5121
J. Phys. Chem. 1992.96, 5121-5129 (19) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice Hall: New York, 1986. (20) Singer, J. V. L.; Singer, K. Mol. Phys. 1972, 24, 357. (21) Hoheisel, C.; Deiters, U. Mol. Phys. 1979, 37, 95. (22) Teja, A. S.; Rowlinson, J. S. Chem. Eng. Sci. 1973, 28, 529.
(23) Clegg, H. P.; Rowlinson, J. S.Faraday SOC.Tram. 1955,51,1333. (24) Gugnoni, R. J.; Eldrige,J. w.;Okay, V. C.; Lee, T. J. AIChE J . 1974, 20, 357. (25) Aftienjew, J.; Zawisza, A. J . Chem. Thermodyn. 1977, 9, 153. (26) Haselden, G. G.; Newitt, D. M.; Shah, S. M. Proc. R. SOC.A 1951, 209, 1.
Deuterium NMR and X-ray Crystallographic Studies of Guest and Host Motions in the Thiourea/l,4-Di-ferf-butylbenzene Inclusion Compound Glenn H. Penner,* James M. Polson,+Cameron Stuart, George Ferguson, and Branko Kaitnert Guelph- Waterloo Centre for Graduate Work in Chemistry, Department of Chemistry and Biochemistry, University of Guelph, Guelph, Ontario N l G 2W1. Canada (Received: October 28, 1991; In Final Form: February 25, 1992)
Deuterium nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation times are used to investigate the guest (DTBB-d4), l,4-di-tert-butylbenzne-dl* (DTBB-d18),the and host molecular dynamics of solid 1 ,4-di-terr-butylbenzene-d4 inclusion compound (TUIDTBB-d4), the thiourea/ 1,4-di-tert-butylbenzene-d~ inclusion thiourea/ 1 ,4-di-tert-butylbenzene-d4 compound (TU/DTBB-dz2),the thiourea-d4/ 1,4-di-tert-butylbenzeneinclusion compound (TU-d4/DTBB), and thiourea-d4 (TU-d4). X-ray crystallographic studies of TU/DTBB-d4 have been carried out at 291 K. In solid DTBB the phenyl ring is essentially static whereas the rert-butyl groups are undergoing rapid reorientation of both methyl and rert-butyl groups. Attempts to analyze the 'H spectra and Tl data for DTBB-dls suggest that the dynamics of the methyl and tert-butyl groups are nearly equivalent, and as a result, a satisfactory analysis, yielding methyl and tert-butyl rotational activation energies, was not possible. X-ray diffraction results for TU/DTBB-d4 suggest that, at 291 K,the phenyl ring is occupying three nearly equivalent sites. The ZHNMR line shapes between 186 and 392 K were interpreted using a model in which the phenyl ring is rapidly flipping between three positions, with one position less favored. At 296 and 186 K the populations are 0.81:1.00.1.00 and 0.201.00.1.OO,respectively. Relaxation times obtained between 1 1 1 and 322 K show no mini",supportingthe assumption of very rapid phenyl ring reorientation. For TU/DTBB-d2z a high-temperature T1minimum is well-defined, and a second minimum,corresponding to tert-butyl group rotation, is reached at the lowest attainable temperatures. Lineshape simulations of the spectrum at 77 K yield methyl and tert-butyl group rotational rates of 1.0 X lo3and 2.0 X 106 s-l, respectively. Analysis of the higher temperature spectra (109-172 K) and T1data (167-300 K) yield methyl rotation activation energies of 12.7 and 12.3 kJ/mol, respectively. Deuterium line-shape studies of the thiourea dynamics in TU-d4 and TU-d4/DTBB yield activation energies for 180' flips about the C-S bond of 47 and 46 kJ/mol, respectively.
Introduction Deuterium NMR has proven to be a very powerful technique for the investigation of molecular motion in partially ordered Such systems may include molecular or ionic crystalline solids,"' glasses,12polymers,'J3 inclusion compounds,leZ2 crystal^.^^*^^ molecules absorbed onto ~ u r f a c e s ? and ~ , ~ liquid ~ Anisotropic molecular motion of the moieties of interest, which are on the order of lo3-lo7 s-l, may affect the 2H NMR line ~hape.2~ Slower motion ( 103-10-1 s-l) can be investigated by spin and faster motion ( 108-1011s-l) may alignment be probed by measurement of the spin-lattice relaxation times.29 Deuterium N M R line shapes are not only affected by the time scale of the motion but also by the type of motion executed by the guest molecule. The prospects for deuterium N M R studies a t natural abundance (0.015%)are usually rather poor. With some synthetic ingenuity this can be turned into a considerable advantage, in that the moiety of interest can be selectively deuterated. Hence, the motion of a particular molecule or part of a molecule can be selectively studied by *HNMR. Urea, thiourea, and selenourea form inclusion compounds with a variety of organic guests.30 The guest molecules are included in the channels formed by the urea, thiourea, or selenourea molecules. These inclusion compounds have received considerable attention and continue to be the focus of much interest. Some effort has been directed toward the study of the motions of guest 'Present address: Dcpartment of Physics, University of British Columbia, 6224 Agriculture Rd., Vancouver. BC Canada V6T 2A6. *Permanentaddress: Laboratory for General & Inorganic Chemistry, Faculty of Science, University of Zagreb, Zagreb, Croatia.
molecules in solid inclusion compounds.31 Calorimetric studies often show phase transitions which are associated with a change in the cavity size or shape and concomitant change in the restricted mobility of the guest molecules. X-ray diffraction studies of inclusion compounds are often unable to locate the atoms of the guest molecule but rather show a smeared-out electron density resulting from fast motion of the guest.32 Deuterium N M R studies of the guest molecule motion in thiourea inclusion compounds of cyclohexane?* ferrocene,20 and adamantane" have recently been reported. We have chosen to study the dynamics of solid, 1,4-di-tert-butylbenzene(DTBB), thiourea (TU), and the TU/DTBB inclusion compound. Fully deuterated thiourea-d4 was studied, as well as TU-d,/DTBB. The guest molecule (DTBB) is selectively deuterated at the ring positions (DTBBd4), a t the tert-butyl positions (DTBB-d18), or fully deuterated (DTBB-dZJ.
Theoretical Background The deuterium NMR spectrum of a static X-D bond is dominated by the quadrupolar interaction between the deuteron nuclear quadrupole moment, eQ, and the electric field gradient, eqzrrat the deuteron. If the quadrupolar tensor is axially symmetric, the spectrum consists of a doublet with spacing
AU
(3$qZ,Q/4h)(3
COS'
J, - 1)
where x = 2qZ,Q/his the quadrupolar coupling constant and J, is the angle between the C-D bond and the magnetic field. For a polycrystallinepowder the spectrum is the weighted sum of many superimposed doublets, yielding the typical Pake doublet, with
0022-3654/92/2096-5 121%03.00/0 0 1992 American Chemical Society
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5122 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
a powerful technique in elucidating the type of dynamics performed by guest molecules loosely held in the channels of urea and thiourea clathrates.
h/\
-150.0
B
M
C
M
D
0.0
Experimental Section
150.0
Frequency IkHz)
Figure 1. Calculated 2HNMR spectra for various rotational models. (A) Rigid lattice limit: x = 170 kHz, q = 0. (B) Rapid methyl rotational: x = 170 kHz,q = 0. (C) Rapid methyl and rert-butyl rotation: x = 170 LHz,q = 0. (D) Rapid phenyl ring rotation: x = 180 Wz, 7 = 0.05. (E)Rapid 180’ phenyl ring flips: x = 180 kHz, q 0.05, yielding an observed spectrum with xcg = 108 k H z and qog = 0.6.
-
characteristic splitting between peaks of 3/4x and shoulders separated by 3/2x. An example of such a powder spectrum is shown in Figure 1A. If the quadrupolar tensor is not axially symmetric, the powder spectrum is characterized by thrce separations: Azql = 3/4X(1 - q ) , L)Y22 = 3/4x(1 q), and Au33 = ’12x, where q is the asymmetry parameter.
+
q = (Av22
- Avll)/Av33
(2)
Figure 1A shows a powder spectrum for the case where x = 170 kHz and q = 0. For the sc-called axially symmetric case AVII = Av22 and q = 0. When there are rapid (>lo7 s-I) jumps of the X-D bond between different orientations in the applied magnetic field, there will be a partial averaging of the powder spectrum. If the static powder spectrum is axially symmetric ( q = 0), then a symmetric motion about some axis will yield another axially symmetric powder spectrum, which is reduced in width by a factor ‘/2(c0s2 B - l), where is the angle between the rotational axis and the X-D bond. This will occur for the case of n-site jumps, where n 1 3 and there is C, symmetry about the rotation axis. Examples corresponding to methyl (e = 70.5O) and phenyl (e = 60°) are shown in Figure 1, B and C, respectively. In a (CH&M group, the methyl group rotation is superimposed on the trimethyl reorientation, and for fast rotation of methyl and trimethyl groups, the width of the powder spectrum is further reduced by a factor of 1/2(cos24 - 1) where 4 is the angle between the rotational axis and the M-C bonds. An example corresponding to superimposed methyl and tert-butyl(4 = 70.5O) rotation is shown in Figure 1D. If the C-D bond is undergoing an asymmetric motion, for example a two-site jump, a large-amplitude vibration, an asymmetric wobble, or exchange between sites of different populations, the overall width of the static powder spectrum will be narrowed and will display a nonzero effective asymmetry (qem # 0). In the case of two-site jumps the reduction of the effective quadrupolar coupling constant,w,and change in q& will depend on the relative orientationsof the C-D bonds for the two sites and on the relative populations of the two sites. An example of a spectrum for a two-site 180’ flipping of a phenyl ring between sites of equal population is shown in Figure 1E. Exchange rates on the order of 103-106 s-l will modulate the line shapes in a less straightforward way; however, the line shapes can be numerically simulated using specific models for the dynamic proce~ses.’~It is, indeed, this sensitivity of the deuterium NMR line shape in the intermediate exchange rate that makes it such
Deuterated samples of 1,4-di-tert-butylbenzenewere prepared by the Friedel-Crafts alkylation of benzene-d6with terr-butyl-d9 chloride and ferric chloride. Products were recrystallized from ethanol and were shown to be pure by high-resolution proton NMR and melting point. Deuterated thiourea was prepared by dissolving thiourea in D,O and removing the solvent under vacuum. The TU/DTBB clathrates were prepared by mixing equal weights of thiourea and the deuterated DTBB in enough methanol to dissolve both solids at room temperature. After slow evaporation the crystals were harvested and washed with pentane and cold water in order to remove any excess DTBB or thiourea, respectively. The TU-d,/DTBB clathrate was prepared by crystallization of DTBB and TU from methanol-Od. Thioum-d, was prepared by dissolving thiourea in D 2 0 and removing the solvent under vacuum. Elemental analysis showed that the thiourea/DTBB clathrate crystallized in a 6: 1 complex. Approximately 500 mg of sample was placed in an 8-mm-0.d. glass tube and sealed. Deuterium NMR spectra were obtained at 41.3 MHz on a home-built spectrometer using the quadrupolar echo pulse sequence” (r/z),-TQ-(*/2),~Q~cquire. Typically, the length of a r/2 pulse was 3.5-4.0 ps. At each temperature the echo signals were collected for a 7Qvalue of 40 ps. In some cases several values of 70, ranging from 40 to 1500 ps, were used. The echo signals were Fourier transformed to obtain the deuterium NMR spectra. Spectra at liquid nitrogentemperature were obtained at 30.7 MHz on a Bruker CXP-200 using a home-built probe. The deuterium TI data were acquired using an inversion recovery pulse sequence modified for quadrupolar nuclei: (*)*~-(r/2),,-7~-aquire. Typically 15 values of T were used to determine TI,at a particular temperature. The pulse spacing, T? for the TI determination was 40 ps. The time between r e p ebtions of the pulse sequence was always greater than 10TI. The data were fit using a nonlinear least-squares (Marquardt) algorithm employing either an exponential fitting function or a sum of two exponentials to obtain the relevant relaxation time parameters. Lineshape simulations of quadrupolar echo spectra, partially narrowed by molecular motion, were simulated by standard metlaodp using the program MXQET.~~The computations employed an IBM 3081-K mainframe. X-ray Expehmk Details of the X-ray experimental conditions and final R factors, etc., are summarized concisely in Table I. The structure of the thiourea host molecule is lcn0wn,3~and initial non-H atomic coordinates of the thiourea molecule were taken from a more recent paper36 which describes a thioureaadamantane complex. After refinement of the thiourea portion of the structure, a difference synthesis revealed the disordered pdi-terr-butylbenzene. For the final stages of the refinement we detenninod C00rdjIlstC8 for the encapulated pdi-tert-butylbmzme from difference m a p and included an idealized molecule (C-C 1.397 or 1.500 A) in the calculations but only allowed its thermal parameters to refine. Atomic scattering and anomalous dispersion factors were taken from the litorature.” All calculations were performed 011 a Silicon Graphics 4D-380 system using the NRCVAX programs.’* Final fractional coordinates are given in Table 11. Thiourea bond lengths and bond angles are given in Table 111.
R d Q md Discuseion l , M l i - d a t - b u Q ~ d(UI’BB-d4). 4 The deuterium NMR spectrum of DTBB-d4 is typical of that expected for phenyl deuterons in the rigid lattice limit. The quadrupolar coupling constant is 185 kHz,and the asymmetry parameter is 0.05. The appearance of the spectrum does not change for all temperatures below the melting point (76 OC, 349 IC). The rotation of the phenyl moiety is hindered by intermolecular interactions; the molecules are stacked in such a way as to have the phenyl ring
Thiourea/ 1,4-Di-tert-butylbenzene Inclusion Compound TABLE I: Summiry of Data Collection, Structure Solution, and Refinement Decllils formula CIOHZIDZN& 3 [(NHz)zC=Sl, 0.5(t-BuC6Dd-t-Bu) 325.5 fw yellow, prism color, habit crystal size, mm 0.78 X 0.31 X 0.25 trigonal cryst syst 30-36" 28 range of the 25 refl in cell determination 15.939 (3) a. A 12.3912 (21) c, A 2726.2 (7) v,A Rgc space group 6 Z thiourea molecules lie on 2-fold molecular symmetry axes, p-tert-butylbenzene molecules (with 0.5 occupancy) lie about sites with 3 symmetry 1038 F(oo00) 1.190 dcllo g cm3 3.9 p , cm-l Enraf Nonius, CAD4 diffractometer Mo K a (A = 0.7093 A) radiation graphite monochromator 4-54 28 range, deg 18 temp, "C 0-17, 17.0-15 hkl range of reflcns 696 reflcns measured 667 unique reflcns 0.019 Rint reflcns with I > 2.5a(I) 512 52 no. of variables in LS 0.0004 k in w = l/(.ZFo + kF,2) 0.039, 0.062, 2.38 R, R,, gof density range in final A map, e A-3 -0.190, 0.240 0.006 final shift/ error ratio TABLE II:
S
Final Fractional
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 5123
d
Figure 2. A view showing how the 1,4-di-tert-butylbenzene-d4 molecules are disordered in the crystal lattice, with an indication of our numbering scheme. The arrows "A" and 'B" show where the cross sections of electron density (shown in Figure 3) were made. The rerr-butyl groups of adjacent DTBB molecules are not interlaced but appear so due to the half-occupancies of the guest molecules.
Coordinates
X
V
z
0.69964 (4) 0.59229 (18) 0.54189 (14) 0.4936 (15) 0.5587 (13) 0.5712 0.6667 0.6667 0.7426 0.5907
0.69964 (4) 0.59229 (18) 0.55914 (14) 0.5064 (15) 0.5926 (13) 0.2537 0.333 0.3333 0.3333 0.3333
0.25 0.25 0.16093 (14) 0.1585 (15) 0.1039 (18) 0.1070 -0.0541 0.0670 -0.1104 -0.1104
6
TABLE IIk Thiourea Bond Distances (A) and Angles (deg) SC(1)-N 120.5 (1) S-C( 1 ) 1.711 (3) C(1)-N 1.311 (2) NC(1)-N'" 119.0 (3) N-Hl(N) 0.81 (2) C(1)-N-Hl(N) 122 (1) N-H2(N) 0.84 (2) C(l)-N-HZ(N) 121 (1) 'Hl(N)-N-HZ(N) 118 (2) "The superscript I refers to an atom a t y , x, 0.5
- z.
rotation hindered by the proximity of tert-butyl groups of nearby DTBB molecule^.^^*^ 1,4-W-terf-butyIbenzeoe-d (DTBB-I Spin-Luttice Relaxation Times. The TI values plotted as a function of inverse temperature are shown in Figure 5. A rather broad, flat T I minimum (2.7 ms) is found at T = 198 K. A linear least-squares fit of the high- and low-temperature extremes of the T I data gave slopes with corresponding activation energies of 15.4 and 15.2 kJ/mol, respectively, with errors of about 5%. Beckman and co-worker~~~ have studied the dynamics of tert-butyl groups in solid DTBB using proton spin-lattice relaxation techniques and have found results similar to those of the present study. At a proton frequency of 31 MHz, for example, a single TI minimum of 14.3 ms at T = 199 K was observed over temperatures ranging from 333 t o 133 K. A strong dependence
Figure 3. A cross section of the electron-density containing (A) the ortho carbon atoms of the 1 ,edi-rerr-butylbenzenc-d4 molecule (corresponding to section A in Figure 2) and (B) the methyl carbons of the tert-butyl group (corresponding to section B in Figure 2). Contour levels are at 0.05 e A-3.
of the relaxation times on the thermal history of the sample was also observed. The TI data were initially analyzed using the BPP spectral density.42 The presence of a single T I minimum implies an equivalence, or near equivalence, of the methyl and tert-butyl rotational rates. Beckman et al.41 have analyzed their proton relaxation results with the assumption that the methyl and tert-butyl groups reorient at the same rate. Assuming that the
Penner et al.
5124 The Journal of Physical Chemktry, Vol. 96, No. 12, 1992
The coefficients A and B are functions of the angles between the C-D directions and the axis describing a particular rotation. We initially assumed that the methyl groups and the tert-butyl groups had tetrahedral geometries. In the case of dynamic equivalence between methyl groups and identical rotation rates for the two motions, the ratio A:B is 0.168: 1. The temperature dependence of the correlation time, T = 1/3k, where k is the exchange rate between the three sites, is assumed to be given by the Arrhenius relation: 7,
=
7,
exp(E,/RT)
(5)
After fitting the high- and low-temperature extremes of TI vs. T1, we find that
-
T1 = Cexp(E,/RT)
(6)
for high temperatures, and T I = D exp(-E,/RT)
a
Figure 4. A view along the crystallographic c direction of (A) the thiourea/ 1,4-di-tert-butylbenzenecrystal structure and (B) the same view with the 1,4-di-tert-butylbenzene molecules removed. The atoms are shown as van der Waals spheres. 100.
50. A
m
v
.--
t--
10.
5.
3. 0
4. 0
5.0
1000/T
6.0
7. 0
8. 0
(l/K)
100.0 50.0 A
m E v
t--
10.0
5.0
3. 0
4.0
6.0
5.0
7. 0
8. 0
1000/T (l/CO Figure 5. Deuterium TIvs 1000/ T for DTBB-d18. Solid curve in upper figure is best fit using eq 8. Solid curve in lower figure is best fit using eq 8 and allowing for a deviation of the tert-butyl group from a tetrahedral geometry.
three methyl groups of the tert-butyl group are dynamically equivalent and have motional rates equal to that of the tert-butyl group, the TI is given by 1/TI = K[Af(wo,7)+ Bf(w0,7/2)1 (3) where ~ ( w , T )= j ( w , ~ )+ 4j(20,~) 87 - 27 (4) 1 + (WT)2 1 + 4(w7)2
+
(7)
for low temperature, where C = 6.68 KT, and D = 6.67 K/(OOT,). Thus, the temperature dependence of Tl is completely determined by fitting the high- and low-temperature extremes of the data. A least-squares fit gave C = 0.176 K-' and D = 8.366 X lo6 K-l. The values of T , and K obtained using eqs 3,4, and 5 are 4.367 X s and 3.687 X 1Olos-', respectively, with an uncertainty of about 5%. The agreement between experiment and theory is excellent at high and low temperatures, but there is a significant discrepancy near the Tl minimum. The experimental Tl values in this region are higher than the predicted values, and the calculated curve does not reproduce the shallowness of the experimental TI minimum. Experimental Tl minima that are shallower than predicted by BPP theory may be attributed to different activation energies for the different methyl groups within a tert-butyl In butylated hydroxytoluene (BHT)41*44 the presence of the hydroxyl group beside the tert-butyl groups induced a conformation in which the rotation of one of the methyl groups was inhibited by the close proximity of a ring hydrogen, the nonequivalence of the methyl resulted in a broad shallow T1 minimum. However, there are no bulky groups ortho to the tert-butyl groups in DTBB; thus, the possibility of inequivalence of methyl groups is not a likely explanation for the T1 behavior. Another possibility, also used to explain anomalous T1behavior in other tert-butyl groups, is a slight inequivalence in correlation times between the methyl and tert-butyl group rotations. Two closely overlapping Tl minima may yield a broad, flat T1minimum. Modifying eq 3 for a tert-butyl group with inequivalent methyl and tert-butyl motions, the relaxation time was found to be 1/Ti = k[Af(~0,7d + Bf(w0~7~2) + cf(~0,7~3)1 (8) where A:B:C = 1:3.89:29.13 and where the functionsf(wo,T) are given by eq 4. The correlation time 7, corresponds to the methyl rotation and T , ~= 1 / 3 kwhere . kl is the exchange rate between three deuteron sites. Similarly, the correlation time Tc2 corresponds = '/3k2, where k2 to the rotation of the tert-butyl group and is the exchange rate between the three methyl group sites. The third correlation time T , ~ ,which takes into account the superposition of the methyl group on the tert-butyl group rotation, is a combination of the previous two; 1 / ~ =, ~l / ~ + , ~1/TC2.The activation energies were fixed to the values obtained from the least-squares fitting of the high- and low-temperature extremes of the Tl versus T 1 curve. The Tl fitting is shown in Figure 5. The fitting parameters were found to be T ~ = , 1.32 X 10l2s, T ~ , = 2.70 X s, and K = 4.10 X lo7 s-~. The fitting curve from this model is considerably better than that obtained from the one-correlation time model, especially in the region of the Tl minimum. Nevertheless, the fit does not quite reproduce the flatness of the experimental T I minimum. A third possibility is that the geometries of the tert-butyl or methyl groups deviate from tetrahedral. In order to reproduce the 10-kHz quadrupolar splitting in the 2H NMR spectra of DTBB (see next section), a tert-butyl bond angle of 113' was used. The T1 fitting, using a bond angle of 113O, is shown in Figure
Thiourea/ 1,4-Di-tert-butylbenzeneInclusion Compound 202.5
173.5
A L R153.4
123.4
116.7
.50.0
0.0
Frequency IkHr)
50.0
-50.0
0.0
50.0
Frequency lkHzl
Figure 6. Experimental and simulated *HNMR spectra for DTBB-d18 at various temperatures. 202.5 K, k = 5.0 X 10'; 173.5 K, k = 1.5 X IO7s-I; 153.4 K,k = 3.0 X 106 s-I; 123.4K,k = 7.5 X lo6 s-I; 116.7 K, k = 3.5 x 106 s-1.
5. The fitting parameters were found to be T~~ = 4.06 X l O I 3 1.431 X l W s , a n d K = 1.1OX 109S-2. Thismodelyields a further improvement in the fit, although the flatness of the experimental TI minimumis still not satisfactorily fit. It is possible that the model is wrrect but that the fitting algorithm just has difficulty resolving the two closely overlapping minima when the minima are not clearly visible. Furthermore, the set of fitting parameters may not represent a unique best fit. 2H NMR Spectra. The *H NMR spectra of DTBB-d18,for the five lowest temperatures, are shown in Figure 6. At temperatures above 202.5 K, the spectra are typical of those expected for fast methyl and tert-butyl rotation (see Figure lC), although the observed quadrupolar splitting of 10 kHz is smaller than that expected for tetrahedral methyl and tert-butyl geometries (14 kHz). As the temperature is lowered, the sharp peaks become less well defined and, by 153 K, have vanished completely, leaving only a smooth Lorentzian-like curve with a width at half-maximum of =10 kHz. As the temperature is further decreased, the line shape continues to narrow until, by 116.7 K, it has reduced to about 3 kHz wide at half-maximum height. At this temperature the spectral intensity is at a minimum. The transverse relaxation time observed by measuring the rate of decay of the spectral intensity as a function of pulse spacing using the quadrupolar echo technique is defined as the T2QE.Generally, the T2QEvalues of the spectra were found to decrease monotonically with decreasing temperature, reaching a T2QEminimum at T = 116.7 K. This is consistent with the spectral intensity minimum found at this temperature. Because of experimental constraints, this was the lowest possible temperature attainable; thus, it is not known whether this is the absolute T2QEminimum, although it is likely to be within 10 K of the true minimum. As mentioned above, the observed quadrupolar splitting is s i g d h n t l y smaller than that expected for rapidly rotating methyl and tert-butyl groups. This suggests the possibility of a third motion, superimposed on the two rotations. The most likely possibility is a small-amplitudelattice vibration in the molecular crystal. The magnitude of the quadrupolar splitting does not change from about 200 K to the melting point at 349 K, implying that the amplitude of the vibration also does not change over this temperature range. The vibrational amplitude is expected to change with temperature, but no change in the appearance of the 2H spectrum of DTBB-d4,due to lattice vibrations, is observed. Another explanation is a deviation of the methyl or tert-butyl groups from having tetrahedral geometries. A survey of X-ray crystal structures for tert-butylbenzene derivatives, having no hindering groups ortho to the tert-butyl moiety, yields several cases of significant deviation of the tert-butyl group from a tetrahedral S,T~.,=
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 5125 geometry.4s A quadrupolar splitting of 10 kHz implies a bond angle of 113'. As mentioned in the previous section, changing the bond angle from 109.5' to 113' gave a better fitting of the Tl data. In order to reliably simulate the 2H NMR spectra, it is necessary to acquire the spectra for the full range of correlation times, from the motionally averaged extreme to the rigid lattice limit. Assuming that the T2QEminimum is near 116.7 K, the tert-butyl groups at these temperatures have correlation times rC= wQ-' = lo4 s, roughly 2 orders of magnitude away from the rigid lattice case. It is precisely in this region that the line shape is most sensitive to changes in the motional rates. In Figure 6 we present the experimental 'H spectra for the five lowest temperatures as well as simulations, where equal exchange rates were assumed for the tert-butyl and methyl rotations and where a tert-butyl bond angle of 113' was employed. The agreement between the experimental and simulated line shape is satisfactory, although it should be pointed out that a number of combinations of tert-butyl and methyl exchange rates may also reproduce the experimental spectra in this temperature range. It would be necessary to obtain *H spectra at temperatures below those presently attainable with our apparatus, in order to precisely determine the rates of the two motions. Thiourea/ 1,4Di-tert-butylbenzened4 (TUIDTBB-d,). Our X-ray analysis establishes clearly how the 1,4-di-tert-butylbenzene-d4 molecule is oriented in the thiourea host. The guest molecule is present with 0.5 occupancy and lies about a 3 symmetry site with each tert-butyl group being very close to another site with 32 symmetry (as shown in Figure 2). A difference synthesis normal to the 3-fold axis and in the plane of the unsubstituted carbon atoms showed a "lumpy donut" of density (Figure 3A), indicating that these benzene carbon atoms were effectively disordered over almost the entire range of rotation angles-but there were six ill-defined maxima (60' apart) in the density torus, consistent with the molecule spending more of its time in these orientations. The tert-butyl methyl carbon atoms gave rise to three maxima (Figure 3B) from whose shape we inferred that the methyl carbons (instead of lying on the 2-fold axis of the site with 32 symmetry) are slightly removed and disordered about the crystallographic 2-fold axis as shown. A view of the clathrate with the atoms shown as van der Waals spheres is shown in Figure 4A. The 1,4-di-tert-butylbenzene-d4guest molecule fits snuggly into the cavity of the thiourea host. (A view of the host with the 1,4-di-tert-butylbenzene-d4 molecules removed (Figure 4B) shows clearly the channels into which the guest molecules are fitted.) The 2H NMR spectra of TU/DTBB-d4 in the temperature range 185.6-392 K are shown in Figure 7. Over this 200 K temperature range a gradual change in both the effective asymmetry parameter, tleff, and the effective coupling constant, Xeff, is observed. The value of qcfr is 0.0 at 185.6 K, increases with increasing temperature, passes through 1.O at 270 K, and then decreases to 0.32 at 392 K. The effective quadrupolar coupling constant changes from 52 kHz at 185.6 K to 26 kHz at 392 K. This kind of gradual change in Teff and xcffwith temperature is indicative of a rapid exchange of the C-D bonds between sites of unequal populations, with the populations changing as a function of temperature. The X-ray diffraction results suggest that the C-D bonds of the phenyl ring are undergoing a six-site exchange (see Figure 4), as a result of phenyl ring jumps between three sites. For the case of equal populations of sites and rapid exchange between sites, a spectrum like that shown in Figure 1D is expected (x,rf 16 kHz, tlcff = 0). Our NMR results indicate that the three positions of the phenyl ring are not equally favored. The simplest models that describe this situation would have one position of the phenyl ring more or less favored than the other two. We have chosen to employ a six-site model in which the C-D bonds execute 60' jumps within the hexagonal channel of the TU host and where two sites (one phenyl position) are less favored than the other four. This model was able to successfully reproduce the experimental spectra. At the highest temperature (392 K) the population ratio
Penner et al.
5126 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
j " l
392.0
) (,
172.3 K
357.5
)
329.7
A
I
295.7
,/)
A
r\, i"\ b! .100.0
/,
L
0.0 Frequency IkHz)
270.3
K
v58.6 K
y38.4 K
2 % K 121.7
249.7
125 kHz
224.0
Figure 8. Representative 2HNMR spectra of TUIDTBB-d, in the lower temperature phase.
203.7 185.6
-
100.0 .100.0
00
100 0
Frequency (kHz)
Figure 7. Experimental and simulated *HNMR spectra for TU/ DTBB-d, at various temperatures. The populations of the least favored site are 392 K (0.91), 357.5 K (OM), 329.7 K (OM), 295.7 K (0.78), 270.3 K (0.69), 249.7 K (0.63), 224 K (OSl), 203.7 K (0.37), and 185.6 K (0.20).
An additional consideration that must be taken into account when the TU channel is significantly distorted from a hexagonal geometry is that the jump angles may no longer be 60° and that the jump angle between positions 1 and 2 may differ from the angle between positions 2 and 3. We have not attempted an analysis with pI # p 2 # p3 and jump angles other than 60°. A third consideration that may be necessary for simulation of the lower temperature spectra, and may improve the agreement between simulation and experiment in the higher temperature region, is that of a small hindering potential for the reorientation of the phenyl ring. Zamir et al.48have addressed the problem of 3-fold reorientation and the appearance of 2H line shapes for various barrier heights, V3. When V, is smaller than kT,line shapes are similar to those obtained for potential-free diffusion. If V3 is much larger than kT,the commonly used discrete-site exchange model is appropriate. When V3is on the order of KT, the spectra are essentially a weighted average over the rotation potential, V(8). For equally populated sites (p, = p 2 = p 3 ) the hindering potential for phenyl reorientation in TU/DTBB takes the form
was 0.91:1.00:1.00, and at the lowest temperature the ratio was 0.20 1.oO:1.@ UnequalI populations . can be rationalized by a slight distortion of the thiourea channel from hexagonal symmetry. At ambient temperatures this distortion results in one phenyl position having about 80% of the population of the other two. The electron V(8) = V6 sin2 38 = (v6/2)(1 - cos 68) (9) density of the phenyl ring is rather smeared out by the dynamics If one phenyl position is more or less favored (pl = p 2 # p 3), of the ring; hence, a population ratio of 0.80: 1.O:l .O would not the potential is be detectable in an X-ray diffraction experiment. Simulations using a model with one phenyl position more favored over the other v(e)= Vi sinZ812 + V6 sinZ38 (10) two invariably yield spectra that were too wide (i.e., xcN too large). For unequal populations (pi # p 2 # p 3 ) The effective asymmetry parameter and quadrupole coupling constant continue to change monotonically as the temperature 38 v(e) = Vi sin2 -e2 + V3sin2 + V, sin2 38 (1 1) is lowered and reach values of 0.70 and 80 kHz, respectively, at 2 122 K (see Figure 8). We were unable to reproduce the spectra The shallowness of the electron density contours between the six below 185.6 K using the three-site, two-population model. It is maxima suggests a rather low potential barrier (see Figure 4). quite pmible that a phase transition occurs below 185.6 K. The 11 suggests that an additional six parameters ( P I ,P2, inclusion compounds of f e r r o ~ e n e ~ ~and , ~ Oc ,y~c~l o h e ~ a n ein~ ~ ~ ~Equation ~ P3, Vi, V,, V6) may be needed to successfully describe the case thiourea undergo phase transitions at 162 and 156 K, respectively. of unequal populations with small finite rotational barriers. In the former, the phase transition is associated with the onset The 2H spin-lattice relaxation times for TU/DTBB-d4 at of reorientation of the ferrocene molecule. The structure of the temperatures between 111 and 322 K are shown as a function of low-temperature phase could not be determined by X-ray difinverse temperature in Figure 9. The T I values decrease confraction methods. In the lower temperature phase of the latter tinuously with temperature over the entire temperature range. The (TU/cyclohexane) (129-156 K),the TU lattice is monoclinic but data points define a good straight line from 121 to 185.6 K. At gradually transforms into a hexagonal form. This transformation higher temperatures there is a negative curvature. The two lowest is accompanied by a continuous transformation of the guest temperature points show a positive deviation from the straight molecules between three different species, corresponding to cyline, suggesting the onset of a T I minimum. The lack of T , clohexane in different dynamic states and apparently also different minimum over this temperature range is consistent with our model lattice sites?' The urea/trioxane inclusion compound undergoes of rapid jumps of the phenyl deuterons between sites of unequal which involves a significant distortion a phase transition at 189 K1* populations. of the channels from hexagonal to orthorhombic symmetry. A Thiourea/1,4Di-tert-butylbenzene-du (TU/DTBB-dS2).*H phase change in TU/DTBB may result in a situation where the NMR Spectra. The 2H spectra of TU/DTBB-& for temperatures three positions of the phenyl ring are in equivalent, requiring a between 171.8 and 109.2 K are shown in Figure 10. A broader model with pi # p 2 # p 3 .
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 5127
Thiourea/ 1,4-Di-rerr-butylbenzeneInclusion Compound 1000.
h
v)
E
v
100.
+ c
!-
,,I
10.
3.0
6.0
5.0
4.0
8.0
7.0
9.0
1000/T (1/K) Figure 9. Deuterium relaxation time vs 1000/T for TU/DTBB-d,.
50 kHz
H
-
-
J I -220.0
I
I 0.0
I
I 210.0
Fmquency (kHz)
Figure 11. (A) Experimental and (B) simulated ’H NMR line sham for TU/DTBB-& at 77 K.
component, due to the ring deuterons, is superimposed on the narrow rerr-butyl ZHresonance. Above 171.8 K the rerr-butyl-d18 component is typical of that expected for rapid rotation of both methyl and rerr-butyl group. The quadrupolar splitting is about 10 IrHz. As with DTBB-d18,this is less than the expected 14-lrHz splitting. The general features of the spectra, as the temperature is reduced, are similar to those for DTBB-d18. The key to successfully simulating these spectra was the analysis of the spectrum at 77 K (shown in Figure 11). The spectrum at 77 K shows that the rigid lattice limit had not yet bcen achieved and reveals significantly more structure than those between 132.7 and 109.1 K. This spectrum could be reproduced by employing methyl and
9 1OOOF
7
5
13
11
Figure 12. Arrhenius plot of methyl jump rate vs inverse temperature for TUIDTBB-d,. The points were obtained by comparison of the observed and simulated spectra (see Figures 10 and 11).
3.0
Figure 10. Experimental ZHNMR spectra for TUIDTBB-d,. Simulations for TU/DTBBdI, are shown on the right-hand side of the figure. Methyl exchange rates are as follows: 171.8 K, k 4.7 X lo7 s-l; 159.3 K,k = 2.0 X lo75-l; 143.7 K, k 7.0 X 106 8’;132.7 K, k = 2.7 X 106 s-l; 122.4 K, k = 1.01 X 106 5-l; 109.1 K, k = 2.35 X 10’ s-l. The terr-butyl exchange rate, k’,was held at 1 X lo9s-’ (fast exchange limit).
’ I
-
6
4.0
5.0
6.0
1000/T
7.0
8.0
9.0
(I/K)
Figme 13. Deuterium relaxation time vs 1000/T for DTBB-dlB/TU. The solid curve corresponds to the best fit of the high-temperature minimum using eq 12.
rerr-butyl three-site exchange rates of k = 1.0 X lo3 s-l and k’ = 2 X 106 cl,respectively. In addition, the rerr-butyl bond angle was h dto 113O, as it was in the analysis of DTBB-d18. With this information at hand, the spectra in Figure 10 could be reproduced. The value of k’was held at 1 X lo9 s-l (in the fast exchange limit), and the best fit values of k varied from 4.5 X lo7 at 171.8 K to 2.35 X lo5 s-l at 109.1 K. A plot of In k versus 1 / T is shown in Figure 12. The Arrhenius activation parameters are = 3.0 X 10” s-l and E, = 12.7 f 0.2 kJ/mol. Spin-Lorrice Relaxation Times. Spin-lattice relaxation times were measured for temperatures ranging from 118 to 293 K and are shown, as a function of reciprocal temperature, in Figure 13. Two TI minima are observed, the fmt one at 200 K has TI(&) = 6 ms, and the second at about 120 K is less well defined and has Tl(min) m 5 ms. The high-temperature minimum is associated with the reorientation of the methyl groups, and an analpis of the deuterium Tl need only consider the methyl reorientation. For this case 1/Ti
4 7 ~ 7 )
(12)
whereflw,.) is defined in eq 4. The correlation time T componds to methyl rotation and T = 1/3k, where k is the exchange rate between the three methyl deuteron sites. The correlation times are related to the sample temperature through eq 5. A fit of the experimental TI data with eqs 12 and 5 gave ko = 2.43 X 10” s-’ and E, = 12.3 kJ/mol, in agreement with the values obtained from simulations of the deuterium NMR line shapa. Unfortunately, the second minimum was not well enough defined to perform an analysis in which both methyl and rerr-butyl rotations are considered (using q s 8 and 5). Both line-shape simulations
Penner et al.
5128 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
TABLE IV: Activation Parameters, Deuterium NMR Parameters, and Bond Angles for the Host Molecules in Several Thiourea and Urea Inclusion Compounds
ko (s-') 2 x 1014 1.65 x 1014 0.84 x 1014
Ea (kJ/mol) TU" (single crystal) TU' (powder) TUIDTBB' TU/ferrocene'
43 47 46 rigid
uread (powder) U/nonodecane' U/trioxand
rigid 23
2
x 1010
x WZ) 212/207 205 200 204 (289 K) 213 (140 K) 212 208 203
(deg) 180 180 180
9
0.154/0.180 0.13 0.16 0.145 0.155 0.145
B (deg) 62.8 60 60
177
59
'Values are given for inner/outer deuterons. Taken from ref 51. 'This work. 'Rigid lattice line shape observed from 140 to 298 K. Taken from ref 19. "Rigid lattice line shape observed at 298 K. Taken from ref 49. CTaken from ref 49. 'Spectra show evidence of two-site flip from 143 to 294 K.
324.8 K
333.8 K
308.2K
318.2 K
294.2K
303.7 K
295.4 K
276.5 K
-
-250.0
0.0
.250.0
I
250.0 -250.0
I
I
0.0
1
I 250.0
Frequency (kHz) Frequency (kHz1 Figure 14. Deuterium NMR spectra of thiourea-d, obtained with a pulse spacing of 40 ps at several temperatures together with simulations employing a model with 180' jumps of the thiourea molecules about the C=S bond. The truncated central feature is likely due to methanol-d, the solvent of crystallization.
and T,data suggest that the activation energy for tert-butyl group rotation is significantly lower than that for methyl rotation. Thiourea-d (TU-d 4) and Thiourea-d 4/ 1,4-Di-tert -butylbeozew/(TU-dJDTBB). The deuterium NMR spectra of T U 4 and TU-d4/DTBB, together with simulations, are shown in Figures 14 and 15, respectively. These spectra are typical of those previously observed for thiourea-d4, urea-d4,and their clathrates, when the host molecules are performing 180' flips about the C=S or C=O bond; Le., the 2H spectra are a superposition of one N-D which lies parallel to the C=S (angle ct is 180') bond and is unaveraged by rotation and one N-D which is inclined at an angle, 8, of 60' to the flipping axis. The simulated spectra were rather sensitive to the N-D bond angles, and an uncertainty of less than 1' can be associated with angles a and 8. Heaton et al.49have discussed the effect of the I4N2H dipolar interaction on deuterium NMR line shapes; the extent of the dipolar dephasing increases significantly with interpulse spacing, T~ We have performed a full dynamic lineshape analysis of the 2Hspectra at pulse spacings of 40 N,where 14N-2Hdipolar dephasing should not contribute significantly to the line shapes. The simulated spectra for TU-d4
,
0.0
250.0 -250.0
0.0
250.0
Figrtre 15. Deuterium NMR spectra of thiourea-d4/DTBB obtained with a pulse spacing of 40 ps at several temperatures together with simulations. The truncated central feature is likely due to methanol-d, the solvent of crystallization.
and TU-d4/DTBB are shown on the right-hand sides of Figures 14 and 15, respectively. The parameters obtained from the fits, together with the corresponding parameters determined for several other thiourea and urea clathrates, are shown in Table IV. The values of x and q do not change significantly from one system to another. The angles ct and j3 are generally near 180' and 60°, respectively. A striking feature of Table IV is the large variation in dynamics of the thiourea and urea molecules for different systems. For example, whereas inclusion of DTBB in thiourea causes little change in the activation parameters, the thiourea molecules in TU-d4/ferrocene are in the rigid lattice limit from 140 to 286 K.19 Similarly, the thiourea molecules in TU-d4/ adamantane are rigid.50 Acknowledgment. This work was supported by grants from the Natural Science and Engineering Research Council of Canada (NSERC). We thank Prof. K.R. Jeffrey for copious amounts of time on the home-built spectrometer. Supplementary Material Available: Table of anisotropic thermal parameters (1 page); tables of final structure factor amplitudes (4 pages). Ordering information is given on any current masthead page.
References and Notes (1) Spiess, H. W. Adv. Polym. Sci. 1985, 66, 23. (2) Davis, J. H. In Isotopes in the Physical and Biomedical Science; Buncel, E., Jones, J. R.,Eds.; Elsevier Science: Amsterdam, 1991; Vol. 2,
Chapter 2.
J. Phys. Chem. 1992,96, 5129-5133 (3) Griffin R. G. Methods Enzymol. 1981, 72, 108. (4) Ratcliffe, C. I. J . Phys. Chem. 1990, 94, 152. ( 5 ) Wendoloski, J. J.; Gardner, K. H.; Hirschinger, J.; Miura, H.; English, A. D. Science 1990, 247, 431. (6) Gruwel, M. L. H.; Wasylishen, R. E. Z . Naturforsch. 1990,45A, 55. (7) Koerfer, M.; Kind, R.; Fuess, H. Z . Naturforsch. 1989, 44A, 1177. (8) Ikeda, R.; Kubo, A.; McDowell, C. A. J. Phys. Chem. 1989,93,7315. (9) Collins, M. J.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. 1989, 93, 7495. (10) Mack, J. W.; Torchia, D. A. J. Phys. Chem. 1991, 95, 4207. (1 1) Kennedy, M. A,; Vold, R. R.; Vold, R. L. J. Magn. Reson. 1991,91, 301. (12) Roessler, G.; Taupitz, M.; Vieth, H.-M. Ber. Bunsen-Gen. Phys. Chem. 1989, 93, 1241. (13) Roy, A. K.; Inglefield, P. T. In Progress in NMR Spectroscopy; Enesley, J. W., Feeney, J., Sutcliffe, L. H., Eds.;Pergamon Press: New York, 1990; Vol. 22. (14) Meirovitch, E.; Rananavare, S. B.; Freed, J. H. J. Phys. Chem. 1987, 91, 5014. (15) Nishikiori, S.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. 1990, 94, 8098. (16) Heyes, S. J.; Dobson, C. M. Magn. Reson. Chem. 1990, S37. (17) Ok, J. H.; Vold, R. R.; Vold, R. L. J . Phys. Chem. 1989, 93, 7618. (18) Gelerinter, E.; Luz, Z.; Poupko, R.; Zimmermann, H. J . Phys. Chem. 1990. 94. 5391. (19) Lowery, M. D.; Wittebort, R. J.; Sorai, M.;Hendrickson, D. N. J . Am. Chem. Soc. 1990,112,4212. (20) Heyes, S.J.; Clayden, N. J.; Dobson, C. M. J. Phys. Chem. 1991,95, 1547. (21) Cannarozzi, G. M.; Meresi, G. H.; Vold, R. L.; Vold, R. R. J. Phys. Chem. 1991, 95, 1525. (22) Poupko, R.; Furman, E.; Miiller, K.; Luz, Z. J . Phys. Chem. 1991, 95, 407. (23) McDaniel, P. L.; Barbara, T. M.; Jonas, J. J . Phys. Chem. 1988.92, 626. (24) Lifshitz, E.; Vega, S.; Luz, Z.; Francis, A. H.; Zimmermann, H. J . Phys. Chem. Solids 1986,47, 1045. (25) Gelerinter, E.; Luz, Z.; Poupko, R.; Zimmermann, H. J. Phys. Chem. 1990,94,8845. 1261 Pouuko. R.: Luz.. Z.:.Swilbera. N.: Zimmermann. H. J . Am. Chem. . SO;. i h 9 , ili,'6094. (27) Wittebort, R. J.; Olejniczak, E. T.; Griffin, R. G. J . Chem. Phys. 1978,86, 5411. (28) Spiess, H. W. J . Chem. Phys. 1980, 72, 6755. 1291 Torchia. D. A.: Szabo. A. J . Maan. Reson. 1981, 42, 381. (30) Takemoto, K.; Sonoda, N. In Inchsion Compounds; Atwood, J. L., Davies, J. E., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: New York, 1984; Vol. 11, Chapter 2. ~
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(3 1) Inclusion Compounds; Atwwd, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: New York, 1984; Vols. 1-111. (32) Hough, E.; Nicholson, D. G. J . Chem. Soc., Dalton Trans. 1978,15. (33) Greenfield, M. S.;Ronemus, A. D.; Vold, R. L.; Vold, R. R.; Ellis, P. D.; Raidy, T. R. J. Magn. Reson. 1987, 72, 89. (34) Davis, J. H.; Jeffrey, K. R.; Bloom, M.; Valic, M. I.; Higgs, T. P. Chem. Phys. Lett. 1976, 42, 390. (35) Elcombe, M. M.; Taylor, J. C. Acta Crystallogr. 1968, ,424, 410. (36) Gopal, R.; Robertson, B. E.; Rutherford, J. S. Acta Crystallogr. 1989, C45, 257. (37) International Tables for X-ray Crystallography; Kynoch Press: Birmingham, 1974; Vol. IV (present distributor Kluwer Academic Publishers, Dordrecht) . (38) Gabe, E. J.; Le Page, Y.; Charland, J.-P.; Lec, F. L.; White, P. S. J. Appl. Crystallogr. 1989, 22, 384-389. (39) Magdoff, B. S.Acta Crystallogr. 1951, 4, 176. (40) Kravers, M. A.; Antipin, M. Yu.; Struchkov, Yu. T. Cryst. Struct. Commun. 1980,9, 955. (41) (a) Aronson, M.; Bechmann, P.; Ross, B.; Tan, S. L. Chem. Phys. 1981,63, 349. (b) Beckmann, P. A.; Fusco, F. A.; ONeill, A. E. J . Magn, Reson. 1984,59, 63. (c) Beckman, P. Chem. Phys. 1981,63, 359. (42) Bloembergen, N.; Purcell, E. M.; Pound, R. V. Phys. Rev. 1948, 73, 679. (43) Beckman, P. J. Magn. Reson. 1979, 36, 199. (44) Polson, J. M.; Fyfe, J. D. D.; Jeffrey, K. R. J. Chem. Phys. 1991, 94, 3381. (45) (a) Flovenicio, F.; Garcia-Blanco, S.; Smith-Verdier, P. Acta Crystallogr. 1976,832,2480. (b) Iwasaki, F. Acta Crystallogr. 1979,835, 2099. (c) Iwasaki, F. Acta Crystallogr. 1980,836, 1700. (d) Jungk, A. E.; Schmidt, G. M. J. Chem. Ber. 1971, 104, 3289. (e) Griffith, E. A. H.; Chandler, W. D.; Robertson, B. E. Can. J . Chem. 1972, 50, 2972. (f) Huffman, J. C.; Nugent, W. A.; Kochi, J. K. Inorg. Chem. 1990,19,2749. (g) Gabe, E. J.; LePage, Y.;Lee, F. L.; Barclay, L. R. C. Acta Crystallogr. 1981,837, 197. (h) Van Koinigsveld, H. Cryst. Struct. Commun. 1982,11, 1423. (i) Dravers, M. A.; Antipin, M. Yu.; Struchkov, Yu, T. Cryst. Struct. Commun. 1980,9, 951. Q) Kravers, M. A.; Antipin, M. Yu.; Struchkov, Yu.T. Cryst. Struct. Commun. 1979,8, 427. (46) Clement, R.; Clande, R.; Mazieres, C. J . Chem. SOC.,Chem. Commun. 1974,654. (47) Clement, R.; Mazieres, C.; Gourdji, M.; Gaibe, L. J. Chem. Phys. 1977.67. 5381. (48) Zamir, S.:Poupko, R.; Luz, Z.; Alexander, S. J. Chem. Phys. 1991, 94, 5939. (49) Heaton, N. J.; Vold, R. L.; Vold, R. R. J. Am. Chem. Soc. 1989,111, ,*, JL1 I . (501 Wasvlishen. R. E. Private communication. (51) OReilly, D: E.; Peterson, E. M.; El Saffar, Z. M. J . Chem. Phys. 1971,54, 1304. 4
Effects of Molecular Conformation on the Packing Density in the Liquid State. 3. Partial Molar Volume Differences of Cis and Trans Conformers at Infinite Dllution Masaharu Ohba; Fumio Kawaizumi,* and Hiroyasu Nomura* Department of Chemical Engineering, School of Engineering, Nagoya University, Chikusa-ku, Nagoya-shi 464, Japan (Received: December 2, 1991; In Final Form: February 24, 1992)
Starting from the PY-like integral equation of RISM-1 type and using the Kirkwood-Buff theory, we evaluated the differences in the partial molar volumes of solute :V of cis and trans isomers. The system investigated consists of a tetratomic A-B-B-A fused hard sphere and a single hard sphere both of which are considered as solvent or solute. To compare the evaluated values with the actual values, the VTs were determined for cis- and trans-decahydronaphthalenedissolved in such solvents as carbon tetrachloride, hexane, and benzene, etc., as well as for hexane andpdioxane in cis- and trans-decahydronaphthalene. The evaluation and experimental results have agreed in the relation that V;(trans) > V:(cis) and also in the magnitude of their differences. Clear correlation was observed between the isothermal compressibility of the solvent and the quantity :V - V,where Vis the molar volume of solute decahydronaphthalene.
Introduction The repulsive forces reflecting the molecular shape and dimension play an essential role in the determination of density, local structure, and properties of liquids. One of the To whom correspondence should be addressed. t Present address: Kawaijuku Educational Institution.
thesent addrm: Iwtitute for ~ 444 Japan.
~fie= ,,
My&i,i-&o, l ~ obzaki, ~
simplest illustrations of the role played by the molecular shape is seen in the different physical behavior of the cis and trans conformers in their liquid state. In our previous work'**(part 1 and Part 2 of this study, hereafter referred to respectively as I and 11), we used the PY-like integral equation of RISM-13 and investigated the differences in packing density' and thermodynamic properties2 of cis and trans conformers in neat liquid state. There, we conc~usionsfor hydrocarbons and hal obtained ~ the following ~ loalkenes: Between cis and trans conformers not only the dif-
0022-3654/92/2096-5 129$03.00/0 0 1992 American Chemical Society
