ORIENTATIONAL ORDER IN p-AZOXYANISOLE, p-AZOXYPHENETOLE AND THEIR MIXTURES IN THE NEMATIC PHASE

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ORIENTATIONAL ORDER IN p-AZOXYANISOLE, p-AZOXYPHENETOLE AND THEIR MIXTURES IN

THE NEMATIC PHASE

S. Chandrasekhar, N. Madhusudana

To cite this version:

S. Chandrasekhar, N. Madhusudana. ORIENTATIONAL ORDER IN p-AZOXYANISOLE, p-

AZOXYPHENETOLE AND THEIR MIXTURES IN THE NEMATIC PHASE. Journal de Physique

Colloques, 1969, 30 (C4), pp.C4-24-C4-27. �10.1051/jphyscol:1969406�. �jpa-00213708�

JOURNAL DE PHYSIQUE

Colloque C 4, supplément au no 11-12, Tome 30, Nov.-Déc. 1969, page C 4 - 24

ORIENTATIONAL ORDER IN p-AZOXYANISOLE, p-AZOXYPHENETOLE AND THEIR MIXTURES IN THE NEMATIC PHASE

S. CHANDRASEKHAR and N. Y. MADHUSUDANA Department of Physics, University of Mysore, Mysore, India

Résumé. - La formule, proposée récemment par Vuks pour le champ de polarisation dans des diélectriques

molécules allongées, est appliquée ici

une mesure du taux d'alignement dans le p.azoxyanisole, le p.azoxyphénétole et leurs mélanges (en phase nématique). Cette formule permet de rendre compte avec une bonne précision des polarisabilités, et d'en extraire des valeurs du paramètre d'ordre

en fonction de la température. On trouve en particulier que, dans les mélanges,

+

où

et

Sont les fractions molaires des deux constituants.

Abstract.

The formula proposed recently

Vuks for the polarization field associated with strongly anisotropic organic molecules has been applied to evaluate the orientational order in p-azoxyanisole, p-azoxyphenetole and their mixtures in the nematic phase. It is found to yield accurate results as is confirmed by the interna1 consistency of the calculations. The degree of order

plotted against the relative temperature (Tc

gives a set of nearly parailel curves, and for a given relative temperature,

is greater the higher the nematic liquid transition point Tc. The degree of order in the mixture is expressible as

+

^wherepl,

are the mole frac- tions of the pure compounds.

1. Introduction. - The first estimates of the orien- tational order in nematic liquid crystals from optical measurements were made by Chatelain [l, 21. If the degree of orientational order is defined as

where

is the angle which the long axis of the molecule makes with the optic axis of the medium,

where

nematic medium, y II,

the principal polarizabilities of the molecule, and 7

1

+

3

showed that it is necessary to take into account the effect of the anisotropic polarization field in evaluating the polarizabilities and assumed an expression similar

to that proposed originally in the theory of Kerr effect in liquids [3, 41. Subsequently, Saupe and Maier

applied the more elaborate form of the polarization field suggested by Neugebauer [6].

Recently, Vuks [7] has proposed a new formula for the polarization field associated with strongly aniso- tropic organic molecules which he has used with success to interpret the light scattering and Kerr effect measu- rements on a number of liquids. The formula is

where

and

1, 2, 3 refers, in the general case, to the three principal refractive indices of the medium and

is the number of molecules per unit volume. In this paper, we apply this simple formula to evaluate the orien- tational order in p-azoxyanisole (PAA), p-azoxyphe- netole (PAP), and their mixtures in the nematic phase.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1969406

ORIENTATIONAL ORDER I N p-AZOXYANISOLE, p-AZOXYPHENETOLE C 4 - 2 5

2. p-azoxyanisole and p-azoxyphenetole. - We shall first summarize the available experimental data on which the present calculations have been based. The refractive indices of PAA and PAP have been deter- mined accurately in the nematic and liquid phases for 6 438, 5 890, 5 086 and 4 800 A by Chatelain and Germain [8] and in the crystalline phase for 6 500, 5 890,5 461 and 4 916 A by ChateIain [9, 101. Absolute densities in the nematic and liquid phases are known for PAA [Il], but only relative measurements have been made for PAP [12] in these phases. The relative values have been converted to an absolute scale using the observed molar volume of PAP at the nematic- liquid transition point [Il]. The density in the crystal- line phase has been derived from X-ray data

for PAA [13] the value is 1,36 and for PAP [IO] it is 1,26.

The nernatic liquid transition point Tc reported by the different investigators Vary slightly. It is assumed here that the different measurements are comparable at corresponding values of the relative temperature (Tc - T ) . Further since the density and the refractive index measurements in the nematic phase have not been made at the same relative temperatures, use was made of empirical formulae for the densities [14], which agree with the observed data to better than 0,02 %, for interpolation or extrapolation.

To test whether the polarization field is accounted for satisfactorily by equation (4), we consider the relation between the refractive indices and densities of the crystalline, nematic and liquid phases. This relation, first derived by Born [15] assuming a Lorentz field, may be expressed in terms of equation (4) as

TABLE 1

Average rnolecufar polarizability

Y X

Crystal, Room Temp.

Nematic, Te

-

7 4 1 Liquid, Tc

+

-

y

x

32,7 Crystal, Room Temp.

32,6 Nematic, Tc - T, 37

32,5 28

32,5 18

32,5 13

32,s 8

32,5 4

32,5 1

32,5

32,4 Liquid, Te

+

where N is the Avogadro's number and M is the molecular weight. Table 1 gives the values of y for the three phases calculated from equation (5) and it can be seen that the agreement is very good. Thus the condition that 7 should be the same in al1 three phases follows naturally from equation (4), whereas this result had to be assumed in previous calcula- tions [5] using Neugebauer's equation.

Since the molecules are parallel to one another in the crystal [16], the molecular polarizabilities can be deduced from the three principal refractive indices.

The calculated values for 5 890 A are

PAA

y, =

20,9 x cc.

PAP

y,,

60,l x cc.

25,O x IOpz4 cc.

Here y, is the average polarizability perpendicular to the length of the molecule. Substituting these values in equation (3), S has been evaluated for different temperatures in the nematic range for 5 890 A. The relative variation of S has been evaluated for the other wavelengths also and brought to the same scale as that for 5 890 A by equating the values at the lowest temperature. The results for the different wavelengths agree to within 1-2 % of the mean. It was also verified that equations (1) and (2) give the same values as equation (3) to within the same limits. The mean values of S are presented in Table II and the corres- ponding curves are shown in figure 1.

The values of S for PAA compare favourably with those of Glarum and Marshall [17] derived from NMR measurements, except that the latter are throughout

FIG. 1.

-

S. CHANDRASEKHAR AND N. V. MADHUSUDANA

TABLE II perature. Therefore the following relation may cer- Degree of order

PAA and PAP tainly be expected to be true

-

PAA PAP ( 1 5 1 )

( l n 2 - 1 )

Tc

407

Tc

438

- P I - ~

T, - T s ^{T, - T} s

+ 2

P +

28 0,680

18 0,637 where pl and

are the molar proportions of PAA 13 0,609 and PAP. The density of the mixture could therefore 8 0,573 be evaluated a t different temperatures. The density 4 0,535 was also evaluated on the assumption that the volumes

0,494 of the two constituents are additive a t the same rela- tive temperature. The two calcuIations agree to slightly higher.

are brought to

within 0,4 % for al1 wavelengths and temperatureS.

However, when the two sets of values The effective principal molecular polarizabilities of the same scale by using a factor the mixture are evidently

\,

the agreement is excellent over the entire nematic (~Jrnix

P ~ ( Y I ) P A A + PZ(YI)PAP range.

From equations (3) and (7) the degree of order in the mixture Sm has been worked out for every tem- 3' Mixtures

p-azoxyaniso'e and p-azoxyphene- perature and composition. The values, averaged for - and are completely in the four wavelengths, are presented in Table III, and the nematic sfate [18, 191. The refractive indices of mix-

corresponding curves for two compositions are shown tures of various compositions have been measured by

in Fig. 1. At a given relative temperature the following Chatdain and Germain Pl. As bas been shown earlier, relation is found

be satisfied to better than 1-2 %

the average molecular polarizability 7 is practically

the same in al1 three phases and independent of tern- Sm

PI SPA, + Pz SPAP (8) TABLE III

Degree of order

mixtures

(*)

(Prof. P. Chatelain has informed us that the compositions reported in the original paper [8] are expressed

as weight fractions,

of PAP. In the present calculations, however, they have been converted to mole fractions p,.)

ORIENTATIONAL ORDER IN p-AZOXYANISOLE, p-AZOXYPHENETOLE C 4 - 2 7

A relation similar to equation (8) connecting the

principal refractive indices of the mixture with those of the pure compounds has been established pre- viously by Chatelain and Germain [SI.

4. Concluding remarks.

From the interna1 consis- tency of the calculations it is concluded that the aniso- tropic polarization field in nematic liquid crystals is represented accurately by the Vuks equation and that the degree of orientational order evaluated on the basis of the equation is quite reliable. The calcula- tions also bring out the fact that the degree of order plotted against relative temperature does not fa11 on a common curve. A similar result has been established by Chen et al. [20] from systematic paramagnetic resonance experiments on a number of nematic liquid crystals. The observed departure from a common curve implies that the intermolecular potential energy func- tion proposed by Maier and Saupe [21] has to be modified. A more general form of the function taking into account the dispersion, dipole-dipole, induction and repulsion interactions has been derived recently by Chandrasekhar et al. [14]. However, contrary to the trend observed by Chen et al. [20], the present

FIG. 2. -- Variation of S with Tc for differcnt relative temprratures.

results appear to show that the higher the nematic- liquid transition point the greater is the degree of order at a given relative temperature (Fig. 2).

Finally, it is a pleasure to express Our thanks to Professor P. Chatelain and Madame Monique Brunet- Germain for giving us additional data on the mixtures of p-azoxyanisole and p-azoxyphenetole, such as tran- sition temperatures etc., which had not been included in their paper [8]. One of us (N. V. M.) is grateful to CSIR (India) for a fellowship.

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