High resolution study of the compression modulus B in the vicinity of the nematic-smectic A transition in 60CB/80CB mixtures

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1 High resolution study of the compression modulus B in the vicinity of the nematicsmectic A transition in 60CB/80CB mixtures H.J. Fromm To cite this version: H.J. Fromm. High resolution study of the compression modulus B in the vicinity of the nematicsmectic A transition in 60CB/80CB mixtures. Journal de Physique, 1987, 48 (4), pp < /jphys: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1987 HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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.

2 On The J. Physique 48 (1987) AVRIL 1987, 647 Classification Physics Abstracts M High resolution study of the compression modulus B in the vicinity of the nematicsmectic A transition in 60CB/80CB mixtures H.J. Fromm Physikalisches Institut der Universität Münster, Domagkstr. 75, D4400 Münster, F.R.G. (Requ le 21 août 1986, accepte le 18 dgcembre 1986) 2014 Résumé. emploie une technique de diffusion de lumière à haute résolution pour étudier la dépendance en température du module de compression B des couches moléculaires de la phase smectique A au voisinage de la transition nématiquesmectique A. En utilisant des mélanges des cristaux liquides 60CB et 80CB, nous trouvons que B suit une loi de puissance de la forme B B0(TcT)~. La grandeur du saut de B à la transition est plusieurs ordres de grandeur plus faible que les valeurs données par Fisch et al. B0 semble ne pas dépendre de la composition des mélanges. Le préfacteur 2014 Abstract. temperature dependence of the compression modulus B of the molecular layers in the smectic A phase has been studied in the vicinity of the nematic to smectic A transition by highresolution lightscattering studies. Using mixtures of the liquid crystals 60CB and 80CB it is shown that B obeys a simple power law of the form B B0(TcT)~. The magnitude of a discontinuity jump of B at the transition temperature compared with values of Fisch et al. is found to be smaller by orders. The prefactor B0 appears to be independent of the concentration of the mixtures. The transition from the nematic phase to the smectic A phase is characterized by the onset of a layered structure at Tc. In contrast to smectic C phases the thickness of the layers is only determined by the length of the molecules or the molecular aggregates [1]. For many applications the layered structure can therefore be regarded as incompressible. Detailed analysis of the transition however shows that the compression modulus is expected to increase continuously in the smectic phase obeying a power law of the form B Bo(TcT) P [2]. Moreover B should be proportional to the inverse of the longitudinal correlation length 61 which shows a critical behaviour according to a critical exponent vi (therefore vi p). Although experimental studies do not yield the expected critical exponent most of them confirm [38] the reported power law dependence. However, Fisch et al. [9] who investigated the temperature dependence of B in mixtures of 80CB (octyloxycyanobiphenyl) and 60CB (hexyloxycyanobiphenyl) found the simple power law to be applicable only in the case of pure 80CB. Increasing the molecular ratio y (60CB/80CB) they had to add a concentration dependent constant BI(y) which increases with increasing y. Such a discontinuity in B at T,, has also been discussed by Halsey and Nelson [10] who investigated the NSA transition in order to identify it with a well defined universality class. As a result of their investigations they found that the possible critical behaviour according to the relation vi 2 v 1. implies a jump discontinuity of B at Tc. vp and v 1. are the critical exponents of the longitudinal and transversal correlation length respectively. It was the aim of the work reported here to check the behaviour of B and from this to deduce some information about the nature of the transition. The particularity of the phase diagram of 60CB/8QCB mixtures which is shown in figure 1, especially the disappearing SA phase at Ymax, increases the interest in this work. The measurements were carried out utilizing lightscattering experiments. Although the compression modulus B cannot be measured directly with this method it has the advantage that the studies can be done on welldefined oriented samples without disturbing the texture. In particular this is important if smectic phases are to be investigated. If we restrict our attention to scattering geometries in which the detected straylight is only caused by Article published online by EDP Sciences and available at

3 648 Fig. 1. Phase diagram of 60CB/80CB. Form of diagram is taken from reference [13] using the optimal density model [14]. splay deformations of the director, the intensity of the scattered light can be described by For small deviations from this geometry (mode 1) one has to replace equation (1) by qj and ql are the projections of the wave vector q in respect to the director n. K1 and K3 are the elastic constants for splay and bend mode fluctuations respectively. Using typical values for K3 and B it can be calculated that K3 q2 can be neglected outside a temperature interval of some mk at the transition small or even point. Within this interval B is vanishes and K3 q2 may be taken into account. In this case K3 is an offset value in respect B (T)lq 2 to and should be detected by high resolution temperature dependent measurements. Keeping in mind that the width r of the Rayleighpeak obtained by dynamic lightscattering is related to the intensity I and the splay viscosity." s by r (ns I )1 [11] and that, q, as well as K1 are not affected by the phase transition one can obtain the temperature dependence of B either by measurements of I or r. Using a sophisticated heterodyne spectrometer including a scaledclipping autocorrelator we are able to measure the relaxation time T and herewith r of splaymode fluctuations independent of static straylight which may eventually occur. The problem of excess straylight which disturbes intensity measurements arises especially in the smectic phase. Therefore we decided to measure r. The sample is mounted in a two stage temperature is controlled by a microcomputer. It can be set and stabilized with an accuracy of oven whose ± 0.3 mk, so that measurements in the vicinity of the transition point can be carried out. Using this procedure the existence of an offset of the quantity BIKl at Tc should be detectable. In the smectic phase the scattered light strongly depends on the scattering geometry as can be seen in equation (2). Therefore the geometry has to be adjusted precisely. As a basic requirement the liquid crystal samples must have a perfectly uniform (homogeneous) alignment. The geometry in which only pure splaymode fluctuations can be detected is calculated for each sample as a function of the temperature. The laser light is polarized normal to the scattering plane and parallel to n ; the analyser lies in the scattering plane. The geometry is optimized in the experiment by maximizing the intensity of straylight in the smectic phase. Starting with this geometry the relaxation time of the dynamically scattered light is measured as a function of q. It is varied by rotating the cell about small angles 0 on an axis orthogonal to the LC cell. Choosing a geometry in which the wave vector kf of the scattered light is orthogonal to the liquid crystal cell, a rotation on the axis kf only affects qi. A representative result of such a measurement is shown in figure 2. The plotted curve is obtained by a least square fit according to equation (2). The minimum of the parabola is proportional to Kl while its curvature directly yields BIKI. For each sample these measurements have been carried out at various temperatures in order to attain some information about the existence of an offset in B or BIK, respectively. While Kl is almost constant in a temperature interval Tc 1 K T Tc + 1 K the quantity B/Kl shows the expected temperature dependence (Fig. 3). It has to be stressed that the large number of individual measure Fig. 2. Line width r as a function of the angle 0 between q and the smectic layers (Nr SA transition).

4 Double Comparison 649 Fig. 3. logarithmic plot of B/Kl of the reduced temperature t (TcT)/Tc. as a function ments necessary for obtaining a plot such as is shown in figure 2 requires very stable and uniform samples especially for y :5 Ymax where even small gradients in the concentration cause a large diffusion induced temporal drift of the transition temperature which can hardly be corrected. Measurements on samples with y > which would seem to be very interesting cannot be carried out with the required degree of accuracy. The temperature range under investigation cannot be extended significantly over three orders of magnitude in the temperature. In the vicinity of 7c the studies are restricted by time dependent shifts of Tc and at lower temperatures by the onset of textural changes which can easily be detected by comparing the results for quasihomodyne and heterodyne measurements. The inevitable drift of 7c with time was between 2mK/h and 2 mklday depending on the quality and concentration of the sample. It was calculated by carrying out the measurements several times. By this the temperature of the individual data points could be corrected within ± 0.4 mk. For each set of experimental data we performed a leastsquare fit over three orders of magnitude in the temperature according to the formulas B Bo. t " and B Bl + Ba t P. Tc is gained as a freely adjusted parameter. B1 is the maximum offset which can be brought into line with the experimental data. The results concerning the NSA transition are shown in table I. For comparison the corresponding values of Bi obtained by Fisch et al. (interpolated) are compared with our values of Bl. The transition temperature obtained by both fitting functions are almost the same. The difference is 2 mk, 0.5 mk, and 0 mk for y 0, and respectively. This implies that both fits are applicable. If one compares the experimental data of independent measurements the values of Bo/ Kl and Bó/ Kl appear reproducable within 10 %. The values of cp and (p have an absolute error of ± A comparison of Bo/Ki and Bi /Ki as well as cp and cp shows that the results of the fits are even rather insensitive to the introduction of an offset Bl. Because of the uncertainty in the absolute values of Kl the absolute values of B1 (y) is well as those of Bí/ B1 can only be estimated within a relative error of 50 %. The quality of the measurement is sufficient to fix the order of the maximum tolerable offset in B. It is clear from the results that a possible offset must be very small and can be neglected in general. This implies that possible influences of the K3 term in equation (2) can also be neglected. Confirmation by experiment of the non existence of an offset is not possible. A course for the decreasing upper limit of Bl with increasing y is due to the fact that with increasing y the value of B/Kl decreases and the intensity (at fixed angle 0) increases as can be seen in equation (2). Therefore the experimental studies can be extended over a larger interval å8 which increases the degree of accuracy of the measurements. A limit is set by the increasing sensitivity to concentration changes. Proceeding from the assumption that Kl does not sighificantly depend on the molecular ratio y one can estimate Bo(y) using extrapolated values of Kl (80CB) [12] using the temperature dependence of Kl (y) determined in our experiments. The results indicate that the dependence of Bo on the concentration of the mixture must be very weak. As stated above measurements on samples with Y 5 ymax, which were desirable, make extremely high demands on the stability of the samples and could not be carried out in the frame of this work. Evaluating the curvature of the parabolas according to figure 2 and equation (2) we found an unexpected behaviour when crossing the transition tem Table I. of the offset values B1( y) of the compression modulus B obtained by a fitting procedure to the experimental data with the according values of Fisch et al. c 1018 m2; c 1011 N1; c" 107 m2fn.

5 650 perature. If we define the curvature as positive in the smectic phase it decreases to zero when approaching Tc. Above the smecticnematic transition (in the nematic phase) it becomes slightly negative in a temperature range of about 102 K and vanishes again for higher temperatures. The maximum negative amplitude corresponds to B/Ki 2 x 1016 m 2 in the smectic phase. A quantitative analysis of this behaviour is the subject of further investigations. Up to now we cannot explain this effect taking all the known influences on the measurements in account. We have shown that the temperature dependence of the compression modulus B can be described by a simple power law without any restrictions. As the experimental data of Fisch et al. as well as ours can be fitted by a power law leading to comparable critical exponents we believe that the difference in the estimated offset value of B does not arise because of the usage of different measurement techniques. On the contrary it may be explained by different temperature ranges used, especially at large values of y. A comparison of the critical exponent of B with values of other authors [38] indicates that cp either does not depend or depends only very weakly on the nature of the liquid crystal. Unfortunately the value cp 0.30 cannot be explained by any known theory. Moreover we have shown that in the mixtures of 80CB and 60CB the prefactor Bo does not depend on the molecular ratio y. Acknowledgments. I would like to express my thanks to Prof. Dr. F. Fischer for his support and stimulating interest in this work. References [1] DE GENNES, P. G., The Physics of Liquid Crystals (Clarendon Press, Oxford) [2] DE GENNES, P. G., Solid State Commun. 10 (1972) 753. [3] BIRECKI, H., SCHAETZING, R., RODELEZ, F., LIT STER, J. D., Proceedings of the Third International Conference on Light Scattering in Solids, edit. M. Balkanski, Flammarion Sciences Paris (1975). [4] BIRECKI, H., SCHAETZING, R., RONDELEZ, F., LIT STER, J. D., Phys. Rev. Lett. 36 (1976) [5] DAVIDOV, D., et al., Phys. Rev. B 19 (1979) [6] LITSTER, J. D., et al., J. Physique Colloque 40 (1979) C3339. [7] LITSTER, J. D., GARLAND, C. W., LUSHINGTON, K. J., SCHAETZING, R., Mol. Cryst. Liq. Cryst. 63 (1981) 145. [8] LITSTER, J. D., Philos. Trans. R. Soc. Lond. A 309 (1983) 145. [9] FISCH, M. R., SORENSEN, L. B., PERSHAN, P. S., Phys. Rev. Lett. 48 (1982) 943. [10] HALSEY, Th. C., NELSON, D. R., Phys. Rev. A 26 (1982) [11] Groupe d Etude des Cristaux Liquides (Orsay), J. Chem. Phys. 51 (1969) 816. [12] MADHUSUDANA, N. V., PRATIBHA, R., Mol. Cryst. Liq. Cryst. 89 (1982) 249. [13] KORTAN, A. R., et al., Phys. Rev. Lett. 47 (1981) [14] PERSHAN, P. S., PROST, J., J. Physique Lett. 40 (1979) L27.