Crystallography of Real Waxes: Branched Chain Packing in

As microcrystalline waxes, Bowax 1018 (Boler Petroleum Company Microwax) from the International Group, Inc., was supplied as a white cake by a colleag...
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Energy & Fuels 2000, 14, 685-691

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Crystallography of Real Waxes: Branched Chain Packing in Microcrystalline Petroleum Wax Studied by Electron Diffraction Douglas L. Dorset Electron Crystallography Laboratory, Hauptman-Woodward Institute, 73 High Street, Buffalo, New York 14203-1196 Received November 9, 1999. Revised Manuscript Received February 29, 2000

Single-crystal electron diffraction patterns have been obtained from oriented samples of two commercial microcrystalline waxes. Their crystal structures, which are also expressed in oriented samples of pure methyl-branched n-paraffins, reveal a bridged lamellar structure reminiscent of low molecular weight linear polyethylene. An interdigitated lamellar packing is proposed that accommodates the methyl branches and nearby vacancies. A parallel study of n-alkyl derivatives of benzene and cyclohexane, on the other hand, reveal that naphthenic components adapt an oblique layer structure unlike the rectangular layer packing found for the petroleum waxes and the branched alkanes.

Introduction Waxes are polydisperse assemblies of polymethylene chain compounds obtained from living and fossilized sources1,2 or as a synthetic product of, for example, the Fischer-Tropsch process.3 To understand the molecular assembly of wax components in the solid state, diffraction4 and spectroscopic5 studies have been carried out. For the synthetic waxes, a four-domain model has been proposed6 which has been adapted to other refined and natural waxes.7 Despite great differences in chemical ingredients found in the large variety of wax types, e.g., the compositional dominance of n-paraffins or fatty acid esters, there seem to be universal physical characteristics, such as thermoplasticity, displayed by them, seemingly justifying this assumption of a common structural model. Recently, single-crystal diffraction studies of wax assemblies have been facilitated by the electron crystallography of oriented thin films.8 Sharp, high-resolution, (1) Hamilton, R. J. Waxes: Chemistry, Molecular Biology and Function; Oily Press: Dundee, 1995. Warth, A. J. The Chemistry and Technology of Waxes; Reinhold: NY, 1947. (2) Pedersen, K. S.; Fredenslund, Aa.; Thomassen, P. Properties of Oils and Natural Gases; Gulf Publishing Co.: Houston, 1989. (3) Le Roux, J. H.; Dry, L. J. J. Appl. Chem. Biotechnol. 1972, 22, 719. Stenger, H. G.; Johnson, H. E.; Satterfield, C. N. J. Catal. 1984, 86, 477. (4) Chichakli, M.; Jessen, F. W. Ind. Eng. Chem. 1967, 59, 68. Retief, J. J.; Le Roux, J. H. S. Afr. J. Sci. 1983, 79, 234. Srivastava, S. P.; Tandor, R. S.; Verma, P. S.; Saxena, A. K.; Joshi, G. C.; Phatak, S. D. Fuel 1992, 71, 533. Craig, S. R.; Hastie, G. P.; Roberts, K. J.; Gerson, A. R.; Sherwood, J. N.; Tack, R. D. J. Mater. Chem. 1998, 8, 859. Dirand, M.; Chevallier, V.; Provost, E.; Bouroukba, M.; Petitjean, D. Fuel 1998, 77, 1253. Gerson, A. R.; Nyburg, S. C.; McAleer, A. J. Appl. Crystallogr. 1999, 32, 296. (5) Lourens, J. A. J.; Reynhardt, E. C. J. Phys. D: Appl. Phys. 1979, 12, 1963. Clavell- Grunbaum, D.; Strauss, H. L.; Snyder, R. G. J. Phys. Chem. 1997, B101, 335. Merk, S.; Blume, A.; Riederer, M. Planta 1998, 204, 44. (6) Le Roux, J. H.; Loubser, N. H. S. Afr. J. Sci. 1980, 76, 157. (7) Basson, I.; Reynhardt, E. C. Chem. Phys. Lett. 1992, 198, 367. Basson, I.; Reynhardt, E. C. J. Phys. D: Appl. Phys. 1988, 21, 1421, 1429, 1434.

electron diffraction patterns of refined linear chain petroleum waxes have been used to determine their crystal structures,9,10 including a three-dimensional determination.11 Such multiple linear chain assemblies pack as well-resolved lamellae, on average with welldefined end planes, and are very similar to the crystal structure of binary n-paraffin solid solutions.12 On the other hand, it is clear that other chain interactions may be possible for the chemically (or compositionally) more complicated natural waxes. For example, beeswax and carnauba wax, crystallized from the melt, pack where chains have only “nematocrystalline” order, i.e., there are no well-resolved chain lamellae and only the continuous lateral “polyethylene” packing of aligned polymethylene chains is expressed on average.10 Nascent lamellar order can be induced by annealing these materials,13 but the endpoint is very similar to the chain packing of low molecular weight linear polyethylene, a single crystal structure recently determined from electron crystallographic data.14 This is a structure where the lamellae are spanned by longer “bridging molecules”. (Indeed, it may be appropriate to ask whether this polydisperse oligomer assembly can also be regarded as a “wax”.) In these preliminary studies, it was assumed that most of the waxes were made up of strictly linear chains. For natural waxes, ester groups also known to be accommodated into a rectangular layer chain packing in the orthorhombic methylene subcell.15 However, another important chemical parameter to be considered is the incorporation of methyl branching on the paraf(8) Dorset, D. L. Macromolecules 1987, 20, 2782. (9) Dorset, D. L. Acta Crystallogr. 1995, B51, 1021. (10) Dorset, D. L. J. Phys. D: Appl. Phys. 1997, 30, 451. (11) Dorset, D. L. Z. Kristallogr. 1999, 214, 362. (12) Dorset, D. L. Z. Kristallogr. 1999, 214, 229. (13) Dorset, D. L. J. Phys. D: Appl. Phys. 1999, 32, 1276. (14) Dorset, D. L. Macromolecules 1999, 32, 162. (15) Aleby, S.; Fischmeister, I.; Iyengar, B. T. R. Lipids 1971, 6, 421.

10.1021/ef9902350 CCC: $19.00 © 2000 American Chemical Society Published on Web 04/21/2000

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Table 1. Melting Points of Waxes and Branched n-Paraffins and Annealing Temperatures for Their Crystallization material Astorwax 3040 Bowax 1018 3 Me C33H67 3 Me C34H69 4 Me C34H69 5 Me C34H69

rotator transition (°C)

melt (°C)

annealing temperature (°C)

54.5 57.1 58.4 51.1

49.9 59.6 62.8 65.9 62.7 59.3

35 45 48 48 48 48

finic chains. This substitution is relevant for the study of Fischer-Tropsch waxes,3 as well as for the high molecular weight “microcrystalline” waxes in petroleum, containing an appreciable amount of naphthenic components.16,17 Again using electron crystallographic procedures, branched chain packing in two real microcrystalline waxes has been determined, as will be described. Materials and Methods Waxes, Component Models, and Their Crystallization. As microcrystalline waxes, Bowax 1018 (Boler Petroleum Company Microwax) from the International Group, Inc., was supplied as a white cake by a colleague in the petroleum industry. Astorwax 3040, received as a light yellow slab was kindly supplied as a research sample from Allied Signal, Inc. Both waxes were slightly tacky and could be plastically deformed. While the latter is described by the manufacturer to contain mostly branched chain hydrocarbons, a description presumably applicable to the former material, there may also be some phenyl and cyclohexyl paraffin derivatives in addition to other naphthenes.2,17 To investigate the crystallization properties of branched chain n-paraffins, small synthetic samples of rac-3-methyl tritriacontane and rac-3-, 4-, or 5-methyl tetratriacontanes were supplied by Dr. J. R. Fryer, Chemistry Department, University of Glasgow. Samples of n-octadecyl benzene, nnonadecyl benzene, and n-nonadecyl cyclohexane were purchased from Fluka AG (Buchs, Switzerland). Initially, these materials were taken up as dilute solutions in light petroleum (heated if necessary to solubilize the material) and thin lamellar microcrystals were formed by evaporation of these solutions onto a carbon-film-covered 300 mesh copper electron microscope grid. Following earlier procedures,18 epitaxially oriented samples of the waxes and methyl-branched n-paraffins were obtained by first evaporating the dilute light petroleum solution onto a freshly cleaved mica sheet to form a thin organic film. With carbon covered electron microscope grids placed face-down onto the organic film, an excess of benzoic acid crystals was distributed over this surface and a sandwich completed by adding the other half of the cleaved mica sheet. Using a thermal gradient the organic solid was first co-melted and then recrystallized to orient the linear chain compounds on the diluent crystal surface, as described by a binary eutectic phase diagram.19 The physical sandwich could then be separated mechanically and the benzoic acid removed by sublimation overnight in a vacuum coating unit. Often the epitaxial orientation achieved by rapid epitaxial growth onto a substrate is insufficient for crystallographic (16) Musser, B. J.; Kilpatrick, P. K. Energy Fuels 1998, 12, 715. Tuttle, J. B. Petroleum Products Handbook; Guthrie, V. B., Ed.; McGraw-Hill: NY, 1960, Chapter 10. (17) Edwards, R. T. Ind. Eng. Chem. 1957, 49, 750. (18) Wittmann, J. C.; Hodge, A. M.; Lotz, B. J. Polym. Sci., Part B: Polym. Phys. Ed. 1983, 21, 2495. (19) Dorset, D. L.; Hanlon, J.; Karet, G. Macromolecules 1989, 22, 2169.

Figure 1. DSC scans of linear chain materials: (a) Astorwax 3040 microcrystalline wax sample. (b) rac-3-methyl-tritriacontane. Note the premelt transition to a “rotator” phase. studies in the electron microscope. As shown earlier with natural waxes13 or low molecular weight linear polyethylene,14 the sample crystallinity could be improved by annealing the linear chain materials (Mettler FP82 heating stage controlled by a FP90 control unit) in the presence of the benzoic acid substrate at a temperature within the onset of the melting endotherm for, e.g., 5 h. (Peak melting points of branched chain alkanes and waxes, determined with a Mettler TA-3300 DSC, are listed in Table 1, with annealing temperatures. Typical DSC scans for a wax sample or a methyl-branched alkane are shown in Figure 1) The benzoic acid was then removed by sublimation in vacuo after the material had been cooled back to room temperature. Attempts to epitaxially orient the ring-substituted alkanes on benzoic acid or naphthalene have been unsuccessful so far. Samples for powder X-ray diffraction measurements were the ones provided by the manufacturer, only ground finer to minimize preferred orientation effects. Diffraction Experiments. Electron diffraction experiments were carried out at 100 kV and at room temperature (20 °C) with a JEOL JEM-100CX II electron microscope, taking usual precautions to minimize radiation damage to the thin organic crystals,20 i.e., use of a small beam current density, a short exposure time, and recording the diffraction patterns on X-ray film (Kodak DEF-5 or CEA Reflex). The selected area most frequently employed sampled a 2.9 µm diameter of the specimen (calibrated by a carbon diffraction replica). All measurements were made at room temperature. Diffraction spacings on electron diffraction patterns were calibrated against an Au° powder standard. Intensity data were measured on the experimental diffraction films with a Joyce-Loebl Mk. IIIC flat-bed microdensitometer, using a triangular fit to the peak profile. Care was taken to establish that the intensity data were internally consistent, as established by suitably low values of Rmerge when two equivalent patterns were compared or Rsym when symmetry equivalent reflections in a single pattern were compared.21 Because the thin organic crystals were plastically (20) Dorset, D. L. Structural Electron Crystallography. Plenum: NY, 1995.

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Figure 2. Diffraction from chain assemblies. Gallery A: Representative chain packing arrays for polymethylene materials. (a) “Nematocrystalline” order with no lamellar separation and/or nascent lamellar order. Mostly the polymethylene subcell packing is expressed. (b) Incomplete lamellar separation restricting the interlamellar gap dimension to ∆z ) 3cs/2, where cs is the methylene chain subcell repeat along the chain axis. The gap distance is restricted by a fraction of bridging chains. (c) Complete lamellar separation where ∆z * 3cs/2. Gallery B: Corresponding 0kl electron diffraction patterns. (a) Nascent lamellar separation. (b) Restricted lamellar separation. (c) Complete lamellar separation. The l indices of 01l reflections are related to the average chain carbon number m (n-CmH2m+2) that would account for the lamellar thickness. deformed, there was no need to apply a Lorentz correction to the intensity data.20 X-ray measurements on the ring-substituted n-alkanes were carried out on a powder diffractometer by Ms. Anne Marie Lanzafame at Eastman Kodak Co. in Rochester, NY. Graphical representations of the peak profiles were provided as well as identified peak reciprocal lattice positions. Structure Analysis. As is typical for electron diffraction patterns from epitaxially oriented rectangular layer polymethylene assemblies8 (see Figure 2), there are two parts of the 0kl patterns which immediately give a qualitative overview of the chain packing. At low angle, the reciprocal spacing of the 00l reflections measures the average lamellar thickness. The intense wide angle 01l and 00l reflections are due to the polymethylene chain subcell packing. If these reflections are not split into two intense peaks, as also found for low molecular weight linear polyethylene,14 then the lamellar separation is incomplete. Indices of the strong 0kl reflections, moreover, are simply related to the average carbon number of the (nascent) lamellar repeat as if it were a pure n-paraffin8 (Figure 2). From the indices of these reflections, by consulting parent orthorhombic n-alkane crystal structures, the space group can be determined to be either A21am for the odd-chainlike structures22 and Pca21 for the even-chainlike structures.23 Polydisperse assemblies of linear chains can crystallize in neighboring microareas as either unit cell, so that several average local structures can exist for a given material.8 Crystallographic direct phasing methods have been used to determine structures of n-paraffins24 and their solid solutions25 (21) Dorset, D. L.; McCourt, M. P.; Li, G.; Voigt-Martin, I. G. J. Appl. Crystallogr. 1998, 31, 544. (22) Dorset, D. L. Z. Kristallogr. 1999, 214, 223. (23) Teare, P. W. Acta Crystallogr. 1959, 12, 294. (24) Dorset, D. L.; Zemlin, F. Ultramicroscopy 1990, 33, 227. Dorset, D. L.; Zhang, W. P. J. Electron. Microsc. Technol. 1991, 18, 142. (25) Dorset, D. L. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 8541.

in this [100] projection. For these materials only the 00l structure factor magnitudes were used initially to calculate a onedimensional Fourier transform to represent the lamellar profile. Following a procedure originally proposed by Robertson,26 algebraic phase values were assigned to reflections within two intensity envelopes (low and wide angle), where approximate centrosymmetry was assumed. For a “reasonable” one-dimensional lamellar profile with carbon peak positions and a suggested occupancy factor, the z/c coordinates of these atoms were obtained. Completing the two-dimensional model required adding y/b carbon positions typical of the orthorhombic even- or odd-chain alkanes in Pca21 or A21am, respectively. For even-chain models, y/b ) 0.186 for odd-numbered carbon positions and 0.314 for the even-numbered positions. For oddchain models, the respective values for y/b are 0.190 and 0.309. These carbon coordinates were then used to calculate the amplitudes of the complete 0kl pattern, the fit measured by the crystallographic residual (R ) ∑||Fobs| - k|Fcalc||/∑|Fobs|). Because there are many more individual atomic positions than there are measured diffraction intensities, the entire sequence of carbon positions obtained from the one-dimensional Fourier transform was regarded as a rigid diffraction grating that could not be varied. Only an atomic occupancy profile and an overall isotropic temperature factor was changed, if necessary, so that the R-value figure of merit would retain some statistical significance.27 Attempts were made to index the powder diffraction patterns with the programs DICVOL and TREOR within the CERIUS2 program package (Molecular Simulations, Inc., San Diego, CA). A constraint was placed on the indexed unit cell based on the hk0 electron diffraction patterns from the ringsubstituted alkanes. (26) Robertson, J. M. J. Chem. Soc. 1945, 607. (27) Hamilton, W. C. Statistics in Physical Science; Ronald, NY: 1964; p 157ff.

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Figure 4. Crystal structures of microcrystalline wax: emphasizing detail near the lamellar interface. Bridging chain entities (carbon positions indicated by arrows) traverse the interlamellar gap in the potential maps calculated from observed amplitudes and model phases. (a) Bowax 1018. (b) Astorwax 3040. Table 2. Observed and Calculated Structure Factors for Microcrystalline Waxes 0kl

Figure 3. Electron diffraction patterns from microcrystalline waxes. (a) Solution crystallized wax: hk0 pattern in projection down the chain axes (Astorwax). (b) 0kl from epitaxially oriented material (Astorwax). Note that the strong 01l reflection is broadened. Inset: detail of single 00l reflection.

Results Microcrystalline Waxes. From dilute solution, both microcrystalline petroleum waxes crystallize in rectangular layers so that the hk0 electron diffraction patterns (Figure 3a), typical of the O⊥ methylene subcell, where a ≈ 7.42, b ≈ 4.96 Å were observed. When samples, epitaxially oriented on benzoic acid, were not annealed, arced diffraction patterns suggestive of poorly oriented polyethylene were observed with no indication of lamellar separation. After annealing, the most intense 0kl reflections were better defined, although the 01l spot was somewhat broadened (Figure 3b). One or two orders of the low angle 00l reflection were also noted. For the Bowax 1018, several local average lamellar structures n-CmH2m+2 were indicated from the 01l reflection indices, where l ) m+2 (see Figure 2Bb), i.e., m ) 44, 45, 46. For the frequently represented m ) 44 (space group Pca21), c/2 ) 58.01 ( 0.08 Å, compared to the 57.72 Å lamellar value predicted for the pure n-paraffin of like carbon number.29 Astorwax 3040 patterns also indicated a distribution of structures, where m ) 51, 52, 53. For the often represented m ) 51 length (space group A21am) the average lamellar spacing was c/2 ) 66.90 ( 0.09 Å, compared to a 66.80 Å value predicted for the model n-paraffin.29 Only one lamellar reflection (28) Harburn, G.; Taylor, C. A.; Welberry, T. R. Atlas of Optical Transforms; Cornell University: Ithaca, NY, 1975; Plate 17. (29) Nyburg, S. C.; Potworowski, J. A. Acta Crystallogr. 1973, B29, 347.

Bowax 1018 00 2 00 4 00 92 01 46 03 46 02 0 Astorwax 3040 00 2 00 106 01 53 03 53 02 0 a

|Fobsd|

|Fcalcd|

phasea

0.83 0.37 0.86 1.48 0.74 3.50

0.91 0.87 0.78 1.57 1.06 3.28

π π π -π/2 π/2 π

1.20 0.81 1.41 0.77 3.19

1.86 0.80 1.23 1.00 2.87

π π π/2 -π/2 π

Closely approximate centrosymmetric value.

was observed in 0kl patterns from this wax, which also contained broadened 01l spots. Crystal structure analyses for the two waxes indicated similar structural details (Figure 4) even though the space groups of even- or odd-chain models are different. In the chain packing model, an interlamellar gap, free of carbon atoms, was always assumed. However, the strong 0kl “polyethylene” reflections were unsplit, and it was clear14,30 that this interlayer distance was an integral value of the projected chain methylene repeat r ) cs/2 where cs ) 2.55 Å, i.e., ∆z ) 3r. The calculated [100] potential maps (Figure 4) always returned carbon atom positions within this gap, even though they had been excluded from the original layer packing model. Moreover, there was always a gradation of partial carbon occupancies just within the nascent lamellar surfaces. These structural features are just those found for low molecular weight linear polyethylene14 with bridging molecules spanning the nascent lamellae. Structure factor calculations with the separated lamellar model, assuming only the linear part of the chains, accounted well for the observed amplitudes in Bowax (R ) 0.17) and Astorwax (R ) 0.20) (see Table 2). Test calculations of unobserved 0kl reflections, based on these models, also indicated that they should be weak. (30) Zhang, W. P.; Dorset, D. L. J. Polym. Sci. Part B: Polym. Phys. 1990, 28, 1223.

Crystallography of Real Waxes

Figure 5. Electron diffraction from model microcrystalline wax components: epitaxially oriented methyl-branched nparaffin (3 Me C33H67). (a) Freshly crystallized samples. Inset: 00l reflections. Note resemblance to 0kl pattern in Figure 3b. (b) Sample after equilibration at room temperature for 5 months indicating the growth of a superlattice. Streaked reflections appear near the center of the 01l row (center arrow) and the formerly broad, intense 01l singlet reflection begins to break up into sharp superlattice reflections (left arrow). Patterns from other methyl-branched paraffins in the series are very similar to a. (c) Electron diffraction pattern from solution-crystallized n-nonadecyl benzene, a model naphthenic component.

Methyl-Branched n-Paraffins. From the crystal structure of an iodinated analog31 (where the iodine would have, approximately, the van der Waals radius of a terminal methyl group32), it might be expected that the methyl-branched n-paraffins will also pack in oblique layers. Nevertheless, samples prepared by the procedures used for the microcrystalline waxes exhibit strikingly similar rectangular layer packing characteristics to the polydisperse wax. Samples crystallized from dilute solution diffract similarly to Figure 3a, establishing the untilted chain packing in the O⊥ methylene subcell (the unit cell of chain-folded polyethylene). Epitaxially oriented samples that were subsequently annealed diffract similar to the microcrystalline wax samples where the 0kl reflections are unsplit and the 01l spot has a shape characteristic (Figure 5a). There are usually several orders (3 to 4) of the lamellar 00l reflections. For the 3-methyl derivatives of the C33H68 and C34H70 alkanes, this blob-like reflection begins to separate into a row of superlattice after the samples equilibrate at room temperature for 5 months, commensurate with the appearance of other superlattice reflections on the same reciprocal lattice row (Figure (31) Abrahamsson, S.; Innes, M.; Nilsson, B. Ark. Kemi 1968, 30, 173. (32) Larsson, K. Acta Chem. Scand. 1968, 18, 272.

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Figure 6. Crystal structures of branched chain n-paraffins, revealing the presence (arrows) of chain segments spanning the lamellar interface. (a) 3 Me C33H67, (b) 3 Me C34H69, (c) 4 Me C34H69, (d) 5 Me C34H69.

5b). The initial crystal growth for the methyl branched alkanes is therefore metastable. Again the lamellar spacings of the branched alkanes were found to correspond to the indices of strong 01l reflections and hence both indicated the average lamellar chain length. For the 3-methyl-C33H67, the most typical lamellar average chain length was m ) 34, where c/2 ) 45.91 ( 0.38 Å. The predicted29 value is 45.02 Å. For the other branched alkanes the average carbon layer m was found from the 01l indices and compared to the measured (predicted29) values for c/2. To summarize other measurements: 3-methyl-C34H69, m ) 35, c/2 ) 47.05 ( 0.18 Å (46.43 Å); 4-methyl C34H69, m ) 36, c/2 ) 47.80 ( 0.30 Å (47.56 Å); 5-methyl C34H69, m ) 37, c/2 ) 48.02 ( 0.33 Å (48.98 Å). Projected crystal structures are strikingly reminiscent of the microcrystalline petroleum waxes (Figure 6). Layer structures based on the analogous n-alkane structure were constructed for calculation of diffraction amplitudes retaining the gaps between lamellae. However, the strong 0kl “polyethylene” reflections were again unsplit so that it was not a surprise to find strong carbon positions within the interlamellar gap in the potential maps (Figure 6). There was also a region with fractional atomic occupancy within region adjacent to the lamellar surfaces. Again, the fit to the observed data for a straight chain model was good for all examples:

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Table 3. Observed and Calculated Structure Factors for the Branched Chain Alkanes 0kl 3 Me C33H67 00 2 00 4 00 6 00 8 00 72 01 36 03 36 02 0 3 Me C34H69 00 2 00 4 00 6 00 8 00 74 01 37 02 74 03 37 02 0 4 Me C34H69 00 2 00 4 00 6 00 76 01 38 03 38 02 0 5 Me C34H69 00 2 00 4 00 6 00 78 01 39 03 39 02 0 a

|Fobsd|

|Fcalcd|

phasea

1.48 1.02 0.61 0.45 1.15 2.02 1.08 3.83

1.46 1.16 0.75 0.42 1.52 1.75 1.75 3.52

π π π π π -π/2 π/2 π

1.22 1.04 0.79 0.37 1.74 3.05 0.98 1.56 4.92

1.60 1.34 1.04 0.70 1.89 2.15 0.99 2.16 4.84

π π π π π -π/2 0 π/2 π

1.33 0.91 0.55 1.40 2.58 1.14 4.27

1.68 1.23 0.72 1.67 1.98 1.99 3.94

π π π π -π/2 π/2 π

1.82 1.26 0.56 2.02 3.68 2.26 6.01

2.52 1.72 0.91 2.09 2.48 2.52 6.09

π π π π -π/2 π/2 π

Closely approximate centrosymmetric value

3-methyl-C33H67 (R ) 0.18), 3-methyl-C34H69 (R ) 0.19), 4-methyl C34H69 (R ) 0.23), 5-methyl C34H69 (R ) 0.17). The structures are again somehow similar to low molecular weight linear polyethylene. Calculated and observed structure factors are listed in Table 3. Ring Substituted n-Alkanes. Although ring substituted n-alkanes are thought form an appreciable part of the naphthenic fraction associated with the microcrystalline waxes,2,16 there was no obvious connection to the average structure found in the wax samples after the analysis of available data. Nevertheless, since there seems to be no published crystallographic information for this class of compounds, a preliminary overview is given here. Both n-nonadecyl benzene and n-nonadecyl cyclohexane crystallize as oblique layers, i.e., with tilted chains. Electron diffraction patterns from solution crystallized samples (Figure 5c) resemble those from polymethylene compounds packing in the Kitaigorodskii34 R[0,(2] layer including the O⊥ methylene subcell. (Another example of molecules with the same layer packing is the Cpolymorph of even chain fatty acids.35) Octadecyl benzene may be polymorphic. A pattern resembling Figure 5c was found but more commonly they indicated a triclinic structure. (33) Dorset, D. L.; Pangborn, W. A.; Hancock, A. J.; Lee, I. S. Z. Naturforsch. 1978, 33c, 39. (34) Kitaigorodskii, A. I. Organic Chemical Crystallography; Consultants Bureau: New York, 1961; p 190. (35) Malta, V.; Celotti, G.; Zannetti, R.; Martelli, A. F. J. Chem. Soc. B 1971, 548.

It was very difficult to index powder X-ray data so that they would agree with the hk0 electron diffraction patterns. In the one seemingly successful analysis, a monoclinic unit cell was determined for n-nonadecyl cyclohexane where a ) 18.09, b ) 5.08, c ) 35.73 Å, and β ) 129.94°, which would correspond to a packing density of 0.94 g/cm3 with 4 molecules in the unit cell. Comparison to observed electron diffraction cell spacings (from patterns very similar to Figure 5c): d100 ) 9.04 ( 0.04; b ) 4.99 ( 0.02 Å, it is obvious that the former cell length is doubled (here assuming an alternative β angle near 90°). In an attempt to assign crystallographic phases to 12 unique h0l amplitudes by the Sayre equation36 (assuming a centrosymmetric [010] projection in space group P21), an array of possible molecular envelopes was found that would indicate an interdigitated bilayer packing. It is clear that reliable intensity data at a resolution greater than 2.0 Å is needed to verify the indexing of all patterns and to complete the structure determinations. Discussion Although microcrystalline waxes are notoriously difficult to crystallize,16 often expressed as “mal-crystalline” forms,17 this electron crystallographic analysis indicates that at least a fraction of the real wax can be crystallized and that the expressed crystalline forms apparently include the interaction of methyl-branched alkanes with normal paraffins. Surprisingly the resultant crystal structure is very similar in form to that of the low molecular weight linear polyethylenes.14 How can this arise from the methyl branching, since the resultant chain packing also seems to be a characteristic of this substitution, as expressed for pure materials? The structure analysis indicates that there must be a bridging entity that spans the nascent lamellae and that also some feature of the chain packing must explain the nonunitary occupancy factors within the first few chain methylene repeats adjacent to the average lamellar surface. A feasible model for the lamellar is suggested after examining previously published crystal structures of a branched-chain fatty acid polymorph, where the branching methyl group must be accommodated at a lamellar interface.37 The chain tilt in these slowly crystallized acids is large enough so that the methyl group is always at the lamellar surface, so that, in a view normal to the chain axes, a large enough vacancy is left in the neighboring chains to accommodate this group. Using data obtained from 3-methyl branched alkanes, metastable crystalline forms with rectangular layer packings can be produced which will eventually transform to a more stable array (perhaps finally more like the X-ray structure of the R-iodinated 3-methyl branched paraffin31). As shown in Figure 7, random penetration of neighboring lamellae with branched segments, incorporating neighboring vacancies to accommodate the pendant group will produce a nascent lamellar structure where the average atomic occupancies will also decrease as the lamellar boundary is approached. The inclusion of methyl group positions, not considered in chain (36) Sayre, D. Acta Crystallogr. 1952, 5, 60. (37) Abrahamsson, S. Ark. Kemi 1959, 14, 65.

Crystallography of Real Waxes

Figure 7. Schematic packing model for the lamellar interface of microcrystalline wax and methyl-branched n-paraffins. Branches can be accommodated by interpenetration into adjacent lamellae with vacancies to compensate for the pendant group. A gradation of chain methylene occupancy factors will result from such an arrangement.

packing models for structure factor calculations, may also be expressed, on average, as random carbon positions protruding from the chain axes. This occurrence of random methyl positions could well account for the characteristic broadening of the 01l reflection in the waxes and methyl-branched paraffinssas was suggested by consulting a reference on optical transforms.18 This identification of methyl branch disorder is also verified with branched chain alkanes since, eventually, the 01l reflection can transform into sharper superlattice reflections as an more ordered packing is reached. This analysis indicates that the most crystalline region of these waxes involves an interpenetration of chains across lamellar boundaries. Although long bridging molecules, that penetrate deeply into the next lamellar layer, are not involved, as they are in polyethylene and some natural waxes, the effect on the electron diffraction pattern is very similar, only because the interlamellar gap is traversed. The role of ring-containing alkane derivatives in microcrystalline waxes is currently unknown. The importance of these naphthenic components has been estimated to be as little17 as 15 mol % or as great2 as 57-75 mol %, compared to a branched chain composition2 of ca. 15-30 mol %. It is interesting that these naphthene components have never been studied by diffraction techniques in the solid state although polar analogues, e.g., alkoxy benzoic acids, certainly have.38 At equilibrium, it is obvious that molecules as dissimilar as the n-alkyl benzenes and the n-paraffins will not be

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co-soluble in the solid state. However, Kitaigorodsky39 has distinguished between true (substitutional) and interblock solid solutions. The latter may be relevant for such molecular admixtures after a rapid crystallization from a co-melt. While the excess molecular volume in interblock solid solutions is presumably accommodated by projection of protruding nonoverlapping molecular moieties into boundaries of crystalline “mosaic blocks”, the expression for nascent lamellar systems might again involve packing of groups within the interface. The possibility for such interactions will be studied in future work with model binary systems. It should be understood, finally, that the observations of a crystalline component in microcrystalline petroleum waxes expressed both a strength and weakness of electron crystallographic methods. The strength of the technique lies in the ability to find microcrystalline regions that are well-ordered. In this study of the microcrystalline waxes, the occurrence of such highly crystalline regions on the electron microscope grid surface did not seem to be unusually sparse. This distribution was, in fact, comparable to the earlier observations9-12 on linear chain waxes. On the other hand, by contrast to powder X-ray methods, a complete overview of the entire solid, including amorphous regions, is less easily appreciated by an electron diffraction probe of microareas. The signal from the most-ordered regions is the most visible and also the most compelling to the experimentalist, particularly when low-dose conditions (low beam current densities) are used. One can only verify that the data from the more crystalline regions are self-consistent after recording numerous electron diffraction patterns. The distribution of local crystal structures in adjacent microareas also did not seem to differ much from those found for the linear chain waxes9-11 or binary paraffin solid solutions.8 Acknowledgment. Research was funded by a grant from the National Science Foundation (CHE-9730317) which is gratefully acknowledged. Dr. John R. Fryer, an anonymous donor, and Allied Signal, Inc. are thanked for providing samples. I thank Ms. Anne Marie Lanzafame for obtaining the powder X-ray patterns from the naphthenic compounds. EF9902350 (38) Bryan, R. F.; Hartley, P. Mol. Cryst. Liq. Cryst. 1981, 69, 47. Bunning, J. D.; Lydon, J. E. J. Chem. Soc., Perkin II 1979, 1621. (39) Kitaigorodsky, A. I. Mixed Crystals; Springer: Berlin, 1984; p 214ff.