NMR AND NEUTRON STUDIES OF WATER DYNAMICS IN DENSE SOLUTIONS

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NMR AND NEUTRON STUDIES OF WATER DYNAMICS IN DENSE SOLUTIONS

L. Schreiner, M. Pintar

To cite this version:

L. Schreiner, M. Pintar. NMR AND NEUTRON STUDIES OF WATER DYNAMICS IN DENSE SOLUTIONS. Journal de Physique Colloques, 1984, 45 (C7), pp.C7-241-C7-248.

�10.1051/jphyscol:1984727�. �jpa-00224292�

N M R AND NEUTRON STUDIES O F WATER DYNAMICS IN DENSE SOLUTIONS

L . J . S c h r e i n e r and M.M. P i n t a r

Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Rdsum6 - On p r 6 s e n t e l a m6thode du groqement-spin en RMN, permettant de mieux c a r a c t d r i s e r l e s r d s u l t a t s des e x p e r i e n c e s de r e l a x a t i o n de s p i n . Les r 6 s u l t a t s d ' d t u d e s de groupement-spin des s o l u t i o n s POE dans l ' e a u e t des c r i s t a u x ~ ' A D N h y d r a t e s s o n t d i s c u t d s c o m e exemples d ' a p p l i c a - t i o n . Enfin des r d s u l t a t s p r g l i n i n a i r e s des expdriences d e neutrons d i f - f u s e s quasi-dlastiquement s o n t r a p p o r t 6 s .

A b s t r a c t - The NMR spin-grouping method, with which t h e r e s o l u t i o n and c h a r a c t e r i z a t i o n of t h e NMR r e l a x a t i o n measurements can be improved, i s presented. Examples of dense H20 s o l u t i o n s of POE and of DNA c r y s t a l s w i t h H20 s t u d i e d by t h i s method and a few p r e l i m i n a r y r e s u l t s of neutron q u a s i - e l a s t i c s c a t t e r i n g experiments a r e discussed.

Nuclear magnetic resonance has been shown t o be a v a l u a b l e technique i n t h e s t u d y of t h e s t r u c t u r e and dynamics of water. This is p a r t i c u l a r l y t r u e f o r r e l a x a t i o n time s t u d i e s of s o l i d s o r very d i l u t e d aqueous s o l u t i o n s . However, i f t h e s t u d i e d systems a r e heterogeneous, e.g. i f t h e s o l u t i o n s a r e dense, t h e NMR measurements have o f t e n been d i f f i c u l t t o i n t e r p r e t due t o problems i n t h e r e s o l u t i o n of t h e N M R s i g n a l s i n t o components corresponding t o t h e d i f f e r e n t s p i n c o n f i g u r a t i o n s and environments. Recently a new NMR approach which improves t h e r e s o l u t i o n of such dense s o l u t i o n s has been developed 111. It is c a l l e d t h e l i n e s h a p e - r e l a x a t i o n c o r r e l a t i o n o r t h e spin-grouping approach. I n t h i s paper we p r e s e n t t h e a p p l i c a t i o n of s p i n grouping i n t h e s t u d y of a dense s o l u t i o n and of a hydrated c r y s t a l .

I - THE SPIN-GROUPING TECHNIQUE

The spin-grouping e x p l o i t s t h e f o l l o w i n g p r o p e r t y of heterogeneous sytems: t h e y u s u a l l y have a magnetization e v o l u t i o n which i s nonexponential and can be c h a r a c t e r i z e d by s e v e r a l time c o n s t a n t s . Generally t h e e v o l u t i o n of t h e t o t a l magnetization can be d e s c r i b e d a s a s u p e r p o s i t i o n of evolving component

magnetizations from d i f f e r e n t s p i n groups each evolving with i t s own r e l a x a t i o n time. The s e p a r a t i o n of t h e t o t a l m g n e t i z a t i o n r e l a x a t i o n i n t o i t s r e s p e c t i v e components can t h e r e f o r e be used t o s e p a r a t e t h e t o t a l (composite) Free I n d u c t i o n Decay (FID) of t h e sample i n t o components, each evolving w i t h a d i f f e r e n t T1 o r Tlp. The NMR s i g n a l i s , t h e r e f o r e , r e s o l v e d i n t o c o n t r i b u t i o n s from d i f f e r e n t s p i n g r o u p s w h i c h a r e c h a r a c t e r i z e d by t h e i r r e s p e c t i v e T l V s or T l p V s , t h e i r T Z 1 s , and t h e r e l a t i v e magnitude of t h e i r magnetizations. This c h a r a c t e r i z a t i o n

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984727

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42%PEG I N H20 - 6 5 C SECOND RUN LONG RR

Fig. 1 - The m a g n e t i z a t i o n r e c o v e r y a t t h e 12 p time window from t h e T1 measurement f o r 42% PEG 400 i n H20 a t -65- C. Two components a r e needed t o c h a r a c t e r i z e t h e decay.

g i v e s improved i n f o r m a t i o n o v e r t h e s t a n d a r d e f f e c t i v e s p i n - l a t t i c e r e l a x a t i o n measurement. T h i s is e s p e c i a l l y t r u e i n t h e d e t e r m i n a t i o n o f t h e m a g n e t i z a t i o n f r a c t i o n c o r r e s p o n d i n g t o a p a r t i c u l a r r e l a x a t i o n t i m e . It should be n o t e d t h a t t h e method r e l i e s on t h e f a c t t h a t t h e t o t a l m a g n e t i z a t i o n ' s e v o l u t i o n can be w e l l s e p a r a t e d ; t h e r e f o r e , t h e r e l a x a t i o n t i m e s of t h e d i f f e r e n t components must be s u f f i c i e n t l y d i f f e r e n t f o r t h e r e s o l u t i o n t o be unique.

The p r i m a r y d i f f e r e n c e of t h e spin-grouping method compared t o t h e s t a n d a r d T1 o r

Tip measurement is t h a t t h e m a g n e t i z a t i o n e v o l u t i o n i s r e c o r d e d s i m u l t a n e o u s l y a t more t h a n one time i n t e r v a l on t h e FID f o r e a c h p u l s e s p a c i n g ,

i n t h e measuring p u l s e sequence. These t i m e i n t e r v a l s on t h e FID a r e c a l l e d o b s e r v a t i o n

"windows". The number of windows r e c o r d e d on t h e FID i s determined by i t s l i n e s h a p e ; FID's w i t h some s t r u c t u r e ( f o r example, b e i n g a s u p e r p o s i t i o n of a s o l i d and a l i q u i d - l i k e l i n e - s h a p e ) a r e r e c o r d e d a t up t o 33 windows ( t h i s number i s l i m i t e d by t h e memory c a p a b i l i t i e s of t h e a q u i s i t i o n computer, i n our c a s e a Hewlett-Packard 98458 computer). The d u r a t i o n o f each time window i s a l s o v a r i a b l e , depending on t h e FID. By t h e end of a spin-grouping e x p e r i m e n t , t h e r e - f o r e , t h e computer h a s r e c o r d e d t h e e l e m e n t s of a two-time d i m e n s i o n a l magnetiza- t i o n e v o l u t i o n m a n i f o l d , M(t,.r), which i s dependent n o t o n l y on t h e p u l s e s p a c i n g

T,

b u t a l s o on t h e p o s i t i o n of t h e window, t. The m a g n e t i z a t i o n e v o l u t i o n i s t h e n a n a l y z e d s e p a r a t e l y a t e a c h window; t h a t i s , i t i s a n a l y z e d a s a f u n c t i o n of T f o r each f i x e d parameter t. For example, i n Fig. 1 t h e m a g n e t i z a t i o n r e c o v e r y i n a T1 e x p e r i m e n t , [{~,(t,-[=-I- MZ(t, r ) } / 2 ~ , ( t , - ) ] a t t h e t = 12 p s window, where

M,(t,m) i s t h e e q u i l i b r i u m m a g n e t i z a t i o n a t t h e t window, i s shown. I f t h e

e q u i l i b r i u m magnetization a t t h e window t. The decomposition of t h e e v o l u t i o n i s achieved through an i n t e r a c t i v e combination of s t a t i s t i c a l and g r a p h i c a l a n a l y s i s of t h e d a t a . The e v o l u t i o n a t a p a r t i c u l a r window i s p l o t t e d and t h e u s e r d e f i n e s

" g r a p h i c a l l y " t h e time regimes of t h e e v o l u t i o n which a r e t o be f i t t e d with a l e a s t - s q u a r e s r e g r e s s i o n , beginning a t t h e t a i l end of t h e e v o l u t i o n ( l a r g e r ' s ) where u s u a l l y only t h e s l o w e s t ( l i q u i d - l i k e ) r e l a x a t i o n component i s s t i l l r e l a x i n g . This a n a l y s i s i s then r e p e a t e d a t each time window on t h e FID. The r e s u l t s of t h e a n a l y s i s a t each window g i v e t h e elements of two m a t r i c e s ; one of which c o n t a i n s t h e r e l a x a t i o n times of a l l components c a l c u l a t e d a t each window, t h e o t h e r which c o n t a i n s t h e magnetization f r a c t i o n s . These r e s u l t s can t h e n be p l o t t e d v e r s u s t h e window p o s i t i o n ( t ) on t h e FID, s e e Fig. 2. The value of t h e s p i n - l a t t i c e r e l a x a t i o n time f o r e a c h r e s p e c t i v e component i s taken a s t h e average of t h e r e l a x a t i o n time over a l l window p o s i t i o n s . The p l o t of t h e window

dependence of t h e magnetization components a c t u a l l y g i v e s t h e decomposed FID's, each corresponding t o a r e s p e c t i v e TI (or Tip). The e q u i l i b r i u m magnetization of t h e components can be determined by e x t r a p o l a t i n g t h e decomposed FID's t o t h e time t = 0, t h a t i s , t o t h e time immediately a f t e r t h e r f p u l s e b e f o r e any magnetization component had t h e chance t o dephase. These t r u e f r a c t i o n s measure t h e number of s p i n s i n a p a r t i c u l a r s p i n group which i s a s s o c i a t e d with a p a r t i c u l a r r e l a x a t i o n time.

Fig. 2a - The r e s u l t s of t h e T1 spin-grouping f o r t h e sample s p e c i f i e d i n Fig. 1.

The v a r i a t i o n of T 1 with window p o s i t i o n . TI long ( 0 ) = 13 i 5 s; T I s h o r t ( 7 ) = 275 + 25 m s .

100 - _-

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42XPEG I N H Z 0 -65C

- SECOND RUN LONG RR -

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0.. . . . . . . . . .

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Fig. 2 (b) - The decomposed FID1s corresponding to part (a). The Gaussian fit to the long TI component (e) is shown. The arrows indicate the magnetization fractions from Fig. 1.

The accuracy of the method depends strongly on the possibility to well define the magnetization components contributing to the total magnetization evolution (spin- lattice relaxation), therefore, it depends on the separability of the nonexponen- tial magnetization evolution into the sum of exponentials. The separation is non-ambiguous if the relaxation times differ by at least a factor of five. As the relaxation times of the different components becone more similar the uncertainties in their determination, and in the resolution of their FID1s, increase. This is especially true if one of the components contributes a minority fraction to the magnetization. It is our experience that the resolution is still quite good if the time constants differ by a factor of 3.5 as long as the magnetization fractions of the different components are at least 30% of the total

magnetization. In systems with two components contributing about equal amounts to the total magnetization it has been possible to resolve the total evolution into components even when they had relaxation times different by only a factor of 2.5;

however, the uncertainties in the component relaxation times and in the

magnetization fractions Ls significant. For this reason, in such situations the method gives components which are useful only if their characteristics can be cross correlated with some other independent information (ideally stoichiometric).

It has been found that it is particularly important to well determine the long relaxation time component. Therefore, it is necessary to measure the

magnetization evolution to within half a percent of the maximum signal, or

better. The errors in the determination of the long T I or Tip component are,

therefore, often quite large. Since the decomposition is repeated over many

windows and the relaxation times of the components are averaged over all windows

it is possible to perform a so-called second iteration step in which the average

the magnetization. By later windows it contributes less than 1%. However, by imposing the value of TI determined at the early windows (small t) into the analysis of the later windows, it is possible to determine the magnetization

fraction at the later windows and so define quite well the shape of the FID corresponding to this T1 component.

I1 - APPLICATION TO DENSE SOLUTIONS

The spin-grouping has been used to study dense solutions 121. Presently the technique is being applied to two model systems: a) aqueous solutions of polyethylene glycol 400 (PEG 400) and b) hydrated oriented NaDNA fibers.

Aqueous solutions of the polymer PEG have been chosen since PEG is soluble in water in all proportions /3/ and since the structure is well defined /4/. In order t6 determine the amount of water which is "bonded" to the PEG molecules PEG 400 was studied over a range of temperatures and concentrations using spin

grouping. In particular the amount of ice and of the "non-freezable" water in the solutions at low temperature was monitored. In Fig. I, the T1 magnetization recovery of a 42% PEG 400 in 58% H20 sample at -65' C is shown. Two components contribute to the magnetization evolution: a slow relaxation component with T 1 = 13 i 5 s and a fast component with T l = 275 + ²⁵ ms. As the two time constants differ by more than one order of magnitude the decomposition is well defined. The results of the spin-grouping are given in Fig. 2. One can see in Fig. 2a that the long T1 has been set to its average over all windows, the short T1 has not yet been averaged and so the scatter in its value has not yet been eliminated in this the second step of the analysis. The decomposed FID's corresponding to this iteration are shown in Fig. 2b. The FID corresponding to the long Ti component decays very rapidly having a Gaussian line-shape typically seen in solids. It has a T2 (defined here as the time taken for the magnetization to decay to half of its maximum value) of only 6 + ² us. From the values of the two relaxation times it

follows that this component can be identified with the ice. The FID corresponding to the short T1 component can be fitted as the sum of an exponential lineshape with T2 = 30 f 2 us and a Gaussian lineshape with T2 = 11 f 2 ps (Fig. 2b). These fits allow us to determine the contributions to the total magnetization at t=O:

the long T 1 component contributes 27 + 5% of the total magnetization, whereas the short T1 component contributes the rest. These magnetization fractions can now be compared to the spin fractions expected from the stoichiometry of the sample: 62%

of the sample's spin mass comes from protons on water molecules. Therefore, about

half of the water protons are not in the ice form. This demonstrates that 16

moles of water per each mole PEG 400, or more explicitly 2 moles water per ether

oxygen in the polymer, are "non-freezable". This is in excellent agreement with

the literature 151. It should be noted that not only has the magnetization

fraction of the non-freezable water been determined but also all the spin groups

C7-246 JOURNAL DE PHYSIQUE

have been c h a r a c t e r i z e d by t h e i r r e l a x a t i o n times. This allows one t o determine t h e environments of t h e s p i n groups. Had t h e measurements been performed a t o n l y one window i t would n o t be p o s s i b l e t o c o r r e l a t e t h e s p i n - l a t t i c e and spin-spin r e l a x a t i o n times and such a d e t e r m i n a t i o n would be much more ambiguous. Note a l s o t h a t , s i n c e t h e deadtime of t h e r e c e i v e r on our instrument i s between 6 and 8 p, a s u b s t a n t i a l amount of t h e magnetization has decayed by t h e time t h e i n s t r u m e n t i s a b l e t o make r e l i a b l e s i g n a l d e t e c t i o n . However, once t h e FID has been d e t e r - mined a t times g r e a t e r than about 8 psec t h e t r u e magnetization can be o b t a i n e d by f i t t i n g t h e line-shape. It has been shown t h a t even f o r r i g i d samples t h e r e s u l t s from t h e spin-grouping experiments a g r e e q u i t e well with those o b t a i n e d when t h e magnetization i s refocussed u s i n g t h e s o l i d echo p u l s e sequence 161.

The PEG 400 s o l u t i o n s have a l s o been s t u d i e d with s p i n grouping a t room tempera- t u r e a t v a r i o u s polymer c o n c e n t r a t i o n s . The r e s u l t s a r e being c o r r e l a t e d w i t h both NMR s p i n echo and neutron q u a s i - e l a s t i c s c a t t e r i n g (NQES) measurements of t h e d i f f u s i o n c o e f f i c i e n t s . With s p i n grouping t h e s i g n a l from t h e water p r o t o n s and from t h e protons on t h e PEG 400 i s s e p a r a t e d . By c o r r e l a t i n g t h e r e l a x a t i o n times observed f o r t h e water s p i n s with t h e d i f f u s i o n c o e f f i c i e n t s measured by s p i n echo i t i s p o s s i b l e t o model t h e r e l a x a t i o n of t h e water s p i n s i n terms of 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 of t h e molecules. Since broadening of t h e neutron q u a s i - e l a s t i c peak measured on t h e time of f l i g h t s p e c t r o m e t e r s I N 5 and IN6 a t t h e

ILL is p r o p o r t i o n a l t o t h e momentum t r a n s f e r squared between .5 < Q < ^{1.0 8;l}

e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s a r e a r r i v e d a t . These measurements on PEG d i l u t e d i n D20 a r e s e n s i t i v e t o t h e segmental motions of t h e PEG 400 molecule and give d i f f u s i o n c o e f f i c i e n t s about t h r e e times l a r g e r than t h o s e o b t a i n e d by NMR s p i n echo, which a r e s e n s i t i v e only t o t h e t r a n s l a t i o n a l motion of t h e whole molecule. W e a r e p r e s e n t l y modelling t h e r e l a x a t i o n of t h e protons on t h e PEG 400 molecule using t h e information from t h e s e d i f f u s i o n measurements.

Fig. 3 - The decomposed FIR'S from t h e Tip s p i n grouping a p p l i e d t o NaDNA

hydrated t o 33% r e l a t i v e humidity. The ( 8 ) correspond t o t h e Tip = 5 m s

component and t h e (r) t o t h e T l = 0.8 ms component.

i n a 33% r e l a t i v e humidity. I n t h i s c r y s t a l t h e r e a r e 4 molecules of water per n u c l e o t i d e ( r e s u l t i n g i n a s p i n mass which has 34% of i t s p r o t o n s on w a t e r mole- c u l e s and 66% on n u c l e o t i d e s ) . The h i g h f i e l d (T1) m a g n e t i z a t i o n r e c o v e r y f o r t h i s sample i s c h a r a c t e r i z e d by a s i n g l e r e l a x a t i o n time w i t h T1 = 8 3 + 5 m s which h a s a two component FID w i t h 35 f 3% of t h e m a g n e t i z a t i o n having a T 2 of 500 f 20

u s ( c h a r a c t e r i s t i c of a s e m i - s o l i d ) , and t h e r e s t of t h e s p i n s having a r i g i d s o l i d T2 of 14 ^f 2 us. The Tip spin-grouping i s i l l u s t r a t e d i n Fig. 3. There a r e two components t o t h e r o t a t i n g frame m a g n e t i z a t i o n decay w i t h T l p t s o f 5.0 ^f 0.3 m s ( c o r r e s p o n d i n g t o 45 f 4% of t h e t o t a l m a g n e t i z a t i o n , Mo) and 0.8 * ^0.1

m s f o r t h e r e s t . The l o n g Tip has a one component FID with a Gaussian l i n e - s h a p e w i t h T2 = 13 + 2 us. The s h o r t Tip h a s a two component FID which i s a s u p e r p o s i t i o n of a n e x p o n e n t i a l FID (T2 = 470 -C 40 us; 36% of M,,) and a Gaussian FID (T2 = 20 f 4 ps; 18% of G ) . The spin-grouping i n d i c a t e s t h a t t h e w a t e r i s i n i n t i m a t e c o n t a c t with t h e DNA f i b e r s . The s h o r t T2 of 470 us c o r r e s p o n d i n g t o t h e water component i n d i c a t e s t h a t i t s motion i s q u i t e r e s t r i c t e d . This h a s a l s o been observed by NQES measurements on t h e sample (performed on IN5 and IN6 a t t h e ILL). Only a s m a l l p a r t of t h e s c a t t e r e d peak is broadened a s i n d i c a t e d by t h e e l a s t i c i n c o h e r e n t s c a t t e r i n g f u n c t i o n (EISF) which remains approximately e q u a l t o one over t h e t o t a l Q regime measured. At h i g h e r h y d r a t i o n s , c o r r e s p o n d i n g t o 11 w a t e r molecules p e r n u c l e o t i d e , t h e w a t e r becomes more mobile. The q u a s i - e l a s t i c peak shows a g r e a t e r broadening i n t h e s h o u l d e r s and t h e Q dependence of both t h e broadening and t h e EISF i n d i c a t e s s c a t t e r i n g from molecules undergoing i s o t r o p i c d i f f u s i o n r e s t r i c t e d t o a s p h e r e w i t h a r a d i u s of -4 A. The i n c r e a s e i n t h e m o b i l i t y of t h e water a t h i g h e r h y d r a t i o n s i s a l s o observed by t h e NMR s p i n - grouping. I n t h i s c a s e t h e m a g n e t i z a t i o n r e c o v e r y a t h i g h f i e l d s ( T I ) i s n o l o n g e r e x p o n e n t i a l . It can be decomposed i n t o two components c o r r e s p o n d i n g t o t h e w a t e r and n u c l e o t i d e protons. The T r p measurements i n d i c a t e , however, t h a t a s m a l l f r a c t i o n of t h e NaDNA c o n t i n u e s t o r e l a x ( i n t h e r o t a t i n g frame o n l y ) w i t h t h e same Tip a s t h e w a t e r , a l t h o u g h t h e r e l a t i v e number of coupled n u c l e o t i d e p r o t o n s d i m i n i s h e s a t t h e l a r g e r h y d r a t i o n s . T h e r e f o r e , t h e w a t e r i s n o t i s o l a t e d from t h e DNA on t h e s m a l l e r time s c a l e s s e e n by Tip. The c o r r e l a t i o n of t h e s p i n r e l a x a t i o n t i m e s T i , Tip and T2 a t v a r i o u s h y d r a t i o n l e v e l s i s making i t p o s s i b l e t o model t h e r e l a x a t i o n of t h e h y d r a t e d NaDNA s i n c e it i s p o s s i b l e t o c l e a r l y i d e n t i f y t h e s p i n groups.

The a p p l i c a t i o n s of s p i n grouping a r e numerous. The most i m p o r t a n t may prove t o be s p i n grouping i n NMR imaging.

ACKNOWLEGEMENTS: We a r e i n d e b t e d t o D r s . A.J. Dianoux and F. Volino f o r many

h e l p f u l d i s c u s s i o n s and s u g g e s t i o n s .

JOURNAL DE PHYSIQUE

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3. F.E. B a i l y Jr. and J.V. Koleske, Poly (Ethylene Oxide), (Academic P r e s s , New York, 1976).

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Zhurn. 38, 44 (1976).

6. N. Funduk, D.W. Kydon, L.J. S c h r e i n e r , H. Peemoeller, L.J. M i l j k o v i c and M.M.

P i n t a r , J. Magn. Res. Med. 1, 66 (1984).