Accurate Fiber X-ray Diffraction Data from Films - ACS Publications

6 Accurate Fiber X-ray Diffraction Data from Films Data Array Calculations

D O N A L D P. MILLER and R O B E R T C. B R A N N O N

1

Downloaded by GEORGETOWN UNIV on February 28, 2018 | https://pubs.acs.org Publication Date: November 17, 1980 | doi: 10.1021/bk-1980-0141.ch006

Clemson University, Clemson, SC 29631

Although diffraction techniques are often chosen for determining the structure of crystalline and paracrystalline mater i a l s , a number of serious difficulties have limited the confidence one may place in the results for fibrous polymers. Such fundamental questions as the relative polarity of adjacent chains and rotational positions of side groups have been afforded little resolution in recent studies (1-7). An excellent example of these difficulties is furnished by recent studies of native and regenerated cellulose. Different studies, from the same photographic data disagreed on chain polarity, though all find the rotatable hydroxymethyl side group in the tg position for which only one single crystal analogue, disordered, has been found. For dissimilar models all yielding R factors below 0.20, data sets are found to disagree by as much as 49%. The same data collection and reduction techniques are commonly used by the same workers for many different polymers. Therefore, data for these other polymers may contain errors on a similar scale, but that the errors have usually, but not always, gone undetected (8). If more than 500 reflections are observed, from single crystals of simple molecules, recognizable electron-density distributions have been derived from visually estimated data classified only a "weak", "medium" or "strong". The calculation of the structure becomes more sensitive to the accuracy of the intensity data as the number of data points approaches the number of variables in the structure. One problem encountered in crystal structure analyses of fibrous polymers is that of a very limited number of reflections (low data to parameter ratio). In addition, fibrous polymers usually scatter x-rays too weakly to be accurately measured by ionization or scintillation counter techniques. Therefore, the need for a c r i t i c a l study of the photographic techniques of obtaining accurate diffraction intensities is paramount. *Current address:

Technical Center, Owens-Corning Corp., Granville, OH 43023

0-8412-0589-2/ 80/47-141 -093$05.00/0 © 1980 American Chemical Society French and Gardner; Fiber Diffraction Methods ACS Symposium Series; American Chemical Society: Washington, DC, 1980.


94

FIBER DIFFRACTION

METHODS

Our g e n e r a l o b j e c t i v e has been t o d e v e l o p methods o f s u f f i c i e n t accuracy i n f i l m data c o l l e c t i o n to allow d i r e c t determinat i o n o f f i b r o u s polymer s t r u c t u r e s ( r a t h e r than i n d i r e c t , w i t h modeling). The o b j e c t i v e can be t h o u g h t o f i n f o u r p a r t s : c o l l e c t x - r a y d i f f r a c t i o n d a t a a r r a y s u s i n g an a c c u r a t e , s t a b l e computer c o n t r o l l e d scanning microdensitometer; process the data through the use o f a h i g h l e v e l computer language chosen f o r i t s a r r a y ( m a t r i x ) m a t h e m a t i c a l c a p a b i l i t i e s ; use t h e p r o c e s s e d d a t a t o d e t e r m i n e d i r e c t l y t h e s t r u c t u r e o f a f i b r o u s p o l y m e r and when t h i s had been a c c o m p l i s h e d t o s u f f i c i e n t a c c u r a c y ; use t h e r e s u l t s t o compare s t r u c t u r e d e t e r m i n a t i o n by t h e t e c h n i q u e s o f a) Peak C e n t e r method, b) Sum I n t e n s i t y method, and c) D a t a A r r a y I n t e g r a t i o n method ( t h e s e a r e d i s c u s s e d b e l o w ) . Visual Estimation of

Intensity

V i s u a l comparison o f d i f f r a c t i o n spots w i t h a graded i n t e n s i t y s c a l e was by f a r t h e most u s e d method t o q u a n t i f y i n t e n s i ties. The human e y e , w h i c h i s a v e r y good c o m p a r a t i v e p h o t o meter, can e s t i m a t e t h e r e l a t i v e o r d e r o f b l a c k n e s s o f a s e r i e s o f s p o t s w i t h g r e a t a c c u r a c y , b u t n o t on a t r u e n u m e r i c a l s c a l e . The o r i g i n o f t h i s method i s unknown and seems a l m o s t i n t u i t i v e . Many a u t h o r s (8-13) s u g g e s t ways t o o b t a i n an i n t e n s i t y s c a l e . F o r many f i l m s e x p o s e d i n t h e r e g i o n o f d e n s i t y where f ^ a r e t h e atom s c a t t e r i n g f a c t o r s , were t h e n c a l c u l a t e d . E - s e c t i o n s , F i g u r e 7 f o r e x a m p l e , were u s e d i n s t e a d o f an e l e c t r o n d e n s i t y b e c a u s e t h i s method e q u a l i z e s t h e e f f e c t i v e s c a t t e r i n g o f a l l a t o m s , m a k i n g l o w a t o m i c number atoms e a s i e r t o l o c a t e . The p o s i t i o n s o f t h e K a n d B r " were f o u n d t o be c o r r e c t a s p r e d i c t e d b y t h e P a t t e r s o n map i n t e r p r e t a t i o n . S e c t i o n s 2A° b y 2A° were s e l e c t e d a n d c o n t o u r e d i n r e g i o n s away from t h e K and B r " i o n s . Approximate l o c a t i o n s o f a l l carbon and o x y g e n atoms were f o u n d i n t h i s manner. No o x y g e n s o f w a t e r o f h y d r a t i o n was f o u n d , s o t h e sample was j u d g e d t o be a n h y d r o u s . Once a new atom was l o c a t e d , t h e s t r u c t u r e f a c t o r p r o g r a m , FHKL, was r u n a g a i n and i n c l u d e d t h e p o s i t i o n o f t h e a d d i t i o n a l atom. A l l a d d i t i o n a l atoms were g i v e n t h e s c a t t e r i n g power o f c a r b o n u n t i l t h e t r u e i d e n t i t y o f t h e atom c o u l d be a s c e r t a i n e d f r o m t h e e l e c t r o n d e n s i t y . Many o f t h e atoms l o c a t e d were n o t members o f t h e same r e s i d u e . The symmetry o p e r a t i o n s o f t h e s p a c e g r o u p were p e r f o r m e d on t h e s e t o f a t o m i c c o o r d i n a t e s and t h e r e s i d u e s were c o n s t r u c t e d b y t r i a l a n d e r r o r g r a p h i c s p l o t s . Various c o n n e c t i v i t i e s were t r i e d u n t i l a c o n n e c t e d r e s i d u e c h a i n was a p p a r e n t . The a t o m i c c o o r d i n a t e s were t h e n s h i f t e d s l i g h t l y i n the d i r e c t i o n needed t o conform t o t h e p r e d i c t e d s t r u c t u r e . A f t e r s e v e r a l c y c l e s o f t h i s p r o c e d u r e t h e R f a c t o r was f o u n d t o be 0.19. The t r i a l s t r u c t u r e was r e f i n e d b y u s i n g a m o d i f i e d v e r s i o n o f t h e f u l l - m a t r i x l e a s t - s q u a r e s f o r t r a n p r o g r a m SFLS ( 3 1 ) . The q u a n t i t y m i n i m i z e d was Q

0

+

F

+

+

French and Gardner; Fiber Diffraction Methods ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

6.

MILLER AND BRANNON

X-ray Diffraction Data from Films

105

0,0


I

^37

'

^

Figure 6. Contoured Patterson section at z = 0.25. X = K* - Br vector peak.


106

FIBER

DIFFRACTION

METHODS


0,0

.1,.78 Figure 7.

Contoured E-section of the region near the 0(5) atom (Z = 0.02)


6.

MILLER

I((F

107


AND BRANNON

2 0

"

F

2 c

)/k),

where k i s a s c a l e f a c t o r . Once t h e c o r r e c t s c a l e f a c t o r h a d been c a l c u l a t e d , t h e c a r b o n a n d o x y g e n a t o m i c c o o r d i n a t e s were a l l o w e d t o v a r y u n t i l t h e change i n a t o m i c p o s i t i o n was l e s s t h a n the c a l c u l a t e d e r r o r i n p o s i t i o n . During f i n a l c y c l e s atomic p o s i t i o n s and i s o t r o p i c temperature f a c t o r s a l l o w e d t o change. The r a t i o o f i n t e n s i t i e s t o v a r i a b l e s was 55/37 ( t h e K a n d B r " p o s i t i o n s were n o t v a r i e d ) . The f i n a l R f a c t o r was 0.058. A t t h i s R v a l u e , n o t a l l bond l e n g t h s a n d bond a n g l e s were a c c e p t able. When t h e g l u c o s e r i n g was a d j u s t e d t o c o r r e c t t h i s p r o b l e m , t h e R v a l u e r o s e t o 0.068. The f i n a l r i n g c o n f o r m a t i o n a n d a d justment w i l l be d i s c u s s e d i n f u t u r e p u b l i c a t i o n s . T a b l e 1. l i s t s t h e i n t e n s i t i e s c a l c u l a t e d f r o m t h e f i n a l atom l o c a t i o n s a n d t e m p e r a t u r e f a c t o r s a n d t h e o b s e r v e d i n t e n s i t i e s s c a l e d t o them. An ORTEP (32) p l o t o f one a m y l o s e c h a i n i n t h e u n i t c e l l a n d n e a r b y K B r i s shown i n F i g u r e 8.


+

C o m p a r i s o n o f D a t a Measurement T e c h n i q u e s . A s t h e i n t e g r a t i o n s o f d i f f r a c t i o n maxima were p e r f o r m e d , t h e peak ( a r r a y m a x i mum) v a l u e o f e a c h was d e t e r m i n e d a n d t h e f i r s t sum o f t h e i n t e g r a t i o n p r o c e s s was d e t e r m i n e d a n d k e p t . These two v a l u e s s h o u l d a d e q u a t e l y r e p r e s e n t i n t e n s i t i e s o b s e r v e d b y t h e Peak C e n t e r t e c h n i q u e a n d b y t h e Sum I n t e g r a t i o n t e c h n i q u e (more t h a n a d e q u a t e , s i n c e , a t t h e t i m e t h e y were d e t e r m i n e d , b a c k g r o u n d h a d a l r e a d y been removed f r o m e a c h d a t a s u b a r r a y ) . These v a l u e s a r e shown i n T a b l e 1. a s P e a k ^ a n d S u m ^ . The peak i n t e n s i t i e s a r e c o r r e c t e d f o r s p o t shape a n d f i b e r t i l t d i s t r i b u t i o n . They may be s c a l e d t o t h e c a l c u l a t e d i n t e n s i t i e s b y d i v i d i n g b y 0.0475 and 0.785 r e s p e c t i v e l y . T h e i r R v a l u e s a r e RPEAK 0.40 a n d SUM 0.31. These were n o t r e f i n e d , b u t d e t e r m i n e d b y u s i n g t h e p o s i t i o n s d e t e r m i n e d f r o m t h e SFLS r e f i n e m e n t a n d v a r y i n g t h e s c a l e f a c t o r s f o r t h e two d a t a s e t s u n t i l R m i n i m i z e d . I f the atoms were a l l o w e d t o a d j u s t i n r e f i n e m e n t w i t h t h e Sum I n t e n s i t i e s , t h e R v a l u e w o u l d a l s o r e d u c e somewhat. Figure 9 shows R e s i d u a l s f o r t h e t h r e e o b s e r v e d d a t a s e t s . I t i s now c l e a r why J a c k o b s , Bumb a n d Z a s l o w were a b l e t o model a n e s s e n t i a l l y c o r r e c t s t r u c t u r e w i t h i n a c c u r a t e i n t e n s i ties. The h e a v y s c a t t e r i n g o f t h e K a n d B r ~ i o n s d e t e r m i n e d t h e i r p o s i t i o n s i n the c e l l s u f f i c i e n t l y t o r e s t r i c t the range on model c o n f i g u r a t i o n s i n t h e r e m a i n i n g u n i t c e l l s p a c e . I n s y s t e m s w h i c h do n o t c o n t a i n h e a v y atoms o r c o n t a i n more atoms (more p a r a m e t e r s ) t h e c o r r e c t s t r u c t u r e was n o t a s e a s i l y obtained. Y e t many s t r u c t u r e s have b e e n s u c c e s s f u l l y ( a p p a r e n t l y ) d e t e r m i n e d b y means o f m o d e l i n g t e c h n i q u e s . The Sum I n t e n s i t y t e c h n i q u e y i e l d s more a c c u r a t e atom p o s i t i o n v a l u e s a n d r e s u l t s i n m o d e l s w i t h R f a c t o r s , i n some c a s e s , as l o w a s 0.15. T h i s s u c c e s s must more be a t t r i b u t e d t o t h e i n put o f a d d i t i o n a l i n f o r m a t i o n i n t o the m o d e l i n g , such as s t e r i c 0

s

0

s

=

R

=

+



108 FIBER DIFFRACTION


METHODS


.02

83.12

37.12

34.44

94.40

305 035

306 036

307 037

3)2 132

28.92

301 031

304 034

124.66

224

12.48

22.96

221

30.57

2018.80

1978.60

69.25

217 127

303 033

1950.71

32.62

16.12

22.69

216 126

302 032

29.43

1500.58

1409.10

59.53

1312.19

746.80

121.70

967.18

2.76

100.10

43.18

2263.10

413.12

2895.10

1540.92

818.46

134.32

1087.22

3.88

113.76

55.12

2831.80

619.98

3465.14

1027.90

1412.58

751.76

134.82

1070.10

6.88

109.32

51.88

2841.40

1344.28

550.69

3364.60

1019.68

2467.40

215 125

858.65

2611.62

9.54

2345.46

214 124

1112.52

4686.74

22.54

90.30

1085.48

4938.14

20.98

213 123

867.56

356^.56

12.67

17.52

313.56

0.38

212 122

211 121

207 027

5.46

2.87

1.15

2.68

12.60

1.15

2.78

4.60

1.87

10.00

5.90

6.30

4.80

9.20

8.60

3.20

3.00

24.90

8

004

JJQ

HQ

18.68

63.13

.05

54.09

8

214.58

,

9-68

9

220

1

56.13

6.02

\IQ

416 246

l\l

iJJ

2

2

' 3

8

78.20

2874.60

762.90

53.20

191.20

3128.00

1

555.50

121.60

7

6

' 0

2

101.10

3275.50

824.68

69.12

204.42

4053.70

1

630.26

128.42


5

2

6

73.39

7

3289.85

753.18

66.58

191.88

4413.21

1

499.25

120.36

8

8

1

.97

6.91

5.40

7.60

1.60

-

5.20

5.70

5.50

FIBER DIFFRACTION

110

METHODS


o Figure 8. ORTEP drawing of amy lose chain and KBr viewed along the b axis. The chain atoms are drawn to 50% probability thermal circles. The K* and Br' ions are drawn to half their ionic radii so as not to obscure the amylose chain.

RESIDUALS VS DSTAR

!°n—i—i—i—i—i—i—i—i—i—i—i

i r

40 -

-40 -

f .60 U 0.8

I

I

1.2

I

I

1.6

i

« I

2.0

I

I

2.4

I

I

2.8

I

I

3.2

L

Figure 9. Residuals, ((I - I AL)/2(ICAL)), for the three data sets (---) PEAK; ( ) SUM; ( ) INTEGRATED). The abscissa, DSTAR = 4*s in 6/k. C



6.

MILLER AND BRANNON


111

h i n d r a n c e s , p s e u d o p o t e n t i a l s , N-H m a p p i n g a n d / o r l i n k e d - a t o m m o d e l s w i t h few p a r a m e t r a l v a r i a b l e s t h a n t o t h e x - r a y d i f f r a c t i o n data. The i n c r e a s e d d a t a t o p a r a m e t e r r a t i o s o f l i n k e d - a t o m r e f i n e m e n t s , w h i c h s h o u l d g i v e more l e a s t s q u a r e s a c c u r a c y , i s o f f s e t , however, by t h e reduced f l e x i b i l i t y o f t h e c h a i n c o n f o r mation i n refinement. The e f f e c t s a p p e a r t o be c o m p e n s a t o r y . C o m p a r i s o n o f t h e SFLS r e f i n e m e n t o f K B r - a m y l o s e w i t h LALS a n d V i r t u a l Bond r e f i n e m e n t s may p r o v e most i n f o r m a t i v e . D a t a a r r a y c a l c u l a t i o n s w i t h c u b i c s p l i n e f i t t i n g and n u m e r i c a l i n t e g r a t i o n a p p e a r s t o y i e l d d a t a o f much g r e a t e r a c c u r a c y . The m e a s u r a b l e r a n g e i s g r e a t l y e x t e n d e d (6500:1 f o r t h e KBra m y l o s e d a t a ) a n d e r r o r s c a n be a c c o u n t e d f o r more a c c u r a t e l y i n the process o f o b t a i n i n g i n t e n s i t y data. T h e s e e r r o r s may e v e n be u s e d i n w e i g h t i n g o f l e a s t - s q u a r e s r e f i n e m e n t c a l c u l a t i o n s a s i s p r e s e n t l y done i n s i n g l e c r y s t a l s t r u c t u r e s t u d i e s . Conclusions T e c h n i q u e s a r e now a v a i l a b l e a n d , t h r o u g h t h e u s e o f contemp o r a r y c o m p u t e r l a n g u a g e s s u c h a s SPEAKEASY, c o n v e n i e n t t o e x t r a c t a c c u r a t e f i b e r x-ray d i f f r a c t i o n d a t a from f i l m s . The a c c u r a c y i s enough t o a l l o w d i r e c t d e t e r m i n a t i o n o f s t r u c t u r e s w i t h d a t a t o p a r a m e t e r r a t i o a s low a s 1.5 i f a p h a s e d e t e r m i n i n g atom ( h e a v y ) i s present. Problems i n s i m p l e r polymer systems, f o r i n s t a n c e t h e q u e s t i o n o f c h a i n c o n f o r m a t i o n i n c e l l u l o s e , s h o u l d now be determinable with greater c e r t a i n t y . I n e v e n more c o m p l i c a t e d systems, the i n c r e a s e i n a c c u r a c y o f the d a t a and the g r e a t e r d a t a m a g n i t u d e r a n g e s h o u l d a l l o w m o d e l i n g t o be c a r r i e d o u t w i t h much more c o n f i d e n c e i n t h e r e s u l t s . Acknowledgements The a u t h o r s w i s h t o t h a n k Dr. A l f r e d F r e n c h f o r t h e KBra m y l o s e sample a n d f o r numerous h e l p f u l s u g g e s t i o n s a n d c r i t i c a l comment, P r o f s . Edw. Vaughn and J . P. M c K e l v e y f o r t h e i r e n c o u r agement, P r o f . M a r i e L a P r a d e f o r u s e o f h e r c o p i e s o f t h e SFLS and ORTEP (32) c o m p u t e r p r o g r a m s a n d h e r e x c e l l e n t s u g g e s t i o n s , Mr. James Eubanks f o r a n e x c e l l e n t e l e c t r o n i c p a c k a g e d e s i g n a n d Mr. James Mann f o r p r e c i s i o n m a c h i n e c r a f t .


112

FIBER DIFFRACTION METHODS

Literature Cited 1. 2. 3. 4. 5. 6. 7.


8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

25. 26. 27. 28. 29. 30. 31. 32.

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RECEIVED May

21,

1980.


Accurate Fiber X-ray Diffraction Data from Films - ACS Publications

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