J. Phys. Chem. 1991, 95,980-983
980
Orlentatlonai Behavior of Naphthalened, Dlssolved in Nematic Solvents C. T. Yim Department of Chemistry, Dawson College, 3040 Sherbrooke St. W.,Westmount, P.Q., Canada H 3 Z 1A4
and D. F. R. Cilson* Department of Chemistry, McGill University, 801 Sherbrooke St. W., Montreal, P.Q., Canada H 3 A 2K6 (Received: April 18, 1990; In Final Form: August 7, 1990)
The orientational order parameters of naphthalene-d8 dissolved in the nematic liquid crystal solvents EBBA, 1 132, and a 55 wt % 1132/EBBA mixture have been measured as a function of temperature. The potential energy parameters, derived from the order parameters, have been analyzed as consisting of two anisotropic terms: a long-range contribution due to the interaction between the molecular quadrupole moment of the solute and the mean electric field gradient of the medium plus a short-range term which depends upon the size and shape of the solute molecule. The results are compared with calculated values based on van der Waals dimensions and with the earlier results on substituted benzenes.
Introduction The solutesolvent interactions responsible for solute orientation in liquid crystal solvents have been the subject of much interest in recent years. Bumell and c~-workers~-~ have demonstrated that, in addition to short-range interactions, there exists a long-range interaction between the solute molecular quadrupole moment and the solvent electric field gradient, which makes an important contribution to the ordering potential, particularly for small molecules. They also showed that the average electric field gradient is zero in a 55 wt % 1132/EBBA mixture at 301.4 K, leaving the short-range interaction as the only contributor to the orientational potential. In recent studies of the orientational behavior of several mono-, di-, Lnd trisubstituted benzenes dissolved in the two nematic solvents, EBBA (a Shiff base) and 1132 (a mixture of phenyl-cyclohexyl cyanides),69 it was shown that the short-range term can be related to the shape and size of the solute molecule and that the model taking into account both long-and short-range contributions yielded calculated order parameters in reasonable agreement with the experimental results. However, since the molecular quadrupole moments were not available for the mono- and disubstituted benzenes, they had to be treated as fitted parameters for these compounds. To further probe the intermolecular interactions involving larger solute molecules, we have measured the orientational behavior of naphthalene in the same solvent systems and in the 55 wt 3 ' 1 1132/EBBA mixture. Naphthalene was chosen as it is one of the few molecules whose molecular quadrupole moment has been determined experimentally l o and t h e ~ r e t i c a l l y . ~ ~ For solute molecules containing eight or more protons, the order parameters can be more easily determined by studying the 2H NMR spectra of the corresponding deuterated species. The two order parameters required to describe the orientation of molecules with less than 3-fold but with at least C,, symmetry are usually ( I ) Burnell, E. E.; de Lange, C. A.; Snijders, J. G. Phys. Reu. 1982, ,425, 2339. (2) Burnell, E. E.; Van der Est, A. J.; Patey, G. N.; de Lange, C. A.; Snijders. J. G. Bull. Magn. Reson. 1987, 9, 4. (3) de Lange, C. A.; Snijders, J. G.; Burnell, E. E. In Nuclear Magnetic
Resonance of Liquid Crystuls; Emsley, J. W . , Ed.; Reidel Publishing Co.: Dordrecht, 1985; Chapter 8. (4) van der Est, J. G.; Kok, M. Y.;Burnell, E. E. Mol. Phys. 1987,60,397. (5) Kok, M. Y . ;van der Est, A. J.; Burnell, E. E. Liq. Cryst. 1988,3,485. ( 6 ) Yim, C. T.;Gilson, D. F. R. Cun. J . Chem. 1987, 65, 2513. (') Yim, C. T.; Gilson, D. F. R. Can. J . Chem. 1989. 67, 54. (8) Yim, C. T.;Gilson, D.F. R. Can. J . Chem. 1988.66, 1749. (9) Yim, C. 7.;Gilson, D.F. R. Can.J . Chem. 1990,68, 875. (10) Calvert, R . L.; Ritchie, G. L. D. J . Chem. Soc., Faraday Trans. 2 1980, 76, 1249.
0022-3654/91/2095-0980$02.50/0
expressed as S j 3and (SI, - SZ2). Here the 3-axis is taken to be the long molecular axis and the 2-axis to be perpendicular to the molecular plane (Figure 1). The order parameters are related to the intermolecular interaction potential, U(e,0), via the following equations s33
= (3/22)(
$
1
~
0 exp(-U(e,@)/kTJ ~ ~ sin 8 d e d e ) - t/2 (1)
(SI1 - SZZ) = (3/2Z)Jl(sin2
0 cos 2 0 exp(-U(e,0)/kq sin 8 d e dO) (2)
where
2 = IJexp(-U((e,@)/kq
sin 8 d e d@
and €3 and 0 are the polar and azimuthal angles specifying the orientation of the molecule-fixed I-, 2-, and 3-axes to the director of the liquid crystal solvent. The intermolecular interaction potential is written as U(e,0) = -ASC1)(cos20
+ B sin2 0 cos 20)
(3)
where S ( ' )is the solvent order parameter and A = ~ [ 3 -] (1/2)(a[l] B = (a[l]
+~[2])
- a[2])/(2a[3] - a [ l ] - a[2])
(4) (5)
The constants a[i] characterize the interaction energy along the corresponding axis. The parameter A reflects the potential energy difference between two solute orientations with the 3-axis parallel and perpendicular to the liquid crystal director and AB the difference between orientations with the 1-axis and 2-axis parallel to the director. Each a [ i ] consists of a long-range contribution, due to the field gradient-molecular quadrupole moment interaction, and a shapesize-dependent short-range Then A = ALR + ASR,and AB = (AB)LR + ( A B ) ~ RThe . short-range interactions are calculated by eqs 4 and 5 by assuming that the a[i]terms are proportional to the van der Waals dimensions9along each axis. The long-range terms are given by ALR = (1/2)(Q33 - (1/2)(Qii + Qzz))Fzz/S(') (AB)LR= ( 1 /4)(Qii
- Qzz)Fzz/S")
(6) (7)
where Q,, are the components of the molecular quadrupole moment tensor, and Fzz is the average electric field gradient along the liquid crystal director, the Z-axis. For both the short- and 0 1991 American Chemical Society
Naphthalene-d8 Dissolved in Nematic Solvents
1
?
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 981 TABLE I: Experimental and Calculated Potential Energy Panmeters of Naphthalene-d8" solvent A B ALR (AB)LR ASR (AB)s, B S R I I32 1.813 0.630 0.371 0.412 1.442 0.730 0.506 EBBA 1.320 0.351 -0.403 -0.447 1.723 0.908 0.527 I I32/EBBA 1.425 0.524 1.434 0.758 0.528
"Units are
5
4 Figure 1. Coordinate system and atomic labeling for naphthalene-d8. long-range interactions, the A parameter will include both solute and solvent contributions, but B should depend only on the solute properties. The solvent molecules are assumed to be rigid and uniaxial.
Experimental Section Naphthalene-da (Aldrich Chemical Co.) was used without further purification. The two liquid crystal solvents used were 1 132, a mixture of cyanophenyl-cyclohexanes and cyanobiphenyl-yclohexanes, which was supplied by BDH Chemicals Ltd., and EBBA (N-(pethoxybenzy1idene)-p-n-butylaniline),which was synthesized and purified according to the literature method." The EBBA employed in preparation of the 55 wt % 1132/EBBA mixture contained about 10% EBBA-d2. The EBBA-d2 was synthesized by first refluxing p-n-butylaniline hydrochloride in D 2 0 for several hours.I2 The resulting p-n-butylaniline-d2 (deuterated at the positions ortho to the amine group) was extracted with ether, purified, and then used to synthesize EBBA-d2. The concentrations of naphthalene-d8 in 1132, in EBBA, and in the 55 wt % 1 132/EBBA mixture were 1.7, 1.7, and 2.0 mol %, respectively. The deuterium NMR spectra were recorded with a Varian XL-300 spectrometer operating at 46.1 MHz, with an 8-ps pulse, an acquisition time of 0.2 s, and spectral widths of 40-80 kHz. To obtain an acceptable signal/noise ratio, 6000-10000 free induction decays were accumulated. Results and Discussion The 2H NMR spectrum of partially oriented molecules is dominated by the large quadrupolar splittings, Au, which can be directly related to the order parameters. For naphthalene the quadrupolar splitting of the deuteron at each inequivalent site can be written as Au = (3/4)(e2qQ/h)(S3,(3 cos2 CY - 1 + q sin2 a / 2 ) + (SI, - Sz2)(sin2CY + q(cos2 CY + 1)/3) (8) where e2qQ/h is the deuteron quadrupolar coupling constant, CY is the angle between C-D bond and the 3-axis, and q is the asymmetry parameter of the electric field gradient at the deuteron. The deuteron quadrupolar coupling constant was taken to be 181 kHzI3 and q to be 0.05,14and the structure of naphthalene-da published by Pawley and YeatsIs was used. A typical experimental spectrum, shown in Figure 2a, consists of four groups of lines symmetrically placed about the center. The outer pair of lines originates from the four equivalent deuterons at positions 2, 3,6, and 7, while the inner pair is assigned to the other set of equivalent deuterons at positions I , 4,5, and 8 (Figure I ) . Both pairs show detailed structure (Figure 2b) caused by the dipolar couplings between the deuterons. Since a personal computer (Olivetti M-24) was used for calculating the spectrum, it was not feasible to take full account of the dipolar couplings among eight interacting deuterons. Therefore, for simulating the spectral pattern of the inner pair, the deuterons I , 2, 7, 8 and 3-6 were ( I 1 ) Kelke, H.; Schuelle, B. Angew. Chem., Inf. Ed. Engl. 1969.8, 884. (12) van der Est, A. J. Ph.D. Thesis, University of British Columbia, 1987. (13) Emsley. J. W.; Hashim. R.; Luckhurst, G. R.;Shilstone, G. N. Liq. Crysf. 1986, I ; 437. (14) Emsley, J. W.; Longeri, M. Mol. Phys. 1981, 42, 315. (15) Pawley, G. S.;Yeats, E. A. Acta Crysrallogr. 1969, 825, 2009.
J molecule-' for A, ALR, (AB)LR,ASR,and ( A B ) ~ R .
TABLE 11: Calculated Potential Energy Parameters Using Molecular Dimensions and van der W u l s Radii" solvent AlvdWl AIAlvdWl BlvdWl AQ1 (AB)a1 Bo' I132 3.67 1.245 0.521 1.616 1.061 0.656 EBBA 3.67 1.107 0.521 0.704 0.130 0.184
"Units are
J molecule-' for ALA[vdW],A=', and (AB)=' and
1O-Io m for A[vdW].
treated as two identical but noninteracting groups, while for the outer pair, the deuterons 1-4 and 5-8 were treated as noninteracting groups.'3 As shown in Figure 2c, the method was found to reproduce the spectral envelope with good precision. Since the spectra are dominated by quadrupolar couplings, any errors caused by neglecting small dipolar couplings are not expected to s i g nificantly alter the magnitudes of the order parameters. The experimental values of S33and (SII - S22)of naphthalene in the three different solvents are plotted against reduced temperature in Figure 3. The plots clearly show that a higher solute orientation occurs in the phenylcyclohexane type solvent. The experimental order parameters at each temperature were used to compute the A and B terms in the potential function via eqs 1 and 2. For EBBA and 1132, the pure solvent order parameters from the literaturei6,'' were used to find the value at the same reduced temperature, since the order parameter of the solvent is a function of reduced temperature only and is independent of the solute and its concentration.I8 For the 1 1 32/EBBA mixture, a solvent order parameter was estimated from the number (mole percent) average of the order parameters of the two components at the same reduced temperature. The values of A and B showed small variations with temperature (a maximum deviation from the average of 5%) similar to that observed in our earlier studies of substituted but since the available data do not permit us to take full account of the small temperature effect on the energy parameters, only the average values of the experimental energy parameters are used in discussing the contributions of the short- and long-range interactions, and these are listed in Table I for each of the systems studied. The molecular quadrupole moment tensor components for naphthalene and the electric field gradients in the solvent are required in order to evaluate the long-range terms, A L R and (AB)LR, via eqs 6 and 7. In the two pure solvents, 1132 and EBBA, the average field gradient, Fzz, decreases with increasing temperature, and it seems reasonable to assume that it is proportional to the solvent order parameter s('), so that Fzz = FOzzS('). It is further assumed that the average electric field gradient in the solvent is independent of the size and shape of the solute molecule, and therefore, the Fzzo values can be taken as solvent-dependent constants. Using the reported datal9 for the two solvents at 298 and 320 K, we found the pzzvalues to be 2.41 X 1 O l a and -2.62 X I O t a V m-2 for 1132 and EBBA, respectively. The published v a l u e ~ 'of~ the , ~ ~molecular quadrupole moments, Q l l ,Q22,and Q33,are 23.9 X IO4, -44.4 X IO4, and 20.5 X IO4' C m2, respectively. The values of ALRand (AB)LR calculated via eqs 6 and 7 are listed in Table I. Since the terms ( Q 3 3 - (1/2NQll + Q22)) and ( Q I I - Q22) are both positive (16) Gilson, D. F. R. Unpublished results. (17) Bahadur, B.; Sarna, R. K.;Bhide. V.G. Mol. Crysf. Liq. Crysf. 1982, 72, 139. Bahadar, 8.;Sarna, R. K.; Bhide, V. C. Mol. Crysf. Liq. Crysf. 1982, 82, 183. (18) Kronberg, B.; Gilson. D. F. R.; Patterson, D. D. J . Chem. Soc., Faraday Trans. 2 1916, 72, 1673. (19) Patey, G. N.; Burnell. E. E.; Snijders, J. G.; de Lange, C. A. Chem. Phys. Lelf. 1983, 99, 271.
982
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991
I 400 HZ I
Yim and Gilson
I
400 HZ
1
Figure 2. (a) 2Hspectrum of naphthalene-d8in EBBA at 317 K. (b) Observed spectral patterns of inner (left) and outer (right) pairs. (c) Simulated spectral patterns of inner (left) and outer (right) pairs.
quantities for naphthalene, the higher orientational orders observed in 1 132 can be explained by the opposite signs of the electric field gradients in the two solvents, which yields a positive long-range contribution to the total potential in 1132 but a negative contribution in EBBA. The ASR term can be written as ASR
= ALA[vdW]
(9)
BsR = B[vdW] (10) where A[vdW] and B[vdW] are given by eqs 4 and 5, respectively, with the a [ i ]terms replaced by van der Waals dimensions. The AL constant reflects the solvent contribution to the short-range interaction energy. If different solutes experience the same mean field, AL should be a constant for a given solvent, and a plot of the experimental ASRvalues versus A[vdW] should yield a strslight line passing through the origin. In the study of substituted benzenes,'*9 reasonable correlations, as shown by the straight lines in Figure 4a,b, were observed for such plots. Using the AL values and 3.02 X IO-" J m-' molecule-' reported earlier9 of 3.40 X in 1 132 and EBBA, respectively, it is possible to derive Acalc(= A,A[vdW] + ALR). (= ALA[vdW]B[vdW] + (AB)LR), and Fa''. These values, as listed in Table 11, have been used to calculate the order parameters S,, and S22. The results are compared with the experimental values in Figure 5. Jn the case of naphthalene in 1 132, good agreement between the calculated and experimental order parameters was obtained. The results for the EBBA solvent were less satisfactory. The short-range contributions ASRand (AB),, can also be obtained by subtracting the corresponding long-range term from the cxpcrinicntal values. These "experimental" short-range pa-
rameters, given in Table I, can be compared with the calculated ALA[vdW] and B[vdW] values. The BSRvalues were found to be 0.506 and 0.527 in 1 I32 and EBBA, respectively. These values are close to the experimental B value of 0.524 in the 55 wt % 1 132/EBBA mixture, which should be equal to BSRif the average field gradient is taken to be zero in this solvent mixture. The calculated value of B[vdW] based on the van der Waals dimensionsZ0is 0.521, which is in excellent agreement with the experimental values in all three solvents. The discrepancy observed for naphthalene in EBBA can be attributed to an unexpectedly high ASRin this system (Table I). This is also clearly shown in Figure 4a,b, where the point for naphthalene in 1132 lies reasonably close to the line, but for EBBA the A S R value is too high. This could be rationalized if it is assumed that naphthalene, and other substituted benzene solute molecules, are subjected to a different local environment in this solvent. A similar conclusion, Le., different solutes are not governed by the same short-range interaction field, was obtained by Burnell and co-workers5 in their study of orientational order of solute molecules dissolved in a 55 wt % 1 132/EBBA mixture at 301.4 K. Therefore, we believe that a reasonable correlation between ASRand molecular dimensions can only be expected for molecules of similar size and properties. I n contrast, the parameter BSRis assumed to be dependent only on the solute properties and should not be sensitive to the variation in the average environments, as observed in this study. In this treatment it has been assumed that the electric field gradient is zero in the 1 132/EBBA mixture over the temperature range studied, and therefore, the average experimental energy (20) Bondi, A. J . Phys. Chem. 1964, 68,441.
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 983
Naphthalene-d8 Dissolved in Nematic Solvents 0.400
0.300
t
x1020 1.500
4RJ/molecule
s33
1.000
0.200
0.500 0.100 1
0.000
0.850
0.880
0.910
0.940
0.970
1.000
0
1
2
3
4
5
6
7
A[ vd W] xl Ot0m
TR
0.400 1132
0-0
EBBA
O....O
1132/EBBA
'
0.100 0.850
0.880
0.910
0.940
1
2.000
A--A
0.970
I 1.000
TR Figure 3. Variation of order parameters (a) Sjj and (b) (SI, - SZ2)of
naphthalene-d, with reduced temperature.
parameters A and B were taken for the AsR and BSRvalues. As mentioned above, the parameter B obtained for naphthalene, and also for the other systems studied, showed a small but definite variation with temperature. Emsley et aI.l3v2Ihave suggested that, for rigid molecules, the temperature dependence of B can be attributed to the neglect of higher rank terms in the orientation potential or to the biaxiality of the solvent molecules. In addition, a different temperature dependence of the short- and long-range interactions22may contribute to the observed temperature dependence of B. To examine the latter effect, we take advantage of the fact that the electric field gradients, Fzz,in the 5 5 wt % 1 132/EBBA-d2 mixture have been measured by Kok et aL5 as a function of the quadrupolar splitting of the deuterons of the EBBA-d2. Therefore, a solvent containing EBBA-d2 was used to prepare a solution of naphthalene-d8 in the 55 wt % 1132/EBBA mixture, and the electric field gradient at each temperature was evaluated from the observed splitting of the deuterium resonance arising from EBBA-d2. The ALR, (AB)LR,ASR,and (A& values a t each temperature were then calculated. The ratio of (AB)sR/AsR gives BSR, the corrected B value, at the corresponding temperature in the 5 5 wt % 1 132/EBBA mixture. The corrected and uncorrected B values are plotted against temperature in Figure 6. It is obvious that the correction reduces but does not eliminate the variation, and thus we conclude that, for naphthalene in 5 5 wt % I 132/EBBA, the observed temperature dependence of B can be attributed partly to the presence of the long-range interactions. The average values of ASR, ( A B ) ~ Rand , ;BsRin the 5 5 wt % 1 132/EBBA mixture are given in Table I. It IS interesting to note that they are almost the same as the short-range interaction parameters in the pure 1 1 32 solvent, which might indicate that (21)Emsley, J. W.; Luckhurst, G. R.; Shilstone, G. N.; Sage, 1. J . Chem. Soc.. Faraday Trans. 2 1987,83, 371. (22)Weaver, A,; van der Est, A. J.; Rendell, J. C. T.; Hoatson, G. L.; Bates, G.S.;Burnell, E. E. Llq. Crysr. 1987,2, 633. (23) Chablo, A,; Cruickshank, D. W. J.; Hinchliffe, A.; Munn, R. W. Chem. Phys. Lett. 1981, 78,424.
.r/
Figure 4. Experimental ASRversus A[vdW]: (a) in solvent 1132; (b) in solvent EBBA. I , benzene; 2, o-dichloro-;3, trichloro-; 4, tribromo-; 5 , o-dicyano-;6, benzoquinone; 7, monochloro-; 8, m-dichloro-;9, monobromo-; IO, monocyano-; 1 I, p-dichloro-; 12, m-dicyano-; 13, p-dibromo-; 14, p-dicyano-; A, naphthalene-d8. &+9
h
02w
/I
f 0.O00
v v)
-0.200
-0.m -0.m
-0.m
0.000
0.200,
0.100
-0.m
-0.200
S(c0l)
0.O00
0.2w
0.m
S(cal)
Figure 5. Experimental versus calculated order parameters for naphthalene-& Triangles are for S22and circles for Sj3. 0.5807
I
I
0.560
B(uncorr)
0-0
B(corr)
0
320
330
0
I
0.540--
B
0.520--
0.500.0.480 300
290
310
340
.
