Fiber Diffraction Methods - American Chemical Society

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Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 28, 2016 | http://pubs.acs.org Publication Date: November 17, 1980 | doi: 10.1021/bk-1980-0141.ch002

Problem Areas in Structure Analysis of Fibrous Polymers E. D. T. ATKINS H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Tyndall Avenue, Bristol BS8 1TL U.K.

Many difficulties are encountered in the elucidation of molecular structure of fibrous macromolecules. Fibrous textures suffer from a variety of faults, distortions and blemishes, the more obvious of which are: limited crystallite size which broadens the diffraction signals, uncorrelated (or worst s t i l l partially correlated) azimuthal orientation of the needle-shaped crystallites about their major axis resulting in the overlay of diffraction signals, and misalignment of crystallites with respect to the fibre direction which produces arcing of the signals. Since x-ray diffraction is the principal technique employed, the experimental data, on which the structure is based, is of considerably poorer quality than that obtained in classical single crystal diffraction. The consequences are rather obvious: the available resolution is less than that desired for detailed structure determination and therefore as many as possible reliable (or what are thought to be reliable) stereochemical and rigid-body constraints are injected into the model building procedures in an attempt to reduce the number of conformations for consideration. This number is often further reduced by empirical energy minimization calculations. Assumptions are made at this stage and therefore some degree of uncertainty (which will be a function of the particular fibrous polymer under consideration) will surround the accuracy of the proposed structure. Thus it is always most desirable to also collect additional experimental information using other methods. Professor Tadakoro's recent book(1) illustrates the considerable advantages and benefits to be gained by coupling infra-red spectroscopy with fibre x-ray diffraction. The increasing availability of Fourier transform infra-red spectrometers allows the same thick samples, suitable for x-ray work, to be used in the spectrometer thus ensuring that both sets of information emanate from the same structure. The delightful selected area electron diffraction patterns obtained from polysaccharides by Dr. Chanzy (2), which exhibit such remarkable resolution and definition, indicate the importance and value of the modern application of electron micro0-8412-0589-2/80/47-141-031$05.00/0 © 1980 American Chemical Society French and Gardner; Fiber Diffraction Methods ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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FIBER DIFFRACTION

METHODS

scopy. F i n a l l y s o l i d - s t a t e NMR has now developed to a l e v e l where we can expect major advances to occur i n the near f u t u r e with r e s p e c t to i t s a p p l i c a t i o n to f i b r o u s polymers. I wish to o u t l i n e a few of the problems that are c u r r e n t l y i r r i t a t i n g the processes of e l u c i d a t i o n i n polymer s t r u c t u r e determination u s i n g f i b r e x-ray d i f f r a c t i o n p a t t e r n s .


1.

R e p r o d u c i b i l i t y and Accuracy of Measured

Intensities

The i n c r e a s i n g use of computerised model b u i l d i n g procedures i n the s t r u c t u r e determination of f i b r o u s polymers i s p r o v i d i n g a welcome improvement i n the r e p r o d u c i b i l i t y and p r e c i s i o n of polymer conformation and s t r u c t u r e and i n t h e i r p r e s e n t a t i o n i n a convenient form. Coupled with t h i s development i s a trend towards more e x t e n s i v e and exhaustive s t r u c t u r e refinements which, i n some cases, have y i e l d e d e x c e p t i o n a l l y d e t a i l e d three-dimens i o n a l model s t r u c t u r e s . For example c e r t a i n p o l y s a c c h a r i d e s t r u c t u r e s have been proposed i n c o r p o r a t i n g s p e c i f i c hydrogenbonded networks. The l o c a t i o n s of c a t i o n s and water molecules w i t h i n the polymer l a t t i c e have apparently been deduced by s t r u c t u r e determination u s i n g c l a s s i c a l s i n g l e - c r y s t a l F o u r i e r d i f f e r e n c e procedures. However p l a u s i b l e such s t r u c t u r e s may appear they cannot be c o n v i n c i n g l y s u b s t a n t i a t e d with respect to the expeimentally a v a i l a b l e x-ray i n f o r m a t i o n , at l e a s t not by u t i l i z i n g the r a t h e r crude methods t y p i c a l l y used f o r measuring the i n t e n s i t i e s o f the broad x-ray d i f f r a c t i o n s i g n a l s from fibres. Major improvements are r e q u i r e d i n the c o l l e c t i o n , p r o c e s s i n g and measurement of the d i f f r a c t i o n i n t e n s i t i e s . Even when such improvements are made, and the extent of the improvement t e s t e d , the accuracy of each proposed s t r u c t u r e w i l l need to be c a r e f u l l y s c r u t i n i z e d . The current vogue of quoting probabi l i t i e s u s i n g s t a t i s t i c a l t e s t i n g procedures r a t h e r than the r e l i a b i l i t y index dragged over from s i n g l e - c r y s t a l d i f f r a c t i o n perhaps o f f e r s a b e t t e r f e e l f o r the confidence placed i n a s t r u c t u r e , but i s no s u b s t i t u t e f o r improvement i n accuracy. Proper e s t i m a t i o n o f the e r r o r s i n v o l v e d i n the measurement of i n t e n s i t y should now be of prime concern to a l l s e r i o u s f i b r e d i f f r a c t i o n i s t s ! The next generation of s t r u c t u r e determinations should not r e l y on a t e s t i n g system based on a s i n g l e column of observed i n t e n s i t i e s , without any e r r o r l i m i t s and with minimum d e s c r i p t i o n concerning t h e i r c o l l e c t i o n and e s t i m a t i o n o f the background s u r f a c e s . Any improvements made w i l l go some way towards b a l a n c i n g the i n c r e a s e d p r e c i s i o n being wielded i n the computerised modelling. There i s no need to labour t h i s p o i n t s i n c e many of the improvements I have o u t l i n e d are d i s c u s s e d i n c o n s i d e r a b l e d e t a i l elsewhere (3-6). Dr. F r a s e r , who should be congratulated f o r p u t t i n g h i s foot i n t h i s p a r t i c u l a r door f i r s t (4), h i g h l i g h t s the advantages of u s i n g a f i l m scanning procedure f o r p r o c e s s i n g i n t e n s i t i e s of f i b r e d i f f r a c t i o n p a t t e r n s and a l l o w i n g a more accurate a p p l i c a t i o n of c o r r e c t i o n f a c t o r s and

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

2.

ATKINS

Structure Analysis Problem Areas

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i n c l u s i o n o f m e r i d i o n a l d i f f r a c t i o n s i g n a l s i n t o the experimenta l l y recorded i n t e n s i t y set ( 3 ) . Two other c o n t r i b u t i o n s (5,6) d i s c u s s the c o l l e c t i o n o f i n t e n s i t i e s from photographic f i l m s with g r e a t e r accuracy than current methods. The use o f mathem a t i c a l l y d e r i v e d s p l i n e s t o represent background s u r f a c e p r o f i l e s i s a l s o d i s c u s s e d i n some d e t a i l and o f f e r s scope f o r better r e p r o d u c i b i l i t y (5).


2.

Intertwining Helices

Since the d i s c o v e r y i n 1953 that DNA c o n s i s t s o f a double h e l i x (7) i n t e r t w i n e d molecular ropes have a t t r a c t e d c o n s i d e r a b l e attention. The s t r u c t u r e o f t r o p o c o l l a g e n c o n s i s t s o f three polypeptide chains i n t e r t w i n i n g about a common a x i s s t a b i l i z e d by i n t e r c h a i n hydrogen bonds (8)and a number o f the a - p r o t e i n s t r u c t u r e s and a c t i n have been i n t e r p r e t e d i n terms o f i n t e r twining molecular ropes (see f o r example 9). T r i p l e strand h e l i c e s have been e s t a b l i s h e d i n p o l y s a c c h a r i d e s f o r the 1,3 linked $-D-xylans and $-D-glucans (10-13) and double strand models f o r carragennan (14), agar (15) and amylose (16) and p a r t i c u l a r polymorphs o f hyaluronate (17). S t r u c t u r a l i n v e s t i gations o f the p o l y s a c c h a r i d e xanthan favoured a 5 s i n g l e h e l i c a l s t r u c t u r e separated from adjacent chains by 1.85nm(18). Thg d e n s i t y o f t h i s model ( p o l y s a c c h a r i d e chains only) i s 0.46gm/cm which i s over three times l e s s than the measured d e n s i t y o f o r i e n t e d f i l m s and the excessive amount of water needed to reduce the d i f f e r e n c e between c a l c u l a t e d and measured d e n s i t i e s i s not c o n s i s t e n t with the behaviour o f the x-ray d i f f r a c t i o n p a t t e r n as a f u n c t i o n o f r e l a t i v e humidity and d r y i n g out o f the sample (19). The mass per u n i t l e n g t h , measured i n s o l u t i o n (20), i s twice that c a l c u l a t e d f o r a s i n g l e c h a i n and r e s u l t s obtained from e l e c t r o n microscopy suggest an i n t e r t w i n i n g o f chains (21). C l e a r l y the s i n g l e chain 5 h e l i x needs t o be re-examined g i v i n g due c o n s i d e r a t i o n to those f a c t o r s . Further d e t a i l s o f the s t r u c t u r e f o r xanthan are given l a t e r i n the proceedings (22). Strong support o f the t r i p l e - s t r a n d 3-D-xylan and 3-D-glucan and the double-strand model f o r hyaluronate (17) came from observable systematic absences y i e l d i n g a space group assignment with some confidence. In t h i s l a t t e r case systematic absences of the type h+k+£=2n i n combination with the u n i t c e l l dimension and the measured d e n s i t y supported a centred t e t r a g o n a l l a t t i c e with two chains placed at each corner and c e n t r e . A s i m i l a r l i n e o f reasoning has been a p p l i e d by Tadokoro i n the case o f i s o t a c t i c poly(methyl methacrylate) the x-ray f i b r e d i f f r a c t i o n p a t t e r n o f which (i-PMMA) has been r e i n t e r p r e t e d i n terms o f an i n t e r t w i n e d double-strand molecule (j.,23). The r e f l e c t i o n s index on an orthorhombic u n i t c e l l and d e n s i t y measurements favour four chains running through the c e l l . Systematic absences of the form h+k=2n support a space group assignment P2 2^2. The agreement between c a l c u l a t e d and measured s t r u c t u r e f a c t o r s i s s t i l l r a t h e r 1


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FIBER DIFFRACTION METHODS

poor o v e r a l l but b e t t e r than a l t e r n a t i v e models with four s i n g l e polymer chains (24). B e t t e r q u a l i t y x-ray f i b r e d i f f r a c t i o n s have been obtained, as shown i n F i g u r e 1, which i n d i c a t e that a number o f r e f l e c t i o n s s p l i t a l l o w i n g a more accurate d e t e r mination o f the u n i t c e l l dimensions, and p r o v i d i n g an improved set o f observed i n t e n s i t i e s on which t o base a s t r u c t u r e r e f i n e ment .


3.

Highly Extended H e l i x o f I s o t a c t i c Polystyrene Found i n Gels

Natta (25)showed that i n c r y s t a l l i n e i s o t a c t i c p o l y s t y r e n e the molecular chains form t h r e e - f o l d h e l i c e s w i t h an a x i a l advance (h) per styrene monomer o f 0.222nm, some 15% below the t h e o r e t i c a l maximum extension o f h = 0.26nm f o r the styrene monomer i n the a l l - t r a n s ( t t ) f u l l y extended c h a i n . X-ray d i f f r a c t i o n p a t t e r n s o f o r i e n t e d g e l s o f i s o t a c t i c p o l y styrene, obtained at high supercoolings i n d e c a l i n , are q u i t e d i f f e r e n t (26)as shown i n F i g u r e 2a) from the t r a d i t i o n a l Natta patterns. In p a r t i c u l a r a pronounced m e r i d i o n a l r e f l e c t i o n at a spacing o f 0.51nm, together with s u c c e s s i v e orders, r e q u i r e d an extended, or n e a r l y extended, c h a i n conformation (26). In a d d i t i o n to the 0.51nm m e r i d i o n a l r e f l e c t i o n l a y e r l i n e s are observed with s i x times t h i s spacing at 3.06nm which equate with twelve styrene u n i t s (27). The 0.51nm m e r i d i o n a l r e f l e c t i o n c o r r e l a t e s with two styrene monomers r o t a t i n g about the c h a i n a x i s t o form a s i x - f o l d h e l i x , the average advance per styrene monomer being 0.255nm only m a r g i n a l l y below the f u l l y extended t t conformation. Extended conformations were r u l e d out on stereochemical arguments (28)and conformational a n a l y s i s (29). Thus A t k i n s (27)considered other c o n f i g u r a t i o n a l l y d i f f e r e n t p o l y s t y r e n e models, i n p a r t i c u l a r s y n d i o t a c t i c and syncephalic (head-to-head) sequences although i n c o n f l i c t with the i n i t i a l C NMR s p e c t r a (30)which i n d i c a t e d no departure from i s o t a c t i c i t y w i t h i n 1-2%. Benson (31) has however reported the presence of low concentrations o f syncephalic sequences i n p o l y s t y r e n e . 1 3

1 3

The a s s e r t i o n o f 98-99% i s o t a c t i c i t y by C NMR prompted A t k i n s (32)to examine the stereochemistry and c a l c u l a t e the energy o f h i g h l y extended i s o t a c t i c chains. In p a r t i c u l a r a t w e l v e - f o l d r e g u l a r h e l i x with an a x i a l advance (h) o f 0.255nm. (Conformationally i t i s simpler to c o n s t r u c t a r e g u l a r twelvef o l d h e l i x and consider s l i g h t m o d i f i c a t i o n s o f environment f o r a l t e r n a t i n g monomers, e i t h e r by v a r i a t i o n o f t o r s i o n a l backbone angles, or r o t a t i o n o f aromatic appendages, o r both). Previous analyses (29,33,34) h i g h l i g h t e d only two conformations, v i z . the Natta t h r e e - f o l d h e l i x and a near a l l trans conformation (33,34) where the l a t t e r , however, does not lead to an extended c h a i n but to a l a r g e c i r c u l a r s t r u c t u r e ( t h i s i s e x p l i c i t i n r e f . 34, but not s t a t e d as such f o r the independently d e r i v e d , b a s i c a l l y i d e n t i c a l bond r o t a t i o n sequence i n r e f . 33^. For the d i s t i n c t i o n of the two kinds o f a l l t t t sequences l e a d i n g t o two b a s i c a l l y


ATKINS


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2.

Figure 1. (a) (top) X-rayfiberdiffraction pattern of i-PMMA. Fiber axis vertical. The layer line spacing is 1.036 nm with a meridional reflection on thefifthlayer line. The model proposed by Tadokoro (\) has a pitch of twice the value for the observed layer line spacing which becomes halved by the symmetry related intertwining chain, (b) (bottom) Higher resolution diffraction pattern of the equatorial region of i-PMMA. The equator is tilted to extend the range on the film. Note that the reflections shown in (a) are now split. (Patterns obtained in collaboration with G. Challa).




Figure 2. X-ray fiber diffraction patterns of i-PS gels, (a) (top) i-PS in transdecalin showing rather weak, odd-order layer lines at 3.06-nm spacing, (b) (bottom) i-PS in cls-decalin showing very strong first order layer line again with 3.06-nm spacing.



2.

ATKINS


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d i f f e r e n t conformations,i.e. c i r c u l a r and extended chains see A t k i n s (32) Conformational a n a l y s i s by A t k i n s (32)have shown that a h i g h l y extended t w e l v e - f o l d h e l i x i s indeed s t e r e o c h e m i c a l l y p o s s i b l e and has low energy. Independent c a l c u l a t i o n s by Sundararajan (35) and C o r r a d i n i (36) have confirmed the e s s e n t i a l f e a t u r e s o f the s t r u c t u r e which i s shown i n F i g u r e 3. In a d d i t i o n L o v e l l and Windle (37) have proposed a model based on a conforma t i o n sequence t t t s where s represents a skew o f 40 - 60 r o t a t i o n from the trans p o s i t i o n . No f u l l s c a l e energy c a l c u l a t i o n s have been undertaken and the stereochemical f e a s i b i l i t y monitored only with CPK space f i l l i n g models. Thus the proposed model must await more r i g o r o u s t e s t i n g before i t can be decided i f i t i s an acceptable a l t e r n a t i v e t o the models d i s c u s s e d above (32,35,36). As an independent approach F o u r i e r transform i n f r a r e d s t u d i e s of i s o t a c t i c p o l y s t y r e n e g e l s favours i s o t a c t i c sequences i n an ordered conformation d i f f e r e n t from the Natta type t h r e e - f o l d h e l i x (38). Two f e a t u r e s o f the p o l y s t y r e n e g e l obtained from t r a n s d e c a l i n deserve comment. F i r s t the m e r i d i o n a l r e f l e c t i o n a t a spacing o f 0.51nm (twice the monomer repeat (h) o f 0.255nm) i n d i c a t e d that the i d e a l i z e d t w e l v e - f o l d h e l i x i s s l i g h t l y d i s t o r t e d with d i f f e r e n c e s between the a x i a l p r o j e c t i o n o f c o n t i g uous monomers reducing the t w e l v e - f o l d symmetry t o s i x - f o l d . Secondly, i n the X-ray f i b r e d i f f r a c t i o n p a t t e r n s ( 3 2 ) i t i s evident that odd order l a y e r s are very weak, i n p a r t i c u l a r the 1st and 3rd. The c a l c u l a t e d c y l i n d r i c a l l y averaged F o u r i e r transform i n t e n s i t i e s o f a t w e l v e - f o l d h e l i x does not give r i s e to a pronounced weakness o f odd order l a y e r l i n e s , and the 1st l a y e r l i n e i s c a l c u l a t e d very s t r o n g . The weakness o f odd order l a y e r l i n e s has prompted s p e c u l a t i o n regarding the p o s s i b i l i t y of two p o l y s t y r e n e chains i n t e r t w i n i n g t o form a double h e l i x (35) s i m i l a r to the w e l l known concept i n DNA. X-ray d i f f r a c t i o n p a t t e r n s obtained from o r i e n t e d i s o t a c t i c p o l y s t y r e n e g e l s prepared from c i s - d e c a l i n (39) e x h i b i t very strong i n t e n s i t y on the 1st l a y e r l i n e as shown i n F i g u r e 2b. Such an o b s e r v a t i o n would not support i n any obvious manner a double h e l i c a l s t r u c t u r e f o r these o r i e n t e d i s o t a c t i c p o l y s t y r e n e gels. X-ray d i f f r a c t i o n r e s u l t s from o r i e n t e d p o l y s t y r e n e g e l s have shown that h i g h l y extended s t r u c t u r e s o f i s o t a c t i c p o l y s t y r e n e chains can e x i s t . These f i n d i n g s are c o n t r a r y t o the t r a d i t i o n a l textbook knowledge o f p o l y o l e f i n s and a l s o t o c o n c l u s i o n s o f recent conformational analyses (29,33,34). The d i f f e r e n c e s between the l a t t e r and our f i n d i n g s a r i s e p a r t l y through the p a r t i c u l a r choice o f non-bonded atomic r a d i i and a l s o from f r e e dom o f r o t a t i o n o f the aromatic s i d e groups about t h e i r l i n k i n g bond. T h i s h i g h l i g h t s the s u b t l e f a c t o r s which may determine the outcome o f conformational c a l c u l a t i o n s i n general (even to


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Figure 3. (a) (top) Projection perpendicular to helix axis of near «//-trans isotactic polystyrene tpl = 23.1° and xf/2 = 11.6°. The helix has 12 monomers in one turn with an axial advance per dimer of 0.51 nm. (b) (bottom) Projection down helix axis.


2.

ATKINS


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the extent of the q u a l i t a t i v e nature o f the c h a i n shape) and i n p a r t i c u l a r to the open-endedness o f conformational p o s s i b i l i t i e s in polyolefins.


4.

Summary

Improvements i n the c o l l e c t i o n and p r o c e s s i n g o f observed i n t e n s i t i e s are now being developed and a p p l i e d . We should expect i n the f u t u r e to request the two-dimensional d e n s i t o meter scan from authors i f one wishes t o re-examine a p a r t i c u l a r s t r u c t u r e determination. I n t e r t w i n i n g chain molecules c r e a t e c o n s i d e r a b l e problems f o r the f i b r e d i f f r a c t i o n i s t . There are two aspects i n t h i s area worth p a r t i c u l a r c o n s i d e r a t i o n . I t i s not d i f f i c u l t to imagine biopolymer chains being b i o s y n t h e s i s e d together and draping around each other. Once formed i t i s l o g i c a l to expect that untwining can occur given the a p p r o p r i a t e c o n d i t i o n s . F o r example c o l l a g e n chains separate on heating t o y i e l d g e l a t i o n . The mounting evidence i n the case o f the c u r d l a n t r i p l e h e l i x ( 1 3 ) i s that the chains can untwist s l i g h t l y (or t w i s t t i g h t e r ) under d i f f e r e n t c o n d i t i o n s g i v i n g r i s e to q u i t e d i f f e r e n t x-ray d i f f r a c t i o n p a t t e r n s as the symmetry i s destroyed. These changes should not be confused with complete untwining o f the c h a i n s . T h i s can be accomplished by more d r a s t i c chemical treatments where degradation a l s o takes p l a c e and untwining occurs o f the short segments (40). There i s no support at present f o r these chains to r e - i n t e r t w i n e (40). An untwining i s envisaged by Sarko (16,41 ) i n the case of A-amylose t o V-amylose. Thus the mechanistic problem o f untwining and r e t w i n i n g i n carrageenan g e l s i s s t i l l a major conceptual problem (42). Recent experiments by Smidsr^d(43)cast s e r i o u s doubt concerning the r e l a t i o n s h i p between untwining and r e t w i n i n g o f i n d i v i d u a l chains to form complexes and the a c t u a l mechanism o f g e l a t i o n (43). S o l u t i o n and g e l a t i o n s t u d i e s by S m i d s r 0 d ( 4 4 ) o f c a r r a geenans favour the i n t e r a c t i o n o f double-strand molecules && the b a s i c mechanism o f g e l a t i o n . C e r t a i n l y such a model eases the t o p o l o g i c a l problems a s s o c i a t e d with the i n t e r t w i n i n g mechanism. I f i t i s c o n v i n c i n g l y proved that i-PMMA i s a double h e l i x t h i s w i l l p r e c i p i t a t e much d i s c u s s i o n and a c t i v i t y concerning the mechanism o f p o l y m e r i z a t i o n . Does one c h a i n s t a r t forming and then act as a s u b s t r a t e t o encourage f a s t e r p o l y m e r i z a t i o n of another c h a i n on the s u b s t r a t e s u r f a c e ? Or do two chains come together with the c o r r e c t p o l a r i t y and i n t e r t w i n e i n order t o lower the f r e e energy ? C e r t a i n l y experiments should be undertaken on i-PMMA t o see i f there i s evidence f o r m e l t i n g apart o f the duplex, which i s only h e l d together by Van der Waals i n t e r a c t i o n s .



40

Acknowledgement s I wish to thank P r o f e s s o r s A. K e l l e r , G. C h a l l a and Dr. P. Lemstra f o r v a l u a b l e d i s c u s s i o n s and the Science Research C o u n c i l f o r f i n a n c i a l support. Literature Cited


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RECEIVED June 10, 1980.


Fiber Diffraction Methods - American Chemical Society

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