Automated Software for Analyzing NMR Spectra of Polymers

Chapter 16

Automated Software for Analyzing NMR Spectra of Polymers 1,3

1

2

Molly W. Crowther , John H. Begemann , and George C. Levy 1

New Methods Research, Inc., 719 East Genesee Street, Syracuse, NY 13210 Department of Chemistry, Syracuse University, Syracuse, NY 13210

Downloaded by UNIV OF SYDNEY on December 24, 2017 | http://pubs.acs.org Publication Date: August 29, 1989 | doi: 10.1021/bk-1989-0404.ch016

2

A general purpose program has been developed for the analysis of NMR spectra of polymers. A database contains the peak assignments, stereosequence names for homopolymers or monomer sequence names for copolymers, and intensities are analyzed automatically in terms of Bernoullian or Markov statistical propagation models. A calculated spectrum is compared with the experimental spectrum until optimized probabilities, for addition of the next polymer unit, that are associated with the statistical model are produced. Spectra can be simulated given the model and probability(les). Databases are created for the polymer at hand through com puter-prom pted input. And, changing the spectrum or applied model is simple. S t e r e o s e q u e n c e in h o m o p o l y m e r s and m o n o m e r s e q u e n c e in c o p o l y m e r s w i l l i n f l u e n c e t h e m e c h a n i c a l and p h y s i c a l p r o p e r t i e s of t h e p o l y m e r . N u c l e a r M a g n e t i c R e s o n a n c e ( N M R ) s p e c t r o s c o p y i s p a r t i c u l a r l y u s e f u l in studying t a c t f c i t y and monomer sequence of p o l y m e r s s i n c e c h e m i c a l s h i f t is s e n s i t i v e t o both c o n f i g u r a t i o n a l and c h e m i c a l e n v i r o n m e n t s , respectively (1,2). Longer sequences are being resolved with larger f i e l d s and a d v a n c e d t w o - d i m e n s i o n a l t e c h n i q u e s are g r e a t l y f a c i l i t a t i n g peak assignments ( 3 - 9 ) . Once peaks are assigned t o sequences, however, the task still remains to analyze intensities for t h e s t a t i s t i c a l model and a d d i t i o n p r o b a b i l i t i e s t h a t a p p r o x i m a t e s t h e polymer propagation. A l t h o u g h longer s e q u e n c e s a f f o r d more i n f o r m a t i o n , a n a l y z i n g t h e s p e c t r a b e c o m e more c o m p l e x and t i m e consuming. T o a s s i s t in t h i s o f t e n n o n - f r i v i a l t a s k o f s e q u e n c e d i s t r i b u t i o n a n a l y s i s , c o m p u t e r methods have been a p p l i e d ( 1 0 - 1 3 ) . One a p p r o a c h i s t o s i m u l a t e s p e c t r a b a s e d on a s t a t i s t i c a l m o d e l a n d p r o b a b i l i t y p a r a m e t e r s until a good match with t h e e x p e r i m e n t a l data is a c h i e v e d . 3

Current address: Department of Chemistry, Drew University, Madison, NJ 07940 0097-6156/89/0404-0160$06.00/0 © 1989 American Chemical Society

Provder; Computer Applications in Applied Polymer Science II ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

16. CROWTHER ET AL.

161 Software for Analyzing NMR Spectra of Polymers


T h i s p a p e r r e p o r t s on a c o m p u t e r p r o g r a m t h a t g e n e r a t e s o p t i m i z e d p r o b a b i l i t i e s f o r e i t h e r B e r n o u l l i a n o r M a r k o v s t a t i s t i c a l m o d e l s by c o m p a r i n g c a l c u l a t e d peak i n t e n s i t i e s t o t h e e x p e r i m e n t a l ones. C o n v e r s e l y , s p e c t r a c a n be s i m u l a t e d f o r d i f f e r e n t m o d e l s g i v e n t h e model p r o b a b i l i t y ( i e s ) and s p e c f r a l l i n e w i d t h . The program applies t o s p e c t r a of homopolymers, for stereosequence analysis, or copolymers, for monomer sequence analysis. No program m o d i f i c a t i o n is r e q u i r e d in c h a n g i n g from p o l y m e r t o p o l y m e r , s p e c t r u m t o s p e c t r u m , o r in c h a n g i n g the statistical model. Each s p e c t r u m , rather, only requires userp r o m p t e d i n p u t f o r each p e a k ' s c h e m i c a l s h i f t and sequence a s s i g n m e n t name. The program is easy t o use, generally a p p l i c a b l e and com m e r c i a l l y a v a i l a b l e . T h e p r o g r a m w i l l be d e m o n s t r a t e d w i t h p o l y ( v i n y l a l c o h o l ) f o r t a c t i c i t y analysis and with c o p o l y m e r vinylidene chloride isobutylene f o r monomer sequence analysis. Peak assignments in C - 1 3 s p e c t r a were o b t a i n e d i n d e p e n d e n t l y by t w o - d i m e n s i o n a l N M R t e c h n i q u e s . In s o m e cases, a s s i g n m e n t s have been e x t e n d e d t o longer s e q u e n c e s and c o n f i r m e d via s i m u l a t i o n of t h e e x p e r i m e n t a l d a t a . E x p e r i m e n t a l and " b e s t - f i t " s i m u l a t e d s p e c f r a w i l l be c o m p a r e d . EXPERIMENTAL Computer Program. The P o l y m e r A n a l y s i s program is w r i t t e n in F O R T R A N 77 a n d c o n t a i n s o v e r 35 s u b r o u t i n e s . (See A c k n o w l e d g m e n t s ) The p r e s e n t v e r s i o n r u n s on V A X o r Sun c o m p u t e r s a n d i s p a r t o f N M R 1 ( R e l e a s e 4.0), w h i c h i s a l a r g e p r o g r a m f o r p r o c e s s i n g a l l t y p e s o f one-dimensional data. Figure 1 illustrates the basic program flow s t a r t i n g from t h e Peak A n a l y s i s module in N M R 1 . The user p i c k s t h e p e a k s in his/her s p e c t r u m and t h e n chooses t h e P o l y m e r A n a l y s i s o p t i o n . B e f o r e e n t e r i n g t h e m a i n menu o f t h e P o l y m e r A n a l y s i s p r o g r a m , a p o l y m e r c l a s s m u s t be s e l e c t e d f r o m t h e u s e r o r d e m o d a t a b a s e . If no c l a s s e x i s t s f o r t h e s p e c t r u m a t h a n d , o n e m a y be c r e a t e d . (Demo s p e c t r a and classes are a v a i l a b l e f o r t r i a l examination.) The user is prompted for all the information required t o define a class. First, general i n f o r m a t i o n such as t h e c l a s s t i t l e ( e . g . P o l y ( v i n y l a l c o h o l ) ) , system (e.g. methine region), nucleus observed (e.g. C - 1 3 ) , s p e c t r o m e t e r , frequency, t e m p e r a t u r e and linewidth is e n t e r e d . N e x t , i n d i v i d u a l peak i n f o r m a t i o n such as t h e s e q u e n c e a s s i g n m e n t , l o c a t i o n and c h e m i c a l s h i f t window is input. The sequence assignment n a m e s may c o n s i s t o f a n y s e r i e s o f t w o c h a r a c t e r s . F o r e x a m p l e , m a n d r may r e p r e s e n t meso a n d r a c e m i c a d d i t i o n s i n a h o m o p o l y m e r t a c t i c i t y s e q u e n c e ( e . g . a m m r r p e n t a d ) a n d , A a n d B may r e p r e s e n t t w o p o l y m e r units in a c o p o l y m e r m o n o m e r s e q u e n c e ( e . g . a A B A A B p e n t a d ) . The a c t u a l p e a k a s s i g n m e n t s e n t e r e d by t h e u s e r may r e p r e s e n t , i n f a c t , t h e toughest part of the analysis. While a s s i g n m e n t s a r e o f t e n deduced by f i t f i n g p e a k i n t e n s i t i e s t o a p r o p a g a t i o n m o d e l , p e a k a s s i g n m e n t s in t h i s s t u d y w e r e m a d e by i n d e p e n d e n t m e a n s a n d , i n r e v e r s e a p p l i c a t i o n , d e d u c i n g t h e p r o p a g a t i o n m e c h a n i s m by t h e p e a k s ' i n t e n s i t i e s . T h e m a i n application of t h e program here, then, is t o c o n f i r m assignments and d e t e r m i n e t h e model of p r o p a g a t i o n and r e a c t i o n p r o b a b i l i t i e s t h a t best f i t s t h e e x p e r i m e n t a l d a t a . T h e p r o g r a m c a n j u s t a s w e l l be u s e d i n t h e r e v e r s e mode. F o r instance, with t h e spectrum o f vinylidene



I—|

CHANGE POLYMER C L A S S AND REASSIGN SPECTRUM

POLYMER C L A S S ? (Select from User a Demo Directory)

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wrorrAnoNSs—n2__jC L A S S TITLE. P E A K

PEAK T A B L E OR DAT) ASSMMVIFNTS

3 "

>a7sl^6CALIBRATE. DELETE/INSTALL P E A K S . . . .

ENTER P R O B A B U T I E S

CALCULATE N A . S . L .

'I

NT1AL GUESSES ENTER P R O B A B U T I E S . , L W . RMS NOISE

Chemical SNA Range:

ENTER P E A K INFORMATION For peak n . Peak Assignment

I CALCULATE PROBABUTY S M U L A T E SPECTRUM

I—eVENTER

Spectrometer end Temperaturrj eta.

System:

TKtC

/ E N T E R C L A S S INFORMATION-

f w

C H O O S E A STATISTICAL M O D E L / fownNUEXNCL / Bemoufflan / ' — First-Order Markov Second-Order Markov

F i g u r e 1. F l o w c h a r t o f t h e P o l y m e r A n a l y s i s p r o g r a m . The program is e n t e r e d f r o m a l a r g e r p r o g r a m , N M R 1 . A d a t a b a s e m u s t be c h o s e n or c r e a t e d f o r t h e s p e c t r u m a t hand and a s t a t i s t i c a l model c h o s e n . O p t i o n s in t h e m a i n menu i n c l u d e c a l c u l a t i o n o f p r o b a b i l i t i e s a s s o c i a t e d with t h e model, s i m u l a t i o n of s p e c t r a , and m o d i f i c a t i o n of t h e peak t a b l e o r d a t a b a s e .

RETURN T O

S T O P N

L O A D POLYMER D A T A B A S E f -

/ S T A R T * N ^POLYMER A N A L Y S E /

1

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1

16. CROWTHERETAL.

Software for Analyzing NMR Spectra ofPolymers


chloride Isobutylene copolymer, partial (triad) assignments were d e t e r m i n e d by i n d e p e n d e n t m e a n s a n d t h e n p e n t a d a s s i g n m e n t s d e d u c e d by f i t to a second-order Markov model. In e i t h e r c a s e , a s s i g n m e n t s m u s t be e n t e r e d w h e t h e r t h e y h a v e b e e n d e t e r m i n e d i n d e p e n d e n t l y , a r e b o r r o w e d f r o m l i t e r a t u r e , o r a r e e n t e r e d f o r e v a l u a t i o n by f i t t i n g t o a propagation model. The peak l o c a t i o n s (in Hz or ppm) are also e n t e r e d a t t h i s p o i n t as w e l l as c h e m i c a l s h i f t w i n d o w s . An option, however, is a v a i l a b l e f o r c o m p u t e r - c a l c u l a t e d w i n d o w s . F i n a l l y , t h e u s e r c h o o s e s a s t a t i s t i c a l m o d e l t o be a p p l i e d in later s i m u l a t i o n s or p r o b a b i l i t y c a l c u l a t i o n s . The c o e f f i c i e n t s ( a - i ) t o t h e p r o b a b i l i t i e s ( P 1 - P 4 ) in E q u a t i o n 1, w h i c h d e f i n e s p e a k i n t e g r a l s , a r e a u t o m a t i c a l l y c a l c u l a t e d d e p e n d i n g on t h e c h o s e n m o d e l . Integral

= a*[P1 ( 1 - P 1 ) ] [ P 2 ^ 1 - P 2 ) ] [ P 3 (1 - P 3 ) ] [ P 4 ( 1 - P 4 ) ] b

C

e

f

g

h

1

(1)

O n l y t h e " a " c o e f f i c i e n t has t h e s a m e m e a n i n g r e g a r d l e s s o f t h e m o d e l . F o r a s y m m e t r i c s e q u e n c e n a m e , e . g . m r r m , t h e " a " c o e f f i c i e n t w o u l d be e q u a l t o 1, a n d 2 f o r any a s y m m e t r i c n a m e . For a Bernoullian model, only one independent probability is d e f i n e d . F o r i n s t a n c e , P1=Pm represents the probability of a meso-addition to the c h a i n . The p r o b a b i l i t y f o r a r a c e m i c a d d i t i o n (Pr) is 1 — P 1 . F o r t h e pentad peak a s s i g n m e n t m r r m , b=2 a n d c=2 i n E q u a t i o n 1. In a f i r s t - o r d e r M a r k o v m o d e l , P1 may be d e f i n e d as P m / r o r t h e p r o b a b i l i t y o f an r a c e m i c addition t o a c h a i n end with t h e last addition being meso. P2 w o u l d be d e f i n e d as Pr/m a n d t h e d e p e n d e n t p r o b a b i l i t i e s , 1-P1 a n d 1 - P 2 a s Pm/m and Pr/r, r e s p e c t i v e l y . C o e f f i c i e n t s f o r t h e m r r m p e n t a d w o u l d be b=1, c=0, d=2, and e=1. F o r a s e c o n d - o r d e r M a r k o v model f o u r i n d e p e n d e n t p r o b a b i l i t i e s may be d e f i n e d , P 1 = P m m / m , P 2 = P m r / m , P 3 = P r r n / m , a n d P4=Prr/m. The corresponding dependent p r o b a b i l i t i e s are 1-P1=Pmm/r, 1-P2=Pmr/r, 1-P3=Prm/r, and 1-P4=Prr/r. The c o e f f i c i e n t s f o r t h e mrrm p e n t a d i n a s e c o n d - o r d e r M a r k o v m o d e l a r e b=0, c = 1 , d=0, e=1, f=0, g=0, h=2, i=0. While d e t e r m i n a t i o n of t h e c o e f f i c i e n t s is not d i f f i c u l t , one can see t h a t manual e n t r y c o u l d g e t o u t of hand. For a spectrum w i t h t e n p e a k s , 99 c o e f f i c i e n t s m u s t be d e f i n e d f o r u s e o f a s e c o n d order Markov model. H e r e , a l l t h e c o e f f i c i e n t s a r e c a l c u l a t e d by t h e p r o g r a m b a s e d upon t h e s e q u e n c e n a m e a n d m o d e l a s s i g n e d . T o c h a n g e t h e s t a t i s t i c a l p r o p a g a t i o n m o d e l , an o p t i o n i s a v a i l a b l e t o c r e a t e an i d e n t i c a l copy of t h e database save t h e model name and c o e f f i c i e n t s w h i c h a r e r e c a l c u l a t e d f o r t h e new m o d e l . T h e d a t a b a s e may be l i s t e d or p r i n t e d . S e v e r a l o p t i o n s a r e now a v a i l a b l e t o t h e u s e r i n t h e m a i n menu o f the program. P r o b a b i l i t i e s c a n be c a l c u l a t e d u s i n g an i t e r a t i v e method, B r o w n ' s m o d i f i e d version of t h e L e v e n b e r g - M a r q u a r d t a l g o r i t h m ( 1 4 - 1 6 ) , by s u b s t i t u t i n g v a l u e s f o r P 1 - P 4 i n E q u a t i o n 1 t o c a l c u l a t e t h e p e a k i n t e g r a l w h i c h a r e t h e n used in E q u a t i o n 2 t o s i m u l a t e s p e c t r a until a good m a t c h b e t w e e n e x p e r i m e n t a l and s i m u l a t e d d a t a i s a c h i e v e d .

N M Data(i) = Z T. i=1 j=1

Intensity(j) (2) Linewidth -4(Peakloc(j)-i) 2

2


163

164

COMPUTER APPLICATIONS IN APPLIED POLYMER Where:

SCIENCE II

D a t a ( i ) i s t h e i t h p o i n t in t h e d a t a a r r a y N is t h e number of data points M is t h e number of peaks P e a k l o c ( j ) is t h e l o c a t i o n o f t h e j " ^ p e a k Intensity(j) = I ntegral(j)/(pf*linew idth)


1

O p t i m u m v a l u e s f o r t h e p r o b a b i l i t i e s may n o t be o b t a i n e d i n t h e c a s e t h a t e x p e r i m e n t a l line widths in t h e s p e c t r u m a r e v e r y d i f f e r e n t s i n c e only a s i n g l e l i n e w i d t h is used f o r t h e s i m u l a t e d s p e c t r a . The c a l c u l a t e d p r o b a b i l i t i e s may be s t o r e d in t h e d a t a b a s e a n d h a r d c o p y r e p o r t s may be p r i n t e d . S i m u l a t e d s p e c t r a c a n be c r e a t e d by a n o t h e r o p t i o n in t h e m a i n menu o f t h e p r o g r a m . P r o b a b i l i t i e s ( P 1 - P 4 ) are p r o m p t e d from t h e user, d e p e n d i n g on t h e m o d e l , i f v a l u e s o t h e r t h a n t h o s e s t o r e d w i t h t h e d a t a base are desired and a s i n g l e l i n e w i d t h is e n t e r e d . Equation 1 and 2 a r e t h e n u s e d t o s i m u l a t e a s p e c t r u m w h i c h c a n be s a v e d , c o m p a r e d t o the experimental spectrum (including overlaying spectra, spectral subtractions, additions, etc.) or p l o t t e d . Calculation of the N.A.S.L. (Number Average Sequence Length) can be p e r f o r m e d , a c c o r d i n g t o t h e d e f i n i t i o n g i v e n by R a n d a l l , g i v e n t h e model p r o b a b i l i t i e s . G e n e r a t i o n o f t h e c o e f f i c i e n t s u s e d in t h e e q u a t i o n r e q u i r e d f o r t h i s o p t i o n , h o w e v e r , has n o t b e e n a u t o m a t e d . H e n c e , i t i s p r e s e n t l y c l u m s y t o use a n d w i l l n o t be p r e s e n t e d h e r e . L a s t , a v a r i e t y of options are a v a i l a b l e t o modify t h e peak t a b l e or polymer database. The f o r m e r include deleting and inserting peaks, c a l i b r a t i o n , and axis u n i t c o n v e r s i o n . Polymer Samples. The p o l y ( v i n y l a l c o h o l ) ( P V A ) is a c o m m e r c i a l material from S c i e n t i f i c Polymer Products. T h e s a m p l e was d i s s o l v e d a t ]Q% w/v in O M S O - c ^ . The s a m p l e of vinylidene c h l o r i d e isobutylene c o p o l y m e r was a k i n d g i f t o f D r s . R. E. C a i s a n d F . A . B o v e y a t A T & T B e l l L a b o r a t o r i e s in Murray H i l l , N J . T h e s a m p l e w a s d i s s o l v e d a t 20% w/v

in

C D C I 3 .

NMR Spectroscopy. A l l proton-decoupled c a r b o n - 1 3 spectra were obtained on a G e n e r a l E l e c t r i c G N - 5 0 0 s p e c t r o m e t e r . The vinylidene c h l o r i d e i s o b u t y l e n e s a m p l e was r u n a t 24 d e g r e e s c e n t i g r a d e . A 45 d e g r e e (3.4us) p u l s e was u s e d w i t h a i n t e r - p u l s e d e l a y o f 1.5s ( p r e p u l s e d e l a y + acquisition t i m e ) . O v e r 2 4 0 0 s c a n s w e r e a c q u i r e d w i t h 16k c o m p l e x d a t a p o i n t s a n d a s w e e p w i d t h o f +/- 5 0 0 0 H z . Measured s p i n - l a t t i c e r e l a x a t i o n t i m e s ( T 1 ) w e r e a p p r o x i m a t e l y 4s f o r t h e n o n - p r o t o n a t e d c a r b o n s , 3s f o r t h e m e t h y l g r o u p s , a n d 0 . 3 s f o r t h e m e t h y l e n e c a r b o n s . T h e P V A s a m p l e w a s r u n a t 55 d e g r e e s c e n t i g r a d e . A 90 d e g r e e ( 6 . 8 u s ) p u l s e was u s e d w i t h a i n t e r - p u l s e d e l a y o f 2 . 1 s . E x a c t l y 800 s c a n s w e r e a c q u i r e d w i t h 16k c o m p l e x d a t a p o i n t s a n d a s w e e p w i d t h o f +/2000 H z . RESULTS

AND

DISCUSSION

E x a m p l e 1, P o l y ( v i n y l a l c o h o l ) . T h e f i r s t e x a m p l e i s g i v e n f o r t h e c a r b o n - 1 3 s p e c t r u m of P o l y ( v i n y l a l c o h o l ) . F i g u r e 2 shows a plot of the carbon s p e c t r u m and a peak listing with assignments from t h e user s database. The assignments c o n s t i t u t e a d i f f i c u l t p a r t of the analysis


16. CROWTHER ET AL.

Software for Analyzing NMR Spectra of Polymers

Polyvinyl alcohol)

OH 4CH2-CH-^


, 14

70.00

65.00

60.00

55.00

50.00

45.00

PPM

**************************************** NMRl P o l y m e r A n a l y s i s R e p o r t ****************************************

#

1 2 3

4 5 6 7 8 9 10 11 12 13 14 15

PPM Intens Assignment 68. 29 16. 83 rrmmrr 68. 23 23. 02 rrmmrm 68. 16 20. 67 mrmmrm 68. 08 25 04 rmmmrr 68. 05 25 27 mmmmrr 24 90 rmmmrm 68. 01 67. 99 20 36 mmmmrm 12 68 rmmmmr 67. 86 13 22 rmmmmm 67. 83 6 66 mmmmmm 67 80 66 44 51 82 ( r m r r ) 66 37 51 .81 ( r m r r ) 66 27 56 .53 (mmrr) (mmrr)+(rmrm) 63 .79 66 22 37 .50 (rmrm) 66 16

16 17 18 19 20 21 22 23 24 25

66 06 64 42 64 26 64 10 46 01 45 75 45 71 45 35 45 27 44 .80

29 54 38 67 50 70 19 48 39 67 71 24 100 00 56 10 79 55 31 .28

mmrm r r rr mr r r mrrm rr r rmr mr r mrm mmr mmm

F i g u r e 2 . T h e C - 1 3 ( 1 2 5 . 7 6 H z ) s p e c t r u m o f a p p r o x i m a t e l y 1 0 ? w/v p o l y ( v i n y l a l c o h o l ) i n D M S 0 - d 6 a t 55°C a n d a p e a k l i s t i n g f r o m t h e Polymer Analysis program.


165


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APPLICATIONS IN APPLIED POLYMER SCIENCE II

and w e r e made ( C r o w t h e r , M . W., 1 9 8 7 , S y r a c u s e U n i v e r s i t y , u n p u b l i s h e d d a t a ) by u s i n g t h e t w o - d i m e n s i o n a l s p i n - l o c k R E L A Y e x p e r i m e n t ( 3 , 1 7 ) , t h e n c o m p a r e d w i t h r e p o r t s in t h e l i t e r a t u r e , and f i n a l l y e v a l u a t e d with the P o l y m e r A n a l y s i s p r o g r a m . Peaks 11-16 were d i f f i c u l t a s s i g n m e n t s s i n c e t h e y r e s u l t f r o m t h e o v e r l a p of f o u r p e n t a d s and sixteen heptads. A s s i g n m e n t s in t h i s r e g i o n w i t h p a r e n t h e s e s , e . g . ( r m r r ) , i n d i c a t e a p e n t a d w i t h h e p t a d s p l i t t i n g . O v e n a l l (18) g a v e t h e s e p e a k s a c o l l e c t i v e rnr t r i a d a s s i g n m e n t . T o n e l l i (19) c a l c u l a t e d c h e m i c a l s h i f t s using the Y - g a u c h e e f f e c t method. His assignments f o r t h e m m r r a n d r m r m p e n t a d s a r e r e v e r s e d b u t w i t h o n l y a 0 . 0 2 pp m difference between t h e m . As with Ovenall, the observed dispersion f o r t h e s e p e a k s a n d f o r t h e m e t h i n e r e g i o n in g e n e r a l i s m u c h g r e a t e r . The o t h e r h e p t a d a n d p e n t a d a s s i g n m e n t s in t h e m e t h i n e r e g i o n a n d t e t r a d a s s i g n m e n t s in t h e m e t h y l e n e r e g i o n a r e in a g r e e m e n t w i t h t h o s e r e p o r t e d by O v e n a l l . A p o r t i o n o f t h e P V A d a t a b a s e i s s h o w n in F i g u r e 3 . B o x e d e n f r i e s indicate required input from t h e user. In t h i s c a s e , a B e r n o u l l i a n model is t h e most l i k e l y c h o i c e . T h e p r o g r a m c o m p l e t e s t h e d a t a b a s e by c a l c u l a t i n g a c h e m i c a l s h i f t window and t h e c o e f f i c i e n t s from E q u a t i o n 1 for each peak. Once c r e a t i o n of t h e P V A database is c o m p l e t e , o p t i m i z e d p r o b a b i l i t i e s may be c a l c u l a t e d f o r t h e e x p e r i m e n t a l s p e c t r u m a t h a n d . S i n c e t h e i t e r a t i v e p r o c e d u r e is r e s t r i c t e d t o a 2048 d a t a p o i n t r e g i o n , z o o m c u r s o r s a r e d i s p l a y e d a n d s e t by t h e u s e r u n t i l t h i s condition is s a t i s f i e d . In t h i s c a s e , t h e m e t h y l e n e r e g i o n was s e l e c t e d and an i n i t i a l g u e s s f o r t h e B e r n o u l l i a n p r o b a b i l i t y (Pr=0.5) and l i n e w i d t h ( 1 3 . 0 H z ) w e r e g i v e n . Optimized values for the p r o b a b i l i t y and l i n e w i d t h w e r e P r = 0 . 5 2 a n d 1 2 . 8 H z , r e s p e c t i v e l y . F i g u r e 4 shows z o o m e d r e g i o n s of t h e e x p e r i m e n t a l and s i m u l a t e d spectra. The m e t h i n e r e g i o n was s i m u l a t e d s e p a r a t e l y using t h e s a m e o p t i m i z e d p r o b a b i l i t y b u t w i t h a l i n e w i d t h o f 8.0 H z . A t this point t h e u s e r may wish t o use t h e s p e c t r a l m a n i p u l a t i o n o p t i o n s ( o v e r l a y , s u b t r a c t i o n , e t c . ) , r e p e a t t h e c a l c u l a t i o n , o r do f u r t h e r s i m u l a t i o n s . E x a m p l e 2. V i n y l i d e n e C h l o r i d e I s o b u t y l e n e C o p o l y m e r . The next e x a m p l e is f o r t h e c a r b o n - 1 3 s p e c t r u m o f c o p o l y m e r v i n y l i d e n e c h l o r i d e isobutylene. F i g u r e 5 shows t h e f u l l s p e c t r u m and t h e peak a s s i g n m e n t l i s t i n g f o r t h e n o n - p r o t o n a t e d v i n y l i d e n e c h l o r i d e c a r b o n in t h e 8 4 - 9 2 ppm r a n g e . T r i a d a s s i g n m e n t s w e r e made ( C r o w t h e r , M . W., 1 9 8 7 , S y r a c u s e U n i v e r s i t y , unpublished data) using t h e t w o - d i m e n s i o n a l C 0 L 0 C (20) e x p e r i m e n t . There are ten v-centered pentads representing different environments for the vinylidene chloride carbon. The i r e p r e s e n t s t h e n o n - p r o t o n a t e d c a r b o n in t h e i s o b u t y l e n e p o l y m e r u n i t . A p o r t i o n o f t h e d a t a b a s e f o r t h i s p o l y m e r i s s h o w n in F i g u r e 6. Literature reports t h a t this polymer follows second-order Markov s t a t i s t i c s (_21_). A n d , in f a c t , p r o b a b i l i t i e s t h a t p r o d u c e d s i m u l a t e d s p e c t r a c o m p a r a b l e t o t h e e x p e r i m e n t a l s p e c t r u m c o u l d n o t be o b t a i n e d with B e r n o u l l i a n or f i r s t - o r d e r Markov models. Figure 7 shows the e x p e r i m e n t a l and s i m u l a t e d s p e c f r a f o r t h e s e t e n p e n t a d s u s i n g t h e s e c o n d - o r d e r M a r k o v p r o b a b i l i t i e s Pff/i=0.60, P i v / i = 0 . 3 5 , P v i / i = 0 . 4 0 , and Pvv/i=0.65 and a l i n e w i d t h o f 14.8 H z .


Software for Analyzing NMR Spectra of Polymers

CROWTHER ET AL.

**************************************** NMRl - POLYMER ANALYSIS DATA BASE

**************************************** Class

3

Poly(vinyl


System: Nucleus: Spectrometer: Frequency: Tempe r a t u r e : Linewidth:

alcohol)

methine/methylene C-13 GN-500 125.76 55 C 12.681234

Model: B e r n o u l l i a n P I : 0.520000 Pr P2:

0.000000

P3:

0.000000

P4:

0.000000

Comment: Peak a s s i g n m e n t s d e t e r m i n e d w i t h 2D S p i n - L o c k R e l a y experiment.

Sequence L e n g t h Names: Nr Nm

Definition

f o r peak number

Assignment: L o c a t i o n (PPM): Window (PPM):

A: B: F:

1.000000 4 C: 2 0 G: 0

Average

1: 3:

1: 3:

0 0

D: H:

2: 4:

E: I:

0 0

coefficients

0.000000 0.000000

sequence l e n g t h c o e f f i c i e n t s (denominator)

0.000000 0.000000

Definition

rrmmrr 68.292000 0.018599

sequence l e n g t h (numerator)

0.000000 0.000000

Average

1

2: 4:

f o r peak number

0.000000 0.000000 2

25 F i g u r e 3. A p o r t i o n o f t h e d a t a b a s e f o r p o l y ( v i n y l a l c o h o l ) . Boxed entries indicate required input from the user. This includes g e n e r a l " h e a d e r " i n f o r m a t i o n and p e a k i n f o r m a t i o n . The d e f i n i t i o n f o r t h e f i r s t peak is s h o w n .


168

COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE II


A

46. 5

46. O

45. 5

45. O

44. 5

44. O

PPM

63. O

68. O

67. O

66. O

65. D

64. O

PPM Figure 4. ( A ) The e x p e r i m e n t a l (top) and s i m u l a t e d ( b o t t o m ) s p e c t r a f o r t h e methylene r e g i o n of p o l y ( v i n y l a l c o h o l ) . The s i m u l a t e d s p e c t r u m i s b a s e d on a B e r n o u l l i a n p r o p a g a t i o n m o d e l w i t h P r = 0 . 5 2 a n d a l i n e w i d t h o f 12.8 H z . (B) T h e e x p e r i m e n t a l ( t o p ) a n d s i m u l a t e d s p e c t r a f o r the methine region of p o l y ( v i n y l a l c o h o l ) . T h e s a m e c o n d i t i o n s as f o r ( A ) w e r e u s e d i n t h e s i m u l a t i o n e x c e p t t h a t a l i n e w i d t h of 8 H z was used.


16. CROWTHER ET AL.


Vinyliclene chloride-isobutylene copolymer CI

CH

3

4CH -C^ + 4CH -CH^


2

2

CI

CH

(v)

(0

CI-C-CI 11111111

CDCI

J1 1 1 1 1 1 1 1 1

90.00

AxJ

Xi

- CC hHU - -

3

CH3-C-CH3

2

I111111111

80.00

3

J1 1 1 1 1 1 1 1 1

70.00

CH

3

J 1 1 1 1 1 1 1 1 1 J 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 11 11 11 11 1 1 J

60.00

50.00

40.00

30.00

20.00

PPM

****************************************

NMRl Polymer A n a l y s i s Report ****************************************

#

1 2 3 4 5 6 7 8 9 10

PPM Intens Assigm 91. 76 11 05 i i v i i 91. 60 33 14 v i v i i 24 85 v i v i v 91. 43 88. 51 66 67 i v v i i 88. 39 100 00 i v v i v 88. 16 53 85 v v v i v 88. 02 35 90 v v v i i 84. 49 29 17 i v v v i 84 42 31 41 v v v v i 84 32 8 46 vvvvv

F i g u r e 5 . T h e C - 1 3 ( 1 2 5 . 7 6 H z ) s p e c t r u m o f a p p r o x i m a t e l y 20% w/v c o p o l y m e r v i n y l i d e n e c h l o r i d e i s o b u t y l e n e i n C D C I ^ a t 24°C a n d a peak listing f r o m t h e P o l y m e r A n a l y s i s p r o g r a m .


169

170

COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE II **************************************** NMR1 - POLYMER ANALYSIS DATA BASE ****************************************


Class

3

VinylideneChloridelsobutylene

System: Nucleus: Spectrometer: Frequency: Temperature: Linewidth:

C l - C - C l Region C-13 GN-500 125.76 24 C 14.687073

Model: Second-Order PI: 0.600000 P i i / i P2: 0.350000 P i v / i P3: 0.400000 P v i / i P4: 0.650000 P v v / i

Markov

Comment: T r i a d assignments were deduced u s i n g the 2 D COLOC e x p e r i m e n t . Sequence Length Names: Nv Ni Definition

f o r peak number

Assignment: L o c a t i o n (PPM): Window (PPM): A: B: F:

1.000000 0 C: 1 2 G: 0

Average

1

iivii 91.760002 0.144003

D: H:

1 1

sequence l e n g t h (numerator)

E: I:

0 0

coefficients

1:

0 . 0 0 0 0 0 0

2:

0 . 0 0 0 0 0 0

3:

0 . 0 0 0 0 0 0

4:

0 . 0 0 0 0 0 0

Average

sequence l e n g t h c o e f f i c i e n t s (denominator)

1:

0 . 0 0 0 0 0 0

2:

0 . 0 0 0 0 0 0

3:

0 . 0 0 0 0 0 0

4:

0 . 0 0 0 0 0 0

Definition

f o r peak number

2 10

F i g u r e 6. A portion of the database f o r vinylidene chloride isobutylene copolymer. Boxed entries are required input from user. T h e p e a k d e f i n i t i o n f o r t h e f i r s t p e a k is s h o w n .


the

Provder; Computer Applications in Applied Polymer Science II ACS Symposium Series; American Chemical Society: Washington, DC, 1989. •

PPM

88.

•

87.

•

8 6 .

•

8 5 .

F i g u r e 7. The e x p e r i m e n t a l (top) and s i m u l a t e d ( b o t t o m ) s p e c t r a f o r t h e n o n - p r o t o n a t e d c a r b o n in t h e v i n y l i d e n e c h l o r i d e p o l y m e r unit. A s e c o n d - o r d e r M a r k o v p r o p a g a t i o n m o d e l w i t h Pff/f=0.60, P i v / i = 0 . 3 5 , P v i / i = 0 . 4 0 , P v v / i = 0 . 6 5 a n d a l i n e w i d t h o f 14.8 H z w a s used f o r t h e s i m u l a t e d s p e c t r u m .

9 0 .


•

i

i

172

COMPUTER

APPLICATIONS IN APPLIED POLYMER SCIENCE II


CONCLUSION The P o l y m e r A n a l y s i s program p r o v i d e s t o o l s f o r a n a l y z i n g s p e c t r a of h o m o - or c o p o l y m e r s . These t o o l s include a peak a s s i g n m e n t database, c a l c u l a t i o n of o p t i m i z e d r e a c t i o n p r o b a b i l i t i e s f o r a given propagation model, s i m u l a t i o n of s p e c t r a given t h e p r o b a b i l i t i e s and model, s p e c t r a l m a n i p u l a t i o n , p l o t t i n g , and p r i n t i n g o p t i o n s . Most i m p o r t a n t l y , t h e p r o g r a m i s e a s y t o use a n d g e n e r a l l y a p p l i c a b l e . While o t h e r p r o g r a m s r e q u i r e m o d i f i c a t i o n of t h e a c t u a l code in c h a n g i n g t h e p o l y m e r , s p e c t r a , o r m o d e l , o n l y c h a n g e s in t h e u s e r database is required here. C h a n g e s in t h e p r o g r a m s i n c e a b r i e f r e p o r t (22) in 1985 i n c l u d e i m p r o v e m e n t o f t h e menu s t r u c t u r e , a d d e d u t i l i t i e s f o r s p e c t r a l manipulations, i n s t i t u t i o n of demo s p e c t r a and database, inclusion of M a r k o v s t a t i s t i c s , and a u t o m a t i o n f o r g e n e r a t i o n of t h e c o e f f i c i e n t s in E q u a t i o n 1. C u r r e n t l i m i t a t i o n s a r e t h a t o n l y t h r e e m o d e l s ( B e r n o u l l i a n , a n d f i r s t - and s e c o n d - o r d e r M a r k o v ) c a n be a p p l i e d , a n d m a n u a l i n p u t i s r e q u i r e d f o r t h e N . A . S. L.. Acknowledgments D r . C h a r l e s D u m o u l i n is a c k n o w l e d g e d f o r w r i t i n g t h e o r i g i n a l v e r s i o n of t h e P o l y m e r A n a l y s i s p r o g r a m . Ann m a r i e L a r e a u made s o m e r e v i s i o n s and d o c u m e n t e d t h e c o d e .

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Bovey, F. A., High Resolution NMR of Macromolecules; Academic Press: New York, 1972. Randall, J. C., Polymer Sequence Determination, Carbon-13 NMR Method; Academic Press: New York, 1977. Crowther, M. W.; Szeverenyi, N. M.; Levy, G. C. Macromolecules 1986, 19, 1333. Mirau, P. A.; Bovey, F. A. Macromolecules 1986, 19, 210. Cheng, H. N.; Lee, G. H. Polym. Bull(Berlin) 1985, 13, 549. Bruch, M. D.; Bovey, F. A. Macromolecules 1984, 17, 978. Gippert, G. P.; Brown, L. R. Polymer Bull(Berlin) 1984, 11, 585. Macura, S.; Brown, L. R. J. Magn. Reson. 1983, 53, 529. Gerig, J. T. Macromolecules 1983, 16, 1797. Cheng, H. N. J. Appl. Polym. Sci. 1988, 35, 1639. Cheng, H. N. J. Chem. Inf. Comp. Sci. 1987, 27, 8. Cheng, H. N. Polymer Bull. 1986, 16, 445. Cheng, H. N.; Bennett, M. A. Anal. Chem. 1984, 56, 2320. Levenberg, K. Quart. J. Appl. Math. 1944, 2, 164. Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431. Brown, K. M.; Dennis, J. E. Numeriche Mathematic 1972, 18, 289. Bax, A.; Davis, D.; Sarkar, S. K. J. Magn. Reson. 1985, 63, 230. Ovenall, D. W. Macromolecules 1984, 17, 1458. Tonelli, A. E. Macromolecules 1985, 18, 1086.


16. CROWTHERETAL. 20. 21. 22.


Kessler, H.; Griesinger, C.; Zarbock, J.; Loosli, H. R. J. Magn. Reson.1984, 57, 331. Kinsinger, J. B.; Fischer, T; Wilson III, C. W. J. Polym. Sci. Part B 1966, 4, 379 and 1967, 5, 285. Levy, G. C.; Begemann, J. B. J. Chem. Inf. Comput. Sci. 1985, 25, 350.


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Automated Software for Analyzing NMR Spectra of Polymers

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