ORDER PARAMETERS IN SA, SC AND N PHASES BY X-RAY DIFFRACTION

HAL Id: jpa-00218742

https://hal.archives-ouvertes.fr/jpa-00218742

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ORDER PARAMETERS IN SA, SC AND N PHASES BY X-RAY DIFFRACTION

A. Leadbetter, P. Wrighton

To cite this version:

A. Leadbetter, P. Wrighton. ORDER PARAMETERS IN SA, SC AND N PHASES BY X-RAY DIFFRACTION. Journal de Physique Colloques, 1979, 40 (C3), pp.C3-234-C3-242.

�10.1051/jphyscol:1979346�. �jpa-00218742�

JOURNAL DE PHYSIQUE Colloque C3, supplément au no 4, Tome 40, Avril 1979, page C3-234

ORDER PARAMETERS IN SA, SC AND N PHASES BY X-RAY DIFFRACTION

A. J. LEADBETTER and P. G. WRIGHTON

Chemistry Department, University of Exeter, Exeter, EX4 4QD, England Résumé. ^- On a mesuré la diffusion des rayons X sur les mésophases nématique et smectique A des trois cristaux liquides :

408 : N-(pl-butoxybenzy1idine)-p-n-octylaniline, TBBA : téréphthal-bis-butylaniline,

IBPBAC : isobutyl-4-(4'-phénylbenzylidèneamino) cinnamate et sur la phase smectique C de TBBA.

Dans tous les cas, la fonction de distribution pour l'orientation des grands axes moléculaires est déterminée et comparée avec la théorie du champ moyen.

Les valeurs de ( P , ) et ( P, ) sont obtenues, et pour 408 sont en bon accord avec les valeurs expérimentales obtenues avec d'autres méthodes.

Dans les phases smectiques, les paramètres d'ordre de la distribution moléculaire dans les couches sont obtenus avec l'assomption d'une distribution gaussienne et sont données les valeurs ( Z 2 ) I l 2 .

Abstract. - X-ray diffraction measurements have been made on the nematic and smectic A phases of three compounds :

408 : N-(pl-butoxybenzy1idine)-p-n-octylaniline, TBBA : terephthal-bis-butylaniline,

IBPBAC : isobutyl-4-(4'-phenylbenzylideneamino) cinnamate.

Additional measurements have been made on the smectic C phase of TBBA.

In al1 cases the distribution function for the orientation of the long molecular axes relative to the director has been determined and compared with the simple mean field theory. Values of ( P2 ) and ( P, ) have also been obtained and for 408 are in excellent agreement with results obtained by other techniques.

For the smectic phases order parameters characterising the distribution of the molecules in the layers have been obtained under the assumption of Gaussian distributions and values for the rms displacements ( 2' )Il2 are given.

1. Introduction. - Following earlier work of Fal- more it was pointed out by McMillan [4] that the gueirettes and de Lord on PAA [l} we have developed smectic layer distribution functions are directly related the use of X-ray diffraction methods to determine to the intensity of the layer reflections [see also 2, 31.

orientational distribution functions of the molecular We have chosen three substances on which to long axes (m) relative to the director (n) for smectic A develop these techniques further. Each has nematic and C phases as well as nematic phases [2, 31. Further- and smectic A phases and TBBA also has a smectic C

phase. They are as follows :

Crystal SB --+ ^{49 "C} SA- ^{63°C N}

-

ii) terephthal-bis-butylaniline

H H

TBBA : H,C4-@N=&-@-&=N-@-C4H9

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979346

ORDER PARAMETERS IN SA, Sc AND N PHASES BY X-RAY DIFFRACTION

iii) isobutyl-4-(4' phenylbenzylideneamino) cinnamate

408 was chosen as an example of the extensively studied n0.m series and the one for which the order parameters ( P,(cos p) ) and ( P,(cos p) ) charac- terising the singlet orientational distribution function have been determined by Shen Jen et al. [6] using a Raman technique. Relative values for ( P , ) from dielectric anisotropy also exist for this compound.

Comparison with these results was intended to demonstrate the validity of Our techniques.

TBBA was examined because this is perhaps the most extensively studied liquid crystalline material and in particular there have been suggestions from analysis of incoherent quasi elastic neutron scattering (IQENS) experiments of unusually low orientational order parameters in the Sc and SA phases [7, 81.

The more ordered smectic phases E and B of IBPBAC have been carefully studied in our laboratory by X-ray and IQENS experiments [9] and the latter

FIG. 1. - A typical intensity contour map of a nematic phase.

C3-236 A. J. LEADBETTER A N D P. G. WRIGHTON

technique has also been applied to the SA phase.

These results have suggested that the smectic phases are relatively highly ordered and we have therefore measured the order parameters in SA and nematic phases as a part of this total programme.

2. Experimental. - CuKa (1.54 A) radiation monochromated by a graphite crystal and collimated to a small ( x 1.5 mm diameter) beam, was used as the X-ray source for the camera. Flat plate photo- graphs were taken with exposure times of 2-4 hours depending on the material. The smectic layer reflec- tions were visible in a few minutes but longer exposures were required for the analysis of the diffuse scattering of the equatorial axes. The optical density of the X-ray photographs was measured by the S.R.C.

microdensitometer service at Daresbury Laboratory from which contour maps (Fig. 1) or intensity along any locus (Fig. 2) are readily obtained. The samples were supplied by Dr. G. W. Gray and were used without further purification. They were contained in 1 mm Lindemann glass tubes which were mounted with a heater and thermocouple in a copper block.

A Eurothenn Temperature Controller was used to maintain a steady temperature

+

Photographs were taken in the nematic phase after cooling the samples in the field ( x 0.3 T) of a small permanent magnet which gave an aligned specimen.

In this phase the magnet remained in position through- out the experiment. For the smectic phase photo- graphs the samples were cooled at 250/h in a 2 T electromagnet from the isotropic into the smectic phase and then transferred into the camera. Once in the camera the alignment did not decrease over the time of exposure, and no in situ magnet was required.

Further details of the experimental techniques have been given in previous work [3].

3. Theoretical background. ^-, 3.1 DISTRIBUTION

NNCTION fd(P) FOR LONG MOLECULAR AXES. - The intensity Z(8) around the diffuse equatorial arc (Fig. 1) is related to the distribution function f,(P) as fol- lows [2, 31

f,(P) secV(tan2 P ^- tan2 8)-11' sin fi dB where fd(P) describes the distribution function for the orientation /? of a smalr volume relative to the director n ( p = O). This volume is the coherence volume, within which the distribution function for the molecular centres is non-random (i.e. g(r) # 1) and typically consists of 5 10 molecules. The above equation may be numerically inverted to give fd(P) and hence ( P2 ), ( P,), etc. It may be compared directly with simple mean field results

f

M(P)

or via the order parameters

<

I(@ (arbitras. scale) against 0 for 408 : a ) nematic at smectic A at 50 OC. The dashed line is the background

intensity.

Earlier work on PAA [1] and on p,n-Heptyloxy and p,n-Octyloxy Azoxybenzene [3] have shown that gene- rally &(P) may be expected to be close to the true singlet distribution function A(/?).

The effect on the analysis of the broadening of the diffraction ring in the n* direction due to poor cor- relations in structure along n may be shown to be negligibly small at least for ( P2 ) 2 0.8 [3].

3.2 THE SMECTIC LAYER DISTRIBUTION FUNC- TION f(z). ^- The distribution function normal to the layers f (z) may be written

with z, = ( cos 2 d z / d ).

ORDER PARAMETERS IN SA, Sc A N D N PHASES BY X-RAY DIFFRACTION C3-237

C3-238 A. J. LEADBETTER A N D P. G. WRIGHTON

PLATE 1 . - (a) 408 Nematic 690 ; (b) 408 Smectic A 490 ; (c) TBBA Nematic 207 OC ; (4 TBBA Smectic A 182 OC ; ( e ) TBBA Smectic A ; ( f ) TBBA Smectic C 159 OC ; (g) IBPBAC Nematic 21 1 OC ; (h) IBPBAC Smectic A 179 OC.

ORDER PARAMETERS IN SA, Sc AND N PHASES BY X-RAY DIFFRACTION C3-239

1t may easily be shown that the intensity of the 001 layer reflection is

where F(001) is the structure factor for a perfect layer and C is a constant.

In general one may choose some mode1 to evaluate F(001) but in order to obtain a very good estimate of z,, especially when there are only few reflections, indicating high disorder, it is a reasonable approxi- mation to take F(001) = constant for al1 1. Then one obtains directly the ratios z , / z 2 , etc. However, by assuming that f ( z ) is Gaussian, then

z, = exp - 2 n2 l 2 ( z2 ) / d 2 z, = 7:"

and ( z 2 ) the rrns displacement of the molecules in the layers. A good estimate of ( z2 )Il2 may in fact be obtained from the number of layer reflections observed in a standard experiment. Thus, we deter- mined experimentally under the standard exposure conditions of Our experiments that if the lth order reflection is not observed then generally

and this enables an estimate of ( z 2 )Il2 to be made very simply.

4 . Results. - The ïntensity measurements obtained from' the microdensitometer were processed and intensity contour maps and profiles were produced.

A typical contour map is shown (Fig. 1) and examples of the photographs obtained for each phase are given in plate 1.

4.1 . 1 408. ^- Typical plots of I(0) are shown for nematic and smectic A phases (Fig. 2). Background intensities which are subtracted prior to data analysis are also shown.

In the nematic phase f,(P) conforms closely to the simple Maier-Saupe mean field distribution. This is illustrated in figure 3 and also shown by the compa- rison of order parameters calculated from the actual distribution and from the best fit Maier-Saupe distri- bution which are given in table 1. The smectic A distribution does not follow so closely the mean field form and although it fits well at low angles, there is a poor fit for fl 3 300 but note that the order parameters are sufficiently high that most of the mole- cules ( fa@) sin P of figure 3) are at fi < 300.

The results for 408 agree very well with Jen et al.'s measurements as shown in figure 4, where the data are plotted against reduced temperature (TIT,,).

The diffraction pattern obtained for the SB phase of 408 is very different from that obtained for the SA and nematic due to the existence of three dimensional order. Order parameters cannot be obtained by the

FIG. 3. -Plots of the experimental distribution function fd(/3) for 408 (+) against fl compared with the best fit mean field distri- bution (solid line). The lower solid line is a plot off,@) sin p.

a) Nematic 69 OC ; b) Smectic A 50 O C , low angle data are not shown ( f d ( / 3 ) +

-

within a few % for /3 < 200.

408 order parameters Phase ( P z ) ( P ? )

- - -

SA 0.76 0.84

SA 0.75 0.82

SA 0.73 0.79

N 0.67 0.68

N 0.63 0.60

N 0.61 0.57

N 0.60 0.54

same type of analysis and these results will not be discussed further here

C3-240 A. J. LEADBETTER AND P. G. WRIGHTON

FIG. 4. - ( PZ ) and ( P, ) against T/T,,. Present expenments : 408 ( p z ) 0

( P 4 >

Data for Nematic phase IBPBAC ( P , ) only are plotted. For SA

and Sc phaseslee tables II Results of Jen et al. [6]

Raman ( P , ) + ( P4) x Dielectric anisotropy O

In both SB and SA phases only two orders of layer reflections are observed but the second order is markedly stronger for the S,. We conclude that

4.1 . 2 Conclusion. - 1. The agreement with Jen et al.'s order parameters which refer to the true singlet distribution is very good which confirms that the technique and analysis used here is valid. Hence fd(P) = f,(P>-

2. The simple mean field theory provides a very good description of the angular distribution function, especially for the nematic phase. It is somewhat less good for the SA phase. It does not however correctly predict the magnitude and temperature dependence of ( P2 ).

4.2 TBBA. - 4.2.1 Sample alignment. - Preli- minary work often showed that when a SA sample was prepared by cooling in a = 0.3 T field then a sharp layer reflection was accompanied by an equa- torial diffuse scattering which was almost isotropic (plate le). This indicates that there must be either other domains whose layer reflections do not intersect the scattering surface or there must be many molecules not in good smectic layers.

However, by careful cooling in a 0.3 T field reasonably good monodomain samples could be obtained and with a 2 T field very good alignment was produced (plate Id).

For the smectic C phase monodomain samples

were produced by tilting the sample in the field on passing through the C + A transition. On cooling through the C phase the monodomain split into a number of separate domains with misalignments of the order of 100 or more. This seems always to occur for wide smectic C ranges and we interpret it as arising from a competition between different ways of increasing the tilt angle with decreasing T : either by increasing molecular tilt relative to the fixed layer normal or by a relative longitudinal displacement of molecules resulting in an increasing tilt of the layer normal.

4.2.2 Nematic phase. - For this phase the form of &(P) fits very well to a simple mean field form as illustrated in figure 5 and shown by the values of ( Pz ) and ( Py ) in table II. The order parameters ( Pz ) and ( P, ) are also included in the plot of

FIG. 5 . - fd(fi) for TBBA : + Experimental ; - Mean field theory. Lower solid line is experimental f,(fi) sin fi. a) Nematic

at 207 OC ; b) SA at 174 OC.

ORDER PARAMETERS IN SA, Sc A N D N PHASES BY X-RAY DIFFRACTION C3-241

TBBA order parametqrs Phase

-

N N N N SA SA SA SA Sc Sc

figure 4. A comparison with the Maier-Saupe mean field mode1 shows that this does not predict very well the absolute values and the temperature depen- dence of ( Pz ).

4.2.3 Smectic A phase. - Samples were prepared in both 0.3 T and 2 T fields. From the sharpness of the 001 layer reflections the alignment appeared equally good but from analysis of I(0) around the equatorial arc the alignment of the samples was found to be field dependent as follows ( Pz ) in field of 2 T z ( Pz ) for 0.3 T

+

The background intensity gives rise to some pro- blems with this substance because there exists diffuse sheets of scattering perpendicular to n* which interfere with I(8) for O 5 60 or 700 and the two components cannot simply be separated. This reshlts in erroneous values of fd(P) at high and too small values of ( Pz ). For reasonably high order parameters (e.g.

( P ) 7 0.7) this effect is not too serious since nearly al1 molecules then have fl values 1ow enough for there to be little interference between I(8) and the diffuse bands. However, the most reliable value of ( Pz ) for the SA phase is probably that given by the fit of the simple mean field distribution to the observed fd(/3) : - (( Py )). This fit is in good agreement with the experimental distribution for

/3 2 400 (Fig. 5) which supports the above view.

These results are given in table II. The order para- meter is not a strong function of T and within the uncertainties of measurement and analysis we may conclude that

throughout the SA phase. This is in good agreement with the results of INQES [8] which gives ( Pz ) < ^0.7

with the long axis fluctuations on a, very rapid time scale (- 10-Il s). Also NQR data [IO] gives ( P, )

-

However, Our results clearly show that the order parameter must be at the upper end of the range

suggested by Volino et al. [8] and furthermore that the distribution function is undoubtedly centred at

= O. Hence the SA phase of TBBA at least is normal in that the molecules are not undergoing rapid pre- cession around a cone with a tilt angle of

-

Such a distribution would be clearly apparent in Our results [3] and can be positively excluded.

4.2.4 Smectic C phase. ^- The analysis of Sc data was very similar to that of S,. The X-ray photo- graphs (plate If) show that reasonable, but not perfect, monodomain samples were obtained and the results are included in table Il.

The apparent decrease in ( Pz ) with falling T is probably spurious and is due at least in part to the decreasing quality of the sample alignrnent discussed above.

In addition to the problems of sample alignment it must be noted that for a smectic C phase some fluctuation must occur of the centre of the distribution f(P) around the layer normal described by the azi- muthal angle a. The data analysis we have used only determines an overall average from the folding of

f (P) and f (a). However, for the monodomains used in Our experiments the tilt direction is in the plane normal to the X-ray beam so that to first order azimuthal fluctuations will have negligible effect on I(8). Taking account of uncertainties in sample alignment we therefore conclude that throughout the Sc phase ( P, ) ? 0.8.

The analysis of INQES data by Volino et al. [7]

suggest an overall ( Pz ) in the Sc phase of 0.3-0.4 which would include the contribution of the azimuthal fluctuations around the layer normal. Nevertheless it is difficult to believe that the latter could be large enough near the Sc-S, transition to give overall fluctuation of the long axis of 50-600 which would also be larger than for the higher temperature SA phase so we conclude that some doubt must be attached to the conclusions derived from the neutron data.

From the observed layer reflections the smectic layer order parameters were determined at

throughout both phases.

4.3.1 IBPBAC. ^- Studies have been made of the nematic and smectic A phases of IBPBAC and typical photographs are s h o w (plate Ig, lh). Values of ( Pz ) and ( P, ) have been obtained for the small nematic range and these are given in table III and included in figure 4.

Further analysis is required for smectic A phase due to interference for 6 > 30-400 from strong diffuse sheets of scattering (which are present in al1 the smectic phases of this compound). These preliminary results are shown in table III and we believe that they are within

+

A. J. LEADBETTER AND P. G. WRIGHTON

TABLE III IBPBAC order parameters

Phase -

N N SA SA SA SA

Smectic layer order parameters have also been obtained for the SA phase. With good alignment a third order reflection is seen and we find

<

+

4.3.2 Conclusion. - 1. The simple mean field theory gives a good description of the shape of f,(P)

for the nematic figure 6 and also for the SA phase for /? ? 250 above which angle reliable data are not yet available.

FIG. 6. - fd( ) for nematic IBPBAC at 21 1 OC : + Experimental ; - Mean field theory. Lower solid line is experimental fd(p) sin P.

2. Of the three compounds investigated here IBPBAC has clearly the most ordered SA phase but the most disordered nematic phase.

References [l] DE LORD, P., FALGUEIRETTES, J., C . R . Hebd. Séan. Acad. Sci.

260 (1965) 2468.

[2] LEADBETTER, A. J., Proceedings of NATO Advanced Study Institute Molecular Physics of Liquid Crystals, Cambridge 1977 (in press).

[3] LEADB~TER, A. J., NORRIS, E. K., Mol. Phys. (in press).

[4] MCMILLAN, W. L., Phys. Rev. A 6 (1972) 936.

[5] DOUCET, J., LEVELUT, A. M., J. Physique 38 (1977) 1163.

[6] JEN, S., CLARK, N. A., PERSHAN, P. S., PRIESTLEY, E. B., J . Chem. Phys. 66 (1977) 4635.

[7] VOLINO, F., DIANOUX, A. J., HERVET, H., J. Physique Colloq.

37 (1976) C3-55.

[8] VOLINO, F., DIANOUX, A. J., HERVET, H., MOI. Cryst. Liq.

Cryst. 38 (1977) 125.

[9] RICHARDSON, R. M., LEADBETTER, A. J., FROST, J. C., Ann.

Phys. 3 (1978) 177.

[IO] SELIGER, J., OSREDKAR, R., ZAGAR, V. and BLINC, R., P h p . Rev. Lett. 38 (1977) 41 1.

VOLINO, F. and DIANOUX, A. J., Phys. Rev. Lett. 39 (1977) 763.