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Molecular solutes in nematic liquid crystals: Orientational order and electric field gradients
CHEMICAL
Volume 99, number 3
PHYSICS LETTERS
5 August 1983
MOLECULAR SOLUTES IN NEMATIC LIQUID CRYSTALS: ORIENTATIONAL G-N. PATEY,
ORDER AND ELECTRIC FIELD GRADIENTS
E-E. BUBNELL
Department of Chemimy.
IJ..-versity of British Cblumbio. 2036 Main Mali. Vancouver. B.C.. Chada V6T I Y6
and J _G_SNIJDERS
and C-A. DE LANGE
Departments of Theoretical and Physical cllemimy. Free U~~iversity. De BoeleIaan 1083. IOSI HVAmterdam, l7ze NetherIan& Received 3 May 1983;in
final form 4 June 1983
The difference between liquidcrystal and gas-phase values for the nuclear quadrupole coupling constant in Dz and HD is used to obtain the mean electric field gradient in various liquid crystals. Order parameters for small molecules dissolved in liquid crystals are calculated assuming that the orientational order arises from the interaction of the molecular quadrupole moment with the averqe tield gradient. The results obtained arc in good agcement with c?lperimental values for hydrogen -and several other solutes.
An understanding of the mechanism of orientational order is of fundamental importance in the theory of liquidcrystalline systems. At present the interactions responsible for orientational ordering are not well understood,and the study of small molecules dissolved in anisotropic environments provides a logical starting point for a systematic investigation. In recent studies of methane [l-3] and hydrogen [3,4] * the observed ordering is attributed to interactions which can be expressed in secondorder tensorial form, but the physical origin of these forces has not been established. Mechanisms previously suggested include interactions with the liquid crystal through dispersion forces [5] , the polarizability anisotropy [I], size and shape [6], and moments of inertia [7,8] of the solute molecule. However, these models do not adequately explain many experimental results. For example, it is difficult to understand the observed negative order parameters found experimentally for the solutes hy-
drogen [4] and acetylene [9] in some liquid crystals; the accepted dogma being that molecules should orient with their axis of greatest polarizability along the director. The results for acetylene were rationalized in terms of a two-site model [9], and for hydrogen by suggesting that it is sufficiently small to sample regions of the solvent with an average electric field different from that experienced by larger molecules [4] _ Neither of these explanations is very satisfactory_ In this letter we rationalize these and other results by showing that the interaction of the mo!ecular quadrupole moment with the average electric field gradient present in the liquidcrystal environment can largely explain the orientational ordering of small solute molecules in some nematic liquid crystals_ A molecule possessing a quadrupole moment interacts with an electric field gradient according to the equation
[lo]
(1) * The vibrational corrections reported for the B/D ratio in ref. [4] are in error. The ratio at 298 K is -2459 and at 320 K is -24.58 for Dz_
0 009-26 14/83/0000-0000/S
03-00 0 1983 North-Holland
where Qas is the molecular quadrupole moment and of the field gradient tensor. If
Fas are components
271
Volume 99. number
CHEMICAL PHYSICS LETTERS
3
the liquid crystal has cylindrical sy_mmetry as is the case in nematic phases. then it is convenient to express Pafl in the coordinate system defined by the space-fured symmetry asis,Z. xvhich will be along the magnetic vector Ho for nematic liquid crystals which orient along IIo. In this coordinate system FmP = 0 if (Y+j3, and in order to satisfy simultaneously symmetry requirements and Laplace’s equation one must have FIya = F,, = - f F,, _Then, if we consider only solute particles of C, and higher symmetry. the quadrupolar hamiltonian reduces to IiQ = -+ Fzz Qz2,, P?(COS 0) _
(3
where P,(cos 0) = 4 (3 co& - I), B describes the orientat&n of the molecular symmetry asis,z, in the space-filed frame, and we have used the relationship Q_XS= rr,, = -f (2, _ In the present theory we take Fzz to be the arem@ field gradient felt by the solute p.uticle. and assume that HQ describes the interaction of the solute particle witb the Iiquidcrystal solvent, Then, the chissioal order parameter describing the orientation of the solute with respect to Z is given by S=(P~(coso))=
J~P2(cosU)esp~--HQ/kT)sir~ j; esp (-fSQjkT)sin
0 d0
6 dO (3)
where T is the absolute temperature and k the Boltunarm constant. We note that if the ratio I;‘zzQzz/k7’ is sufficiently small eq. (3) reduces [ 1 I] to S = I;;,Q2,,/10kT.
(9
in a recent study of the 1fi and 21-i isotopes of molecular hydrogen dissolved in several nematic solvertts [-&Iit ~-as found that the measured ratio of the nuclear qt’sdrupole coupling constant to the direct dipole-dipole coupling constant between tbe two nuclei WJS about sis percent lower than the gas-phase value obtained from molecular-beam magnetic resonYice measurements [13-J 3] . If we assume that this drfference results from the estramolecular electric field grctdient present in the liquid crystal. an experimental estimate of Fzz can be obtained_ The observed quadrupolar splittings are written in the form
.Y(obs) = LS(intramolecular) - f~Q,F~~lh where ~(illtrarl~olecu~r) = f (ee’qQp/il)S _ 273
,
(5)
5
Ausust 1983
In eq. (6) we use the value of S obtained from the experimental [4] dipole-dipole coupling constant in HD or D2 using the appropriate value of (l/R3) (R is the internuclear separation in hydrogen) averaged over vibrations and centrifugal distortion (see ref. [43)_ The value of the nuclear quadrupole coupling constant in the molecule, e”&&,flr, is obtained by least-squares fitting the q’(R) data of ref. [14] to the quadratic,
where R, is the equilibrium separation and .$= (R - R,)/R,_ Eqs. (9)-(14) of ref. [4] then yield the vibrationally averaged values of e2qQDlil used in eq. (6)_ This calculation of B(intramolecular) is not strictly correct [ 1 ,l S] since it assumes that S does not depend upon internuclear separation and a more rigorous calculation might lead to slightly different values of Fzz_ However. such effects should not be large. For esample, if vibrational averaging is ignored and the cquifibrium value of R is used, F,, is = 10% smaller [2f than we report. Another possibility is to use averages for the jOO>vibration-rotation state which give numbers for Fzz =s 10% larger than those we report _ For HD and D2 dissolved in various liquid crystals, values of Fzz obtained from eqs. (5) and (6) as described above are listed in table 1. These field gradients together with eq. (3) yield classical values for the order parameter_ For hydrogen quantum-mec~lanical effects are significant but a classical value consistent with our mechanism can be extracted from the experimental data [43 _ In table 1 these classical order parameters for D2 are compared with those obtained from eq. (3) The agreement between experiment -and theory is quite good in all Iiquid crystals, particularly when one considers that )IO adjtisrtzbie parameters are involved_ We have simply used the discrepancy between liquid-crystal and gas-phase values for the mrclear quadrupole coupling constant to calculate the average external electric field gradient. Eq. (3) then satisfactorily predicts the value of the order parameter which, experimentally, is obtained directly from the measured dipolar coupling constants. A further test of the theory is given in fig_ 1 where experimental order parameters are compared with theoretical results for several solutes in p-ethoxybenzy~dene-~‘-~z-butyla~~ne (EBBA). The theoretical
CHEMICAL
Volume 99, number 3
PHYSICS
LETTBRS
5 August 1983
Table 1 Averag,e electric field zzadients in various liquid crystals together wvitbcalculated and esperimental Fz
Liquid crystel a)
(1011
298 320
EBBA
a) b) c, d)
-6.39t0.13 -5.68kO.l
10 3 Sfor
esuQ
from HD
I
6.15+0.16 5.051to.39
order pammeters for D2
Ds
from Da
espt_c!
theory d)
-6.42t0.32 -6.20+0.17
-14.0 -11.9
-10.0 -8.7
1132
298 320
6.07+0_17 4.7 21.3
V
298
-5.72t0.23
-S-63+0.48
1167
310 330
-3 .OOtO.O2 -2.68t0.08
-2_96+0.04 -2.5 kO.3
10.8 8.1 -12.3 _ 5.‘ -4.2
9.7 7-2 -89 -4.5 -3.7
See ref. f4] for more infomration on the liquid crystals. I esu = 1 statvdt cm-a = 2.998 x LO6 V m”. This is the order parameter for the classical limit from table V of ref. 141 (see text). From eq. (3) using the average of the Fzz values from HD and Ds_ The vahres Q=, = 0649 x 10Az6 esu for Dz and 0.6555 x lO-26 esu for HD (ref. [ 161: He value taken for HD is the average of those reported for Dz and Hz) and &!D = (0.2860 + O_OOlS) X 1O-26 cm2 (ret [ 141) have been used_
results are obtained from eq. (3) with Fzz takento be the average of the experimental vaIues for D, and ND at 298 K (cf. table 1). We note that, except for benzene (see below), the present theory gives the correct general trend even for molecules which possess a
-8
0 26 Q,r x 10 esu
-4
4
I
8
I+$. 1. Theoretical and experimental order parameters as a function of the molecular quadrupole moment, Q,,, for several solutes iu EBBA at = 298 6. The solid line represents the theoretical result obtained from eq. (3) and the solid dots are elrpcrimentsl literature values for the molecular qua&upole moments (first reference) ;md order parameters (second reference) for the molecules C&is f17,lSj. NsO [ 17,191, Na ~20,21].CH3~~17~221~D~ [16,43,CFaH [17,22],aud CzH2
12391.
permanent dipole moment. Hence a dipolar mechanism does not appear to be important in this case. The observed negative order parameters for hydrogen and acetylene are predicted by the quadrupolar mecbanism and it is not necessary to invoke “two-site” or other models in which the orientational mechanism for these molecules is assumed to be different from that of other solutes. It is possible that some of the observed discrepancies between theory and experiment result from inaccurate values for the molecular quadrupole moments_ In particular for CH3F and CFs H the quoted f 17 ] experimental unce~a~t~es are rather large and for acetylene there is experimental evidence for values of QZZranging from 3.0 X 10vZ6 (cf. refs. ]16,Z4]) to 8.4 X lo-“” esu (cf. ref. [25]) with recent quantumchemical calculations [23] giving 734 X 10-Z6 esu_ We note that if the smaller values are correct then the calculated order parameter for acetylene is in better agreement with the experimental result_ The experimental and theoretical values for benzene are in total disagreement. In this case QZ. is negative and according
to our model
the benzene
mole-
cule should line up such that the normalto thering is parallel to the director. We would expect such an orientation to involve extra energy needed to ‘>I& aside the liquid-crystal rod-hikemolecules_ It is likely 273
Volume 99. number 3
CHEMICAL PHYSlCS LETTERS
that Iinrar ~~~~fecules cm more easily orient perpendieular fo the director by simpfy fitting between the liquid-crystal rods. We conclude that the interactian between the molecular qundrupole moment and the electric field gradient accounts for much of the orientational ordering of molecular hydroge:en dissolved in several liquid crystals. This is also shown to be the case for several other simple solutes in EBBA. It is also worth noting that the values of Fzz in table f. used in conjunction with methane results [26] lead to a consistent description of the quadrupolar coupliigs observed in deutcrated methanes in various liquid crystals [z] _However. the benzene result indicates that other effects can also play a decisive role and a systematic investigation of the various physical interactions contributing to the orientational ordering of small solute molecules is in progress. Financial support from the North Atlantic Treaty Or~lli~tioll (Grant No. 1954, EEB and CAdL) and from the Natural Sciences and Engineering Research Council of Canada (GNP and EEB) is gratefully acknowledged.
References
[ 21 J .G Snijdcr\. C..%. dc Lange and C.E. BurnelI. to be
puhlicb~d_ 13 j 3.G. SniJdcrs. C’.A. de Lanse snd EE. l.krnell. fsr& J. Chcm., to bc published. I-l] IX. IfurncIl. C..+. dc Lange and J-G. Snijdcrs. Phys. Kcv. AX (19SZ) 2339.
274
151 A. Saupe, Mol. Cryst.
1 (1966) 527.
CT_ Yim and D.F.R. Gibson, Can. 1. Chem.49 (1971) 2345 171 J.hI_ Anderson, J. %fagn. Reson.4 (1971) 231, [6J J-C. Robertson,
[S] E-T. Samulksi. Ferroelectrics 30 (1980) 83. 191 P. DiehI. S. Sskora, W. Niederberaer and E.E. BumeII. J. Magn_ Reson. 14 (1974) 260_ A.D. Buc~i~~l~, in: Advances in chemical physics, Vol. 12, intermoIecuIar forces, ed. J-0. ff irschfelder
335. N.F. Ramsey. BIolccuIar beams (Oxford Univ. Press, London, 1956). and references therein. R-F. Code and N.F. Ramsey, Phys. Rev. A4 (1971) 19-U. D.&l. Bishop and L-M. Cheung, Phys. Rev. A20 (X979) 381: R.V_ Reid Jr_ and XL. Vaida, P&s. Rev. A7 ( 1973) E.E. Burnell and C.A. de Langx Cbem_ Phys Letters 76 t1980) 268_ DE. Stogryn and A.P. Stogyn. Mol. Phys_ I1 (1966) 371. W.H. FIygxe. Chcm, Rev. 74 (1974) 653. P. Diehl, H. B%gcr and H. Zimmcrm*~~. J. Magn. Rc son. 33 (1979) 113. P-K. Bhattacbaryya and B.P. Dailey, J. Chem. Pbys. 59 (1973) 5620. W.H. Flygarc and R.C. Benson. Mol. Phys. 20 (1971) 225. E.E. Burncll and C.A. de Lange, unpublished resuIts_ N.Y.C. Lee and E-E. Burncll, unpubkbcd rcsuits. R-D. _4mos and J-H. Wiliiarns, Chcm. Phys. Letters 66 (1979) 371. .I-F.J.hf. van Pelt. J-J. Brondijk, V.WW. Ciaessen and J. Bicmond, J. Chem. SOC. Faraday Trans. II 77 (1981) 1789. S-L. Hartford, Wm.C. AlIen, CL_ h’orris, E.F. Pwrson and W-H. FIygare. Chcm- Phys. Letters 18 (1973) 153, E.E. IlurneIl -and Clri. de Lzuge, J _Chem. Phys. 76 (1982) 3474.
Volume 99, number 3
PHYSICS LETTERS
5 August 1983
MOLECULAR SOLUTES IN NEMATIC LIQUID CRYSTALS: ORIENTATIONAL G-N. PATEY,
ORDER AND ELECTRIC FIELD GRADIENTS
E-E. BUBNELL
Department of Chemimy.
IJ..-versity of British Cblumbio. 2036 Main Mali. Vancouver. B.C.. Chada V6T I Y6
and J _G_SNIJDERS
and C-A. DE LANGE
Departments of Theoretical and Physical cllemimy. Free U~~iversity. De BoeleIaan 1083. IOSI HVAmterdam, l7ze NetherIan& Received 3 May 1983;in
final form 4 June 1983
The difference between liquidcrystal and gas-phase values for the nuclear quadrupole coupling constant in Dz and HD is used to obtain the mean electric field gradient in various liquid crystals. Order parameters for small molecules dissolved in liquid crystals are calculated assuming that the orientational order arises from the interaction of the molecular quadrupole moment with the averqe tield gradient. The results obtained arc in good agcement with c?lperimental values for hydrogen -and several other solutes.
An understanding of the mechanism of orientational order is of fundamental importance in the theory of liquidcrystalline systems. At present the interactions responsible for orientational ordering are not well understood,and the study of small molecules dissolved in anisotropic environments provides a logical starting point for a systematic investigation. In recent studies of methane [l-3] and hydrogen [3,4] * the observed ordering is attributed to interactions which can be expressed in secondorder tensorial form, but the physical origin of these forces has not been established. Mechanisms previously suggested include interactions with the liquid crystal through dispersion forces [5] , the polarizability anisotropy [I], size and shape [6], and moments of inertia [7,8] of the solute molecule. However, these models do not adequately explain many experimental results. For example, it is difficult to understand the observed negative order parameters found experimentally for the solutes hy-
drogen [4] and acetylene [9] in some liquid crystals; the accepted dogma being that molecules should orient with their axis of greatest polarizability along the director. The results for acetylene were rationalized in terms of a two-site model [9], and for hydrogen by suggesting that it is sufficiently small to sample regions of the solvent with an average electric field different from that experienced by larger molecules [4] _ Neither of these explanations is very satisfactory_ In this letter we rationalize these and other results by showing that the interaction of the mo!ecular quadrupole moment with the average electric field gradient present in the liquidcrystal environment can largely explain the orientational ordering of small solute molecules in some nematic liquid crystals_ A molecule possessing a quadrupole moment interacts with an electric field gradient according to the equation
[lo]
(1) * The vibrational corrections reported for the B/D ratio in ref. [4] are in error. The ratio at 298 K is -2459 and at 320 K is -24.58 for Dz_
0 009-26 14/83/0000-0000/S
03-00 0 1983 North-Holland
where Qas is the molecular quadrupole moment and of the field gradient tensor. If
Fas are components
271
Volume 99. number
CHEMICAL PHYSICS LETTERS
3
the liquid crystal has cylindrical sy_mmetry as is the case in nematic phases. then it is convenient to express Pafl in the coordinate system defined by the space-fured symmetry asis,Z. xvhich will be along the magnetic vector Ho for nematic liquid crystals which orient along IIo. In this coordinate system FmP = 0 if (Y+j3, and in order to satisfy simultaneously symmetry requirements and Laplace’s equation one must have FIya = F,, = - f F,, _Then, if we consider only solute particles of C, and higher symmetry. the quadrupolar hamiltonian reduces to IiQ = -+ Fzz Qz2,, P?(COS 0) _
(3
where P,(cos 0) = 4 (3 co& - I), B describes the orientat&n of the molecular symmetry asis,z, in the space-filed frame, and we have used the relationship Q_XS= rr,, = -f (2, _ In the present theory we take Fzz to be the arem@ field gradient felt by the solute p.uticle. and assume that HQ describes the interaction of the solute particle witb the Iiquidcrystal solvent, Then, the chissioal order parameter describing the orientation of the solute with respect to Z is given by S=(P~(coso))=
J~P2(cosU)esp~--HQ/kT)sir~ j; esp (-fSQjkT)sin
0 d0
6 dO (3)
where T is the absolute temperature and k the Boltunarm constant. We note that if the ratio I;‘zzQzz/k7’ is sufficiently small eq. (3) reduces [ 1 I] to S = I;;,Q2,,/10kT.
(9
in a recent study of the 1fi and 21-i isotopes of molecular hydrogen dissolved in several nematic solvertts [-&Iit ~-as found that the measured ratio of the nuclear qt’sdrupole coupling constant to the direct dipole-dipole coupling constant between tbe two nuclei WJS about sis percent lower than the gas-phase value obtained from molecular-beam magnetic resonYice measurements [13-J 3] . If we assume that this drfference results from the estramolecular electric field grctdient present in the liquid crystal. an experimental estimate of Fzz can be obtained_ The observed quadrupolar splittings are written in the form
.Y(obs) = LS(intramolecular) - f~Q,F~~lh where ~(illtrarl~olecu~r) = f (ee’qQp/il)S _ 273
,
(5)
5
Ausust 1983
In eq. (6) we use the value of S obtained from the experimental [4] dipole-dipole coupling constant in HD or D2 using the appropriate value of (l/R3) (R is the internuclear separation in hydrogen) averaged over vibrations and centrifugal distortion (see ref. [43)_ The value of the nuclear quadrupole coupling constant in the molecule, e”&&,flr, is obtained by least-squares fitting the q’(R) data of ref. [14] to the quadratic,
where R, is the equilibrium separation and .$= (R - R,)/R,_ Eqs. (9)-(14) of ref. [4] then yield the vibrationally averaged values of e2qQDlil used in eq. (6)_ This calculation of B(intramolecular) is not strictly correct [ 1 ,l S] since it assumes that S does not depend upon internuclear separation and a more rigorous calculation might lead to slightly different values of Fzz_ However. such effects should not be large. For esample, if vibrational averaging is ignored and the cquifibrium value of R is used, F,, is = 10% smaller [2f than we report. Another possibility is to use averages for the jOO>vibration-rotation state which give numbers for Fzz =s 10% larger than those we report _ For HD and D2 dissolved in various liquid crystals, values of Fzz obtained from eqs. (5) and (6) as described above are listed in table 1. These field gradients together with eq. (3) yield classical values for the order parameter_ For hydrogen quantum-mec~lanical effects are significant but a classical value consistent with our mechanism can be extracted from the experimental data [43 _ In table 1 these classical order parameters for D2 are compared with those obtained from eq. (3) The agreement between experiment -and theory is quite good in all Iiquid crystals, particularly when one considers that )IO adjtisrtzbie parameters are involved_ We have simply used the discrepancy between liquid-crystal and gas-phase values for the mrclear quadrupole coupling constant to calculate the average external electric field gradient. Eq. (3) then satisfactorily predicts the value of the order parameter which, experimentally, is obtained directly from the measured dipolar coupling constants. A further test of the theory is given in fig_ 1 where experimental order parameters are compared with theoretical results for several solutes in p-ethoxybenzy~dene-~‘-~z-butyla~~ne (EBBA). The theoretical
CHEMICAL
Volume 99, number 3
PHYSICS
LETTBRS
5 August 1983
Table 1 Averag,e electric field zzadients in various liquid crystals together wvitbcalculated and esperimental Fz
Liquid crystel a)
(1011
298 320
EBBA
a) b) c, d)
-6.39t0.13 -5.68kO.l
10 3 Sfor
esuQ
from HD
I
6.15+0.16 5.051to.39
order pammeters for D2
Ds
from Da
espt_c!
theory d)
-6.42t0.32 -6.20+0.17
-14.0 -11.9
-10.0 -8.7
1132
298 320
6.07+0_17 4.7 21.3
V
298
-5.72t0.23
-S-63+0.48
1167
310 330
-3 .OOtO.O2 -2.68t0.08
-2_96+0.04 -2.5 kO.3
10.8 8.1 -12.3 _ 5.‘ -4.2
9.7 7-2 -89 -4.5 -3.7
See ref. f4] for more infomration on the liquid crystals. I esu = 1 statvdt cm-a = 2.998 x LO6 V m”. This is the order parameter for the classical limit from table V of ref. 141 (see text). From eq. (3) using the average of the Fzz values from HD and Ds_ The vahres Q=, = 0649 x 10Az6 esu for Dz and 0.6555 x lO-26 esu for HD (ref. [ 161: He value taken for HD is the average of those reported for Dz and Hz) and &!D = (0.2860 + O_OOlS) X 1O-26 cm2 (ret [ 141) have been used_
results are obtained from eq. (3) with Fzz takento be the average of the experimental vaIues for D, and ND at 298 K (cf. table 1). We note that, except for benzene (see below), the present theory gives the correct general trend even for molecules which possess a
-8
0 26 Q,r x 10 esu
-4
4
I
8
I+$. 1. Theoretical and experimental order parameters as a function of the molecular quadrupole moment, Q,,, for several solutes iu EBBA at = 298 6. The solid line represents the theoretical result obtained from eq. (3) and the solid dots are elrpcrimentsl literature values for the molecular qua&upole moments (first reference) ;md order parameters (second reference) for the molecules C&is f17,lSj. NsO [ 17,191, Na ~20,21].CH3~~17~221~D~ [16,43,CFaH [17,22],aud CzH2
12391.
permanent dipole moment. Hence a dipolar mechanism does not appear to be important in this case. The observed negative order parameters for hydrogen and acetylene are predicted by the quadrupolar mecbanism and it is not necessary to invoke “two-site” or other models in which the orientational mechanism for these molecules is assumed to be different from that of other solutes. It is possible that some of the observed discrepancies between theory and experiment result from inaccurate values for the molecular quadrupole moments_ In particular for CH3F and CFs H the quoted f 17 ] experimental unce~a~t~es are rather large and for acetylene there is experimental evidence for values of QZZranging from 3.0 X 10vZ6 (cf. refs. ]16,Z4]) to 8.4 X lo-“” esu (cf. ref. [25]) with recent quantumchemical calculations [23] giving 734 X 10-Z6 esu_ We note that if the smaller values are correct then the calculated order parameter for acetylene is in better agreement with the experimental result_ The experimental and theoretical values for benzene are in total disagreement. In this case QZ. is negative and according
to our model
the benzene
mole-
cule should line up such that the normalto thering is parallel to the director. We would expect such an orientation to involve extra energy needed to ‘>I& aside the liquid-crystal rod-hikemolecules_ It is likely 273
Volume 99. number 3
CHEMICAL PHYSlCS LETTERS
that Iinrar ~~~~fecules cm more easily orient perpendieular fo the director by simpfy fitting between the liquid-crystal rods. We conclude that the interactian between the molecular qundrupole moment and the electric field gradient accounts for much of the orientational ordering of molecular hydroge:en dissolved in several liquid crystals. This is also shown to be the case for several other simple solutes in EBBA. It is also worth noting that the values of Fzz in table f. used in conjunction with methane results [26] lead to a consistent description of the quadrupolar coupliigs observed in deutcrated methanes in various liquid crystals [z] _However. the benzene result indicates that other effects can also play a decisive role and a systematic investigation of the various physical interactions contributing to the orientational ordering of small solute molecules is in progress. Financial support from the North Atlantic Treaty Or~lli~tioll (Grant No. 1954, EEB and CAdL) and from the Natural Sciences and Engineering Research Council of Canada (GNP and EEB) is gratefully acknowledged.
References
[ 21 J .G Snijdcr\. C..%. dc Lange and C.E. BurnelI. to be
puhlicb~d_ 13 j 3.G. SniJdcrs. C’.A. de Lanse snd EE. l.krnell. fsr& J. Chcm., to bc published. I-l] IX. IfurncIl. C..+. dc Lange and J-G. Snijdcrs. Phys. Kcv. AX (19SZ) 2339.
274
151 A. Saupe, Mol. Cryst.
1 (1966) 527.
CT_ Yim and D.F.R. Gibson, Can. 1. Chem.49 (1971) 2345 171 J.hI_ Anderson, J. %fagn. Reson.4 (1971) 231, [6J J-C. Robertson,
[S] E-T. Samulksi. Ferroelectrics 30 (1980) 83. 191 P. DiehI. S. Sskora, W. Niederberaer and E.E. BumeII. J. Magn_ Reson. 14 (1974) 260_ A.D. Buc~i~~l~, in: Advances in chemical physics, Vol. 12, intermoIecuIar forces, ed. J-0. ff irschfelder
335. N.F. Ramsey. BIolccuIar beams (Oxford Univ. Press, London, 1956). and references therein. R-F. Code and N.F. Ramsey, Phys. Rev. A4 (1971) 19-U. D.&l. Bishop and L-M. Cheung, Phys. Rev. A20 (X979) 381: R.V_ Reid Jr_ and XL. Vaida, P&s. Rev. A7 ( 1973) E.E. Burnell and C.A. de Langx Cbem_ Phys Letters 76 t1980) 268_ DE. Stogryn and A.P. Stogyn. Mol. Phys_ I1 (1966) 371. W.H. FIygxe. Chcm, Rev. 74 (1974) 653. P. Diehl, H. B%gcr and H. Zimmcrm*~~. J. Magn. Rc son. 33 (1979) 113. P-K. Bhattacbaryya and B.P. Dailey, J. Chem. Pbys. 59 (1973) 5620. W.H. Flygarc and R.C. Benson. Mol. Phys. 20 (1971) 225. E.E. Burncll and C.A. de Lange, unpublished resuIts_ N.Y.C. Lee and E-E. Burncll, unpubkbcd rcsuits. R-D. _4mos and J-H. Wiliiarns, Chcm. Phys. Letters 66 (1979) 371. .I-F.J.hf. van Pelt. J-J. Brondijk, V.WW. Ciaessen and J. Bicmond, J. Chem. SOC. Faraday Trans. II 77 (1981) 1789. S-L. Hartford, Wm.C. AlIen, CL_ h’orris, E.F. Pwrson and W-H. FIygare. Chcm- Phys. Letters 18 (1973) 153, E.E. IlurneIl -and Clri. de Lzuge, J _Chem. Phys. 76 (1982) 3474.