532
J. Phys. Chem. B 2000, 104, 532-537
Internal Heteroatom Substitution and the Layer Packing of Polymethylene Chains Douglas L. Dorset* Electron Diffraction Department, Hauptman-Woodward Medical Research Institute, Inc., 73 High Street, Buffalo, New York 14203-1196
Dolores Clavell-Grunbaum and Robert G. Snyder Chemistry Department, UniVersity of California, Berkeley, California 94720-1460 ReceiVed: September 21, 1999; In Final Form: NoVember 23, 1999
In an investigation of methylene replacement by small heteroatom insertions the crystal structures of N,Ndioctadecylamine, (C18H37)2NH, and dihexadecyl ether, (C16H33)2O, were determined by electron crystallography and infrared spectroscopy. Crystals of the amine, epitaxially oriented on naphthalene, are characteristic of the analogous odd-chain n-paraffin in its high-energy orthorhombic B-polymorph. Cell constants are a ) 7.52(2), b ) 5.04(1), and c/2 ) 50.0(4) Å and the extinction rules for the 0,k,l reflections (k + l ) 2n + 1) are consistent with the space group A21am. Carbon and nitrogen coordinates in a paraffin-like model match observed data reasonably well (R ) 0.22). A binary phase diagram reveals that the secondary amine is continuously cosoluble with the n-paraffin of the same chain length (n-C37H76). The ether, crystallized on benzoic acid, is polymorphic. The major monoclinic form, which forms a eutectic solid with n-C33H68, crystallizes in space group Aa with a ≈ 5.59, b ≈ 7.40, and c ) 88.66 Å and β ) 116.2°. Its projected crystal structure includes a twisted chain conformation in an oblique layer (R ) 0.26). The orthorhombic form in space group A21am (c/2 ) 45.1 Å) resembles the odd-chain paraffin and may be continuously co-soluble with it.
Introduction Substitution of methylene or methyl groups in paraffins and their derivatives by heteroatoms or different functional groups is very important for the understanding the molecular chain packing of natural products such as plant and insect waxes, as well as functionalized polymers. Long-chain fatty acid esters are found to coexist with n-alkanes in a polydisperse combination,1 somehow promoting the formation of a solid solution.2 Heteroatom substitution has also been useful for the design of growth modifiers,3,4 e.g., in diesel fuels. Insertion of functional groups such as a ketone provides a probe of chain flexibility in dielectric measurements, also assuming that some amount of the probe is cosolubilized in a paraffin crystal lattice.5 Ether links inserted into polymethylene chain sequences form the basis for an important class of polymers6 and nonionic detergents.7 In the early crystallographic investigations of the lipids, such substitutions have also been valuable for the solution of the crystallographic phase problem via isomorphous replacement. While terminal halogen substitutions have a van der Waals radius similar to a methyl group, strict isomorphism is often found,8 but substitution of a methylene group by a sulfur atom proves a much less successful retention of the methylene chain packing of the native compound.9 In a phenomenological overview of this substitution problem, it is sometimes difficult to understand what factors promote cosolubility of a simple derivative with the analogous n-paraffin. For example, ketones are known to pack well in an orthorhombic paraffin layer packing with only slight lateral expansion of the unit cell dimensions.10 Ester groups can also be accommodated in an untilted orthorhombic layer packing, provided that they occur in asymmetrically substituted compounds11 (i.e., different alcohol and fatty acid chain lengths). Otherwise, an oblique layer
packing is formed. Substitution by very small groups such as an ether oxygen, however, can initiate an oblique layer chain packing.12 While the substitution may favor nonplanar chain conformations in the vicinity of this group, it would appear that both large and small van der Waals radii of hetero groups may also affect the chain layer packing. In this paper, the effect of a substitution of a methylene group by a secondary amine or ether on polymethylene chain packing is explored. Material and Methods Compound and Crystallization. N,N-Dioctadecylamine (>99% pure), (C18N37)2NH, was purchased from Fluka (Buchs, Switzerland) and dihexadecyl ether (a.k.a dicetyl ether) (purity unspecified), (C16H33)2O, was purchased from Pfaltz & Bauer (Stamford, CT). Both were received as colorless crystalline plates. For calorimetric investigations (see below), samples were weighed into aluminum pans, either pure or in various molar combinations with the analogous n-paraffins, i.e., n-tritriacontane, n-C33H68 (>99% pure) (Supelco, Bellefonte, PA), and n-heptatriacontane (>99% pure), n-C37H76, also purchased from Fluka. For investigations of the solution-grown crystal habit, thin lozenges were formed by evaporation of dilute solutions in either chloroform or light petroleum onto carbon-film-covered electron microscope grids. For diffraction studies, to obtain the structurally most informative projection onto the molecular chain axes, the two substances were oriented on specific substrates that nucleate the chain packing by lattice matching so that the chain axes lie in the plane of the largest crystal face, rather than normal to it. Epitaxial orientation of the dioctadecylamine employed naphthalene as a substrate, adapting Fryer’s procedure.13 Two carbon-
10.1021/jp993379o CCC: $19.00 © 2000 American Chemical Society Published on Web 12/31/1999
Substitution and Packing of Polymethylene Chains covered electron microscope grids were placed in the bottom of an aluminum DSC pan. A very small amount of the amine was added to the pan after an excess (approximately 10 mg) of naphthalene was weighed on top of these grids. The pan was then sealed and the crystallization from the comelt was carried out via a temperature program on the DSC. That is, the sample was held at 25 °C for 1 min, raised to 100 °C and held there for 1 min, and then recooled to 25 °C at 5 °C/min. The pan was then opened and placed into an evacuable chamber, whereupon the naphthalene was removed by sublimation in the vacuum provided by a floor pump. Dicetyl ether was epitaxially oriented on benzoic acid, adapting an earlier procedure.14 A dilute solution in light petroleum was evaporated to dryness on a freshly cleaved mica sheet, and carbon-film-covered copper electron microscope grids were placed face down on the organic layer. An excess of benzoic acid was distributed around these grids. The second half of the mica sheet covered these components to form a sandwich, which was then placed at the hot end of a thermal gradient (metal bar spanning a hot plate and a thermoelectric cold plate), first to comelt the organic components and then to crystallize the hypo-eutectic solid.15 The linear chains are also specifically oriented on the benzoic acid crystal surface. After cleaving the sandwich, the excess benzoic acid was removed by sublimation overnight in vacuo. Differential Scanning Calorimetry. DSC measurements on the secondary amine and its molar combinations with the n-heptatriacontane, or the dicetyl ether combined with ntritriacontane, were made with a Mettler TA-3300 instrument. The binary combinations were fused in the sealed pans at 100 °C. After the samples had been equilibrated at room temperature for some time (e.g., months), scans were made from 0 to 100 °C at 5 °C/min. Endotherm peak positions were located with a min/max function in the Mettler STARe software running on a Dell PC. After calibrating the temperature scale with 18 known n-paraffins and n-perdeuterioparaffin standards, these transition points were used to construct binary phase diagrams, as described earlier.15 (These diagrams, however, may not describe fully equilibrated binary systems.) Electron Diffraction and Microscopy. Selected area diffraction experiments were carried out at 100 kV and at room temperature with a JEOL JEM-100CX II electron microscope, employing a selected area with a 2.9 µm diameter (calibrated with a carbon grating replica). Bright field images were obtained for some specimens at 10 kX direct magnification by blocking all but the undiffracted incident beam with an aperture to provide contrast. Low dose operating conditions were followed to minimize radiation damage to the specimens.16 This included use of a screenless X-ray film (CEA Reflex or Kodak DEF-5) to record diffraction patterns and bright field images. Data Reduction and Crystal Structure Determination. Diffraction films were scanned on a Joyce Loebl Mk. III C flatbed microdensitometer to obtain the peak profiles of the diffraction spots. Integrations were made as a triangular approximation of the peak shape and, as usual, no Lorentz correction was applied to the raw intensities (due to the curvilinear distortion of the crystals). Diffraction patterns from several crystals were compared to one another, as outlined recently,17 to establish the self-consistency of the intensity data, and an average was made over scaled diffraction patterns and over symmetry equivalents of unique reflections in single patterns. The positions of carbon and nitrogen atoms in the chains along the longest unit cell axis were found after assigning the
J. Phys. Chem. B, Vol. 104, No. 3, 2000 533 approximately centrosymmetric phases to the 0,0,l reflections that would be found for the analogous n-paraffin and then computing a one-dimensional potential map. From this information and the space group symmetry, the chain packing model could be easily constructed. For calculation of structure factors, Doyle-Turner18 electron scattering factors were used. Infrared Spectroscopy. Infrared measurements were carried out at room temperature or lower on melt-crystallized thin-layer samples between two KBr windows. The instrument was an evacuable Nicolet model 8000 FTIR spectrometer equipped with a MCT/B detector. Operating parameters were chosen to provide a resolution of 1.0 cm-1. Band assignments made in previous studies19 were consulted as the spectra of the heteroatom paraffin analogues were compared to those of the odd-chain n-alkanes of equal length. Of particular interest were the methylene wagging modes near 1350 cm-1 and the symmetric methyl group bending mode (“umbrella band”) near 1370 cm-1. Splitting of the methylene rocking band near 720 cm-1 indicated that the methylene subcell packing was O⊥ for crystalline compounds. A weak N-H stretching mode near 3290 cm-1 was also monitored for the secondary amine. Results Crystal Habit and Layer Packing. Monolamellar lozenge crystals obtained by evaporation of dilute solutions closely resembled those found for orthorhombic paraffins.20 The dominant crystal face for the secondary amine was (0,0,1) wherein chain ends terminate. The lateral chain packing was bounded by {1,1,0} faces. Electron diffraction patterns from them were typical of the [0,0,1] projection of the orthorhombic perpendicular (O⊥) methylene subcell21 (Figure 1a). From measurements of patterns calibrated with an internal gold powder diffraction standard, a ) 7.52(2) and b ) 5.04(1) Å. From systematic absences on reciprocal axes, the layer symmetry group was found to be pgg. Diffraction patterns from solution-crystallized dihexadecyl ether (Figure 1b) were characteristic of the Kitaigorodskii22 R[(1,0] layers, with chains inclined approximately 27° to the methyl end plane normal (parallel to the viewing direction). A similar layer packing and electron diffraction pattern have been found for cetyl palmitate (hexadecyl hexadecanoate).23,24 In earlier electron diffraction studies of this ether,23 a ) 5.64 and b ) 7.43 Å, in accord with results of this study. Also in agreement with earlier work,23 the crystal habits were poorly defined. There was also evidence for a second rectangular layer packing for this material from h,k,0 patterns resembling Figure 1a. Binary Phase Behavior. From DSC measurements, the melting point of n-heptatriacontane was 77.5 °C compared to a predicted25,26 value of 77.0 °C. The measured transition enthalpy was 230.1 J/g vs a predicted value of 258.7 J/g. (Predictions were based on curve fits to experimental data in earlier studies.26) The dialkylamine melted at 72.6 °C with a transition enthalpy of 264.9 J/g. For the n-alkane, a rotator phase transition was observed 1.7 °C below the melt. After the solid was equilibrated at room temperature for over a week, the constructed binary phase diagram (Figure 2a) revealed a linearly continuous melting curve between the pure components, indicating that the two materials were nearly ideally cosoluble over the whole concentration range. This identified close adherence to Raoult’s law was similar to observations made on n-paraffins copacking with n-perdeuterioparaffins having the same chain length.27 (Actually, the secondary amine and n-paraffin did appear to fractionate at a lower temperature. This may be due to the gradual emergence of incompatible polymorphic forms
534 J. Phys. Chem. B, Vol. 104, No. 3, 2000
Dorset et al.
Figure 1. Electron diffraction patterns from heteroatom-substituted polymethylene chains crystallized from dilute solution: (a) N,Ndioctadecylamine; (b) dihexadecyl ether.
Figure 2. Binary phase diagrams of heteroatom-substituted chains with n-paraffins of the same chain length. The size of individual endotherms is associated with the type of binary interaction (see ref 42). Large transition enthalpies are indicated schematically by “b”. For a continuous solid solution, nearly the same value is retained for intermediate compositions. For eutectic interactions, the enthalpies (schematically: “×” for intermediate values, “O” for small values) become smaller for the liquidus curve, or correspondingly larger for the solidus curve, as the eutectic point is approached. (a) N,Ndioctadecylamine with n-heptatriacontane. This forms a continuous solid solution from the melt. (The points marked “2” indicate a small endotherm that appears in aged samples, perhaps denoting fractionation; the points marked “×” are an identified rotator transition.) (b) Dihexadecyl ether with n-tritriacontane. While these components form the eutectic when the ether packs in oblique layers, an additional transition line (notation), superimposed on the diagram describing interactions between major polymorphs, indicates that the minor rectangular layer packing form may be cosoluble with the n-paraffin.
for the two substances, a topic to be investigated in future work. The nearly-ideal continuity of the melting line was used independently here to establish the close structural and volumetric similarity of the two compounds in their pure forms and in their binary solutions.22) The n-paraffin, n-tritriacontane, melted at 70.9 °C vs a predicted value of 70.3 °C. The observed transition enthalpy (rotator plus melting) was 239.5 J/g vs a predicted value of 254.5 J/g. A rotator phase appeared at 67.2 °C. The dicetyl ether melted at 53.2 °C with a transition enthalpy of ∆H ) 237.7 J/g. The binary phase diagram of the ether with n-C33H68 (Figure 2b) revealed that the major, monoclinic, polymorph of the ether was completely insoluble in the n-paraffin. However, a minor orthorhombic component may be continuously cosoluble with the n-paraffin (see notation in Figure 2b). Analysis of Diffraction from Epitaxially-Oriented Samples. The 0,k,l pattern from samples grown on naphthalene closely resembled those obtained from odd-chain n-paraffins, oriented in a similar way28 (Figure 3a). The lamellar spacing c/2 ) 49.97(35) Å agreed well with the value (49.0 Å) expected for n-C37H76 in an untilted orthorhombic form.29 The extinction rule for reflections in the [1,0,0] zone, k + l ) 2n + 1, moreover, was in accord with A21am space group symmetry of the Bpolymorph of the odd-chain n-paraffin with the same chain length.28 In infrared measurements, the N-H stretching band
was asymmetric at room temperature. At lowered temperature the frequency shifted by 8 cm-1 as the band became more symmetric, perhaps indicating a thermal motion effect on the amine group. The wagging modes indicated that there were no gauche conformations in the chains. Although the major umbrella band at 1375 cm-1 supported the orthorhombic chain layer packing, a shoulder at 1371 cm-1 may indicate an additional monoclinic form, unobserved by crystallography. After applying the approximately centrosymmetric crystallographic phases expected for the analogous n-paraffin model to the 0,0,l reflections, a series of atomic positions along z were clearly visualized, although some disorder is indicated in the terminal methyl position. Using the z/c positions from the onedimensional Fourier transform, and giving y/b values of 0.190 or 0.309 (from analogous n-paraffin crystal structures), respectively, for odd or even carbon positions (also the former for the central nitrogen position), the agreement of the model to the observed diffraction amplitudes (Table 1) was reasonably good (R ) 0.22). For the structure factor calculation, an isotropic thermal parameter B ) 3.5 Å2 was applied to all atomic positions, and a partial occupancy of 0.6 was given to the outer methylene to simulate the disorder (possibly due to end twists of the chain). The projected layer packing, shown in Figure 4a, reveals that the chains pack with planar zigzag conformations. Many of the electron diffraction patterns from epitaxially
Substitution and Packing of Polymethylene Chains
J. Phys. Chem. B, Vol. 104, No. 3, 2000 535
Figure 4. Projected chain packing for heteroatom-substituted chains: (a) N,N-dioctadecylamine; (b) dihexadecyl ether. (The chain zigzag is apparent in this potential map with methylene centers occurring at the peak maxima. The nonregularity of this sequence, particularly comparing the chain ends with the chain centers, indicates a molecular twist.)
TABLE 2: Observed and Calculated Structure Factor Magnitudes for Dihexadecyl Ether
Figure 3. Electron diffraction patterns (0,k,l) from epitaxially oriented samples, where the c*-axis is oriented horizontally, accounting for the closely spaced row of “lamellar” 0,0,l reflections: (a) N,N-dioctadecylamine; (b) dihexadecyl ether, monoclinic form; (c) dihexadecyl ether, orthorhombic form.
TABLE 1: Observed and Calculated Structure Factor Magnitudes for N,N-Dioctadecylamine 0,k,l
|Fobs|
|Fcalc|
0,k,l
|Fobs|
|Fcalc|
0,0,2 0,0,4 0,0,6 0,0,8 0,0,10 0,0,12 0,0,14 0,0,16 0,0,18 0,0,20 0,0,22 0,0,24 0,0,26 0,0,28 0,0,30
0.57 0.47 0.40 0.40 0.36 0.37 0.31 0.33 0.27 0.31 0.23 0.24 0.20 0.15 0.17
0.41 0.44 0.37 0.39 0.32 0.32 0.24 0.24 0.17 0.16 0.11 0.10 0.06 0.05 0.02
0,0,74 0,0,76 0,0,78 0,1,35 0,1,37 0,1,39 0,2,0 0,2,2 0,2,4 0,2,76 0,2,78 0,3,35 0,3,37 0,3,39
0.46 0.68 0.80 0.44 0.54 1.26 2.31 0.17 0.15 0.49 0.56 0.37 0.47 1.01
0.25 0.84 0.63 0.24 0.49 1.04 2.65 0.16 0.16 0.44 0.33 0.23 0.50 1.06
oriented dihexadecyl ether (Figure 3b) were consistent with an oblique layer structure projecting down the b ≈ 7.4 Å axis such that (c/2) sin β ) 39.8(2) Å and β* ) 63.8°, comparing well to
h,0,l
|Fobs|
|Fcalc|
h,0,l
|Fobs|
|Fcalc|
0,0,2 0,0,4 0,0,6 0,0,8 0,0,10 0,0,12 0,0,14 0,0,16 0,0,18 0,0,20 0,0,22 0,0,24 0,0,26 0,0,28 0,0,30
0.45 0.56 0.47 0.46 0.37 0.36 0.31 0.27 0.23 0.30 0.21 0.17 0.23 0.27 0.08
0.52 0.52 0.39 0.56 0.36 0.49 0.25 0.47 0.24 0.32 0.25 0.12 0.15 0.18 0.09
0,0,32 0,0,34 0,0,36 0,0,68 0,0,70 2,0,-34 2,0,-2 2,0,0 2,0,2 2,0,4 2,0,6 2,0,8 2,0,34 2,0,36
0.36 1.06 0.56 0.74 0.66 1.28 0.43 2.38 0.89 0.63 0.65 0.45 0.63 0.76
0.08 0.73 0.87 0.15 0.34 0.91 0.58 2.66 1.04 0.74 0.69 0.37 0.34 0.76
values obtained earlier from X-ray patterns12 ((c/2) sin β ) 39.1 Å, β* ) 63.1°). These patterns were often twinned and, moreover, there was also clear evidence for a second orthorhombic form (Figure 3c), crystallizing in space group A21am, where c/2 ) 45.1(3) Å. (The corresponding value29 for the orthorhombic n-tritriacontane is c/2 ) 43.9 Å.) Coexistence of two polymorphs for the ether was also indicated by the doubling of wagging bands in the infrared spectra. These may point to two different chain conformations as well. Moreover, there were also two umbrella bands supporting orthorhombic and monoclinic layer stackings. Indices of observed h,0,l reflections from the monoclinic form of the ether were consistent with the monoclinic space group Aa. The unit cell dimensions a ) 5.59, b ) 7.40, and c ) 88.66 Å and β ) 116.2° were accepted for the structure factor calculations. A model based on the continuous chain of ethyl stearate30 was constructed with appropriate elongation to obtain the initial phasing model (R ) 0.36). One cycle of Fourier refinement, where atomic positions were picked from the potential map, lowered the crystallographic residual to R ) 0.26 (Table 2) when the isotropic temperature factors B ) 6.0 Å2 were assigned to both heavy atom types. It is apparent that the chain conformation is not entirely a planar zigzag but, instead, is one that incorporates an overall conformational twist (Figure 4b). Discussion Volumetrically, replacement of an essentially tetrahedral methylene group carbon by an approximately tetrahedral amine nitrogen is obviously not sufficient to destroy the overall orthorhombic paraffin-like nature of this secondary amine in a way analogous to the oblique layer packing induced in the symmetric long chain ethers12 or fatty acid esters.31 The heteroatom to carbon (C-N) single bond distances, quoted32
536 J. Phys. Chem. B, Vol. 104, No. 3, 2000 as 1.46-1.47 Å for simple dialkylamines to 1.50 Å for the hydrobromide of this compound,33 are compared to a slightly larger 1.54 Å distance for the C-C single bond, and the 111° C-N-C and N-C-C bond angles are very close to those found experimentally for paraffinic C-C-C sequences. Zefirov34 distinguishes between the van der Waals radii of carbon and nitrogen in organic molecules, respectively: 1.50 and 1.71 Å. The C-H and N-H distances are very close to one another (values given from 1.04 to 1.08 Å), so that an internal methylene or secondary amine would not differ greatly in local crosssectional area. The only volume deficit, in comparison to the polymethylene chains, would be the removal of a hydrogen position within the substituted amine function, where it would be replaced by a lone electron pair. Substitution of a carbon by nitrogen has been investigated previously for binary solids of aromatic molecules. For example, a slight substitutional cosolubility can be found for biphenyl in R,R′-dipyridyl35 (and vice versa), but although both molecules crystallize in the same space group, the differences in unit cell constants and mode of molecular packing precludes continuous cosolubility over all concentrations.36 The phase diagram is eutectic. Of more interest are the anthracene-acridine binary solids.37 Although both molecules pack in unit cells with different dimensions, there are large continuous solubility domains across the concentration range. As found also for n-paraffins, this cosolubility is fostered by the possibility for polymorphism. A discontinuity of cosolubility, leading to a limited eutectic isotherm, also demonstrates that it is easier to accommodate voids in a binary crystalline solid than an increase in packing density (e.g., insertion of anthracene into an acridine lattice). The continuity of the melting curve for N,N-dioctadecylamine in n-heptatriacontane (Figure 2a) can be understood as a system where both pure components have the same unit cell dimensions, molecular packing motif, and space group symmetry. Cosolubility of the components of the binary solid merely involves the insertion of small vacancies as the amine concentration increases, but these are not as large as found for two cosoluble paraffin homologues, for example. However, since this insertion is made at the center of the chain, where conformational defects are least likely to be stabilized,38 local packing differences at low temperature may induce fractionation, perhaps explaining the function of the amine as a crystal growth modifier. On the other hand, an ether linkage including an oxygen with a van der Waals radius of 1.29 Å with no protruding hydrogens would amount to a greater difference in nonoverlap volume. There is also a lower rotational barrier in the ether bond linkages to permit nonplanar chain conformations to occur in this region of the molecule.39 With a local cross-sectional expansion of the chain due to conformational disorder, an oblique layer packing is preferred, as also found for the symmetric fatty acid esters.11 Thus, the fractionation of the monoclinic dicetyl ether in comixtures with the orthorhombic n-paraffin of equal length would resemble the case of a symmetric fatty acid ester with an n-alkane, already studied.40 On the other hand, there must also be the possibility for a more planar chain conformation to exist that is energetically close to that of the nonplanar form. This will permit the observed orthorhombic structure to crystallize and a continuous cosolubility to occur with the n-alkane of the same chain length. According to Kitaigorodskii and Myasnikova,41 the configurational (entropic) effect of comixing in the stable solid solution must outweigh other factors that could lead to fractionation of the ether and n-alkane. One such factor is the energy change due to the molecular conformation of the
Dorset et al. ether impurity. Other influences, such as the energy differences contributed by void-induced stresses, the change in molecular vibrational energy, or differences in the free energy of crystal packing, should be minimal. Thus, slight changes in conformation at the molecular center will nucleate different layer packings and lead to quite dramatic changes in cosolubility with alkanes. Similar subtle differences, e.g., asymmetric vs symmetric inclusion, are also found for the fatty acid esters, affecting how they would be incorporated into polydisperse waxes.1 Thus, even with conformational disorder, it may be that an asymmetric ether inclusion into a polymethylene chain may also allow cosolubility with the n-paraffin of comparable chain length. Acknowledgment. Research was funded by a grant from the National Science Foundation (CHE-9730317) to HWI and from the National Institutes of Health (G-27690) to UC Berkeley, which are gratefully acknowledged. References and Notes (1) Warth, A. A. The Chemistry and Technology of Waxes; Reinhold: New York, 1947. (2) Dorset, D. L. Acta Crystallogr. 1995, B51, 1021. Dorset, D. L. J. Phys. D: Appl. Phys. 1997, 30, 451. Dorset, D. L. J. Phys. D: Appl. Phys. 1999, 32, 1276. (3) Kern, R.; Dassonville, R. J. Cryst. Growth 1992, 116, 191. (4) Bennema, P.; Liu, X. Y.; Lewtas, K.; Tack, R. D.; Rijpkema, J. J. M.; Roberts, K. J. J. Cryst. Growth 1992, 121, 679. Simon, B.; Grassi, A.; Boistelle, R. J. Cryst. Growth 1974, 26, 90. (5) Strobl, G. R.; Trzebiatowski, T.; Ewen, B. Prog. Colloid Polym. Sci. 1978, 64, 219. (6) Tadokoro, H. Structure of Crystalline Polymers; Wiley: New York, 1979. (7) Dorset, D. L. J. Colloid Interface Sci. 1983, 96, 172. (8) Larsson, K. Acta Chem. Scand. 1964, 18, 272. (9) Abrahamsson, S.; Westerdahl, A. Acta Crystallogr. 1963, 16, 404. (10) Malta, V.; Cojazzi, G.; Zannetti, R.; Amati, L. Gazz. Chim. Ital. 1974, 104, 921. (11) Aleby, S.; Fischmeister, I.; Iyangar, B. T. R. Lipids 1971, 6, 421. (12) Kohlhaas, R. Chem. Ber. 1940, 73, 180. (13) Fryer, J. R. Inst. Phys. Conf. Ser. (EMAG) 1981, 61, 19. (14) Wittmann, J. C.; Hodge, A. M.; Lotz, B. J. Polym. Sci., Polym. Phys. Ed. 1983, 21, 2495. (15) Dorset, D. L.; Hanlon, J.; Karet, G. Macromolecules 1989, 22, 2169. Dorset, D. L. Macromolecules 1990, 23, 623. (16) Dorset, D. L. Structural Electron Crystallography; Plenum: New York, 1995. (17) Dorset, D. L.; McCourt, M. P.; Li, G.; Voigt-Martin, I. G. J. Appl. Crystallogr. 1998, 31, 544. (18) Doyle, P. A.; Turner, P. S. Acta Crystallogr. 1968, A24, 390. (19) Snyder, R. G.; Schachtschneider, J. H. Spectrochim. Acta 1963, 19, 85. Schachtschneider, J. H.; Snyder, R. G. Spectrochim. Acta 1963, 19, 117. (20) Dawson, I. M. Proc. R. Soc. (London) 1952, A214, 72. (21) Cowley, J. M.; Rees, A. L. G.; Spink, J. A. Proc. Phys. Soc. (London) 1951, A64, 609. (22) Kitaigorodskii, A. I. Organic Chemical Crystallography; Consultants Bureau: New York, 1961; p 190. (23) Schoon, Th. Z. Phys. Chem. 1938, B39, 385. (24) Dorset, D. L. Bioorg. Khim. 1976, 2, 781. (25) Dorset, D. L. Macromolecules 1990, 23, 623. (26) Broadhurst, M. G. J. Res. Natl. Bur. Stand. 1966, 70A, 481. Dollhopf, W.; Grossmann, H. P.; Leute, U. Colloid Polym. Sci. 1981, 259, 262. (27) Dorset, D. L. Macromolecules 1991, 24, 6521. (28) Dorset, D. L.; Zhang, W. P. J. Electron. Microsc. Techn. 1991, 18, 142. Dorset, D. L. Z. Kristallogr. 1999, 214, 223. (29) Nyburg, S. C.; Potworowski, J. A. Acta Crystallogr. 1973, B29, 347. (30) Aleby, S. Acta Chem. Scand. 1968, 22, 811. (31) Kohlhaas, R. Z. Kristallogr. 1938, 98, 418. (32) Sutton, L. E., Ed. Tables of Interatomic Distances and Configuration in Molecules and Ions; The Chemical Society: London, 1958. (33) Nyburg, S. C. Acta Crystallogr. 1996, C52, 192. (34) Zefirov, Yu. V. Crystallogr. Rep. 1994, 39, 939. Zefirov, Yu. V. Crystallogr. Rep. 1997, 42, 122. (35) Remyga, S. A.; Myasnikova, R. M.; Kitaigorodskii, A. I. SoV. Phys. Crystallogr. 1968, 12, 784.
Substitution and Packing of Polymethylene Chains (36) Kitaigorodsky, A. I. Molecular Crystals and Molecules; Academic: New York, 1973; p 96. (37) Myasnikova, R. M.; Kitaigorodskii, A. I. SoV. Phys. Crystallogr. 1958, 3, 157. (38) 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.
J. Phys. Chem. B, Vol. 104, No. 3, 2000 537 (39) Smith, G. D.; Boyd, R. H. Macromolecules 1990, 23, 1527. (40) Dorset, D. L. J. Polym. Sci. B: Polym. Phys. 1989, 27, 1161. (41) Kitaigorodskii, A. I.; Myasnikova, R. M. SoV. Phys. Crystallogr. 1961, 5, 610. (42) Tammann, G. A Textbook of Metallography; Chemical Catalog Co.: New York, 1925.
