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J. P h p . Chem. 1983,87,1390-1396
good a fitting as for ellipsoidal symmetry, and the experimental temperature dependence of pap: cannot be reproduced by the change of equilibrium constants only. Good fitting at various temperatures can be achieved by a considerable change in the value of IJ (about Z O O ) . Thus, the assumption concerning the geometry of multimers is essential and strongly modifies the dependence of pap: on concentration. This is illustrated in Figure 6 for the model of linear multimers. Conclusions This paper presents an example of fruitful common interpretation of spectroscopic and dielectric measurements. Spectroscopic determination of equilibrium constants for self-association enabled us to discuss the conformation of chain multimers of N-methylacetamide. This discussion shows that neither the model of rigid chains (like in crystalline amide) nor the model in which the
formation of all conformers is equally probable described the results of dielectric studies. However, the model of “elongated” multimers, proposed by Bass and co-workers for the interpretation of dielectric properties of pure liquid amides, appears to work also for dilute NMA solutions. This is a quite simple model, but nevertheless it takes into account the most important properties of multimers, their shape and the dependence of dipole moment on the number of elements in the association chain. Our consideration also showed the strong influence of assumptions concerning the geometry of multimers on the theoretical dependence of pap: on concentration.
Acknowledgment. This work was supported by the Polish Academy of Sciences within the framework of Project MR-1.9. Registry No. N-Methylacetamide, 79-16-3; carbon tetrachloride, 56-23-5.
A Hydrogen-2 Nuclear Magnetic Resonance Study of Conformational and Dynamic Characteristics of Cyclohexane While Trapped within Thiourea Inclusion-Compound Channels Eva Meirovitch,’ Tamar Krant, and Shimon Vega The Weizrnann Institute of Science, Isotope Department, 76 100 Rehovot, Israel (Received: July 16, 1982; In Final Form: November 2, 1982)
We report on 2HNMR spectra from a polycrystalline powder of the thiourea-cyclohexane-dI2inclusion compound within the temperature range 134-345 K. Drastic changes in these spectra as a function of temperature are interpreted in terms of cyclohexane becoming engaged gradually in various uncoupled dynamic modes and undergoing several conformational alterations. At the lowest temperatures, chair-form conformers with a geometry consistent with minimal energy calculations (mec) prevail; the cyclohexane rings are in an upright position within the channels, with the triad axis z’lying parallel to the channel axis d, about which they spin rapidly. At 137 K the guest molecules tip over suddenly so that z’ becomes tilted at an average angle a relative to d with a concomitant onset of nonuniform reorientation about d. Over the next 125 K the average intrachannel orientation of cyclohexane changes gradually with a determined to an accuracy of f1.5’. We also find that at 159 K the motion about d becomes uniform and detect an increase of about 2’ in the angle between the axial and equatorial C-D bonds. At approximately 240 K, onset of rapid ring inversion is observed.
Introduction In isotropic liquids molecules reorient basically as individual entities, as described by the Stokes-Einstein and Debye equations, with rates governed by activation energies which are characteristic for the particular solvent used. In ordered solvents, such as the various liquid crystalline phases, molecules reorient in the presence of local ordering potentials but otherwise the main features of the reorientation process are conserved. Among many other techniques, nuclear magnetic relaxation has been used extensively to study molecular motion in isotropic fluids’ and recently in ordered fluids as ell.^^^ Can one infer from these studies the dynamic behavior of molecules in the solid state? (1)L. M. Jackman and F. A. Cotton, Ed., ‘Dynamic Nuclear Magnetic Resonance Spectroscopy”, Academic Press, New York, 1975. (2)(a) Z. Luz, R. Naor, and E. Meirovitch, J. Chem. Phys., 74,6621 (1981);(b) R. Poupko and Z. Luz, ibid., 75,1975 (1981). (3)R.R. Vold, R. L. Vold, and N. M. Szeverenyi, J . Phys. Chem., 85, 1934 (1981)
This question has been addressed in the past with nuclear magnetic resonance (NMR) spectroscopy using broad-line NMR, relaxation-time measurement^,^^^ and, very recently, complete line shape analysis6-10which became practical due to the development of the high-resolution solid-state NMR techniques. However, the number of studies focussing on the dynamics of molecules in solids (4)H.S.Gutowsky and G. E. Pake, J. Chem. Phys., 18,162(1950). (5)E.R. Andrew, J. Chem. Phys., 18,607 (1950). (6)(a) R. G. Griffin, L. Powers, and P. S. Pershan, Biochemistry, 17, 2718 (1978);(b) G.M. Gall, J. A. Verdi, and S. J. Opella, J. Am. Chem. SOC.,103,5039 (1981). (7)(a) D.E. Wemmer, D. J. Reuben, and A. Pines, J. Am. Chem. Soc., 103,28 (1981);(b) A. D. English and A. J. Vega, Macromolecules,12,353, 3 (1979). (8)H.W. Spiess, Chem. Phys., 6,217(1974);H.W Spiess, R. Grosescu, and U.Haeberlen, ibid., 6, 226 (1974);H.W. Spiess and H.Sillescu, J . Magn. Reson, 42,381 (1981). (9)(a) S.Alexander, A. Baram, and Z. Luz, Mol. Phys., 27,441 (1974); (b) A. Baram, Z. Luz, and S. Alexaner, J. Chem. Phys., 64,4321 (1976). (IO) (a) R. F. Campbell, E. Meirovitch, and J. H. Freed, J . Phys. Chem., 83,525 (1979);(b) E. Meirovitch and J . H. Freed, Chem. Phys. Lett., 64,311 (1979).
0022-3654/83/2087-1390$01.50/00 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983
Cyclohexane Trapped in Inclusion Compounds 0 5i -+
U
-
L
I
58
*
NH;
Flgure 1. Schematic illustration of (a) the thiourea-cyclohexane inclusion compound, (b) the chair-former of cyclohexane, and (c) the location of the cyclohexane molecules within the channels.
is small and only few compounds have been studied up till now. Among these are some vacancy-containing molecular solids known as inclusion compound^^'-'^, where guest molecules are trapped within cavities or channels wherein they are likely to experience various dynamic processes. Molecular motion in these compounds has been studied up till now mainly with broad-line NMR,14b,where the second moment of the NMR spectrum is being measured. Due to the significant contribution of interspin interactions, implying knowledge of interatomic distances, this technique is limited in the nature and the uniqueness of the information it can provide. On the other hand, solid-state 2H NMR is dominated by the quadrupole interaction alone, enabling one to use the much more informative approach of line shape a n a 1 ~ s i s . l ~ ~ It is this latter technique, applied to the thioureacyclohexane-d12(TCIC-d12)inclusion compound, we have used in this work, with particular emphasis on the dynamic and structural characteristics of the cyclohexane guest trapped within the channels formed by the thiourea host. The channel-type structure of this compound is illustrated schematically in Figure la, and the chair-form conformer of cyclohexane is shown in Figure lb. TCIC has been studied previously with X-ray crystallography15J6,differential thermal analysis (DTA),17a14N NQR,17"and wide-line 'H NMR.16J7b Calculations of the conformation of this compound were performed by Cope et al.18 Abrupt changes in the X-ray pattern and in the NQR and NMR spectra were observed a t approximately 123 K. The X-ray results pointed out that the rhombohedral unit cell parameters alter suddenly a t that temperature. An endothermic DTA peak was observed a t 129 K with protonated TCIC and a t 125 K with thiouread,-cyclohexane. The six 14N NQR lines merged into a single line, and the broad-line 'H NMR results indicated (11)S. G. Frank, J.Pharmacol. Sci., 64,1585 (1975). (12)D. D. McNicol, J. J. McKendrick, and D. R. Wilson, Chem. Soc. Reu., 7,65 (1978). (13) N. G. Parsonage and L. A. K. Staveley, "Disorder in Crystals", J. S. Rowlinson and J. E. Baldwin, Ed., Clarendon Press, Oxford, 1978. (14)(a) J. A. Ripmeester, R. E. Hawkins, and D. W. Davidson, J. Chem. Phvs.. 71.1889 (1979):(b) D. W.Davidson.' S. K. Grae. and J. A. Ripmeester, J . Mugn. Reson.', 31, 399 (1979). (151 H. V. LenCe. Acta Crvstulloar.. 7. 1 (1954). (16)R. ClEment,'C. Maziires, MY Gourd,$, and L. Guib6, J . Chem. Phys., 7,5381 (1977). (17)(a) R. CICment, M. Gourdji, and J. GuibE, J . Mugn. Reson., 20, 345 (1975);(b) R. CICment, M. Gourdji, and L. GuibC, Mol. Phys., 21,247
-
(1 ~ 971 - --,.1.
(18)(a) A. F.G. Cope, D. J. Cannon, and N. G. Parsonage, J. Chem. Thermodyn., 4, 829 (1972);(b) ibid., 4, 843 (1972).
1391
a sudden drop in the second moment at 123 K. A second-order phase transition was observed at 153 K where the I4N NQR line disappears and the 'H NMR second moment levels off. The X-ray results showed that between 123 and 153 K the rhombohedral unit cell parameters change continuously and that the phase transition at 153 K involves a smooth transformation of the rhombohedral unit cell into a monoclinic one belonging to the P 2 / c space group, with a nearly twofold increase in its volume. Regarding the motional characteristics of cyclohexane in liquids, high-resolution NMR showed that the overall tumbling motion and the ring inversion process are essentially the same in i ~ o t r o p i c and ' ~ ~ orderedzb ~~ liquids. There is no indication from these former studies that cyclohexane assumes any conformation other than the geometry obtained from minimal energy calculations (mec). It is our objective to find out whether any of these characteristics alter upon going from the lquid to the solid state. Should cyclohexane be mobile within the thiourea channels, one would expect the rates at which it reorients to be considerably lower than in liquids. Also, cyclohexane is likely to experience orientational restrictions. Furthermore, overall molecular reorientation may be slowed selectively relative to internal motions which become thus amenable for detailed studies. In liquids these motions are often "masked" by the rapid molecular tumbling. It has been found in this study that within the clathrate cyclohexane undergoes various dynamic processes and several conformational changes from 134 to 345 K. Our results complement those obtained with the above-mentioned methods by providing new types of information related to the nature of the motions experienced by this molecule and to its conformation, removing ambiguities and rectifying incorrect interpretations. In section I1 we summarize experiment1 details; in section I11 we present our results. A conclusive discussion appears in section IV. 11. Experimental Section Cyclohexane-d,, was purchased from Merck Sharp and Dohme, Canada, and used without further purification. Analytical grade thiourea and methanol from Aldrich were used. The clathrate was allowed to precipitate from a methanol solution of thiourea and cyclohexane-d,,, as described in ref 15-18, to obtain a polycrystalline powder. Excess methanol was then removed on a vacuum line at a torr pressure. Gravimetric and NMR measurements indicated a stochiometric thiourea to cyclohexane-d,, ratio of 3:1, as expected. Formation of the thiourea clathrate was also proven by performing X-ray powder diffraction measurements on the precipitate, to obtain a typical pattern characteristic of thiourea inclusion compounds. The 2H NMR experiments were performed on a modified Bruker SXP-90 spectrometer. The deuterium Larmor frequency was 13.82 MHz. The polycrystalline powder sample was tightly packed within a 7.5" 0.d. NMR tube to a height of 1.5 cm. All ,H NMR spectra were obtained by the quadrupole echo (goo,, T , 90"J experiment, with a delay time T of 100 ps, with a 90' pulse length of 3.5 ps, and by Fourier transformation of the nonquadrature detected echo signal after t = 27. Each spectrum was obtained by 200 accumulations and alternation of the phase (19)(a) F.D. L. Anet and R. Anet, ref 1, chapter 14;(b) F. A.L. Anet and J. R. Brown, J . Am. Chem. Soc., 89,760 (1967). (20)D. Hofner, S. A. Lesko, and G. Binsch, Org. Mugn. Roson., 11,179 (1978).
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Should the C-D bearing molecule reorient rapidly about an arbitrary axis z', tilted at an angle y relative to the C-D bond, and should this motion be uniform (Brownian motionlo or planar jumpsgJObetween equivalent sites of symmetry higher than or equal to C3J partial averaging of the original tensor Qo to an effective axially symmetric tensor Q1, with its principal axis along z', will occur. A reduced spectrum, analogous in shape to that illustrated in Figure 2a, will be obtained with the frequency distance of the main peak from vo becoming 6, = 3/8Q1,where Q1 relates to the original quadrupole constant Qo by means of the equation
I
I I I
Q1
I
I
= &01/(3cos2 Y - 1)
(2)
From the experimental value of 61 one can thus readily obtain the tilt angle y of z'relative to the C-D bond. If in addition to the rapid motion about a zl' axis another rapid motion occurs about a second diffusion axis z2', stepwise shrinking of the full tensor Qo first to Q1 and then to Q2 will take place. By measuring the corresponding values and J2, the angle a between zl' and z i can be obtained from
I
b I I
-
i 6 2 = 61(1/2)(3 COS2 - 1) (3)
0
I20
Y(K H z 1
Flguro 2. (a) One-half of the symmetric theoretical isotropic rigid limit powder spectrum obtained with a quadrupole constant 0,= 165 kHz and a natural line width T2*-l = 0.21 kHz; 6, = 3/eQo and zero denotes the position of the Larmor frequency. (b) Experimental 2H NMR spectrum obtained at 134 K (phase I V ) from a polycrystalline powder of thiourea-cyclohexane-d,, (-); spectrum calculated by superimposing two axially symmetric powder patterns with Q,B = 0,= 164.3 kHz and Qoe= Q I I = 54.4 kHz, T2*-'(a) = 0.14 kHz and T 2 * - ' ( e )= 0.42 kHz (- - - -).
of the first 90" pulse was performed to reduce distortions in the echo signals due to dead time effects after the second pulse. The different temperatures of the samples were obtained by a flow of cold dry N2 gas and stabilized by a Bruker B-ST 100/700 temperature control unit. Accuracy of the temperature during an experiment was about f1.5
K. 111. Results and Discussion A . General Background. The spin Hamiltonian of a deuterium nucleus in a solid is usually dominated by the quadrupole interaction.21 The NMR spectrum of a deuteron in a C-D bond, oriented at a unique d relative to the external field H,,consists of two frequency lines with spacing A = (3e2qQ/2h)(1/2)(3 cos2 0 - 1)
(1)
where e2qQ/h is the quadrupole interaction constant of the axially symmetric quadrupole tensor Q (from now on this constant will be simply denoted by Qo) and d the angle between the magnetic field and the principal axis of Qo. In an isotropic polycrystalline powder all orientations in space are equally probable, and the deuterium NMR spectrum will be given by a superposition of doublets resulting in a spectrum such as that illustrated in Figure 2a (obtained for typical values of Qo = 165 kHz and T2*-l = 0.21 kHz). Shown is half of the spectral pattern which is symmetric about the Larmor frequency vo, defined arbitrarily to be zero. The dominant feature in the line shape is a strong peak at a frequency distance ?j0,which for an axially symmetric tensor Qo is given by a0 = 3/sQo. (21) See, for example, S. Hsi,H. Zimmermann, and Z. Luz, J. Chem. Phys., 69, 4126 (1978), and references cited therein.
Should the investigated molecule contain two types of C-D bonds differing in their orientation relative to a unique diffusion axis z' but with identical quadrupole coupling constants Qo,the 2H NMR spectrum will consist of a superposition of two axially symmetric powder spectra corresponding to the respective partially averaged tensors, say QI and QII. From the experimental values of QI and QII, the respective tilt angles yI and yII of the two C-D bonds relative to z ' can be obtained with
61 = 60(1/2)(3 COS2 71- 1)
(4)
and the same for 6n. In the particular case of the diffusion axis z 'lying within the plane determined by the two C-D bonds, the interbond angle 6 will be given by p = yII - yr. This applies, for example, for the axial and equatorial C-D bonds in cyclohexane when z ' is parallel to the triad axis, as shown in Figure lb. Nearly all experimental 2H NMR spectra of deuterated cyclohexane in the thiourea clathrate observed in this study are given by two superimposed axially symmetric powder spectra. These are interpreted to correspond to partially averaged quadrupole tensors of the axial and equatorial C-D bonds resulting from rapid reorientation about one or two diffusion axes. The experimental spectra recorded as a function of temperature shall be discussed below and interpreted in terms of values assumed by the angles a and 6. Four distinct temperature ranges, characterized by typical spectra, were identified, in accord with the results of Cldment et al." who studied the 14NNQR spectrum of the thiourea-cyclohexane clathrate and observed four phases labeled IV-I upon increasing the temperature. We shall adopt this nomenclature. B. Phase IV. The 2H NMR spectrum obtained a t 129 K is shown in Figure 2b and the line shapes obtained between 134 and 154 K are shown in Figure 3. Temperatures lower than 129 K were not attainable with our equipment. The 129 and 134 K spectra were found to be identical and to consist of two superimposed axially symmetric powder patterns with 61 = 61.6 kHz and 611 = 20.4 kHz, as illustrated in Figure 2b and in the top trace of Figure 3. This value of dI corresponds to a quadrupole constant Qo = 164.3 kHz, typical for aliphatic C-D bonds. On the other hand, hII is reduced considerably, indicating that the cyclohexane deuterons experience selective mo-
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983
Cyclohexane Trapped in Inclusion Compounds
from which only the absolute value of the function 1/2(3 cos28 - 1)(with 8 denoting either a or y) can be obtained, there is an ambiguity in the value of 8 in that both 54.7 - {and 54.7 f with f < 54.7’ provide the same mathematical solution of 1’/2(3 cos2 8 - 1)1(54.7 is the “magic angle” for which 3 cos2 8 - 1 = 0). On the other hand, the 13C NMR line shape is different for 6 = 54.7 - { and 8 = 54.7 + {. This two-fold ambiguity in 8 can therefore be resolved by using carbon-13 (which is an I = nucleus) rather than deuterium (which is an I = 1 nucleus) as the NMR probe. Since our interpretation relates mainly to changes in geometry, choosing consistently the smaller angle implies the least gradual conformational modification and we adopt this view. C. Phase III. At 137 K and 2H NMR spectrum changes dramatically. Superimposed on the 134 K spectrum a new component, of a smaller overall spread along the frequency axis, is observed, indicating that a phase transformation has occurred from phase IV to a new phase 111. This transition has been observed with all the previously used methods at a somewhat lower temperature (the discrepancy in the precise value of the transition temperature is, most likely, an isotope effect?) and was found to correspond to an abrupt change in the monoclinic unit cell parameters. We discuss below the phase I11 spectra, present our interpretation, and outline possible implications. In general, the line shapes in phase I11 consist of a major peak and broader absorbances located at higher (relative to v,) frequencies. Our first attempt was to interpret these spectra in a way similar to our interpretation of the phase IV spectra, by assigning the overall “shrinking” to a sudden tilt of z‘ from d and a concomitant onset of rapid and uniform reorientation about d, besides the rapid motion about z’. Then, as outlined previously, a reduced axial tensor Qle = QOe((1/2)(3cos2 a - l),with Qoedenoting the quadrupole coupling constant corresponding to the equatorial deuterons in phase IV and a the tilt angle between z’and d, is expected to be obtained. By measuring ale, the distance of the main peak from u,, we have estimated a = 35’ a t 139 K (we disregard the second mathematical solution of CY = 74.4O = 54.7 {). The shape of the 143 K spectrum is similar to that of the 139 K one, except for a further shrinking of the pattern, and the experimental value of 6: gives a = 42’. However, contrary to our results in phase IV, where the overall line shape could be simulated by superimposing two axial powder patterns corresponding to Qoe and Qoawith Qoe/Qoa= (3 cos2 yI - 1)/(3 cos2 yII - 1)and p = yII - yI, neither the 139 nor the 143 K spectra could be simulated satisfactorily with the above-mentioned estimates for a and with 6I and an in the vicinity of their mec values. Close examination of the 139 and 143 K line shapes reveals a “shoulder” located on the high-frequency slope of the main peak and an overall spread of the spectrum along the frequency axis smaller than expected and richer in features than the 134 K line shape. These characteristics could be accounted for by superimposing two nonaxial powder patterns with, however, no particular relationship between their respecitve principal values. Good fits with the experiments were obtained by superimposing two orthorhombic tensors with DI = 18.0 kHz, E1 = 0.7 kHz, DII = 25.0 kHz, and EII= 3.0 kHz a t 139 K and the respective values of 16.0, 1.50,21.0, and 2.5 kHz at 143 K, with D and E as defined in ref 6b. T2*-l(I) was taken to be 0.4 kHz and T2*-’(II) = 1.5 kHz. Slow (on the H2 NMR timescale) motions may lead to line shapes which are not readily predictable. However,
+
:I-, .
I54
,
I
0
27
I
54 v(KHz)
1
81
Figure 3. Experimental ‘H NMR spectra obtained at the temperatures line shapes calculated by superimposing two orthorhombic powder patterns with D , = 18.07, E , = 0.68,T2*-’ = 0.41 and D,,= 25.5, E,, = 2.77, T2*-’ = 1.38, all in kHz units (----).
denoted in the figure (-);
tional averaging. From Figure l b it can be seen that motion about the triad axis z ’would differentiate between the six axial and the six equatorial C-D bonds. Furthermore, since mec22indicate that the axial bonds are tilted at an angle of 2.6’ relative to the triad axis z’whereas the equatorial ones are tilted a t 109.7’, one would expect a minor effect of a rapid motion about this axis on the quadrupole tensor of the axial deuterons and a considerable effect on the equatorial deuterons. This expection is indeed borne out by the experiment: using eq 4 with yI = 2.6’ and yII = 109.7’ (i.e., p = 107.1’) we obtain the theoretical value of R = QI/Q11 = 3.025, in excellent agreement with the experimental value of 2.95 obtained from the Figure 2b spectrum. Also, with eq 4 we obtain for the axially symmetric quadrupole interaction constant of the C-D bonds a value Qo = 164.8 kHz from bI and Qo = 165.1 kHz from an. This is in agreement with the value Qo = 167 kHz cited by Mantsch et al.23 Further support comes from a complete line shape simulation, as illustrated by the reasonably good fit between the full (experimental) and dashed (calculated) lines in Figure 2b, with the latter obtained by superimposing two equally intense powder spectra corresponding to QI = = 1.64.3 kHz and QII = */36II = 54.4 kHz. These results strongly support the view that the effective tensors QI and QI1associate respectively with the axial and equatorial deuterons of frozen-in chair-form conformers obtained by mec. We note, as a general comment, that since the anisotropic feature in the full deuterium NMR spectrum is a splitting between two equally intense frequency lines (26,) (22) The geometrical parameters for the cyclohexane molecule were calculated with a computer program described in S. R. Niketic and K. Rasmussen, “The Constant Force Field A Documentation”, in “Lecture Notes on Chemistry”, G. Berthier, Et al., Ed., Vol. 3, Springer, Berlin, 1977. (23) H. H. Mantsch, H. Saito, and I. C. P. Smith, Progr. Nucl. Magn. Reson. Spectrosc., 11, 211 (1977).
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TABLE I : Effective Quadrupole Constants Q,Angles (y. between the Triad Axis z' and the Channel Axis d, and Natural Line Widths T,*-' Used To Calculate Theoretical Spectra at the Various Temperatures in Phases IV and I1 T,*' (II), k H z T , * - (I), k H z temp, K
QI.
kHz
134 159 172 183
164.3 30.0 26.5 25.4
195 210 225 240
23.7 22.9 21.2 20.5
R = QI/QII.
QII,
kHz
54.4 8.9 7.9 7.7 7.45 6.8 6.6 5.7
Ra
"I0
ab
a
b
a
b
0.0 36.8 38.65 39.4
0.41 1.4 1.3 1.25
0.0 1.1 1.1 1.1
1.38 3.9 3.6 3.6
0.0 3.0 3.0 3.0
40.2 41.0 41.75 42.9
1.17 1.1 1.0 0.97
1.0 0.9 0.8 0.7
3.6 3.6 3.6 3.6
3.0 3.0 3.0 3.0
@IIO
2.95 3.37 3.35 3.30
0.0 35.8 37.6 38.8
Phase IV 0.0 37.8 39.7 40.0
3.18 3.37 3.21 3.60
39.8 40.3 41.4 41.8
Phase I1 40.6 41.8 42.1 13.9
a is the arithmetic mean of CYIand "11.
in the slow-motional regime they are very sensitive to changes in the motional rates and varying the temperature leads typically to considerable alterations in these ~ h a p e s . ~ In - l ~our case the shape of the phase 111spectra is nearly preserved by lowering the temperature, indicating that slow-motional effects are apparently not dominant. On the other hand, both the invariance of the line shape pattern and the low symmetry of the partially averaged tensors are consistent with a nonuniform but rapid reorientation about d, a considerable tilt between z ' and d a t 139 K, and a further increase in this angle upon increasing the temperature to 143 K. These results certainly warrant further experimental work on other magnetic nuclei such as 13Cand on other guest which have molecular conformations similar to cyclohexane. Nonuniform reorientation about a mean diffusion axis has been observed previously for pentamethylbenzene in the solid state by 13C NMR.24
D. Phase 11. At about 159 K the uncommon phase I11 pattern changes and the line shapes shown in Figure 4 are obtained. These are reminiscent of the 134 K spectrum. Furthermore, the spectral pattern is nearly preserved from 159 through 240 K, except for a gradual reduction in the overall width. Indeed, the experimental spectra obtained in this temperature range could be simulated by superimposing two axially symmetric powder patterns with parameters listed in Table I. The good fits between the series of experimental and calculated spectra are shown in Figure 4. The scaling down of the spectra is then interpretable in terms of a further increase in a as a function of temperature. The accuracy in a is high and we estimate the precision to be better than f1.5'. Table I contains values of a obtained independently from the two tensors Qla and Qle. These values do not differ by more than 1.5'. The fourth column in Table I contains values of R = QI/QII which were found to be nearly constant and equal to 3.4 f 0.1 throughout phase 11. On the other hand, at 134 K (and below that temperature) R was found to be equal to 2.95, in agreement with the theoretical value of 3.025 based on mec. This increase in R can be interpretated by a 2' increase in the angle fi (see eq 4) which becomes equal to 109' in phase 11, implying a change in the molecular geometry. The fit between calculated and experimental spectra could be improved considerably by allowing for an angular dependence of the natural line width T2*-'of the type T2*-' = la - b cos2 8'1 with 0' denoting the angle between d and H. The best fit values of a and b are given in Table I. The (24) D. E. Wemmer, Ph.D. Thesis, University of California, Berkeley,
1975.
I
0
,
1
9.0
1
18.0
I
I
27.0
u(KHz) Flgure 4. (a) Experimental and calculated *H NMR spectra obtained in phase I1 at the temperatures denoted In the figure. The theoretical spectra (- - - -) are calculated with the parameters listed in Table I.
simplest interpretation for the angular dependence of T2*-' would be to assume that it stems from a mosaicity effect, i.e., a distribution of diffusion axes z' about a mean orientation associated with an average tilt angle CY. Then, one would naturally postulate a 1/2(3cos2 8' - 1) dependence of that part of T2*-l related to the mosaic spread: T2*-' = I(TZo)-'+ (T29-l(1/2)(1 - 3 cos2 0')l For the spectral component associated with the equatorial deuterons we found that a = (T,O)-l+1/2(T2m)-1 and b = 3/2(T2")-1 were about 1 kHz, implying that (TZm)-' = 0.6 kHz and (TZ0)-l= 0.6 kHz. From a quadrupole echo T2experiment we obtained (T,O)-lto be of the order of 0.5 kHz, supporting the hypothesis outlined above. The values b for the axial deuterons are about 3 kHz, three times larger than the values for the equatiorial ones. This is consistent with a mosaicity effect knowing that the ratio
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983
Cyclohexane Trapped in Inclusion Compounds
L
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244" K
r,,,_
II
k
5
I
I
I\\
-
259
I
I I
1
0
1
1
9.0
I
I8 0
I
270
u ( KHz)
Flgure 5. Experimental 2H NMR spectra obtained in the two-phase region extending between 240 and 265 K.
between the effective quadrupole constant is also about three. In fact, such a distribution relates to a spread in diffusion axes z'about a mean orientation given by the a values listed in Table I. We have carried out spectral simulations with an orientation independent T2*-' set to 0.6 kHz and both a Lorentzian and a Gaussian spread in z'. Although the Lorentzian distribution function gave a better fit than the Gaussian one, no substantial improvement over the angular-dependent T2*-' simulations was achieved. We tentatively attribute the discrepancy between theory and experiment to a more complex and, at this stage, unpredicatable form of the distribution function. These results, we feel, warrant further studies, including the use of other magnetic nuclei, such as 13C as well as theoretical calculation aimed, on one hand, at elucidating the nature of the potential operating on cyclohexane and, on the other hand, a t a more realistic modeling of the dynamic process. We note that the discrepancy between the experimental and the calculated spectra in Figure l b are likely to stem from a similar origin. E. Phase I. At about 240 K a centrally located structureless symmetric line, superimposed on the typical phase I1 spectral envelope appears, as illustrated in Figure 5. This is the temperature at which according to Clement et al.16 the '*N NQR v+ line disappears and which has been associated with the phase 11 to phase I transition. The relative intensity of this new component increases gradually upon increasing the temperature to 265 K, where the spectrum is given by a single line located a t the Larmor frequency. Complete vanishing of the quadrupole splitting would occur for an isotropically and rapidly reorienting cyclohexane molecule.23 However, this simple hypothesis is inconsistent with the evolution of the experimental 2H NMR spectrum upon further increasing the temperature, as shown by the full lines in Figure 6. Instead of the common decrease in width of an absorption line in the motional narrowing region, the line first broadens, then becomes structured, and ultimately develops at about 330 K into a unique axially symmetric powder pattern. In comparison with the line shapes in Figure 2, this is consistent with a rapid anisotropic motion of a single type of C-D bonds. This can only arise by assuming that in phase I rapid interconversion between the chair-form conformers occurs which averages out the axial and equatorial bond
I
1
0
I
90 v ( KHz)
180
Flgure 6. Experimental H ' NMR spectra obtained in phase I between 265 and 345 K (-): spectra calculated with the parameters listed in Table I1 (----).
6ot
I
i
501 U0
1
401
i 1
I !
I
dol
'
'
150 ' '
! '
'
' 200 '
' ' ' 250 ' T
'
i ' ' ' 300 ' '
'
,
( O K )
Flgure 7. Plot of the angle a between the triad axis z'and the channel axis d as a function of temperature in the various phases.
orientations to a single average C-D orientation. Should the previously observed temperature evolution of a be carried on to phase I, its value in the vicinity of 270 K must be close to the magic angle, for which the typical powder pattern in expected to collapse to a single line. This is in full accord with our experimental observations. Further alteration of a (to occur upon further increasing the temperature) should cause recovery of the powder pattern structure, as is indeed borne out by the experiment. We determined a with complete line shape analysis by using eq 3 with 61 = 6,,. The angle a was varied to obtain the experimental value of &. Axially symmetric poweder patterns for an effective quadrupole constant Q = 3/a62 and various T,*-'values were then calculated. The best fit
1396
The Journal of Physical Chemistty, Vol, 87,No. 8, 1983
TABLE 11: Effective Quadrupole Constants Q and Angles CY Used To Calculate Theoretical Spectra at the Various Temperatures in Phase I temp, K
Q, k H z
265 270 290 310 325 335
0.81 1.55 2.24 3.63 6.01 5.71
__a'
'
54.1 53.6 53.1 52.1 51.1 50.6
55.3 55.8 56.3 57.3 58.3 58.8
' Two series of possible angles a , displaced symmetricall y about the "magic angle" of 5 4 . 7 " , are obtained as explained in the text. results shown in Figure 6 were obtained with the parameters given in Table 11. The value of CY at 240 K was found to be 42.9'. Although we have not simulated in detail the spectra in the two-phase region extending from 244 to 265 K, it can be seen that the shape of the broad phase I1 component is practically invariant throughout this temperature range. The value of CY a t 265 K is found to be either 54.1 or 55.8' and it changes to 50.6 or 58.8" at 345 K. To be consistent with previous considerations we are inclined to choose the smaller value, implying that CY decreases from 54.1' at 256 K to 50.6' a t 345 K. However, due to the small change in CY throughout phase I, an increase from 55.8" a t 265 K to 58.8' at 345 K is equally plausible. We note again the sensitivity of the 2H NMR spectrum to CY in the vicinity of the "magic angle". Accuracy as high as 0.5' can be achieved with a macroscopically isotropic system. The quadrupole echo T2 experiments indicate that throughout phase I the intrinsic line width is of the order of 0.5 f 0.1 kHz. Best fit theoretical spectra were obtained with T,*-' values of this order of magnitude. However, the 310 K simulation required a slightly higher value T2*-' = 0.8 kHz. Similar to our phase I1 observations, this apparent anomaly may also be indicative of a spread in CY with a nontrivial shape. Alternatively, these observations can be caused by slow motional effects, undetectable due to the near vanishing of the quadrupole structure at 270 K. That the effect of slow motion is to wash out line structure and broaden the spectrum is illustrated in ref lob. Our experimental results do not allow us to determine the nature of this slower process, neither to distinguish between the dynamic and the static nature of the spread tilt angles. IV. Discussion As outlined in the text, we interpret our results in terms of the angle CY specifying the orientation of the cyclohexane ring within the channels (see Figure IC),the angle @ between the axial and the equatorial C-D bonds (see Figure Ib), and the conformation of the cyclohexane ring. No information on the two latter aspects was obtained with X-rays,15J6 14N NQR,17* broad-line lH NMR,16 and DTA16J7awhereas only partial and in some cases inadequatez5 information was derived regarding intrachannel orientation. The temperature dependence of a is depicted in Figure 7. The physical meaning of this angle as the most probable tilt of z'relative to d, which is shifted to higher values upon increasing the temperature, was discussed previously. We suggest that below 137 K (phase IV) cyclohexane is oriented in an uprigt position within the channels and __________ ( 2 5 ) H.Nakajima, J . Phys. SOC.Jpn., 555 (1965).
Meirovitch et al.
spins rapidly about its triad axis 2' whereas about 137 K (phase 111) it is tilted by approximately 35" relative to the symmetry axis of the channel. Phase I11 was found with all the previous methods to be an obscure region.16J7 Although all the former physical methods reported on changes occurring in the respective spectra in this range of temperatures, none pointed out the nature of the microscopic characteristics likely to induce these changes. Our results suggest that, upon crossing the phase IV to phase I11 transition, the rapidly spinning cyclohexane rings tip over within the channels and reorient in some nonuniform manner about the channel axis d. A second abrupt transition occurs a t 240 K. This was only detected with 14NNQR17aand related to a flip of the whole thiourea molecules about the C=S bond. Our results point out a profound change in the conformation of the guest molecules, consisting in onset of rapid ring inversion. Thus, the conformational freedom of the cyclohexane molecules seems to be rather intimately related to the mobility of the channel-forming host molecules. The hypothesis that near room temperature cyclohexane reorients rapidly and i s ~ t r o p i c a l l yis~definitely ~ proven to be incorrect. On the other hand, our 2H NMR results are in accord with the work of Clement et al.l6>l7 We would again like to stress the high precision of 0.5-1.5' in the value of CY in phases I1 and I as well as the strong evidence that the transitions at 137 and 240 K are of first order. None of the previous methods provided information on the geometry of the chair-form cyclohexane conformers. We found that in phase IV the angle betweent he axial and the equatorial C-D bonds is 107.1', whereas in phase I it increases to 109'. As already mentioned, there is no previous evidence for ring interconversion taking place within the thiourea channels. We would like, at this point, to comment on the uniqueness of our interpretation of the "scaling factors" yielding partially averaged quadrupole constants. Throughout this presentation we have associated these with mean tilt angles between triad and channel axes. It is, however, possible to envisage a different picture by assuming that what is being measured in these experiments is an "order parameter", rather than a mean tilt angle, analogous to the physical situation prevailing in a liquid crystalline phase. z would then be defined as the ordering axis, with rapid intrachannel reorientation of the cyclohexane molecules and preferential alignment of z along d. High ordering at lower temperatures would then reflect a highly peaked distribution centered at d and a decrease in the ordering upon increasing the temperature would signify an increase in the width of this distribution. The deuterium NMR experiment alone cannot differentiate between these two models. We also note that our results cannot differentiate between uniform reorientation about z'and/or d and discrete jumps between three equivalent sites (which for the motion about d is physically plausible in view of the 32 site symmetry), since we only observe the effect of the dynamic process in the motionally narrowed limit.$ We believe to have c o n t r i b ~ t e d in l ~ ~illustrating the potential of solid-state deuterium NMR in vacancy containing solid matrices. The questions to be addressed next relate to the correlation of these conformational and dynamic features with the various properties and functions of these molecular crystals. Registry No. Cyclohexane-thiourea, 1618-80-0.
