THE p,T, c-DEPENDENCE OF DEUTERIUM SPIN-LATTICE RELAXATION RATES IN SUPERCOOLED LiCl-, NaCl- AND MgCl2-D2O SOLUTIONS

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THE p,T, c-DEPENDENCE OF DEUTERIUM SPIN-LATTICE RELAXATION RATES IN SUPERCOOLED LiCl-, NaCl- AND MgCl2-D2O

SOLUTIONS

E. Lang, W. Fink, H.-D. Lüdemann

To cite this version:

E. Lang, W. Fink, H.-D. Lüdemann. THE p,T, c-DEPENDENCE OF DEUTERIUM SPIN-LATTICE

RELAXATION RATES IN SUPERCOOLED LiCl-, NaCl- AND MgCl2-D2O SOLUTIONS. Journal

de Physique Colloques, 1984, 45 (C7), pp.C7-173-C7-177. �10.1051/jphyscol:1984719�. �jpa-00224284�

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THE p,T,c-DEPENDENCE OF DEUTERIUM SPIN-LATTICE RELAXATION RATES I N SUPERCOOLED L i C 1 - , NaC1- AND MgC12-D20 SOLUTIONS

E.W. Lang, W. Fink and H.-D. ~ G d e m a n n

I n s t i t u t fur Biophysik und Physikalische Biochemie, Universitat Regensburg, Postfach 397, 0-8400 Regensburg, F.R.G.

Resume

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On mesure l a dependance en pression e t temperature des temps de r e l a x a t i o n spin-reseau du deuterium dans des s o l u t i o n s e l e c t r o l y t i q u e s

aqueuses, dans une grande gamme de c o n c e n t r a t i o n (LiC1 : c

5

11M, NaC1: c < 5M MgC12: c < 5M, p ( 225 MPa, 283 K

2

T

2

180 K). Les r e s u l t a t s sont compGes avec l e comportement de D20 surfondue. On donne des r e s u l t a t s d e t a i l l e s de l a dependance des v i t e s s e s de r e o r i e n t a t i o n des mol@cules D20 en f o n c t i o n de l a temperature, l a pression e t l a composition pour l e systeme LiC1-D20.

On en t i r e des conclusions au s u j e t de l ' i n f l u e n c e de l a s t r u c t u r e e t de l a temperature de t r a n s i t i o n v i t r e u s e sur l e s mouvements moleculaires.

A b s t r a c t

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The p ,T-dependence o f d e u t e r i um s p i n - l a t t i c e re1 a x a t i on times of aqueous e l e c t r o l y t e s o l u t i o n s over a l a r g e c o n c e n t r a t i o n range (LiC1:

c < 11M, NaC1: c < 5 M, MgC12: c < 5 M, p < 225 NPa, 283 K > T > 180 K) i s r e p o r t e d . The r e s u l t s are comparFd w i t h t h e behaviour o f supFrcoEled D20.

D e t a i l e d account o f t h e dependence o f the r e o r i e n t a t i o n r a t e s o f D20 molecules on T,p and composition i s given f o r the system LiC1-D20 and con- c l u s i o n s a r e drawn r e g a r d i n g the i n f l u e n c e o f s t r u c t u r e and the glass t r a n - s i t i o n on molecular motions.

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

From the study o f the supercooled 1 iq u i d range i n t e r e s t i n g i n f o r m a t i o n r e g a r d i n g the p h y s i c a l behaviour o f water and aSueous s o l u t i o n s can be obtained /1-3/. I n supercooled l i q u i d s molecular motions can o f t e n be slowed down t o a time s c a l e where nuclear magnetic resonance measurements become frequency dependent and can y i e l d s p e c i f i c i n f o r m a t i o n about t h e s t r u c t u r e and dynamics o f t h e l i q u i d phase / 4 - l l / .

I n t h i s i n v e s t i g a t i o n a p p l i c a t i o n o f h i g h h y d r o s t a t i c pressure and t h e glass- forming a b i l i t y o f concentrated aqueous e l e c t r o l y t e s o l u t i o n s /12/ have been used t o explore molecular motions over a wide range o f temperatures w i t h r e l a x a t i o n time measurements. Herein the p,T,c-dependence o f t h e deuterium n u c l e a r r e l a x a t i o n r a t e of D20 i n supercooled LiC1-, NaC1- and MgCl~-D20 s o l u t i o n s i s reported.

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

A l l s o l u t i o n s were prepared from a stock s o l u t i o n of t h e anhydrous s a l t (Suprapur, Merck, Darmstadt) and D20 (99,96 %, Merck, Darmstadt). Experimental d e t a i l s con- c e r n i n g sample p r e p a r a t i o n and T1 measurements a r e given i n the previous paper by Ludemann and Lang ( t h i s volume)

.

The TI measurements a r e accurate t o

+

5 % f o r temperatures T > 220 K and t o

*

¹⁰% a t the lowest temperatures. The temperatures were measured w i t h a m i n i a t u r e chromel-alumel thermocouple ( P h i l i p s , Kassell and a r e r e l i a b l e t o

+

1 K. The pressure was measured w i t h a ' p r e c i s i o n

our don

gauge (Heise, Connecticut) t o

*

^{0.5 MPa.}

R E S U L T S A N D D I S C U S S I O N

The deuterium ( 2 ~ ) s p i n - l a t t i c e r e l a x a t i o n times TI have been obtained f o r a l l s o l u t i o n s i n the pressure range 0.1 MPa p - < 225 MPa and a t temperatures Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984719

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C7-174 JOURNAL DE PHYSIQUE

180 K < T < 283 K. LiC1-D20 s o l u t i o n s were i n v e s t i g a t e d a t t h e concentrations 0.3 m,- 3 i,5 m, 8 m and 11 m (m-molality = moles s a l t / l kg D20). Two

a d d i t i o n a l s o l u t i o n s (0.1 m, 1 m) were i n v e s t i g a t e a a t p = 0.1 HPa o n l y . NaC1-020 s o l u t i o n s had concentrations 0 . 1 m, 3 m and !4gC12-D20 s o l u t i o n s had compositions 0.1 m, 0.3 m, 0.6 rn, 1 m, 2 m, 3 m, 5 m.

F i g u r e 1 d i s p l a y s the isothermal pressure dependence o f the L i C l -D20 s o l u t i o n s f o r a l l concentrations and t h r e e temperatures. The T i - d a t a o f n e a t D20 under these c o n d i t i o n s are i n c l u d e d also. Besides de-creasing w i t h fa1 1 in g temperature, the

r e l a x a t i o n t i m e - T1 i n LiC1-D20 a l s o de- creases w i t h i n c r e a s i n g c o n c e n t r a t i o n i n t h e normal l i q u i d range a t a l l pressures s t u d i e d . Deeply undercool ed s o l u t i o n s , however, e x h i b i t a q u i t e d i f f e r e n t behaviour. Here T; i s found l o n g e r i n t h e aqueous s o l u t i o n s than i n neat D20 a t low pressure whereas a t h i g h e r Fressure t h e ambient temperature behaviour i s reestablished.

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^LICI-DZOS O I U ~ . Also the p o s i t i v e pressure depen-

dence o f T1 becomes i n c r e a s i n g l y l e s s pronounced w i t h the a d d i t i o n o f s a l t u n t i l i t vanishes a t a c o n c e n t r a t i o n 5 m c c c 8 m .

F i g u r e 2 shows t h e pressure dependence o f T1 a t temperatures T =

A 283 K, 238 K and 218 K f o r 3 v o l a l so- l u t i o n s o f LiC1, NaC1, MgC12 and CsBr corresponding t o a cornposi t i o n R = , , , ,

0 100 200 16.67 ( R = moles C20/moles s a l t ) . A t

T = 283 K t h e " s t r u c t u r e forming" s a l t s LiC1, NaCl and MgC12 a r e seen t o ex- Figure 1

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Pressure dependence o f deuterium

hibit shorter relaxation times than s p i n - l a t t i c e r e l a x a t i o n times T l i n LiC1-D7O neat D20 whereas the ,,structure brea- s o l u t i o n s a t various concentrations ( c moial ) king,, salt CsBr possesses a

anger and t h r e e s e l e c t e d temperatures.

Thus the former s o l u t e s reduce the nlobil i t y o f water molecules a t ambient temperature whereas t h e l a t t e r enhance t h e i r mobi 1 i t y . Furthermore t h e i n - f l u e n c e o f the s t r u c t u r e forming s o l u t e s upon molecular motions i n water i s i n t h e order MgC12 > L i C l > NaCl as already e s t a b l i s h e d e a r l i e r /13/. Also no i n f l u e n c e o f pressure upon T1 i s d e t e c t a b l e i n these s a l t s o l u t i o n s . B u t the whole p a t t e r n changes i f one e n t e r s

HUU( the supercooled s t a t e . The s p e c i f i c i n - f l u e n c e o f t h e ions upon T i i s much more pronounced a t low t mperatures.

- A t ambient pressure t h e FH-Tl o f neat D20 have a s t r o n g e r temperature depen-

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dence than any 3 m s a l t s o l u t i o n s t u d i e d h i t h e r t o . I n t h e 238 K-isotherms one thus f i n d s f o r CsSr, LiC1, NaCl and t o s m a l l e r e x t e n t even f o r MgC12 a h i g h e r m o b i l i t y f o r t h e water molecules than observed i n neat D20. A t h i g h hydro-

0 100 200 0 100 200 0 100 200 s t a t i c pressure the p a t t e r n observed a t

-'p'MPa' ambient temperature i s r e e s t a b l i s h e d F i g u r e 2

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Pressure dependence o f except t h a t a t low temperatures NaCl d e u t e r i um spin-1 a t t i c e r e l a x a t i o n has a s t r o n g e r i n f l u e n c e on m o b i l i t y times TI i n various e l e c t r o l y t e so- than LiC1. We w i l l n o t e n t e r a d e t a i l e d 1 u t i o n s a t constant c o n c e n t r a t i o n d i s c u s s i o n o f these e f f e c t s b u t r a t h e r ( c = 3 m o l a l ) and t h r e e selected c o n f i n e our discussion t o t h e 225 MPa temperatures.

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can be measured t o t h e lowest temperatures obtained. The m o b i l i t y o f t h e water molecules can be slowed down t o a t i m e s c a l e where t h e 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 o f t h e D20 molecules become comparable t o the Larmor p e r i o d o f t h e deuterium nucleus.

T h i s i s i n d i c a t e d by a minimum i n t h e temperature dependence o f t h e 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 TI which was observed i n a l l s o l u t i o n s . The r e l a x a t i o n times TI obtained f o r d i f f e r e n t concentrations a r e t a b u l a t e d i n Table 1 t o g e t h e r w i t h t h e minimum temperature Tmin. I t i s seen t h a t TI a t Tmin increases and t h a t Tmin s h i f t s t o h i g h e r temperature as t h e s o l u t i o n s become more concentrated.

Table 1

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Concentration dependence o f minimum s p i n - l a t t i c e r e l a x a t i o n timeTl and corresponding temperature Tmin a t p = 225 MPa.

Furthermore t h e minimum becomes broader w i t h i n c r e a s i n g concen- t r a t i o n . These f e a t u r e s a r e s i m i l a r t o those observed a1 ready i n h i g h l y concentrated, p l ass-forming LiC1- D20 s o l u t i o n s by Boden and Mortimer / 9 /

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225 MPo Isobars of Deuteron-Tl in :H~O/L~CI Solutions

The f u r t h e r d i s c u s s i o n i s r e - s t r i c t e d t o the system LiC1-D20 be- cause the q u a n t i t a t i v e e v a l u a t i o n o f t h e data has o n l y been done f o r these s o l u t i o n s u n t i l now. Figure 3 shows t h e 225 #Pa i s o b a r s o f t h e LiC1-sol u t i o n s . I t i s we1 1 known, t h a t the i n t e r a c t i o n o f the l i t h i u r i o n w i t h n e x t neighbour water mole:

cules i s s u f f i c i e n t l y s t r o n g f o r the l i f e t i m e o f the h y d r a t i o n sphere t o become much l o n g e r than the c o r r e l a t i o n times o f t h e water molecules /14,15/. S c a t t e r i n g techniques p r o v i d e a d e t a i l e d p i c t u r e o f the geometrical arrangement o f the molecules i n the hy- d r a t i o n sphere /16,17/. From NMR F i g u r e 3

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Temperature dependence o f d e u t e r i um s p i n 1 a t t i c e r e l a x a t i o n times T a t constant pressure (p=ZZ5 h ~ a ) i n LiCl-DZO s o l u t i o n s a t various concentrations.

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C7-176 JOURNAL DE PHYSIQUE

experir,~ents i t has been deduced t h a t the water molecules i n the h y d r a t i o n sphere r e o r i e n t about an a x i s p o i n t i n g r a d i a l l y outward from the c a t i o n along the L i - 0 d i r e c t i o n /13,18/. We propose a simple motional model o f the water molecules i n the h y d r a t i o n sphere o f t h e l i t h i u m i o n which neglects completely the i n f l u e n c e o f the C1- anion on the dynamics o f the water molecules. This seems t o be j u s t i f i e d be- cause i t has been concluded f r o n Pi:.lR experiments /13/ t h a t t h e i n f l u e n c e o f the C1- anion i s much s m a l l e r than t h a t o f the L i + c a t i o n . Recognizing t h a t the w a t e r - c a t i o n r a t i o R o f the 11 m LiC1-D20 s o l u t i o n i s 4.55 i t i s assumed t h a t a l l water molecules i n t h i s system belong t o t h e h y d r a t i o n sphere o f the c a t i o n . Then t h e r e - o r i e n t a t i o n a l motions o f t h e water molecules a r e modelled by a d i f f u s i o n a l r e - o r i e n t a t i o n 8bout t h e L i - 0 a x i s w i t h the d i p o l e moment d i r e c t i o n t i 1 te d a t an angle O 52

/ l o /

away from the L i - 0 d i r e c t i o n and an i s o t r o p i c o v e r a l l r e o r i e n - t a t i o n a l d i f f u s i o n o f t h e h y d r a t i o n complex. Furthermore small amp1 i tude 1 ib r a t i o n a l o s c i l l a t i o n s o f t h e 0-D bond d i r e c t i o n about i t s average d i r e c t i o n are considered t o account f o r a p o s s i b l e l i b r a t i o n a l averaging o f t h e deuterium quadrupole c o u p l i n g constant. C h a r a c t e r i z i n g i n t e r n a l and o v e r a l l r e o r i e n t a t i o n s by two c o r r e l a t i o n times ~i and ^{T r}r e s p e c t i v e l y the f o l l o w i n g expression f o r the r e l a x a t i o n r a t e 1/T1 o f t h e h v d r a t i o n water i s deduced:

2

w i t h --- qeffQ the 1 ib r a t i o n a l l y averaged quadrupole coup1 i n g constant and h

The temperature dependence o f the c o r r e l a t i o n times T, and ~i i s assumed t o f o l l o w the VTF-equation: T = T~ exp(B/(T-To)) w i t h To s p e c i f y i n g t h e glass t r a n s i t i o n temperature where the molecules become a r r e s t e d i n an amorphous arrangement and are unable t o explore t h e phase space any f u r t h e r /19/. The e x p e r i m e n t a l l y observ- a b l e glass t r a n s i t i o n temperature T i s f o r k i n e t i c reasons always Tg > To. Both q u a n t i t i e s depend on t h e compositio# o f t h e s o l u t i o n s /12/.

F o l l o w i n g a suggestion o f Boden and Mortimer /9/ the r e l a x a t i o n r a t e s i n a l l s o l u t i o n s o f lower c o n c e n t r a t i o n should be given by

w i t h ( l / T l ) h y d . corresponding t o t h e 11 molal s o l u t i o n and ( l / T l ) b u l k t h e r e l a x a t i o n r a t e observed i n n e a t D20 w i t h a c o r r e l a t i o n time .T, I t ' s temperature dependence i s again described by t h e VTF-equation. The above r e l a t i o n w i l l h o l d o n l y i f a l l r e l a x a t i o n r a t e s a r e evaluated a t t h e same reduced temperature (T-To(R)), w i t h To(R) the i d e a l glass t r a n s i t i o n temperature o f t h e s o l u t i o n o f composition R.

A m o d i f i e d Arrhenius diagram ( T i @ 1/(T-T,(R)) r e v e a l s t h a t a1 1 curves ex- h i b i t t h e same slope on the h i g h temperature s i d e o f the minimum f o r s u i t a b l y choosen To(R). This suggest t h a t t h e parameter B should be independent o f concen- t r a t i o n and t h a t t h e e f f e c t o f composition upon the temperature dependence of T i i s determined predominantly by i t s e f f e c t on t h e glass t r a n s i t i o n temperature. Thus a l e a s t squares f i t t i n g e x e r c i s e has been done w i t h the r e l a x a t i o n times obtained i n 11 m LiC1-D20 t o f i x the parameters -cro, T~ and To(R = 4.55). The q u a n t i t i e s

T~,, B and To have been used as obtained r e c e n t l y f o r n e a t D20. Also t h e deuterium quadrupole c o u p l i n g constant has been assumed t o be u n a f f e c t e d by t h e presence of ions, as has been suggested by t h e o r e t i c a l c a l c u l a t i o n s /20/. The r e s u l t i n g tempe- r a t u r e dependence o f T i i n t h e various s o l u t i o n s i s shown as a s o l i d l i n e through the data i n F i g u r e 3. The agreement i s reasonably good and suggests t h a t most of the e f f e c t s i n f l u e n c i n g the temperature and composition dependence o f T i i n these s o l u t i o n s a t h i g h pressure i s i n c o r p o r a t e d i n t o the model. I t i s i n t e r e s t i n g t o note t h a t no pressure dependence o f TI i s found i n t h e 8 molal and 11 molal solu- t i o n s and t h a t i t i s very small i n t h e 5 molal s o l u t i o n s . Hence the anomalous

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temperature Tg of the system /21/. Thus t h e present model accounts w e l l f o r t h e temperature dependence o f t h e r e l a x a t i o n r a t e s i n these systems. I t should be noted f u r t h e r t h a t the e f f e c t o f pressure upon t h e dynamics o f water i n t h e more d i l u t e s o l u t i o n should be c o n f i n e d t o i t s i n f l u e n c e on (l/Tl)bulk as (?/Tl)hyd. shows no pressure dependence i n t h i s pressure range.

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

We a r e indebted t o M r . S. Heyn, R. K n o t t and E. Treml f o r t h e i r e x p e r t t e c h n i c a l help. The l e a s t squares f i t s (NAG E04FCF) were performed a t t h e Computer Center o f the U n i v e r s i t a t Regensburg. Generous f i n a n c i a l support by the DFG and t h e Fonds der Chemie are g r a t e f u l l y acknowledged.

R E F E R E N C E S

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