Crystal Structures and Glassy Phase Transition Behavior of

Dec 15, 2007 - Didcot, Oxfordshire, OX11 0QX, United Kingdom, School of Chemistry, The UniVersity of Edinburgh,. King's Buildings, West Mains Road, ...
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Crystal Structures and Glassy Phase Transition Behavior of Cyclohexene Richard M. Ibberson,*,† Mark T. F. Telling,† and Simon Parsons‡ ISIS Facility, STFC-Rutherford Appleton Laboratory, Harwell Science and InnoVation Campus, Didcot, Oxfordshire, OX11 0QX, United Kingdom, School of Chemistry, The UniVersity of Edinburgh, King’s Buildings, West Mains Road, Edinburgh, EH9 3JJ, United Kingdom

CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 2 512–518

ReceiVed June 18, 2007; ReVised Manuscript ReceiVed September 24, 2007

ABSTRACT: The complex phase behavior of cyclohexene, C6H10, has been characterized between 2 K and its melting point at 170 K using complementary high-resolution neutron powder diffraction and single-crystal X-ray diffraction techniques, and the crystal structures of the three known ambient-pressure phases have been determined. Phase II is the sole orientationally ordered structure of cyclohexene, crystallizing in the triclinic space group P1j. Phase I and metastable phase III may be characterized by the mode of orientational disorder corresponding to free uniaxial rotation and ring inversion of the molecules, respectively. Phase I is cubic with space group Pa3j, and the molecule is located on a 3-fold axis with Z′ ) 1/3. Phase III is monoclinic with Z′ ) 2 and space group P21/c, but with pseudocubic character inherited from the phase I structure. In this phase, only one of the molecules in the asymmetric unit is disordered and exhibits ring inversion which freezes at the glass transition temperature around 80 K. Introduction Cyclohexene, C6H10, is one of the fundamental structures in the stereochemistry of organic compounds. Accordingly, the molecular geometry and conformational characteristics has been the subject of extensive experimental and theoretical studies. Cyclohexene is also of interest as one of the family of organic molecular crystals with pseudospherical cage or monocyclic ring structures that typically exhibit order–disorder phase transitions in the solid state (see, for example, ref 1). Indeed, this type of phase transition in cyclohexene was observed and characterized by Huffman using calorimetric methods as early as 1948.2 More recent and extensive studies by Haida et al.3,4 using differential thermal analysis (DTA) and adiabatic calorimetry revealed a more complex phase behavior involving metastable and glassy crystalline states dependent on the thermal history of the sample (see Figure 1). It was found that by slowly cooling a sample through the melting point at 170 K an orientationally disordered phase I forms that transforms reversibly to a metastable phase III at 112 K. Cyclohexene-III exhibits glassy crystalline behavior if cooled below 83 K. A sample cooled rapidly however may be quenched into a glassy crystalline form of phase I, termed gI, which on warming undergoes a series of often overlapping transitions as shown in Figure 1. The stable low-temperature phase II forms irreversibly from phase I at 120 K and was observed down to the low-temperature limit of the experiment of 60 K. The phase I to phase II transition was also found to be dependent on both the thermal history of the sample and its purity and gives rise to different thermal behavior in the temperature range 120–140 K. Thus, cyclohexene is shown to have two glassy orientationally disordered crystalline phases and one fully ordered low-temperature form. Cyclohexene can also exhibit a third glassy liquid state when prepared using vapor condensation methods,3,4 and remarkably, the glass transition temperatures in all cases are very similar. The molecular motion and phase transition behavior of cyclohexene has also been studied using spectroscopic tech* To whom correspondence should be addressed. Tel.: +44(0)1235 445 871. Fax: +44 (0)1235 445 383. E-mail: [email protected]. † ISIS Facility. ‡ University of Edinburgh.

Figure 1. Phase behaviour of cyclohexene for rapidly (>7 K/min) and slowly cooled samples after the work of Haida et al.4

niques. NMR temperature-dependent measurements of the second moment and spin–lattice relaxation5 are in broad agreement with the calorimetry results for a rapidly cooled sample, although an anomaly reported at 128.5 K was not observed in the calorimetric study. The NMR results suggest that in cyclohexene-I the molecules undergo uniaxial rotation about an axis normal to the plane of the molecule; whereas, in phase III, the molecules undergo ring inversion between mirror images of the half-chair molecular conformation. Vibrational spectra (FTIR and Raman)6 also confirm this complex phase behavior. Spectra corresponding to the stable phase II structure were noted as being distinctive from all other phases and suggest the crystal structure to be monoclinic or triclinic (C2h or Ci) with two molecules per primitive unit cell. In contrast, phase I is characterized by asymmetric line shapes of the internal vibrational bands and the presence of broad peaks in the lowfrequency region of the Raman spectra indicative of the molecules undergoing anisotropic rotation. The frequency of the ring inversion mode was noted as being highly phasedependent. Here, we report the crystal structures of the three lowtemperature phases of cyclohexene. The low melting point and

10.1021/cg0705512 CCC: $40.75  2008 American Chemical Society Published on Web 12/15/2007

Structure and Phase Behavior of Cyclohexene

Crystal Growth & Design, Vol. 8, No. 2, 2008 513 Table 1. Crystallographic Data for the Phases of Cyclohexene-d10

crystal system space group a (Å) b (Å) c (Å) R (deg) β (deg) γ (deg) V (Å3) Z Dcalc (g/cm3) T (K)

Figure 2. Typical diffraction thermogram recorded on OSIRIS on warming. Peaks corresponding to phase III change abruptly to phase I at 120 K. Peaks corresponding to phase II are observed between 130 and 145 K, and the sample reverts to single phase I at 150 K.

complex phase behavior, including first-order phase transitions, of cyclohexene represent particular technical difficulties for both powder and single-crystal diffraction techniques. However, the complementary use of both techniques has enabled a full and detailed structural study to be completed including a description of the nature of the glassy behavior in phase III of the compound. Experimental Details Cyclohexene, C6H10, is a clear colorless liquid with a melting point of 170 K and a boiling point of 356 K. Samples of normal (99+%) and perdeutrocyclohexene (C6D10, 99+%) were obtained from SigmaAldrich for the single-crystal X-ray and neutron powder diffraction studies, respectively. Neutron Powder Diffraction Measurements. A 2 g portion of cyclohexene-d10 was sealed in an 11 mm diameter vanadium sample can containing glass wool to promote the growth of fine crystallites on freezing. The sample was loaded in a vanadium-tailed “orange” cryostat and a series of time-of-flight neutron powder diffraction scans were collected initially using the OSIRIS spectrometer7 at the ISIS pulsed neutron source in order to characterize the low-temperature phase behavior. When run in diffraction mode, the OSIRIS instrument operates typically with its two disk choppers rotating at 25 Hz providing a 2 Å wide d-spacing band of diffraction data, the limits of which are determined by delays to the opening of the disk apertures relative to the source. A complete diffraction pattern may thus be recorded by merging a series of these data sets covering the full spectral range of the instrument. For the present studies however, a novel configuration was adopted in which the disk choppers were spun at 10 Hz to provide a 5 Å wide d-spacing band offering a more efficient data collection strategy to rapidly survey the phase diagram with counting times of typically 10 min per temperature. Data were recorded at backscattering, ) 160°, over a time-of-flight range of between 12 and 112 ms, corresponding to a useable d-spacing range of between 0.7 and 5.7 Å. Under these experimental settings, the instrumental resolution, ∆d/d, is approximately constant and equal to 2 × 10-3. Additional powder diffraction data for the phase II and phase III structures were recorded at 2 K using the high-resolution powder diffractometer (HRPD),8 at ISIS. Data on HRPD were recorded at backscattering, ) 168°, over a time-of-flight range of between 30 and 230 ms, corresponding to a d-spacing range between 0.6 and 4.6 Å. Under these experimental settings, the instrumental resolution, ∆d/d, is approximately constant and equal to 8 × 10-4. Figure 2 shows a representative thermogram of diffraction data recorded on OSIRIS. Following a series of runs using both rapidly and slowly cooled samples, the occurrence of the three low-temperature phases, as proposed in the adiabatic calorimetry studies4 was confirmed. An assemblage of phases, II and III and I and II, was readily produced

phase I

phase II

phase III

cubic Pa3j 10.3208(1) 10.3208(1) 10.3208(1) 90.00 90.00 90.00 1099.35(3) 8 1.120 150

triclinic P1j 6.4010(1) 7.5029(2) 6.3419(1) 109.085(2) 118.370(2) 79.326(3) 253.109(1) 2 1.214 2

monoclinic P21/c 10.6258(6) 10.1493(5) 9.6366(5) 90.00 90.822(5) 90.00 1039.1(1) 8 1.185 2

in line with the calorimetry findings, and this most likely explains previous inconsistencies in the reported phase behavior using spectroscopy. It proved difficult using the present experimental setup to achieve the required cooling rate of faster than 7 K/min over the temperature range 200-80 K required in order to produce the phase gI. Attempts to prepare crystalline phases through quenching samples directly in liquid nitrogen were not successful, yielding diffraction patterns with no Bragg peaks and consistent with amorphous glassy material. The diffraction patterns recorded on OSIRIS at 2 K (for phases III and II) and at 150 K (phase I) were indexed based on the positions of the first 20 peaks using TOPAS-Academic9 and unit cell constants for the three phases are given in Table 1. The crystal structures of phases II and III were solved by simulated annealing implemented by TOPASAcademic using a z-matrix format molecular template based on calculated coordinates of an isolated molecule determined by using density functional theory (DFT) methods.10 The phase II structure was solved in the space group P1j with one molecule in the asymmetric unit. The final structure was then refined, against the HRPD data, without constraints and using two isotropic displacement parameters for respective carbon and deuterium atoms. The diffraction pattern was significantly line broadened, as can be seen in Figure 3, and this loss of information accounts for the use of isotropic displacement parameters and reduced precision in the derived molecular dimensions. The final profile fit is shown in Figure 3. The phase III structure was solved in the space group P21/c with two independent molecules in the asymmetric unit. However, attempts to refine the structure in detail, with reference to the anticipated structural disorder, produced ambiguous results and thus single-crystal methods were chosen in order to determine more reliable structural information for this phase. The final profile fit of the 2 K phase III data recorded on HRPD is shown in Figure 4. The 150 K data recorded on OSIRIS are shown in Figure 5 and, in line with spectroscopic observations, are characteristic of a plastic and an orientationally disordered phase, exhibiting a high

Figure 3. Observed (circles) and calculated (line) diffraction patterns for cyclohexene-d10 phase II measured on HRPD at 2 K. The line at the bottom of the diagram is the difference between observed and calculated patterns. Vertical bars mark the calculated Bragg peak positions (the equivalent d-spacing range shown in the figure is 0.7–2.3 Å).

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Figure 4. Observed (circles) and calculated (line) diffraction patterns for cyclohexene-d10 phase III measured on HRPD at 2 K. Note the high background of these data in comparison to phase II (Figure 3). The line at the bottom of the diagram is the difference between observed and calculated patterns. Vertical bars mark the calculated Bragg peak positions (the equivalent d-spacing range shown in the figure is 0.8–2.3 Å).

Figure 5. Observed (circles) and calculated (line) diffraction patterns for cyclohexene-d10 phase I measured on OSIRIS at 150 K. The line at the bottom of the diagram is the difference between observed and calculated patterns. Vertical bars mark the calculated Bragg peak positions (the equivalent d-spacing range shown in the figure is 2.2–5.5 Å). background attributable to diffuse scattering and weak intensity at the high-Q end of the diffraction profile. The phase I structure was solved in the space group Pa3j with one-third of a molecule in the asymmetric unit and the molecule constrained to lie on a 3-fold axis. Given the paucity of data, the scattering of the uniaxially disordered molecules was modeled simply using a six-membered ring of carbon atoms, each with a site occupancy factor of one-third. The position of the ring on the 3-fold axis was refined along with the radius of the ring and a common isotropic displacement parameter for each atom. Attempts to fit the data using more sophisticated models, for example using a molecular fragment that included deuterium atoms, yielded poorer results. The final profile fit is shown in Figure 5. X-ray Single-Crystal Measurements. Single-crystal X-ray diffraction data were collected with Mo KR radiation (λ ) 0.71073 Å) on a Bruker SMART Apex CCD diffractometer equipped with an Oxford Cryosystems variable-temperature device and an OHCD laser-assisted crystal growth device. The sample used was C6H10, rather than C6D10. The crystal was grown over the course of 25 min, from a sample of the liquid, in a capillary held at 160 K using the Boese laser-assisted zone-refinement method.11 The crystal was indexed initially as the cubic phase I structure and was then cooled to 110 K where it had transformed to the monoclinic phase III structure. Diffraction data were collected at 110 K, but the crystal was found to have become polycrystalline after 3.5 h of data collection, though a complete set of data had been obtained prior to this.

Ibberson et al.

Figure 6. Refined phase I structure of cyclohexene. The six-membered rings represent the uniaxially disordered molecules forming a herringbone motif. The phase III structure was solved by direct methods in P21/c (SHELX-97)12 and refined by full-matrix least-squares against |F|2 (SHELX-97). The unit cell is metrically nearly orthorhombic, and the structure was refined as a pseudomerohedral twin, with a 2-fold axis along [100] as the twin law; the twin scale factor was refined to 0.320(3). It was evident from difference maps that one molecule in the asymmetric unit is ordered, and the second is disordered over two orientations with slightly different positions. Similarity restraints were applied to all chemically equivalent bonds and angles. Rigid body and bond restraints were applied to the anisotropic displacement parameters (adps) in the disordered molecule. Molecular Packing Calculations. Calculations were performed only for the ordered phase II structure of cyclohexene. Structural parameters derived by neutron diffraction were used to calculate the molecular electron density by standard quantum chemical methods using the program GAUSSIAN9813 at the MP2/6-31G** level of theory. The electron density model of the molecule was then analyzed using the program package OPiX14 which allows the calculation of dimer and lattice energies. Lattice energy calculations employed a cluster of molecules of radius 18 Å. The output from these calculations yields a total energy and a breakdown into its electrostatic, polarization, dispersion, and repulsion components. Topology calculations were carried out with the program TOPOS-Pro,15 and Hirshfeld surfaces were calculated using CrystalExplorer.16 Software and Other General Procedures. The structures were visualized using the programs MERCURY17 and DIAMOND.18

Results and Discussion Cyclohexene-I: The Cubic Phase. The arrangement of the molecules in the phase I structure is shown is Figure 6. The molecules are arranged in a herringbone motif; however, a detailed description of the structure is vitiated by the limited diffraction data available from this plastic phase. The disordered molecules are modeled simply as a six-membered (carbon) ring of radius 1.852(3) Å, centered on an 8c position in the unit cell with x ) 0.0921(5), and with large isotropic displacement parameters for the atoms of 0.09(1) Å2. This model is consistent with the likely configurational freedom suggested by NMR studies5 that comprises both ring inversion and free rotation of the molecules along an axis perpendicular to the plane of the molecule. Since carbon and deuterium have essentially the same scattering length for neutrons, this simple model can be considered as approximating to an annulus of scattering density corresponding to the freely rotating molecules within the structure. This finding is also consistent with the residual entropy of the glassy phase, Ig, being greater than R ln 24 indicative of disorder above that attributable solely to ring inversion. In the phase I structure, the accommodation of uniaxially disordered

Structure and Phase Behavior of Cyclohexene

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Figure 8. Refined phase II structure of cyclohexene. Figure 7. Molecular volume of cyclohexene as a function of temperature. Run 1 corresponds to a slowly cooled sample showing the transition of phase III (circles) to phase I (filled squares). Run 2 is a sample first annealed at 120 K, showing the transition of phase II (triangles) to phase I (open squares). Solid lines are fits to the phase III and phase II data (2–60 K) using a Debye model (see text). Dotted lines denote the extrapolation of the fits (60–170 K).

molecules within a primitive cubic cell is analogous to phase I of cyclohexene oxide (C6H10O)19 which has a primitive cubic lattice constant of 10.69 Å at 215 K. The equilibrium conformation for both molecules is a half-chair (twisted form). In contrast, the removal of the endocyclic double bond in the six-membered rings of cyclohexane (C6H12)20 and cyclohexanone (C6H10O)21 results in a (full) chair equilibrium conformation, and the phase I structures are face-centered cubic with lattice constants of 8.61 Å at 195 and 225 K, respectively. Thus as the degree of puckering within a particular series of monocyclic compounds increases, the tendency is for the molecules to become spherically disordered in the high-temperature plastic phases and to adopt the more usual face-centered cubic structures associated with pseudospherical cage hydrocarbons such as adamantane. The volume of a cyclohexene molecule in all three phases as a function of temperature is shown in Figure 7. The coexistence of all three phases, around 120 K, permits a direct comparison of the packing density and shows that phase I has the lowest density at this temperature corresponding to a molecular volume of 135.23 Å3. The subtle interplay between the phases is readily apparent in that the transition from phase III to phase I is accompanied by only a 1.3% decrease in packing density and a 4.3% decrease in the transition from phase II to I. Cyclohexene-II: The Triclinic Phase. The derived molecular dimensions within the phase II structure are unexceptional with a CdC double bond length of 1.334(4) Å and an average CsC single bond length of 1.50 Å with an rms deviation of 0.03 Å. The average CsD bond length is 1.109(4) Å. The refined molecular half-chair conformation has C1 symmetry with a twist angle of 62.3(4)°; however, it is in close agreement (within three estimated standard deviations) of the DFT calculations using C2 symmetry10 and, in this case, the twist angle is 63.4°. Searches of the Cambridge Structural Database (CSD; version 5.28 of January 200722) yields 10 structures of organometallic complexes containing cyclohexene and another in which cyclohexene is contained as a solvent molecule. The half-chair conformation of cyclohexene is observed in all these structures with an average twist angle of 61.11° with an rms deviation of 6.7°.

Figure 9. Molecular coordination in cyclohexene-II. The centroids of the molecules are labeled X1. . .X12, where X1 makes the strongest contact to the central reference molecule and X12 makes the weakest; the numbering follows Table 2. H-atoms have been omitted for clarity.

The arrangement of the molecules in the phase II structure is shown is Figure 8. The molecules are arranged to form chains running parallel to the crystallographic a-c plane with D. . .D close-contact distances between neighboring molecules along the chain of 2.374 and 2.423 Å. The chains stack, approximately along the b axis, with a contact between two CdC bonds in which the distance between the two bond midpoints is 3.74 Å and with a D. . .D close-contact distance of 2.320 Å. Voronoi-Dirichlet partitioning23 reveals that the molecular coordination number in cyclohexene-II is 14, though two contacts are much weaker than the other twelve and the topology is approximately cubic close-packed with a coordination sequence of 12–42–92. Each molecule is surrounded by six molecules in the (010) plane, related by lattice translations along [100], [001], and [101]. The central molecule also forms contacts to three molecules above and three molecules below the plane, in the ABC type stacking arrangement characteristic of CCP topology (Figure 9). The PIXEL procedure, which has been developed recently by Gavezzotti,24 enables further insight to be gained on molecular packing by calculation of intermolecular interaction energies. The method also enables these energies to be broken down into electrostatic, polarization, dispersion, and repulsion contributions. In a PIXEL calculation, the electron density in an isolated molecule is first calculated using a quantum mechanical package such as GAUSSIAN. This electron density model is then placed in a crystal structure and divided into pixels of electron density. Each energy term is obtained by summing over energies calculated between pairs of pixels in neighboring

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Table 2. Results of PIXEL Calculations on Cyclohexene-II no.

centroid-centroid distance (Å)

coulombic energy (kJ/mol)

polarization energy (kJ/mol)

dispersion energy (kJ/mol)

repulsion energy (kJ/mol)

total energy (kJ/mol)

symmetrya

1 2 3 4 5 6 7 8 9 10 11 12

4.334 5.056 5.381 5.029 6.338 6.338 5.332 6.397 6.397 6.266 6.525 6.525

-2.2 -6.3 -1.2 -3.5 -2.0 -2.0 -2.7 -2.0 -2.0 -1.2 -2.0 -2.0

-1.7 -2.9 -0.6 -1.3 -0.8 -0.8 -1.2 -1.0 -1.0 -0.4 -1.3 -1.3

-22.4 -21.0 -11.2 -14.9 -11.1 -11.1 -13.1 -10.0 -10.0 -7.4 -9.6 -9.6

15.1 21.5 5.4 12.7 8.2 8.2 11.5 7.6 7.6 4.1 8.4 8.4

-11.2 -8.8 -7.7 -7.1 -5.7 -5.7 -5.5 -5.4 -5.4 -4.9 -4.5 -4.5

-1 [1, -1, -2] -1 [1, 0, -1] -1 [1, 0, -2] -1 [2, 0, -1] 1 [0, 0, 1] 1 [0, 0, -1] -1 [2, -1, -1] 1 [-1, 0, 0] 1 [1, 0, 0] -1 [2, -1, -2] 1 [-1, 0, -1] 1 [1, 0, 1]

a

Symmetry operator with cell translation in square brackets.

Figure 10. Hirshfeld surfaces, colored according to shape index, illustrating the two strongest intermolecular interactions in cyclohexeneII.

molecules. Details on the PIXEL method have been given by Dunitz and Gavezzotti24 and Gavezzotti.24,25 PIXEL calculations (Table 2) support the topological view of the packing in cyclohexene-II described above. The twelve nearest neighbors have interaction energies in the range -4.5 to -11.2 kJ/mol; the thirteenth strongest contact has an interaction energy of -2.2 kJ/mol. The lattice energy is calculated to be -43.0 kJ/mol; this quantity does not appear to have been determined experimentally, though it compares to values of -37.6 kJ/mol for cyclohexane, -45 kJ/mol for benzene (average value), and -42.6 kJ/mol for cyclopentane.26 The lattice energy is dominated by the dispersion term (-80.9 kJ/mol), while the electrostatic, polarization, and repulsion terms are -14.8, -7.4, and +60.0 kJ/mol, respectively. Analysis of the Hirshfeld surface27 calculated for the molecules in cyclohexene-II reveals that H. . .H contacts comprise the majority (93.3%) of intermolecular interactions. Though C. . .C contacts contribute only 0.7% of the surface, PIXEL calculations indicate that they correspond to the strongest interaction (no. 1 in Table 2), a stacking contact between two CdC bonds in which the distance between the two bond midpoints is 3.74 Å (Figure 10a). This is dominated by a dispersion term, and its energy (-11.2 kJ/mol) is similar to a medium-weak hydrogen bond. This interaction is also revealed by a red crescent-shaped region on the top of a Hirshfeld surface colored according to shape index27 (Figure 10a). The second and third strongest interactions also involve the CdC moieties. Notably, interaction no. 2 features a H. . .CdC contact, which is presumably responsible for the relatively large electrostatic term of -6.3 kJ/mol, a contact which is also clearly visible as a large red indentation in the shape index Hirshfeld surface plot

shown in Figure 10b. Interaction nos. 4–12 in Table 2 all refer to pairs of molecules in which CdC. . .CdC distances are more than 6.3 Å, and can be described as van der Waals contacts between alkyl moieties with energies in the range -4.5 to -7.1 kJ/mol, and which correspond to H. . .H contacts on Hirshfeld surfaces. No evidence of disorder in phase II was found in the refined 2 K structure, and this was also supported following refinement of the variable-temperature data for this phase. The volume of the cyclohexene molecule in phase II as a function of temperature is shown in Figure 7. These data are well-fitted using a Debye model28 with the refined parameters V0K ) 126.540(3) Å3 and θD ) 137.19(1) K. The refined parameters describing the thermal expansion were obtained by fitting the data over a low-temperature interval, in this case 2-60 K, and were then used for a baseline extrapolation against which any anomalous behavior could be assessed. The observed variation of molecular volume with temperature is seen to follow very closely the extrapolated baseline (Figure 7) with only marginally significant deviations from this idealized behavior in the region of the transition to phase I where both phases are found to coexist. The characterization of phase II based on the current diffraction data is in good agreement with findings from other experimental techniques. Calorimetric studies4 found that cyclohexene-II has no residual entropy and is therefore fully ordered. Analysis of the Raman spectrum,6 which has six singlet external modes, predicts a centrosymmetric structure in either the triclinic or monoclinic systems. The vibrational spectroscopic studies also noted that while the internal modes show only small frequency shifts corresponding to the phase transitions, the transition from phase II to phase I was the most pronounced. The shifts are generally less than 5 cm-1; however, the ring inversion mode in particular was strongly affected. This mode was observed in the Raman spectrum at 185 cm-1 in the liquid and phase I, at 193 cm-1 in phase III, and at 208 cm-1 in phase II. The increase in frequency of the ring inversion mode supports the current diffraction findings that crystals of phase II have the highest density and, more generally, highlights the significant effect of the crystal structures and associated crystal packing effects on the ring inversion process. Cyclohexene-III: The Monoclinic Phase. The arrangement of the molecules in the phase III structure is shown is Figure 11, and the pseudocubic nature and similarity with the phase I structure (Figures 6 and 13) is apparent. The molecular packing is reminiscent of the motif from phase I; however, in this phase, the contents of the asymmetric unit comprise one fully ordered molecule and a second molecule which is disordered as shown in Figure 12. The disordered molecule adopts both the normal and inverted forms of the half-chair conformation with the centroids of each ring displaced by 0.3 Å and rotated relative

Structure and Phase Behavior of Cyclohexene

Figure 11. Refined phase III structure of cyclohexene determined from single-crystal X-ray diffraction at 110 K. Ordered molecules are denoted by carbon atoms drawn with lines of the boundary ellipse.

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Figure 13. Overlay of the unit cell and contents of phase III (black) and phase I (light grey) illustrating the close relationship between the monoclinic and cubic structures (atoms of the disordered molecule in phase III are denoted by +).

Figure 12. Asymmetric unit of phase III determined from single-crystal X-ray diffraction at 110 K. The disordered molecule (shown right) exhibits both the half-chair conformation (light shading) of the ordered molecule of the unit (shown left) and also adopts the inverted form (darker shading).

the CdC double bond by some 60° in the plane of the rings. A common molecular conformation was refined for all components in the asymmetric unit with C1 symmetry and with a twist angle of 61.35(4)°, in good agreement with the values determined for phase II and in DFT calculations described earlier. As shown in Figure 11, the molecular packing can be characterized as a series of zigzag planes of ordered and disordered molecules respectively running along approximately the a-c crystallographic planes. The centroids of two of the ordered molecules retain the alignment from the cubic phase, as shown in Figure 13, and these and the other ordered molecules remain largely isolated in the structure with no C. . .H close-contact distances less that 3 Å. In contrast, the disordered molecules are characterized by a network of C. . .H close contacts for each carbon atom of between 2.65 and 3.03 Å. The glassy behavior observed previously in cyclohexene-III using other experimental techniques is evidently associated with the disorder in the structure. The average volume of the cyclohexene molecules in phase III as a function of temperature is shown in Figure 7 and once more is fitted using a Debye model over the low-temperature region, with the refined parameters V0K ) 129.89(3) Å3 and θD ) 115.6(1) K. In this case, there is clear deviation from the extrapolated baseline above 80 K, the region of the glass transition, which may be attributed to the onset of inversion between the two molecular

Figure 14. Fractional occupation, pCH1, of the more favorable conformation in phase III as a function of temperature.

conformational forms and manifested by an increase in the average molecular volume. Further evidence for the glassy behavior in phase III is provided following refinement of the fractional occupancy of each conformation of the disordered molecule, using the variable-temperature powder diffraction data from OSIRIS. A constrained structural model, based on the single-crystal results, is used in which all the molecules are defined as rigid bodies and only three translational and three rotational components are refined for each molecule along with the sum of the occupancies for the disordered components (constrained to unity) and two isotropic displacement parameters for respective carbon and deuterium atoms. Figure 14 shows the temperature variation of the population fraction of the more energetically stable conformational arrangement for a slowly cooled sample recorded on warming. Below the glass transition temperature, the proportions of the two orientations are clearly fixed. Above the glass transition temperature, Tg, the decrease in major conformational fraction may be expressed in terms of a Boltzmann distribution assuming thermal equilibrium is achieved. The energy difference

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between the two conformational arrangements, ∆G , is given by the equation pHC2/pHC1 ) ([1/pHC1] - 1) ) exp(-∆G/kT)

(1)

∆G ) - kT ln([1 ⁄ pHC1] - 1)

(2)

thus

A least-squares fit assuming ∆G to be constant between 80 and 120 K gives a reasonable fit (Figure 14) and a derived energy difference of 107(2) K (corresponding to 9.22 meV). There is a clear departure from this idealized behavior, and relaxation effects are evident at temperatures above 65 K. This indicates that the cooling rate while preparing the sample, ca. 1 K/min, is significantly faster than the heating rate, ca. 0.5 K/min, determined by the duration of each measurement, and hence, the system begins to unquench at a lower temperature. A similar behavior has also been observed in neutron powder diffraction studies of C6029 which also exhibits an orientational glass transition. In this latter case, the use of higher-precision data recorded using finer temperature steps enabled relaxation rates to be obtained and hence the reorientational activation energy to be determined. The present description of the phase III structure, comprising one ordered and one disordered molecule in the asymmetric unit, accounts also for the apparent discrepancy in the residual entropy of this phase reported by Haida et al.4 The relaxation phenomenon of the ring inversion was observed calorimetrically, suggesting that the energy difference between orientations within phase III was of the order of thermal energy. However, while complete disorder of the ring inversion mode contributes to the entropy by R ln 2 (5.8 J/(K mol)), the residual entropy determined for phase III is only 2.7 J/(K mol), that is, approximately half the value for complete disorder. The occurrence of both ordered and disordered molecules in the asymmetric unit of molecular crystal structures is well-known and indeed is observed in the sold-state phase diagram of methane, the simplest organic compound.30,31 Conclusions In summary, the crystal structures of the three solid-state phases of cyclohexene at ambient pressure have been successfully determined and characterized as a function of the temperature. The combination of X-ray single-crystal methods and variable-temperature high-resolution neutron powder diffraction has enabled the subtle details of orientational order within the various phases to be understood, and this complete description is found to be consistent with both spectroscopic deduction6 and observations based on calorimetry.4 In particular, the apparent anomalous residual entropy observed for cyclohexene-III4 can be attributed to orientational disorder in only half the asymmetric unit. In general, the weakly scattering nature of plastic and substantially orientationally disordered structures makes their study by powder diffraction especially challenging. The success of the present study demonstrates that, with ever-increasing count rates available on current powder diffractometers and with new high-flux spallation neutron sources due on line in the next few years, the expectation of studies on this type of compound is for the provision of detailed and quantitative structural results. Acknowledgment. This research was supported by the Science and Technology Facilities Council (STFC) with the provision of neutron beam time. Supporting Information Available: Crystallographic information file (CIF) for the phase II (2 K) and phase III (120 K) structures. These files contain a full listing of intramolecular bond lengths and bond angles. This material is available free of charge via the Internet at http: //pubs.acs.org

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