HIGH PRESSURE S P I N - L A T T I C E - R E L A X A T I ON TIME STUDIES
IN SUPERCOOLED H20 AND D20 ENRICHED WITH 0-17
E. L a n g and H.-D. Ludemann
I n s t i t u t f l i r B i o p h y s i k und P h y s i ka 1 i s c h e B i o c h e m i e U n i v e r s i t a t R e g e n s b u r g , P o s t f a c h 3 9 7 , D-8400 R e g e n s b u r g
The s p i n - l a t t i c e r e l a x a t i o n times (T-,) have been s t u d i e d f o r the 17
gO-nuclei i n l i g h t and heavy water i n the temperature range between 240 K and 450 K and a t pressures up to 250 MPa ( 1 ) . Furthermore 1H s p i n - l a t t i c e r e l a x a t i o n times have been measured i n H^^O enriched to 25 % and 50 % w i t h ^ 0 i n the temperature range 193 K to 343 K and pressures up to 250 MPa.
The experimental d i f f i c u l t i e s i n s t u d y i n g supercooled water are s i g - n i f i c a n t l y reduced when i t i s p o s s i b l e to apply the measurements t o water emulsions. NMR-measurements can take f u l l advantage o f the emulsion technique. Thereby small w a t e r d r o p l e t s are suspended i n an i n s o l u b l e c a r r i e r (50 % w/w cyclohexane/cyclopentane) and prevented from c o a l e s c i n g by e m u l s i f i c a t i o n w i t h s o r b i t a n t r i s t e a r a t e . The sample i s contained i n a strengthened g l a s s c a p i l l a r y which i s i n - corporated i n a Cu/Be-high pressure c e l l d e s c r i b e d p r e v i o u s l y ( 2 ) . From the 0-17 TJs obtained the o r i e n t a t i o n a l c o r r e l a t i o n times xQ, which are the zero-frequency F o u r i e r transforms of the corresponding s p e c t r a l d e n s i t y f u n c t i o n s , have been c a l c u l a t e d w i t h i n the r o t a - t i o n a l d i f f u s i o n model. The water molecules have been t r e a t e d as s p h e r i c a l - t o p s and are assumed to r e o r i e n t i s o t r o p i c a l l y on the average. Experimental evidence s u p p o r t i n g these assumptions has been presented elsewhere ( 3 ) . In the course of the c a l c u l a t i o n of these e f f e c t i v e c o r r e l a t i o n times Tq a value of - p ~ - = (6,6±0,1) MHz f o r the 0-17 quadrupole c o u p l i n g constant (QCC) has been used i n a c c o r -
2
dance w i t h the r e s u l t found f o r H-QCC i n supercooled heavy water ( 4 ) . T h i s assumption has r e c e n t l y been c o r r o b o r a t e d by H a l l e and
Wennerstrbm ( 5 ) . The e f f e c t i v e c o r r e l a t i o n times Tq i n c r e a s e w i t h d e c r e a s i n g temperature i n a non-Arrhenian f a s h i o n . T h e i r pressure dependence r e v e a l s a decrease w i t h i n c r e a s i n g pressure w i t h a pressure c o e f f i c i e n t t h a t i n c r e a s e s w i t h f a l l i n g temperature a t low p r e s s u r e s . In the p r e s s u r e range p = 150-200 MPa they run through a minimum and f u r t h e r i n c r e a s e w i t h r a i s i n g p r e s s u r e as i s normally found i n l i q u i d s . Furthermore the e f f e c t i v e c o r r e l a t i o n times Tq i n
17 9
Do 0 are i d e n t i c a l a t the r e s p e c t i v e temperatures and pressures to 2
the e f f e c t i v e c o r r e l a t i o n times xQ c a l c u l a t e d from H-T^ measurements i n D2O. T h i s r e s u l t s t r o n g l y supports the i s o t r o p i c nature o f the o r i e n t a t i o n a l f l u c t u a t i o n s of the water molecules. However i t does not r u l e out the p o s s i b i l i t y o f a n i s o t r o p i c r o t a t i o n a l motion on a s h o r t e r time s c a l e .
Thus a t low pressures (p < 150 MPa) the d i f f e r e n t i s o b a r s can be d e s c r i b e d w i t h a f r a c t i o n a l power law TQ = Ts^ - y - ^ Y w i t h a s i n g u - l a r temperature T i m p l y i n g a A - l i k e anomaly i n l u p e r c o o l e d water
17
( 6 ) . The e f f e c t i v e c o r r e l a t i o n times Tq i n H0 0 a r e found to be
17 6
s h o r t e r than those i n Do 0. However a t low p r e s s u r e s they c o u l d a l s o be f i t t e d t o the f r a c t i o n a l power law mentioned above, a l l parameters being equal except the s i n g u l a r temperatures Tg which were found t o be lower by about 7 K i n l i g h t water. T h i s shows t h a t the l a r g e dynamic i s o t o p e e f f e c t found can i n the low p r e s s u r e region be accounted f o r by the i n f l u e n c e o f the i s o t o p i c s u b s t i t u - t i o n upon the s i n g u l a r temperature, t h e i n f l u e n c e o f the i s o t o p e e f f e c t upon the dynamic behaviour o f the watermolecules i n super- cooled water a t low pressures i s d i s c u s s e d .
At high p r e s s u r e s (p > 200 MPa) the temperature dependence of Tq r e - sembles the dynamics o f normal viscous l i q u i d s ( 7 ) . I t c o u l d be d e s c r i b e d by the VTF-equation xQ = TQe x p (B/ T - TQ) which i m p l i e s a divergence o f T0 a t the i d e a l g l a s s t r a n s i t i o n temperature TQ. The l a t t e r has a l s o been found to be lower i n H20 than i n D20 by about 5 K. In the high p r e s s u r e r e g i o n the dynamic i s o t o p e e f f e c t becomes more complicated i n t h a t i t does not o n l y appear i n the e h a r a c t e -
r i s t i c temperatures TQ but a l s o i n t h e other parameters. The r e s u l t s are d i s c u s s e d i n terms o f a c o n s t a n t l y r e a r r a n g i n g random network o f hydrogen-bonded molecules. In a d d i t i o n proton s p i n - l a t t i c e r e -
F i g . 1: Isotherms o f pro- ton s p i n - l a t t i c e r e l a x a t i o n times i n supercooled H2 1 60 (A) and H2 1 70 (o) with 50 % 0-17 enrichment
(A) data from r e f . (8)
0.01 \ , , , r — 0 5 0 100 ISO 200
• p ( M P o )
Taxation times have been measured i n H2*70 e n r i c h e d w i t h 25 % and 50 % 0-17 r e s p e c t i v e l y . The data have been analyzed w i t h t h e a s - sumption t h a t t h e i n t e r a c t i o n between 0-17 and t h e protons i s t o a f i r s t approximation an a d d i t i o n a l i n t r a m o l e c u l a r r e l a x a t i o n path which leads t o a s h o r t e r r e l a x a t i o n time T1 than i n H2*60 . F i g . 1 shows a few ^ - T , isotherms i n H9 1 60 and H9 1 70 (50 % e n r i c h e d ) . Thus
1 7 - 1 l o
the d i f f e r e n c e between T1( H2 0) - T^ ( H2 0) measures a p u r e l y 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 from which the e f f e c t i v e c o r r e l a t i o n times T Q can be e x t r a c t e d . In t h e temperature range o f o v e r l a p these e f f e c t i v e c o r r e l a t i o n times Tq a r e i d e n t i c a l a t t h e r e s p e c t i v e temperatures and pressures t o t h e c o r r e l a t i o n times c a l c u l a t e d from the 0-17 T^ i n H2 1 70 . With these c o r r e l a t i o n times t h e i n t r a - and i n t e r m o l e c u l a r c o n t r i b u t i o n s t o t h e measured r e l a x a t i o n times T, i n
16
H« 0 can be e v a l u a t e d . A n a l y s i s o f t h e data shows, t h a t i n t h e
c 1
supercooled l i q u i d t h e H - r e l a x a t i o n i s dominated by the 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 . T h i s i n d i c a t e s t h a t t r a n s l a t i o n a l d i f f u s i o n i s slowed down much more r a p i d l y than i s r o t a t i o n a l d i f f u s i o n .
ACKNOWLEDGEMENT
F i n a n c i a l s u p p o r t by t h e DFG and the Fonds der Chemie i s g r a t e f u l l y acknowledged.
REFERENCES
(1) E. W. Lang and H.-D. Llidemann
Ber. Bunsenges. Phys. Chem. 85, 603 (1981) (2) E. W. Lang, R. Rauchschwalbe and H.-D. Llidemann
High Temperatures-High Pressures 9, 519 (1977) (3) E. W. Lang
D i s s e r t a t i o n 1980, U n i v e r s i t a t Regensburg (4) E. W. Lang and H.-D. Ludemann
Ber. Bunsenges. Phys. Chem. 84, 462 (1980) (5) B. H a l l e and H. Wennerstrbm
J . Chem. P h y s . , i n press
(6) C. A. A n g e l l , i n :
Water - A Comprehensive T r e a t i s e , V o l . 7 (1981) F. Franks ed., Plenum P r e s s , New York ( i n press) (7) G. H a r r i s o n
The Dynamic P r o p e r t i e s o f Supercooled L i q u i d s Academic P r e s s , London (1976)
(8) E. W. Lang and H.-D. Ludemann J . Chem. Phys. 67, 718 (1977)
