Structural Properties of Low-Temperature Phase Transitions in the

Dec 23, 2007 - The stable phase at ambient temperature (phase I) undergoes a second-order transition to phase II at ca. 148 K, and phase II undergoes ...
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J. Phys. Chem. C 2008, 112, 839-847

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Structural Properties of Low-Temperature Phase Transitions in the Prototypical Thiourea Inclusion Compound: Cyclohexane/Thiourea Zhigang Pan,† Arnaud Desmedt,‡ Elizabeth J. MacLean,§ Franc¸ ois Guillaume,*,‡ and Kenneth D. M. Harris*,† School of Chemistry, Cardiff UniVersity, Park Place, Cardiff CF10 3AT, Wales, Institut des Sciences Mole´ culaires, UniVersite´ Bordeaux 1, CNRS UMR 5255, 351 cours de la Libe´ ration, 33405 Talence Cedex, France, and Synchrotron Radiation Source, Daresbury Laboratory, Daresbury, Warrington WA4 4AD, England ReceiVed: August 21, 2007; In Final Form: October 24, 2007

The prototypical thiourea inclusion compound, cyclohexane/thiourea, in which cyclohexane guest molecules are located within tunnels in a hydrogen-bonded thiourea host structure, is known to exist in three phases (denoted I, II, and III). The stable phase at ambient temperature (phase I) undergoes a second-order transition to phase II at ca. 148 K, and phase II undergoes a first-order transition to phase III at ca. 127 K. The structural properties of phases I-III have been determined in the present work from synchrotron X-ray powder diffraction data, employing the Rietveld refinement technique. The structural properties determined for phase I are in agreement with those reported previously from single-crystal X-ray diffraction data. The structures of the two low-temperature phases (phases II and III) have not been reported previously, and we emphasize the advantages of using X-ray powder diffraction techniques in these cases due to the occurrence of crystal twinning on entering these phases. In phase II, the observed distortion of the thiourea tunnel is consistent with an increase of orientational ordering of the guest molecules in comparison with phase I, although a unique determination of the disordered guest substructure could not be established. On entering phase III, however, the Rietveld refinement indicates a further distortion of the thiourea tunnel structure, which is associated with ordering of each guest molecule in a single discrete orientation. Importantly, structural aspects of the guest substructure in this phase (particularly concerning the tilt angle of the C3 axis of the guest molecule relative to the tunnel axis) are in excellent agreement with results on the orientational characteristics of the guest molecules in phase III deduced from a previous single-crystal 2H NMR study.

1. Introduction Crystalline organic inclusion compounds, in which the host substructure forms one-dimensional tunnels densely loaded with guest molecules, exhibit a wide range of important physicochemical properties.1-6 In recent years, a substantial amount of research in this field has focused on studies of structure, dynamics, and phase transition mechanisms in incommensurate urea inclusion compounds.3-6 At present, however, much less is known about the corresponding properties of thiourea inclusion compounds. In thiourea inclusion compounds, an extensively hydrogen-bonded arrangement of thiourea molecules forms a crystalline “host” structure, within which there are unidirectional, nonintersecting tunnels. Suitable “guest” molecules are located inside these tunnels, and examples include branched hydrocarbons, cyclohexane and some of its derivatives, and small organometallic molecules such as ferrocene. For most guest molecules (particularly those with fairly isotropic molecular shape), the structure of the thiourea inclusion compound is rhombohedral at ambient temperature and the guest molecules are orientationally disordered. In many cases, this rhombohedral structure transforms to a monoclinic structure at * To whom correspondence should be addressed. E-mail: [email protected] (K.D.M.H.), [email protected] (F.G.). † Cardiff University. ‡ Universite ´ Bordeaux 1. § Daresbury Laboratory.

low temperature. Most thiourea inclusion compounds are commensurate, with two guest molecules per unit repeat distance of the thiourea host structure along the tunnel and a guest/ thiourea molar ratio of 1:3. While the host tunnel in urea inclusion compounds is fairly cylindrical (with only small fluctuations in tunnel diameter on moving along the tunnel), the rhombohedral thiourea tunnel structure has prominent bulges (diameter ≈ 7.1 Å) and constrictions (diameter ≈ 5.8 Å) at different positions along the tunnel.7 As a consequence, many properties of thiourea inclusion compounds are more directly understood by considering the thiourea host structure to be of “cage” type rather than “tunnel” type. The thiourea inclusion compound containing cyclohexane as the guest component has generally been regarded as the prototypical member of this family of inclusion compounds, and the present paper is focused on structural rationalization of this material in the two low-temperature phases. Three distinct thermotropic structural phases of cyclohexane/thiourea were identified several years ago,8,9 and recent differential scanning calorimetric (DSC) studies10 confirmed this conclusion. Thus, the DSC data show exotherms (peak maximum temperatures with associated enthalpy changes in brackets) at 148 K (-0.1 J g-1) and 127 K (-3.6 J g-1). The three phases are denoted phase I (above Tc1 ) 148 K), phase II (between Tc1 ) 148 K and Tc2 ) 127 K), and phase III (below Tc2 ) 127 K). On heating cyclohexane/thiourea from phase I, endotherms are

10.1021/jp076706y CCC: $40.75 © 2008 American Chemical Society Published on Web 12/23/2007

840 J. Phys. Chem. C, Vol. 112, No. 3, 2008 observed in the DSC data at 130 K (3.6 J g-1) and 149 K (0.06 J g-1). Clearly, there is thermal hysteresis in the transition at Tc2. Early single-crystal X-ray diffraction studies11 showed that, at ambient temperature (phase I), the host substructure is the conventional rhombohedral thiourea tunnel structure with space group R3hc, as also found for other thiourea inclusion compounds at ambient temperature.12 Phase II is monoclinic with twice the volume of the rhombohedral unit cell of phase I, and phase III is also monoclinic.9 The space groups and structures of the lowtemperature phases II and III were not determined in this early work, but the space groups of both phases II and III were recently reported10 to be P21/a from analysis of X-ray powder diffraction data. To date, however, the structures of phases II and III have not been reported. Dynamic properties of the cyclohexane guest molecules in the three phases have been investigated by wide-line 1H NMR,9,13 2H NMR,10,14,15 including studies exploiting the advantages of single-crystal 2H NMR,10 molecular dynamics simulations,16 and incoherent quasielastic neutron scattering.17-20 Recently,10 progress was made in understanding the relationship between the dynamics of the guest molecules and the symmetry in each phase, allowing a microscopic model for the phase transition mechanisms to be established within the framework of Landau theory. In this work, the transitions were described in terms of order parameters defined on the basis of the symmetry principles of Landau theory, and theoretical analysis of the crystal strain occurring at the phase transitions allowed comparison between the experimental temperature-dependence of the lattice parameters and the classical interpretation derived from Landau theory. Powder and single-crystal 2H NMR studies of samples of cyclohexane/thiourea containing perdeuterated cyclohexane guest molecules (C6D12) showed that in phase I, the motionally averaged quadrupole coupling tensor is axially symmetric. On passing from phase I to phase II, the 3-fold symmetry axis of the space group of phase I is lost, such that the motionally averaged quadrupole interaction tensor is not axially symmetric in phase II. The relative orientations of the guest molecules deduced from the single-crystal 2H NMR spectra were found to be consistent with the site-symmetry properties of the structure and the proposed modes of crystal twinning, and the results demonstrated that there is only one type of dynamic species of guest molecule in phase II (thus disproving earlier erroneous claims in the literature15). In phase III, there is evidence of a greater degree of orientational ordering of the cyclohexane guest molecules, and geometric information relating to the guest molecule orientation was deduced. Thus, the tilt angle (denoted λ; Figure 1) of the C3 axis of the guest molecule relative to the tunnel axis was determined to be λ ) 70°, and the projection of the C3 axis of the guest molecule on to the plane perpendicular to the tunnel axis was deduced to form an angle (denoted φp; Figure 1), with respect to a reference axis in this plane, of either φp ) 30° or 90°. By consideration of the symmetry of the inclusion compound, the dynamics of the guest molecules were described using simple jump models (i.e., multidimensional pseudospin models) in all three phases, from which the temperature dependences of the order parameter components were established. To determine the structures of the low-temperature phases of cyclohexane/thiourea, the present work has employed X-ray powder diffraction rather than single-crystal X-ray diffraction, recognizing that transformations from high-symmetry to lowsymmetry phases are often associated with crystal twinning, which can lead to difficulties in structure determination from

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Figure 1. Definition of the geometric variables λ and φp, which characterize the orientation of the cyclohexane guest molecule relative to the thiourea host tunnel structure.

single-crystal X-ray diffraction data. Indeed, the single-crystal 2H NMR studies discussed above provided direct evidence that, starting from a single crystal in phase I, crystal twinning is introduced in phases II and III. The occurrence of crystal twinning in the low-temperature phases, however, does not pose problems in the application of X-ray powder diffraction techniques for structure determination. 2. Experimental Section The cyclohexane/thiourea inclusion compound was prepared by slowly cooling a solution containing cyclohexane and thiourea in methanol from ca. 55 °C to ambient temperature over a period of about 1 week. Needle-shaped crystals with typical diameters between ca. 2 and 5 mm were obtained. The crystals were kept in the crystallization solution until required for the X-ray powder diffraction experiments and were washed with methanol prior to these experiments. Preliminary X-ray powder diffraction patterns were recorded at several temperatures between 250 and 30 K on a Siemens D5005 diffractometer (Cu KR radiation) operating in reflection mode in the range of 5° e 2θ e 40°, with step size 0.036° and counting time 4 s per step. The temperature was controlled by a helium cryostat with accuracy ca. 0.1 K. Although the phase transitions were clearly identified, the resolution was not sufficient to allow a detailed interpretation of the structural changes in the low-temperature phases in terms of space group determination. For this reason, synchrotron X-ray powder diffraction data were recorded on Station 2.3 at the Synchrotron Radiation Source, Daresbury Laboratory. The X-ray powder diffraction patterns were recorded in transmission geometry for a finely ground sample of cyclohexane/thiourea in a glass capillary sample holder. A high-quality X-ray powder diffraction pattern was recorded at one temperature in each phase (phase I, 293 K; phase II, 140 K; phase III, 100 K), with wavelength 1.40 Å (for 293 and 140 K) and 1.30 Å (for 100 K). The total data range was 5° e 2θ e 70°, with step size 0.01° and counting time per step 4 s. The same powder sample was used to record the data for phases I and II, whereas a fresh sample was used to record the data for phase III. An X-ray powder diffraction pattern recorded at ambient temperature on the sample used to record the data for phase III confirmed that this sample was identical to that used to record the data for phases I and II.

Phase Transitions in Cyclohexane/Thiourea

Figure 2. Synchrotron X-ray powder diffraction patterns recorded for cyclohexane/thiourea at 293, 140, and 100 K. Peaks marked with asterisks are due to pure thiourea; peaks marked with circled asterisks are due to pure cyclohexane.

3. Results 3.1. Preliminary Analysis of Structural Properties. The low-angle regions of the experimental synchrotron X-ray powder diffraction patterns are shown in Figure 2. The X-ray powder diffraction pattern at 293 K (Figure 2a) is indexed by the following unit cell with rhombohedral metric symmetry: a ) 10.04 Å and R ) 104.09°. Systematic absences are consistent with space group R3hc, as determined previously from singlecrystal X-ray diffraction.11 We note that the low-intensity peaks indicated by asterisks in Figure 2a are not indexed by this rhombohedral unit cell and are assigned as pure thiourea, which is known to form as a decomposition product of thiourea inclusion compounds under X-ray irradiation.21 Indeed, these low-intensity peaks are indexed by the reported orthorhombic unit cell (a ) 7.659 Å, b ) 8.557 Å, and c ) 5.489 Å) of pure thiourea (space group Pnma).22,23 Changes in the X-ray powder diffraction pattern on crossing the phase transition at Tc1 comprise splitting of peaks and the appearance of new peaks. For example, the peaks indexed as (11h0), (200), or (21h1h) in phase I each split into two peaks in phase II (Figure 2b). The X-ray powder diffraction pattern at 140 K (phase II) is indexed by a unit cell with monoclinic metric symmetry: a ) 9.99 Å, b ) 15.55 Å, c ) 12.43 Å, and β ) 114.63°. All peaks in the X-ray powder diffraction pattern, except those marked by asterisks or circled asterisks in Figure 2b, are indexed by this unit cell. At 140 K, pure thiourea (peaks indicated with asterisks in Figure 2b) is orthorhombic (a ) 7.52 Å, b ) 8.53 Å, and c ) 5.46 Å) with space group P21ma.22,23 In addition, new peaks of very low intensity appear in phase II and are attributed to pure cyclohexane. Decomposition of cyclohexane/thiourea under X-ray irradiation produces pure thiourea and pure cyclohexane, which is cubic at 280 K and undergoes a phase transition to a monoclinic structure below 186 K with space group C2/c.24 The two peaks marked with circled asterisks in Figure 2b are indexed as (200) and (1h11) for pure cyclohexane. From consideration of systematic absences in the X-ray powder diffraction pattern of cyclohexane/thiourea, the space group of phase II is assigned as P21/a.

J. Phys. Chem. C, Vol. 112, No. 3, 2008 841 In phase III, the number of reflections is the same as that for phase II (Figure 2c), and only shifts of peak positions are observed. The phase transition at Tc2 is characterized by an abrupt change of lattice parameters,10 and the X-ray powder diffraction pattern at 100 K is indexed by the following unit cell with monoclinic metric symmetry: a ) 10.22 Å, b ) 15.00 Å, c ) 12.41 Å, and β ) 115.17°. As noted above for phases I and II, the X-ray powder diffraction pattern for phase III contains some low-intensity peaks due to pure thiourea (peaks indicated with asterisks in Figure 2b), although no peaks due to pure cyclohexane are detectable for phase III.25 From the conditions for systematic absences, the space group of phase III is assigned as P21/a. In summary, phase I of cyclohexane/thiourea is rhombohedral with space group R3hc in agreement with earlier single-crystal X-ray diffraction studies,11 and the primitive unit cell contains two cyclohexane molecules and six thiourea molecules. Phase II is monoclinic with space group P21/a (Z ) 4), which is a subgroup of R3hc. From the temperature-dependence of the lattice parameters,10 it is clear that the transition at Tc1 is continuous, and recalling that the enthalpy change at Tc1 is only ca. 0.1 J g-1, the transition between phases I and II is characteristic of a second-order phase transition. The transition at Tc2 produces phase III, which is also monoclinic with the same space group as phase II and Z ) 4 (i.e., an isostructural phase transition). The abrupt change in lattice parameters and the strong thermal anomaly at Tc2 are characteristic of a first-order phase transition. Rietveld refinement for each phase was carried out using the GSAS program26 as discussed below. In each case, a two-phase refinement was carried out, including the known structure of pure thiourea as a second phase in addition to the cyclohexane/ thiourea inclusion compound, thus accounting directly for the presence of peaks due to pure thiourea as discussed above. Although the X-ray powder diffraction pattern for phase II contains a few peaks due to pure cyclohexane, all of these peaks have very low intensity, and the refinement did not include this phase explicitly. Thus, peaks due to pure cyclohexane will contribute to the difference plots for Le Bail fitting and Rietveld refinement for phase II. 3.2. Structure Determination of Phase I (293 K). Le Bail fitting of the X-ray powder diffraction pattern for phase I using the unit cell and space group (R3hc) discussed above led to a good fit (Figure 3a; Rwp ) 14.89%, Rp ) 11.17%, χ2 ) 5.86). The initial structural model for Rietveld refinement of phase I comprised only the host substructure (i.e., the empty thiourea tunnel structure) taken from a previously reported structure determination of the rhombohedral thiourea tunnel structure.12 Standard geometric restraints were applied to the bond lengths and bond angles of the thiourea molecule (which included hydrogen atoms in fixed positions relative to the non-hydrogen atoms of the molecule). The Rietveld refinement converged steadily, but did not lead to a good fit to the experimental data, as the guest component makes a significant contribution to the X-ray powder diffraction pattern. With the use of the refined host-only structural model, a difference Fourier map was calculated and the position of the strongest peak within the tunnel was added to the structural model as a carbon atom. The position and occupancy of this carbon atom were allowed to refine with the isotropic displacement parameter fixed, and then the occupancy was fixed at the refined value and the position and isotropic displacement parameter were allowed to refine. This procedure was repeated until convergence was achieved for both the occupancy and isotropic displacement parameter. At this stage, the difference Fourier map was recalculated, and

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Figure 3. Results from fitting the X-ray powder diffraction data for phase I at 293 K: (a) Le Bail fit and (b) final Rietveld fit.

the position of the strongest peak within the tunnel was again added to the structural model as a carbon atom and was subjected to the same refinement procedure described above, with common values of occupancy and isotropic displacement parameter refined for both “guest” carbon atoms. At this stage, the highest peak in the difference Fourier map was not located in the tunnel, but close to the sulfur atom of a thiourea molecule, and no further atoms were added to the structural model from the difference Fourier map. Thus, a total of two carbon atoms (with high refined values of isotropic displacement parameter) were included in the final refined structural model to represent the disordered guest substructure in phase I. We emphasize that no physical significance should be assigned to the actual positions of the carbon atoms introduced into the structural model to represent the scattering from the guest substructure, nor the refined values of the common occupancy and common isotropic displacement parameter for these atoms. A similar refinement strategy has been employed previously in the structure determination of solid inclusion compounds with disordered guest substructures from single-crystal X-ray diffraction data.12,27 It is well established from other techniques10,16-19 that the cyclohexane guest molecules exhibit substantial dynamic disorder in phase I, and refinement of an accurate disorder model

for the guest substructure was not the aim of the present work. Nevertheless, an adequate representation of the average guest electron density is required to achieve an acceptable quality of fit to the experimental X-ray powder diffraction pattern and hence to obtain an acceptable description of the thiourea host substructure in phase I. The final refined structural parameters at 293 K are given in the Supporting Information, and the experimental and calculated X-ray powder diffraction patterns are compared in Figure 3b (Rwp ) 16.22%, Rp ) 12.74%, χ2 ) 7.02). The final refined structure viewed along the tunnel axis is shown in Figure 4. The final refined lattice parameters (hexagonal setting) are a ) 15.83591(14) Å and c ) 12.45581(15) Å. 3.3. Structure Determination of Phase III (100 K). We discuss the Rietveld refinement for phase III at this stage, as results obtained in this refinement are used subsequently for the refinement of phase II (see Section 3.4). Le Bail fitting of the X-ray powder diffraction pattern for phase III using the unit cell and space group (P21/a) discussed in Section 3.1 led to a good fit (Figure 5a; Rwp ) 11.02%, Rp ) 7.84%, χ2 ) 2.85). Initially, Rietveld refinement was carried out for a host-only structural model, with the fractional coordinates of atoms of

Phase Transitions in Cyclohexane/Thiourea

Figure 4. Structure of cyclohexane/thiourea in phase I (at 293 K) viewed along the tunnel axis. The physical interpretation of the refined positions of atoms within the tunnel is discussed in the text.

the thiourea molecules taken from the previously reported structure determination of the low-temperature monoclinic phase of the chlorocyclohexane/thiourea inclusion compound28 (together with the unit cell discussed in Section 3.1 for phase III of cyclohexane/thiourea at 100 K). Standard geometric restraints were applied to the bond lengths and bond angles of the thiourea molecules (which included hydrogen atoms in fixed positions relative to the non-hydrogen atoms of the molecule). Following this host-only refinement, a difference Fourier map was calculated, which was found to contain several peaks within the tunnel corresponding approximately to the geometry of a cyclohexane molecule. Thus, six carbon atoms were added to the structural model in the positions of these peaks and representing a cyclohexane/thiourea stoichiometry of 1:3 (with the occupancy of the cyclohexane guest fixed at 1). In the following Rietveld refinement using the complete structure (i.e., refinement of both host and guest substructures), standard geometric restraints were applied to the thiourea molecules as described above. Initially, no geometric restraints were applied to the cyclohexane molecule, but the refinement led to a nearly planar ring with C-C distances ranging from 0.97 to 1.55 Å. At this stage, standard geometric restraints were applied to the bond lengths and bond angles of the cyclohexane molecule, which then led to satisfactory refinement. A common isotropic displacement parameter was refined for all carbon atoms of the cyclohexane molecule. Finally, hydrogen atoms were added to the cyclohexane molecule in fixed positions and with a fixed isotropic displacement parameter. The final refined structural parameters at 100 K are given in the Supporting Information, and the experimental and calculated X-ray powder diffraction patterns are compared in Figure 5b (Rwp ) 13.89%, Rp ) 10.54%, χ2 ) 4.40). The final refined crystal structure viewed along the tunnel axis is shown in Figure 6a, and the guest substructure is shown in Figure 6b. The final refined lattice parameters are a )10.2129(15) Å, b ) 14.9786(22) Å, c ) 12.4066(18) Å, and β ) 115.1763(9)°. 3.4. Structure Determination of Phase II (140 K). Le Bail fitting of the X-ray powder diffraction pattern for phase II using

J. Phys. Chem. C, Vol. 112, No. 3, 2008 843 the unit cell and space group (P21/a) discussed in Section 3.1 led to a good fit (Figure 7a; Rwp ) 8.80%, Rp ) 6.20%, χ2 ) 1.96). The initial Rietveld refinement was carried out for a hostonly structural model, with the fractional coordinates of the atoms of the thiourea molecules taken from the previously reported structure determination of the low-temperature monoclinic phase of chlorocyclohexane/thiourea28 (together with the unit cell determined here for phase II of cyclohexane/thiourea at 140 K). Standard geometric restraints were applied to the bond lengths and bond angles of the thiourea molecules (which included hydrogen atoms in fixed positions relative to the nonhydrogen atoms of the molecule). Three different models (denoted models A, B, and C) were then considered for introducing guest electron density within the structural model. Model A. Following the host-only refinement, a carbon atom was added into the tunnel in the position of the highest peak in the difference Fourier map. Rietveld refinement was then carried out, with the position, occupancy, and isotropic displacement parameter of this carbon atom refined (but with the occupancy and isotropic displacement parameter not refined simultaneously), employing the strategy described for phase I in Section 3.2. This procedure was repeated, adding individual carbon atoms to the structural model at the position of the highest peak in the difference Fourier map, until the highest peak in the difference Fourier map was not located in the tunnel. In total, nine carbon atoms were added to the structural model in this procedure. As discussed above for phase I, all carbon atoms added to the tunnel had a common occupancy and a common isotropic displacement parameter, which were both refined (although not simultaneously). Thus, model A represents a disordered guest substructure, but as discussed above for phase I, no direct physical interpretation should be attached to the specific positions occupied by the carbon atoms that represent the guest electron density in this model; rather, these atoms represent the overall resultant “smeared out” distribution of guest electron density in the disordered description, so physical interpretation should only be attached to the overall distribution of the set of carbon atoms (including the distribution implied by the atomic displacement parameter) that represent the guest substructure in this model. The final refined structural parameters are reported in the Supporting Information, the structure is shown in Figure 8, and the final Rietveld difference plot is shown in Figure 7b (Rwp ) 10.87%, Rp ) 8.05%, χ2 ) 2.98). The final refined lattice parameters are a ) 9.99428(18) Å, b ) 15.5797(4) Å, c ) 12.43400(14) Å, and β ) 114.6449(16)°. Model B. Following the host-only refinement, a single cyclohexane molecule was added to the host tunnel using the fractional coordinates of the cyclohexane guest molecule obtained in the Rietveld refinement for phase III (Section 3.3). Thus, model B represents a fully ordered guest substructure (with the guest molecule having an occupancy of 1). Rietveld refinement was then carried out using the procedure described in Section 3.3 for phase III, with standard geometric restraints applied to the bond lengths and bond angles of the thiourea and cyclohexane molecules. The final refined structural parameters are given in the Supporting Information, and the final Rietveld difference plot is shown in Figure 7c (Rwp ) 13.18%, Rp ) 9.44%, χ2 ) 4.61). The final refined lattice parameters are: a ) 9.9938(20) Å, b ) 15.5785(32) Å, c ) 12.4340(25) Å, and β ) 114.6447(20)°. Model C. This model represents a disordered guest substructure in which the guest molecule is disordered between two

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Figure 5. Results from fitting the X-ray powder diffraction data for phase III at 100 K: (a) Le Bail fit and (b) final Rietveld fit.

discrete orientations (but with the center of the guest molecule located at the same position in the tunnel). Thus, one component was taken as the position/orientation of the ordered guest molecule in phase III, and the other component was obtained by a 180° rotation of this molecule about an axis parallel to the c axis (i.e., the tunnel axis). The basis for considering this disorder model is that the overall orientation of the guest molecule and region of space occupied within the host tunnel are rather similar for these two orientations of the guest molecule. Initially, each disorder component was given an occupancy of 0.5, but the occupancy was refined subject to the constraint that the total occupancy of the two disorder components was 1 (i.e., refined occupancies x and 1 - x). Rietveld refinement was carried out with this guest substructure added to the structure obtained in the host-only refinement, with standard geometric restraints applied to the bond lengths and bond angles of the thiourea and cyclohexane molecules. The final refined structural parameters are given in the Supporting Information, and the final Rietveld difference plot is shown in Figure 7d (Rwp ) 12.61%, Rp ) 9.10%, χ2 ) 4.16). The final refined occupancies of the two guest components are 0.53 and 0.47, and the final refined lattice parameters are a ) 9.9938(20) Å, b ) 15.5785(32) Å, c ) 12.4340(25) Å, and β ) 114.6447(20)°.

4. Discussion Initially, it is relevant to recall that diffraction experiments of the type discussed here are generally unable to distinguish between dynamic disorder and static disorder, but that other techniques are required to provide definitive information in this regard. Thus, for the cyclohexane/thiourea inclusion compound, it is well established from solid-state 1H NMR,9,13 13C NMR29 and 2H NMR,10,14,15 incoherent quasielastic neutron scattering,17-20 and molecular dynamics simulations16 that the nature of the disorder of the guest molecules in this inclusion compound is dynamic in character. In this context, the most detailed insights into the dynamic properties of the cyclohexane guest molecules in this material have been established from single-crystal 2H NMR studies,10 and it is relevant here to recall some of the main conclusions from this work. In phase I, the disorder of the guest molecules is described in terms of a model of jumps of the molecular C3 axis between six orientations of equal probability according to the D3 point group symmetry of the site occupied by the cyclohexane molecule within the thiourea host structure, together with rapid reorientation of the cyclohexane molecule about its C3 axis. In phase II, dynamic disorder of the cyclohexane guest molecules involves reorientation among six inequivalent orientations (the populations of which are

Phase Transitions in Cyclohexane/Thiourea

Figure 6. (a) Structure of cyclohexane/thiourea in phase III (at 100 K) viewed along the tunnel axis (note the well-defined orientation of the cyclohexane guest molecules, in contrast to the disorder observed for the cyclohexane guest molecules in phases I and II). (b) Structure of cyclohexane/thiourea in phase III (at 100 K) showing the orientation of the cyclohexane guest molecules (the tunnel axis is the c-axis).

unequal as a consequence of the lowering of the symmetry of the host structure), together with rapid reorientation about the molecular C3 axis. The transition from phase II to phase III is strongly first order, and abrupt ordering of the orientation of the C3 axis of the cyclohexane guest molecule takes place in phase III, as the motion of this axis relative to the host structure becomes frozen. However, rapid reorientation of each cyclohexane molecule about its C3 axis still occurs in phase III. An important structural property is the tilt angle λ, which defines the orientation of the C3 axis of the cyclohexane guest molecule relative to the tunnel axis (Figure 1). From previous 2H NMR results,10 the value of λ is determined to be around 60° in phase I and remains close to this value (in the region ca. 55-60°) in phase II. The transition from phase II to phase III, however, is associated with an abrupt orientational ordering of the C3 axis, with the tilt angle changing to λ ≈ 70°. The results reported in the present paper provide a complete structural understanding of the three phases of the cyclohexane/ thiourea inclusion compound. As discussed in Section 1, the structure of phase I was previously reported from single-crystal X-ray diffraction data, and the structural properties determined here from X-ray powder diffraction data concur well with the

J. Phys. Chem. C, Vol. 112, No. 3, 2008 845 previous structural results. The description of the time-averaged guest substructure as extensively disordered is also in good agreement with conclusions (as discussed above) from several different techniques (including 2H NMR10) that there is dynamic disorder of the guest molecules in phase I, with each individual guest molecule disordered between six orientations within the host tunnel structure. Although the Rietveld fit is improved by including electron density within the tunnel to represent the contribution to the diffraction pattern from the disordered guest substructure, the description of the guest electron density is equivalent to a highly diffuse distribution, and no attempt has been made to deduce more detailed information (for example, orientational distribution functions) relating to this structural aspect from the X-ray powder diffraction data, as such analysis would be more satisfactorily attempted from single-crystal X-ray diffraction studies. The structure of phase II clearly demonstrates that there is a small distortion of the thiourea host structure in comparison with phase I, but that the time-averaged guest substructure remains substantially disordered. However, there is evidence that the time-averaged description of the guest electron density distribution becomes somewhat more localized, with some orientational preference which appears to reflect the manner in which the host tunnel is distorted (Figure 8). Thus, for example, the widest part of the guest distribution is oriented along the widest part of the distorted host tunnel. As discussed in Section 3.4, three structural models were considered in the Rietveld refinement calculations for phase II, representing different degrees of disorder within the guest substructure, ranging from a disordered model (model A) handled in a manner analogous to the refinement for phase I to an ordered model (model B) handled in a manner analogous to the refinement for phase III. Clearly, all three models give a reasonable fit to the data, although the best fit is obtained for model A. However, the Rietveld refinement for model A involved a greater number of refined parameters than the Rietveld refinements for models B and C, which may in part contribute to the better fit obtained. Nevertheless, for the model (model B) comprising a single orientation of the guest molecule, a reasonable fit is achieved only with a very high value of the refined isotropic displacement parameter, which suggests that a single discrete orientation of the guest molecule does not represent an adequate description of the structure of phase II. Model C, which considers disorder in terms of two discrete guest molecule orientations, provides a more satisfactory description than model B (giving a better fit to the data and maintaining a reasonable value of the refined isotropic displacement parameter). From the evidence available, however, we cannot deduce that model C provides a better description than model A. Thus, at the level of information that may be deduced unambiguously from the X-ray powder diffraction data, we conclude that the guest substructure in phase II still exhibits a significant degree of disorder, but is probably substantially more ordered than phase I, and the time-averaged distribution of the guest molecules is significantly more anisotropic, presumably as the distortion of the host tunnel promotes some orientational preference for the guest molecules. This conclusion is consistent with the results from 2H NMR, which suggest that, while the guest molecules are still distributed among six distinguishable orientations in phase II, these different orientations are not equally populated. In the structure of phase III, it is clear that the thiourea host tunnel is distorted significantly from the rhombohedral tunnel structure in phase I and that, in phase III, each cyclohexane guest molecule adopts a single well-defined orientation (with a

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Figure 7. Results from fitting the X-ray powder diffraction data for phase II at 140 K: (a) Le Bail fit, (b) final Rietveld fit for model A, (c) final Rietveld fit for model B, and (d) final Rietveld fit for model C.

C3 axis and the tunnel axis) in the refined structure is λ ) 68° (λ is defined in Figure 1), in close agreement with the value of λ ≈ 70° determined for phase III from single-crystal 2H NMR.10 Furthermore, the structure determined here confirms that the projection of the C3 axis of the guest molecule on to the plane perpendicular to the tunnel axis forms an angle φp ≈ 30° (φp is defined in Figure 1), again in excellent agreement with one of the values (φp ) 30° or 90°) deduced from single-crystal 2H NMR. We recall that, due to the nature of the crystal twinning and the properties of the 2H quadrupole interaction tensor, single-crystal 2H NMR could not distinguish which of these values of φp is correct. Acknowledgment. We thank Drs. Benson Kariuki and Michel Couzi for helpful discussions in connection with the work described in this paper and Daresbury Laboratory for the provision of beamtime for recording X-ray powder diffraction data. Financial support from EPSRC, Cardiff University, and Universite´ Bordeaux 1 is gratefully acknowledged.

Figure 8. Structure of cyclohexane/thiourea in phase II (at 140 K) viewed along the tunnel axis. The structure shown is the result from the Rietveld refinement for model A. The physical interpretation of the refined positions of atoms within the tunnel is discussed in the text.

reasonable refined value of the isotropic displacement parameter). Single-crystal 2H NMR results10 suggest that rotation of the cyclohexane molecule about its C3 axis still occurs in phase III, but such motion (in the form of 120° jumps) is compatible with a single orientation of the molecule in the time-averaged structure, as the symmetry of the jump motion is identical to the molecular symmetry. Importantly, the tilt angle of the cyclohexane molecule (i.e., the angle between the molecular

Supporting Information Available: Structural data (CIF files) from the Rietveld refinements of phase I at 293 K, phase II at 140 K (results for each of the models A, B, and C considered in the refinement), and phase III at 100 K. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Fetterly, L. C. Non-Stoichiometric Compounds; Mandelcorn, L., Ed.; Academic Press: New York, 1964; p 491. (2) Takemoto, K.; Sonoda, N. Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: New York, 1984; Vol. 2, p 47. (3) Hollingsworth, M. D.; Harris, K. D. M. ComprehensiVe Supramolecular Chemistry; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Vo¨gtle, F., Eds.; Pergamon Press: Oxford, 1996; Vol. 6, pp 177-237. (4) Harris, K. D. M. Chem. Soc. ReV. 1997, 26, 279.

Phase Transitions in Cyclohexane/Thiourea (5) Guillaume, F. J. Chim. Phys. Phys.-Chim. Biol. 1999, 96, 1295. (6) Harris, K. D. M. Supramol. Chem. 2007, 19, 47. (7) George, A. R.; Harris, K. D. M. J. Mol. Graphics 1995, 13, 138. (8) Cle´ment, R.; Jegoudez, J.; Mazie`res, C. J. Solid State Chem. 1974, 10, 46. (9) Cle´ment, R.; Mazie`res, C.; Gourdji, M.; Guibe´, L. J. Chem. Phys. 1977, 67, 5381. (10) Desmedt, A.; Kitchin, S. J.; Guillaume, F.; Couzi, M.; Harris, K. D. M.; Bocanegra, E. H. Phys. ReV. B: Condens. Matter Mater. Phys. 2001, 64, 054106. (11) Lenne´, H.-U. Acta Crystallogr. 1954, 7, 1. (12) Harris, K. D. M.; Thomas, J. M. J. Chem. Soc., Faraday Trans. 1990, 86, 1095. (13) Cle´ment, R.; Gourdji, M.; Guibe´, L. Mol. Phys. 1971, 21, 247. (14) Meirovitch, E.; Krant, T.; Vega, S. J. Phys. Chem. 1983, 87, 1390. (15) Poupko, R.; Fourman, E.; Mu¨ller, K.; Luz, Z. J. Phys. Chem. 1991, 95, 407. (16) Soetens, J.-C.; Desmedt, A.; Guillaume, F.; Harris, K. D. M. Chem. Phys. 2000, 261, 125. (17) Jones, M. J.; Guillaume, F.; Harris, K. D. M.; Aliev, A. E.; Girard, P.; Dianoux, A.-J. Mol. Phys. 1998, 93, 545. (18) Jones, M. J.; Camus, S.; Guillaume, F.; Harris, K. D. M.; Dianoux, A.-J. Physica B 1998, 241-243, 472. (19) Desmedt, A.; Guillaume, F.; Combet, J.; Dianoux, A. J. Physica B 2001, 301, 59. (20) Desmedt, A.; Soetens, J. C.; Guillaume, F.; Lechner, R. E.; Dianoux, A. J. Appl. Phys. A 2002, 74, S1357.

J. Phys. Chem. C, Vol. 112, No. 3, 2008 847 (21) Harris, K. D. M. J. Solid State Chem. 1990, 84, 280. (22) Kunchur, N. R.; Truter, M. R. J. Chem. Soc. 1958, 517, 2551. (23) Truter, M. R. Acta Crystallogr. 1967, 22, 556. (24) Kahn, R.; Fourme, R.; Andre´, D.; Renaud, M. Acta Crystallogr. 1973, B29, 131. (25) It is noteworthy that the powder X-ray diffraction pattern shown in Figure 2 for phase III does not show evidence for pure solid cyclohexane, whereas the powder X-ray diffraction patterns shown in Figure 2 for phases I and II do show evidence for pure solid cyclohexane. In this regard, we recall that the powder X-ray diffraction pattern shown in Figure 2 for phase III was recorded for a different sample from that used to record the data for phases I and II. It is reasonable to propose that partial decomposition of the inclusion compound occurs while handling the material at higher temperatures, prior to cooling in the X-ray powder diffraction experiments, producing solid thiourea and liquid cyclohexane. The fact that in some cases no pure solid cyclohexane is observed (e.g., phase III discussed here) may be due to vaporization of the liquid cyclohexane decomposition product prior to cooling in the X-ray powder diffraction experiments. (26) Larson, A. C.; Von Dreele, R. B. General Structure Analysis System (GSAS); Los Alamos National Laboratory Report LAUR 86-748, 1994. (27) Harris, K. D. M.; Thomas, J. M. J. Chem. Soc., Faraday Trans. 1990, 86, 2985. (28) Jones, M. J.; Shannon, I. J.; Harris, K. D. M. J. Chem. Soc., Faraday Trans. 1996, 92, 273. (29) Aliev, A. E.; Harris, K. D. M.; Apperley, D. C.; Harris, R. K.; Su¨nnetc¸ iogˇlu, M. M. J. Chem. Soc., Faraday Trans. 1993, 89, 3791.