Volume 182,number 3,4
CHEMICALPHYSICSLETTERS
2 August 1991
21NeNMR spectroscopy: temperature dependence of the 21Nequadrupole coupling and electric field gradient in a liquid crystal P. Ingman,
J. Jokisaari
I, 0. Pulkkinen
NMR Laboratory and Department oSphysics, University of Oulu, SF-90570 Oulu, Finland
P. Diehl and 0. Muenster Department of Physics, University of Basel, CH-4056 Basel, Switzerland
Received 23 April 1991
The “Ne NMR spectrum of Z’Ne-enrichedneon gas dissolved in the anisotropic phase of the thermotropic liquid crystalZLII 167 was recorded at various temperatures. The curve obtained by plotting the absolute value of the quadrupole coupling constant, 1x1,as a function of temperature is found to possess a maximum in the nematic range. This is considered as an indication of at least two contributions to the total electric field gradient at the nucleus. After the transltion to the smectic A phase, 1x1starts to increase without detectable discontinuity to low temperature. The results are compared to the corresponding ones measured earlier for 83Krand “‘Xe.
1. Introduction It has earlier been found that the *H quadrupole coupling of some deuterated methyl compounds [ l31, of deuterated methanes [4,5] and of the deuterated hydrogen molecule [ 6,7] are dependent upon the liquid-crystal (LC) solvent which is used to orient molecules and to make the quadrupole splitting in the *H NMR spectra (or in the spectra of any other quadrnpolar nuclei) observable. Two reasons for this are given: the correlation of the vibrational and reorientational motions (the so-called deformational contribution) and the external electric field gradient (efg) created by a liquid-crystalline environment. Information about the latter effect can be derived by dissolving quadmpolar noble-gas isotopes in a liquid-crystal solvent; in a liquid-crystalline environment, the NMR spectrum of an isotope with spin I is split into 2lcomponents because of the interaction of the nuclear quadrupole moment with the efg at the nuclear site. To whom correspondence should be addressed.
We were recently successful in recording 131Xeand 83Kr NMR spectra of the natural xenon and krypton gases in Merck ZLI 1167 as well as in a few other liquid crystals [ 8,9 1, These experiments yielded the temperature dependence of the quadrupole coupling constants (qcc) which can be explained only by introducing at least two efg contributions of different origin. One of them is the just-mentioned
external
from the collisions of the atoms with the LC molecules. In order to be able to separate the various contributions, it is helpful and even necessary to use various isotopes as probes and to detect their resonances in single-component and mixed liquid crystals. In particular, the latter ones look promising, since in proper mixtures the external efg can be changed in a controlled manner. The relaxation of the quadrupolar noble-gas isotopes is dominantly caused by the interaction of the nuclear quadrupole moment with a fluctuating efg. According to the origin of the efg, models applied to explain relaxation behaviour are classified as electrostatic (corresponding to the external efg contriefg, whereas the other one arises probably
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bution) and electronic (corresponding to the deformation of the electron cloud because of collisions). The present study on total efgs experienced by “Ne on the one hand, and by 13’Xeand s3Kr on the other [ 8,9], gives hints that a model based on a single contribution exclusively cannot produce satisfactory results. We report here, for the first time, *‘Ne NMR spectra of neon in a liquid crystal. On the whole, the number of papers dealing with “Ne NMR spectroscopy is small; to our knowledge, there exist only two papers, one by Henry and Norberg [lo] on liquid and solid neon, and a very recent one by the present authors on gas-to-solution shifts of neon [ II].
2. Experimental The liquid crystal Merck ZLI 1167 [mixture of 4n-alkyl-trans,trans-bicyclohexyl-4’-carbonitriles] was placed into a heavy-wall NMR tube (outer diameter 10 mm, wall thickness 1.5 mm) and degassed in a vacuum line. *‘Ne-enriched (95 atom percent) neon gas (delivered by Isotec Inc.) was transferred to the sample in a vacuum line so that the final pressure was ~0.5 atm. The *‘Ne NMR spectra were recorded on a Jeol GX400 spectrometer (operating at 31.56 MHz for “Ne) form a nonspinning sample without locking. Depending on temperature, 65000 to 100000 FIDs were accumulated applying the frequency window of 40 kHz and collecting Sk points. In between the approximately 90” observation pulse and the start of the FID acquisition, a dead time of 200 ps was used in order to avoid baseline waving. The final time-domain signal was multiplied by a combination of a trapezoidal and an exponential window function before Fourier transformation.
3. Results and discussion The NMR spectrum of a quadrupolar noble-gas isotope i (spin I,) in a liquid crystal is a multiplet with 21, components. The separation of tow successive peaks, the quadrupole splitting B,, can be represented as 254
2 AugustI99I
CHEMICAL PHYSICSLETTERS
5,=g,y,P,(cosa)
1 1j(21[-I)
’
where P2 (cos a) is the second-order Legendre polynomial with (Ybeing the angle between the magnetic field and the liquid-crystal director, and x, is the nuclear quadrupole coupling constant (qcc) defined as x,= eQ,v;:'lh .
(2)
In eq. (2), Q, is the nuclear quadrupole moment, Vf is the total electric field gradient at the nuclear site in the direction of the LC director, and e and h are the electron charge and Planck constant, respectively. Vr depends upon the degree of order of the liquid crystal and the collision of neon with LC molecules, and, consequently, also upon temperature. Taking into account the induced efg (the external efg induces a quadrupole moment in the electronic distribution of neon which in turn induces an efg at the nucleus), we can write Vj:’ in the form, (3) where yooj is the Sternheimer shielding (or antishielding) factor, V f is the efg produced by the LC molecules, and Vg takes into account the efg due to the deformation of the electron distribution through collisions. The *‘Ne NMR spectrum of neon gas in a liquidcrystalline environment is a 3 :4: 3 triplet, as shown in fig. 1. The absolute value of the “Ne qcc, 1~~~1, determined in ZL11167 liquid crystal, is presented as a function of temperature, T, and reduced temperature, T*= T/T,, (TN, is the nematic-isotropic transition temperature), in fig. 2. Table 1 lists the 1~~~1and efg values, Vr, at various temperatures. The curves in fig. 2 display maxima in the nematic
Volume 182, number 3,4
Table 1 Experimental quadrupole coupling constant, lxNe1,of “Ne, and the total electric field gradient, V;p’, experienced by *‘Ye in the ZLII 167 liquid crystal at various temperatures. Experimental error for the two quantities is estimated to be approximately 0.5%
Iqcc”kHz ‘3.o
7I
T(K)
mc’ 300
1 305
310
1 315
320
’ 325
1
1
330
335
I 340
345
350
355
360
T/K (4 IqccllkHz 13.0,
,o.sC 0.84
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CHEMICAL PHYSICS LETTERS
I
I 0.86
0.88
0.90
0.92
0.94
0.96
0.98
352 348 345 343 340 335 333 330 325 320 317 315 313 311 310 309 307 305 c’ 303
T*
a,
0.989 0.977 0.969 0.963 0.955 0.941 0.935 0.927 0.913 0.899 0.890 0.884 0.879 0.874 0.871 0.868 0.862 0.857 0.851
V$
b’
IXNFI (kHz)
(10’8Vm~‘)
10.94 11.86 12.25 12.38 12.48 12.48 12.42 12.32 12.08 11.a2 11.66 11.58 11.51 1I .48 11.46 11.48 1 I S6 11.74 11.93
3.19 4.11 4.24 4.28 4.32 4.32 4.30 4.26 4.18 4.09 4.04 4.0 1 3.99 3.98 3.96 3.98 4.01 4.06 4.14
1.00
T* (b)
Fig.2. The absolutevalueof the *‘Nequadrupolecouplingconstant, IX+ 1, as a function of (a) absolute and (b) reduced
a) T*= T/T,,, where r,, was measured to be 356 K. b, Calculated from eq. (2). c, Pure ZLIl167 possesses a smectic A-nematic transition at Ts,,=305 K.
temperature.
LC [ 51. Furthermore, the ratio of the qccs of the isotopes i and j should be range, as also do the corresponding curves for 83Kr and 13’Xe in the same LC [9]. The maxima are shifted when the qccs of various isotopes are drawn as a function of T. On the contrary, it is interesting to note that when using reduced temperature, the maxima appear at about the same T*. The shift of the maxima is due to the fact that the pressure of gas varies from one sample to another and, furthermore, the solubility of the three gases is remarkably different and, therefore, i-,, changes. The curve in fig. 2 also shows the effect of the S,-N phase transition on the efg; after the transition, the magnitude of the efg starts to increase with decreasing temperature. The shape of the curve 1x1versus T or T* (in the nematic range) can be explained by introducing two contributions to the total efg: If it were only due to the external efg produced by the liquid-crystal solvent, it should behave as the degree of order of the
(4) where Q, equals -0.12x10-**, 0.26~10-~~ and 0.09~10-~~ m*, and JJ~, -168.5, -79.98 and -9.14 [ 121 for i= 13’Xe, 83Kr and *‘Ne, respectively. The ratios calculated from eq. (4) are: Ix~Jx~~I =0.966, Ix~Jx.A =22.3 and Ix~JxN~I = 23.1. The average experimental ratios (the individual ratios vary a bit, less than IO%, however, with temperature) are 0.78, 13.0 and 16.7, respectively, deviating 19, 42 and 28% from the theoretical ones. The biggest deviation exists between xenon and neon, and the smallest one between xenon and krypton. On the other hand, if the total field gradient is assumed to arise purely from the deformation of the neon electron distribution because of collisions, the qcc 255
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should be proportional to ( r -3) p,, the average value of r -3 over the p-electron wavefunctions of the atom i [ 131. Consequently,
&=
Q, (r-3&
Xl
Q,
II IIV3>p,.
contribution, temperature.
which
increases
with
decreasing
4. Conclusions
(5)
With the Q, values given before and the ( re3,Jpi values from ref. [ 141, eq. (5) leads to the following ratios (in parentheses are shown the values obtained when relativistic corrections are taken into acl~x.Jz~~ I = count): lzJzKr I =0.547 (0.581), 2.70 (2.61) and ~~~~~~~~ I =4.93 (4.49). These are clearly smaller than the corresponding experimental values. It has been proposed that the external efg, i.e. the efg created by the LC and enhanced by the Sternheimer factor, is about the same in the case of various small molecules, such as hydrogen and methane [ 5 1. Thus, it is logical to assume that this is the case also for noble gases. Then, the abovementioned deviations in the qcc ratios stem from the second effect on the total efg. i.e. from the average deformation of the electron cloud of the atom during collisions with LC molecules. Further measurements using all three quadrupolar noble-gas isotopes in various pure and mixed liquid crystals are needed before one will be able to make models explaining the efg behaviour and to separate and quantify the possible efg contributions. The pure ZLI 1167liquid crystal possesses a smectic A phase between TCsA= 298 K and TsAN= 305 K. These temperatures, of course, change when solutes are added to the LC. The amount of neon is so small that the transition temperatures are affected only slightly. On the contrary, the pressure of xenon and krypton gases in the previous experiments was so high that the transition to the S,&phase could not be detected. Fig. 2 shows that the S,-N transition causes the efg to increase with decreasing temperature. This may arise from the expulsion of neon atoms from the more-dense core region to the less-dense chain region in the smectic phase.Thus, the deformation of the neon electron-cloud contribution to the total efg may become less important than the external efg
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CHEMICAL PHYSICS LETTERS
This work on 2’Ne in combination with the ones on 83Kr and 13’Xe in the liquid-crystal ZLIll67 shows that the total electric field gradient is a sum of at least two contributions. Therefore, it is obvious that the consideration of a single contribution to the electric field gradient cannot satisfactorily explain the relaxation of the nuclei. Moreover, no abrupt change in the efg could be detected at the smectic .4nematic transition.
Acknowledgement The authors are grateful to the Academy of Finland and to the Swiss National Science Foundation for financial support.
References [I ] J.B. Wooten, Ph.D. Thesis, Clemson University ( 1977). [ 21 I. Joklsaari, P. Diehl, J. Amrein and E. ljas, J. Magn. Reson. 52 (1983) 193. [3]J. Jokisaari and Y. Hiltunen, J. Magn. Reson. 60 (1954) 307. [4] J.G. Snijders, C.A. de Langeand E.E. Bumell, Israel J. Chem. 23 (1983) 269, and references therein.
[S] J. Lounila and P. Diehl, J. Chem. Phys. 94 ( 1991) 1785. [6] E.E. Burnell, CA. de Lange and J.G. Snijders, Phys. Rev. A25 (1982)2339. [ 71 G.N. Patey, E.E. Burnell, J.G. Snijders and C.A. de Lange, Chem. Phys. Letters 99 ( 1983) 27 1. [B] P. Diehl and J. Jokisaari, Chem. Phys. Letters 165 (1990) 389. [91 P. Ingman, J. Jokisasari and P. Diehl. J. Magn. Reson. 92 (1991) 163. [IO] R. Henry and R.E. Norberg, Phys. Rev. B 6 ( 1972) 1645. [ 111 P. Diehl, 0. Muenster and J. Jokisaari, Chem. Phys. Letters 178 (1991) 147. [ 121 D. Kolb, W.R. Johnson and P. Shorer, Phys. Rev. A 26 (1982) 19. [ 131 C. Deverell, Mol. Phys. I6 ( 1969) 491. [ 141 C.J. Jameson and 1. Mason, in: Multinuclear NMR, ed. I. Mason (Plenum Press, New York, 1987) ch. 3.