Temperature-dependent T1 measurements of 13C and 14N in acetonitrile dissolved in a thermotropic...

JOURNAL OF MAGNETIC RESONANCE 33 27-39 (1979)

Temperature-Dependent TI Measurements of 13C and 14N in Acetonitrile Dissolved in a Thermotropic Liquid Crystal

H. A. LOPES CARDOZO, J. BULTHUIS, AND C. MACLEAN

Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083, Amsterdam, The Netherlands

Received November 28, 1977; revised April 21, 1978

The methyl r3C and the r4N longitudinal relaxation times in acetonitrile, dissolved in a thermotropic liquid crystal, were studied as a function of temperature under the condition of proton decoupling. The r4N longitudinal relaxation time could be derived from the cyano r3C linewidth due to the incomplete averaging of the dipolar interactions in the nematic phase. The correlation times for the reorientation of the r3C-H vector and for the reorientation about an axis perpendicular to the principal molecular axis were obtained using standard relaxation theory, with allowance for the ordering in the nematic phase and applying extreme narrowing arguments. The results strongly indicate that the equations derived for the isotropic phase, assuming rotational diffusion, cannot be applied to a molecule dissolved in a nematic phase merely by taking into account the partial orientation.

INTRODUCTION

NMR of molecules dissolved in liquid crystals is a well-established technique for determining molecular geometries. In some cases, however, the results show considerable deviations from those of other techniques (I, 2) and even measurements in different liquid crystals may be conflicting (3, 4). Several attempts, some of them successful, have been made to explain the observed discrepancies, e.g., by accounting for vibrational corrections (5), By proposing a two-site model (3,4), or by assuming distortion of the dissolved molecule (6). A study of the dynamical behavior of the molecules dissolved in a liquid crystal might contribute to a better understand- ing of these effects.

Relatively little is known about the dynamical behavior of small molecules in liquid crystals, although there is a growing interest in this field (7-15). In the present study an attempt is made to determine the anisotropic motion of acetonitrile from 13C relaxation measurements in Merck’s Licrystal, Phase V. This liquid crystal has a large nematic range which permits measurements of the temperature dependence of the relaxation rates. Acetonitrile was studied because it is a simple nonspherical molecule. Moreover, its anisotropic motion in isotropic solvents has already been studied extensively (16-19). Assuming that the reorientation of acetonitrile can be described by a rotation-diffusion equation, as is normally applied to the isotropic phase, the two principal diffusion constants Dll and D, can be deduced from the correlation times of two different relaxation vectors. The term Dt corresponds to a reorientation about the principal molecular axis. and D, to a reorientation

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28 LOPES CARDOZO, BULTHUIS, AND MACLEAN

perpendicular to this axis. In the following we refer to these motions as parallel and perpendicular reorientations, respectively. The two correlation times can be determined by relaxation time measurements of the two carbon-13 nuclei, provided that the various contributions to these relaxation times can be separated. Measurement of the longitudinal relaxation time of the methyl r3C then gives the correlation time of the C-H relaxation vector.

The transverse relaxation of the cyano 13C is dominated by the 14N quadrupole longitudinal relaxation as a result of the nonvanishing dipole-dipole interaction between the 14N and 13C nuclei in the nematic phase. So in measuring the linewidth of the cyano 13C the correlation time of the perpendicular reorientation is obtained.

EXPERIMENTAL

All r3C measurements were made using a Varian XL-loo-12 WG spectrometer operating at 25.2 MHz in the FI mode.

The proton-decoupled 13C relaxation times were measured by using the modified Freeman-Hill IRFT pulse sequence (20). The logarithms of the measured intensities were plotted against the delay time. Strongly deviating data points were excluded from the analysis. The error in the 2-i measurements is estimated to be less than *5%. Within the experimental accuracy, all Tr measurements show an exponential decay.

Proton decoupling has two major experimental advantages. First, it gives a large enhancement of the signal-to-noise ratio as a result of the coalescence of the 13C multiplet and because of the nuclear Overhauser enhancement. Second, there is no additional line broadening, which is characteristic of liquid crystal NMR spectra with large line splittings, probably caused by temperature fluctuations and gradients in the sample.

Proton decoupling in the nematic phase cannot be achieved by broadband irradiation because the standard Varian decoupling accessory has insufficient power. The protons, however, constitute a fully equivalent group of nuclei. Therefore it is possible to decouple them by irradiating at a single frequency, exactly at the centre of the ‘H spectrum (21). The power used was about 10 W. With each new measurement the irradiation frequency had to be adjusted with great care until the most intense and narrowest methyl 13C line was obtained. Figure 1 shows the decoupled 13C line for different irradiation frequencies.

The NOE measurements were carried out using the gated decoupling technique (22). The reproducibility of the measurements was unsatisfactory, giving a value of n ranging from 1.6 to 2.1.

The sample tubes (Wilmad; 5-mm o.d.) were treated with aqua regia to remove all paramagnetic impurities introduced in the polishing process used by the manufac- turer. The sample tube was filled with a weighted amount of liquid crystal and degassed by five freeze-pump-thaw cycles. Then a known volume of acetonitrile was distilled into the tube, which was sealed after freezing and pumping. Two samples were prepared: one with 13CH3CN, sample A, and the other with CH3i3CN, sample B (both 90% enriched), each containing 15 mole% acetonitrile in Licrystal nematic phase V (Merck, Darmstadt). 13CH3CN was purchased from Merck, Sharp & Dohme (Canada) and CH313CN from Prochem (London).

1

J + 0,e

I

j-

0.0

- I J

c 50

l-k

1

-dd

FC

3 n

FIG.

1. Me

thyl

13C

line

(samp

le A,

7°

C)

as a

func

tion

of the

pr

oton

deco

uplin

g fre

quen

cy

relat

ive

to the

fre

quen

cy

F, of

the

cente

r of

the

proto

n sp

ectru

m.

The

deco

upler

off

set

is va

ried

from

(F,-

10)

Hz

to (F

,+ 10

) wi

th

steps

of

2 Hz

. ? i4


The temperature of the sample could be held constant within *O.l”C by using the standard Varian variable-temperature accessory, provided measures were taken to maintain the nitrogen stream at a constant temperature and flow. The temperature and temperature gradient in the probe were measured by inserting a thermocouple into a 5-mm tube filled to the same height with Licrystal as the sample tube containing the acetonitrile solution.

When the decoupling power was turned on, the temperature increased by about SC, and the temperature gradient was about 25°C over the filling height of 26 mm. The gradient was dependent on the sample temperature. The temperature gradient was minimized to 0.5 to 1°C by inserting the sample tube into a lo-mm outer tube, filled with D20 or CDCls (below 0°C) to provide a lock signal, and only spinning the outer tube

THEORY

From the observed NOE we conclude that the intramolecular dipole-dipole interactions between the methyl 13C and the protons provide the dominant contribution to the 13C relaxation of the methyl group. Furthermore, the exponential behavior of the relaxation indicates that cross-correlation effects can be ignored (23). Thus we describe the methyl r3C relaxation behavior as 3 times the contribution from one methyl proton.

With standard relaxation theory (24) the dipolar relaxation of the 13C by one of the methyl protons under the conditions of proton decoupling is described by

1/T1(‘3C) = &:,h2{‘J ( 3 0 WH-WC)+J1(OC)+2J2(WH+WC)}, [II

with the spectral density defined as

Jq(w4) = [ +a F’q’(0)F’-4’(7) e-i”4rd7, J-CC

where

is the correlation function and

F(o'z: (3cos2 e-11 2 & I

F(*')= 0 2 1’2sin e cos 8 eFrd 2 & '

1/24n2 eeT2id

r&3 .

m

[31

[41

The symbols have their usual meanings. A difference between the isotropic phase and the nematic phase is the partial

orientation of the solute molecule in the latter, resulting in an incomplete averaging

ACETONITRILE RELAXATION IN THERMOTROPIC PHASE 31

of the dipole-dipole interaction, which is described by the Hamiltonian

Hclip = 1 Dij{IziI,i -~(Ii+Ij-+ I[Ij+)}, i<j

where

Dij = zh((l - 3 COS2 eij)/r;i,

where 8ij is the angle between the vector connecting nuclei i and j and the magnetic field. The quantity Dij can be written as (25)

(7)

where

s,, = ((3 cos2 e - 1)/2) PI is the order parameter and 8 is the angle between the z axis and the magnetic field; x, y, and z are Cartesian coordinates in the molecular frame. The threefold symmetry axis is chosen as the z axis.

The above relations show that we have to average the correlation functions [3] with respect to the orientation in the nematic phase. From the assumption that the reorientation of the molecule can be described by a rotation-diffusion equation, it follows that the correlation function decays exponentially with a time constant rcq, the rotational correlation time

F(q)(0)F(-q)(7) = {lF’q’(o)12 -F’4’oF’-q’(0)6q,o} .eT’Q. [91 Using Eqs. [2], [4], and [9], one obtains for the spectral density functions the expressions

JObH - 4 = 1 --

-g-- rCH l+

27co $0~~ eCH-60S2ZH}, (wH-wc)2Tzo 4

J1(oc)=l rCH 1+

274 -{COS 3- eCH--ii&?cH}, (uC)2& 2

1 J2(wH + WC> = 6

27c2 ‘{sin4 @on}. rcH 1 +(wH+wC)27z2 8

[lOI

Following Egozy ef al. (7), we assume that the motion of the C-H vector is isotropic in the sense that we can describe the correlation functions by one 7,. Furthermore we assume that (WH - wc)‘rz w&z and (WH + oc)*rz << 1. In other words we use extreme narrowing arguments. Substitution of Eq. [9] into Eq. [l] gives for the correlation time rc of the C-H relaxation vector under the condition of proton decoupling the simple expression

9 &Yh 2 l/z-J3C) =- 6

8 rCH h (1 -&&2‘H}Tc, [Ill


which, for the isotropic phase in the extreme narrowing limit, shades off into the well-known result

As stated above, we describe the relaxation time of the methyl 13C under proton decoupling as 3 times the result for one i3C-H vector

[=I

The longitudinal relaxation of the cyano 13C nucleus is probably determined by intermolecular dipole-dipole interactions and chemical shift anisotropy, whereas the intramolecular dipole-dipole interactions will be of minor importance. This makes the interpretation of the relaxation time very difficult because the contributions cannot be easily separated. Moreover it turns out that the linewidth of the 13C resonance in the nematic phase is very broad, which makes it difficult to measure Ti reliably. In the nematic phase the proton-decoupled cyano i3C spectrum consists of a single Lorentzian line with a strongly temperature-dependent linewidth. The multiplet splitting between the 14N and 13C nuclei is not observed because of the rapid 14N quadrupolar relaxation. This is also normally observed in the isotropic phase (26).

The multiplet splitting is described by

Hspl = Hdip + J{IzS,z + (1/2)(I+S- + I-S+)},

where J is the scalar coupling between spins I and S and Hdip is the dipolar coupling, defined in Eq. [5]. The splitting is temperature dependent through the temperature dependence of S,, (Fig. 2). Using Abragam’s arguments for the isotropic phase (24) we derive for the longitudinal and transverse relaxation of the cyano 13C caused by the rapidly relaxing 14N nucleus the expressions

T2(14N)

1 +(tic-~~)~T;(i~N)’

Td14N) 1 + (oe - w~)‘T;(~~N)

+ ${Jc, + DcN)~ TI(‘~N).

iI31

The first term on the right-hand side of Eq. [ 141 is negligibly small with respect to the second term, and the linewidth of the cyano 13C is given by

&/2= 1/~7’&~C)= (~T~/~){J~N+D~N}~T~(~~N); iI51 DCN varies between -213 and -428 Hz (Table 2) and JcN = 12.48 Hz (27,X?). These values show that the dipolar 13C-N coupling contributes significantly to the linewidth of the i3C nucleus. In the isotropic phase DcN = 0 and the contribution to the cyano 13C linewidth from JCN is not detectable. In the nematic phase, however,


14

12

1C

N

9

x E

z In

E

L

;

C

c

I-

I-

I-

) - I I I I I I I I 1 I

-40 -30 -20 10

0°C

10 20 30 40 50

FIG. 2. Plot of the ordering parameter S,, vs temperature. The dots are from proton measurements on sample B (CH313CN), the squares from proton measurements on sample A (13CH3CN), and the triangles from the methyl 13C measurements on sample A. The estimated error in S,, is f 1%.

the linewidth varies from 57.5 to 7 Hz, depending on the temperature. The quadrupole contribution to the longitudinal relaxation for an I = 1 nucleus subjected to an axially symmetric electric field gradient is given by

where e*qQ/h is the quadrupole coupling constant. The spectral densities are defined in Eqs. [l] and [2], but here the FCg)‘s are

F-(O) = $(3 cos* 8 - l),

Using the same arguments as those used in the derivation of Eq. [ll], we obtain for TI(r4N) as a function of the correlation time 71 and the ordering parameter S,, the expression

[181


RESULTS AND DISCUSSION

The results of the methyl r3C relaxation measurements are given in Table 1, together with the calculated correlation times 7,. Table 2 shows the results of the linewidth measurements of the proton-decoupled cyano 13C, the calculated i4N longitudinal relaxation times, and the calculated correlation times r1 for the perpendicular reorientation. The given linewidths were corrected by 1 Hz (which is about the linewidth of the methyl 13C in the nematic phase), to account for other broadening mechanisms.

For sample A the ordering parameter S,, was obtained from the undecoupled r3C spectra and from the ‘H spectra. For sample B, only the ‘H spectra could be used to calculate S,,. In Fig. 2 the ordering parameter is given as a function of the temperature for both samples. The temperature dependences for 7c and rL are shown in Figs. 3 and 4, respectively.

If the reorientation of the molecule is assumed to be a thermally activated process, T = r. exp(-E,/RT). The curves in Figs. 3 and 4 are represented by two linear parts

TABLE 1 T1(13C) AND 7, VALUES OF 13CH3CN (SAMPLE A) AS A

FUNCTION OF TEMPERATURES

Temperature cc,

Tl (se4 (1O’sec)

G7.4 8.3 2.3 t62.3 8.1 2.3 +54.6 1.4 2.5 +50.1 6.7 2.8 +45.2 6.1 3.1 +43.5 6.5 2.9 +38.7 6.2 3.0 +30.1 5.7 3.2 +26.2 5.3 3.5 +25.6 5.0 3.7 +20.2 4.7 3.9 +14.0 3.7 5.0 +12.6 4.1 4.5

+9.4 3.3 5.6 f6.4 3.0 6.2 f4.5 2.1 6.8 1-1.8 2.6 7.1 +0.5 2.4 7.7 -1.0 2.2 8.4 -4.2 2.1 8.8 -5.4 2.0 9.2

-14.0 1.4 13.2 -20.5 1.1 16.7

a The 7, values are calculated using Eq. [12] with the 13C-H distance taken as 1.125 8, (33). The stability in the temperature is estimated to be *O.l”C. The estimated error in Tl(13C) is less than *5%.


TABLE 2 A VI/Z OF 13C11W, L, DCN. T,(14N), AND r1 FOR CHst3CN (SAMPLE B) AS A FUNCTION OF

TEMPERATURE“

Temperature h/2

03 (Hz)

S ZL DCN

0-w

T,(“N)

(10m4 set) (lo-‘set)

+38.5 51 0.071 -213 1.51 37 +36 55 0.077 -231 1.37 41 +32.5 55 0.084 -252 1.14 50 +29.5 56.5 0.089 -267 1.04 55 +26.5 56 0.093 -278 0.95 60 +22 54 0.099 -296 0.80 72 +18 50 0.103 -309 0.68 85 +13 44 0.108 -324 0.54 108

+9 38 0.112 -336 0.43 135 +6.5 35.5 0.114 -342 0.39 150 +4 33 0.117 -351 0.34 171 +0.5 28 0.120 -360 0.28 213 -2.5 24 0.123 -368 0.23 261 -4.5 21 0.124 -372 0.19 306

-11 15.3 0.130 -390 0.13 468 -18.5 19 0.137 -410 0.076 795 -26.3 6 0.143 -430 0.041 1468

a The DCN. Tl(14N), and r1 values are calculated using Eqs. [7], [15], and [18], respectively. The quadrupole coupling constant was taken as 3.60 MHz (31) and the ‘sCfN distance as 1.133 A (33). The stability in the temperature is *O.l”C. The uncertainty in AV 1,s is estimated to be 1 Hz above 0°C and 0.5 Hz below 0°C.

2.7 2.6 2.9 30 3.1 3.2 3.3 3.4 X6 3.6 3.7 3.6 3.9 *I)

7000/T, K-’

FIG. 3. Semilogarithmic plot of rc vs (1000/T) K-l. The nematic-isotropic transition temperature is approximately 42.5”C.


“C 50 25 0 -25 -40

2, I-

10 I I 8 1

3.0 3.1 3.2 3.3 3.4 3.5 se 3.7 3.8 3.9 4.0 4.1 4.2 4.3

10001 T, K-’

FIG. 4. Semilogarithmic plot of 71 vs (1000/T) K-‘. The nematic-isotropic transition temperature is approximately 42S”C.

each, so that approximate values can be calculated for the activation energies in the corresponding temperature ranges. The values for the reorientation of the 13C-H vector are 5.1 and 2.1 kcal/mole below and above 26.2”C, respectively. For the perpendicular reorientation the activation energy is 9.6 kcal/mole below 0.X and 7.6 kcal/mole above 0S”C. These values are considerably higher than those in pure acetonitrile, namely, 1.37 kcal/mole for the reorientation of the C-D vector and 2.0 kcal/mole for the perpendicular reorientation (I 7). For comparison, the value of the activation energy for the relaxation of the radical PD-Tempone dissolved in Licrystal phase V is 9.6 kcal/mole in the nematic phase and 8.0 kcal/mole in the isotropic phase (8).

The reason for the change in the slope of Fig. 3 above 26°C is not clear. In principle it may be caused by a contribution of spin-rotation relaxation, which has a temperature dependence opposite to that of the dipolar mechanism. This, however, is not likely in view of the rather large value of T=, compared to neat acetonitrile. The


scatter in the measured NOE values is too large to permit one to draw any conclusions concerning the relative contribution of spin-rotation interaction to the 13C relaxation. The importance of this mechanism can be verified by deuterium relaxation measurements, as a function of temperature.

For an isotropic liquid under the condition of anisotropic rotational diffusion Woessner (17,29) derived a relation between the correlation time and the components of the diffusion tensor. As acetonitrile is a small molecule and the degree of order is rather low, it seems reasonable to try to fit the results to this relation.

Accordingly we can write for the methyl 13C relaxation time, instead of Eq. [12],

27 Y&L 2 1/TJ3C) = s -& h (1 -cos2:&(6D,)-‘+&(5D,+D,,)-’

+$(20,+40,,)-‘1, P91

where TV = (60,)-l, 711 = (6011)-~ - and cos &u=$(l -$S,,). In fact Woessner’s derivation (29) has to be modified for the case of the partial orientation of the molecules in the nematic phase; i.e., there is an anisotropic distribution of orien- tations instead of an isotropic random distribution. When this is done one obtains

3 rxl 2 1/m’3c)=~ --&- h [(2 - S&60,)-’ + (2 - fS&(5D, + II,,)-’

+ (2 + s,, )g(20, + 40,,)-‘]. WI

For small values of S,, this result is only slightly different from that of Eq. [19]. Equation [18], relating the T1 (14N) to r I, remains valid. It should be noted that although the average value of cos4 19 appears in the expressions for the spectral density functions, this is not the case for the expressions for T1(13C) and T1(i4N).

According to Eqs. [19] and [20] the minimum value of T= is about O.lr,, which is attained only under the condition Dll >>DI. However, over the entire temperature range measured, r,< 0.1~~. This inconsistency is even more serious: if r, were determined by rL only, the slopes of the plots of rc and r1 vs l/T would be similar, which is not the case. There is an additional indication why 7c is not likely to be determined by D, only. If Dll>> D, the methyl 13C would, according to Werbelow and Grant (23), decay nonexponentially because of cross-correlation effects, and this is not observed.

One possibility is that the quadrupole coupling constant in this system is much larger than 3.60 MHz, as measured by Gerace and Fung (31) in a lyotropic liquid crystal. It is indeed a well-known fact that 14N quadrupole coupling constants in liquids may be medium dependent (32). Assuming DIJDl = 10.35, as in the case of pure liquid acetonitrile at 25°C (17), the quadrupole coupling constant must be 8.6 MHz, which is highly improbable, as appears also from the values of 3.74 MHz measured in the solid phase (34) and 4.35 MHz in the gaseous state (35). Even if Q/Dl is assumed to be much larger than 10.35, e.g., 50, the value of the quadrupole coupling constant has to be unreasonably large, so that the inconsistency is unlikely to be attributable to a solvent dependence of the quadrupole coupling constant.


The value of the quadrupole coupling constant given by Gerace and Fung was measured in the lyotropic phase, where the ordering is much smaller than in the nematic phase. Hence in the former phase the ordering can hardly play an important role in the relaxation mechanism. Therefore it seems worthwhile to repeat the same experiments in the lyotropic phase, although one may wonder whether, with the dipolar 13C-14N coupling much smaller, the TZ of the cyano 13C can be measured in the same way.

CONCLUSION

The relaxation times of the 13C and 14N are discussed in terms of the reorientation of two independent vectors. Assuming that the anisotropic reorientation can be described by Eq. [19] or [20] these relaxation times should in principle suffice to determine the components Dll and D, of the diffusion tensor. The results show that the assumptions underlying Eqs. [19] and [20] are not applicable to the nematic phase. A more elaborate theoretical treatment, like the one developed by Freed (36) which takes into account correlations between reorientational motions of acetonitrile and the liquid crystal molecules, seems to be necessary.

We hope that 13C and *H measurements on our new 180-MHz NMR spectrometer (Bruker WH 180), which we will carry out shortly, will give us additional information concerning the importance of the spin-rotation mechanism in relaxing the methyl 13C nucleus above 26°C and of the frequency dependence of the T1 (14N) which should manifest itself in a change of the linewidth of the cyano 13C.

The experiments in Licrystal V show that, although 14N cannot be measured directly, much information can be obtained from linewidth measurements on a nucleus coupled to the 14N nucleus in the nematic phase. A great advantage is the possibility of changing the coupling between the quadrupole nucleus and the nucleus under study, by changing the ordering, which in turn is a function of temperature, concentration, and solvent. Another possibility is that of changing the coupling by spinning the sample tube.

ACKNOWLEDGMENTS The authors gratefully acknowledge helpful discussions with Dr. W. M. M. J. Bovte and the

experimental assistance of Mr. J. van der Giessen.

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Temperature-dependent T1 measurements of 13C and 14N in acetonitrile dissolved in a thermotropic...

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