Orientational order in the nematic phase of 4-methoxy-4′-cyanobiphenyl: A deuterium NMR study

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3 February 1984

ORIENTATIONAL ORDER IN THE NEMATIC PHASE OF 4-METHOXY-4'-CYANOBIPHENYL: A DEUTERIUM NMR STUDY J.W. EMSLEY, K. HAMILTON, G.R. LUCKHURST, F. SUNDHOLM *, B.A. TIMIMI and D.L. TURNER Department of Chemistry, The University, Southampton, S09 5NH, UK

Received 17 October 1983; in final form 3 December 1983

The deuterium NMR spectrum of 4-methoxy-da-3,5-dz-4'-cyanobiphenylhas been recorded as a function of temperature in its monotropic nematic phase. The particularly simple molecular structure for this nematogen allows three elements of the Saupe ordering matrix to be determined from the spectral splittings. The temperature dependence of the major element of the ordering matrix is well predicted by theory provided allowance is made for the molecular biaxiality.

There have been many attempts to develop molecular theories for the order-disorder transition exhibited by nematic liquid crystals [ 1]. In the majority of these theories the molecules are assumed to be rigid and cylindrically symmetric while, in practice, nematogenic molecules are flexible and of low symmetry. As a consequence, an unambiguous test of such theories against the properties of real nematics is rarely possible. However, the advent of computer simulation studies of model liquid crystals with rigid particles of high symmetry has meant that the validity of the approximations employed in the theories may now be checked [2]. Nonetheless, such comparisons provide no direct information on the form of the pair potential for real nematogens. Therefore, it is important to be able to investigate the behaviour of materials with relatively simple molecular structure. For example, p-quinquephenyl does possess a nematic phase but the transition temperatures (TcN = 388°C; TNI = 423°C [3]) are inconveniently high and its thermal stability is uncertain [4] ; it is not therefore a particularly easy material to study. The mesomorphic range and possibly the structural simplicity of compounds exhibiting liquid crystal phases may be enhanced by working at high pressures. This possibility obtains because the nematic-isotropic transition increases more rapidly * Permanent and present address: Department of Chemistry, University of Helsinki, Helsinki 10, SF-00100, Finland. 136

with pressure than the crystal-isotropic transition and so materials which are not nematic at atmospheric pressure may be at an elevated pressure. Thus the relatively simple, 4-methoxy-4 -cyanoblphenyl (10CB) melts to an isotropic liquid at atmospheric pressure but to a nematic at ~ 4 kbar [4]. The orientational order in this high pressure nematic has been investigated using proton NMR but the spectra were poorly resolved and it was not possible to determine the Saupe ordering matrix [4,51. An alternative to the use of high pressure is to prepare the metastable or monotropic nematic phase by supercooling the isotropic liquid. Indeed, the monotropic nematic-isotropic transition has been observed for 10CB at 85.5°C [6] although Wallis and Roy [7] were unable to record NMR spectra from the monotropic nematic phase except by working at pressures greater than 0.5 kbar. However, we have been able to obtain the monotropic nematic phase at atmospheric pressure by slowly cooling 10CB contained in a standard NMR tube. In view of the structural simplicity of 10CB, we have synthesised a partially deuterated sample and present here the results of a deuterium NMR study of the monotropic nematic phase. 4-me thoxy-d 3-3, 5-d2-4'-cyanobiphenyl ( 10CB-d5 ) was prepared by first deuterating 4-hydrogen-4'-cyanobiphenyl (2 g) in the 3,5 positions by refluxing with a mixture of deuterium oxide (8 ml) and deuterotrifluoroacetic acid (10 ml) for eight hours [8]. The •

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reaction mixture was allowed to cool and subsequently poured into water (50 ml); the precipitated solid was filtered off, washed with water (50 ml) and dried. This procedure was repeated four times and resulted in ~95% deuteration at the 3,5 positions. The cyano group is partially hydrolysed by this method and so the hydrolysis product was removed from the 4hydroxy-3,5-d2-4'-cyanobiphenyl by dissolving the mixture in a small quantity of methanol, followed by precipitation with water. 10CB-d 5 was prepared by adding the deuterated 4-hydroxy-4'-cyanobiphenyl (0.57 g) and then methyl iodide-d 3 (0.2 ml) to a suspension of finely powered sodium hydroxide (0.70 g) in dimethyl sulphoxide (15 ml) [9]. The mixture was stirred at room temperature for 30 rain, diluted with water (15 ml) and then extracted with ether (3 X 250 ml). The organic phase was washed, dried and the solvent evaporated. The crude product was recrystallized from ethanol with decolourizing charcoal. The resulting 10CB-d 5 (0.52 g) was contaminated with products formed by the hydrolysis of 4-hydroxy-4'-cyanobiphenyl. It was purified by extracting the solid product with chloroform, the solution was concentrated and then passed through a silica column. Elution with chloroform gave 10CB-d 4 while a 1 : 1 mixture of methanol and chloroform produced the more polar product which is 4'-(4-methoxy-d3-3,5-d2-phenyl) benzamide. The melting point of the purified 10CB-d 5 is 104.5-105.5°C and is in good accord with the literature value for 10CB [6]. The deuterium NMR spectra of 10CB-d 5 were measured as a function of temperature at 30.7 MHz using a Bruker CXP 200 spectrometer. The sample was first melted and the temperature was then lowered. The monotropic nematic-isotropic transition was observed at 86°C and invariably the sample did not freeze until 66°C. A typical spectrum, recorded at 71°C, is shown in fig. 1. This was obtained by averaging 600 transients following 50 ° pulses of 6/~s duration with a delay of 0.1 s between pulses. The spectral width was 25 kHz accumulated into 4 kbyte of computer store, which limits the precision on line positions to 12 Hz. The spectrum contains a quadrupolar doublet from the methoxy deuterons, and each component of the quadrupolar doublet from the aromatic deuterons is split into a further doublet by the dipolar interaction with the protons at positions 2 and 5. The low intensity of the peaks from the aromatic deuterons relative to those

3 February 1984 2 kHz

Fig. 1. The deuterium NMR spectrum of 4-methoxy-d3-3,5d 2-4'-cyanobiphenyl in the monotropic nematic phase at 71° C.

from the methoxy deuterons reveals that 240% of the aromatic deuterons were lost during the synthesis of 10CB from deuterated 4-hydroxy-4'-cyanobiphenyl. The variation of the two quadrupolar splittings and the dipolar splitting with temperature is shown in fig. 2. For one temperature near the nematic-isotropic transition, a spectrum containing peaks associated with both the nematic and the isotropic phases was recorded. This observation is of particular value because the temperature dependence of the orientational order and hence the splittings is extremely small in the twophases region; in consequence, it is possible to determine the splittings at the nematic-isotropic transition with high precision. The two-phase region is less than I°C in width and results, presumably, from a trace impurity. The analysis of the observed splittings to obtain the ordering matrix is a difficult task which depends on the nature and distribution of the molecular conformers [ 10]. For example, if the molecule exists in a discrete number of conformations then the partially averaged component of any second rank tensor A parallel to the director for a uniaxial phase is -

Atl =A 0 + ~

PnAn'S n •

(1)

Here Pn is the normalised probability of the nth conformation, S n is its Saupe ordering matrix and A 0 is the scalar component, which strictly is averaged over all conformations. The tensors An and S n are given in 137

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( TNI-T )/K Fig. 2. The temperature dependence of the quadrupolar splittings for the aromatic (o) and methoxy (o) deuterons together with the hydrogen-deuterium dipolar splitting (o) observed for 10CB-d5. a molecular axis system which is the same for all conformations. For mesogens such 4-n-pentyl-4'-cyanobiphenyl Pn, Sn and A n have a pronounced conformational dependence and there is insufficient data to extractPn and S n from the observed magnetic interaction All [ 1 1 ]. Instead the partial averages Atl have to be coinpared with values calculated using theoretical models for the conformational distribution and • the ordering matrices of each conformer [ 12]. One of the major advantages in studying 10CB is that we do not need to develop such elaborate models provided we make quite reasonable assumptions concerning the conformations which 10CB can adopt. Two of these conformations are shown in fig. 3; the methoxy group is in the plane of the aromatic ring to which it is attached, in accord with the structure o f other anisole 138

derivatives [13]. The second ring is inclined to the first at an angle q~or n - ~b. The other conformations are derived from these by rotations of the rings about the para axis through 180 °. The shapes of all eight conformers are identical, and so the probability of a particular conformer is independent of the conformation and equal to 1/8. It is convenient to divide the conformers into two sets, those with an inter ring angle of ~b(denoted by n+) and those with an angle 180 ° - ~ ( n ) . The conformational set n+ have identical shapes and so will have the same ordering matrix S + provided the molecular reference frame is attached to the methoxy group (cf. fig. 3). Similarly, one ordering matrix S - suffice for the set n _ , but this is not identical to $+. In fact, S+ and S - differ only in the x y and y z off-diagonal elements, which are equal but

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z

"~ = Szz(q~z)+ g(Sxx _ Syy)((qAxx) (q_yy)).A ×

The off-diagonal terms in S x z do not appear in this result because the conformational averaging of q produced by ring rotation through 180 ° reduces (qxAz) to zero. The remaining averages are related to the principal components of q for an aromatic deuteron by

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opposite in sign [ 11 ]. The magnetic nuclei studied in this investigation of 10CB are located in the anisole fragment and so the magnetic tensors for conformations n+ and n_ are identical in the x y z frame. Consequently, it is the average ordering matrix ½(S + + S - ) which is needed in the expression for Air. This reduces to 2

All = A 0 + g S • (A),

(2)

where $ denotes the average ordering matrix, for which y is a principal axis and (A) is the conformationally averaged tensor. We now use the result in eq. (2) to analyse the observed splittings. We begin with the p r o t o n - d e u t e r i u m interaction. The scalar coupling is less than 0.2 Hz and may be ignored, the dipolar splitting is then just twice the parallel component of the dipolar tensor, /~HD. In the x y z frame the total H - D dipolar tensor is independent of the conformation and is cylindrically symmetric about the z axis; consequently g r i d = --THTD S z z / 4 n 2 r 3 D .

(3)

The H - D dipolar splitting gives immediately one diagonal element of the average ordering matrix $. The quadrupolar splitting is just three halves the quadmpolar interaction which for the aromatic deuterons, is

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(5)

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The principal axes abc are shown in fig. 3 together with 7, the angle between the C - D bond and the z axis. Therefore the quadrupolar splitting from the aromatic deuterons provides us with the other diagonal elements of the average ordering matrix. The remaining off-diagonal element S x z is obtained from the observed quadrupolar tensor component for the methoxy deuterons; this is given by

= ( Szz(3

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where 0 is the angle between the O - C D 3 bond and the z axis. It is assumed that the CD 3 group rotation about this bond is governed by a barrier with threefold symmetry, and so q = ~ qCD(3 c o s 2 a - 1).

(7)

Here, a is the angle made by the C - D bond with the three-fold axis and qCD is the quadrupolar interaction for the methoxy deuterons. In using these equations to extract the elements of the averaged ordering matrix from our results we have employed the following values for the geometric parameters: rHp = 2.48 A [ 1 4 ] , 7 = 60 °, 0 = 55 ° [13] and a = 70.U, which assumes a tetrahedral geometry for the methyl group. The principal components of the quadrupolar tensor for the aromatic deuterons were taken to be qaa = - 9 0 . 2 kHz, qbb = 186 kHz, qce = - 9 5 . 8 kHz [ 15] and for the methoxy deuterons qCD = 168 kHz [16]. The absolute signs of the splittings are not determined from our experiments and so they are assigned in accord with our expectations for the ordering of a molecule such as 10CB in its nematic phase. Thus, the hydrogen-deuterium dipolar 139

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splitting is assumed to be negative because we expect

Szz , the order parameter for the long molecular axis, to be positive. It was possible to show that the quadrupolar splitting for the aromatic deuterons has the same sign as the dipolar splitting by means of selectively irradiating the protons in the 2,6 positions while monitoring the deuterium spectrum [17]. Although the proton spectrum is poorly resolved, two broad bands separated by the large ortho p r o t o n proton dipolar splitting and a central band covering ~ 4 kHz can be distinguished. The central band resuits, presumably, from the protons which are ortho to the deuterons, and irradiating its high frequency edge using ~1 W of continuous power caused partial collapse of the high-frequency deuterium doublet, while irradiation of the low-frequency edge partially collapsed the low-frequency doublet. However, irradiation outside the central band had no significant effect on the deuterium spectrum. Thus, although the proton band is unresolved, the proton-deuterium dipolar coupling clearly dominates its structure and since the weak irradiation selectively perturbs connected deuterium transitions we conclude that the two splittings have the same signs [17]. This gives a biaxiality Sxx - Syy of ~0.06, which is identical to the value found for the aromatic ring attached to the cyano group in 4-n-pentyl-4'-cyanobiphenyl [ 11 ]. In marked contrast, if the quadrupolar splitting is positive the biaxiality in S is calculated to be ~0.14, which we believe to be unreasonably large for 10CB; this supports our determination of the relative sign for the quadrupolar splitting. Finally, we must obtain the off-diagonal element Sxz from the quadrupolar splitting for the methoxy deuterons. If the methoxy splitting is negative Sxz is small (~0.05) and negative, whereas, if the splitting is positive Sxz is also small (~0.03) but positive. It is impossible to make an unambiguous choice between these two. However, a positive value of Sxz corresponds to the major principal axis for S being tilted several degrees away from the z axis towards the methoxy group. This orientation of a principal axis seems intuitively correct and so we have taken the quadrupolar splitting of the methoxy deuterons to be positive. The components of the averaged ordering matrix calculated with this choice of signs are listed in table 1. It is not possible to extract the ordering matrix for the n+ or n_ conformers from these results without 140

3 February 1984

Table 1 The temperature dependence of the elements of the Saupe ordering matrix for 10CB TNI_T(K)

Sz z a)

Sxx_Syy a)

Sx z a)

0.1 1.1 2.1 3.1 4.1 6.1 7.1 8.1 9.1 10.1 11.1 12.1 13.1 14.1 15.1 16.1 17.1 18.1 19.1 20.1 21.1 22.1 23.1

0.326 0.337 0.371 0.391 0.41 0.431 0.438 0.448 0.459 0.459 0.471 0.481 0.494 0.504 0.512 0.504 0.514 0.519 0.527 0.528 0.54 0.538 0.544

0.059 0.054 0.059 0.060 0.062 0.061 0.060 0.060 0.061 0.059 0.060 0.061 0.063 0.063 0.064 0.059 0.061 0.060 0.061 0.060 0.061 0.059 0.059

0.012 0.017 0.019 0.020 0.021 0.024 0.025 0.026 0.026 0.028 0.028 0.028 0.028 0.029 0.029 0.031 0.031 0.032 0.032 0.032 0.033 0.034 0.034

a) The errors in Szz, Sxx-Syy and Sxz are less than 1%, 2% and 3% respectively. making additional assumptions concerning the location of the principal axes for S+ or S - . However, such information should be available from the proton NMR spectrum. Indeed, we have been able to obtain a highresolution p r o t o n - {deuterium) spectrum of 10CB-d 5 in its monotropic nematic phase. The spectrum is complex partly because there are six proton spins but also because the extent of ring deuteration is not complete, and so some of the molecules contain more than six protons. Nonetheless, we are confident that, given time we should be able to analyse this spectrum and so obtain detailed information on the structure and orientational ordering for one of the simplest nematogens. It is of interest to compare the orientational order in 10CB with that in a cyanobiphenyl with an alkyl chain so as to see the influence, if any, of the chain on the order. 4-n-pentyl-4'-cyanobiphenyl (5CB) is the only nematogen for which comparable information is available, although it is the ordering matrix for

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T/TNI Fig. 4. The dependence of the order parameter Szz for the para axis of the methoxy ring in IOCB (o) and the cyano ring in 5CB (G) on reduced temperature, T/TN1.The dependence predicted by the Luckhurst-Zannoni-Nordio-Segre theory (6 = 0.15) is shown as the solid line while the broken line gives the prediction of the Maier-Saupe theory (5 = 0). the cyano ring which is known [ 11 ]. However, the two rings in cyanobiphenyl derivatives must share a common para axis, and so we are able to compare the order parameter for this axis in 10CB and 5CB. The two sets o f results are shown in fig. 4 plotted as a function o f the reduced temperature T/TNI. At the n e m a t i c - i s o t r o p i c transition the order parameters for both nematogens are the same to within experimental error but as the temperature is lowered the order parameter for 5CB increases more rapidly than for 10CB. It is tempting to ascribe this variation in behaviour to the flexibility o f the n-pentyl chain in 5CB. However, it might also result from different isobaric expansivities for the two nematogens, which should cause the average anisotropic interactions and hence the order parameters to possess different temperature dependences [ 18].

Although the diagonal elements of the average ordering matrix which we have determined for 10CB are not the principal components for either set of conformers, they might be expected to approximate closely to them. In conclusion, therefore we compare the predictions o f the L u c k h u r s t - Z a n n o n i N o r d i o - S e g r e theory [19] with the observed temperature dependence ofSzz. We use this theory rather than that o f Maier and Saupe or its other variants [ 18] since it allows for molecular biaxiality which is necessary for 10CB because o f the observed biaxiality, albeit small, in S. According to this theory, the potential o f mean torque is U(/37) = u200 [d02,0 +

26d2,2cos(2T)]

X [d02,0(/~) + 28d2,2(/3)cos(2~,)l,

(8)

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where/3, 7 are the spherical polar angles which the director makes in the principal molecular frame [ 19]. In this expression the major order parameter Szz is denoted by • ~/~ - and the biaxiality S x x - S yy is 61/2 × o,o d2,2 cos(27) where d2m,n([3) is a reduced Wigner rotation matrix. The biaxiality in the molecular interactions is characterized by the quantity 6 which is temperature independent and vanishes in the limit o f molecular cylindrical symmetry. The strength parameter u200 is the average of a coefficient in the anisotropic pair potential over all molecular separations. The principal components o f the ordering matrix are obtained by solving the consistency conditions and the n e m a t i c isotropic transition temperature from the orientational free energy [ 19]. For a given 8, the biaxiality Sxx - Syy is a unique function of Szz which can be used to estimate 8; from the results listed in table l, 6 is found to be 0.15. Using this value we have calculated the dependence o f Szz on the reduced temperature; these results are shown as the solid line in fig. 4 and are clearly in good agreement with experiment. It is often argued that because the observed biaxiality in the ordering matrix is so small the l:nolecules may be assumed to be cylindrically symmetric [ 20]. To demonstrate the limitations o f such an argument we also show as a broken line in fig. 4 the temperature dependence of Szz predicted when 8 is zero, i.e. by the M a i e r - S a u p e theory. There is clearly a large difference between the major order parameter Szz predicted for uniaxial molecules and that for biaxial particles even though the biaxiality in $ is indeed small. We are grateful to the Science and Engineering Research Council for the award of an Advanced Research Fellowship to DLT as well as providing a fellowship for KH and a grant towards the cost of the NMR spectrometer. FS thanks the Royal Society for support under the European Science Exchange Pro-

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gramme. We are especially grateful to BDH Chemicals Limited for a gift o f 4-hydroxy-4'-cyanobiphenyl.

References [1] G.R. Luckhurst and G.W. Gray, eds., The molecular physics of liquid crystals (Academic Press, New York, 1979). [2] G.R. Luckhurst, S. Romano and P. Simpson, Chem. Phys. 73 (1982) 337, and references therein. [3] T. Nozaki, Bull. Chem. Soc. Japan 35 (1962) 1788. [4] P.L. Sherrell and D.A. CreUin, J. Phys. (Paris) 40 (1979) C3-211. [5] G.P. Wallis, Ph.D. Thesis, cambridge University (1978). [6] G.W. Gray and A. Mosley, J. Chem. Soc. Perkin Trans. II (1976) 97. [7] G.P. Wallis and S.K. Roy, J. Phys. 41 (1980) 1165. [8] V. Gold, in: Eriedal-Crafts and related reactions, ed. G.A. Olah (Interscience, New York, 1963) p. 1253. [9] R.G. Gillis, Tetrahedron Letters (1968) 1413. [10] J.W. Emsley and G.R. Luckhurst, Mol. Phys. 41 (1980) 19. [11] J.W. Emsley, G.R. Luckhurst and C.P. Stockley, Mol. Phys. 44 (1981) 565. [12] J.W. Emsley, G.R. Luckhurst and C.P. Stockley, Proc. Roy Soc. A381 (1982) 117. [13] J.W. Emsley, C.M. Exon, S.A. Slack and A.M. Giroud, J. Chem. Soc. Perkin Trans. II (1978) 928. [14] P. Diehl and W. Niederberger, J. Magn. Reson. 9 (1973) 495. [15] J.W. Emsley and M. Longeri, Mol. Phys. 42 (1981) 315. [16] L.J. Burnett and B.H. Muller, J. Chem. Phys. 55 (1971) 5829. [17] J.W. Emsley, J.C. Lindon and J. Tabony, Mol. Phys. 26 (1973) 1485. [ 18 ] G.R. Luckhurst, in: The molecular physics of liquid crystals, eds. G.R. Luckhurst and G.W. Gray (Academic Press, New York, 1979) ch. 4. [19] G.R. Luckhurst, C. Zannoni, P.I ~'~-rdioand U. Segre, Mol. Phys. 30 (1975) 1345. [20] W.H. de Jeu, Physical properties of liquid crystalline materials (Gordon and Breach, New York, 1980).