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Anisotropic molecular reorientations of quinuclidine in its plastic solid phase : 1H and 14N NMR relaxation
study
C. Brot, J. Virlet
To cite this version:
C. Brot, J. Virlet. Anisotropic molecular reorientations of quinuclidine in its plastic solid phase : 1H and 14N NMR relaxation study. Journal de Physique, 1979, 40 (6), pp.573-580.
�10.1051/jphys:01979004006057300�. �jpa-00209141�
Anisotropic molecular reorientations of quinuclidine
in its plastic solid phase :
1H and 14N NMR relaxation study
C. Brot
Laboratoire de Physique de la Matière Condensée, Parc Valrose, 06304 Nice Cedex, France
and J. Virlet
Service de Chimie Physique, Division de Chimie,
Centre d’Etudes Nucléaires de Saclay, B.P. 2, 91190 Gif sur Yvette, France
(Reçu le 27 octobre 1978, accepté le 22 février 1979)
Résumé. 2014 Dans la phase solide plastique de la quinuclidine, la mesure des temps de relaxation en RMN de 14N et de 1H a permis de montrer que les réorientations n’étaient certainement pas isotropes. A partir des résul-
tats de RMN, on a calculé les temps de corrélation pour plusieurs modèles de mouvements anisotropes. Le meil-
leur accord avec les valeurs déduites des mesures de diffusion des neutrons (article précédent), utilisant les mêmes modèles, est obtenu pour le modèle où les molécules se réorientent par sauts de ± 90° autour des axes C4 du
cristal avec un temps de résidence de (22,2 ± 2). 10-12 s, et par sauts de ± 120° autour de l’axe moléculaire
C3 avec un temps de résidence de (5,25 ± 2,8). 10-12 s, à température ordinaire. L’enthalpie d’activation est de 15,3 kJ/mole pour les sauts de ± 90°, un peu plus élevée pour les sauts de ± 120°. Les temps de corrélation de translation ont aussi été mesurés à haute température.
Abstract. 2014 14N and 1H NMR relaxation times have been measured in quinuclidine in its plastic phase. These
measurements rule out isotropic motion. Correlation times for several anisotropic reorientational models are
calculated from these NMR data. The best agreement with the values calculated from neutron scattering experi-
ments (preceding paper) is obtained for a model where the molecules reorient by ± 90° jumps about the crys-
tallographic C4 axes with a residence time of (22.2 ± 2).10-12 s, and by ± 120° jumps about the molecular C3
axes with a residence time of (5.25 ± 2.8).10-12 s, at room temperature. The activation enthalpy is 15.3 kJ. mol.-1 for the ± 90° jumps, and higher for the ± 120° jumps. Translational correlation times have also been measured at high temperature, below the melting point.
Classification
Physics Abstracts
76.60
1. Introduction. - The determination of molecular reorientation rates in plastic crystals by Nuclear Magnetic Relaxation measurements has a long history [1-3]. These studies have however been limited in the
following senses :
i) Correlation times were obtained, without much definition about which quantity the correlation times
were related to. Alternatively, the results were often presented under the form of a rotational diffusion,
constant, despite the fact that this notion has a mean-
ing only in the case of a mechanism of dif’usive rota- tion (by infinitesimal angular steps). In that case, the
Hubbard relations [4] relating the decay times of the
spherical harmonics of successive order are fulfilled.
But in crystals, or even in plastic phases diffusive
rotation is probably exceptional, so that such lan- guage is likely to be misleading.
ii) When the molecule is a spherical top and the crystal has cubic symmetry (e.g. plastic adamantane) the rotations or reorientations evidently have iso- tropic (endospherical) probabilities. However, in globular molecules forming plastic crystals but without
having Td or Oh symmetry, anisotropic angular
motion is likely. It is then necessary to measure the relaxation rates of nuclei at différent sites in the molecular frame, to get the two (or three) rates des- cribing the motion. This kind of study has become commonplace in recent work on molecular liquids, but up to now has not, to our knowledge, been attempt-
ed for plastic crystals.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004006057300
574
In this paper we present measurements of 1 H and 14N nuclear magnetic relaxation times and an analysis
of the reorientational motion of the symmetric top molecule quinuclidine HC(CH2CH2)3N, in the plastic phase. We have taken advantage for the interpretation,
of the recent X-ray determination of the allowed
positions of the molecule in the crystal cell (preceding
paper, p. 557) [5]. This X-ray study showed that the
reorientational motion occurs by angular jumps
rather than by diffusive rotation. The NMR measure-
ments reported here show that this motion is aniso-
tropic. These results will be compared with those of
an neutron scattering study (preceding paper, p. 563) [20]. The translational diffusion rates were also obtain- ed at higher temperature, below the melting point.
2. Expérimental procédure and new data. - Qui-
nuclidine was prepared from its hydrochloride deri-
vative bought from Fluka. It was purified by double
sublimation under vacuum. Amounts of 3 to 5 g were transferred under vacuum into measuring tubes which
were then sealed.
14N NMR measurements were made at 4.35 MHz
on 14 mm o.d. samples, using a home built NMR spectrometer with an extemal 2D field-frequency lock.
Signal averaging was performed with a « 1070 »
Nicolet Signal Averager.
The transverse relaxation rate T2 of 14N was
measured directly on the accumulated free induction
decay, recorded about 10 to 100 kHz off-resonance.
Care was taken to reduce the decay time and parasitic
mechanical oscillations which follow the radio fre- quency pulse. The z/2 pulse duration was 21 gs.
The longitudinal and transverse relaxation times
Tl and T2 of 1 H were measured at 6.23 MHz by the
usual pulse sequences (n/2, L, n/2) and (rc/2, r, n) for
six temperatures from 75,DC to 122 OC. Measurements at higher temperature were precluded by the occur-
rence of a darkening of the sample which began at
about 120 OC and cannot be avoided by careful puri-
fication of the sample and sealing it under vacuum.
For lower temperature, we use the values of Tl already
measured [6].
3. Translational diffusion. - The line narrowing (or T2 lengthening) observed for 1H above 75 OC
(Fig. 1) gives unambiguous evidence for translational motion of the molecules.
The NMR relaxation data can be interpreted using Torrey’s calculation [7] for the spectral density of a
diffusive motion : in his calculation Torrey assumes jumps of definite length 1 but of any direction ; this is a good approximation for diffusion by jumps to
the 12 neighbouring sites in a f.c.c. cubic crystal, especially if, as here, an average has to be taken after- wards over all the orientations of crystallites in a powder sample.
As Tl is much longer than T2, the motion is slow
Fig. 1. -1H longitudinal (0) and transverse (0) relaxation times measured in quinuclidine. The full line indicates previous measu-
rements [6].
(co,r » 1) ; in this limit, the relaxation times Tl and T2 are given by :
where r is the jump time, co, the Larmor frequency
and the constant C is given by :
with k = 0.742 80 for a f.c.c. lattice ; a = 8.91 Â is the lattice cell constant of quinuclidine [5] ; 1 = a/
is the jump length ; n = 4 is the number of molecules per lattice cell and c, the number of protons spins
per molecule, is 13 ; as usual, we consider the c protons of the rapidly reorienting molecule to be at the centre
of mass of the molecule.
Using the expression (1) for the transverse relaxa- tion time T2, one gets the values of the translational correlation time which are given on figure 3. The
activation enthalpy is 73.5 kJ.mol.-’.K-’, and the
value of r extrapolated to the melting point is
r =8.2 x 10-7 s, of the same magnitude (~5 x 10-’ s)
as that reported for other f.c.c. plastic crystals [8-11].
From these values of r, the contribution of the trans-
lational motion to the longitudinal relaxation rate
Tf1, is easily calculated using (1). Then, by différence,
the rotational contribution may be written :
and is plotted on figure 1. The agreement with the
previously measured values for Tl at lower tempe-
ratures [6] is excellent.
4. Angular motions. Qualitative conclusions. - From the slope of the 1 H log TI-l 1 vs. T-l plot, it
is evident that, as already shown in the preceding study of 1 H relaxation [24, 6], the reorientational motion of quinuclidine in its plastic phase is fast and, therefore, the NMR condition of extreme narrowing is fulfilled.
The measured linewidth of the 14N NMR is much
higher than it would be if it were due to the dipolar interactions and is therefore due to the quadrupole
relaxation. Indeed the contribution due to the static intermolecular dipolar interaction with the proton is for l4N, lower by the factor (2/3) (YN/y.J than the proton linewidth ; it is further reduced by the flip-flop
motion of protons [12, 13]. The residual 14N line- width can easily be calculated using the calculation of Merhing and Sinning for adamantane [14] as qui-
nuclidine has the same f.c.c. structure in its plastic phase. It is found that the dipole interaction with the protons leads to a quasi-Lorentzian line whose width
is b = 1/nT2 with T2 = 7.8 ms. At high temperature the translational motion will further narrow the 14N line. In this case the dipolar contribution to the transverse relaxation time can be easily calculated
from that of protons and is given in the slow motion range (coH, WN 1/LTRANS) by
Fig. 2. -14N transverse relaxation time T2Q in quinuclidine.
Also indicated is the calculated proton-nitrogen dipolar contri- bution to the linewidth calculated as explained in the text.
The calculated dipolar contribution (without and
with diffusive motion) to the linewidth of 14N is plotted in figure 2. It is always smaller by a factor of
20 than that measured and therefore can be neglected
in the interpretation of the results.
The experimental transverse relaxation of the 14N is thus due to the quadrupolar relaxation induced by
the random reorientations of the molecule. If we assume a single correlation time for the molecule, thus considered as a spherical top, we have for 14N (S = 1 ) :
In the quinuclidine molecule, the quadrupole
interaction is axial, with its axis lying on the C3
molecular axis and therefore r, is the reorientation time of the molecular axis. For the value of the qua-
drupolar coupling constant, one can take, in the
absence of a measured value for quinuclidine, the
value obtained in triethylenediamine [15]
another value, measured in the non-bridged molecule triethylamine [15] is 5.02 MHz so that the error on (e2 qqlh) may be estimated to be less than 2 % and
the error on T2,, (or TROT) less than 4 %. This yields
Fig. 3. - Correlation times for diffusion (-..-) and for « C4 » anisotropic reorientation. (0) « C4 » cubic residence time and (p)
« C3 » self-reorientation residence time as defined in the text.
Note different scales for diffusion and reorientations.
576
We consider now, in a first crude approach, the
information which can be drawn from the spin-lattice
relaxation times of the protons. For this the reorien- tational contribution to the proton longitudinal relaxa-
tion has been derived from the experimental values
in section 3. This contribution is due to the random reorientations of the molecules acting on the inter- proton dipolar interactions. It contains an intra- molecular part, which is the larger, and a smaller
intermolecular part.
We will also, here temporarily consider, the mole- cule as a spherical top and will describe its motion
by a single correlation time T,. This amounts to sup-
posing that the reorientations are ruled by a diffusion equation, or if we consider solid definite angle jumps
that we are in the any well jump or with memory loss [3, 8, 16] hypothesis : in this hypothesis, at each jump,
a molecule can go to any one of its allowed positions, losing memory of its initial position. r, must then be
the same as the correlation time for the motion of the direction of the molecular axis as determined by 14N relaxation rate. We assume also, for simplicity,
that the reorientational motions of neighbouring
molecules are uncorrelated and unconcerted [8,17,16]
(wholy independent reorientations) so that the corre-
lation times for a vector joining two protons in diffe-
rent molecules is Te/2-
At this stage we can use the fact that if the correla- tion time is unique, the spin lattice relaxation time
can be related to that part of the second moment which is averaged out by the motion considered. In the case of protons, and for a crystalline powder,
this relation reads :
For the reduction of the intramolecular second mo- ment AM2 INTRA we calculate AM2 INTRA: = 18.24 G 2 ;
from reference [24] the reduction of the intermolecular second moments AHINTER is 5.5 ± 2 G2.
Using the experimental values of Tl measured here and in [1] ] we get r, = 20 x 10-12 1 /Tl ROT. · These
values of Te are too low by more than a factor two
with respect to the values obtained through the
relaxation of l4N. If, instead of independent jumps
for neighbouring molecules we adopt the hypothesis
of concerted or correlated reorientations, then the intermolecular correlation time is r, and we find LC = 17.7 x 10-12 Ti-’ RO T ; LC values are 20 % lower
than in the preceding case so that the agreement would be still worse. We conclude that the hypothesis
of isotropic rotational motion has to be abandoned : therefore, the relaxation of the protons is due at least in part to a fast motion which is without ef’ect on the
quadrupole interaction. As this interaction is axial, about the C3 axis of the molecule, one has thus experi-
mental evidence for an angular motion about the
molecular axis faster than the motion of the axis itself. This conclusion is not too surprising if one
remembers that in the low temperature phase of quinuclidine, where the motion of the molecular axis is blocked, there still exist threefold reorientational
jumps of the molecules about their C3v axes.
5. Angular motion, detailed analysis of the molecular reorientations. - At this stage we know that the
angular motion of the molecules is anisotropic but
this situation can exist both for reorientational jumps
and for continuous diffusive motion. As has been recalled above in the X-Ray study (preceding paper,
p. 557 [5]), it was concluded that the allowed orien- tations of the molecules are finite in number (spheri- cally isotropic probabilities yielded a worse residual factor). Consequently it follows that the angular
reorientations can only take place by short duration
jumps between these discrete allowed orientations.
The latter are related by the symmetry operations of
the cubic cell F432, and are 24 in number (distinguish-
able orientations). The jumps can a priori have diffe- rent probabilities per unit time to occur for the difi’e- rent rotations of this crystallographic group.
Moreover we assume, as suggested in the preceding section, that there exists also a reorientational motion about the molecular C3 axis occurring by 2 n/3 jumps
which bring the molecule into crystallographically
identical positions, but which contribute strongly to
the nuclear relaxation. Except for the nitrogen atom,
the tertiary carbon and its proton, all atoms in the molecule have thus 3 x 24 = 72 possible positions corresponding to 3 x 24 NMR-distinguishable orien-
tations of the molecule.
Group theoretical methods can be used to compute any desired correlation time function [3, 8, 16-19]. It
will be assumed here that all the operations in the
same class s have the same probability per unit time
is 1 of occurring.
We consider first, the simpler case of the motion
of the molecular axis, for which only 24 positions are
allowed. The NMR relaxation of 14N is sensitive
only to this motion. Under reorientation the quadru- pole interaction behaves as second spherical harmo-
nics.
It has been shown [3, 16, 19] that under the opera- tion of the cubic group of rotation, the correlation function of a second order spherical harmonic is for
a powder :
where TF2 and LE are decay times characteristic of the irreducible representations F2 and E of the cubic
group. In terms of the jump probabilities Ls-l for
each operation in class s, one has [3, 16, 17] :
No other mode (irreducible representation) is
involved in NMR. The relative weights of the two
active modes depend on the exact orientation of the
reorienting unit vector (X, Y, Z) in the cell, and are given by [3, 16, 19] :
For the direction joining the centre of mass to the nitrogen atom (molecular C3v axis) one has, from the structural data [5] :
i.e. the molecular axis is only some 10° off the 111 direction, and then
In the extreme narrowing condition one can use
eq. (5) with
At this point we consider two variants of the present jump model, the any-well jump or memory loss model
and the « C4 » model.
In the former model all 24 reorientational jumps including the identity jump to the initial well are
supposed to be equally probable, the molecule losing
memory of its original orientation when being excited
in a rotational jump
Then, all irreducible representations J1 have the
same decay rate
and eq. ,(11) reduces to
At room temperature (25 OC), from eqs. (5), (11)
and figure 2, one has r,, z- 17 ps, hence TAW = 408 ps.
The probability of going in any one of the 24 orien-
tational wells is the same for any jump, and then the
probability of going back to the initial orientation is
dtlLAw where as the probability of going into a diffe-
rent well is 23 dt/rAW - TAW/23 = 17.73 ps may be called the residence time.
This result is in disagreement with the result of the neutron study of the preceding paper which, with the same hypothesis, yields Très = 28.4 ps.
We are consequently led to discard the any well
jump hypothesis. In the same way, C3, C2, C2 models
are discarded which assume that only C3 or C2 or C’2 jumps are allowed.
On the other hand, if we consider the C4 model, assuming that only jumps belonging to the class C4
are allowed, i. e. r2 ’= i 2-1 1 = T31= 0, then combin-
ing eq. (9) with eq. (11) we get
At room temperature this yields :
This value is in perfect agreement with that deduced
for T4 in the same model from the neutron study,
We conclude that this model is very likely to be
realistic.
Note that if NMR measurements allow us to
discard isotropic motion models they alone cannot
enable a choice between the anisotropic motion models ; for this choice one needs extra information
(here from neutron scattering) which used together
with NMR results, allows a more precise description
of the motion.
Since there are 6 equally likely C4 operations, the
mean time between two successive jumps of the class
C4 (résidence time in a well)
at room temperature.
At 100 °C and - 23 OC, one finds respectively
T4 = 38.4 ps and 436 ps ; the activation enthalpy of
this cubic C4 reorientation is 15.3 kJ . mol. -1.
We investigate now the self-reorientation of the molecule. Here we call, self reorientation, the three- fold angular jumps about the molecular axis. Infor- mation about this motion can be extracted from a
detailed analysis of the proton 1 H spin lattice relaxa-
tion.
This relaxation rate has two contributions : the intramolecular one and the intermolecular one.
Consider first the intramolecular contribution to the 1 H NMR relaxation, T;-,’ NTRAI which arises from the proton-proton dipole interaction modulated by
the random reorientations of the molecule among the 72 allowed orientations, induced by the combined
cubic + self-reorientations.
The longitudinal (or Zeeman) relaxation rate of
dipolar origin T1-1Z which we will call shortly dipolar
relaxation rate is given generally by [12, 8] :
where N is the number of spins over which the sum
E is taken
ïj
