Electron Crystal Structure Analysis of Linear ... - ACS Publications

22 Electron Crystal Structure Analysis of Linear Polymers—An Appraisal D O U G L A S L . D O R S E T and B A R B A R A MOSS

Downloaded by TUFTS UNIV on October 19, 2016 | http://pubs.acs.org Publication Date: June 1, 1983 | doi: 10.1021/ba-1983-0203.ch022

Medical Foundation of Buffalo, Inc., Electron Diffraction Department, Buffalo, N Y 14203 Many microcrystalline linear polymers have been found to give good single crystal electron diffraction patterns; yet such intensity data are used only rarely for crystal structure analysis. Although the earliest assumptions made for such data are not rigorously true, the kinematical diffraction approach used in x-ray crystallography often will yield correct structural results. Thus, standard phasing methodologies—for example, use of Patterson maps, direct phasing,—can be quite satisfactory. Two important perturbations to diffracted intensities, resulting from n-beam dynamical scattering and elastic crystal bending, must be recognized and minimized to guarantee the derivation of real crystal structures. The first-named perturbation is minimized by restricting crystal thickness and/or selecting an appropriate electron wavelength. Because elastic bends of a few degrees are always present in thin molecular crystals, the latter perturbation is most noted when the unit cell length in the direction of the incident beam is large. Fortunately, a short unit cell repeat in this (fiber axis) direction is often found for polymer crystals. The influence of n-beam dynamical scattering and elastic crystal bending is demonstrated by model calculations on cytosine and representative polymer structures.

JELECTRON D I F F R A C T I O N is u s e d frequently i n p o l y m e r physics to d e termine the u n i t c e l l dimensions and symmetry for molecular p a c k i n g i n single microcrystals. A s frequently p o i n t e d out (J), the e n h a n c e d scattering cross-section o f matter for electrons (compared to x-rays or neutrons) allows the a c q u i s i t i o n of information u n o b s c u r e d b y the overlap of reflections w i t h near-reciprocal spacing found i n p o w d e r diffraction patterns. 0065 - 2393/83/0203-0409$06.00/0 © 1983 American Chemical Society

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.


410

POLYMER CHARACTERIZATION

D e s p i t e its popularity, electron diffraction is u n d e r u t i l i z e d b y p o l y m e r scientists. Quantitative use of intensity data for crystal struc ture analysis is attempted only rarely a n d then by only a very small n u m b e r of research groups i n the w o r l d . T h i s situation is difficult to comprehend g i v e n the potential for a crystal structure analysis. P o l y mer crystals, after a l l , are not often grown to sizes large enough for single-crystal x-ray experiments. Reluctance to use such intensity data reflects a basic m i s u n d e r standing of their d o m a i n of validity. E a r l y use of such data for organic crystal structure analysis (2), w h i c h demonstrated the promise of the technique, adopted too many assumptions used for x-ray crys tallography. Resultant analytical procedures seemed to vary from c o m p o u n d to c o m p o u n d . D e s p i t e this situation, the agreement be t w e e n observed a n d calculated structure factor m o d u l i often r e m a i n e d poor. F u r t h e r m o r e , most crystal structures reported h a d b e e n deter m i n e d previously u s i n g x-ray data. T h e s e factors a l l contributed to w i d e s p r e a d mistrust of the technique. O v e r the past few years, w e have sought a realistic understanding of the perturbations that l i m i t the use of such data for ab initio crystal structure determination. Although this work continues, a self-consis tent overview emerges that shows w h y some of the conceptual models used i n x-ray crystallography are not appropriate for electron crystallog raphy. O n the other hand, minimization of data perturbations allows the use of electron diffraction intensities for crystal structure analysis, as is also demonstrated b y the increasing n u m b e r of p o l y m e r crystal structures d e r i v e d from such data (3—11). η-Beam Dynamical

Scattering

H i g h - e n e r g y electron beams have small wavelengths compared to x-ray$ (at 100 k V , 0.037 Â vs. 1.54 A for C u K a x-rays), resulting i n a E w a l d s a m p l i n g sphere that is approximately a plane (i.e., many diffracted beams are excited simultaneously instead of one). G i v e n the larger scattering cross-section of matter for electrons (2) (f i/fx-ray 10 ), a d y n a m i c a l description of many beam interactions s h o u l d be more appropriate than the k i n e m a t i c a l one, w h i c h assumes the i n d e p e n d e n c e of all diffracted beams (12). Unfortunately, adherence to the kinematical approximation allows the most direct determination of a crystal structure from diffraction data. E x p e r i m e n t a l conditions must be established to approach this i d e a l to ensure the success of the analysis. Originally, researchers thought that t h i n microcrystals used for electron diffraction w o u l d conform to the mosaic m o d e l used i n x-ray crystallography. E a c h microblock i n a mosaic was i m a g i n e d to be so oriented that only one strong reflection was excited from it (13) and e

3


=


22.

DORSET A N D MOSS

Electron Crystal Structure

Analysis

411

was used as a justification for the kinematical scattering approxima tion. If mosaic block sizes were large enough to cause interaction b e t w e e n the i n d i v i d u a l diffracted beams and the i n c i d e n t beam, then a two-beam d y n a m i c a l correction was made (i.e., a primary extinction correction). H o w e v e r , experimental application of this correction was inconsistent and s h o w e d a w i d e variability i n the relation b e t w e e n corrected structure factor magnitudes and the measured diffraction intensities. Sometimes mosaic block shapes were incorporated as an additional variable (14). C e r t a i n l y , organic microcrystals contain de fects that w o u l d account for a mosaic of domains w i t h i n t h e m , but their concentration does not appear large enough to justify this m o d e l (J5). T h e crystals used for electron diffraction experiments are largely perfect; the mosaic block size is generally larger than the coherence w i d t h of the i n c i d e n t b e a m (12). Consistent w i t h the notion of crystal perfection, η-beam interac tions may be demonstrated i n t h i n molecular crystals, for example, i n experiments w i t h monomolecular layers of orthorhombic n-paraffins, w h i c h may be regarded as an oligomeric form of polyethylene. U s e of such crystals has established the presence of η-beam effects i n four ways (to be discussed i n d i v i d u a l l y i n the f o l l o w i n g sections). F i t of O b s e r v e d D a t a w i t h C a l c u l a t i o n . η-Beam d y n a m i c a l c a l culations of the m u l t i s l i c e type (12) or using the phase grating ap proximation (12) give the best explanation of specific diffraction i n tensities that differ from their kinematical values. This has been shown for paraffins as w e l l as short- a n d long-chain polyethylenes (16, 17). Intensity Change w i t h Increasing E l e c t r o n Accelerating Voltage. E l e c t r o n diffraction intensities from paraffin taken w i t h beam acceler ating voltages up to 1000 k V are accordant w i t h the η-beam d y n a m i c a l theory (18). T h e r e is no actual realization of kinematical diffraction at h i g h voltage as w o u l d be predicted by the two-beam diffraction theory. B e h a v i o r of C o n t i n u o u s l y E x c i t e d Diffracted Beams w i t h Change of Crystal Orientation. I f a row of diffraction beams coincides w i t h a tilt axis for the crystal, t h e n the continuously excited intensities w i l l change d u r i n g tilt only i f η-beam d y n a m i c a l interactions are present. T h i s behavior was shown for t h i n crystals of a wax (17). T h e demonstration of η-beam interactions has b e e n important for the conception of a realistic crystal m o d e l . H o w e v e r , their influence on ab initio crystal structure analyses also is important. Rigorous n beam dynamical calculations were carried out for a representative molecular crystal structure, cytosine, considering a projection d o w n the shortest u n i t c e l l axis at two accelerating voltages. S u c h data were sampled at increasing crystal thicknesses and used naively as i n p u t diffraction data for an automated direct phasing computer program. A t



412


100 k V , these diffraction data y i e l d e d false crystal structures for thicknesses above 75 Â; at 1000 k V the m a x i m u m acceptable crystal thickness is around 300 Â (J 9). T h e importance of η-beam dynamical scattering also can be as sessed for p o l y m e r structures solved from electron diffraction data. F o u r such structures are s u m m a r i z e d i n T a b l e I. M u l t i s l i c e n-beam calculations generally do not change the agreement between ob served and calculated structure factors appreciably. T h e polymers listed have far fewer repeats w i t h i n the reported crystal thicknesses than polyethylene (40 repeats for a 100-Â thickness). Therefore, the diffraction data are not changed appreciably by d y n a m i c a l scattering, e v e n though this description of the scattering process is the most r i g orous. A n exception is found for poly(e-caprolactone) for w h i c h best agreement w i t h experiment was obtained at a thickness of 156 Â or n i n e u n i t c e l l repeats. H o w e v e r , for the hkO zone, there is effectively a s u b c e l l of length 2.47 Â i n the beam direction, so that the structure factors at 156 Â thickness are indicative of 63 repeat units. T h i s f i n d i n g explains the great difference b e t w e e n the d y n a m i c a l (R = 0.16) and kinematic (R = 0.27) results. Elastic Crystal

Bending

A l t h o u g h t h i n crystals used for electron diffraction experiments are often nearly perfect i n terms of defect concentration, they are also commonly deformed b y the substrate surface. E l a s t i c b e n d i n g of such crystals is observed easily i n low-magnification diffraction contrast electron micrographs taken at low-beam doses. Because such bends are only over a few degrees, this property can cause a severe change i n the diffracted intensities, particularly i f the u n i t c e l l repeat along the i n c i dent beam direction is large (20). U s i n g an analytical procedure proposed by C o w l e y (20), w h i c h considers a Patterson function altered b y a Gaussian term dependent on the crystal curvature a n d the unit c e l l length along the i n c i d e n t beam, b e n d i n g was s h o w n to explain apparent diffraction coherence restrictions from various paraffinic crystals for w h i c h the true u n i t c e l l is m u c h longer than the c h a i n zig-zag repeat (17, 21). These c a l c u l a tions show that solution growth of molecular crystals gives the least favorable projection for a n electron diffraction experiment because the longest u n i t c e l l axis is commonly normal to the best-developed crystal face. E p i t a x i a l crystal growth, w h i c h forces a shorter axis i n this d i r e c t i o n , allows the collection of diffraction data that are more representative of the total u n i t c e l l (17). M a x i m u m Patterson vector components i n the beam direction, and thus the attenuation of them caused b y the crystal b e n d i n g , are smaller. C o n s e q u e n t l y , bends have less impact on the diffracted intensity for these zones.



Best agreement (R = 0.21) at b e n d ±2° a n d temperature factor Β = 6 A ; originally c i t e d R ~ 0.25 Best agreement Β = 12 A at b e n d ± 8 ° , R = 0 . 2 5 ; significant improvement

N o significant i m p r o v e m e n t ; however, only six monomer repeats for c i t e d crystal thickness; b e s t R = 0.25 Best agreement R = 0.36 at t = 56 A (estimated thickness of 80 A only four monomer repeats); R = 0.34 c o m p a r i n g data to kinematical model A considerable i m p r o v e m e n t over the k i n e m a t i c m o d e l ; R = 0.16 compared to R = 0 , 2 7 at t = 156 A ; n i n e unit c e l l repeats

A n h y d r o u s nigeran a = 17.76 A , b = 6.0 A c(fiber) = 14.62 A

Polytrimethylene terephthalate a = 4 . 6 4 A , b = 6.27 A , c(fiber) = 18.64 A a = 98.4°, β = 93.0°, y = 111.1°

Poly(€-caprolactone) a = 7.496 A , b = 4.974 A , c(fiber) = 17.297 A

2

Best agreement Β = 5 A at b e n d ±3°, R = 0.23

2

A l s o , no real i m p r o v e m e n t ; crystals d e s c r i b e d as b e i n g particularly rigid

I n agreement w i t h original f i n d i n g , o n l y a slight improvement; however, o n l y 14 m o n o m e r repeats for c i t e d crystal thickness

a-Poly[3,3-bis(chloromethyl) oxacyclobutane] a = 17.85 A , & = 8.15 A , c(fiber) = 4.78 A

2

Correction for Crystal Bending

Structure

Multislice η-Beam Calculation

Table I. Attempted Intensity Data Corrections for Published Polymer Structures


414


Fortunately, the fiber repeat of many p o l y m e r structures is s m a l l enough to a l l o w collection of useful diffraction-intensity data. H o w ever, for the three structures i n T a b l e I w i t h longest fiber repeats, a correction for elastic b e n d i n g p r o d u c e d a significantly i m p r o v e d fit of observed and calculated data.


Crystal Structure

Analysis

I f the caveats m e n t i o n e d earlier are observed, the electron diffraction intensity data from t h i n organic crystals are useful for structure analysis. I n fact, the tendency of polymers to form extremely t h i n microcrystals of the order of 100 Â makes them particularly suitable. T h e experiment also i m p l i e s a m i n i m i z a t i o n of radiation damage by use of fast photographic films a n d l o w electron beam doses, as is d i s cussed often. P r e l i m i n a r y " L o r e n t z factor" corrections were not found useful (16). Intensities are taken directly from integration of densitometer scans across a diffraction film w i t h due attention p a i d to the possible errors caused b y nonlinearities, as described b y Wooster (22). Phasing of diffraction data can be approached i n as many ways as used i n x-ray crystallography. B o t h Patterson techniques and trial a n d error have b e e n successful. I f there are an adequate n u m b e r of large n o r m a l i z e d structure factors i n the experimental diffraction data for each atom i n the asymmetric unit, direct phasing methods can be used (19, 23). Z o n a l diffraction data from l i n e a r p o l y m e r crystals, however, often represent a s m a l l n u m b e r of reflections per atom. T o create a realistic n u m b e r of variable parameters for such l i m i t e d diffraction data, k n o w n skeletal structures of monomers or oligomers are assumed to be unchanged i n the p o l y m e r , but their mutual conformations are v a r i e d b y rotations about linkage bonds. I n such a p h a s i n g procedure, a match of p a c k i n g energy m i n i m u m w i t h R - v a l u e m i n i m u m is u s e d to specify the best structural m o d e l (9). Refinement of the structures must incorporate corrections for either η-beam scattering or crystal b e n d i n g , d e p e n d i n g on w h i c h perturbation w i l l have the most effect on the experimental intensities. Such corrections a l l o w construction of structural models w i t h p h y s i cally realistic thermal parameters (see T a b l e I), a feature d i s a l l o w e d i n earlier k i n e m a t i c a l treatment of such data (7—11, 16), a n d stress the importance of their i n c l u s i o n i n a crystallographic analysis. F o r this refinement, however, additional information should be k n o w n about the crystals, i.e., there must be some estimate of crystal thickness a n d also diffraction contract micrographs to estimate crystal curvature. B o t h corrections i m p l y that the structure is k n o w n i n three d i m e n sions. C u r r e n t l y , this third d i m e n s i o n is inferred from a structural


22.

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Analysis

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m o d e l but s h o u l d be directly obtainable from three-dimensional dif fraction data resulting from a tilt experiment.


Future

Investigations

Several directions for future work are clearly indicated. O n e of these areas is a c o m b i n e d treatment of b e n d i n g and d y n a m i c a l dif fraction to assess h o w these perturbations to intensity data may inter act. C a l c u l a t i o n of the η-beam d y n a m i c a l interactions from a c u r v e d paraffin crystal and representative linear polymers, now i n progress, may give insight into these interactions. A n o t h e r very important consideration is the o p t i m i z e d collection of three-dimensional electron diffraction intensities. T h i s gathering w o u l d , of course, a l l o w a m u c h more accurate determination of a crystal structure a n d , w i t h an increased n u m b e r of data, may a l l o w the general use of direct phasing methods for organic crystals, i n c l u d i n g linear polymers. A short u n i t c e l l axis i n the beam direction, posited by epitaxial growth for molecular organic crystals, or p r o v i d e d already b y the fiber repeat of many polymers, gives more confidence i n the intensity data from slightly curved crystals. T i l t of a crystal up to the commonly found 60° goniometer l i m i t c o u l d double the crystal repeat along the beam. I f this value remains tolerably small, then a threed i m e n s i o n a l data set c o u l d be used. T h e utility of such threed i m e n s i o n a l data has b e e n demonstrated already for t h i n protein crys tals (24). Acknowledgments Research was supported by P u b l i c H e a l t h Service Grant N o . G M - 2 1 0 4 7 from the N a t i o n a l Institute of G e n e r a l M e d i c a l Sciences and by N a t i o n a l Science F o u n d a t i o n Grant Nos. P C M 7 8 - 1 6 0 4 1 and CHE79-16916. Literature Cited 1. Brisse, F.; Marchessault, R. H. In "Fiber Diffraction Methods"; French, A. D.; Gardner, Κ. H., Eds.; ACS SYMPOSIUM SERIES No. 141, ACS: Washington, DC, 1980; p. 267. 2. Vainshtein, Β. K. "Structure Analysis by Electron Diffraction"; Pergamon: Oxford, 1964. 3. Tatarinova, L. I.; Vainshtein, Β. K. Vysokomole. Soedin., 1962, 4, 261. 4. Vainshtein, B. K.; Tatarinova, L. I. Sov. Phys. Crystallogr. 1967, 11, 494. 5. Claffey, W.; Gardner, K.; Blackwell, J.; Lando, J.; Geil, P. H. Philos. Mag. 1974, 30, 1223. 6. Claffey, W.; Blackwell, J. Biopolymers 1976, 15, 1903. 7. Roche, E.; Chanzy, H.; Boudeulle, M.; Marchessault, R. H.; Sundararajan, P. Macromolecules 1978, 11, 86. 8. Poulin-Dandurand, S.; Perez, S.; Revol, J. F.; Brisse, F. Polymer 1979, 20, 419. 9. Perez, S.; Roux, M.; Revol, J. F.; Marchessault, R. H. J. Mol. Biol. 1979, 129, 113.


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10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Day, D.; Lando, J. B. Macromolecules 1980, 13, 1483. Noe, P., Mc.Sc. Thesis, Univ. of Montréal, Montréal, Canada, 1979. Cowley, J. M. "Diffraction Physics"; North-Holland: Amsterdam, 1975. Vainshtein, Β. K. Sov. Phys. Crystallogr. 1956, 1, 15. Lobachev, A. N.; Vainshtein, Β. K. Sov. Phys. Crystallogr. 1961, 6, 313. Dorset, D. L. J. Polym. Sci., Polym. Phys. Ed. 1979, 17, 1797. Dorset, D. L. Acta Crystallogr. 1976, A32, 207. Ibid., 1980, A36, 592. Dorset, D. L. J. Appl. Phys. 1976, 47, 780. Dorset, D. L.; Jap, B. K.; Ho, M.-S.; Glaeser, R. M. Acta Crystallogr. 1979, A35, 1001. Cowley, J. M. Acta Crystallogr. 1961, 14, 920. Dorset, D. L. Z. Naturforsch. 1978, 33A, 964. Wooster, W. A. Acta Crystallogr. 1964, 17, 878 Dorset, D. L.; Hauptman, H. A. Ultramicroscopy 1976, 1, 195. Unwin, P.N. T.; Henderson, R. J. Mol. Biol. 1975, 94, 425.


20. 21. 22. 23. 24.

RECEIVED for review October 14, 1981. ACCEPTED December 16, 1981.


Electron Crystal Structure Analysis of Linear ... - ACS Publications

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