A Binary n-Alkane Phase Revisited. Overcrowding and Molecular

12418

J. Phys. Chem. B 2001, 105, 12418-12426

A Binary n-Alkane Phase Revisited. Overcrowding and Molecular Deformation in the β-Phase of C24H50:C26H54 Stanley C. Nyburg,* Angela Carstensen, and Carolyn A. Koh* Department of Chemistry, King’s College, UniVersity of London, Strand, London WC2R 2LS, England ReceiVed: June 5, 2001; In Final Form: September 27, 2001

The first single-crystal X-ray diffractometric structure analysis to be performed on a binary n-alkane phase was carried out on 0.77:0.23 C24H50:C26H54 in our laboratories in 1994. New insights are now provided from a detailed examination of the atomic coordinates. It is shown how impossibly short hydrogen-hydrogen atom intermolecular distances rule out certain types of end-to-end molecular packing. Even when these restrictions are taken into account, H‚‚‚H contacts exist which, although not short enough to rule out the molecular packing in question, are almost certainly responsible for anomalous temperature factors and for bending the otherwise normally straight backbone of these molecules. Our analysis shows that, as in the pure n-alkanes themselves, the molecular chains have the all-trans conformation. A proposal by Dorset that the chains in the binary phase have terminal gauche conformations is examined and dismissed.

Introduction

For n even

Ever since Smith2 examined the melting point curve of C16: C18 (Cn ) CnH2n+2) over the whole composition range, there has been considerable interest shown in solid phases containing two (or more) different n-alkanes. Temperature/composition phase diagrams have been determined by differential scanning calorimetry (DSC) and by X-ray powder diffraction. Where the latter are interpretable, phases have been allocated to crystal systems. Freshly prepared binary phases prepared from the melt sometimes show diffraction patterns that change on standing; others appear to be stable indefinitely. The published literature on n-alkane binary phases is far too large for complete citation here. Full references can be found in extensive lists published in the most recent papers by Dirand and co-workers3 and Dorset and co-workers.1 Phase diagrams fall into two groups, those showing a number of solid solutions and those showing eutectic behavior. Typical of the former is the C20:C22 system illustrated in Figure 1.4It is generally agreed that the smaller the difference in the number of carbon atoms in the two components the more likely are solid solutions to be formed. Larger differences cause immiscibility in the solid phase and the formation of a eutectic. From a simple model of n-alkane binary phases, Matheson and Smith5 derived an equation for the limits placed on the difference in chain length for solid solution (rather than eutectic) formation to be possible. The number of carbon atoms in the longer alkane, cNmax, is governed by the number in the shorter alkane, cNmin, by cNmax < 1.22 cNmin - 0.411. C40:C50 marginally violates the inequality.6 Much is known of the crystallography of the pure n-alkane components themselves and some generalizations can be made. For CnH2n+2 , systems and space groups are as follows. For n odd

n g 11, orthorhombic, Pbcm or Pbnm * Corresponding authors. E-mail: [email protected]. Phone: +44-0-207-848-2161. E-mail: [email protected]. Phone: +44-0-207848-2380. Fax: +44-0-207-848-2810.

6 e n e 26, triclinic P1h n g 26 monoclinic monoclinic P21/a or orthorhombic Pbc21 Key crystal structures are known in each of these groups, and from them the unit cell dimensions and crystal structures of all the others can be derived.7 In all cases, the molecules have planar all-trans conformations and are packed with their backbones parallel to form layers. In some cases the unit cell spans two such layers The longest cell dimension is conventionally designated as c. X-ray powder diffraction patterns show that the solid solution binary phases have the same overall layer-type structure as the pure components themselves. However, it was not until we obtained qualitatively determined intensities from X-ray diffraction precession photographs from single crystals of the β and βo phases of C20:C224 that the crystal structure of any solid solution binary structure was known in complete detail. Both phases are orthorhombic, despite the fact that the pure components crystallize in the triclinic system. The β phase shows the same type of bilayer structure as the pure alkanes with n odd but in space group Bb21m, having a different relative disposition of the two layers. Single crystals of the corresponding β phase of C24:C26 were later subject to full three-dimensional X-ray diffraction examination.8 This proved to be isostructural with the β phase of C20:C22, and it is the details of this former structure that are now being examined in this paper. The βo phase crystallizes in orthorhombic Fmmm and is highly disordered. The only other single-crystal studies of binary n-alkane phases of which we are aware are those of Dorset using thin epitaxially grown microcrystals for electron diffraction. He has found9 C32: C36 and C33:C36 binary phases to be isostructural with our C24:C26 β phase. He has ascribed10 another C32:C36 microcrystal to a different orthorhombic space group, Pca21, based only on two-dimensional diffraction data.

10.1021/jp012150h CCC: $20.00 © 2001 American Chemical Society Published on Web 11/15/2001

Binary n-Alkane Phase of C24H50:C26H54

J. Phys. Chem. B, Vol. 105, No. 49, 2001 12419

Figure 1. Temperature/composition phase diagram of C20:C22. [This is Figure 2 (p 341) of Lu¨th et al.4Copyright 1974 Gordon & Breach Science Publications Ltd., Dordrecht, Holland. Reproduced with permission.]

In an Abstract, Smith11 reports on 0.5:0.5 and 0.67:0.33 mixtures of C24 and C26, giving c cell dimensions of 137.2 and 202.0 Å, respectively. These are almost exactly 2.0 and 3.0 times the value we have consistently found. We can only assume Smith observed Bragg reflections that interleave ours. A superstructure with a c spacing of 445.2 Å has been reported for C30:C36.12 Denicolo et al.13 examined the C23:C24 system by DSC and X-ray powder photography. Their phase diagram closely resembles that of β-C20:C22 (and presumably C24:C26). However, to the phase in that region of their phase diagram corresponding to our β-phase, they assign to a primitive orthorhombic cell, whereas ours is B-centered. If their assignment is correct, it would be a matter of considerable interest because we show below that our binary phase at least could not crystallize in the primitive-cell space group Pbcm shown by the pure odd-numbered n-alkanes. In our 1994 paper we did not fully explore the molecular implications of the crystal structure. We did point out obvious limitations on the way in which the two types of component molecule could pack. As a consequence of our renewed interest in alkane waxes, of which these binary phases can be considered prototypes, we were in the process of reappraising the results when Dorset’s paper1 came to our attention. In his paper, Dorset claims there is doubt as to whether our 1994 structure is wholly correct. This has given us an added incentive to reappraise the structure.

Crystal Structure None of the single crystals of this phase 0.72:0.28 C24:C26 that we were able to prepare from solution were ideal for structure analysis. The habit is platy and the crystals commonly consist of several slightly misaligned components that cannot be separated without fracture. Uniform extinction in crossed polarized light is uncommon. Such genuinely single crystals as could be obtained were always very thin and fragile and often slightly bowed. Diffraction data were also commonly not ideal. Bragg 2θ profiles were often not smooth, indicative of the presence of more than one crystal component. Low values of the residual R cannot therefore be expected. The crystals are orthorhombic, unit cell 4.992(1), 7.503(3), and 67.448(8) Å, and space group Bb21m. The chemical composition and crystal density (ca. 1 g./ml.) show that there are, on average, Z ) 4 molecules per cell. Using the NRCVAX crystal structure system14 least squares refinement gave a final R value of 0.11. The binary structure shows close similarity to that of many pure odd-numbered n-alkanes with space group Pbcm. In particular, both kinds of structure are bilayered, each layer having the molecules lying parallel to c and packed sideby-side in exactly the same way. The difference between the crystal structure of these pure alkanes and that of the binary phase lies in the symmetry operation connecting two adjacent layers. As we shall see, there are cogent reasons for this difference. Structure analysis reveals four 27-peak motifs per unit cell. According to the International Tables,15 in this space group,

12420 J. Phys. Chem. B, Vol. 105, No. 49, 2001

Nyburg et al. TABLE 1: Numbering, Fractional Coordinates, Isotropic Temperature Factors (Å2), and Occupancies for Carbon Atoms in the Fourteen Independent Peak Positions of the Motif C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12) C(13) C(14)

x

y*

z

Biso, Å2

occupancy

0.82(3) 0.72(2) 0.82(1) 0.692(6) 0.816(6) 0.704(6) 0.811(6) 0.693(6) 0.818(6) 0.695(6) 0.813(6) 0.705(6) 0.819(6) 0.698(7)

0.000(2) 0.109(9) -0.027(7) 0.046(5) -0.043(5) 0.030(5) -0.059(5) 0.028(5) -0.052(5) 0.029(5) -0.060(5) 0.032(5) -0.061(4) 0.020

0.245(2) 0.2260(9) 0.2082(6) 0.1875(4) 0.1705(4) 0.1517(4) 0.1319(4) 0.1128(4) 0.0940(4) 0.0763(4) 0.0572(4) 0.0372 0.0189 0.0

5(3) 18(3) 8(1) 6.6(3) 6.6(3) 6.6(3) 6.6(3) 6.6(3) 6.6(3) 6.6(3) 6.6(3) 6.6(3) 6.6(3) 2.8(7)

0.22(4) 0.75(7) 0.75(4) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

a In the space group Bb21m the position of the origin on the y axis is arbitrary. It has been chosen to coincide with the molecular backbone.

TABLE 2: Hydrogen Atom Fractional Coordinates Generated by NRCVAXa 1a 1b 1c 2a 2b 2c 3a 3b 3c Figure 2. Electron density section at y ) 0. [This is Figure 4a of Gerson & Nyburg.8 Copyright 1994 The International Union of Crystallography. Reproduced with permission.]

four motifs must lie in special equivalent positions and have mirror planes of symmetry normal to z through their centers. Figure 2 is the electron density section at y ) 0 showing three half-motifs. One has its center on the mirror plane lying at z ) 0, the other two with their centers lying on the next layer, with a mirror plane at z ) 1/2. Peaks in the motifs are numbered from 1 at one end to 14 (at the center) and then, primed, from 13′ to 1′. The C26 molecules have two choices of occupying the 27-peak motif (1 through 2′ and 2 through 1′). The C24 molecules have four such choices (1 through 4′, etc.). This choice is revealed by the fractional occupancies of carbon atoms located at the outer ends of the motif. Fractional atomic coordinates, occupancies and temperature factors of carbon atoms assigned to the peak positions are given in Table 1. It is clear that, using normal nonbonding interatomic distances, the terminal peaks lying close together near z ) 1/4 (Figure 2) cannot all be simultaneously occupied by carbon atoms in the same unit cell. We discuss this in detail below. Hydrogen Atom Interactions Any intermolecular conflicts that might arise in the crystal structure will be due to unacceptably short H‚‚‚H distances. Unfortunately, the F data and the extensive disorder in the structure are such as to prevent our determining hydrogen positions directly by Fourier analysis especially at the outer ends of the motifs. The positions of hydrogen atoms that are potentially liable to close H‚‚‚H intermolecular contacts were those generated by NRCVAX and are given in Table 2.

x

y

z

0.7502 0.0360 0.7547 0.5052 0.8156 0.7831 0.75015 0.0360 0.7488

0.8663 0.9731 0.0888 0.1260 0.23778 0.0413 0.8394 0.9731 0.0666

0.24790 0.24410 0.25663 0.22579 0.22496 0.23930 0.21114 0.2073 0.2192

a Note hydrogen atoms of type c are only present if a methyl group is allocated to the peak.

We have carried out a survey of H‚‚‚H nonbonded distances retrieved from the Cambridge Organic Structure Database16 (Nyburg et al.17). Distances range from about 2.0 Å for headto-head contact (C-H‚‚‚H-C) to about 2.6 Å for sideways contact. The region of potential conflict is close to the plane z ) 1/4 (and z ) 3/4). Figure 3 shows four motifs in the z-projection. Motifs are designated according to their general equivalent positions:

[

A x B 1-x

z

/2 + y

z

1

y

1

1 /2 - x

1

D x - /2 E

y

1

1

/2 + y

/2 - z /2 - z

1

]

C1-C2 bonds such as A1-A2 point away from the viewer, bonds 1′ to 2′ such as D1′-D2′ toward the viewer. It is convenient to group the H‚‚‚H interactions into two types. First those occurring between hydrogen atoms in motifs having the same equivalent y-coordinates such as A‚‚‚D‚‚‚A‚‚‚D‚‚‚ or (symmetrically equivalent) B‚‚‚E‚‚‚B‚‚‚E‚‚‚ Second those between hydrogen atoms in motifs having different equivalent y-coordinates such as A (or D)‚‚‚E‚‚‚(A or D)‚‚‚E or (symmetrically equivalent) A (or D)‚‚‚B‚‚‚A(or D)‚‚‚B‚‚‚. As to the first group, in all the known crystal structures of pure n-alkanes the hydrogen atoms of the terminal methyl groups are staggered with respect to those of the adjacent methylene.



Figure 3. z-projection showing unacceptably the short H‚‚‚H intramolecular distances that prevent the carbon atom occupation of juxtaposed A1/D1′ and E1′/B2 locations along the x-axis.

This is due to the approximately 3.5 kcal mol-1 barrier to rotation of the methyl hydrogen atoms.18 If peak positions 1 in A and 1′ in D (or equivalently 1 in B and 1′ in E) are occupied by terminal methyl groups, there will be impossibly short H‚‚‚H contacts of 1.40 and 1.44 Å between methyl hydrogen atoms, as shown in Figure 3. When such impossibly short distances are invoked, the possibility of rotation of the methyl hydrogen atoms must be considered. Rotation, if it occurs, will be such as to reconcile the opposing requirements of minimizing the repulsive intermolecular interactions with maximizing the most favored molecular conformation. However in this case, if free rotation of the methyl group hydrogen atoms is allowed, it can be shown (in-house software) that the longest H‚‚‚H contact possible is still unacceptable at 1.76 Å. Clearly, adjacent motifs having the same equivalent y-coordinates cannot have methyl carbon atoms simultaneously at positions 1 and 1′. The A1-toD1′ methyl hydrogen conflict is also illustrated in y-projection, Figure 4. The same type of potential source of conflict is that between methyl hydrogen atoms at site positions 1 and 2′ or, equivalently, 1′ and 2. For methyl hydrogen atoms in their most stable conformation, there are again unacceptable H‚‚‚H contacts of 1.74 and 1.75 Å. Figure 3 is a composite z-projection showing both A1‚‚‚D1′ and E1′‚‚‚B2 (same as A1‚‚‚D2′ by symmetry) conflicts. Figure 5 shows the A1‚‚‚D2′ conflict in the yprojection. Thus for adjacent motifs having the same ycoordinates, they can neither have both 1 and 1′ positions occupied by methyl groups nor can 1 and 2′ positions. Last, in the same group, we examine 1 and 3′ or 1′ and 3 site occupancies (not illustrated). Here, the shortest H‚‚‚H contact is 2.60 Å, which is perfectly acceptable. A similar situation arises with a peak 2 to peak 2′ juxtaposition (when compared to a 1 to 3′ juxtaposition, this simply entails the same reduction in z-coordinates of both motifs). Thus the shortest H‚‚‚H distances are virtually the same at 2.67 Å and perfectly acceptable. Clearly then, the ability for the carbon atoms of the C24 and C26 molecules to occupy the 27-atom peak positions of the motif is in no way random. If an A molecule has position 1 occupied by a methyl group, the adjacent D molecules cannot have their methyl groups in positions 1′ or 2′. Position 3′ is

allowed and it is presumably the 1 to 3′, 2 to 2′, and 3 to 1′ contacts that govern the c dimension of the unit cell. For a 1 to 3′ juxtaposition the number of atoms between z ) 0 and peak 1 is 13 1/2 and between peak 3′ and z ) 1/2 is 11 1/2, making 25 atoms in all. It is of interest and importance to note that the c cell parameter of pure C25H52 is 67.41 Å,19 virtually identical to ours. This almost exact match is somewhat surprising since C25H50 crystallizes in a different space group, Pbcm, where the end-to-end molecular packing is different from that in the binary phase. (A similar observation has been made for the C20:C22 system, where the c-spacing matches that of pure C21H4420). Possible reasons why the C24:C26 binary phase does not also crystallize in Pbcm are given later. We turn now to the second group of possible interactions, those between hydrogen atoms on motifs with different equivalent y-coordinates. In this group we have to concern ourselves not only with methyl hydrogen atoms but also with methylene hydrogen atoms. We concentrate on A(or D)‚‚‚E‚‚‚A(or D)‚‚‚E because A(or D)‚‚‚B‚‚‚ interactions are the same. We have seen that adjacent A‚‚‚D‚‚‚A positions (and B‚‚‚E‚‚‚B positions) cannot be randomly occupied. Even so, we are left with a large number of packing possibilities. It turns out, however, that all such possibilities can be covered in just three diagrams, Figure 6a-c. These three diagrams show, in turn, the three allowed A‚‚‚D‚‚‚A juxtapositions, namely, A1‚‚‚D3′, A2‚‚‚D2′, and A3‚‚‚D1′ It will be seen that there is a large number of H‚‚‚H contacts shorter than 2.4 Å. (Some contacts recur even though the A‚‚‚D‚‚‚A packing is different.) We consider that none of these contacts are sufficiently short to prevent atoms from occupying the positions shown, especially as rotation of methyl hydrogen atoms will lengthen some contact distances. We believe, however, that they affect temperature factors and molecular geometry. Temperature Factors; Molecular Distortion Dorset1 (loc. cit. p 233) comments on the fact that in our structure analysis, the carbon atoms in peak 1 and peak 1′ positions have, unusually, lower temperature factors than those in positions 2 and 2′. These factors were given by least-squares analysis and we believe have a rational explanation. Figure 3


Nyburg et al.

Figure 4. A1/D1′ conflict in y-projection.

Figure 5. A1/D2′ conflict in y-projection.

assumes the methyl groups all to be in the most favored conformation. Doubtless there will be rotations of the methyl groups in order to lessen H‚‚‚H conflicts and the conformational requirements will be in opposition to such rotations. It is virtually impossible to assign final conformations for any of the packing possibilities with any degree of confidence except perhaps to assume that after such rotations, the shortest H‚‚‚H distances will still be the shortest. This allows us to make some general observations. First, a methyl group at E1′ is enclosed by three very short contacts 2.09, 2.10, and 2.10 Å (Figure 6a), and this could conceivably explain why a carbon atom at peak 1 (and, by symmetry, peak 1′, Table 1) has an uncharacteristically small temperature factor. Second, parts a-c of Figure 6 show clearly that the short H‚‚‚H contacts to motif E are very asymmetrically distributed. We believe it is this asymmetry of these short interactions that has brought about a significant distortion of the molecule. In our original paper,9 we did not examine the geometry of the 14 independent positions of the 27-peak motif in detail. If the motif were planar with its backbone parallel to the z-axis, the x and y coordinates of all peak positions would be the same. Table 1 shows this is not so. We find that the outer peaks of the motif are not coplanar with the remainder. Table 3 shows the deviations of all the peak sites from the best least-squares plane of atoms C4 through C13. Terminal atoms C2, C2, and C3 are strikingly out-of-plane. This can be seen in Figure 7.

these, an accurate value of d(001) can be obtained. If the phase is known to belong to the orthorhombic system, as is commonly the case, then d(001) equals the c cell parameter. (If the system is of lower symmetry, this is not so.) For a given phase, c can be determined as a function of composition. According to Vegard’s Rule,21 if the phase is a solid solution, the c parameter should be a linear function of the composition. Many such determinations have been made, but few, if any, appear to obey this rule. In some cases the dependence is erratic, some values of c lying above a smooth curve connecting values at the extremities, others below. Possible reasons are that the samples were not all properly annealed or that there is some uncertainty in the exact composition of that region of the phase which is in the X-ray or electron beam. Another important possibility for deviations from Vegard’s Rule is that, as the proportion of the longer alkane chain increases, there comes a point where the crystal motif is not long enough. If this is so, and there is no change in structure type, there will be a sudden lengthening of the motif by two methylene groups, one at each end. This will increase the c cell parameter by 2.54 Å. There appear to be no really convincing examples of this but some that are suggestive. Thus C32:C37, studied by Dorset6 (loc. cit., Figure 5a) has c values that, around C37 ) 0.1, are 45 Å and that increase somewhat erratically to 50 Å at C37 ) 0.9. This might reasonably be due to two steps increasing by 2.5 Å each time. A somewhat less convincing example is provided by C28:C34.

The c Cell Parameter

Inability of the Binary Phase To Crystallize in Pbcm

It is normally a simple matter to identify and index the 00l reflections on the X-ray powder diagram of a binary phase. From

The binary phase crystallizes in a different orthorhombic space group from that, Pbcm of a large number of odd n-alkanes



Figure 6. All the short H‚‚‚H intramolecular distances experienced by a molecule at site E from neighboring A and D molecules in allowed positions: (a) For methyl groups at ‚‚‚A1‚‚‚D3′‚‚‚A1‚‚‚. (b) For methyl groups at ‚‚‚A2‚‚‚D2′‚‚‚A2‚‚‚. Hydrogen atoms HE1′b and HE3′b overlap in this projection. H‚‚‚H distances to HD2′b are 2.31 and 2.26 Å, respectively. (c) For methyl groups at ‚‚‚A3‚‚‚D1′‚‚‚A3‚‚‚. H‚‚‚H distances to HD2′b are as for (b). Hydrogen atoms HD1′b and HD3′b also overlap in this projection. Distances to HE2′b are 2.31 and 2.26 Å, respectively.


Nyburg et al.

TABLE 3: Atom Deviations (Å) Deviations of Atoms C4-C13 from Their Best Least Squares Plane C4 0.019 C5 0.040 C6 -0.005 C7 -0.047 C8 -0.044 C9 0.026 C10 -0.020 C11 -0.021 C12 0.044 C13 0.008 Deviations of Outer Atoms from This Plane C1 0.247 C2 0.272 C3 0.123

such as C25H52.19 Cell dimensions for this structure, a ) 4.97(5), b ) 7.478(5), c ) 67.41(10) Å, closely resemble those for the binary phase. As in the binary phase, the structure is bilayered but the relation between the upper and lower layers is different. It is this fact that prevents the binary phase from crystallizing in Pbcm. In the binary phase the chains in the lower layer lie between z ) -1/4 and +1/4. The upper layer is formed from the lower by B-centering, that is by a translation of x ) 1/ and z ) 3/ . The upper layer therefore lies between z ) 1/ 4 4 4 and 3/4. In C25H52, the lower layer lies between z ) 0 and 1/2 and the upper layer is formed from this by the action of a center of symmetry at (1/2, 1/2, 1/2) causing it to lie between z ) 1/2 and 1. From atomic coordinate data provided by Smith,19 it is easy to add extra fictitious methyl groups to the ends of the 25 carbon atom chain to give an all-trans 27-peak motif like that found in the binary phase. Using the now different general equivalent positions for the new Pbcm space group we assign four motifs as follows:

[

A x

y

B 1-x

1

D x

1

E

1-x

z

/2 + y z /2 - y 1 - z

1-y

1-z

]

As before, peaks are numbered from the end of the motif inward. The region of potential conflict is z ∼ 1/2. Atoms lying below this are unprimed; those above are primed. As before, we first consider A, D conflicts. If both motifs have peak positions 1 occupied by methyl groups there is a drastic clash between HA1a and HD1′a of 0.58 Å. (This latter hydrogen atom is not shown in Figure 8 but, in z-projection, it will have the same position as HD3′a. This shows clearly why HA1a to HD1′a is so short.) If now the terminal methyl group on motif D is at position 2′, there is still an unacceptable conflict HA1a to HD2′c of 1.39 Å. Last, if the terminal methyl group of motif D is at position 3′, there are no unacceptably short H‚‚‚H distances. To this extent, the packing in Pbcm would be akin to that in Bb21m of the binary phase. However, given that A has a terminal methyl at position 1 and a terminal methyl position on D at position 3′, there are still quite unacceptable H‚‚‚H distances between hydrogen atoms between motifs A and E. (Figure 8). (By symmetry, the same unacceptable distances, not shown in Figure 8, occur between motifs B and D.) Figure 8 shows A to E H‚‚‚H clashes for all possible methyl group occupancies. Clearly, however, as in the binary phase, there is a large number of different occupancies possible around any one particular peak occupied by a methyl group. Some of

Figure 7. Three terminal atoms at each end of the motif significantly out-of-plane with the rest. This will be more clearly seen if the figure is viewed at glancing angle.

these will not involve unacceptable H‚‚‚H distances. Thus, for example, as in Figure 8, if motif A has position 1 occupied and the neighboring E motif has position 3′ occupied, no unacceptable clashes result. However, this type of occupancy cannot happen everywhere throughout the crystal if both C24 and C26 molecules are to be accommodated. Hence the type of clashes shown in Figure 8 would be bound to occur in many sites. This demonstrates clearly why the binary phase does not crystallize in Pbcm, which would entail replacing the B-centered translation relating upper and lower layers by a center of symmetry. Gauche Conformation and Raman Spectra Dorset1 has prepared crystalline samples of 0.75:0.25 C24: C26 (i.e., close in composition to our crystals) by epitaxial growth and subjected the samples to electron diffraction. He assigned phases to 12 photographically measured 00l diffraction amplitudes from which he obtained a one-dimensional potential plot. This consisted of 25 strong peaks, 12 either side of a central peak. Although outside the last peak the potential was still positive, it was deigned too vestigial to be part of an all-trans chain. This observation forms the first basis of Dorset’s questioning of our 27-peak motif. Dorset’s second basis is his use of our X-ray F data to carry out (apparently all two-dimensional) Fourier summations. Again he found an only 25 strong peak motif. We believe these apparent differences in results arise from Dorset’s use of two-



Figure 8. Short H‚‚‚H distances in the hypothetical C24:C26 phase in orthorhombic space group Pbca.

dimensional data, which give Fourier plots far less accurate than those using all the three-dimensional data. He also states (loc. cit. p 234) that if F phases are calculated for a C25H52 motif, the resultant Fourier plot shows no further peaks. This is hardly surprising. The crucial test would be to use three-dimensional data to obtain the ∆F plot, followed by least-squares refinement. Dorset states (loc. cit. p 234) that we assumed that the “chains are conformationally extended as all-trans entities”. This is categorically not so. No molecular assumptions of any kind were made apart from the empirical chemical composition. Most of the motif was obtained by direct methods (which involve no assumptions as to molecular geometry) and the remaining peaks established from three-dimensional ∆F plots and least-squares refinement. Clearly, a 25-peak motif cannot completely describe the crystal structure since C26H54 molecules have to be accommodated. Dorset’s explanation is that the terminal carbon atoms of the motif are not trans-coplanar to the remainder but are, to some unspecified extent, gauche. The basis for this proposal seems to relate to certain Raman spectra discussed below. A gauche conformation, of necessity, requires there to be a significant torsion angle between the two planes, peaks 1,2,3 and peaks 2,3,4, achieved by rotating the bond between peaks 1 and 2 about the peak 2-3 axis. Because, at torsion angles (60°, there is an energy barrier estimated at 3.31 kcal/mol,18 the most likely two places to find such a peak would be those generated by torsion angles of (120°. It is a relatively simple matter to calculate the trajectory of peak 1, which would result from any such rotations. We had previously made a careful study of this region of the unit cell and found neither F nor ∆F peaks. In view of Dorset’s paper,1 we removed the peak 1 carbon atom and its attendant hydrogen atoms from the calculation of F’s and then performed the ∆F synthesis. Peak position 1 was restored and no other significant peaks found for the entire range ((180°) of torsion angles. Dorset gives no coordinates for a carbon atom in his postulated gauche conformation. He does, however, give a two-dimensional y-projection of electron density obtained from our intensity data, which shows vestigial peaks outside the 25-peak motif (loc. cit. Figure 5). By implication,

Figure 9. Gauche conformations of a carbon atom at A1 for every 40° rotation about A2-A3. Note that the greater the gauche rotation, the more the z-coordinate of the atom differs from 0.25.

these vestigial peaks are gauche positions. They appear to lie exactly on z ) 0.25. But such peaks cannot result from any gauche rotation. This is shown clearly in Figure 9, where, as can be seen, the greater the rotation, the further will the terminal carbon atom be from z ) 0.25. Quite apart from the fact that we can find no evidence for any gauche conformations in the crystal structure, it should be


Nyburg et al.

Figure 10. Raman spectrum in the methyl rocking region of the binary phase 40:60 C24,C26. Conformations: t, trans; g, gauche.

stressed that even a modest movement of any terminal carbon atoms toward a gauche conformation will seriously disrupt the structure given here. Thus a mere 20° rotation of carbon atom A1 about A2-A3 will seriously decrease the H‚‚‚H distance of HA1c to HE1′a (Figure 6a) from 2.10 Å to an impossible 1.84 Å. Clearly, atom E1′ would have to move to accommodate this conflict and this movement itself will invoke movements elsewhere in the crystal structure. As noted above, the basis of Dorset’s1 attribution of a gauche conformation to the terminal carbon atom of the C24:C26 binary phase is related to certain Raman spectra of alkane mixtures examined, among others, by Snyder and co-workers.22 They prepared a number of binary and tertiary alkane solid phases from the melt. Their Raman spectra show, in addition to the intense band at 890 cm-1 attributed to the all-trans chain conformation, weaker bands in the region down to 800 cm-1. These are attributed to the presence of a gauche conformation at the ends of alkane chains. These Authors nowhere state categorically that gauche conformations are present in the truly crystalline phase. In fact they are ascribed to “the interlamellar region”, with which we agree if this refers to the boundaries of the crystal mosaic blocks. We have also found weak Raman bands in the region down to 800 cm-1 from the 40:60 C24:C26 binary phase (Figure 10). We have also noted that these bands are increased slightly in intensity when the crystals are either crushed or solidified after melting. (Sudden drastic cooling had no effect.) These results, it seems to us, are simply due to reduction in size of the mosaic blocks and hence to an increase in the extent of boundaries between them. This theme is being developed in an article currently in preparation. Gauche conformations have also been identified in the Raman spectra of urea complexes, to a small extent with n-alkanes23 but to as much as 50% with certain halagenoalkanes.24 Although diffraction studies of single crystals of multiple alkane phases are still limited in number, it is striking that (see Dorset1) there is not a single example where, using threedimensional data, not only the presence but also the actual fractional coordinates of such any carbon atom in gauche conformation have been determined. In short, we believe the claim that such gauche conformations occur in the truly crystalline regions of these materials remains unproven. Conclusions Binary n-alkane solids that crystallize in the orthorhombic space group Bb21m with a ∼ 5 Å and b ∼ 7.5 Å are almost

certainly isostructural with that described here. Multicomponent n-alkane solids (i.e., the alkane waxes) meeting these criteria, almost certainly have the same type of structure. They form a unique class of molecular crystal where the molecules are in all-trans conformation. There is no evidence for any parts of the molecules to be in gauche conformation. Potential molecular conflict restricts the choice of molecular site and gives rise to significant molecular distortion. Acknowledgment. Financial assistance from Chevron Petroleum Technology Research, Houston and the Gas Research Institute, Chicago, IL, is gratefully acknowledged. References and Notes (1) Dorset, D. L. Z. Kristallogr. 1999, 214, 229-236. (2) Smith, J. C. J. Chem. Soc. 1932, 737-741. (3) Chevallier V.; Petijean, D.; Bouroukba, M.; Dirand, M. Polymer 1999, 40, 2129-2137. (4) Lu¨th, H.; Nyburg, S. C.; Robinson, P. M.; Scott, H. G. Mol. Cryst., Liq. Cryst. 1974, 27, 337-357. (5) Matheson, R. R, Jr.; Smith, P. Polymer 1985, 26, 288-292. (6) Dorset, D. L. Macromolecules 1990, 23, 623-633. (7) Nyburg, S. C.; Potworowski, J. A. Acta Crystallogr. 1973, B29, 347-352. (8) Gerson A. R.; Nyburg, S. C. Acta Crystallogr. 1994, B50, 252256. (9) Dorset, D. L. Macromolecules 1987, 20, 2782-2788. (10) Dorset, D. L. Proc. Natl. Acad. Sci. 1990, 87, 8541-8544. (11) Smith, A. E. Acta Crystallogr. 1957, 10, 802-803. (12) Dorset, D. L.; Snyder, R. G. J. Phys. Chem. 1996, 100, 98489853. (13) Denicolo, J.; Craievich, A. F.; Doucet, J. J. Chem. Phys. 1984, 80, 6200-6203. (14) Larson, A. C.; Lee, F. L.; Le Page, Y.; Webster, M.; Charland, J. P.; Gabe, E.; White, P. S. NRCVAX; Ottawa, Canada, 1994. (15) International Tables for Crystallography; D. Reidel Publishing Co.: Dordrecht, The Netherlands, 1984-. (16) 3D Search & Research using the Cambridge Structural Database. Allen, F. H.; Kennard, O. Chemical Design Automation News 1993, 8, 3137. (17) Nyburg, S. C.; Faerman, C. H.; Prasad, L. Acta Crystallogr. 1987, B43, 106-110. (18) Smith, G. D.; Jaffe, R. L. J. Phys. Chem. 1996, 100, 18718-18724. (19) Smith, A. E. J. Chem. Phys. 1953, 21, 2229. (20) Gerson, A. R.; Sherwood, J. N.; Roberts, K. J.; Hausermann, D. J. Cryst. Growth 1990, 99, 145-149. (21) Vegard, l. Z. Phys. 1921, 5, 17. (22) Clavell-Grunbaum, D.; Strauss, H. L.; Snyder, R. G. J. Phys. Chem. B 1997, 101, 335-343. (23) Kobayashi, M.; Koizumi, H.; Cho, Y. H. J. Chem. Phys. 1994, 93, 4659-4672. (24) Smart, S. P.; El Baghdadi, A.; Guillaume, F.; Harris, K. D. M. J. Chem. Soc., Far. Trans. 1994, 90, 1311-1322.

A Binary n-Alkane Phase Revisited. Overcrowding and Molecular

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