NMR observations of molecular motions and Zeeman-quadrupole cross relaxation in 1,2- difluorotetrachloroethane

We report measurements of "F NMR relaxation times Tu Tlf, TID, and T2 in the plastic crystal CFCL2-CFCL2 . From the data near the melting point, we obtain the jump time for translational selfdiffusion. At lower temperatures, we observe on the cold side of the T, and Tif minima an unusual field dependence which is substantially less than the normal field-squared dependence. We also observe a reduction in T\ near 40 MHz due to cross relaxation between the Zeeman levels of the "F spins and quadrupole levels of the 3 5C1 and 3 7C1 spins. We measured the cross relaxation times TIS as a function of field and found good agreement with our theoretical calculation of TIS.

NMR observations of molecular motions and Zeeman-quadrupole cross relaxation in 1,2- difluorotetrachloroethanea) Harold T. Stokes,b) Thomas A. Case, and David C. Ailion Department of Physics, University of Utah, Salt Lake City, Utah 84112 C. H. Wang Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received 6 November 1978) We report measurements of 19F NMR relaxation times ^lp> ^"lD' and T2 in the plastic crystal CFCL2-CFCL2. From the data near the melting point, we obtain the jump time for translational self­diffusion. At lower temperatures, we observe on the cold side of the T, and rlp minima an unusual field dependence which is substantially less than the normal field-squared dependence. We also observe a reduction in T, near 40 MHz due to cross relaxation between the Zeeman levels of the 19F spins and quadrupole levels of the 35C1 and 37C1 spins. We measured the cross relaxation times tis as a function of field and found good agreement with our theoretical calculation of r/s. I. INTRODUCTION Solids composed of molecules of approximate spheri­cal shape often form a plastic crystalline phase (as de­fined by Timmermans1) prior to melting. In such a phase, the molecules sit in a regular lattice, usually cubic, but reorient rapidly in a manner characteristic of a liquid. Thus, a plastic crystal exhibits transla­tional order but orientational disorder. At some lower temperature Tt, the crystal undergoes an order-disorder transition below which the orienta­tion of the molecules becomes ordered. It is possible normally to supercool the plastic crystal below Tt by lowering the temperature rapidly. In a few cases2 where this has been done, a glass phase transition has been observed at a temperature Tt < Tt, below which a glassy crystalline phase (as defined by Adachi et al.3) is formed. Such glassy crystals are in a metastable state in which the rate of molecular reorientation be­comes so small that a transition to the more thermo­dynamically stable ordered crystalline state is not ob­served over the time scale of a given experiment.2 Thus the molecules are "frozen" into a state of orientational disorder. The compound CFC12-CFC12 forms a plastic crystal­line phase below its melting point Tm = 298 °K. The order-disorder phase transition occurs at Tt = 170°K. However, the plastic crystalline phase is so easily su­percooled that the ordered crystalline phase is difficult to achieve.4,5 In the supercooled plastic crystalline phase, a glass phase transition occurs at Tf = 90°K be­low which molecular reorientations are frozen out.4'5 Another relaxation phenomenon was observed in heat capacity measurements4'5 at 130°K and has been a,A preliminary report of the results contained in this paper was presented in September 1978 at the XXth Ampfere Con­gress in Tallinn, USSR and will appear in the proceedings of that conference. wCurrent address: Department of Physics, University of Illinois, Urbana, Illinois 61801. ascribed to the freezing of conversion between the trans and gauche conformers of the molecule. In this paper, we report NMR measurements in CFC12-CFC12 from its melting point Tm down to 77°K. We interpret our results in terms of molecular motions (e.g., translational self-diffusion near Tm and molecu­lar reorientations at lower temperatures). In addition, we observe cross relaxation between the Zeeman ener­gy levels of 19F and the quadrupole levels of 35C1 and 37C1. We compare our data with a theoretical calcula­tion of the cross relaxation time and find good agree­ment. Previous NMR measurements in CFC12-CFC12 have been made by others: namely second moments6,7 and linewidth measurements4 as well as Ti and Tu relaxa­tion times.4 We compare our results with these wher­ever applicable. II. SECOND MOMENT CALCULATION The structure of the CFC12-CFC12 molecules has been determined by electron diffraction8 from which the posi­tion coordinates of the atoms are obtained (see Table I). In the solid phase, these molecules lie in a body-cen- TABLE I. The position coordinates of the atoms in a CFC12- CFC12 molecule for the two isomers. The z axis is chosen along the C-C bond with the origin at the midpoint. Atom trans Position (in A) gauche X y z X y z C 0 0 0.77 0 0 0.77 C 0 0 -0.77 0 0 -0.77 F 1.31 0 1.18 1.31 0 1.18 F -1.31 0 -1.18 0.67 1.12 -1.18 Cl -0.76 1.45 1.43 -0.76 1.45 1.43 Cl -0.76 -1.45 1.43 -0.76 -1.45 1.43 Cl 0.76 1.45 1.43 0.85 -1.39 -1.43 Cl 0.76 -1.45 -1.43 -1.63 0.10 -1.43 J. Chem. Phys. 70(8), 15 Apr. 1979 0021-9606/79/083563-09$01.00 © 1979 American Institute of Physics 3563 3564 Stokes, Case, Ailion, an d Wang: NMR o f 1 ,2 -d iflu o ro te tra ch lo ro e th an e TABLE II. Contributions to the second moment (in G2) of the 19F NMR line shape. Intramolecular F-F F-Cl Intermolecular F-F F-Cl Chemical shift anisotropy Total Isotropic Rotation 0 0 0.134 0.006 0 0.140 Rigid Trans 0.16 0.073 0.32 0.016 0.18 0.75 Lattice Gauche 0.84 0.063 0.32 0.016 0.18 1.44 tered cubic (bcc) lattice with a cell constant a0 = 7.18 ±0.04 A at 15°C as determined by x-ray diffraction.4'5 (The cell constant a0 is defined to be the distance be­tween lattice points along the [100] direction.) In calculating the second moment of the NMR line shape, we consider two cases. The first case is the plastic crystalline phase. In this phase, the molecules reorient very rapidly; hence, the nuclear dipolar spin- spin interaction is averaged over the motion. If we as­sume the reorientations to be isotropic, we find that the intramolecular interactions average to zero. The inter- molecular interactions, on the other hand, average to a value which can be calculated exactly by placing all nu­clear spins at the centers of their respective mole­cules. 9-11 Thus we readily obtain expressions for the second moment of the ,9F line shape due to l-l interac­tions (/ refers to 19F spins), Af,„ = 2x3/(/+l)rJ*VSi , (1) and that due to I-S interactions (S refers to 35C1 or 37C1 spins), Mus = 4/s |S(S + l)y| H2a0iSi. (2) In the above expressions, yr and ys are the gyromagnetic ratios of the I and S spins, respectively; fs is the frac­tional abundance of the Cl isotope under consideration; and Sj is a summation over bcc lattice sites, Si=E (^)6[K3cos%-1)]2. Here rjk is the distance between lattice sites j and k, and 9]k is the angle between rJh and H0, the external dc magnetic field. The factors 2 and 4 in Eqs. (l) and (2), respectively, refer to the number of F and Cl atoms in a molecule. has been calculated to be 5.809 for a powdered sample.12 Evaluation of Eqs. (l) and (2) gives a total second moment M2I= 0.140 G2 as shown in Table n. Now consider the case of a rigid lattice (i.e., all mo­tions are slow compared to the inverse linewidth). The intramolecular contribution is easily calculated from the following expressions for a powder sample: (3) Mm(intra) = 3/(/+ l)y2 K2|r^ , and M2rs (intra) =/s jS(S + l)yi H1 r 0 »*1 (4) (5) nuclei in the molecule. These expressions are evalu­ated and given in Table II. The calculation of the intermolecular contribution presents some problems. The orientations of the mole­cules are disordered, and thus we do not know the rela­tive positions of nuclei. However, if we assume that the molecules are oriented randomly relative to each other (i.e., there are no preferred directions of orien­tation relative to each other), we can calculate the in­termolecular contribution by averaging the second mo­ment of each pair interaction over all possible orienta­tions of the molecules. (Note that this is basically dif­ferent from the previous case of rapid motion where we averaged the interaction rather than the second mo­ment.) Thus, for a powder sample, we have Mu /inter) = 3/(/+ 1 )y}K2 (rf„), and MlIS (inter) =/s | S(S + 1 )y\ K2 \ £ <r$J), (6) (7) where the term rjk in Eq. (4) is the F-F distance and in Eq. (5) the F-Cl distance, summed over the four Cl where the summation in Eq. (6) is over I spins and in Eq. (7) is over S spins. The term (rjjj) is the average of r'jl over all orientations of the two molecules to which spins j and k are attached, (r'jl) can be calculated by an integration over the surfaces of two spheres, St and Sk, generated by rotating the two molecules containing the j and k sites. Thus the radii Rs and Rh of the two spheres are the distances of the j and k sites from the centers of their respective molecules. In the following paper,13 we carried out such an inte­gration and from Eq. (42) of that paper, we obtain -6 r R jk*R j r P*R j = arrr j dP f (8> JRJk.Rj JfRj Evaluating this integral, we have (fe)6)=te)6 [i - +r*)+^ ■ R> ~ ^ + Rf,(R] + Rl-Ri]Rl-R2}Ri)] x[l -2R-jUR] + Rl) + i$(ii2 -i?J)2]'3 . (9) Thus, using Eq. (9) we evaluate Eqs. (6) and (7) and give the results in Table II. One more contribution to the rigid-lattice second mo­ment needs to be considered: that of the chemical shift J. Chem. Phys., Vol. 70, No. 8, 15 April 1979 Stokes, Case, Ailion, and Wang: NMR o f 1 ,2 -d iflu o ro te tra ch lo ro e th an e 3565 FIG. 1. Block diagram of pulse spectrometer. anisotropy. Assuming axial symmetry in the chemical shift a, we write M2l(o) = ±(on-aJ2Hl , (10) where cr,, -has been measured7 in CFC12-CFC12 to be 2.4x io"4. The evaluation of Eq. (10) is given in Table n. Adding together all the contributions, we obtain a total second moment Mit = 0.75 and 1.44 G2 for the trans and gauche isomers, respectively, as shown in Table n. Since the crystal contains a mixture of trans and gauche isomers, the experimental second moment should lie somewhere in between. The values calculated in Table II agree favorably with those calculated by Gutowsky and Takeda,6 Andrew and Tunstall,7 and Kishimoto.4 We differ only in the inter- molecular contribution to the rigid-lattice value, which they only estimated. They then obtained different values for the trans and gauche isomers. Under our assump­tion of random orientation, we see clearly that the value should be independent of isomer, as shown in Table II. III. EXPERIMENTAL PROCEDURES The sample of CFC12-CFC12 was obtained originally from PCR, Inc. It was then purified and transfered to a glass tube where it was sealed under vacuum. (The details of this sample preparation are given in an earlier paper.14) Even though the sample was grown into a single crystal from the melt, it melted and recrystal­lized during the course of the NMR measurements. As a result, most of the data reported here was taken on a polycrystalline sample. However, because of the orien­tational disorder that exists in CFC12-CFC12, anisotropy effects in a single crystal are probably negligible. This is supported by the fact that we observed no anisotropy (to within 10%) in T2I at 116 °K or in Tu at 100 °K in a freshly grown single crystal. All of the NMR data was taken with a standard pulse spectrometer (see Fig. 1), using single-coil probes tuned to 50 n. Some of the 7\ data was taken using a transmission-line probe.15-17 This probe was construct­ed by winding 13 turns of copper ribbon (0. 5 mm wide) on a 12-mm o.d. glass tube (see Fig. 2). This was covered with a layer of insulator (single layer of 0. 5- mil Mylar obtained from a 400-V Mylar capacitor) and then with brass foil which was connected to ground. This arrangement gives the coil a distributed capaci­tance to ground and hence forms a transmission line, Ground 50ft Resistor 50-ft Coxial Cable Glass Tube Brass Foil Mylar FIG. 2. Broadband NMR probe. Copper Ribbon J. Chem. Phys., Vol. 70, No. 8, 15 April 1979 3566 Stokes, Case, Ailion, and Wang: NMR o f 1 ,2 -d iflu o ro te tra ch lo ro e th an e w/27t(MHz) FIG. 3. The VSWR of the broadband NMR probe. which, as we will see, has a characteristic impedance Z0 = 50 O. By terminating the coil with a 50-0 resistor connected to ground, the input impedance Zin of the coil would be close to 50 O over a wide range of frequency. We measured Zln with a vector impedance meter as a function of frequency and expressed the result in terms of the voltage-standing-wave ratio (VSWR) in dB, using VSWR=2°K»g..[■:g:l t;;g;,']. «« where Z0 = 50 O. Since the VSWR in Fig. 3 is small, the input imped­ance of the probe is fairly close to 50 0 over the entire frequency range shown. Using this probe in the pulse FIG. 4. 19F NMR relaxation data. 2 FIG. 5. Tu at 24 MHz. □ First day of measurements; ■ subsequent measurements. 8 9 10 II 12 13 I000/T (°K"') spectrometer, we could easily make NMR measurements over a wide range of frequencies. In particular, we measured the Tl of 19F in CFC12-CFC12 over the range 18-80 MHz. Using wide-band amplifiers, only the quarter-wavelength cables needed to be changed for dif­ferent frequencies. We should note that none of the T1(J or TlD data were taken using this transmission-line probe. IV. RESULTS We measured the spin-lattice relaxation time Tu, the rotating-frame relaxation time Tlp/, the dipolar re­laxation time T1d, and the spin-spin relaxation time Tu of 19F in CFC12-CFC12 over a wide temperature range (see Fig. 4). Kishimoto4 previously measured Ti{ (at cu0//2ff = 6O MHz) and Tur (at HXI= 5. 42 G) over approxi­mately the same temperature range. For the most part, his measurements are consistent with our data but lack some of our detail. However, there are two major dif­ferences: (1) his TUl data for T 5100°K has a much greater slope than ours, and (2) his Tu data (60 MHz) for T Sil30°K falls almost exactly on top of our Tu data for 80 MHz and is thus shifted upward from our expected positions for 60 MHz data. Concerning this last point of disagreement, we observed ourselves a sample-his­tory dependence of Tu in this temperature region. On our first day of measurements, we obtained measure­ments of Tu at 24 MHz, shown in Fig. 5 as open squares. Three days later, we took more measurements and found that Tu was now significantly lower in value. These and all subsequent measurements (even months later) of Xu at 24 MHz are shown in Fig. 5 as filled squares and fall on a straight line. Kishimoto's T(/ (60 MHz) data is consistent with our Tu (24 MHz) data taken the first day. In the following sections, we examine in detail some of the features of our NMR data and discuss its physical significance. A. Second moments We measured T2l of the 19F NMR free induction decay (FID) at 24 MHz as a function of temperature (see Fig. J. Chem. Phys., Vol. 70, No. 8, 15 April 1979 S to k e s, Case, Ailion, and Wang: NMR o f 1 ,2 -d iflu o ro te tra c h lo ro e th a n e 3567 4). At temperatures below about 90 °K, we find T2t = 50 Msec. We observed the shape of the FID to be approxi­mately Gaussian. (This is common for FID's in sol­ids. 18'13) If we assume a Gaussian line shape, then we find Mu=Vy)TlI. (12) Using T2i= 50 Msec, we obtain M2/= 1.26 ±0.08 G2. From Table II we see that this value is consistent with a rigid-lattice second moment arising from a mixture of the two isomers (M2i= 0. 75 and 1. 44 G2 for the trans and gauche isomers, respectively). Note that Gutowsky and Takeda6 measured M2i= 1.4 G2, and Andrew and Tunstall7 measured M2r = 1.3 G2 for this temperature region. (They reported 1,1 G2 which had been corrected for chemical shift anisotropy.) At about T = 100°K, we see from Fig. 4 that T2J in­creases (the line narrows) to a value T2/s 145 Msec. Using Eq. (12), we find that M2I = 0.13 ±0.01 G2. From Table II we see that this value agrees closely with the second moment for isotropic rotation (M2i= 0.140 G2). Thus we conclude that the motion responsible for nar­rowing the line at T= 100 °K is isotropic molecular re­orientation. This is consistent with heat capacity mea­surements4' 5 which indicate a "freezing out" of molecu­lar reorientation at 90 °K. Note that Gutowsky and Takeda6 measured M2/ = 0.18 G2 for this temperature region. At T=:200oK, we see from Fig. 4 another increase in T2/, this time due to translational self-diffusion which we will discuss in the next section. B. Translational self-diffusion In plastic crystals, translational self-diffusion usually becomes a dominant spin-lattice relaxation mechanism near the melting point. Such is also the case in CFC12- CFC12 (see Fig. 4). This occurs in the temperature region of rapid molecular reorientation, where, as dis­cussed in Sec. II, the intramolecular dipolar interac­tions are averaged to zero and the intermolecular inter­actions are averaged to values which one would obtain by placing all spins at the centers of their respective molecules. Thus, in this case, theories for relaxation in monoatomic crystals may be applied. The dominant self-diffusion mechanism in plastic crystals is thought to be motion of vacancy defects.20-22 Accordingly, we will use relaxation theories for vacancy diffusion in a monoatomic bcc lattice of a polycrystalline sample. It is evident from Fig. 4 that all the data is on the low-temperature side of the minima. Thus, we need expressions for relaxation times only in the limit a,o/ri» where ri is the average time between diffu­sion jumps of a molecule. For high-field relaxation, we obtain from the random- walk theory of Wolf23 T\\ = 2xfy4fc2/(/+ l)oj^*aJ6(25.6), (13) T 2\ = 2 x |y4 K2I(I + 1 )T„af (39. 0). (14) Furthermore, T \ \ , = T-2\ , (15) lOOO/TCK'1) FIG. 6. Jump time t„ for translational self-diffusion. in the limit co1/ri« 1, and T;1,=2xfy4tf2/(/+ i)w;Jt;V(i8. 9), (16) in the limit couTi» 1. In the above expressions, u)u = y,HXJ, where Hu is the magnitude of the rf field ap­plied at frequency o>0/. A factor 2 was included in Eqs. (13)-(16) to account for the two fluorine nuclei in each molecule of CFC12-CFC12. The F-Cl dipolar interac­tions are negligible here and are thus neglected. Note that our a0 as defined in this paper is twice the aQ in Ref. 23. For low field relaxation, we obtain from the encounter model24 rii, = T-> (0.822) (17) in the limit Ti» T2i. Using Eqs. (13)-(17) we can calculate t4 from the ex­perimental values of Tu, T2I, and TiD. (We also includ­ed the TUI data of Kishimoto.4) As seen in Fig. 6, over six decades the result exhibits Arrhenius behavior, Tt = t0 exp(EA/kT), (18) where t0 = 2. Ox 10"15 sec and the activation energy EA = 43.0 ±0.3 kJ/mole. From linewidth measurements, Kishimoto4 obtained EA = 44 kJ/mole for self-diffusion. C. Zeeman-quadrupole cross relaxation At low temperatures, we observed in Tu at 40 MHz anomalous behavior (see Fig. 4) which we attribute to cross relaxation between the Zeeman levels of the 19F spins and the quadrupole levels of the 35C1 and 37C1 J. Chem. Phys., Vol. 70, No. 8,15 April 1979 3568 Stokes, Case, Ailion, an d Wang: NMR o f 1 ,2 -d iflu o ro te tra ch lo ro e th an e ojoi/2tt (MHz) FIG. 7. Effect of Zeeman-quadrupole cross relaxation on TtI. spins. This cross relaxation causes a large reduction in the apparent Tu. Similar effects have been observed in a number of experiments.25-31 To investigate this ef­fect further, we measured Tu as a function of co0/ at two different temperatures (see Fig. 7) and observed a brqad minimum in Tu centered at about 40 MHz. As­suming that the quadrupolar Tls is much less than the cross relaxation time tis, we see that the apparent re­duction in TtI is limited by tiS. (Actually, the relaxa­tion time is limited by the sum, Tis + Tis, where Tis is the spin-lattice relaxation time of the chlorines. Nor­mally, for quadrupolar relaxation, Tls is very short and can be neglected compared to tis.) In particular, +T ^(normal), (19) where Tl7(normal) is the "normal" spin-lattice relaxa­tion time shown as the dashed line in Fig. 7. By sub­tracting Tj1/normal) from T\\, we obtain r}'s, which we plot in Fig. 8. Note that r/s is temperature independent as we would expect. Generally, cross relaxation occurs at fields H0 where the Zeeman splitting oj07 of the I spins is equal to the quadrupolar splitting ioQS of the S spins. Of course, the presence of H0 also splits the quadrupole resonance and, in the case of CFC12-CFC12 where the molecules are orientationally disordered, broadens the quadrupole resonance considerably, making it possible to satisfy the cross relaxation condition u>07 = toos over a wide range of co0/. Hence we see a very broad minimum in tis (Fig. 8). We derived a theoretical expression for the cross re­laxation time t/s (see the following paper13). All param­eters in the theory are well-known physical constants except for coQS, the quadrupole splitting of 35C1 and 37C1. Using a pulse NQR spin-echo technique,32 we attempted to find directly the pure quadrupole resonance of 35C1 at 77 °K and thus determine c*>os. We were unable to find this resonance, possibly because of the line broadening due to random orientations of the CFC12-CFC12 mole­cules in the glassy crystalline phase. From NQR mea­surements in other chlorinated ethanes33-35 we find that generally <x>QS/2ir = 40 MHz for 35C1 in these compounds. Using this value (and hence a)os/27r = 31. 5 MHz for 37C1), we calculated tis (see the following paper13) and plotted the result as a solid line in Fig. 8. Considering that there are no adjustable parameters in the theoretical calculation, the agreement with experimental data is ex­cellent. The cross relaxation effect disappears at T > 125°K. In this temperature region, the rate of molecular re­orientation is greater than 40 MHz and the Cl quadrupole splitting is thus motionally narrowed and "smeared" out (see pp. 67-68 in Ref. 36). D. Molecular reorientation At low temperatures (below 200°K for TXI and below 150°K for TlpI and TtD) we find some very unusual re­laxation phenomena (see Fig. 4). Perhaps one of the most striking features present is the reduced field de­pendence on the cold side of the minima. If we plot, for example, lnrlff/ vs Ini/,, at r=83°K (see Fig. 9), we find it falls on a straight line with a slope a = 1. This means that approximately TieI<xHu. Similarly, from a plot of lnT)7 vs lno>07 at T = 100°K (the lower dashed line in Fig. 7), we obtain TtIccH" with as 1.2. Furthermore, the field dependence between the Tu and Tlp/ data also follows an approximate relation TiI/TleI = only with as 1.1. The field dependence of Tu and TUI is thus self-consistent and indicates that both Tir and Tlp/ are probably due to the same relaxa­tion mechanism in this temperature region. This con­clusion is further supported by the fact that the Tlr and (jJ01/2tt (MHz) FIG. 8. The cross relaxation time tis as a function of w0/. J. Chem. Phys., Vol. 70, No. 8, 15 April 1979 Sto k es, Case, Ailion, an d Wang: NMR o f 1,2 -d iflu o ro te tra ch lo ro e th a n e 3569 Tlp/ data have similar slopes: 11.7 and 9. 5 kJ/mole, respectively. The values of Tu and T1(J/ at their minima also follow an unusual field dependence. Plotting in Tu,imln vs lnffl7 (see Fig. 10), we see that with /3=0.83 ±0.05. Also, from the ratio of the Tu values at their minima at 80 and 24 MHz, we find TiIimiaccHl with 0=0.76 ±0.05. Again, the similar field dependence of Tlo/i mi„ and Tu>mln is further evidence of a single relax­ation mechanism for both TJpl and Tu. Another unusual aspect of the relaxation data is the large asymmetry in slopes on the two sides of the Tip minima. The slope on the hot side of the minima (33 kJ/mole) is more than three times the slope on the cold side. It appears that this asymmetry cannot simply be explained just in terms of an additional relaxation mechanism. Now we note that the low-field TUJ minima occur near the onset of motional narrowing at T= 100°K. This sug­gests37 that the same motion which is narrowing the line at 100 °K is also responsible for the TUI relaxation. In Sec. IV A we showed that this motion is indeed molecu­lar reorientation. Thus we conclude that the relaxation mechanism responsible for Tu and TUI in the low tem­perature region is likewise molecular reorientation. This conclusion is in some ways not surprising since one often finds in plastic crystals that molecular reori­entation provides a strong relaxation mechanism at low temperatures. However, one usually also finds that the relaxation data is consistent with a Bloembergen, Pur­cell, and Pound-type theory38 (BPP), i.e.,39 t-• (2<" and tui ~3 y/AAf2" [21+4wj|/rj+21+wirf+rnrfe] ■ (21) HU(G) FIG. 9. TipJ as a function of Hu at 83 °K. The line is a best fit to the data. FIG. 10. T1d/,mln as a function of Hu. The line is a best fit to the data. where rr is the correlation time of the reorientation and AMm is the part of MUl which is modulated by the re­orientation. These expressions have been successfully used in NMR studies of a number of plastic crystals.40-45 Our data follows some of the general aspects of the BPP-type theories given by Eqs. (20) and (21). TXI and TlpI are field independent on the hot side of the minima (ct>o/Tr« 1 and u>l7Tr« 1) and are field dependent on the cold side of the minima (co0/rr» 1 and couTr» 1) with TXI and TUI increasing with increasing field. However, in some ways, our data deviates substantially from this theory. Equations (20) and (21) predict that Tu<x.H\ and TiPloch\j on the cold side of the minima and that Tu,^ Furthermore, they pre­dict that the slopes of each relaxation time are equal in magnitude on both sides of the minimum. As we have already pointed out in this section, our data departs sharply from these predictions of Eqs. (20) and (21). We are not presently able to explain these phenomena theoretically. However we briefly discuss here a cou­ple of possibilities. First of all, consider the possibili­ty that these features arise from the nature of the mo­tion involved in the molecular reorientation process. As an example, Walstedt et al.*6 measured Tt of 23Na in Na0-alumina at 17.2 and 25. 5 MHz. They observed an asymmetry in the slopes on the two sides of the T, min­ima and also observed on the cold side of the minima a field dependence which is substantially less than the BPP-type field-squared dependence. They explained their data in terms of a distribution G{EA) of heights of the barriers to the motion. Assuming that, at each value of Ea, their relaxation follows a BPP-type behav­ior, they obtained (22) Using an appropriate distribution function G(Ea), they were able to make a good fit of Eq. (22) to their data. We would find it much more difficult to fit such a theory to our data, since our unusual field dependence covers a range af over four orders of magnitude in field (fflf = 1.6 G to H0 = 20 kG). (It should be noted that a reduced field dependence of T, has also been observed by others47*48 in some polymers.) J. Chem. Phys., Vol. 70, No. 8, 15 April 1979 3570 Stokes, Case, Ailion, an d Wang: NMR o f 1 ,2 -d iflu o ro te tra ch lo ro e th an e FIG. 11. Correlation time Tr of the molecular reorientation. The dashed line is from Ref. 5. Another approach to the explanation of our data may involve the nature of the interaction itself rather than the motion. For example, each fluorine nucleus in CFC12-CFC12 is in close proximity to two chlorine nu­clei. As we commented in the previous section, the Cl quadrupolar relaxation time Tls is normally very short. The modulation of S due to Tls processes can cause /-spin relaxation via the I-S dipolar interaction. Such an indirect relaxation process has been called "dipolar relaxation of the second kind"49 and has been observed in a number of cases.49"54 A field-squared dependence typically has been observed49-52 for this kind of relaxa­tion. However, these observations have been made in systems undergoing motional narrowing. In our case of "slow" motion where Tls s rr (see Ref. 55), it may be possible to obtain a different result which could produce some unusual features in TipI and Tl7, such as the ones that we have observed. Even though we do not have a theory to explain our data, we can still learn something about the general be­havior of the correlation time rr of the molecular reori­entation. First of all, we know that Tr~ T-ii at the onset of motional narrowing. Thus we obtain tt = 50 /xsec at T = 95°K. Second, we know that wlxrrs 1 at the Tlp/ minima and cowrr = 1 at the Tu minima. Hence we ob­tain approximate values of rr at those points. In addi­tion, we measured T2S of the 35C1 NMR FID at 8 MHz near the melting point Tm and obtained T2S = 20 jjsec. Such a short T2S is caused by lifetime broadening due to a strong quadrupolar relaxation in rapidly tumbling molecules. For this case of extreme narrowing, we have56 for S = f, , (23) from which we obtain rr = 2. Ox 10‘12 sec. We plot these values of rr obtained from T2l, the Tip[, and Tu minima, and T2s in Fig. 11. Satija and Wang14 also obtained val­ues of rr from depolarized Rayleigh scattering data over the range T = 265 to 297°K. Their results are shown as a dashed line in Fig. 11 and are seen to be in fair agree­ment with our T2S result. We now have in Fig. 11 the general behavior of rr over a wide range of temperature. As we can see, the activation energy EA is not constant but seems to in­crease with decreasing temperature. Near the melting point, light scattering data14 gives EA = 7.3 ±0. 5 kJ/ mole. At low temperatures, we can see from Fig. 11 that Ea = 35 kJ/mole. Note that we could not obtain EA directly from the slopes of the Tu and Tlfl data without knowing their r dependences. For example,57 any rela­tionship of the type Tuccrvr would give us a straight line on a plot of lnTj, vs T"1 (as we observed) but with a slope i>Ea. Without a theory to explain the data, we do not know the value of v and thus cannot determine EA from the slope of the TXI data. Note that there seems to be a sudden change in EA near T = 125°K. This is very close to the temperature where the conversion between the trans and gauche con- formers are frozen out (r = 130°K). Thus these two phenomena may be related. ACKNOWLEDGMENTS We thank Dr. S. K. Satija for his assistance in pre­paring the samples used in this work. We also thank Professor G. A. Williams for generously allowing us the use of some of his facilities. We appreciate the assistance of Professor J. S. 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