An Introduction to NMR Spectroscopy of Solid Samples - ACS

NMR and Macromolecules Downloaded from pubs.acs.org by YORK UNIV on 12/15/18. For personal use only.

2 An Introduction to NMR Spectroscopy of Solid Samples DANIEL J. O'DONNELL Phillips Petroleum Company, Bartlesville, OK 74004

Complex solid sample NMR techniques used in other chapters of this text are discussed. These techniques are presented using conceptual arguments, rather than mathematical equations, so that those unfamiliar with NMR spectroscopy might get a quick grasp of the nature of the experiment. Figures and charts are given which depict the interactions present in the solid state and which show how these interactions are manipulated in the NMR experiment to yield the desired information. The p a p e r s p r e s e n t e d i n t h i s volume r e p r e s e n t a f r a c t i o n o f t h e a p p l i c a t i o n s d e v e l o p e d f r o m new t e c h n i q u e s i n NMR s p e c t r o s c o p y over t h e past decade. T h i s f l o o d o f new methods h a s g e n e r a t e d new terms w h i c h , t h o u g h m a t h e m a t i c a l l y w e l l d e f i n e d , a r e d i f f i cult tovisualize physically. As a r e s u l t , t h e advantages o f the newer methods ( a n d t h e i n f o r m a t i o n t o be g l e a n e d f r o m them) are o f t e n l o s t t o the s c i e n t i s t n o t i n t i m a t e l y f a m i l i a r w i t h NMR s p e c t r o s c o p y . The o b j e c t i v e o f t h i s c h a p t e r i s t o p r o v i d e a g u i d e f o r t h e NMR layman t o t h e methods u s e d i n t h e f o l l o w i n g c h a p t e r s . Mathem a t i c a l d e r i v a t i o n s h a v e been a v o i d e d i n f a v o r o f d e s c r i p t i o n s and d i a g r a m s t o p r o v i d e c o n c e p t u a l d e f i n i t i o n s . The d i s c u s s i o n will concentrate on t h e t e c h n i q u e s used i n the following c h a p t e r s , a n d t h e r e f o r e w i l l n o t a t t e m p t t o be c o m p r e h e n s i v e . R e a d e r s a r e r e f e r r e d t o s e v e r a l t e x t s and a r t i c l e s f o r d e t a i l e d treatments o f the subjects ( 1 - 5 ) .

0097 6156/84/0247 0021 $06.25/0 © 1984 American Chemical Society

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NMR

High Resolution

AND MACROMOLECULES

NMR S p e c t r o s c o p y o f S o l i d s

Haeberlin (5) expressed the p r e v a i l i n g attitude o f the spectroscopist i n 1976 with the statement, "Narrow i s beautiful." Although t h i s a t t i t u d e s t i l l p r e v a i l s , i t has long been r e c o g n i z e d that a wealth of information i s contained i n NMR l i n e shapes b r o a d e n e d by s p e c i f i c i n t e r a c t i o n s i n s o l i d s . E x t r a c t i n g t h a t i n f o r m a t i o n has been d i f f i c u l t , s i n c e a v a r i e t y o f mechanisms c o n t r i b u t e t o t h e l i n e s h a p e , and e a c h must be selectively removed from the others to decipher the information. The methods u s e d t o d e c o n v o l u t e t h e c o m p l e x l i n e s h a p e s i n v o l v e m a n i p u l a t i o n s t o remove some b r o a d e n i n g w h i l e r e t a i n i n g other information. Several o f these techniques a r e d i s c u s s e d below. Contributions

t o NMR L i n e W i d t h s i n t h e S o l i d

Dipole-Dipole

Interactions

State

E a c h N M R - a c t i v e s p i n % n u c l e u s i n an e x t e r n a l m a g n e t i c f i e l d , H , a c t s as a m a g n e t i c d i p o l e w h i c h a l i g n s w i t h H i n specific states. F o r p r o t o n s , c a r b o n s and o t h e r s p i n h n u c l e i , two states e x i s t : p a r a l l e l or a n t i p a r a l l e l to H . Since each n u c l e u s , as a d i p o l e , h a s a l o c a l f i e l d a s s o c i a t e d w i t h i t , t h e a c t u a l f i e l d e a c h n u c l e u s e x p e r i e n c e s i s a sum o f t h e e x t e r n a l f i e l d , H , and c o n t r i b u t i o n s f r o m a l l t h e s u r r o u n d i n g d i p o l e s . T h i s d i p o l e - d i p o l e i n t e r a c t i o n i s h i g h l y d e p e n d e n t upon t h e a n g l e between t h e d i r e c t i o n o f H and t h e i n t e r n u c l e a r v e c t o r b e t w e e n a d i p o l e p a i r , and i s a l s o h i g h l y d e p e n d e n t upon t h e d i s t a n c e between t h e d i p o l e s . I n an abundant n u c l e a r species s u c h as p r o t o n s , e a c h p r o t o n h a s many n e i g h b o r s w h i c h i n t e r a c t w i t h i t a n d , b e c a u s e o f t h e dépendance o f a n g l e and d i s t a n c e , a wide v a r i e t y o f d i p o l e - d i p o l e i n t e r a c t i o n s are p o s s i b l e . In l i q u i d s , t h e s e s p e c i f i c i n t e r a c t i o n s a r e a v e r a g e d by m o t i o n s which c o n s t a n t l y change a n g l e s and d i s t a n c e s , resulting i n narrow l i n e s . I n s o l i d s , t h e a n g l e s and d i s t a n c e s a r e f i x e d , r e s u l t i n g i n an enormous number o f d i f f e r e n t l o c a l m a g n e t i c e n v i r o n m e n t s , e a c h o f w h i c h i s o b s e r v e d i n t h e NMR s p e c t r u m . The d i f f e r e n c e s i n l o c a l f i e l d s i n d u c e d by d i p o l e - d i p o l e i n t e r a c t i o n s r e s u l t i n a r a n g e o f s i g n a l s i n t h e NMR spectrum, c o v e r i n g 40 K H i n some c a s e s . As was m e n t i o n e d p r e v i o u s l y , i n f o r m a t i o n a b o u t i n t e r n u c l e a r d i s t a n c e s c a n be o b t a i n e d from the d i p o l e - d i p o l e i n t e r a c t i o n s between two i s o l a t e d d i p o l e s . The p r o b l e m i s i n d e c o u p l i n g a l l t h e o t h e r d i p o l e - d i p o l e i n t e r a c t i o n s , so t h a t one d i p o l e - d i p o l e c o u p l i n g c a n be o b s e r v e d . 0

Q

0

0

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Chemical S h i f t

Anisotropy

The s e c o n d m a j o r c o n t r i b u t o r t o NMR l i n e w i d t h s i n s p e c t r a o f s o l i d m a t e r i a l s i s c h e m i c a l s h i f t a n i s o t r o p y , CSA. CSA r e s u l t s

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NMR Spectroscopy of Solid Samples

f r o m t h e i n t e r a c t i o n between m a g n e t i c f i e l d s f r o m e l e c t r o n s i n m o t i o n a r o u n d a n u c l e u s and t h e n u c l e a r s p i n . The d i s t r i b u t i o n of e l e c t r o n s around the nucleus w i l l depend upon c h e m i c a l b o n d i n g , and a s a r e s u l t w i l l n o t be u n i f o r m i n a l l d i r e c t i o n s . As an e x a m p l e , c o n s i d e r a c a r b o n y l bond. Electronically, this bond i s h i g h l y d i r e c t i o n a l , and how i t i n t e r a c t s w i t h t h e s t a t i c f i e l d , H , w i l l be s t r o n g l y d e p e n d e n t upon t h e a n g l e b e t w e e n t h e bond and t h e d i r e c t i o n o f H . R a p i d m o t i o n s i n t h e liquid state result i n t h e o b s e r v a t i o n o f a n e t average interaction (i.e., narrow l i n e s ) . I n the s o l i d s t a t e a l l possible orientations are "frozen" i n place, resulting i n a wide v a r i e t y o f l o c a l i n t e r a c t i o n s which a r e observed i n t h e spectrum ( i . e . , wide l i n e s ) . Although information concerning b o n d i n g and m o l e c u l a r symmetry a r e c o n t a i n e d i n t h e CSA l i n e s h a p e , t h e o v e r l a p o f CSA l i n e s h a p e s i n a c o m p l e x s y s t e m makes interpretation difficult. The l i n e w i d t h s i n d u c e d b y CSA i n t e r a c t i o n s a r e d i r e c t l y p r o p o r t i o n a l t o H , so t h a t h i g h e r f i e l d s do n o t improve r e s o l u t i o n . 0

Q

Q

N u c l e a r Quadrupole E f f e c t s The discussion so f a r h a s c e n t e r e d on t h e n o n - s y m m e t r i c distribution of local fields surrounding a given nucleus r e s u l t i n g f r o m o t h e r n u c l e i ( d i p o l e - d i p o l e i n t e r a c t i o n s ) and from e l e c t r o n s ( c h e m i c a l s h i f t a n i s o t r o p y , C S A ) . I n a d d i t i o n , t h e n u c l e u s i t s e l f may n o t be s y m m e t r i c , r e s u l t i n g i n a n o n symmetric nuclear charge distribution, i . e . , an electric q u a d r u p o l e moment. F o r n u c l e i w i t h a s p i n quantum number, I , o f h ( e . g . , * H a n d ^ C ) t h e q u a d r u p o l e moment i s z e r o , and no consideration need be g i v e n t o quadrupolar interactions. However, i n t h e c a s e o f d e u t e r i u m , I e q u a l s 1, and t h e e f f e c t s o f t h e q u a d r u p o l e must be t a k e n i n t o a c c o u n t . S i n c e t h e quadrupole i s e l e c t r i c i n nature, i tinteracts d i r e c t l y only with electric field g r a d i e n t s and n o t w i t h t h e magnetic field. However, t h e m a g n e t i c e n e r g y l e v e l s o f t h e n u c l e u s a r e c o u p l e d to t h e q u a d r u p o l a r e n e r g y l e v e l s , r e s u l t i n g i n s p l i t t i n g s i n t h e NMR s p e c t r a . These s p l i t t i n g s c a n be v e r y l a r g e , r e s u l t i n g i n s p e c t r a ~200 K H w i d e f o r D , and 5 M H f o r ^ N . A t t h i s p o i n t one m i g h t a s k why q u a d r u p o l a r i n t e r a c t i o n s s h o u l d be c o n s i d e r e d , s i n c e they a r e d i f f i c u l t t o o b s e r v e , and i n t h e case o f deuterium, r e q u i r e i s o t o p i c l a b e l l i n g . The answer l i e s in the fact that i f the e l e c t r i c f i e l d g r a d i e n t about t h e q u a d r u p o l e i s f l u c t u a t i n g due t o m o l e c u l a r m o t i o n , l i n e n a r r o w i n g o c c u r s w h i c h i s e x t r e m e l y s e n s i t i v e t o t h e f r e q u e n c y and amplitude o f that motion. The r e a d e r i s r e f e r r e d t o t h e chapter by J e l i n s k i and c o - w o r k e r s i n this v o l u m e , and r e f e r e n c e s t h e r e i n f o r examples and f u r t h e r d i s c u s s i o n s . 2

Z

Z

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NMR

AND MACROMOLECULES

L i n e N a r r o w i n g Methods I n t h e above d i s c u s s i o n s o f t h e s o u r c e o f l i n e - b r o a d e n i n g i n s o l i d s t a t e NMR s p e c t r o s c o p y , i t was p o i n t e d o u t t h a t a l l o f t h e i n t e r a c t i o n s were h i g h l y o r i e n t a t i o n a l l y d e p e n d e n t . In the case o f d i p o l e - d i p o l e i n t e r a c t i o n s , the o r i e n t a t i o n of the i n t e r n u c l e a r v e c t o r between two d i p o l e s w i t h r e s p e c t t o H gave r i s e t o wide l i n e s . F o r CSA i n t e r a c t i o n s , t h e o r i e n t a t i o n o f t h e c h e m i c a l bond w i t h r e s p e c t t o H was i m p o r t a n t . Finally, the o r i e n t a t i o n o f t h e n u c l e a r e l e c t r i c q u a d r a p o l e w i t h r e s p e c t to t h e s u r r o u n d i n g e l e c t r i c f i e l d g r a d i e n t gave r i s e t o s p l i t t i n g s i n t h e NMR s p e c t r a . I n e v e r y c a s e i t was n o t e d that m o l e c u l a r m o t i o n , e s p e c i a l l y random r o t a t i o n a l and t r a n s l a t i o n m o t i o n as e x p e r i e n c e d i n t h e l i q u i d s t a t e , r e s u l t e d i n l i n e n a r r o w i n g by t i m e - a v e r a g i n g . To o b t a i n n a r r o w l i n e - w i d t h s i n t h e s o l i d s t a t e , i t i s t h e n up t o t h e s p e c t r o s c o p i s t t o m i m i c the e f f e c t o f motion i n a l i q u i d t o time-average t h e d i f f e r e n t interactions. Q

Q

Dipolar

Decoupling

The s i m p l e s t means o f r e m o v i n g d i p o l a r i n t e r a c t i o n s between two n u c l e i i s t o d e c o u p l e t h e i n t e r a c t i o n by a means entirely a n a l o g o u s t o s c a l a r d e c o u p l i n g u s e d i n ^ C NMR s p e c t r o s c o p y t o remove J - c o u p l i n g f r o m bonded p r o t o n s ( 6 ) . A strong radio frequency ( r f ) pulse a t the resonance frequency o f the protons i s t u r n e d on d u r i n g a c q u i s i t i o n o f t h e c a r b o n s i g n a l . The d e c o u p l i n g r f p u l s e promotes r a p i d s p i n t r a n s i t i o n s o r f l i p s between s p i n s t a t e s by t h e p r o t o n s p i n s , t h e r e b y a v e r a g i n g t h e static dipolar i n t e r a c t i o n s to zero. This decoupling c o n s t i t u t e s a r a p i d random m o t i o n i n " s p i n s p a c e " , as opposed to t h e random m o t i o n c h a r a c t e r i s t i c o f m o l e c u l e s tumbling i n r e a l space. U n f o r t u n a t e l y , i t c a n o n l y be u s e d t o remove heteronuclear dipole-dipole interactions. I n c a s e s where t h e i s o t o p i c c o n c e n t r a t i o n o f NMR a c t i v e s p e c i e s i s l o w , s u c h a s ( 1 . 1 % o f a l l c a r b o n s ) , homonuclear d i p o l e - d i p o l e i n t e r actions are not s i g n i f i c a n t . The l i n e - s h a p e s l e f t i n t h e NMR s p e c t r a o f s o l i d when d i p o l a r d e c o u p l i n g o f t h e p r o t o n s i s used therefore normally only reflect the chemical shift a n i s o t r o p y (CSA). The

Magic Angle

Although d i p o l a r d e c o u p l i n g removes d i p o l a r i n t e r a c t i o n s , i t does n o t remove CSA, n o r does i t p e r m i t o b s e r v a t i o n o f abundant s p i n s p e c i e s s u c h as p r o t o n s , s i n c e o b s e r v a t i o n and d e c o u p l i n g c a n n o t be done a t t h e same t i m e . D i f f e r e n t , more s e l e c t i v e means a r e needed t o remove t h e s e i n t e r a c t i o n s .

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O'DONNELL


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I t c a n be shown ( 1 - 5 ) t h a t t h e m a g n i t u d e o f a n y o f t h e above anisotropic interactions have a very specific angular dépendance w i t h r e s p e c t t o : 1. the s t a t i c f i e l d ( C S A ) , 2. o t h e r n u c l e a r s p i n s ( d i p o l e - d i p o l e i n t e r a c t i o n s ) o r 3. w i t h surrounding e l e c t r i c f i e l d gradients (quadrupole i n t e r a c t i o n s ) . Among o t h e r terms d e s c r i b i n g t h e o r i e n t a t i o n a l dependence o f these a n i s o t r o p i c i n t e r a c t i o n s i n each o f t h e r e s p e c t i v e H a m i l t o n i a n o p e r a t o r s i s t h e t e r m (3cos ® - 1 ) . The a n g l e θ h a s a d i f f e r e n t m e a n i n g d e p e n d i n g upon t h e t y p e o f i n t e r a c t i o n b e i n g considered. For dipole-dipole interactions, t h e angle i s b e t w e e n a v e c t o r j o i n i n g two d i p o l e s and t h e d i r e c t i o n o f H (Fig. 1 A ) . I n t h e c a s e o f CSA i n t e r a c t i o n s , t h e a n g l e m i g h t be b e t w e e n t h e b o n d i n g a x i s and H ( F i g . l b ) . F i n a l l y , t h e a n g l e i n quadrupolar i n t e r a c t i o n s i s b e t w e e n t h e q u a d r u p o l e moment and t h e d i r e c t i o n o f t h e e l e c t r i c f i e l d g r a d i e n t ( F i g . 1 c ) . I n each case, i f t h e angle θ i s chosen such t h a t : 2

0

0

2

3 cos e

-1=0

a l l a n i s o t r o p i c c o n t r i b u t i o n s t o t h e NMR s p e c t r u m w i l l r e d u c e to z e r o . T h i s a n g l e , 54.7°, i s j u s t l y c a l l e d t h e m a g i c a n g l e . Since a l l values of θ are possible i n the n o n - c r y s t a l l i n e or powdered s o l i d , v e r y few i n t e r a c t i o n s n a t u r a l l y r e d u c e t o z e r o . However, i f , o v e r t i m e , t h e a v e r a g e v a l u e o f θ = 54.7°, t h e anisotropic static contributions w i l l again reduce t o zero. T h i s c a n be done i n r e a l s p a c e by h i g h speed sample r o t a t i o n a t an a n g l e 54.7° f r o m t h e d i r e c t i o n o f t h e f i e l d ( _ 3 ) ; or i n s p i n s p a c e , by m a n i p u l a t i o n o f t h e s p i n s u s i n g r f p u l s e s ( J 7 ) . In F i g . 2, a r e p r e s e n t a t i o n o f t h e e f f e c t o f s p i n n i n g on t h e t i m e a v e r a g e d v a l u e o f an i n t e r n u c l e a r v e c t o r i s shown. Rotation a b o u t t h e a x i s R c a u s e s t h e n u c l e i and t h e i n t e r n u c l e a r v e c t o r to c i r c l e t h e a x i s . O v e r a p e r i o d o f one r o t a t i o n , t h e a v e r a g e p o s i t i o n o f e a c h n u c l e i l i e s a l o n g R, and t h e t i m e a v e r a g e i n t e r n u c l e a r v e c t o r w i l l t h e r e f o r e a l s o be a l i g n e d w i t h R. The anisotropic static i n t e r a c t i o n s mentioned above will be c o h e r e n t l y m o d u l a t e d a t s p i n n i n g r a t e s l e s s t h a n ~ one h a l f o f the l i n e w i d t h ( i n H z ) , r e s u l t i n g i n s p i n n i n g s i d e bands. At s p i n n i n g r a t e s g r e a t e r t h a n t h e l i n e w i d t h , t h e s i d e bands disappear. T h e o r e t i c a l l y , i t i s p o s s i b l e t o remove a l l o f t h e above a n i s o t r o p i c i n t e r a c t i o n s b y sample s p i n n i n g a t t h e m a g i c angle. Realistically, s p i n n i n g r a t e s have b e e n l i m i t e d b y m a t e r i a l p r o b l e m s , so t h a t r a t e s o f 3 t o 5 K H a r e n o r m a l . These rates are sufficient to attenuate o r remove lineb r o a d e n i n g due t o CSA, b u t a r e f a r s h o r t o f t h e ~ 2 0 K H necessary t o remove dipolar interactions, with a few exceptions(_1 ) . Z

Z

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NMR AND MACROMOLECULES

A .

X

Β .

F i g u r e 1 . O r i e n t a t i o n a l dependence o f a n i s o t r o p i c i n t e r a c t i o n s on t h e a n g l e Θ : a. D i p o l e - d i p o l e interac t i o n ; b. c h e m i c a l s h i f t a n i s o t r o p i c i n t e r a c t i o n ; c. e l e c t r i c q u a d rupolar interaction.

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Figure 2. The t i m e - a v e r a g e d r e s u l t randomly o r i e n t e d i n t e r n u c l e a r v e c t o r , t i o n a l a x i s , R.

of rotation ab, about a

of a rota-


28 Line Narrowing i n Spin Space - WAHUHA

Sample spinning induces a time dependent e f f e c t on the r e l a tionship between a nuclear spin f i x e d along H and its "surroundings" by moving the "surroundings" about the magic angle. I f the "surroundings" are now f i x e d , the same type o f time dependent behavior can be induced by s p e c i f i c r o t a t i o n o f the nuclear spins about the magic angle. In F i g . 3, a repre s e n t a t i o n o f magic angle sample spinning i s given from the viewpoint o f the sample. Since the magic angle vector i s a locus o f points e q u i d i s t a n t from a l l three coordinates, a view down the magic angle r e v e a l s the three coordinate axis to be e q u a l l y spaced about the "magic" v e c t o r . As the sample s p i n s , the a p p l i e d f i e l d , H , appears to be " r o t a t i n g " through each o f the c o o r d i n a t e s . The nuclear spins remain a l i g n e d along H , so that the s p i n magnetization, M, a l s o appears to be r o t a t i n g through the three c o o r d i n a t e s . Q

0

0

In 1968, Waugh and co-workers(7) devised a means of " r o t a t i n g " M through each of three coordinate a x i s . Because nuclear spins precess about H a t the Larmor or resonance frequency, the co ordinate system used when s p i n manipulations are i n v e s t i g a t e d must also r o t a t e a t the Larmor frequency. This a l s o permits us to view r f pulses at the Larmor frequency as a p p l i e d f i e l d s along the axes o f t h i s r o t a t i n g frame (when the r o t a t i n g frame i s used, the axes w i l l be designated x , y and ζ ) . Q

f

f

1

C l a s i c a l l y , when an r f pulse i s a p p l i e d , e.g. along the x' a x i s , t h i s r f f i e l d , H]_, w i l l cause the net s p i n magnetization, M, a l i g n e d along H to precess as shown i n F i g . 4 a . A pulse of s p e c i f i c d u r a t i o n f o r a given H| w i l l cause M to precess e x a c t l y h r e v o l u t i o n , so that M l i e s on the y axis ( F i g . 4 b ) . Changing the phase of the o f pulse 180° w i l l cause M to precess i n the opposite d i r e c t i o n , r e t u r n i n g i t to the ζ ' axis ( F i g . 4c). The same type o f pulse sequence can be a p p l i e d along the y' a x i s , r o t a t i n g M into the x a x i s . By proper use of pulses and delays, M can be made to spend equal amounts of time on each of the r o t a t i n g frame axes. As can be seen, t h i s mimics i n s p i n space the r e s u l t s obtained by sample r o t a t i o n i n r e a l space. The necessary pulses are diagramed i n F i g . 4 d . I f the pulses are short enough and the delays, τ, are kept to a min imum, the " r o t a t i o n r a t e " o f the process can be made f a s t enough to e f f e c t i v e l y decouple homonuclear d i p o l e - d i p o l e i n t e r actions . This technique and other, more complicated pulse sequencesQ) have been used to narrow l i n e s i n proton s p e c t r a . The method i s also important i n that i t removes only homonuclear d i p o l e - d i p o l e broadening, but does not e f f e c t heteronuclear d i p o l e - d i p o l e i n t e r a c t i o n s . In the chapter by Schaefer and coworkers i n t h i s text, the WAHUHA pulse sequence 0

1

1

O'DONNELL


Figure 3. V i e w down m a g n e t i z a t i o n , M, and i s r o t a t i n g ccw w i t h The a n g l e o f R f r o m a l

t h e r o t a t i o n a l a x i s , R, o f t h e n e t t h e a p p l i e d f i e l d , Ho. The v i e w e r r e s p e c t t o the c o o r d i n a t e system. l three axis i s 5 4 . 7 ° .


A .

fH

Ζ 0

M ' χ'-X' W/2 P U L S E

t

1

+ X ' W/2

PULSE

Β .

j

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c.

W/2 X' 4

W/2 -X' W/2 !

4 Π

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ψ

7Γ/2 -Y' 4

2Ψ

ACQUIRE DATA Figure 4. The WAHUHA e x p e r i m e n t : a . The a c t i o n o f a TT/2 r f p u l s e a p p l i e d t o a s p i n s y s t e m a l o n g t h e +x' a x i s i n t h e r o t a t i n g frame; b. t h e a c t i o n o f a ïï/2 p u l s e a p p l i e d a l o n g - x a x i s . c . The WAHUHA p u l s e s e q u e n c e . 1

2.

was

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NMR

Spectroscopy of Solid Samples

u s e d t o remove 1 H - * H d i p o l e couplings.

couplings,

31

while

retaining ^-H-

F i n a l l y , i t s h o u l d be p o i n t e d o u t t h a t t h e above d i s c u s s i o n s are vast over-simplifications which are (hopefully) conceptually easy t o grasp. unfortunately, they are not theoretically satisfying. A d d i t i o n a l reading i s urged t o pro v i d e a more i n d e p t h understanding(1-5). Cross P o l a r i z a t i o n C l a s s i c a l l y , t h e n e t magnetization, M , o f a s p i n system r e s u l t s f r o m t h e sum o f t h e i n d i v i d u a l s p i n s w h i c h p r e c e s s a b o u t t h e applied field, H (see F i g . 5a). The f r e q u e n c y of the precession, called t h e Larmor f r e q u e n c y (OJL? F i g . 5 a ) , i s d e p e n d e n t upon t h e m a g n e t i c moment o f t h e i n d i v i d u a l s p i n s , and the a m p l i t u d e o f H . I n a d d i t i o n , the amplitude or p o l a r i z a t i o n o f M w i l l depend upon t h e v a l u e o f t h e n u c l e a r m a g n e t i c moment a s w e l l . I n t h e case o f a p r o t o n s p i n system, t h e n e a r l y 100% n a t u r a l abundance and l a r g e m a g n e t i c moment r e s u l t i n a p o l a r i z a t i o n that gives a large net magnetization, MJJ (Fig. 5a). The m a g n e t i c moment o f a l ^ C p i on t h e o t h e r h a n d , i s a b o u t one f o u r t h as l a r g e a s t h e p r o t o n moment, r e s u l t i n g i n a n e t m a g n e t i z a t i o n , M , t h a t i s one f o u r t h t h a t o f p r o t o n s i n t h e same H f o r an e q u a l number o f n u c l e i . To make m a t t e r s w o r s e , t h e n a t u r a l abundance o f ^ C n u c l e i i s o n l y 1.1%. F i n a l l y , t h e l e n g t h o f time f o r t h e carbon s p i n system t o r e c o v e r f r o m t h e p e r t u r b a t i o n n e c e s s a r y t o make a m e a s u r e ment c a n be 10 t o 100 t i m e s l o n g e r t h a n t h a t t i m e needed f o r a proton s p i n s y s t e m i n t h e same m o l e c u l e (see s p i n - l a t t i c e relaxation, below). This creates a time b o t t l e n e c k when repeated samplings a r e taken o f the ^ C magnetization. Q

Q

S

n

>

c

0

From t h e above d i s c u s s i o n , i t i s e v i d e n t t h a t i f t h e p r o t o n s p i n s y s t e m c o u l d be u s e d as a s o u r c e o f m a g n e t i z a t i o n and a s a means o f r e l a x a t i o n f o r t h e c a r b o n s p i n s y s t e m , a n enhancement o f t h e c a r b o n N M R s i g n a l and a s a v i n g s i n t i m e c o u l d be achieved. T h i s energy t r a n s f e r i n t h e s t a t i c f i e l d , H , i s n o t p o s s i b l e due t o t h e l a r g e m i s m a t c h i n t h e L a r m o r frequencies for t h e two d i f f e r e n t n u c l e i . I n order f o r a t r a n s f e r to o c c u r , t h e two s p i n s y s t e m s must have some p r e c e s s i o n a l compo nents that a r e equal i n frequency. As l o n g a s t h e s p i n s a r e precessing about t h e s t a t i c f i e l d , H , t h i s i s impossible. However, s p e c i f i c m a g n e t i c f i e l d s may be a p p l i e d by u s i n g r a d i o frequency ( r f ) pulses. I n F i g . 5a, the magnetization ofthe p r o t o n s was shown i n a c o o r d i n a t e s y s t e m s e t i n t h e l a b o r a t o r y ; the laboratory reference frame. An r f p u l s e a t a given f r e q u e n c y i n t h e l a b o r a t o r y frame w i l l a p p e a r a s a f i e l d o f magnitude H, r o t a t i n g a b o u t the Ζ axis a t the applied Q

Q

NMR A N D MACROMOLECULES

f

A .

"^3w'^ H

T

"

Ho

13

f

CROSS POLARIZATION

4/H = 4»C

F i g u r e 5. S p i n l o c k i n g o f t h e p r o t o n s p i n s y s t e m and subsequent c r o s s polarization between t h e p r o t o n and carbon s p i n s : a. The i n i t i a l p r o t o n m a g n e t i z a t i o n on t h e ζ' a x i s , a l i g n e d w i t h t h e f i e l d , Ho; b. Α π / 2 p u l s e i s a p p l i e d along the χ axis of the proton rotating f r a m e , f o l l o w e d by an r f f i e l d , H ç , a p p l i e d a l o n g t h e y a x i s o f t h e carbon r e f e r e n c e frame; c. Spin locking of t h e p r o t o n s p i n s b y H J J and c r o s s p o l a r i z a t i o n w i t h t h e carbon s p i n s . 1

2.

O'DONNELL

33


frequency. I f t h e c o o r d i n a t e s y s t e m were r o t a t i n g a t t h e a p p l i e d f r e q u e n c y ( a r o t a t i n g r e f e r e n c e f r a m e ) , t h e n Έ.\ w o u l d a p p e a r a s a f i e l d a l i g n e d a l o n g e i t h e r t h e x ' o r y' a x i s . In Fig. 5b, a n r f f i e l d a t t h e p r o t o n f r e q u e n c y , H J J , i s shown along the χ a x i s . T h i s f i e l d , a s shown i n f i g . 5b, a p p l i e s a torque t o MJJ, t h e n e t p r o t o n m a g n e t i z a t i o n , making i t r o t a t e into the y axis. A t t h a t p o i n t , t h e r f f i e l d c a n be s h i f t e d 90°, so t h a t i t a l s o l i e s a l o n g t h e y a x i s ( F i g . 5 c ) . Because HJJ i s a m a g n e t i c f i e l d t h a t i s c o - l i n e a r w i t h t h e n e t m a g n e t i z a t i o n , Mj|, t h e i n d i v i d u a l s p i n s r e p r e s e n t e d b y M|j w i l l p r e c e s s about Hj| a t a new p r e c e s s i o n a l f r e q u e n c y , that i s determined by t h e amplitude o f H . I f another r f f i e l d i s a p p l i e d a t t h e carbon f r e q u e n c y , such t h a t t h e p r e c e s i o n a l f r e q u e n c y , U ) , o f t h e c a r b o n s p i n s a b o u t H e q u a l s (jOg, t h e n an e f f i c i e n t t r a n s f e r o f magnetization can occur ( F i g . 5c). 1

1

1

H

C

c

The p r o c e s s o f h o l d i n g a n e t m a g n e t i z a t i o n a l o n g a n a x i s o f t h e r o t a t i n g frame u s i n g a n r f f i e l d i s c a l l e d s p i n - l o c k i n g . The match o f r f f i e l d i n t e n s i t i e s H and H s u c h t h a t (% = 0 ) i s c a l l e d a Hartman-Hahn m a t c h ( 8 ) . The p r o c e s s o f t r a n s f e r r i n g m a g n e t i z a t i o n from t h e p r o t o n s p i n s t o t h e carbon s p i n s i s called cross polarization(9). The r a t e of transfer i s characterized by a contact time, T , which S c h a e f e r and coworkers used t o s t u d y s p i n - s p i n c o n t r i b u t i o n t o T^p ( s e e b e l o w and c h a p t e r b y S c h a e f e r , e t a l , t h i s v o l u m e ) . C

H

c

c p

The c r o s s p o l a r i z a t i o n , o r CP, p r o c e s s may be u s e d w i t h a n y o r a l l o f t h e l i n e n a r r o w i n g t e c h n i q u e s t o o b t a i n NMR s p e c t r a o f s o l i d s w i t h r e s o l u t i o n approaching that of liquidsC3). A combination o f c r o s s p o l a r i z a t i o n ( C P ) , magic angle s p i n n i n g (MAS) and d i p o l a r d e c o u p l i n g were u s e d t o o b t a i n t h e s p e c t r u m o f a v e r y i n s o l u b l e p o l y p h e n y l e n e s u l f i d e ( R y t o n ) a s shown i n F i g . 6.

34

NMR

NMR M e a s u r e m e n t s o f M o t i o n

AND

MACROMOLECULES

i n Polymers

All o f the i n t e r a c t i o n s discussed above have a strong dependency on m o t i o n , ( o r l a c k o f m o t i o n ) i n s o l i d s . I t i s not s u r p r i s i n g then that the motions that a r e present i n a s o l i d c a n be d e t e c t e d by m o t i o n - s e n s i t i v e NMR m e t h o d s . The methods u s e d i n t h i s volume c a n be d i v i d e d i n t o two c a t a g o r i e s ; l i n e shape a n a l y s i s and r e l a x a t i o n s t u d i e s . Line-Shape A n a l y s i s B e c a u s e o f t h e s t r o n g o r i e n t a t i o n a l dependancy o f t h e l i n e b r o a d e n i n g mechanisms d i s c u s s e d a b o v e , t h e NMR l i n e shape w i l l r e f l e c t changes i n t h e o r i e n t a t i o n w i t h t i m e . I f the frequency o f a m o t i o n i n a s o l i d i s lower than the range o f f r e q u e n c i e s (i.e., line-width in H ) i n d u c e d b y an i n t e r a c t i o n (e.g., e l e c t r i c quadrupolar i n t e r a c t i o n s ) , a small, but measurable narrowing might occur. As t h e f r e q u e n c y and a m p l i t u d e o f t h e motion i s i n c r e a s e d by h e a t i n g t h e s a m p l e , a d d i t i o n a l line narrowing w i l l occur. D r a m a t i c l i n e - s h a p e changes o c c u r a s t h e motional frequency nears the l i n e - w i d t h frequency. Above t h e l i n e - w i d t h frequency, s u b s t a n t i a l l y narrower l i n e shapes a r e observed. C o n v e r s e l y , t h e m o l e c u l a r m o t i o n may be r a p i d comp a r e d t o t h e l i n e w i d t h a t room t e m p e r a t u r e ( n a r r o w l i n e s ) and the t e m p e r a t u r e dependency o f t h e l i n e shape may be b e s t i n v e s tigated by l o w e r i n g t h e t e m p e r a t u r e . In this t e x t , Dr. J e l i n s k i and c o w o r k e r s u s e d l i n e - b r o a d e n i n g from n u c l e a r e l e c t r i c q u a d r u p o l a r i n t e r a c t i o n s t o i n v e s t i g a t e motions about a bond b e t w e e n c a r b o n s isotopically enriched with deuterium. T h i s s t u d y was p a r t i c u l a r l y i n t e r e s t i n g , b e c a u s e two r e g i o n s o f t h e p o l y m e r e x i s t e d ; one t h a t gave a r e l a t i v e l y n a r r o w NMR l i n e - w i d t h ( " f a s t " m o t i o n ) and one t h a t y i e l d e d a much b r o a d e r NMR l i n e w i d t h ( " s l o w " m o t i o n ) . T h i s i n d i c a t e d two r e g i o n s i n the polymer w i t h d i s t i n c t l y d i f f e r e n t m o t i o n a l c h a r a c t e r i s t i c s . z

S c h a e f e r and c o w o r k e r s , i n a n o t h e r c h a p t e r i n t h i s t e x t , u s e d *H - l ^ C d i p o l e - d i p o l e " l i n e s h a p e s " o b t a i n e d i n a v e r y c l e v e r way t o i n v e s t i g a t e r o t a t i o n a l m o t i o n o f t h e a r o m a t i c r i n g s i n polystyrene. The method u s e d a WAHUHA p u l s e s e q u e n c e t o decouple proton-proton d i p o l a r i n t e r a c t i o n s , cross p o l a r i z a t i o n t o enhance s i g n a l a c q u i s i t i o n and an o v e r a l l s a m p l i n g t e c h n i q u e s y n c h r o n o u s w i t h t h e sample r o t a t i o n . The ^ C - *H d i p o l e d i p o l e i n t e r a c t i o n was mapped i n r o t a t i o n a l s i d e b a n d s p e c t r a o b t a i n e d f r o m 16 " n o r m a l " CP/MAS s p e c t r a . The method, t h o u g h somewhat i n v o l v e d , p r o v i d e d a measure o f d i p o l e - d i p o l e lineshapes w h i c h c a n be i n t e r p r e t e d i n terms o f s i d e - c h a i n r o t a t i o n i n the polymer.

2.

O'DONNELL

35

N M R Spectroscopy of Solid Samples

R e l a x a t i o n and M o t i o n i n S o l i d s S p i n - L a t t i c e R e l a x a t i o n - Ί·\ I n F i g . 5 a , a r e p r e s e n t a t i o n o f t h e n e t m a g n e t i z a t i o n , M, o f a n u c l e a r s p i n system i s g i v e n . The v a l u e o f M i s t h e sum o f t h e i n d i v i d u a l s p i n s p r e c e s s i n g a t t h e Larmor f r e q u e n c y , U)L, about the a p p l i e d field, H . The i n d i v i d u a l s p i n s r e p r e s e n t an e x c e s s o f s p i n s i n t h e l o w e n e r g y s t a t e o f a s y s t e m where t h e spins are distributed (Boltzman d i s t r i b u t i o n ) b e t w e e n two states (spin % nucleus). The s y s t e m , a s shown i n F i g . 5 a , i s at equilibrium. I f an r f p u l s e , Η χ , a t i s now a p p l i e d , t h e system w i l l a b s o r b some o f t h e e n e r g y f r o m t h e p u l s e ( t h e resonance c o n d i t i o n ) , t h a t i s , t h e system w i l l "heat up". I n F i g . 5b t h i s i s r e p r e s e n t e d by a t i p p i n g o f t h e m a g n e t i z a t i o n i n t h e r o t a t i n g f r a m e . The m a g n i t u d e o f M a l o n g H i s e q u a l t o z e r o i n F i g . 7b. The s y s t e m i s c l e a r l y n o t i n e q u i l i b r i u m w i t h H , and i f t h e r f f i e l d , H|, i s removed a t t h i s p o i n t , t h e s y s t e m w i l l be l e f t i n a d i s o r d e r e d s t a t e . To r e - e s t a b l i s h t h e equilibrium condition, some o f the i n d i v i d u a l spins must exchange e n e r g y , o r " c o o l down." The p r o b a b i l i t y o f a s p i n g i v i n g up e n e r g y i n t h e f o r m o f d i s c r e t e r f r a d i a t i o n ( a phonon) i s v e r y l o w . T h u s , s i n c e e n e r g y must be c o n s e r v e d , t h e e n e r g y must be d i s s i p a t e d i n some o t h e r f o r m . I t may be dissipated as thermal energy t o the atomic framework, o r l a t t i c e , i f a s u i t a b l e mechanism e x i s t s f o r t h e t r a n s f e r . The mechanism must be m a g n e t i c i n n a t u r e , and must f l u c t u a t e a t t h e L a r m o r f r e q u e n c y ( i . e . , i t must f l u c t u a t e a t a r a d i o f r e q u e n c y i n t h e megahertz r a n g e ) . The m a g n e t i c f i e l d s o u r c e s a v a i l a b l e on t h e a t o m i c s c a l e a r e n u c l e a r d i p o l e s and u n p a i r e d e l e c t r o n s . I f there i s r o t a t i o n , v i b r a t i o n or t r a n s l a t i o n i n the l a t t i c e a t t h e L a r m o r f r e q u e n c y , U3L, t h e n r e l a x a t i o n o f t h e s p i n s y s t e m to t h e e q u i l i b r i u m s t a t e can occur by passage o f t h e excess energy t o t h e l a t t i c e system; i . e . , s p i n - l a t t i c e relaxation occurs. The r e l a x a t i o n process usually appears t o be exponential i n n a t u r e , and i s u s u a l l y c h a r a c t e r i z e d by a 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|. The v a l u e f o r Ύγ r e p r e s e n t s t h e t i m e n e c e s s a r y f o r t h e m a g n e t i z a t i o n t o r e t u r n t o w i t h i n ( 1( 1/e)) o r 6 3 % o f i t s m a g n i t u d e a t e q u i l i b r i u m . Thus, f o r f u l l r e s t o r a t i o n o f M a l o n g t h e f i e l d , H , one must w a i t several t i m e s t h e v a l u e o f Τ j ( u s u a l l y 5 · T]_ i s s u f f i c i e n t ) . Q

N

0

Q

N M R A N D M A C R O M O L E C U I ES Τ

— J

L

180.0

160.0

_ _ _ J

140.0

L

.

120.0

1

!

1

J

1 80.0

60.0

100.0

CHEMICAL SHIFT -

I

—I

Γ

I

40.0

L_ 20.0

PPM

Figure 6 . A CP/MAS NMR spectrum of Ryton (polyphenylene sulfide). The s i g n a l s occur at ~135 and ~133 ppm ( from an e x t e r n a l reference of TMS).

F i g u r e 7. A mapping of the carbon magnetization during a Τι measurement : a. The carbon magnetization, M Q , locked on the y axis by an r f f i e l d , H Q , a f t e r cross p o l a r i z a t i o n ; b. Mfj a l i g n e d along the a p p l i e d f i e l d , Ho, a f t e r a π/2 r f pulse along -x'; c. Mç a f t e r T j r e l a x a t i o n f o r a time p e r i o d , τ; d. Mç, a f t e r a π/2 r f pulse, a l i g n e d along y . This permits the amplitude of M Q to be measured. 1

f

2.

O'DONNELl.

37

N M R Spectroscopy of Solid Samples

For the individual interested i n molecular motion, the important feature of spin-lattice relaxation (or other r e l a x a t i o n mechanisms) i s t h e dependency on m o l e c u l a r m o t i o n t o p r o v i d e an e f f i c i e n t e n e r g y pathway f o r r e l a x a t i o n . Thus, m o l e c u l a r motions a t t h e Larmor frequency f o r i n d i v i d u a l carbon atoms i n a m o l e c u l a r framework may be mapped b y T j m e a s u r e ments. Since t h e frequency o f m o l e c u l a r motion i s temperature d e p e n d e n t , a d d i t i o n a l thermodynamic and k i n e t i c i n f o r m a t i o n may be o b t a i n e d by m e a s u r i n g T\ v a l u e s f o r d i f f e r e n t c a r b o n s o v e r a range o f t e m p e r a t u r e s . I n t h e p a p e r b y L y e r l a and c o w o r k e r s i n t h i s v o l u m e , Ύγ measurements made f o r t h e f i r s t t i m e o v e r a range o f low temperatures y i e l d e d s p e c i f i c i n f o r m a t i o n about m o t i o n i n t h e backbone and s i d e c h a i n s o f a s e m i - c r y s t a l l i n e and a g l a s s y p o l y m e r . The d a t a was t a k e n a t a L a r m o r f r e q u e n c y o f 15.1 MHz f o r nuclei. I t was a l s o n o t e d i n t h i s p a p e r t h a t t h e T\ v a l u e s measured f o r t h e g l a s s y p o l y m e r showed n o n e x p o n e n t i a l b e h a v i o r . As s t a t e d i n t h e paper, t h i s r e p r e s e n t e d a d i s t r i b u t i o n o f T| v a l u e s due t o t h e many d i f f e r e n t e n v i r o n m e n t s , and t h e r e f o r e t h e many d i f f e r e n t T\ m e c h a n i s m s , p r e s e n t i n the polymer. R e l a x a t i o n i n t h e R o t a t i n g Frame-T]ρ As v a l u a b l e a s T| measurements c a n be i n a n a l y z i n g m o l e c u l a r motions, they suffer from a significant d r a w b a c k ; t o map motions a t other frequencies, different magnetic field s t r e n g t h s , H , must be u s e d . T h i s r e q u i r e s t h e use o f a d i f f e r e n t magnet ( i . e . , a d i f f e r e n t s p e c t r o m e t e r o p e r a t i n g a t a d i f f e r e n t Larmor f r e q u e n c y ) . I n addition, the l i m i t a t i o n of t h e Tji measurements t o m o l e c u l a r m o t i o n s i n t h e 10^ h e r t z f r e quency r a n g e ( f o r ^ C ) r e s t r i c t s t h e u s e o f T\ s t u d i e s t o o n l y a few t y p e s o f m o t i o n s . Motions i n the k i l o h e r t z r e g i o n a r e therefore inaccessible. Q

The f r e q u e n c y r a n g e o f m o t i o n a v a i l a b l e f o r s t u d y b y Ί\ mech anisms i s governed by t h e p r e c e s s i o n a l (Larmor) frequency o f the i n d i v i d u a l s p i n s about t h e a p p l i e d f i e l d , H . I f a means c o u l d be f o u n d t o make t h e s e s p i n s p r e c e s s a b o u t a much l o w e r field i n t h e presence o f H , then t h e f r e q u e n c y dependent n a t u r e o f t h e r e l a x a t i o n mechanism c o u l d be a l t e r e d t o a l l o w motions i n t h e KHz r a n g e t o be s t u d i e d . S u c h a means h a s a l r e a d y b e e n d i s c u s s e d — s p i n l o c k i n g ( s e e F i g . 5 ) . I n t h e CP e x p e r i m e n t , t h e p r o t o n s p i n s a r e f i r s t " l o c k e d " a l o n g an r f f i e l d , H||, r o t a t i n g a t t h e L a r m o r f r e q u e n c y . As shown i n F i g . 5b, H|| a p p e a r s a s a m a g n e t i c f i e l d a l i g n e d a l o n g an a x i s o f a Q

Q


38

coordinate system r o t a t i n g at the proton Larmor frequency about H (the *H r o t a t i n g frame). As shown i n 5c, the i n d i v i d u a l porton spins w i l l precess about H J J at a frequency, directly p r o p o r t i o n a l to the amplitude of H . In a d d i t i o n , the carbon spins at the end of the cross p o l a r i z a t i o n trans fer are a l s o " l o c k e d " along an r f f i e l d , Hç, such that the i n d i v i d u a l carbon spins are precessing about Hç at a frequency, U)fj, p r o p o r t i o n a l to H p There are two important features about the s p i n - l o c k c o n d i t i o n that make i t a t t r a c t i v e f o r r e l a x a t i o n s t u d i e s ; 0

W

1.

The l o c k i n g r f f i e l d s can have a range of amplitudes. Thus a range of motional frequencies can be i n v e s t i g a t e d by simply changing the amplitude of Hj| or H Q .

2.

The magnetization locked along the a p p l i e d r f f i e l d s are at a magnitude generated by a much l a r g e r f i e l d , H . T h i s means that the magnetization, M , i s much too large i n prop o r t i o n to the r f f i e l d s , H J J and H Q , and M must d i m i n i s h v i a a r e l a x a t i o n mechanism to a l e v e l that matches the amplitude of H J J or H Q . 0

The process of r e l a x a t i o n of M to a value p r o p o r t i o n a l to the a p p l i e d r f f i e l d s i n the r o t a t i n g frame i s c a l l e d s p i n - l a t t i c e r e l a x a t i o n i n the r o t a t i n g frame. The mechanisms a v a i l a b l e f o r t h i s form of r e l a x a t i o n are e n t i r e l y analogous to those a v a i l able f o r simple s p i n - l a t t i c e r e l a x a t i o n as described above. S i m i l a r l y , r o t a t i n g frame r e l a x a t i o n i s c h a r a c t e r i z e d by a time constant analogous to T j , and i s c a l l e d T j p , or the spinl a t t i c e r e l a x a t i o n time i n the r o t a t i n g frame. Typically, Tjp values obtained from protons i n s o l i d samples are not of much use, since communication between the abundant protons tends to average the r e l a x a t i o n process, so that individual proton r e l a x a t i o n mechanisms cannot be observed. For ^ C , however, the n a t u r a l low abundance of l^C l i m i t s the degree of communic a t i o n , and separate T^p values can be obtained for each observed carbon s p e c i e s . As noted i n the papers by Schaefer and coworkers and by L y e r l a and coworkers, T j p data may be complicated by the f a c t that mechanisms other than s p i n - l a t t i c e i n t e r a c t i o n s (namely s p i n spin r e l a x a t i o n ) are p o s s i b l e which don't map motional charact e r i s t i c s . In the case of p o l y s t y r e n e , Schaefer and coworkers conclude that the spin-spin contributions are negligible, whereas L y e r l a and coworkers f i n d that the l e v e l s of s p i n - s p i n and s p i n - l a t t i c e c o n t r i b u t i o n s for i s o t a t i c polypropylene and a t a t i c polymethyl methacrylate were temperature dependent.

2.

O'DONNELL

39


Measurement o f R e l a x a t i o n The methods t o measure T j and T^p i n t h e s o l i d s t a t e a r e somewhat u n i q u e . The i n i t i a l step f o r both experiments c o n s i s t s o f enhancement o f t h e magnetization v i a - *H c r o s s p o l a r i z a t i o n ( F i g . 5 ) . A t t h e end o f t h e c r o s s p o l a r i z a t i o n p e r i o d , t h e carbon m a g n e t i z a t i o n i s e i t h e r allowed t o c o n t i n u e t o i n t e r a c t w i t h t h e r f f i e l d , Hç w h i l e t h e p r o t o n r f f i e l d i s removed ( F i g . 7 a ) , o r an r f p u l s e i s a p p l i e d t o r o t a t e it to align with H ( F i g . 7b). I n t h e f i r s t c a s e , t h e magnet i z a t i o n a l i g n e d a l o n g Hç d e c a y s v i a a T j p mechanism, and t h e r a t e o f d e c a y i s m o n i t o r e d by c h a n g i n g t h e l e n g t h o f t i m e H Q i s applied. The p u l s e s e q u e n c e u s e d i s o u t l i n e d i n t h e p a p e r by S c h a e f e r and c o - w o r k e r s and i s r e p e a t e d h e r e ( F i g . 8 c ) . The r e a d e r i s r e f e r r e d t o o t h e r r e f e r e n c e s f o r a more d e t a i l e d a c c o u n t (_3). Q

I f t h e m a g n e t i z a t i o n M Q i s moved t o t h e ζ a x i s t o a l i g n w i t h H , t h e i n d i v i d u a l s p i n s w i l l now p r e c e s s a t ωχ^ a r o u n d H ( M H frequencies). Remembering t h a t t h e m a g n e t i z a t i o n represented by M Q i s t h e r e s u l t o f a f o u r - f o l d enhancement f r o m t h e c r o s s p o l a r i z a t i o n w i t h t h e p r o t o n s p i n s , then i t i s e v i d e n t t h a t M Q does n o t r e p r e s e n t t h e n o r m a l e q u i l i b r i u m m a g n e t i z a t i o n f o r t h e carbon s p i n system. R e l a x a t i o n o c c u r s ( F i g . 7 c ) , and s a m p l i n g o f t h e p r o c e s s i s done by r o t a t i n g t h e r e m a i n i n g m a g n e t i z a t i o n v i a a ïï/2 r f p u l s e i n t o t h e x , y p l a n e ( F i g . 7 d ) . 1

0

0

f

Z

1

The p u l s e s e q u e n c e s f o r m e a s u r i n g T\ and T j p , enhancement p u l s e s , a r e g i v e n i n F i g . 8.

including

t h e CP

Conclusions T h i s s h o r t o v e r v i e w o f s o l i d sample NMR t e c h n i q u e s h a s been an attempt t o e x p l a i n t h e experiments used i n t h i s t e x t i n terms t h e layman c a n u n d e r s t a n d . A s c a n be s e e n b y t h e t i t l e s o f t h e p a p e r s on s o l i d sample NMR s p e c t r o s c o p y , t h e m a i n t h r u s t o f r e s e a r c h i n t h i s a r e a as a p p l i e d t o polymers i s t h e i n v e s t i g a t i o n o f motions i n polymers. The e x p e r i m e n t s o u t l i n e d i n t h i s and f o l l o w i n g c h a p t e r s h a v e been shown t o be u s e f u l f o r i n v e s t i g a t i n g m o t i o n s c o v e r i n g a f r e q u e n c y r a n g e o f 1 0 ^ t o 10^ H z . Most o f these experiments a r e pre-programmed into the commercial instruments a v a i l a b l e today. New a n d even more e x c i t i n g experiments are p o s s i b l e w i t h the f l e x i b i l i t y a f f o r d e d by t h e s t a t e o f t h e a r t c o m p u t e r c o n t r o l l e d s y s t e m s . Hopefully, as these instruments become more commonplace, these

NMR A N D MACROMOLECULES

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F i g u r e 8. P u l s e d i a g r a m s f o r s o l i d sample NMR e x p e r i ments: a. ^H-l^c cross polarization with dipolar d e c o u p l i n g ; b. WAHUHA % - *H d i p o l a r d e c o u p l i n g ; c . Τ r e l a x a t i o n sequence ( t i m e p e r i o d , τ, i s v a r i e d ) ; d. Τχ r e l a x a t i o n s e q u e n c e ( t i m e p e r i o d , t , i s v a r i e d ) .

2.

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41


types o f experiments they deserve.

will

gain

the wider

acceptance

and

use

Literature Cited 1.

Mehring, M. "High Resolution NMR Spectroscopy in Solids"; Diehl, P.; Fluck, Ε . ; Kosfeld, R . , Eds.; NMR, Vol. XI, Springer-Verlag, New York, 1976.

2.

Abragam, A. "The Principles of Nuclear Magnetism"; Clarendon Press: Oxford University, London, 1961.

3.

Schaefer, J ; Stejskal, Ε. O. in "topics in Carbon 13 NMR Spectroscopy"; Levy, G . , E d . ; Wiley-Interscience: New York, 1978; Chap. 4.

4.

Goldman, M. "Spin Temperature and Resonance in Solids"; Clarendon Press: London, 1970.

5. J.

Nuclear Magnetic Oxford University,

Haeberlin, U. in "Advances in Magnetic Resonance"; Waugh, S., Ed.; Acedemic: New York, 1976; V o l . I, pg. v.

6.

Block, F . Phys. Rev. 1958, III,

7.

Waugh, J. S.; Huber, L . M.; Haeberlen, Letters 1968, 20, 180.

8.

Hartmann, S. R.; Hahn, E . L .

9.

Pines, Α . ; Gibby, 1973, 59, 569.

RECEIVED November 18, 1983

841. U.

Phys. Rev. 1962,

M. G . ; Waugh,

J.

S.

J.

Phys.

Rev.

128, 2042. Chem. Phys.

An Introduction to NMR Spectroscopy of Solid Samples - ACS

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