The Structures of Cellulose - American Chemical Society

Chapter 2

X-ray Diffraction Studies of Ramie Cellulose I 1

2

2

A. D. French , W. A. Roughead , and D. P. Miller 1

Southern Regional Research Center, U.S. Department of Agriculture, P.O. Box 19687, New Orleans, LA 70179 Department of Physics and Astronomy, Clemson University, Clemson, SC 29631

Downloaded by CORNELL UNIV on September 29, 2016 | http://pubs.acs.org Publication Date: June 22, 1987 | doi: 10.1021/bk-1987-0340.ch002

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Current fiber x-ray diffraction studies, including new calculations by the authors, are reviewed. Because of different conventions used to describe the crystal structure of native cellulose, the preferred parallel structure described as "up" by Gardner and Blackwell for Valonia corresponds to the "down" structure that was strongly rejected for ramie by Woodcock and Sarko. A variety of assumptions were tested, as were results from the different computer programs used for fiber diffraction. These results were compared with those from a computer program written for single crystal work, and the comparisons were satisfactory. A major reason for the differences in reported structures for celluloses comes from differences in the diffraction intensity data sets taken at the various institutions. C e l l u l o s e f i b e r s have been been s t u d i e d w i t h x - r a y d i f f r a c t i o n s i n c e 1913 ( 1 ) . Over t h e p a s t dozen y e a r s , a number o f f u l l f l e d g e d s t u d i e s o f n a t i v e c e l l u l o s e have been p u b l i s h e d , each without apparent f a u l t , but with c o n t r a d i c t o r y i n d i c a t i o n s o f c h a i n p a c k i n g mode. A t t h e same time, s p e c t r o s c o p i s t s have c h a l l e n g e d some o f t h e fundamental assumptions and a p p a r e n t l y c l e a r r e s u l t s o f the d i f f r a c t i o n s t u d i e s . T h i s r e p o r t i s p a r t o f a n e f f o r t by s e v e r a l f i b e r c r y s t a l l o g r a p h e r s t o b e t t e r u n d e r s t a n d t h e v a r i a b l e outcome from t h e s e s t u d i e s and s p e c i f i c a l l y t o a s c e r t a i n t h a t r e s u l t s a r e n o t dependent on t h e p a r t i c u l a r computer program u s e d . R. M i l l a n e a t Purdue and A. Sarko a t S y r a c u s e a r e a l s o a n a l y z i n g a d a t a s e t o b t a i n e d by Roughead and M i l l e r from d i f f r a c t i o n photographs t a k e n by F r e n c h ( t h e RMF d a t a ) (2) i n o r d e r t o l e a r n more about t h e methodology and about c e l l u l o s e i t s e l f . I n t h i s r e p o r t some r e s u l t s w i l l be d i s c u s s e d based on t h a t d a t a as w e l l as some c o m p a r a t i v e r e s u l t s based on o t h e r d a t a s e t s . S e l e c t i o n o f Ramie C e l l u l o s e f o r Study. Ramie c e l l u l o s e was s e l e c t e d f o r s t u d y because i t i s h i g h l y o r i e n t e d and f a i r l y

0097-6156/87/0340-0015$06.50/0 © 1987 American Chemical Society

Atalla; The Structures of Cellulose ACS Symposium Series; American Chemical Society: Washington, DC, 1987.


16

THE STRUCTURES OF CELLULOSE

crystalline. A l t h o u g h ramie i s not as c o m m e r c i a l l y i m p o r t a n t as c o t t o n , c o t t o n f i b e r s have a c o m p l i c a t e d e x t r a l e v e l o f s t r u c t u r e t h a t d e c r e a s e s the amount o f i n f o r m a t i o n a v a i l a b l e from a d i f f r a c t i o n study. I f t h i s f i b e r s t r u c t u r e i n cotton i s destroyed w i t h a Waring b l e n d e r (making x - r a y f i b e r d i f f r a c t i o n i m p o s s i b l e ) , an e l e c t r o n d i f f r a c t i o n p a t t e r n n e a r l y i d e n t i c a l t o t h a t from ramie may be o b t a i n e d ( 3 ) . I n c o n t r a s t , e l e c t r o n d i f f r a c t i o n p a t t e r n s (and x - r a y p a t t e r n s , t o o ) from a l g a l and b a c t e r i a l c e l l u l o s e s d i f f e r from ramie and c o t t o n , even though they a l l have the main f e a t u r e s i n common. I n f r a r e d s p e c t r a from ramie and c o t t o n a r e a l s o s i m i l a r t o each o t h e r and d i f f e r e n t from t h o s e o f the a l g a l and b a c t e r i a l c e l l u l o s e s ( 4 ^ . Thus, the s t r u c t u r e o f ramie s h o u l d a c c u r a t e l y resemble c o t t o n a t the m o l e c u l a r and c r y s t a l l i t e l e v e l s , w h i l e t h e r e i s some doubt as t o whether such c l o s e s i m i l a r i t y a p p l i e s between the s t r u c t u r e s o f a l g a l and c o t t o n c e l l u l o s e s . Review o f P r e v i o u s Work Unit C e l l . V a r i o u s workers (2,5-6) have d e t e r m i n e d s i m i l a r d i m e n s i o n s f o r the ramie u n i t c e l l . As shown i n T a b l e I , however, the a_ and _b dimensions have ranges o f about 0.07 A. (The a_ and t> d i m e n s i o n s o f the MGW (Mann, Gonzalez and W e l l a r d ) and RMF c e l l s have been i n t e r c h a n g e d t o conform t o s t a n d a r d c r y s t a l l o g r a p h i c n o t a t i o n (7^) as d i s c u s s e d below.)

Authors

Table I.

U n i t C e l l s f o r Ramie

Mann* Gonzalez Wellard (MGW)

Woodcock Sarko (WS)

Roughead* Miller French (RMF)

Dimension a b c Y

7.846 8.171 10.34 96.38

7.78 8.20 10.34 96.5

7.794 8.248 10.33 96.77

* The a and b dimensions have been i n t e r c h a n g e d the r e p o r t e d v a l u e s f o r t h i s c o m p a r i s o n .

from

The base plane o f the u n i t c e l l f o r c e l l u l o s e I i s o f t e n drawn w i t h the o r i g i n o f the axes p l a c e d i n the lower l e f t c o r n e r , w i t h the x a x i s to the r i g h t and the y a x i s up and t o the l e f t with monoclinic angle being obtuse. However, Sarko's group i n S y r a c u s e has used s t a n d a r d c r y s t a l l o g r a p h i c c o n v e n t i o n , w i t h the o r i g i n i n the upper l e f t , the y a x i s t o the r i g h t , and the x a x i s down and t o the l e f t . I n both c a s e s , the z a x i s i s toward the viewer i f the x and y axes a r e i n the p l a n e o f the p a p e r . T h i s paper u s e s the s t a n d a r d c o n v e n t i o n , shown i n F i g u r e 1, as used i n S y r a c u s e . The a, b, and c



2. FRENCH ET AL.

X-ray Diffraction Studies of Ramie Cellulose I

F i g u r e 1. Drawing of the c e l l u l o s e I u n i t c e l l , a c c o r d i n g to the s t a n d a r d c r y s t a l l o g r a p h i c c o n v e n t i o n i n r e f . 7, by B i l l Garner, Martin Marietta Corporation.


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dimensions a r e the r e p e a t i n g d i s t a n c e s a l o n g the x, y, z axes, r e s p e c t i v e l y .

and


Chain Conformation. From computer m o d e l i n g s t u d i e s o f c e l l u l o s e ( 8 ) , we know t h a t the c e l l u l o s e m o l e c u l e has l i m i t e d f l e x i b i l i t y . Only a few r e g u l a r ( i n t e r n a l l y symmetric) c o n f o r m a t i o n s a r e a l l o w e d f o r c e l l u l o s e , a b e t a 1 , 4 - l i n k e d g l u c a n , and s t r u c t u r e s s i m i l a r t o the t r a d i t i o n a l 2 - f o l d h e l i x a r e the o n l y ones i n a c c o r d w i t h the observed z a x i s s p a c i n g . Such c h a i n s resemble f l a t r i b b o n s . C r y s t a l S t r u c t u r e . I n the c u r r e n t models from x - r a y d i f f r a c t i o n , a t o t a l o f two c e l l u l o s e c h a i n s h a v i n g a t o m i c p o s i t i o n s c l o s e t o t h o s e r e s u l t i n g from 2 - f o l d screw symmetry pass through each o f the unit cells. These c h a i n s a r e bound i n t o s h e e t s by hydrogen bonding between the edges o f the r i b b o n s ; t h e r e a r e no hydrogen bonds proposed t o c o n n e c t the s h e e t s t o each o t h e r ( 6 , 9 - 1 1 ) . The r e m a i n i n g c o h e s i v e n e s s i s a p p a r e n t l y p r o v i d e d by vander Waals attraction. I n o r d e r t o form t h e s e s h e e t s , the 06 h y d r o x y l group i s r o t a t e d i n t o the t g p o s i t i o n , where i t forms both i n t r a - and i n t e r - m o l e c u l a r hydrogen bonds. A l t h o u g h the t g 06 p o s i t i o n i s somewhat c o n t r o v e r s i a l because i t i s r a r e l y found i n s i n g l e c r y s t a l s t u d i e s o f s m a l l e r c a r b o h y d r a t e s , i t has been r e p o r t e d i n a l l recent x-ray s t u d i e s of c e l l u l o s e I . P a c k i n g Mode. The s t r u c t u r e s f o r n a t i v e ramie c e l l u l o s e d e s c r i b e d by Woodcock and Sarko (6) (WS) and f o r V a l o n i a c e l l u l o s e by Gardner and B l a c k w e l l (11) have been c a l l e d " p a r a l l e l - u p " , as opposed t o " p a r a l l e l - d o w n " and t o " a n t i p a r a l l e l " arrangements ( 1 1 ) . However, t h e i r proposed s t r u c t u r e s used the d i f f e r e n t a x i a l c o n v e n t i o n s d e s c r i b e d above. I f both s t r u c t u r e s a r e d e s c r i b e d u s i n g the same c o n v e n t i o n , the p a c k i n g i n one o f the c e l l s i s p a r a l l e l - u p and and the o t h e r i s packed p a r a l l e l - d o w n . I n o t h e r words, the p a r a l l e l - u p s t r u c t u r e p r e f e r r e d by G a r d n e r and B l a c k w e l l c o r r e s p o n d s t o the p a r a l l e l - d o w n s t r u c t u r e s t r o n g l y r e j e c t e d by Woodcock and S a r k o . Work by F r e n c h (9) showed a s m a l l p r e f e r e n c e f o r an a n t i p a r a l l e l arrangement. I d e n t i c a l , hydrogen-bonded s h e e t s t r u c t u r e s can be formed i n each o f t h e s e p a c k i n g arrangements, but the between-sheet i n t e r a c t i o n s are d i f f e r e n t . C e l l Symmetry. F o r many y e a r s , i t was a c c e p t e d t h a t the c e l l u l o s e m o l e c u l e embodied 2 - f o l d screw symmetry ( s p a c e group P 2 ) . Later, Honjo and Watanabe (12) showed e l e c t r o n d i f f r a c t i o n diagrams t h a t i n d i c a t e t h a t V a l o n i a c e l l u l o s e c r y s t a l l i z e s i n the PI space group t h a t does n o t c o n t a i n symmetric c h a i n s . The u n i t c e l l a l s o c o n t a i n e d 8 c h a i n s . Other d i f f r a c t i o n work showed the p r e s e n c e o f f a i n t m e r i d i o n a l r e f l e c t i o n s on the odd l a y e r l i n e s t h a t a l s o i n d i c a t e t h a t the c h a i n s do not have e x a c t 2 - f o l d screw symmetry. While the v a l i d i t y o f t h i s e v i d e n c e has been a c c e p t e d f o r V a l o n i a , i t has not been used i n s t r u c t u r a l s t u d i e s because o f the low i n t e n s i t i e s o f the s p o t s t h a t i n d i c a t e the l a r g e c e l l and t h a t break the symmetry. I t has been argued t h a t the d e v i a t i o n s from symmetry must be r e l a t i v e l y s m a l l ( 1 1 ) ; assumptions r e g a r d i n g the c e l l s i z e have been n e c e s s a r y i n o r d e r f o r the needed computations to be manageable. 1


2. FRENCH ET AL.


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I n Woodcock and Sarko's work on ramie (6) and i n u n p u b l i s h e d work by F r e n c h , the improvement i n f i t between o b s e r v e d and c a l c u l a t e d i n t e n s i t i e s was i n s i g n i f i c a n t when the model was a l l o w e d to d e v i a t e from 2 - f o l d symmetry. On the o t h e r hand, s p l i t t i n g i n the nmr peaks and o t h e r s p e c t r a l e v i d e n c e (13,14) has g i v e n s t r o n g i n d i c a t i o n t h a t the m o l e c u l e s a r e not n e a r l y as symmetric as thought. G i v e n the above c o n t r a d i c t i o n s , q u e s t i o n s o f g e n e r a l i n t e r e s t regarding c e l l u l o s e structure include:


a.

b. c.

d.

e.

What i s the p a c k i n g mode o f the c h a i n s ? I s the p a c k i n g mode d i f f e r e n t i n c e l l u l o s e I and I I ? I f so, how i s the c o n v e r s i o n effected? What i s the e x t e n t o f d e v i a t i o n from a symmetric P2^ s t r u c t u r e ? What i s the n a t u r e o f f i b r i l s ? A r e they extended o r f o l d e d ; what i s the s o u r c e o f l e v e l i n g o f f degree o f p o l y m e r i z a t i o n ? Why i s i t d i f f e r e n t f o r c e l l u l o s e I and I I ? What i s the f i b r i l l a r s t r u c t u r e from the s t a n d p o i n t o f m i l d reactions? Which oxygen atoms a r e a v a i l a b l e f o r m i l d r e a c t i o n s such as c r o s s l i n k i n g a f a b r i c ? I s the h y d r o g e n bonding scheme i m p o r t a n t i n d e t e r m i n i n g the r e a c t i v i t y ? What i s the cause o f d i f f e r e n c e s i n r e s u l t s among the o t h e r p h y s i c a l methods? What a r e the d i f f e r e n c e s among the v a r i o u s c e l l u l o s e s t h a t cause d i f f e r e n c e s i n t h e i r IR and nmr s p e c t r a ?

Some o t h e r a s p e c t s a r e p r i m a r i l y o f i n t e r e s t crystallographers: a. b.

to

fiber

What i s the s o u r c e o f the s u b s t a n t i a l e r r o r r e m a i n i n g i n our studies? What i s the meaning o f the temperature f a c t o r s t h a t r e s u l t ?

F i b e r x - r a y d i f f r a c t i o n can be e x p e c t e d to p r o v i d e a t l e a s t some e v i d e n c e r e l a t i v e t o a l l the above q u e s t i o n s . W i t h the a v a i l a b l e r a t i o o f d a t a t o p a r a m e t e r s , however, some q u e s t i o n s may w e l l r e m a i n unanswered. Samples o f f a r h i g h e r c r y s t a l l i n i t y would be needed to a c c o m p l i s h a complete d e t e r m i n a t i o n , and t h e r e i s some danger t h a t such samples would not c o m p l e t e l y c o r r e s p o n d t o samples o f more g e n e r a l i n t e r e s t . Computer T e c h n i q u e s Program D e s c r i p t i o n . I n o r d e r t o d e t e r m i n e polymer c r y s t a l s t r u c t u r e s , e a c h o f the p a r t i c i p a t i n g i n s t i t u t i o n s u s e s computer programs t h a t r e f l e c t d i f f e r e n t r e s o u r c e s and a b i l i t i e s as w e l l as philosophies. Models to be used f o r c a l c u l a t i o n o f i n t e n s i t i e s a r e c o n s t r u c t e d i n v a r i o u s ways, and each has a d i f f e r e n t s t r a t e g y f o r f i n d i n g the b e s t r e s u l t . E a c h o f the methods has some unique a b i l i t i e s and some d i s a d v a n t a g e s . The SHELX program (15) i s used a t Clemson U n i v e r s i t y . I t was d e s i g n e d f o r s i n g l e c r y s t a l s t u d i e s and can s w i f t l y r e a c h a good match between o b s e r v e d and c a l c u l a t e d d a t a but has no s t e r e o c h e m i c a l component i n the d e t e r m i n a t i o n and was n o t d e s i g n e d to accommodate polymers which have the same m o l e c u l e p a s s i n g t h r o u g h many u n i t c e l l s . I t was s l i g h t l y m o d i f i e d f o r o v e r l a p p e d



20


intensities. S t a r t i n g models must be f a i r l y c l o s e , because t h e r e i s no s e a r c h i n g based on o v e r a l l parameters o f a polymer, such as chain r o t a t i o n or chain t r a n s l a t i o n . The program used a t the S o u t h e r n R e g i o n a l R e s e a r c h C e n t e r (SRRC) was w r i t t e n f o r s i m p l e c e l l u l o s e s t r u c t u r e s (9) m o s t l y by V. G. Murphy, now a t C o l o r a d o S t a t e U n i v e r s i t y . It quickly c a l c u l a t e s R v a l u e s f o r changes i n v a r i a b l e s such as c h a i n r o t a t i o n and c h a i n t r a n s l a t i o n . L i k e SHELX, i t has no s t e r e o c h e m i c a l component. M o d e l i n g i s based on the v i r t u a l - b o n d method ( 1 6 ) , and r e l i e s on s u b s t i t u t i o n o f d i f f e r e n t c o o r d i n a t e s e t s from s i n g l e c r y s t a l s t u d i e s o f model compounds such as c e l l o b i o s e i n o r d e r t o p r o v i d e f i n e i n t e r n a l a d j u s t m e n t s o f a t o m i c c o o r d i n a t e s . The SRRC program uses v a r i a t i o n space s e a r c h i n g t o f i n d the b e s t c o m b i n a t i o n of c h a i n r o t a t i o n and t r a n s l a t i o n i n s t e a d o f a l e a s t s q u a r e s minimization. Because i n d i v i d u a l a t o m i c p o s i t i o n s ( e x c e p t 06) a r e not v a r i e d d i r e c t l y by the program, such a s i m p l e program i s n o t w e l l - s u i t e d f o r determining structures with r e l a t i v e l y high r a t i o s of data to v a r i a b l e parameters. I t i s , however, u s e f u l f o r e x a m i n i n g the e f f e c t s o f d i f f e r e n t assumptions o r q u i c k l y f u r n i s h i n g s t a r t i n g models f o r a more e l a b o r a t e program. It i s a l s o v e r y easy t o p r e p a r e a new d a t a s e t . At S y r a c u s e and Purdue, the computer programs a r e h i g h l y s o p h i s t i c a t e d f o r s t u d y o f polymers i n g e n e r a l . Both c a n combine d i f f r a c t i o n i n t e n s i t y c a l c u l a t i o n s and s t e r e o c h e m i s t r y t o o p t i m i z e intermolecular i n t e r a c t i o n s f o r structures that simultaneously y i e l d a good f i t between the o b s e r v e d and c a l c u l a t e d d i f f r a c t i o n intensities. These s t u d i e s u s u a l l y weight the d i f f r a c t i o n d a t a and the s t e r e o c h e m i c a l s t u d i e s e q u a l l y . The PS-79 program used a t S y r a c u s e was w r i t t e n by P e t e r Zugenmaier and Tony Sarko ( 1 7 ) . I t uses t e c h n i q u e s d e s i g n e d f o r speed and i m p l e m e n t a t i o n on a r e l a t i v e l y s m a l l computer. The m o d e l i n g method a l l o w s v a r i a t i o n i n monomeric geometry t h r o u g h changes i n the d i s t a n c e between the l i n k a g e oxygen atoms. A l l the a t o m i c p o s i t i o n s c a n be v a r i e d w i t h c o n s t r a i n t s t o accommodate s t e r e o c h e m i c a l and x - r a y d a t a . The L i n k e d Atom L e a s t Squares (LALS) program (18,19) by A r n o t t and c o a u t h o r s i s used a t s e v e r a l i n s t i t u t i o n s , i n c l u d i n g Purdue, where i t was d e v e l o p e d , and Case Western Reserve U n i v e r s i t y , where i t was used by Gardner and B l a c k w e l l . I t i s b e s t implemented on a l a r g e computer; the C o n t r o l Data C o r p o r a t i o n supercomputer a t Purdue h a n d l e s i t v e r y r a p i d l y . S e t t i n g up a new model w i t h LALS i s more c o m p l i c a t e d t h a n w i t h the o t h e r programs, but LALS a p p e a r s to p r o v i d e r e a l i s t i c m o l e c u l a r f l e x i b i l i t y . R Factors. Each program d e t e r m i n e s the e x t e n t o f agreement between the o b s e r v e d and c a l c u l a t e d i n t e n s i t i e s (the R f a c t o r ) i n a s l i g h t l y d i f f e r e n t way. The e x a c t method o f c a l c u l a t i o n i s i m p o r t a n t i n the magnitude o f R t h a t i s a t t a i n e d , making i t d i f f i c u l t t o compare r e s u l t s from d i f f e r e n t l a b o r a t o r i e s . While the minima i n t h e s e d i f f e r e n t R f a c t o r s u s u a l l y a r i s e from v e r y s i m i l a r s t r u c t u r e s , each a l g o r i t h m may, as seen below, i n d i c a t e a d i f f e r e n t p r e f e r e n c e among competing models. D i f f e r e n c e s i n the magnitude o f R a r i s e from d i f f e r e n t methods f o r c a l c u l a t i n g the c o n t r i b u t i o n s from s p o t s t h a t a r e too weak t o be o b s e r v e d b u t have a c a l c u l a t e d i n t e n s i t y g r e a t e r t h a n the t h r e s h o l d o f o b s e r v a t i o n . Such r e f l e c t i o n s a r e c a l l e d the unobserved d a t a . V e r y minor


2. FRENCH ET AL.


21

d i f f e r e n c e s r e s u l t from the t e c h n i q u e u s e d t o s u p p l y t h e s c a t t e r i n g f a c t o r s t o the c a l c u l a t i o n s . Two o t h e r s o u r c e s o f d i f f e r e n c e i n the magnitude o f r e p o r t e d R v a l u e s a r e the method u s e d t o s c a l e the o b s e r v e d i n t e n s i t i e s to the c a l c u l a t e d ones ( s c a l e f a c t o r ) , and the method f o r compensating f o r t h e r m a l m o t i o n and p o s i t i o n a l d i s o r d e r (temperature f a c t o r ) . The SRRC program c a l c u l a t e s 5 d i f f e r e n t R v a l u e s , shown i n T a b l e I I . They a r e : a s i m p l e R, ( R o b s ) , based on o n l y r e f l e c t i o n s t h a t a r e o b s e r v e d , an R f o r o n l y the unobserved d a t a (Runobs), t h e i r t o t a l ( R t o t ) , the w e i g h t e d t o t a l R" (R"wt) and the u n i t - ( o r un-) w e i g h t e d t o t a l R (R"unwt). A weighted Rtot i s c a l c u l a t e d i n some o t h e r programs. By k e e p i n g the Robs and Runobs s e p a r a t e , the e f f e c t s o f two somewhat independent s e t s o f d a t a may be o b s e r v e d . At SRRC the square r o o t s o f the o b s e r v e d and c a l c u l a t e d i n t e n s i t i e s are s c a l e d t o each o t h e r w i t h a l e a s t s q u a r e s f i t t h a t i n c o r p o r a t e s an e x p o n e n t i a l term (9). T h i s s i m u l t a n e o u s l y produces a low magnitude o f R", a s c a l e f a c t o r , and a temperature f a c t o r . As shown i n F i g u r e 2, c o a r s e d e t e r m i n a t i o n s o f c h a i n r o t a t i o n a l p o s i t i o n c o u l d be a c c o m p l i s h e d w i t h any o f these R v a l u e s . When R values are c a l c u l a t e d at f i n e increments o f r o t a t i o n ( F i g u r e 3 ) , however, the c h o i c e o f type o f R f a c t o r d e t e r m i n e s which c h a i n r o t a t i o n s a r e chosen t o r e p r e s e n t the b e s t s t r u c t u r e .


M

W e i g h t i n g Schemes. R"wt i s p r e f e r r e d by s t a t i s t i c i a n s because i t g i v e s e x t r a p e n a l t y t o proposed s t r u c t u r e s t h a t have a few l a r g e d i s c r e p a n c i e s between o b s e r v e d and c a l c u l a t e d i n t e n s i t i e s i n s t e a d of a normal d i s t r i b u t i o n o f e r r o r s . T h i s e f f e c t a r i s e s from the use o f the square o f the d i f f e r e n c e s . A l s o , the w e i g h t i n g i n c r e a s e s R"wt h e a v i l y when the d i s c r e p a n c y p e r t a i n s t o the more a c c u r a t e l y d e t e r m i n e d s p o t s and p e n a l i z e s l i g h t l y when the s p o t s are p o o r l y r e s o l v e d . Only the RMF d a t a s e t i n c l u d e s s t a n d a r d d e v i a t i o n s f o r the i n t e n s i t y measurements. These v a l u e s , d i v i d e d by t h e square r o o t of the o b s e r v e d i n t e n s i t y and i n v e r t e d , c a n be used t o w e i g h t the R value c a l c u l a t i o n . F o r c e l l u l o s e I , which has a few dominant s p o t s , t h i s i n e v i t a b l y r e s u l t s i n a l a r g e range o f w e i g h t s . Other w e i g h t i n g schemes can be a d o p t e d . F o r the Mann, G o n z a l e z and W e l l a r d (20) (MGW) and the WS d a t a s e t s , the 4 t h r o o t o f the i n t e n s i t y was u s e d t o g i v e a s m a l l range i n w e i g h t s t h a t would p a r t i a l l y r e f l e c t the e r r o r s due t o c o u n t i n g s t a t i s t i c s . The scheme f i n a l l y adopted f o r the RMF d a t a u s e d the r e c i p r o c a l s o f the f r a c t i o n a l e r r o r , e x c e p t t h a t a c e i l i n g was s e t a t 0.20 o f the weight o t h e r w i s e c a l c u l a t e d f o r the s t r o n g e s t r e f l e c t i o n . Such w e i g h t i n g s t y p i c a l l y d e c r e a s e the s e n s i t i v i t y o f the R f a c t o r t o v a r i a t i o n s i n the model. A l s o , the w e i g h t e d R" i s u s u a l l y n u m e r i c a l l y s m a l l e r t h a n the u n i t - w e i g h t e d R" which, i n t u r n , i s s m a l l e r than R t o t . Comparison o f Programs. The purpose o f the comparison o f the r e s u l t s d e r i v e d t h r o u g h these 4 d i f f e r e n t computer programs i s t o l e a r n t o what e x t e n t r e s u l t s a r e independent o f the computer program. There a r e a c t u a l l y two s i m i l a r q u e s t i o n s . The f i r s t i s whether s i m i l a r R f a c t o r s w i l l r e s u l t from i d e n t i c a l i n p u t structures. The second c o n s i d e r s the s i m i l a r i t y o f s t r u c t u r e s s e l e c t e d as the f i n a l b e s t model i n each program. A t p r e s e n t , we can comment b e s t on the f i r s t q u e s t i o n .


THE STRUCTURES OF CELLULOSE Table

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The Structures of Cellulose - American Chemical Society

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