynamic properties of supercooled water by a fractional power law, a s used in the theory of c r i t i c a l phenomena:

T-T -y

.2 =

(+)

⁽¹⁰⁾

S

The s i n g u l a r i t y temperature TS a t ambient pressure i s found f o r al1 properties studied h i t h e r t o a few degrees below TH, the homogeneo~ls nucleation temperature.

Fig. 7 includes TS f o r l i g h t and heavy water as obtained from l e a s t squares f i t t i n g t o the rotational correlation time f o r 0 . 1 (MPa) < p < 150 (MPa). For higher pressures the f i t becomes progressivly worse. A t p > 150 MPa The VTF equation pro- vides obviously a superior f i t . Comparing the f i t s of ~2 f o r l i g h t and heavy water t o equ. (10) reveals, t h a t a t constant pressure only TS for the two l i q u ~ d s i s

(9)

C7-48 JOURNAL DE PHYSIQUE

d i f f e r e n z . A t c o n s t a t ??essure t h e -r2 f o r l i g h t and heavy w a t e r f a 1 1 i n a l o g ~2 v e r s . l o g ( T - T ~ ) . T ~ - ~ p l o t on a s i n g l e s t r a i g h t l i n e , i f f o r TS t h e s i n g u l a r i t y temperatures g l v e n i n F i g . 7 a r e i n s e r t e d . The dynamics o f t h e w a t e r molecules a r e thus i d e n t i c a l i n t h e two systems a t equal d i s t a n c e f r o m t h e s i n g u l a r i t y temperature.

F i g . 8 c o l l e c t s a s e t o f T ~ - i s o b a r s i n t h i s r e p r e s e n t a t i o n . C O N C L U D I N G R E M A R K S

The e v a l u a t i o n o f t h e d a t a d e r i v e d from t h e NMR-experiments i s s t i l l i n a rudimen- t a r y s t a t e , s i n c e f o r a s u c c e s s f u l and c o n c i s e d e s c r i p t i o n o f t h e r e s u l t s o b t a i n e d one w o u l d need a v a r i e t y of thermodynamic and s p e c t r o s c o p i c data, t h a t a r e s t i l l l a c k i n g f o r t h e e x t r e m e l y supercooled range. The e x p e r i m e n t a l d i f f i c u l t i e s en- countered i n t h i s area o f t h e phase diagram a r e enormous, e s p e c i a l l y i f one cannot make use of t h e emulsion technique. Our group i s i n t h e process o f s t u d y i n g super- c o o l e d s a l t s o l u t i o n s and s o l u t i o n s o f hydrophobic mode1 compounds i n w a t e r . The r e - su1 t s o b t a i n e d i n t h e s e areas a r e presented i n two s h o r t communications a t t h i s workshop.

A C K N O W L E D G E M E N T

The work p r e s e n t e d h e r e was o n l y f e a s i b l e t h r o u g h t h e e x p e r t t e c h n i c a l a s s i s t a n c e o f Mr. S. Heyn, R. K n o t t and E. Treml. The c a l c u l a t i o n s were performed a t t h e Computer-Center o f t h e U n i v e r s i t a t Regensburg. Generous f i n a n c i a l s u p p o r t was ob- t a i n e d f r o m t h e DFG and t h e Fonds d e r Chemie.

R E F E R E N C E S

/ 1/ C.A. ANGELL, i n F. Franks ed. "Water

-

A Comprehensive T r e a t i s e " , Plenum Press, New York 1982, V o l . 7, p. 1 f f

/ 2/ C.A. ANGELL, Ann. Rev. Phys. Chem. 1983, 34, 593

/ 3/ E.W. LANG, H.-D. LÜDEMANN, Angew. Chemie I n t . Edn. 1982, 21, 315

/ 4/ D.H. RASMUSSEN, A.P. McKENZIE, i n H.H. J e l l i n e k : "Water S t r u c t u r e and t h e Water Polymer I n t e r f a c e , Plenum Press, New York 1972, p. 126 f f

/

5/ H. KANNO, R.J. SPEEDY, C.A. ANGELL, Science, 1975, 189, 880 / 6/ C.A. ANGELL, H. KANNO, Science 1976, 193, 1121

/ 7/ J.C. HINDMAN, A. SVIRMICKAS, J . Phys. Chem. 1973, 77, 2487 / 8/ J.C. HINDMAN, J. Chem. Phys. 1974, 60, 4488

/ 9/ E.W. LANG, H.-D. LÜDEMANN, Ber. Bunsenges. Phys. Chem. 1980, 84, 462 /IO/ E.W. LANG, H.-D. LÜDEMANN, J. Chem. Phys. 1977, 67, 718

/Il/ E.W. LANG, H.-D. LÜDEMANN, B e r . Bunsenges. Phys. Chem. 1981, 85, 603 /12/ H. YAMADA, Rev. S c i . I n s t r u m . 1974, 45, 640

/13/ E.W. LANG, H. -D. LÜDEMANN, L. PICULELL, J . Chem. Phys., i n p r i n t

/14/ A. ABRAGAM, "The P r i n c i p l e s o f N u c l e a r Magnetism", O x f o r d U n i v e r s i t y Press,l961 /15/ H.W. SPIESS, i n : P. D i e h l , E. F l u c k , R. K o s f e l d eds."NMR-Basic P r i n c i p l e s and

Progress", S p r i n g e r B e r l i n 1978, Vol. 15, p. 55 f f /16/ D.W.G. SMITH, J.G. POWLES, Molec. Phys. 1966, 10, 451 /17/ R. HAUSSER, Z. N a t u r f o r s c h u n g A, 1963, 18, 1143

/18/ H. HAUER, E.W. LANG, H.-D. LÜDEMANN, B e r . Bunsenges. Phys. Chem. 1979, 83,1262 /19/ J . HAUER, E.W. LANG, H.-D. LÜDEMANN, Chem. Phys. 1981, 62, 195

/20/ D.T. EDMONDS, A.L. MACKAY, J . Maon. Resonance 1975, 20, 515

/21/ P. THADDEUS, L.C. KRISHER, T.H.N. LOUBSER, J . Chem. Phys. 1964, 40, 257 /22/ R.J. SPEEDY, C.A. ANGELL, J . Chem. Phys. 1976, 65, 8 5 1

/23/ T. DeFRIES, J. JONAS, J. Chem. Phys. 1977, 66, 896 /24/ T. DeFRIES, J. JONAS, J . Chem. Phys. 1977, 66, 5393

/25/ J . JONAS, T. DeFRIES, D.J. WILBUR, J . Chem. Phys. 1976, 65, 582