MOLECULAR PROPERTIES OF SOME NEMATIC LIQUIDS. I. MAGNETIC SUSCEPTIBILITY ANISOTROPY AND ORDER PARAMETER

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MOLECULAR PROPERTIES OF SOME NEMATIC LIQUIDS. I. MAGNETIC SUSCEPTIBILITY ANISOTROPY AND ORDER PARAMETER

I. Ibrahim, W. Haase

To cite this version:

I. Ibrahim, W. Haase. MOLECULAR PROPERTIES OF SOME NEMATIC LIQUIDS. I. MAG- NETIC SUSCEPTIBILITY ANISOTROPY AND ORDER PARAMETER. Journal de Physique Col- loques, 1979, 40 (C3), pp.C3-164-C3-168. �10.1051/jphyscol:1979333�. �jpa-00218729�

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JOURNAL DE PHYSIQUE Colloque C3, supplkment au no 4, Tome 40, Avril 1979, page C3-164

MOLECULAR PROPERTIES OF SOME NEMATIC LIQUIDS. I

(").

MAGNETIC SUSCEPTlBILITY ANISOTROPY AND ORDER PARAMETER

I. H. IBRAHIM and W. HAASE

Institut fiir Physikalische Chemie, Technische Hochschule Darmstadt, Germany

Abstract. - The diamagnetic susceptibility of a number of 4,4'-disubstituted phenyl benzoates and two isomers of 4,4'-disubstituted phenyl thiobenzoates are reported as a function of temperature in the solid, nematic and isotropic phases. The Merck nematic phases ZLI 1052 and ZLI 389 are also studied. The order parameters are calculated using an estimated value for the molar susceptibility anisotropy. The effect of the terminal substituents and central groups on the magnetic anisotropy is discussed. For compounds with similar chemical framework the order parameters in the case of thioesters and nitriles are higher than in the case of esters and alkoxides.

1. Introduction. - Anisotropy is the basic cha- racter of liquid crystals. It is a result of angular correlations between the molecules. Its characte- rizing order parameter can be determined by several techniques [I]. A macroscopic anisotropy is caused by subjecting a liquid crystal to an external magnetic or electric field. Under proper alignment one may obtain information about the order parameter from measurements of diamagnetic susceptibility, electric permitivity and refractive index. A knowledge of the effective molecular magnetic or electrical properties in the liquid crystalline phase and a description of the internal field are required for the order parameter determination. The internal field effects are small in the magnetic case whereas the problem of the internal electric field remains in the case of electrical permitivity and refractive index measurements.

Basically we are interested in the long-range orientational order in the nematic phase. The work to be reported here will concentrate on the study of the parameters that characterize this kind of order.

We report measurements on the diamagnetic susceptibility of four compounds of 4,4'-disubstituted phenyl benzoates

0

R = OCH3 and R' =C5Hll , (1) R=OC6H13 and R ' = C , H l l , (11) R = C,H, and R' = OC,H1, , (111) R=C5H11 and R' = OC,Hl, , (IV)

(*) Part II (Refractive Index and Order Parameter) of this series is published in the Journal de Physique, tome 40, fevrier 1979, p. 191.

nematic phase ZLI 1052 (mixture of (I) and (11)) , (V) nematic phase ZLI 389 (mixture of 86 "/, of (V) and

14 "/, of a substance with three benzene rings) (VI)

and two isomers of 4,4'-disubstituted phenyl thiobenzoates

R = C N and R t = C 5 H l 1 , 0111) R=C,H,, and R ' = C N . (VIII) These compounds were chosen in order to study the influence of the central and terminal groups.

We present in this paper new measurements on the susceptibility for the compounds 1-111 which were measured earlier in quartz ampoules [2]. The significant source of error in the old measurements was the dissolved oxygen during the sealing process.

As far as we know no susceptibility measurements were made before for the other compounds.

2. Basic equations. - The macroscopic tensor order parameter Q can be defined as

Q = G x a . (1)

where the constant G can be determined by setting

Q,,

= 1 in a perfectly aligned state and

xa

^{is the}

anisotropic part of the diamagnetic susceptibility tensor

x

(per unit volume). Hence

Q,, = G& , ^a,

B

⁼x. v, z

.

(2) G is given by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979333

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MOLECULAR PROPERTIES OF SOME NEMATIC LIQUIDS C3-165

N is the number of molecules per unit volume and

xll, x~~

^and

x~~

are the principal volume susceptibilities of an isolated molecule. If we define the macroscopic diamagnetic susceptibility anisotropy of a completely ordered nematic phase as

we obtain

This definition of the macroscopic order parameter is independent of any assumption about the rigidity of the molecules.

Rotating the diamagnetic susceptibility tensor of a single rod-like molecule by an arbitrary rotation R(cp, 0, $), where cp, 8 and $ are the Euler angles of the rotation, and then taking a statistical average, we find [3]

where

zll

and X, are the volume susceptibilities parallel and perpendicular to the director, respectively, and 0 is the angle between the long molecular axis and the director. The microscopic order parameter S is defined by

Introducing definition (7) in eq. (6) gives

Thus we can derive

and

x , = ~ - ~ S A X . ( 9 4 The average susceptibility is given by

Therefore

3 . Experimental. - The diamagnetic susceptibility was measured as a function- of temperature by the Faraday method at about 10 kOe. The net force F acting on a sample of volume V placed in a strong inhomogeneous magnetic field H that has a field gradient d H / a x in the vertical direction x is determined by

Eq. (12) can be rewritten in terms of the mass sus- ceptibility X, as

where X, = ~ / p , p is the density, and m is the inass of the sample.

The force F and the mass m were measured with an electrobalance (Cahn RG-2000). The electrobalance contributed to the accurate measurement of weight changes better than 0.002 mg. The cali-

d H

bration of H - was carried out by a measurement ax

of the force on a standard substance. The magnetic standard used was HgCo(CNS),,

The studied sample was taken to be as far as possible of the same volume as that of the standard substance and at the same place between the poles of the magnet (Bruker electromagnet B-E-20 va). The sample was put in a cylindrical quartz container which has nearly 0.1 cm3 volume. It was suspended from the balance by a quartz fibre. The measurement was carried out in vacuum to avoid any oxygen impurities in the sample. The temperature of the sample was maintained at f 0.1 OC by a heating system and a period of 15-25 min was allowed for the sample to reach the thermal equilibrium. The temperature was measured with a Chromel-Alumel thermocouple put near the sample. The accuracy of the susceptibility measurement was about 1

%.

Since the magnetic field was strong enough to align the director parallel to H, the mass susceptibility measured, with the method shown above, in the nematic phase was ( x , ) ~ ~ . In the isotropic phase as in the solid phase the molecules are randomly oriented and

?i,

was measured.

4. Evaluation of AX,. - susceptibility anisotropy may be accurately determined by mass susceptibility measurements on a single crystal. The single crystal X-ray and magnetic data for the studied compounds are not available. If AX, is not known, the order parameter cannot be separated. We shall discuss in the following three possibilities to evaluate AX,.

a) A molecule with two benzene rings is magneti- cally considered to be equivalent to the biphenyl molecule, provided that there is no conjugation between the two benzene rings of the biphenyl [5]

and the susceptibility anisotropy is completely due to the delocalized n-electrons of the benzene rings as far as the contribution of the end and central groups to the magnetic anisotropy is small with respect to those of the benzene rings.

a hat-is

[6]

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C3-166 I. H. IBRAHIM A N D W. HAASE

The molar susceptibility anisotropy AX, = AX, x M, M is the molecular weight.

b) A theoretical order parameter is predicted by Maier-Saupe (MS) theory. This order parameter depends on the parameter TVz(T)/TN, V,"(T,,). VN(T) is the molar .volume in the nematic phase at temperature T. The 'theoretical order parameter is calculated by using the density data (see part 11). By substituting this S and the susceptibility data in eq. (9a) we obtain Ax,.

c) It has been shown that log (SAX,) appears to be proportional to log (- z ) in the temperature

region z < - 0.016 [2, 71, where z = ( T - TNI)/TN,.

If the straight line section of the log (S Axg)-log ( - z) curve is extrapolated to the absolute zero, where S = 1, the intercept will yield AX,.

In an attempt to evaluate AX,,

dk

Jeu and Claas- sen [8] have used the value of 59.7 x cm3 mol-I as the sum of the anisotropies of two benzene rings in the p,pf-di-n-alkyl azoxybenzenes. This procedure may lead to an overestimation of the magnetic anisotropy. Values of the order of 50 to 55 x cm3 mol-' are found for AX, of related molecules with two benzene rings [9].

The mass susceptibilities [lo-' cm3 g- I] as a function of temperature

I 11 I11 IV

- Xg t

rOcl

- - ^Xg t PC1 Xg t PC1

-

- XP

- 6.337 41 .O - 6.639 22.0 - 6.589 27.0 - 6.748

- 6.337 48.6 - 6.639 29.5 - 6.589 37.4 - 6.748

- 6.000 49.0 - 6.519 30.4 - 6.201 38.0 - 6.536

- 5.621 50.0 - 6.037 31.0 - 5.966 39.0 - 6.095

- 5.640 51.8 - 6.054 33.8 - 5.984 42.0 - 6.109

- 5.661 53.4 - 6.072 36.0 - 6.001 43.9 - 6.121

- 5.686 55.2 - 6.089 38.2 - 6.019 45.6 - 6.131

- 5.724 56.4 - 6.106 40.8 - 6.047 48.1 - 6.148

- 5.775 58.4 - 6.140 43.1 - 6.071 52.0 - 6.180

- 5.817 60.0 - 6.192 44.8 - 6.097 54.3 - 6.204

- 5.860 61.0 ^-6.226 46.5 - 6.142 56.9 - 6.239

- 6.309 62.1 NI - 6.605 47.6 - 6.186 59.4 - 6.275

- 6.309 70.0 - 6.605 48.5NI - 6.556 60.8 - 6.306

60.0 - 6.556 61.6 - 6.342

62.5NI - 6.712 70.0 - 6.712 .

v

v 1 VII VIII

Xs t ^Xg t ["C]

. - - ^{X P} t PC1

- XP

- - -

- 5.802 20.0 - 5.888 56.0 - 6.476 61.0 - 6.574

- 5.809 24.4 - 5.897 64.8 - 6.476 74.0 - 6.574

- 5.819 29.1 - 5.931 65.4 - 6.296 74.6 - 6.271

- 5.841 33.9 - 5.943 66.0 - 5.632 75.5 - 5.755

- 5.858 38.6 - 5.964 68.0 - 5.639 77.4 - 5.771

- 5.900 43.4 - 6.009 70.2 - 5.652 79.8 - 5.788

- 5.929 48.1 - 6.047 72.0 - 5.672 83.0 - 5.812

- 5.958 51.6 - 6.074 74.8 - 5.679 85.6 - 5.820

- 6.011 54.2 - 6.093 76.8 - 5.692 87.0 - 5.837

- 6.050 57.6 - 6.159 80.0 - 5.719 89.0 - 5.870

- 6.094 59.5 - 6.200 82.2 - 5.732 91.6 - 5.881

- 6.511 61.0 - 6.243 86.5 - 5.752 93.9 - 5.919

- 6.511 62.ONI - 6.646 90.0 - 5.772 96.1 - 5.935

70.0 - 6.646 92.0 - 5.786 97.0

-

^5.976

96.3 - 5.815 98.2 - 6.046

100.2 - 5.915 99.0 NI - 6.525

101.0 - 5.972 110.0 - 6.525

102.ONI - 6.462 110.0 - 6.462

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MOLECULAR PROPERTIES O F SOME NEMATIC LIQUIDS

The nnisotrop-v of the dinmngnetic susceptibility AX, [low6 cm3 mol-l]

Compound I I1 111 IV V VI VI I VIII

- - - - - - - -

(4 55.1 55.1 55.1 55.1 55.1 58.9 55.1 55.1

Procedure (b) 52.2 -1 0.4 54.0 f 0.8 50.3 f 0.9 51.8 f 1.5 52.6 f 1.3 54.8

+

^1.4 ^57.4

+

^0.5 ^56.0^f^1.0

(c) 53.7 55.1 51.2 56.0 52.0 59.3 55.7 54.9

5. Results and discussion. - The mass susceptibilities of the compounds studied in the solid, nematic and isotropic phases are reported in table I. The values of Ax,, for the studied compounds. obtained from the three procedures described in section 4, are summarized in table 11. According to eqs. (8) and (1 I), the order parameters are calculated using the estimated values for the molar susceptibility anisotropies (procedure (a)). These values for S are shown in figures 1-3. The theoretical curve for S obtained from the MS theory is indicated in the figures

FIG. I. - Order parameter vs. reduced temperature for compounds I (A), I1 ( 0 ) and V (m). The broken line is from the MS theory.

FIG. 2. - Order parameter vs. reduced temperature for compounds I1 (O), 111 ( 0 ) and IV (a). Broken line (MS).

as a broken line. The temperature dependence of S is in satisfactory agreement with that predicted from the MS theory, but differs at temperatures close to TNl.

Values of S as a function of a reduced temperature ⁽⁷⁾for the mixture V and its components I and I1 (see Fig. 1) are found to justify the additivity rule

with

E x i = 1

i

where xi and Si are the mole fraction and the order parameter of component i, respectively.

Figures 1-3 show that the order parameters of compounds VII and VIII are higher than those of compounds I-V.

It is shown from figures 2 and 3 that the order phrameters of the isomeric compounds are nearly identical within the experimental error. This means that the order parameter is independent of the position of the terminal substituents with respect to the central group.

In the same homologous series the order parameter increases with increasing the nematic-isotropic transition temperature (Fig. 1).

Procedure (b) gives values for AxM that vary from one compound to another. The mean value for the susceptibility anisotropies of compounds VII and VIII (56.7 x cm3 mol-I) is higher than that for compounds I-V (52.2 x crn3 mol-I). This is attributed to the fact that the thioester and cyano groups in the former correspond to the ester and alkoxy groups in the latter. This indicates that the contribution of the various groups must be taken into account.

Eventhough the extrapolation procedure (c) has

0.70

0,60:

050 0.40 0.30

- o.100 - 0.07 5 - 0.050 - 0.025 O elements of the susceptibility tensor. To evaluate AX,

FIG. 3. - Order parameter vs. reduced temperature for compounds from the bond susceptibility data we draw a figure

VII (A) and VIII (V). Broken line (MS). of the molecule assuming standard values for the

- A

-

A -a

s PQ-AP,

t

^\VA- ^-em_At,V _A

- , v '

<\

_\

- 4

I I I -T

no theoretical basis, it leads to reasonable values for AxM. No information about the contribution of the various groups to the magnetic anisotropy can be obtained from this method.

The average susceptibility of a molecule can be accurately determined by adding of group susceptibility terms, assigned to atoms or bonds [lo]. An addjtive scheme can be applied to the diagonal

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C3-168 I. H. IBRAHIM A N D W . H A A S E

bond lengths and angles. The molecular axis is taken along the line joining the outer para carbon atoms of the two benzene rings assuming the molecule to be rigid. The sum of the susceptibility contributions of all the various bonds and groups parallel to the molecular axis gives (x,)

,,.

Also the sum of all contributions normal to the molecular axis gives (x,), ;

We have assumed that the contribution of the alkyl groups to be effectively isotropic, i.e. AX, = 0.

Using for benzene the value

Calculated susceptibility anisotropies for the studied groups

Group AxM [lop6 cm3 mol-'1

-

for C-0, C=O, C-S and C z N bonds the data C-C=N of Flygare et al. 1121 and for C--C bonds the value

R-C

the magnetic anisotropies are estimated to be 53.3 x 10-6cm3 mol-' for compounds I-V and 50.9 x cm3 mol-

'

for compounds VII and VIII (table 111). We selected the data from the here- mentioned references because they lead to the most convincing results.

Table I11 shows that the contribution of the ester group to AxM is nearly identical with that of the thioester group. Comparison of the calculated magnetic anisotropy for compounds I-V with that for compounds VII and VIII shows greater anisotropy for the former than for the latter. This is because the absolute contribution of the alkoxy group to AxM of a molecule is smaller than that of the cyano group. The contribution of the alkoxy group may be somewhat smaller, as the molecular structure is not known.

If the values of

AX, (55.1 and 53.3 x cm3 mol-')

for compounds I-V obtained, respectively, from the two procedures (a) and calculated are compared, we conclude that the order parameters displayed in figures 1 and 2 are reasonable. Also comparison of thevalues of AxM (55.1 and 50.9 x cm3 mol-') for compounds VII and VIII obtained from the same procedures, respectively, indicates that the order parameters presented in figure 3 are somewhat lower.

In general, we can say that for compounds which have similar chemical framework the order parameters in the case of thioesters and nitriles are higher than in the case of esters and alkoxides.

Acknowledgments. - One of us (I.H.I.) grate- fully acknowledges the financial support by the Mission Department of Egypt. We thank E. Merck, Darmstadt, for providing compounds. Part of this work was supported by the Deutsche Forschungs- gemeinschaft.

References

[ I ] See for example :

(a) DE GENNES, P. G., The Physics of Liquid Crystals (Cla- rendon, Oxford) 1974, Chap. 2 ;

(b) J E N , S., CLARK, N . A,, PERSHAN, P. S. and PRIESTLEY, E. B., J. Chem. Phys. 66 (1977) 4635 ; '$

(c) SAUPE, A. and MAIER, W . , Z. Naturyorsch. 16a (1961) 816.

[2] IBRAHIM, I. H. and HAASE, W., Z. Naturforsch. 31a (1976) 1644. ,

[3] PRIESTLEY, E. B., W O J F W I C Z , P. J. andSmNG, P.,,Introduction to Liquid Crystals (Plenum Press, New Y o r k ) 197411975, p. 74-76.

[4] FIGGIS, B. N . and NYHOLM, R. S., J. Chem. Soc. (London) Pt. IV (1958) 4190.

[5] See the crystal structure o f the biphenyl :

HARGREAVES, A. and RIZVI, S. H., Acta Cryst. 15 (1962) 365.

[6] LASHEEN, M . A., Phil. Trans. Roy. Soc. A 256 (1964) 357.

[7] HALLER, I., HUGGINS, H . A., LILIENTHAL, H. R. and MCGUIRE, T . R., J. Phys. Chem. 77 (1973) 950.

[8] DE JEU, W . H . and CLAASSEN, W . A. P., J. Chem. Phys. 68 (1978) I02.

[9] HABERDITZL, W., in Theory and Applications of Molecular Dia- magnetism, edited by Mulay, L. N . and Boudreaux, E. A.

(Wiley, New Y o r k ) 1976, Sec. 3.5 E.

[lo] PASCAL, P., Chimie GPnPrale (Masson et Cie, Paris) 1949.

[ I l l W E I S S , A. and W I T T E , H., Magnetochemie (Verlag Chemie, Weinheim) 1973, p. 74.

[I21 SCHMALZ, T . G . , NORRIS, C . L. and FLYGARE, W . H., J. Am.

Chem. Soc. 95 (1973) 7961.

[13] DAVIES, D. W., MoI. Phys. 6 (1963) 489.