J. phys. Chem. 1083, 87, 689-695
ruthenium(1) complexes. It remains to be investigated why this is so. Acknowledgment. P. A. Jacobs and R. A. Schoonheydt acknowledge a research position as Senior Research Associate from the Belgian National Fund of Scientific Re-
689
search. This research was supported by the Belgian Government (Geconcerteerde Onderzoehakties, Ministerie voor Wetenschapsbeleid). Registry No. CO, 630-08-0; HzO, 7732-18-5; Ru(NH3):+, 18943-33-4; R ~ ( N H ~ ) ~ ( c31418-66-3; ~ ) ~ + , RU(NH,)~(OH)~+, 38331-41-8.
structure of Rotator Phases in n-Alkanes Goran Ungar RMBr Boskovic Institute, 41001 Zagreb, Yugoslavia (Received: June 8, 1982; In Final Form: September 28, 1982)
Polymorphic behavior of crystalline odd-numbered n-alkanes from CllHa to C&52, as well as of binary mixtures, was studied by X-ray diffraction, differential scanning calorimetry (DSC), and infrared (IR) spectroscopy. With increasing temperature alkanes up to C21H44 undergo one first-order transition into an orthorhombic plastic (“rotator”)phase with a face-centered unit cell, space group Fmmm (phase denoted FCO). Longer n-alkanes (C23H48 and C25H52) undergo a further weak first-order transition into a rhombohedral (trigonal)modification 3-5 K below melting point. Its space group is R3m and it has a hexagonal subcell, while the unit cell extends through three molecular layers. In the shortest paraffin, CllH24, the ratio of lateral unit-cell parameters ao/bo in the FCO phase is 1.45-1.47 and is lower than in the ordered orthorhombic form (1.49). However, in the FCO phase of longer alkanes this ratio increases steeply with temperature, the increase being accelerated as ao/boapproaches the hexagonal lattice value of 3lI2. Another C-face-centered plastic phase is present in C23H48 between 39.5 and 41 “C. It is also observed in CzsHszon cooling. The more highly ordered modification, which appears in C26H52 1-2 K below the transition into the plastic state, and which is also found in longer alkanes, is shown by X-ray diffraction to be the modification B previously described in C33H68.
Introduction Odd-numbered n-alkanes with 9 to approximately 4 3 carbon atoms, as well as even ones with 22 to approximately 4 0 C atoms, exist in an orientationally disordered (plastic) crystalline state at temperatures several degrees below their melting points.’ Muller2 first observed that orthorhombic paraffin crystals tend toward, and in some cases reach, hexagonal symmetry on approaching melting temperature. He also proposed that molecules in the hexagonal phase rotate as rigid rods around their long axes and hence the name “rotator” phase for the disordered crystal form. The disordered phase has ever since received continuous attention and has been studied by a number of experimental techniques, as well as theoretically. One of the outstanding studies on polymorphic transitions in n-alkanes is that of Strobl and co-workers (see ref 3 for a review) performed on n-C33H68,where four crystal modifications were found and studied in detail. The highest-temperature modification can be classified as the rotator phase (the term “rotator” phase as used here does not imply existence of free rotation of molecules), but it is not hexagonal and the paraffin chains are tilted with respect to the molecular layer normal. Also, it was found to contain a considerable proportion of nonplanar molecules with one or two gauche bonds. As regards shorter paraffins, much less reliable information exists about the rotator phase. A number of theoretical studies however were performed in the past.44 Recently two primarily vibrational studies were reported, one by Zerbi and co-workers on C1gH4o7and the other by (1)M. G. Broadhurst, J. Res. Natl. Bur. Stand., Sect. A, 66, 241 (1962). (2)A. Miiller, h o c . R. SOC.London, Ser. A , 138,514 (1932). (3)B. Ewen, G.R. Strobl, and D. Richter, Faraday Discuss. Chem. SOC., 69,19 (1980). (4)J. D. Hoffman, J. Chem. Phys., 20, 541 (1952). (5)D. W.McClure, J. Chem. Phys., 49,1830 (1968). (6)D. H.Bonsor and D. Bloor, J. Mater. Sci., 12,1552 (1977). 0022-3654f 8312087-0689$01.50/0
Snyder and co-workers on odd alkanes C17H36 through C29HW8 Whereas previous papers, with the exception of that by Pecholde and the above-mentioned paper of Strobl and c o - ~ o r k e r sviewed ,~ the molecules as rigid all-trans forms displaying rotational and translational motion,lOJ1 the newest studies reveal a considerable fraction of molecules with some gauche bonds both near the chain ends7y8 and, in longer alkanes, also in the chain interior.8 Concerning the structural aspects, already in 1948 Mazee12observed that the rotator phase in nJ&HG and nC23H48has a base-centered orthorhombic unit cell. Subsequently, however, Larsson13 reported that C19H4,possesses a hexagonal subcell above the rotator transition but that the overall unit cell, which extends through two molecular layers, has orthorhombic symmetry due to the mode in which neighboring layers are stacked. While the present work was in progress, Doucet and co-workers14reported the rotator phase in C17H36, C1gH40, and C21H44 to have a base-centered orthorhombic unit cell, space group Ccmm, which in CsHu and C25H525 transforms into a hexagonal modification of undetermined structure a couple of degrees below the melting point. In the present study all odd-numbered n-alkanes from CllHU to C25H52, as well as selected binary mixtures, were investigated by X-ray diffraction, differential scanning calorimetry (DSC), and infrared (IR) and Raman spec(7)G. Zerbi, R.Magni, M. Gwoni, K. Holland Moritz, A. Bigotto, and S. Dirlikov, J . Chem. Phys., 76, 3175 (1981). (8)R.G. Snyder, M. Maroncelli, S. P. Qi, and H. L.Strauss, Science, 214,188(1981);M. Maroncelli, S.P. Qi, H. L. Strauss, and R. G. Snyder, J. Am. Chem. SOC.,104,6237(1982). (9)S. Blasenbrey and W. Pechold, Rheol. Acta, 6,174 (1967). (10)J. D. Barnes and B. M. Fanconi, J . Chem. Phys., 56,5190(1972). (11)J. D. Barnes, J. Chem. Phys., 58, 5193 (1973). (12)W.M. Mazee, R e d . Trau. Chim. Pays-Bas, 67,197 (1948). (13)K.Larsson, Nature (London),13,383 (1967). (14)J. Doucet, I. Denicolo, and A. Craievich, J. Chem. Phys., 75,1523 (1981). (15)J. Doucet, I. Denicolo, A. Craievich, and A. Collet, J. Chem. Phys., 75, 5125 (1981).
0 1983 American Chemical Society
6QO The Journal of phvslcal Chemlsby, Vol. 87, No. 4, 1983
Ungar
-j-
--
- .~
I
L
50
LO
-T
P
('C)
Flgwe 1. DSC thermogram of nCmH, showing five dlscontlnuous phase transitions. A hIgh-sensitMty recording is shown to emphasize the small endotherms. The phases are as follows: PO = primitive orthomombk, ccm(7) = Gfacecentered rotator phase (struchre not determined), fco = all-facecentered ortho"&, r = hombohedral, and Ilq
= liquid phase.
troscopy. Preliminary experiments were also made with n-C27H6sand n-C31HB4.This paper is only a limited account of mainly X-ray diffraction results so far derived. The work will be reported in full elsewhere.lB
Experimental Section All n-alkanes were obtained through Sigma Chemicals and were of approximately 99% purity. Analysis by gas chromatography and DSC revealed that only ClgHu and C27HW were of lower purity. DSC runs were performed on a Perkin-Elmer DSC-2 instrument in the mode for heat capacity measurements at a heating rate of only 1.25 K/ min and with 10-mg samples. Powder X-ray diagrams were recorded with a Guinier-Lenne-type low/high-temperature camera, either isothermally or in a continuous slow heating or cooling mode. A high-temperature powder diffractometer was also used. Temperature readout was accurate to within 0.1 K. Results Thermal Analysis. DSC thermograms of odd n-alkanes up to and including CzlHcrshow only one large endotherm, 8-14 K below melting point, which marks the rotator phase transition. From CBH4 onward the thermograms become much more complex, indicating a number of phase transitions with smaller heat effects. These additional transitions are found both below and above the main rotator one. As an example the thermogram of n-CBHB is shown in Figure 1. In all paraffins, as well as in their binary mixtures, the specific heat is found to be exceptionally high above the rotator transition, reaching up to 4.7 J/(g K) at temperatures far from any first-order transitions. The temperatures and heats of the main rotator transition for paraffins studied in this work agree well with those reported in the review by Br0adhurst.l X-ray Diffraction. Although the X-ray study was restricted to polycrystalline material, indexing of reflections and further analysis was facilitated by the following circumstances: (a) the unit cell in longer paraffins is always largely extended in, or nearly in, the chain direction; (b) advantage was taken of the existence of a sublattice in paraffin crystals, (c) the chain-length dependence and (d)
__
- _
~
~
_
_
-
__
.
m e 2. hh/ plane of the reciprocal lattlce in CPIHU. Only the section wlth (hhO), subcell reflection groups Is shown. Circles denote the observed reflecttons In the FCO phase. The 11 1, 1 13, and 115 arcs are shown In order to illustrate the extent of line separation in a powder dtffraction pattern. the temperature dependence of reflection positions have been measured and are known. An illustrative exposition of the sublattice concept can be found in ref 17. It seems worthwhile, however, to describe it briefly here. Let us first consider a perfect extended-chain polyethylene crystal whose reciprocal lattice consists of an array of points. Let the crystal now become lamellar through a shortening of the chains to the length encountered in n-alkanes. We thus obtain an isolated paraffin crystal layer and, instead of points, the reciprocal lattice consists of spikes oriented perpendicularly to the layer surface. The real paraffin crystal is a onedimensional lattice of such layers stacked on top of each other. What used to be the unit cell in polyethylene now becomes the subcell. In reciprocal space the one-dimensional lattice is represented by a series of parallel planes mutually separated by co*, the inverse of the layer repeat distance cW Nonzero diffraction intensity can only occur where both the conditions of the sublattice and of the above-mentioned one-dimensionallattice are satisfied. In reciprocal lattice terms, the result is that a sublattice spike samples out a series of points from the set of parallel planes which it intersects, as shown in Figure 2. In this way a group of discrete reflections is obtained. Such a subcell reflection group w i l l hereafter be denoted by the subscript s. It should be noted that, in the idealized paraffin crystal described above, we implied that the repeat distance co relates to only one layer spacing, whereas it relates to two layer spacings in most paraffin structures (see below). Also, the crystallographic axes need not be orthogonal. Ordered Crystalline Phases. It was confirmed that the lowest-temperaturemodification of all pure odd paraffins studied agrees with the orthorhombic structure determined for n-C23H,8by Smith,18having the space group Pcam. This will hereafter be referred to as the PO (primitive orthorhombic) phase. The binary mixtures, on the other hand, crystallize in a different orthorhombic modification, the structure of which we have not yet determined. This change in structure we regard as one of the reasons for the unusually large depression of the rotator transition temperature upon admixture of another paraffin of slightly different chain length.1gy20 A few degrees below the rotator transition a small en(17)W.Pieeczek, G.R. Strobl, and K. Malzahn, Acta Crystallogr.,
(16)G. Ungar and N. Vene, in preparation.
Sect. B, 30, 1278 (1974).
(18)A. E.Smith, J. Chem. Phys., 21, 2229 (1953).
~
Structure of Rotator Phases in +Alkanes
dotherm (AH= 1 J/g) is found in CBHa (at 34 "C, Figure 1) and in C25H52 (at 38.5 "C). The endotherm is absent in shorter alkanes. This transition was recently also observed by Snyder and co-workers8 in paraffins C25H52, CnHB, and C& and was termed 6 transition. The above authors detect a small increase in the number of endgauche bonds a t this transition using IR spectroscopy. On the other hand, we observe no discontinuity in temperature scans of X-ray diffraction that could be associated with this transition; neither the position nor the intensity of diffraction lines changes. The source of cooperativity that leads to the relatively sharp first-order transition remains unclear. The transition entropy, according to our measurement, amounts to only R In 1.13 and is thus too low to be assigned to the acquisition of any new orientational degree of freedom. Starting with n'C25H52 onward a new crystalline phase appears below the rotator transition. In our sample of C25H52 it is stable between 46.2 and 47.8 "C. An isotropic lateral lattice expansion occurs during the transition from the PO phase, the cross section per chain increasing by 0.6%. Snyder et a1.8 find a substantial fraction of molecules with end-gauche bonds in this, as they call it, phase IV. Our diffraction patterns show that its structure is monoclinic with an A-face-centered unit cell based on an orthorhombic subcell and thus c o n f m the suggestion8that it is isomorphous with the modification B first discovered by Piesczek, Strobl, and Malzahn'? in n-CSHm The latter authors determined the full structure of this modification, ascribing to it the space group Aa. It has been proposed3 that the molecules perform 180" rotational jumps between two equally probable orientations, which already brings this crystal modification out of the class of fully ordered phases. Orthorhombic Rotator Phase. It is now clear that there is more than one rotator phase with different crystal structures and that several rotator modifications can succeed each other with increasing temperature in a single system. Such is the case with n-CBHa and longer alkanes, as well as with binary mixtures starting with the system C19H40 + C21H44. Great attention was paid in this work to determiningthe packing mode in the most abundant of all rotator phases, the only plastic phase found in n-paraffins up to C2'H4 and which we find in a certain temperature range in CBHa and C25H52, as well as in the corresponding paraffin mixtures. In C23H48 this modification is stable between 41.0 and 44.5 "C (314.2-317.7 K, the range denoted fco in Figure 1). The position of diffraction lines for this phase agrees well with an orthorhombic structure with unit-cell dimensions similar to those below the rotator transition. Thus, there are four molecules per unit cell, two in the lower and two in the upper layer. A straightforward determination of the space group was possible thanks to the large range of paraffins studied and especially to the shortest ones in the group (CllHU, CI3HB, ...). In shorter alkanes the rotator phase occurs a t lower temperatures and has a higher degree of order, thus showing some of the lines a t larger Bragg angles which are not observed in longer alkanes. An even more important advantage of X-ray patterns from short alkanes is that the individual reflections within the same subcell reflection group (e.g., reflections 110, 111, 112 ... of the group 110,) are better resolved (see the diffraction pattern from CllHU, Figure 3), since the reciprocal axis co* is longer. The latter statement is readily visualized in Figure 2, which shows (19) W.M. Mazee, Anal. Chim. Acta, 17, 97 (1957). (20) D.H.Bonsor and D.Bloor, J. Mater. Sci., 12, 1559 (1977).
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983 691
0
..I I--
0 Q
L A,,o --cv
Figure 3. Section of a powder diffraction pattern of CllH,,
recorded with the temperature continuously increasing. Some of the reflections of the PO and FCO phases are indexed in the figure. R denotes a reflection of the supporting platinum mesh.
TABLE I: Measured and Calculated Reticular Distances in the FCO Phase of C,,H, at 238 K (Range 4.5 > d > 2.2 A ) 110 111 113 200 202 204 020 311
4.166 3.906 3.707 3.612 3.357 2.548 2.219
0.005 f 0.005 f 0.005 f 0.005 0.005 ~t0.003 f 0.003 f
4.201 4.165 3.906 3.708 3.611 3.360 2.550 2.219
the reciprocal lattice in C2'H4. In the shortest alkane, CllHU, the layer-line separation co* is approximately twice as large as in C2'H4; this results in a better resolution of individual reflections in the former paraffin. On the other hand, a larger number of reflections is usually observed within a subcell reflection group in longer alkanes. A sample list of measured and calculated reticular distances is given in Table I for CllHU at -35 "C (238 K). It was established that the general reflection conditions (hkl) are h + k = 2n and h + I = 2n. This reduces the choice to only three space groups: Fmmm, F222, and Fmm2. The special positions with multiplicity 4 (four molecules per unit cell) have the same spatial arrangement in all these space groups. The arrangement is depicted in Figure 4A. We now resort to the IR and Raman spectroscopic evidence that the molecules are found primarily in the alltrans straight-chain conformation or a t least that gauche bonds, where present, are not positioned in a regular fashion in the crystal, which might otherwise reduce the symmetry of the average m o l e c ~ l e . Consequently, ~~~ a mirror plane perpendicular to the chain axis exists in an average odd n-alkane molecule, which leaves the space group Fmmm (0;;)as the single possible choice. This all-face-centered orthorhombic phase will hereafter be referred to as the FCO phase. In Figure 4A the bow-shaped motifs schematically represent the orientation probability density function of the molecular vector r' which originates in the center of mass of the molecule and bisects the LCCC angle (see Figure 4C). The true orientation function cannot, of course, be determined from the present data, but it must be consistent with the site point group mmm, where the coordinate axes are parallel to those of the crystal lattice. It is important to note that the orientation function is identical for all
692
Ungar
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983
x
I
31
I
25
A
I
A
220
280
260
240
300
320
T (lo
Figure 6. Temperature dependence of lateral unit-cell dimensions a and bo for n-alkanes C11H24 to C25H52. Vertical broken lines mark the discontinuous phase transitions. For the rhombohedral phase in CBHa and C25H52 the orthohexagonalvalues a , and bo are shown (cf. Figure 3B). Largest error margins, f0.01 A.
ah b0
I
I - r
1
I
I
25 21
a0
Figure 4. Schematic representation of molecular arrangements in the FCO phase (A) and in the rhombohedral phase (B). View along c axis (i.e., chain axis). Full symbols represent molecules in the first layer, open ones those in the second, and the ones drawn with broken lines represent molecules in the third layer. (C) Illustration of the molecular vector i .
’.I c11
220
25OrV290
I
I
310
I
I
T(K)
330
Figure 7. Temperature dependence of the a olbocell parameter ratio for n-alkanes C11H2,, C21H44, and C25H52.
-
Qs
Figure 5. Side view (schematic) of the subcell in the low-temperature PO form (A) and in the rotator phase (B).
molecules, i.e., that, as far as X-ray crystallography is concerned, all molecules are equivalent. The symmetry of the “average” molecule in the FCO phase presupposes a reduction of the subcell dimension c,. Compared with the PO modification, c, is probably halved, as shown schematically in Figure 5, although an even greater reduction in c, cannot be excluded. Halving of c, implies disappearance of all reflections belonging to what in the PO form used to be the (hkl),groups with odd I (e.g., group (hkl),). The diffraction pattern from the rotator phase indeed does not show any such reflection. In fact, only reflections belonging to the (hkO),groups are observed. However, it must be remarked that groups (hkl), with I 2 2 are not expected to be seen anyway in disordered phases of an unoriented paraffin sample since the line intensity at the correspondingly large scattering vectors is already too low. Thus, the question whether c, is even more than halved in the rotator phase (in which case reflection groups (hk2), would also be forbidden) cannot be answered at present. The described FCO modification shows several interesting features. Firstly, the lateral unit-cell dimensions undergo drastic changes in a small temperature interval (Figure 6). Meanwhile, the length of the unit cell, co,
jumps up by only 0.0-0.6 A (0.00-0.01%) upon the PO FCO transition (“rotator transition”) in paraffins CllH24 to C25H52, respectively. There is further continuous small increase in co with increasing temperature in the FCO phase (the largest increase is from 57.59 to 57.84 A in C21H44). The ao/bo ratio in the FCO phase increases steeply with temperature, tending toward 31/2,the value characterizing a hexagonal subcell. Figure 7 shows temperature dependence of the ao/boratio for three selected n-alkanes: CllH24,C21H44,and C25H52. Compared to its value in the PO phase, the ao/boratio of the FCO phase is higher in C17H36 and longer paraffins, but it is lower (lattice is “less hexagonal”) in C11H24 and C13H28. For C15H32 the ao/boratio is similar in both phases. It is because only higher members of the series were considered in the past that the name “hexagonal”, or “pseudohexagonal”,phase came into use for denoting the high-temperature modification in n-alkanes. The transition into the rotator state is accompanied by a considerable increase in unit-cell volume, which is almost entirely due to transverse expansion. The increase in basal FCO transition is larger in area aobo during the PO longer and smaller in shorter alkanes; thus, for C25H52 the product aobojumps up by 0.9 Hi2, and for CllH24 by only 0.65 Hi2. This appears to be the reason for the observedl but so far unexplained increase in latent heat of the rotator transition, in J/g, with increasing chain length in the series of odd n-alkanes. The temperature expansion coefficient of the FCO phase varies with temperature, but it is typically 2-3 times as
-
Structure of Rotator Phases in n-Alkanes
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983
large as that of the low-temperature PO phase. Accordingly, the FCO phase is marked by high specific heat, as mentioned previously. Some information about the stacking of molecular layers can already be derived from a qualitative consideration of the 001 reflections. The transition from the low-temperature to the rotator phase is accompanied by some broadening of the 001 lines, particularly those with larger 1. The integral intensity also decreases more steeply with increasing 1 so that, e.g., the 008 line of the FCO phase in C23H48is barely visible, whereas reflections up to 1 = 12 are observed in the PO phase. The steep decrease in intensity with increasing 1 indicates a “rough” layer surface in the rotator phase.21 Even within the same FCO phase a higher-order 001 line is found in some cases to fade out with increasing temperature. For example, in CZ1H4the 0 0 10 reflection is clearly visible just above the PO-FCO transition but disappears a few degrees below melting point. Thus, it is concluded that the interlayer becomes progressively more diffuse (“rougher”) with increasing temperature in the rotator phase. Judging by the temperature scans of CBHMand c25H62 the same trend is also continued through the hexagonal transition (see below). As to the 001 line intensity extrapolated to 1 = 0, it actually increases slightly upon the PO-FCO transition. This is ascribed to some thickening of the interlayer whose electron density is lower than that within a layer.21 A detailed quantitative analysis of the 001 reflections will be the subject of a separate study. The above-mentioned preliminary observations are so far in agreement with the recent spectroscopic evidence of a certain fraction of not fully stretched (kinked) molecules in the rotator phase8 and of some chains protruding out of their surface and twisting their end^.^,^ Both effects are expected to cause a roughening of the layer interface. Hexagonal Phase. The crystals of paraffins up to nCZ1Humelt before becoming hexagonal. However, in the case of CZ3HM and C25H52 the melting point is sufficiently high to allow the existence of a modification with a truly hexagonal subcell within a range of 3-5 “C. With increasing temperature the FCO phase gradually transforms toward hexagonal symmetry until the ao/bo ratio of 1.69 is reached. At this point a discontinuous transition brings about the hexagonal modification which is characterized by only one strong diffraction line instead of the two strong lines 111 and 200 of the FCO phase. In agreement with the recent report by Doucet et al.15this first-order transition is manifested as a small but very sharp endotherm in the DSC thermogram. In our sample of CBHMit occurs at 48.1 “C, with a at 44.5 OC (see Figure 1) and in CP5H52 transition enthalpy of only 1.0 J/g, or 0.08kcal/mol. Our X-ray results relating to the hexagonal transition, i.e., attainment of hexagonal subcell symmetry, differ from those of Doucet et al. in that these authors record neither the discontinuous change in lattice parameters nor the change in layer stacking mode (see below). The change in layer spacing upon the FCO hexagonal transition is negligible and is within the limits of experimental error of 0.05 A (
