3282
J. Phys. Chem. B 1999, 103, 3282-3286
Phase Separation of a Metastable Three-Component n-Paraffin Solid Solution Douglas L. Dorset* Electron Diffraction Department, Hauptman-Woodward Medical Research Institute, Inc., 73 High Street, Buffalo, New York 14203-1196
Robert G. Snyder Chemistry Department, UniVersity of California, Berkeley, California 94720-1460 ReceiVed: December 16, 1998
An equimolar combination of n-C28H58/n-C32H66/n-C36H74, crystallized from the melt, initially forms a solid solution. Electron diffraction data from the epitaxially oriented [100] projection can be used to determine its crystal structure, a pseudo n-C33H68 layer in space group A21am (a ) 7.42, b ) 4.96, c ) 87.40 Å). After 6 days at room temperature, a superlattice is formed (c ) 351.1 Å). Its crystal structure, suggested from the direct Fourier transform of 00l reflections, is a sequence of solid solution lamellar layers. After 16 months, another superlattice is observed with a spacing double the one found earlier. Its crystal structure appears to be a sequence of nearly pure n-alkane chain layers. While the behavior resembles the case of n-C30H62/ n-C36H74 solids, where n-C28H58/n-C32H66 1:1 is a pseudocomponent, the sequence of phase separation within the miscibility gap is more complicated than that of the binary combination.
Introduction As a model for the nonpolar part of amphiphilic molecules or, in their own right, as a component of petroleum waxes, mixed chain n-paraffins have been studied extensively for many years in order to determine what symmetry and/or molecular volume factors ensure their cosolubility in the solid state. Attempts to generalize these principles were made as early as 1960 when Mnyukh1 reviewed the already extensive experimental literature and applied principles for stabilization of solid solutions proposed by Kitaigorodskii.2 The absolute volumetric difference tolerated in a stable solid solution has been shown to be a function of the mean chain length.3,4 Although phase diagrams can appear to be continuous with concentration, the solutions themselves are discontinuous in unit cell symmetry,5-7 contrasting with original predictions.1,2 In some cases, a rectangular layer packing is maintained over all concentrations but with local variations in the unit cell symmetry within the crystalline solid.5 Quantitative crystal structures exist for such binary solids.8 In other cases, the oblique packing found for the pure components reverts to a rectangular layer packing when enough of the second component is added.6 For multicomponent waxes,9 the crystal structures also resemble the orthorhombic binary solid solutions. When a limiting boundary of relative molecular volume difference is crossed,4 the solid solutions can become metastable, slowly fractionating in the solid state into a superlattice-like array.4,10 This phenomenon was first noted by Mazee11 in his study of the C30H62/C35H72 binaries but shown later to exist for a number of other chain combinations.4,10 After numerous qualitative characterizations of this phase separation, a crystal structure has been reported12 for two nonequal combinations of C30H62/C36H74, the model fully in accord with earlier vibrational spectroscopic measurements.13 With greater differences in molecular volume, eutectic behavior begins to be observed,4,10 again at a boundary, delineating
this behavior from the metastable solid solution, which is rather sharp.14 This sensitivity to slight volume changes is underscored by the triggering of eutectoid behavior by just isotopic substitution (D for H) of the shorter chain component, e.g., in the C30H62/C36H74 binaries. The crystal structure of such a solid has also been reported.15 In the sequence of structures reviewed above, there is no case where “mechanical mixtures” of components can be found. While increasing volume differences of binary solids can lead to different chain layer assemblies, each is always a closely packed crystal structure where the presence of voids is kept to an absolute minimum. Because natural products are almost always polydisperse, it might be imagined that the structure of binary solids may serve only as a first approximation of the solids formed from multicomponent assemblies. In true solid solutions, however, there is very little evidence for any great difference. Again, the crystal structures of two petroleum waxes and a mineral (montan) wax, in addition to that of a synthetic “flat” wax (with equimolecular combination of components), have shown that the packing in the mixed chain monolayer is very much like that of the binary solid,9 recently verified in a three-dimensional structure analysis.16 This includes the formation of local crystal structures with different unit cell symmetries (i.e., mimicking either an average odd or even orthorhombic paraffin structure5). Is this similarity also true for the metastable solution; does the phase separation take place in a fashion similar to that of the binary when there are more than two components in the solid? The phase separation of a three-component assembly, composed of equimolar amounts of n-C28H58, n-C32H66, and n-C36H74, is described as a sequence of their crystal structures in order to detect similarities and differences. Materials and Methods Crystallization of n-Paraffin Combinations. Commercial sources, purities, and physical properties of the pure n-paraffins,
10.1021/jp9847639 CCC: $18.00 © 1999 American Chemical Society Published on Web 04/01/1999
Phase Separation of an n-Paraffin Solid Soluton
J. Phys. Chem. B, Vol. 103, No. 16, 1999 3283
Figure 1. DSC scans of n-C28H58/n-C32H66/n-C36H74 1:1:1, comparing an aged sample to one just recrystallized from the melt. The major difference is a small “mixing” endotherm (arrow) near 40 °C.
n-Octacontane (n-C28H58), n-dotriacontane (n-C32H66), and nhexatriacontane (n-C36H74), have been given in previous publications.4 The three paraffins were combined physically by weighing as equimolar quantities and then fused by melting. DSC measurements (made with a Mettler TA3300 instrument) on the solid formed just after comelting reveal the presence of a two endothermic transitions, a small one at 55.9 °C corresponding to transition from the orthorhombic to hexagonal “rotator” phase and a larger one at 65.6 °C which is due to the true melt (Figure 1). Upon being allowed to stand for 6 days, a very small “mixing endotherm” appears near 40 °C (Figure 1), much as observed, e.g., in n-C30H62/n-C36H74 solids,13,17 i.e., characteristic of the metastable behavior found for the binaries. (Similar behavior is found when hydrogen in either of the two largest paraffin components is completely replaced by deuterium.) For electron crystallographic characterization of the solid, microcrystals of the three-component combination were epitaxially oriented on benzoic acid substrates, as a variant of the procedure originally devised by Wittmann, Hodge, and Lotz.18 After crystallization of this paraffin/diluent eutectic on carbonfilm-covered electron microscope grids, the diluent was removed by sublimation in high vacuum to leave the oriented paraffin microcrystalline films. Electron Crystallographic Structure Determination. Procedures for electron crystallography have been reviewed in a recent monograph.19 Selected area electron diffraction patterns from the eptaxially oriented films (3-9 µm diameters sampled) were recorded at 100 kV on Kodak DEF-5 X-ray film using a JEOL JEM-100CXII electron microscope. Compared to X-ray diffraction, the spatial coherence of this method (Young’s fringe experiment) is very high, with coherence lengths typically 1.0 µm or greater.20 Care was taken to minimize the electron dose given to these specimens in order to reduce the likelihood of radiation damage. As shown by Glaeser and Thomas,21 the angular divergence of the incident beam is minimized by the condenser lens settings used for “low-dose” diffraction studies, thus optimizing further the spatial coherence of the electron beam. Diffraction spacings were calibrated against a gold powder diffraction standard. After measurement of unit cell constants and symmetry determination, diffraction intensities were measured on the films by scanning them with a Joyce Loebl Mk. IIIC flat-bed microdensitometer and then integrating the peak areas on the scans. No Lorentz correction was necessary, owing to the curvilinear distortion of the crystalline plates due to elastic bending.19 In the ensuing structure analysis, it was assumed that these intensities were close to the single scattering (kinematical)
Figure 2. Electron diffraction of n-C28H58/n-C32H66/n-C36H74 1:1:1 freshly crystallized on an epitaxial substrate to reveal solid solutionlike behavior.
Figure 3. One-dimensional Fourier transform of solid solution 00l reflections in Figure 2, revealing carbon positions in a single lamellar layer.
approximation, as justified by the final crystallographic residual R ) ∑||Fcalc| - k|Fobs||/∑|Fcalc|. Crystal structures of these solids have been determined by direct methods.8 For example, the average solid solution structures have been reported, either for binary or multicomponent solids, crystallizing either in space groups Pca21 (for even-chain orthorhombic structures22) or A21am (for odd-chain orthorhombic structures23). On the basis of previously established procedures,12 the structure of the superlattice-like solid that emerges from the metastable solid solution is determined in the following way. Structure factor amplitudes of the superlattice along the (00l) row are assigned indices that are nearly commensurate with an appropriate long unit cell repeat. Reflections in the diffraction row are then assigned crystallographic phases according to the phase envelope of the pure n-paraffin that models the parent solid solution layer repeat. (Although both space groups cited above are noncentrosymmetric, these phases are very close to the centrosymmetric 0, π values.) After computation of the reverse Fourier transform to a one-dimensional potential distribution, a likely chain repeat model is found by comparing nodes of the lamellar profiles with the known lamellar spacings of pure paraffins. This sequence is then used to construct a model for calculation of all 0kl structure factors, comparing these with the observed data.
3284 J. Phys. Chem. B, Vol. 103, No. 16, 1999
Dorset and Snyder
Figure 5. Layer structure found from analysis of lamellar row in Figure 4a. The equivalent n-paraffin chain lengths are indicated by the lines spanning the density minima. (The profiles are generated at lower spatial resolution than in Figure 3 to indicate just the lamellar envelope but not individual carbon positions.)
TABLE 2: Indices of Superlattice Reflections and Their Crystallographic Phases l
d*obs
d*calc
|Fobs|
phase
8 14 16 21 24 29 32 37 272 280
0.0232 0.0404 0.0460 0.0600 0.0684 0.0828 0.0902 0.1051 0.7752 0.7974
0.0228 0.0399 0.0456 0.0598 0.0684 0.0826 0.0911 0.1054 0.7747 0.7974
0.96 0.27 0.70 0.26 0.55 0.29 0.36 0.26 1.16 1.02
π π π π π π π π 0 π
TABLE 3: Observed and Calculated Structure Factors for Superlattice of Three Paraffins
Figure 4. Electron diffraction patterns, showing lamellar reflections after fractionation: (a) initial appearance of superlattice after 6 days at room temperature (Inset shows enlarged 00l row); (b) after solid equilibrates for 16 months.
TABLE 1: Observed and Calculated Structure Factors for the C28/C32/C36 1:1:1 Solid Solution 0kl
|Fo|
|Fc|
00 2 00 4 00 6 00 8 00 68 00 70 01 31 01 33 01 35 01 37 02 0 02 68 02 70 03 33 03 35
1.10 0.75 0.36 0.29 0.78 0.66 0.34 0.68 1.26 0.34 2.97 0.44 0.38 0.49 0.81
1.02 0.54 0.45 0.42 1.18 0.94 0.32 0.82 1.60 0.16 2.51 0.49 0.40 0.52 1.03
Results Electron diffraction patterns from freshly crystallized samples of the three-component paraffin combination, recorded to d* ) 0.894 Å-1 resolution, clearly resemble those of other solid solutions (Figure 2). The 00l lamellar row near the central beam in these 0kl patterns is attenuated in resolution, due to the presence of unequal chain lengths within individual lamellae. The lamellar spacing of many individual diffraction patterns, c/2 ) 43.70 ( 0.48 Å, is very close to the literature value24 for pure n-C33H68 (43.89 Å), but also there is a minor component of microcrystals that diffract as if the average structure is n-C34H70. Using the (m, m + 2) rule5 for indices of the most
0kl
|Fo|
|Fc|
00 8 00 14 00 16 00 21 00 24 00 29 00 32 00 37 00 272 00 280 01 124 01 132 01 140 01 148 02 0 02 272 02 280 03 132 03 140
0.96 0.27 0.70 0.26 0.55 0.29 0.36 0.26 0.78 0.66 0.34 0.68 1.26 0.34 2.97 0.44 0.38 0.49 0.81
1.11 0.12 0.91 0.24 0.69 0.20 0.46 0.12 0.45 0.44 0.28 0.55 1.13 0.07 2.93 0.24 0.23 0.59 1.24
intense reflections of the 01l row (where m is the average carbon number of a layer composed of n-CmH2m+2), the resemblance average n-C33H68 layer is again established. The crystal structure of the solid solution was modeled therefore with an orthorhombic unit cell in space group A21am, based on the carbon and hydrogen positions23 of n-C33H68. Here, the unit cell spacings are a ) 7.42, b ) 4.96, c ) 87.40 Å. Fractional atomic occupancies were assigned to carbon and hydrogen positions, viz: 0.50 at the terminal methyl positions and a respective increase by 0.79, 0.82, 0.85, 0.87, 0.89, 0.91, 0.94, 0.95, 0.96, 0.99, 1.00 for successive methylene positions as the center of the carbon chain was approached from either terminus. These occupancies were used to mimic the copacking of unequal chainlengths,6,8,25,26 giving a nearly Gaussian distribution of average vacancies in each lamella. Isotropic thermal parameters assigned to each atom type were BC ) 2.0 Å2 and BH ) 4.0 Å2. As shown in Table 1, the match of calculated and observed structure factor magnitudes, R ) 0.23, is quite reasonable. Chain carbon z/c positions, as well as their fractional carbon occupancies, are indicated in the one-dimensional Fourier transform based on phased 00l reflections (Figure 3).
Phase Separation of an n-Paraffin Solid Soluton
J. Phys. Chem. B, Vol. 103, No. 16, 1999 3285
Figure 6. Layer structures found from analysis of the lamellar row in Figure 4b. Again equivalent paraffin chain lengths are suggested (lines spanning deep density minima). However, it is possible to construct several alternative models to explain the packing of lamellae terminating in a shallow minimum. In any case, a lateral phase separation is indicated for this region.
The solid that is formed after equilibrating at room temperature for several days is betrayed by the electron diffraction patterns in Figure 4 a, i.e., a superlattice-like repeat is found for the 00l reflections. The overall resolution limit to the entire pattern does not change. All of the superlattice reflections are as sharp as those from the original solid solution. There are no signs of lateral or longitudinal “shape-transform” effects that would be due to extremely small, isolated subdomains with a unique structure. (All reflections were assigned a phase value of π radians, except for (00 68) with a 0 rad phase value.) If just the lamellar reflections are evaluated, a large lattice repeat could be specified with c ) 351.12 Å so that the reflection positions could be assigned nearly integral values (see Table 2). If the structure factor amplitudes were assigned crystallographic phases according to the phase envelope in the above solid solution structure, the reverse one-dimensional Fourier transform to the potential map clearly shows the sequence of lamellae. Using the known lamellar repeats of the pure orthorhombic n-alkanes,24 model lamellar repeats for the superlattice unit cell would be as shown in Figure 5a, identified by interlamellar interfacial density minima at dimensionally reasonable positions. A structural model was constructed, based on the lamellar sequence in Figure 4, and assuming a orthogonal cell with spacings a ) 7.42, b ) 4.96, c ) 351.12 Å, permitting just the x, y, z; 1/2 + x, -y, z symmetry operations for each layer. Using only carbon positions for the alkane chains in the successive lamellae, with fractional occupancies starting from the successive chain termini, respectively, 0.25, 0.50, 0.75, 1.00, ..., the agreement of calculated and observed structure factor magnitudes was again quite reasonable (R ) 0.24) as shown in Table 3. If the solid is allowed to equilibrate at room temperature for e.g., 16 months, there are further changes in the 00l superlattice pattern. The overall resolution of the pattern does not change. However, the resolution of reflections within the 00l row does increase (Figure 4b), indicating that the lamellar interfaces are more ordered. Furthermore, the previous indexing to simulate a nearly commensurate superlattice is no longer valid. If the c spacing is doubled (702.2 Å), the 00l indices again have nearly integral values. From the reverse Fourier transform (Figure 6), a sequence of paraffin chain lengths is again found, matching closely literature values for the pure orthorhombic lamellae.24 An ambiguity at a shallow-density minimum will be interpreted below. Discussion Selection of the three paraffins for construction of the metastable solid solution was not accidental. For example, it is well-known4 that the separate binary interactions of n-C28H58/ n-C32H66 and n-C32H66/n-C36H74 form solid solutions that remain stable for many years. In addition, the former 1:1 combination, which may often crystallize as an average n-C30H62-like layer, might be considered a “quasicomponent” to form, on average,
something like an n-C30H62/n-C36H74, binary with the longest n-paraffin chain. This was the operational premise from which the study began. On the other hand, it is also well-known that the greatest volume difference between chains would not favor stable continuous n-C28H58/n-C36H74 solid solutions4 and indeed a eutectic of solid solutions might be envisioned so that local combination of the extreme chain lengths may instead fractionate rather rapidly. As proposed, the presence of the intermediate chain length allows a metastable solid solution to be formed when the combination is crystallized from the melt. It is interesting that the average lamellar length of this solution is one methylene unit longer than that of the pure intermediate component (or perhaps two) but never equal to it. Otherwise, the crystal structure is the same as that found for any other paraffin solid solution of this kind, presuming that the average structure mimics the odd-chain orthorhombic model. The difference in behavior of binary and ternary combinations is found when the metastable solution begins to separate. As shown in recent descriptions of the binaries, the phase separation tries to sequester the individual chains into pure components, either as lateral islands13 or sequences of longitudinal domains.12 For the ternary system, solid solution behavior remains in each average layer. While average C33H68 layers are still found in the sequence, there will also be shorter C31H64- and longer C34H70-like layers interspersed to account for domains rich in either the short- or long-chain components. This is only a “snapshot” after a few days of separation. The segregation of components will continue over a much longer time frame so that the structure itself evolves to some final endpoint, where the layers again are dominated by chain lengths corresponding to nearly pure components. While the sequence of solid solutions found after initial phase separation seems to be uniform laterally (evidenced by the depth of the density wells between lamellae in Figure 5), the separation into layers that contain mostly one pure ingredient also contains domains where lateral separation must also be involved. (However, their dimensions are large enough so they are not detected via elongated diffraction spots, as stated above. In other words, the segregation appears to be incorporated into an average structure that is representative of the whole sample.) This would account for the shallow density in the center of the superlattice (Figure 6). Such behavior was observed earlier for binary solids observed within a miscibility gap12 or in eutectoid solids.15 Acknowledgment. Research was supported in part by grants from the National Science Foundation (CHE94-17835) to the Hauptman-Woodward Institute and the National Institutes of Health (GM-27690) to the University of California at Berkeley, both of which are gratefully acknowledged. References and Notes (1) Mnyukh, Yu. V. Zh. Strukt. Khim. 1960, 1, 370. (2) Kitaigorodskii, A. I. Organic Chemical Crystallography; Consultants Bureau: New York, 1961; pp 231-240.
3286 J. Phys. Chem. B, Vol. 103, No. 16, 1999 (3) Matheson, R. R., Jr.; Smith, P. Polymer 1985, 26, 288. (4) Dorset, D. L. Macromolecules 1990, 23, 623. (5) Dorset, D. L. Macromolecules 1987, 20, 2782. (6) Lu¨th, H.; Nyburg, S. C.; Robinson, P. M.; Scott, H. G. Mol. Cryst. Liq. Cryst. 1974, 27, 337. Gerson, A. R., Nyburg, S. C. Acta Crystallogr. 1994, B50, 252. (7) Dirand, M.; Achour, Z.; Jouti, B.; Sabour, A.; Gachon, J.-C. Mol. Cryst. Liq. Cryst. 1996, 275, 293. (8) Dorset, D. L. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 8541. (9) Dorset, D. L. Acta Crystallogr. 1995, B51, 1021. Dorset, D. L. J. Phys. D: Appl. Phys. 1997, 30, 451. Dorset, D. L. Z. Kristallogr., in press. (10) Dorset, D. L. Macromolecules 1986, 19, 2965. (11) Mazee, W. M. Am. Chem. Soc. DiV. Petrol. Chem. Prepr. 1958, 3 (4), 35. (12) Dorset, D. L.; Snyder, R. G. J. Phys. Chem. 1996, 100, 9848. (13) Snyder, R. G.; Goh, M. C.; Srivatsavoy, V. J. P.; Strauss, H. L.; Dorset, D. L. J. Phys. Chem. 1992, 96, 10008. (14) Dorset, D. L.; Snyder, R. G. Macromolecules 1995, 28, 8412. (15) Dorset, D. L. J. Phys. Chem. B 1997, 101, 4870.
Dorset and Snyder (16) Dorset, D. L. Z. Krist, in press. (17) Snyder, R. G.; Conti, G.; Strauss, H. L.; Dorset, D. L. J. Phys. Chem. 1993, 97, 7342. (18) Wittmann, J. C.; Hodge, A. M.; Lotz, B. J. Polym. Sci., Polym. Phys. Ed. 1983, 21, 2495. (19) Dorset, D. L. Structural Electron Crystallography; Plenum: New York, 1995. (20) Cowley, J. M. Diffraction Physics, 3rd ed.; Elsevier: Amsterdam, 1995; p 82. (21) Glaeser, R. M.; Thomas, G. Biophys. J. 1969, 9, 1073. (22) Teare, P. W. Acta Crystallogr. 1959, 12, 294. (23) Dorset, D. L.; Zhang, W. P. J. Electron. Microsc. Tech. 1991, 18, 142. (24) Nyburg, S. C.; Potworowski, J. A. Acta Crystallogr. 1973, B29, 347. (25) Asbach, G. I.; Geiger, K.; Wilke, W. Colloid Polym. Sci. 1979, 257, 1049. (26) Craievich, A.; Doucet, J.; Denicolo, I. J. Phys. (Paris) 1984, 45, 1473.
