Proc. Natl. Acad. Sci. USA Vol. 88, pp. 5499-5502, July 1991 Chemistry Electron crystallography of linear polymers: Direct structure analysis of poly(E-caprolactone) (electron diffraction/direct methods/crystal structure analysis/polymer crystal structure) DOUGLAS L. DORSET Electron Diffraction Department, Medical Foundation of Buffalo, Inc., 73 High Street, Buffalo, NY 14203 Communicated by Herbert A. Hauptman, April 8, 1991 (receivedfor review, January 21, 1991) ABSTRACT Three-dimensional electron diffraction inten- was reported (5) based on the direct phasing of three- sity data from poly(e-caprolactone) are used for an ab initio dimensional electron diffraction data. Although it might be phase determination based on the probabilistic estimate of argued that this is a special case, where the essentially three- and four-phase structure invariants in space group single-atom structure favors the success ofthe ab initio phase P212121. From the initial phase set of 30 reflections (two of determination, the notion that this direct analysis may have which are incorrect) of the 47 in the total data set, computed wider application in the electron crystallography of linear electrostatic potential maps produce a recognizable structure polymers is demonstrated in this paper, which describes the that can be refined by Fourier techniques and atomic displace- crystal structure analysis of poly(E-caprolactone). ment. The final structure (R = 0.21), which is very similar to one found in an earlier fiber x-ray study, shows that the polymer chain must adopt a nonplanar conformation around MATERIALS AND METHODS the ester linkage. As described in an earlier paper (6), samples of poly(E- Because of the difficulty in crystallization of linear polymers, caprolactone) [Mw (weight-average molecular weight) = electron diffraction techniques have been often used to obtain 14,600; Mn (number-average molecular weight) = 9300] were single-crystal information from lamellar plates grown by the epitaxially oriented on benzoic acid by the technique of self-seeding technique, enabling one to take advantage of the Wittmann et al. (7), and the crystallinity of the samples was favorable scattering cross-section of matter for electrons to improved by annealing the polymer at 500C in the presence of obtain a useful scattering signal from a thin microcrystal. this substrate. Selected area electron diffraction patterns Intensity data in these electron diffraction patterns have been from these microcrystals (estimated to be <100 A thick), used in quantitative structure analyses, initially in two- obtained at 100 kV on a JEOL JEM-100CXII, could be dimensional projections down the chain axes but more recently recorded from the (Okl) reciprocal plane (untilted crystals) or in three dimensions, with data taken from tilted single micro- the (hhl) reciprocal plane (obtained when the crystals are crystals (1). Even though single-crystal electron diffraction data tilted 30-35° around c*, the reciprocal unit cell axis along the from such samples permit the unit cell and space group to be molecular chain). [Prints of these electron diffraction pat- defined unequivocally because the diffraction peaks are well- terns were published earlier (6).] Solution-crystallized sam- separated from one another (in contrast to a fiber diffraction ples, similarly, could be used to record hk0 data. The pattern), the number ofmeasured intensities is still rather small intensity data were quantitatively measured from scans ofthe when compared with the number of measurements used for a diffraction films with a Joyce Loebl MkIIIC flat-bed micro- typical x-ray crystal structure analysis. densitometer. To avoid saturation of the photographic film Given the small number of intensity data and the resultant response to the scattered electrons, differently timed expo- statistical problems encountered thereby in defining the best sures were used to record the diffraction patterns. fit of a model to the experimental measurements (2), a rather The noncentrosymmetric orthorhombic space group of the elaborate procedure is used to determine polymer crystal unit cell is P212121 (D2, no. 19 ofref. 8). Unit-cell constants, in structures with electron diffraction data. Generally, the x-ray good agreement with fiber x-ray determinations (9, 10), are: crystal structures of a monomer or a number of oligomeric segments are determined first to determine molecular geo- a = 7.48 ± 0.02, b = 4.98 + 0.02, c = 17.26 ± 0.03 A. metric parameters, which can be assumed to remain rigidly fixed in an analysis of the infinite polymer structure (3, 4). It should be emphasized that all unit-cell measurements were These invariant molecular moieties are then concatenated made from the electron diffraction patterns. into the infinite chain via "linkage bonds," at which confor- Direct phase determination was based on the probabilistic mational twists are permitted. Rotational orientations around estimate of three (triplet)- and four (quartet)-phase structure these linkage bonds are then monitored by simultaneous invariants in this space group (11, 12)-i.e., respectively minimizations of an internal energy (calculated with non- bonded atom-atom potential functions) and the crystallo- 1 = Ohl + h2 + h3 graphic R factor to determine which chain conformer is most likely to be correct. and There is very little experience, on the other hand, with ab initio structure analyses based solely on the electron diffrac- 4, = Ohl + 4h3 + 1h3 + Oh4 tion intensity with no assumptions made about the molecular geometry. Recently, the crystal structure of polyethylene where Xi hi 0 applies to the Miller index values. These invariants are ranked according to the values of The publication costs of this article were defrayed in part by page charge 2 payment. This article must therefore be hereby marked "advertisement" A = N12 in accordance with 18 U.S.C. §1734 solely to indicate this fact. lEhEh,2Eh3 5499 Downloaded by guest on September 23, 2021 5500 Chemistry: Dorset Proc. Natl. Acad. Sci. USA 88 (1991) and B = - + + IEh+I - 2], N IEh1Eh2Eh3Eh4I[IEh,+l2 IE+h3I2 with the highest values being most probable, where N = 32 is the number of nonhydrogen atoms in the unit cell. The normalized structure factors JEhl are calculated from ob- served amplitudes IFhI as usual-i.e., IEhI2 - FhJN scaled such that (JEhJ2) = 1.0. 6i Here, fi are atomic scattering factors, and e is a multiplicity factor accounting for translational space group symmetry (E = 2 for hOO, OkO, and 001 reflections in P212121 and E = 1 for all other hkl reflections). To obtain initial phases Oh in order to find other phase values from the simultaneous equations above, one is per- mitted to set the values of three reflections having allowable Miller index parity (11) to define the origin. Ifh, = h1kl1, then these index values cannot be all even (e); nor can 7,i hi = eee. For the noncentrosymmetric space group, a fourth reflection can be chosen to fix the enantiomorph. For this assignment, some Xi hi eee is allowed, but the summation of phases must be ±+r/2 for this structure to be semi-invariant so that FIG. 1. Final electrostatic potential map for poly(E-caprolactone) in the projection down the a = 7.48-A axis. Most of the atomic it corresponds to a unique choice of enantiomorph. positions (which are indicated for one polymer chain) are well resolved in this projection. PHASE DETERMINATION all involve the 4210 phase value and, if 25 correct quartet Because of the geometry ofthe diffraction experiment, zonal invariants are used to Bmin = 2.05, this phase is correctly reflections in the list of 47 reflections belong to the index assigned the value 0 by the weight of seven correct assign- groups Okl and hkO. Since these have restricted centrosym- ments vs. four incorrect ones. All hkO data, therefore, are metric phase values (8), representatives of these groups are given phase values from these invariants. The Okl reflections used to define the origin and enantiomorph. For origin are found mostly in triplets incorporating nonzonal, noncen- selection H1elo, 40320, and 0017 are defined, and the value of trosymmetric hkl reflections. By using the enantiomorph- 4038, which forms a semi-invariant with the first two reflec- defining reflection given above, the approximate phase val- tions, is used to specify the enantiomorph. Next, so-called ues of many three-dimensional reflections can be found, but "sigma 1 (h1)" three-phase invariants (11) were generated a few are related to one another by an algebraic unknown c where h, = h2 = -Y/2h3. From these triplets, the value of one (Table 1) which requires the calculation of two Fourier maps phase, 02m = ir, was accepted for the highest positive Al = from the 30 phased structure-factor amplitudes to find a [(IEhl)2 - 1)]IE2hI/N1/2 = 4.48. Thus, the five values are used recognizable molecular geometry. This occurs for c = 0. to evaluate the Y2 three-phase invariants (where, in general, Note also that two initial phase estimates in Table 1 are h, = h2 i h3), as well as the four-phase invariants, defined incorrect. above. The most prominent phase relations in the triplet and quartet invariants are among the hkO reflections, representing STRUCTURE REFINEMENT a projection down the polymer chain. Of these 45 X2 triplets Although all the measured hkO reflections are assigned phase evaluated to Amin = 0.20, 4 were found to be incorrect. These values, it is not possible to resolve individual projected chain Table 1. Initial phase set from analysis of triplets and quartets atoms in the electrostatic potential map calculated in the [001] projection. However, the general positions of the chain Origin: 011o = 1r/2, 1320 = ir/2, 4017 = ir/2 density in the unit cell are clearly defined. Calculation of the Enantiomorph: 0038 =-/2 map with Okl data is more informative since atomic positions 21 triplet: (200 = T along the zig-zag are resolved. This allows one to find hk0 zonal 12 triplets and quartets: Table 2.