J. Phys. Chem. B 2001, 105, 5139-5143
5139
Crystal Structure of Wax Lamellar InterfacessA Residual Petroleum Fraction Characterized by Electron Crystallography Melanie Rademeyer Department of Chemistry and Biochemistry, Rand Afrikaans UniVersity, P.O. Box 524, Auckland Park 2006, South Africa
Douglas L. Dorset*,† Electron Crystallography Laboratory, Hauptman-Woodward Medical Research Institute, Inc., 73 High Street, Buffalo, New York 14203-1196 ReceiVed: NoVember 17, 2000; In Final Form: March 26, 2001
After a multicomponent paraffin assembly was constructed to model a petroleum residue wax (Mw/Mn ) 1.009), its structure was characterized by electron crystallography. Consistent with a single lamellar spacing, two endotherms in a DSC scan are typical of paraffin chain solid solutions and represent the premelt transition to a “rotator” phase and the true melt. The average chain packing in the crystal structure is that of the paraffin n-C32H66, in space group Pca21 with a ) 7.42, b ) 4.96, and c ) 85.0 Å. An attempt to account for the lamellar disorder with a chain-end occupancy model based on the chemical distribution of chain lengths is only partially successful. A better fit is found when lower chain-end occupancies are used. This discrepancy could be due to conformational defects in which the chain end atoms do not lie on strict methylene subcell lattice sites.
Introduction Recently, single-crystal electron diffraction data from polydisperse assemblies of linear alkanes have effectively distinguished the structure of true lamellar waxes from those in which well-defined layers are never formed.1 It is now clear why the former, exemplified by relatively narrow petroleum distillate cuts, are physically deformable solids whereas the latter, exemplified by as-synthesized Fischer-Tropsch products and low-molecular-weight linear polyethylene, are brittle solids. With lamellar layering, defects due to chain length differences, including nonplanar conformations, are concentrated at a layer surface.2-4 For the brittle solids in which lamellae are never formed, there is only an average “nematocrystalline” ordering of the chain axes, leading to an internally reinforced chain packing array, despite an often larger polydispersity value.1 The distribution of chain disorder has often been studied in lamellar waxes. It readily became apparent that, in terms of diffraction experiments, a suitable model at layer surfaces for dissimilar chain lengths within a lamella would include a distribution of fractional methylene atomic occupancies,5 with the greatest deviation from unity occurring at the surface. Spectroscopic measurements, on the other hand, indicate that the packing arrangement might be more complicated than just partial methylene group occupancies. A more realistic structure would include, for example, nonplanar conformational defects.4 Recently,2 a Gaussian model for fractional occupancy was correlated to a lamellar disorder term described by Strobl and co-workers6 and was shown to account well for the falloff of lamellar diffraction peaks in patterns from a number of paraffin waxes. Later, the accuracy of this model was questioned3 * Author to whom correspondence should be addressed. † Current address: ExxonMobil Research and Engineering Co., 1545 Route 22 East, Annandale, NJ 08801.
because, in principle, this distribution of chain methylene positions should be related to the actual chemical distribution of chain lengths within the solid. After examination of a polydisperse artificial wax with very low polydispersity (Mw/Mn ) 1.003)3 based on one characterized earlier by Stokhuyzen and Pistorius,7 it was decided that a model accounting for the actual chain length distribution was more accurate than the best Gaussian distribution of methylene occupancies. In this paper, a wax with a broader distribution is studied to evaluate this chemically based model further. Materials and Methods Model Wax and Its Crystallization. The model paraffin wax used in this study was based on a residual petroleum wax, termed “Wax J” when originally characterized by Gupta and Severin8 using high-temperature gas chromatography and supercritical fluid chromatography to determine the carbon chain distribution. The original residual wax comprised a distribution of chains from n-C21H44 to n-C39H80, with the assayed concentrations of individual species tabulated by these authors.8 For this study, a closely similar chain distribution (Figure 1) was obtained by weighing pure n-paraffins into a vial. This mixture was then co-melted on a hot plate, cooled, broken up and stirred, and remelted several times to obtain a uniform solid solution. From the known chain length distribution, the calculated polydispersity9 (Mw/Mn) is 1.009. A DSC measurement of the reconstructed wax (Figure 2) yields results typical of narrow distillate cuts8 where one can discern a premelt transition of an orthorhombic solid to a rotator phase before the true melt. The appearance of the premelt transition indicates the presence of a stable paraffin solid solution, as is also supported by diffraction measurements. The premelt temperature of 55.6° and the melt temperature of 65.7
10.1021/jp004233o CCC: $20.00 © 2001 American Chemical Society Published on Web 05/09/2001
5140 J. Phys. Chem. B, Vol. 105, No. 22, 2001
Rademeyer and Dorset
Figure 1. As-weighed chain length distribution for paraffin model for a previously characterized8 petroleum residual wax.
Figure 2. DSC of the model paraffin wax with an endotherm due to a premelt rotator phase followed by one due to the true melt.
°C in the artificial chain assembly can be compared to the respective values 53.4 and 64.7 °C for the actual residual wax sample.8 The model residual wax was crystallized for electron diffraction study using an epitaxial orientation method originally designed by Wittmann, Hodge, and Lotz.10 First a dilute solution of the material was prepared in light petroleum, and a drop of this soution was evaporated onto the surface of a freshly cleaved mica sheet to leave a thin film of the paraffinic mass. Carbonfilm-covered 300-mesh electron microscope grids were then placed face-down on the wax film, and an excess of benzoic acid crystal was distributed over this surface. After the other half of the mica sheet was placed over this assembly to create a sandwich, the total organic mass was first melted and then rapidly cooled by sliding the sandwich along a thermal gradient created by spanning a hot plate and thermoelectric cold plate with an aluminum bar. Epitaxial nucleation of the chains was therefore achieved on the benzoic acid diluent crystals as described by a phase diagram.11 After the mica sheets were separated to reveal the organic solid, the benzoic acid was removed by sublimation in high vacuum overnight. The electron microscope grids, containing the oriented crystals, could then be inserted into the electron microscope for electron diffraction studies. Electron Diffraction and Intensity Measurements. All electron diffraction experiments were carried out at 100 kV and room temperature with a JEOL JEM-100CX II electron microscope equipped with a (60° tilt goniometer stage. Low beam dose conditions were maintained to minimize radiation damage to the specimens.12 Selected areas for these experiments had nearly 10 or 3.0 µm diameters, as calibrated by carbon replicas of diffraction gratings. Diffraction patterns were recorded on Kodak DEF-5 X-ray film, which was then developed in an
Figure 3. Experimental electron diffraction patterns for epitaxially oriented model residual wax: (a) 0kl, (b) hhl.
Industrex developer. Ultimately, all diffraction spacings were calibrated against a gold powder diffraction standard, but it was also useful to use the d020 spacing from the wax as an internal secondary standard,2 assuming it to be near 2.48 Å. For collection of three-dimensional electron diffraction data from the epitaxially oriented wax samples, both the 0kl (0° tilt around c*) and hhl (33° tilt around c*) orientations were sampled (Figure 3). The latter experiments utilized a Gatan 650 Mk 1 sample holder that permitted continuous rotation of the grid at any tilt angle to align c* with the tilt axis of the specimen rod. Although other zonal projections could be accessed experimentally, the above orientations are the most informative diffraction nets for structure analysis. Diffraction peak intensities were measured from the films by scanning them on a Joyce-Loebl Mk III C flat-bed microdensitometer. Peak areas were approximated by triangular fits, and as is usual for selected area diffraction experiments on organic crystals,13 the internal consistency of the diffraction data (for symmetrically equivalent reflections and equivalent diffraction patterns, respectively) was ascertained by Rsym and Rmerge, where
R)
∑h ||F(h)1| - g|F(h)2||/∑h |F(h)1|
Agreements with R e 0.15 were sought.13 As is usual, no Lorentz correction was made to the raw intensities because of the elastic bend deformation of the microcrystalline samples.12 Crystal Structure Analysis. Although it is possible, in principle, to determine the crystal structures of n-paraffins and
Crystal Structure of Wax Lamellar Interfaces
Figure 4. Overall chain packing scheme for model wax based on pure n-C32H66 paraffin in space group Pca21: (a) [100] projection, (b) [010] projection.
Figure 5. Potential map, [100] projection, for model residual wax, revealing fractional occupancies for chain positions near the lamellar surfaces.
their solid solutions by direct methods from electron diffraction intensities,14 the carbon framework of the waxes can be simply related to that of the analogous pure paraffin. In this study, attention was focused on finding the best model to account for the observed falloff of low-resolution 00l “lamellar” intensities. Details of such model construction will be reviewed below. Results Representative electron diffraction patterns from two zonal projections of reciprocal space are shown in Figure 3. For each pattern, only a single lamellar repeat was observed, indicating again that the co-mixture crystallized as a solid solution. Measured lamellar spacings have an average value of c/2 ) 42.5 ( 0.2 Å. Using previously established indexing rules for the 01l row,2 i.e., l ) m, m + 2 for the strongest reflections, the most commonly found layer structure mimicking that of a pure paraffin n-CmH2m+2 was found at m ) 32. Accordingly, the lamellar spacing for orthorhombic n-C32H66 was calculated by Nyburg and Potoworowski15 to be 42.49 Å, identical to the result cited above. Observed reflection indices for 0kl and hhl patterns are consistent with space group Pca21, the common orthorhombic polymorph of even-chain paraffins.16 Unit cell constants of a ≈ 7.42, b ≈ 4.96, and c ) 85.0 Å were used for the crystal structure determination. Using the crystal structure packing for orthorhombic n-C36H74 scaled to the n-C32H66 homologue to give atomic coordinates, an R value of 0.32 was observed for BC ) 2.0 and BH ) 4.0 Å2. All atoms were given unitary occupancy. (For successive calculations, these isotropic temperature factors were retained.) The chain packing model, assuming unitary occupancies, is shown in Figure 4. If the crystallographic phases from this model are applied to the observed structure factor amplitudes, the potential map in Figure 5 is observed. Note that the unitary occupancy model is not reproduced at the chain ends. It was obvious that a fractional occupancy model was required for the chain packing to account for the distribution of chain lengths in a single lamella. In keeping with the recent study by Stokhuyzen and Pistorius3 of a wax with a polydispersity of 1.003, an occupancy model was constructed from the known chain length distribution. The chains were considered to be rigid
J. Phys. Chem. B, Vol. 105, No. 22, 2001 5141
Figure 6. Two chain occupancy models used in the analysis of the model wax: (2) Statistical occupancy based on known composition, (b) random occupancy model used to minimize the crystallographic R value.
and in an all-trans extended conformation. Chains shorter than C32 were placed with the terminal methyl group at the surface of the C32 lamella and shifted by one methylene group at a time to build up a distribution, stopping when the methyl end reached the opposite surface of the average lamella. For chains longer than C32, one end of the chain was placed at the lamellar surface, and the chain was shifted in increments of one methylene group until the mirror image of the starting position was reached. Molar percentages of each chain length were then also computed considering the experimental concentrations in the mass (Figure 1). From this calculation, the chain-end occupancies were computed (Figure 6). Neglecting any mass beyond the lamellar surface to construct a more realistic, bounded lamellar structure, however, did not change the agreement appreciably. The crystallographic R value was found to be 0.25 when carbon positions were used for the calculation and 0.27 when hydrogens were included. Another statistical model that considers the greatest possible disorder was constructed by placing all chain ends at a lamellar surface and then calculating the distribution of chains at the other lamellar surface, again including the known concentration of individual species. This model fit the observed data with R ) 0.27 when carbon positions were used for the structure factor calculation and with R ) 0.31 when hydrogens were included. A Gaussian occupancy model, similar to the ones discussed earlier,2 was also calculated. First, the theoretical interlamellar gap for pure n-C32H66 was calculated from ds ) L - 1.275(m - 1) and then the value ds′ ) ds/2 was obtained. A scale factor k was then obtained from the extrapolation of I(00l) to the zero scattering angle, where k ) (ds)2/I(000). Using the experimental I(00l) value from the model wax, an extrapolated I(000) value was also determined. From this value, dav ) [kI(000)]1/2 was found, as well as dav′ ) dav/2. The ratio dav′/ds′ for the model wax is 1.74, similar to the value found for binary paraffin solid solutions or pure paraffins crystallized from the melt.2 This indicates that the defect distribution is rather shallow within the lamellar surface. A Gaussian model in agreement with the defect distribution depth dav′ ) 2.60 Å results in R ) 0.28 when carbon or both atomic species are used for the structure factor calculation. Interestingly, a slightly more disordered lamellar interface produces a better agreement, i.e., R ) 0.23. Finally, a sequential search was made for an occupancy model to minimize the crystallographic R value. That is, the atomic occupancy of one atom was varied while the other values were kept constant until a minimum was found; then the next atom occupancy was changed, and the process was repeated until all atoms had been considered. The best model (Figure 6) was
5142 J. Phys. Chem. B, Vol. 105, No. 22, 2001
Rademeyer and Dorset
TABLE 1: Observed and Calculated Structure FactorssBest Chain Occupancy for Model Wax
occurrence of mass distributions in the chain ends that do not coincide with the periodic lattice points of the polymethylene chain subcell will not reinforce the Bragg signal but will instead contribute to a general continuous diffuse scattering background. Because such diffuse signals are more or less related to the Fourier transform of the molecular chains, it is often difficult to distinguish one disorder model from the other.19 Nevertheless, the need to place less mass at periodic polymethylene sites than stipulated by chemical composition is actually in accord with the results of spectroscopic measurements on paraffin solid solutions and waxes.4 From spectroscopic measurements on such polydisperse solid solutions, it has been found that nonplanar conformational defects occur at lamellar surfaces with concentrations greatest at the lamellar surface.4 With partial folding or twisting of the chain ends to fill in the partial void spaces left by the co-mixing of dissimilar chain ends, it is clear that the molecular chain end segments need not lie precisely on the polymethylene sites expected for a pure paraffin lamella. In fact, increased polydispersity, and hence larger possible “void” spaces, should further emphasize the nonplanarity of the chain ends. This contrasts with the less polydisperse wax studied before,3 for which there would be more spatial constraints within this region. Thus, Bragg diffraction measurements can only reveal the most ordered part of the chain packing in such solidssa limitation that should be acknowledged. The hopes of finding a more accurate chain distribution model based on chain distribution as some kind of average “image”, therefore, is frustrated by the inability of crystallographic measurements to account accurately for the average conformational defect distribution. A more realistic model, including all aspects of the lamellar interface, can be constructed only after spectroscopic and crystallographic results are carefully compared to one another to come to an answer in consistent agreement with all data.
a
hkl
|Fobs|
|Fcalc|
phasea
00 2 00 4 00 6 00 8 00 10 00 12 00 64 00 66 00 68 00 70 01 28 01 30 01 32 01 34 01 36 02 0 02 2 02 4 02 66 02 68 03 32 03 34 11 1 11 3 11 5 11 32 11 34 22 0
1.67 1.55 0.99 0.61 0.34 0.26 0.37 1.65 1.30 0.33 0.36 0.48 1.21 3.78 0.37 2.60 0.51 0.49 1.81 0.52 0.74 1.22 3.07 0.80 0.51 0.67 1.70 0.97
1.72 1.39 1.00 0.64 0.39 0.25 0.39 1.67 1.28 0.36 0.30 0.57 1.28 2.36 0.24 3.11 0.44 0.36 0.65 0.50 0.82 1.55 4.24 1.10 0.39 0.70 1.29 0.96
π π π π π π 0 0 π π π/2 π/2 π/2 -π/2 -π/2 π 0 0 π 0 -π/2 π/2 π π π π/2 -π/2 π
Approximate centrosymmetric value.
found to give R ) 0.21 when carbon positions were used and R ) 0.22 when hydrogens were included. (Although electron diffraction intensity data are less than ideal under a kinematical approximation,12 the stablility of the model when hydrogen atoms are added is a favorable indication of a self-consistent structural prediction.) Note that the occupancy factors for the terminal atoms are actually lower than those predicted from an extended-chain model based on the chemical composition (Figure 6). The calculated and observed structure factors for this optimized model are listed in Table 1.
Acknowledgment. This research was funded by a grant from the National Science Foundation (CHE-9730317), which is gratefully acknowledged. References and Notes
Discussion It is clear that the previously claimed3 improvement over a Gaussian occupancy model by one based on chemical composition was a fortuitous result, perhaps facilitated by the very low polydispersity of the wax examined in that study. The present analysis of a wax with a higher polydispersity detects flaws in any assumption that all disorder at the lamellar surface in any paraffinic solid solution can be accounted for only by the fractional occupancy of methylene chain positions. The difficulty with the crystallographic atomic occupancy model is that the chain atoms are assumed to lie on periodic lattice sites, i.e., on the methylene subcell positions of a pure orthorhombic paraffin,17 to reinforce the Bragg peak signal in the diffraction patterns. However, if the occupancy model can be improved by placing less mass on these periodic sites than suggested by an experimentally measured chain length distribution, then other features of a structure must be considered that might not be easily accessible to a diffraction experiment. If a constant scattering mass is assumed for an object, then the radiation scattered by it should also be a constant value,18 no matter what local changes are imposed by disorder and/or temperature. (With the conservation of molecular orientation in a crystal, this should also be approximately true for individual zonal projections.) The
(1) Dorset, D. L. J. Phys. Chem. B 2000, 104, 10543. Dorset, D. L. Z. Kristallogr. 2001, 216, 234. (2) Dorset, D. L. Z. Kristallogr. 2000, 215, 190. (3) Dorset, D. L. J. Phys. Chem. B 2000, 04, 8346. (4) Maroncelli, M.; Strauss, H. L.; Snyder, R. G. J. Phys. Chem. 1985, 89, 5260. Kim, Y. S.; Strauss, H. L.; Snyder, R. G. J. Phys. Chem. 1989, 93, 485. Clavell-Grunbaum, D.; Strauss, H. L.; Snyder, R. G. J. Phys. Chem. B 1997, 101, 335. Basson, I.; Reynhardt, E. C. J. Chem. Phys. 1991 95, 1215. (5) Piper, S. H.; Chibnall, A. C.; Hopkins, S. J.; Pollard, A.; Smith, J. A. B.; Williams. E. F. Biochem. J. 1931, 25, 2072. Craievich, A.; Doucet, J.; Denicolo, I. J. Phys. (Paris) 1984, 45, 1473. (6) Strobl, G. Koll. Z. Z. Polym. 1972, 250, 1039. Strobl, G.; Ewen, B.; Fischer, E. W.; Piesczek, W. J. Chem. Phys. 1974, 61, 5257. (7) Stokhuyzen, R.; Pistorius, C. W. F. T. J. Appl. Chem. 1970, 20, 1. (8) Gupta, A. K.; Brouwer, L.; Severin, D. Petrol. Sci. Technol. 1998, 16, 59. Gupta, A. K.; Severin, D. Petrol. Sci. Technol. 1997, 15, 943. (9) Billmeyer, F. W., Jr. Textbook of Polymer Science, 2nd ed.; WileyInterscience: New York, 1971; pp 65-67, 78. (10) Wittmann, J. C.; Hodge, A. M.; Lotz, B. J. Polym. Sci. B: Polym. Phys. 1983, 21, 2495 (11) Dorset, D. L.; Hanlon, J.; Karet, G. Macromolecules 1989, 22, 2169. (12) Dorset, D. L. Structural Electron Crystallography; Plenum Press: New York, 1995. (13) Dorset, D. L.; McCourt, M. P.; Li, G.; Voigt-Martin, I. G. J. Appl. Crystallogr. 1998, 31, 544. (14) ,Dorset, D. L.; Zemlin, F. Ultramicroscopy 1990, 33, 227. Dorset, D. L.; Zhang, W. P. J. Electron Microsc. 1991, 18, 142. Dorset, D. L. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 8541.
Crystal Structure of Wax Lamellar Interfaces (15) Nyburg, S. C.; Potoworowski, J. A. Acta Crystallogr. B 1973, 29, 347. (16) Teare, P. W. Acta Crystallogr. 1959, 12, 294. (17) Abrahamsson, S.; Dahlen, B.; Lo¨fgren, H.; Pascher, I. Prog. Chem. Fats Other Lipids 1978, 16, 125.
J. Phys. Chem. B, Vol. 105, No. 22, 2001 5143 (18) Guinier, A. X-ray Diffraction in Crystals, Imperfect Crystals and Amorphous Bodies; W. Freeman: San Francisco, CA, 1963; p 33. (19) Dorset, D. L.; Hu, H. L.; Ja¨ger, J. Acta Crystallogr. A 1991, 47, 543.
