J. CHEM. SOC. FARADAY TRANS., 1993, 89(20), 3801-3804 Proton Spin Relaxation, Internal Motion and Structure 1,2,4,5=TetraisopropyI benzene Hania A. Al-Hallaq and Peter A. Beckmann* Department of Physics, Bryn Ma wr College,Bryn Mawr, PA 19010-2899, USA The temperature dependence of the solid-state proton Zeeman relaxation rate in polycrystalline 1,2,4,5tetra- isopropylbenzene has been measured at Larmor frequencies of 8.5 and 53 MHz. The isopropyl groups are immobile on the NMR timescale. The data are interpreted with a very small distribution of barriers for all eight methyl groups and this is consistent with a molecular geometry which has the isopropyl lone protons in neigh-bouring pairs, facing each other in the plane of the aromatic ring. It was also possible to interpret the data with a two-site model consistent with the much less sterically hindered arrangement whereby the isopropyl group lone protons are rotated by ca.45" in opposite directions out of the plane of the ring. These matters are discussed and the models are compared with results from other spectroscopic measurements. This and other isopropyl systems are compared with related ethyl and tert-butyl systems. Also, the observation of non-exponential nuclear spin relaxation is discussed. Proton spin relaxation is a good technique for investigating local interactions in molecule solids.' In this study, we inves- tigate internal motion and molecular structure in poly-crystalline 1,2,4,5-tetraisopropylbenzene (1,2,4,5-TIB). In previous papers, polycrystalline 1,4-diisopropylbenzene (1,4- DIB) and 1,3,5-triisopropylbenzene (1,3,5-TIB) were ~tudied.~.~In these two molecules, the isopropyl groups have proton neighbours on the aromatic ring and the measured barriers for methyl reorientation in the solid state were in the range 13-15 kJ mol-'.Methyl reorientation in solid ethyl- benzenes is characterized by similar barrier^.^ In these ethyl- and isopropyl-substituted benzenes, the barrier for methyl reorientation is dominated by the intraalkyl electronic barrier, corresponding to ca. 4 kJ mol-' per bond overlap (as in ethane'). This suggests that the methyl groups are well away from the aromatic plane and that intermolecular inter- actions in the solid state contribute no more than a few kJ mol-'.This same barrier is found for the out-of-plane methyl groups in many tert-b~tylbenzenes.~" 1,2,4,5-TIB has two pairs of neighbouring isopropyl groups with each pair separated by a ring proton. Compared with 1,4-DIB and 1,3, 5-TIB, 1,2,4,5-TIB provides a more crowded intramolecular environment for the isopropyl groups and their constituent methyl groups. Experimental We have measured the temperature dependence of the Zeeman proton spin-lattice relaxation rate R at Larmor fre- quencies o/2n of 8.5 and 53 MHz in polycrystalline 1,2,4,5- TIB as shown in Fig. 1. Standard pulse techniquesa*' and thermometry4 were used. 1,2,4,5-TIB was obtained from Aldrich; the quoted purity was 96% and the sample was a solid at room temperature. Two samples were sealed in a vacuum after several melt-freeze-pump cycles, but one with several more cycles than the other.The two samples were indistinguishable in terms of their R us. T properties. The perturbed nuclear magnetization relaxed exponentially below 175 K (lo3 T-' = 5.7 K-') and as such R is uniquely defined at lower temperatures. The free-induction decay was characterized by a T, of ca. 10 ps, indicating rapid spin diffu- sion. In this range, the uncertainty in R is ca. +3% except at the lowest temperatures at 8.5 MHz where R becomes pro- gressively smaller and the fractional uncertainty becomes progressively greater. The lowest-temperature data point at 8.5 MHz has the largest uncertainty (ca. +25%).This was not a problem at 53 MHz where the signal-to-noise ratio is considerably greater. For all but the three lowest-temperature 8.5 MHz data points in the temperature range below 175 K, the scatter in R us. T-', which is in the range 2-8%, is a good indicator of the uncertainty. Above 175 K, non-exponential relaxation was observed and became more pronounced as the temperature increased. In the range 175 < T/K < 230, the non-exponential relax- ation was characterized by a well defined initial exponential decay and this is the value shown by the data points in Fig. 1. The uncertainty in these R values is ca. & 10% because of the limited initial decay time duration over which R was com- puted. Again, the scatter is a good measure of the uncer- tainties.The nature of the relaxation process changed at the very highest temperatures and by 250 K (lo3 T-' = 4 K-') there is a less well defined initial slope. Very careful measurements at the highest temperatures at 53 MHz where the signal-to- noise ratio is considerably better than at 8.5 MHz, showed that a sum of two exponentials fits the relaxation data very well. For example, -in one experiment at 244 K (lo3 TIK 250 200 150 300 100 10 30 .-40 v)I '22e E Q L-10 100 3 400 1 1000 4 5 6 7 8 9 10 lo3 KIT Fig. 1 Proton spin-lattice relaxation rate R us. temperature T in solid 1,2,4,5-tetraisopropylbenzeneat 8.5 (A) and 53 MHz (m). The solid line corresponds to theoretical models as discussed in the text.T-' = 4.10 K-'), the long-time behaviour of the magne- tisation is very well characterized by an R value of 3.0 & 0.1 s-'. Subtracting this recovery from the short-time recovery gave a decay very well characterized by an R value of 12 f1 s -Three high-temperature experiments were analysed in this fashion but the two relaxation rates in each case are not presented in Fig. 1. Rather, for consistency with the rest of the data presented in Fig. 1, these three experiments are rep- resented by an R value that characterizes the initial decay as well as possible. They have a significant uncertainty since this initial decay is not exponential. Note that the tem-peratures here are well below the melting point of 392 K ( lo3 T-' = 2.55 K-').Theoretical Models Origins of the Non-exponential Relaxation We will present two dynamical models for the observed R us. T behaviour in 1,2,4,5-TIB. Since these models assume expo- nential relaxation, a comment is in order concerning the observation of non-exponential relaxation at higher tem-peratures. In the middle-temperature region, the non-exponential relaxation most likely originates from the correlated motions of the three proton-proton vectors in the methyl groups. This is very common in methyl systems and has been adequately discussed in the literature."-14 In this case, the initial decay of the nuclear magnetisation, whose characteristic R values are presented in Fig. 1, is the appro- priate one to use if the effects of correlated motions are to be excluded. The effect of the correlated motions is to retard the relaxation at long times.The non-exponential relaxation observed at the highest temperatures probably has a different origin. It probably results from the additional motion brought about by the onset of some form of premelting.'5,'6 The observation of two well defined relaxation rates suggests either two motions or two distinct parts of the sample. There was no liquid line component to the NMR free-induction decay as there was in 1,4-DIB2*3 and the situation is more analogous to the situ- ation in 1,3,5-TIB2 in that as temperature increases (at least one of) the observed relaxation rates is significantly greater than that predicted by fits to the whole R us.T curve based on methyl reorientation only. The most likely candidate for an extra motion is whole-molecule rotation about an axis perpendicular to the ring. This motion is well documented in solid and 1,2,4,5-TIB has a molecular shape which could permit this motion. If there were appreciable translational diffusion, a liquid-like NMR line would have been observed. We will fit the data in Fig. 1 assuming only internal motion is occurring on the NMR timescale. Methyl and Isopropyl Reorientation Models We fit the relaxation data to a model whereby only the eight methyl groups are reorienting. We are able to rule out models which assume either isopropyl group or whole-molecule reorientation. Adding either of the latter two motions would result in a predicted relaxation rate which is about twice the observed rate.We have presented a detailed discussion of this matter for proton spin relaxation in ethyl- benzenes4 On the basis of equivalent calculations for isopro- pyl groups, we are able to conclude that only the methyl groups are reorienting in 1,2,4,5-TIB. Also, all eight of them are reorienting. Finally, the observed barriers presented below show that the isopropyl groups must be oriented such that the constituent methyl groups are free from significant steric interactions with (1) the ring, (2) the neighbouring iso- propyl group and (3) atoms on neighbouring molecules. J. CHEM. SOC. FARADAY TRANS., 1993, VOL. 89 Mathematical Models The proton spin-lattice relaxation rate is given by4 R = A[J(o,z) + 4J(20, z)] with the theoretical value of A,called A,given by4 A=--( n-9 fi)-y4A2 40 N 4n r6 The proton-proton separation in a methyl group is r, po is the permeability of free space and y is the proton magneto- gyric ratio.The number of protons in methyl groups involved in the motion is n and the number of protons in the molecule in N. The parameter A = (n/N)3.80 x lo9 sF2. For an ensem- ble of methyl groups characterized by a correlation time 2,' LLJ(0, z) = -(3)1 + W2T2 with 7 related to the temperature by z = z, exp(E/kT) (4) where E is the barrier and z, is the pre-exponential factor. For a single term using eqn. (1)-(4), there are, at most, three adjustable parameters; E,z, and A.If there are enough different barriers, then it is more conve- nient, and involves fewer adjustable parameters, to assume a distribution of barriers. A particularly useful phenomenologi- cal spectral density is given by 2 sin[& arctan(oz)] (5)J(0, z) = -0 (1 + 02z2)E'2 which is discussed in detail elsewhere.' The additional parameter is E, where 0 < E < 1 characterizes the distribution of barriers (or correlation times). As E + 1, the spectral density in eqn. (5)reduces to that given by eqn. (3).l TekelyI6 has suggested that a distribution of correlation times might be due to the presence of more mobile spins at the sites of crystal imperfections. The molecules on crystallite surfaces could provide such an environment where the inter- molecular contribution to the barrier is slightly smaller than in the perfect-crystal environment.This is reasonable, but the breadth of the distribution observed in the present experi- ment (when the distributed z model discussed above is used) is so very small that many physical models could be invoked. Experiments such as those reported here cannot be used to distinguish between these models. Data Analysis and Interpretation Fits of the In R us. T-' Data We present two equally valid fits of the R us. T data in Fig. 1. A single term for R using eqn. (1)-(4) does not fit the data at all; it will not even fit the data at one frequency. A single-term fit using eqn. (1)-(3) and (5) is shown by the solid lines in Fig. 1.The parameters are E = 13.3 kJ-mol-', z, = 3.1 x s, E = 0.90 and A/A= 1.0, where A is given by eqn. (2) with n = 8 methyl groups x3 protons per methyl group = 24 methyl protons and N = 30 total protons. The uncertainties are ca. f15% for E and A, ca. f20% for E and ca. +25% for z,. This value of E = 0.90 suggests an extremely small distribution of barriers E, so small that for all intents and purposes, the value of 13.3 kJ mol-' may be con- sidered as unique. The distribution for E = 0.85 is presented J. CHEM. SOC. FARADAY TRANS., 1993, VOL. 89 el~ewhere.~The fact that a spectral density characterized by an extremely narrow distribution of z values is successful, whereas a single z spectral density is unsuccessful is testament to the extreme sensitivity of the experimental technique.The other fit assumes two chemically inequivalent sets of methyl groups. Rapid spin diffusion then results in the obser- vation of a single relaxation rate having two terms each given by eqn. (1) and (3), each with their own value of z. We take A, = A, = A with n = 12 (instead of 24 when there is a single term) and N = 30 as before. The fit is statistically indistin- guishable from the preceding fit and is visually identical to that shown in Fig. 1 given the thickness of the solid line. The fitted parameters are El = 14.8 kJ mol-', 7,' = 1.4 x s, E, = 12.2 kJ mol-' andz,, = 4.1 x s. The uncer- tainties are ca. +5%2,' and +25% for E,andElfor and Molecular Geometry and Methyl-group Reorientation Seeman et ~1.~'discussed three orientations of an isopropyl group which they call planar, perpendicular and gauche, based on the orientation of the isopropyl group with respect to the aromatic plane.In the planar arrangement, the two methyl groups are on opposite sides of the aromatic plane with the lone proton in the plane adjacent to a ring proton. We call this + = 0 for the orientation of the isopropyl group. In the perpendicular arrangement, + = 90"; the lone proton lies 90" from the plane of the aromatic ring on one side and the two methyl groups lie 30" from the plane on the other side. In the gauche arrangement, 0 < +/degrees < 90. All three of these arrangements are sterically reasonable for a single isopropyl group such as that found in isopro-pylbenzene (IB).On the basis of their molecular jet laser spec- troscopy experiments, Seeman et al. conclude that the planar zm2.The values of z, in both these fits are in the range of values expected for methyl group reorientation. They can be compared with simple theories for tm21 and they are all arrangement occurs in IB. In 1,2,4,5-TIB, however, the neigh- bouring pairs of isopropyl groups provide quite a different within a factor of three or so. We emphasize that all these fits use only the more exten- intramolecular environment than realized by the lone isopro- pyl group in IB or the pair of isopropyl groups in 1,CDIB. Asive a/(2n) = 8.5 MHz data. The data at 53 MHz are predic- tions and can be used to reinforce the fit but it can also be planar arrangement in 1,2,4,5-TIB where the lone protons of the isopropyl groups face each other (i.e.+ = 0 for one iso- used to rule out many forms of spectral densities; namely propyl group and 4 = 180" for the other) is consistent with those that do not predict that R is independent of o at high our single-barrier fit, but the two lone protons are very close and this geometry seems highly unlikely. A planar arrange- temperatures and those that do not predict the R(o)depen-dence at low temperatures.' Alkyl Group Reorientation We can use these experiments to gain some insight into the molecular geometry of 1,2,4,5-TIB. The role of the solid state ment where the two isopropyl groups have identical orienta- tions with respect to the aromatic ring (both 0") is inconsistent with either of our fits since in this case the two methyl groups in one isopropyl group facing the lone proton in the neighbouring isopropyl group would have a much higher rotational barrier than we observe.A staggered per- pendicular arrangement (+ = 90" for one isopropyl group and +is first of all to make the centres of mass of the molecules = 270" for the other) is also in compatible with our immobile on the NMR timescale. We have shown above that the isopropyl groups are also immobile. This is consistent with the crowded intramolecular geometry (i.e. adjacent pairs of isopropyl groups), but we note that this same result is data since in this case the barrier to methyl reorientation would again be very much higher than observed.However, if neighbouring isopropyl groups in a 0", 180" planar arrange- ment are rotated in the same rotational sense by ca. 45" to bring the lone protons out of the plane of the ring on opposite sides, steric interactions between the two isopropyl found when isopropyl groups have only proton neighbours on the ring as in 1,4-DIB., This same situation is realized for ethyl groups in several polycrystalline ethyl benzene^.^ Whereas tert-butyl groups in closely related tert-lone protons are reduced very significantly. At the same time, the rotation is not large enough to bring one of the two butylbenzenes do reorient in the solid state at rates compara- methyl groups in each isopropyl group close enough to the tble with their constituent out-of-plane methyl gro~p,~*~~-'~ ring to result in a significant steric effect.A space-fillingethyl and isopropyl groups have a lower symmetry than tert- model suggests that the neighbouring isopropyl groups could librate as much as f15", but this motion would likely occur butyl groups. During crystallization, neighbouring molecules can approach the molecule nearer at the alkyl, non-methyl too quickly on the NMR timescale to have an observable effect on the Zeeman relaxation rates. proton position(s) than they can at the methyl position(s). Alkyl-group reorientation for ethyl and isopropyl groups could then be strongly hindered in the solid state compared with the gas phase.The tert-butyl groups, on the other hand, have three-fold symmetry and even though they are larger, they require no additional space in the crystal to reorient. Based on experiments in tert-butyl systems, we can conclude that in order to appear motionless on the NMR timescale in these relaxation experiments, the barrier for isopropyl group reorientation in 1,2,4,5-TIB, 1,4-DIB2 and 1,3,5-TIB' is greater than ca. 50 kJ mol-'. This value can be compared with a value of 1.0 f0.6 kJ mol-' obtained from gas-phase low-resolution microwave spectroscopy experiments in 33- dibromoisopropylbenzene.26It can also be compared with the values of 8.2 f0.8 kJ mol-' in i~opropylbenzene~~ and 21 7 kJ mol-' in 2,6-difl~oroisopropylbenzene,~~both obtained from liquid-state NMR studies of J splittings.All these values seem quite reasonable and completely consistent. t The factor a, should be inserted inside the summation in eqn. (5) in ref. 24. This gauche geometry suggests that each isopropyl group does indeed contain two slightly inequivalent methyl groups, as suggested by our second fit since one methyl group will be closer to the ring. Presumably, the 14.8 kJ mol-' methyl group has a few kJ mol-' of this barrier coming from steric interactions with a ring proton. Of course, we can only say that this interpretation is consistent with this particular fit of the data. When neighbouring molecules are considered, one can imagine many geometric models which give rise to two sets of dynamically inequivalent methyl groups.In particular, we cannot rule out models that suggest that the crystal structure makes the two sides of the molecule inequivalent with the four methyls in one adjacent pair of isopropyl groups having a greater barrier than the eight methyl groups on the other side of the molecule. The crystal structure of 1,2,4,5-TIB is unknown. Summary We have investigated the temperature and Larmor frequency dependence of the proton spin-lattice relaxation rate in 1,2,4, 3804 5-tetraisopropylbenzene.Only the methyl groups are reo-rienting. However, all eight methyl groups are reorienting. The barriers for methyl reorientation are in the range of those found in a wide variety of alkyl-substituted planar aro- matic molecules when the methyl group is well away from the aromatic plane.The rotational barrier is dominated by the intraalkyl electronic barrier of ca. 12-15 kJ mol-' with a contribution of perhaps a few kJ mol- from other intramol- ecular and intermolecular steric sources. Thus, there are no strong intramolecular or intermolecular steric contributions to the barrier. One model proposed here suggests a very narrow distribution of barriers and another suggests two unique, but not very different, barriers. The two-site model is particularly inviting in that a likely geometry for the mol- ecule is such that in order for the lone protons to sit slightly out of the plane, one methyl group will be slightly closer to the plane than the other.No other geometry seems to lead to a situation free of a large intramolecular (steric) component to the barrier. References 1 P. 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