この論文は国立情報学研究所の電子図書館事業により電子化されました

Hayashi, Kenichi

Hidaka, Yoshiki

Kai, Shoichi

Kyoto University Research Information Repository

TitleELECTROHYDRODYNAMIC CONVECTION IN PLANARAND HOMEOTROPIC SYSTEMS OF NEMATIC LIQUIDCRYSTALS(Session III : Complex Fluids, The 1st TohwaUniversity International Meeting on Statistical PhysicsTheories, Experiments and Computer Simulations)Author(s)Hayashi, Kenichi; Hidaka, Yoshiki; Kai, ShoichiCitation物性研究 (1996), 66(3): 504-505Issue Date1996-06-20URL http://hdl.handle.net/2433/95793RightType Departmental Bulletin PaperTextversionpublisherKyoto UniversityELECTROHYDRODYNAMIC CONVECTION IN PLANAR ANDHOMEOTROPIC SYSTEMS OF NEMATIC LIQUID CRYSTALSKenichi Hayashi, Yoshiki Hidaka and Shoichi KaiDepartment ofApplied Physics, Faculty ofEngineering,Kyushu University,Fukuoka 812-81, JapanIntroductionWhen the voltage above a critical value is applied to a thin layer of nematic liquid crystals, theelectrohydrodynamic convection (EHC) occurs due to their anisotropies of viscosities, dielectric, andelastic constants. This instability, especially in a planar alignment (PA) system, has been studiedextensively for the typical subject of the nonlinear-nonequilibrium phenomena [1,2]. On the otherhand, less studies in a homeotropic alignment (HA) system have been done so far, because EHC inHA has been thought that it was nothing different from one in PA. But recently some new theoreticalpredictions have been proposed and they have demonstrated important differences between EHCs inPA and HA by use of computer simulations. Thus EHC study in the homeotropic structure also beginsto attract our interests [3-5t.'We experimentally investigate the stability and formation processes of convective patterns in PAand HA in this background and try to compare our experimental results with theoretical ones.Fig. 1 : Stability diagram of nonnal rolls inone-dimaosional planar system.0.40.30.0 0.1 0.2Q=(q - qc) / qcI./-/Ix .4x x :.x xl.>oo<xxx x x x x/ •>oo<xx x X X X ~ •)O()(x X X X X x... •. eo<xxx x x ./••'-tIP<X x X x x Z' •~:~ ~ ~ ~"'..">e.x ~..1<0.00 .....................~-...L_~ ...............................................~-0.2 -0.10.05I~ 0.15'-'II 0.10~S? 0.200.30"u~ 0.25Planar Alignment CaseFirstly in PA system, weakly nonlinear aspects can be modeled for example by the Swift-Hohenbergequation and TOOL equation, and in one dimensional system the stability diag~ of convective rollsis theoretically obtained from these equations. In the real system, however, it has been difficult torealize the pure one-dimensional situation. Thus, the comparison between theoretical and experimentalresults in one-dimensional system has not yet done so far..Here, we tried experimentally to obtain the stability diagram of one-dimensional EHC in PA usinga transparent electrode prepared specially by following manners. We used the nematic liquid crystal,MBBA with its parallel conductivity 3.30x1o-9 Q-1cm-1and perpendicular one 2.34 x 10-9 Q-1cm-1bydoping of TBAB 0.012 wt%. Then it is filled between two glass plates both of which were coated withtransparent electrodes. One of them was lithographically etched as a form of stripe in 30 ± 2 pm widthand in 1cm length. The layer thickness waschosen as 50pm so as to be one-dimensionalsystems.In order to investigate the stability of normalrolls with a given wave number q. thecharacteristics in EHO was used such that thewave number of normal rolls depend on theapplied frequency. First, we prepare normalrolls with a given wave number q by setting thefrequency f1" Then the frequency are changedto the standard frequency fo with maintainingthe deviation s from threshold. We call this thefrequency-jump meth~. In this manner we cancompulsively prepare the normal rolls with thedesired deviation of wave number Q(=(q-q)/q).- 504-and test its stability. Where qo is a critical wave number at/a, and in our experiment,jo has beenchosen as 800Hz. Repeating this procedure for many different values of q,jand voltage V, we candetermine the stability range of normal rolls as a function of q and V, i.e. the Busse balloon.We clarified that the normal rolls state exhibits three kinds of behavior by using this experimentalprocedure. The first situation is that after a convective pattern entirely disappears new convectivepattern with a different wave number appears. The second is that the wave number changes throughthe annihilation or the nucleation of rolls after the frequency of the applied field was jumped. Thirdly,essentially no change of initial patterns happens for the jump of the frequency of the applied field.These behavior is classified clearly as three areas on the stability diagram as shown in Fig. 1. Open,closed circles and crosses show the first, second and third situation respectively. The two boundaries,such as Neutral and Eckhaus boundary, well agree with the theoretical prediction.Fig. 2 : Phase diagram ofEHe in homeotropic system.2000•.6• •• •L!I.•o6·500 1000 1500Frequency (Hz)• Normal roll[J Zig-zag pattern... Wavy pattern• Chain patternL!I. BamboO pattern1535+o6 •• 06•+[J..[J.+[J._ [J.... Y [J •...... lil·............ [Jglil10 [J [J [J [J30Homeotropic Alignment CaseIn a homeotropic alignment system, a very different scenario can be observed for the onset of EHCfrom the planar configuration. To begin with, the homeotropic alignment becomes unstable at acritical voltage VI where the director starts to reorient and acquires a planar component. It's called asthe Freedericksz tr,ansition. With further increase of voltage V, a secondary instability leading EHCtakes place. The EHC mode with finite wavenumber is superimposed on the Freedericksz mode withzero-wavenumber (the so-called Goldstonemode). Therefore, more richness of phenomenawill expected than "in 9Je planer case.First of all, we shall classify the patterns inhomeotropic case. We experimentally investigatethe phase diagram of a two-dimensionalhomeotropic system for the applied voltage andfrequency. In order to achieve the ideal >-Freedericksz deformation we used the magnetic .'Z' 25field. By applying magnetic field to the sample Ncell in the x-directiQn, the uniform tilting of ~ 20director is set to the x-direction. Therefore,patterns could be classified distinctly and easilyanalyzed quantitatively.Fig. 2 shows the phase diagram obtained bythe above procedure. Although each pattern inthe diagram shows very interesting behavior, thedetail will be given in the complete reportpublished in the near future because of limitationof space. However we would like to stress herethat the phase diagram was quite different fromone of planar case.References(1] K. Hirakawa and S. Kai : Mol. Cryst. Liq. Cryst., 40 (1977) 261.[2] S. Kai and W. Zimmermann: Prog. Theor. Phys. 5upplement No.99 (1989) 458.[3] H. Richter, N. Klopper, A. Hertrich and A. Buka: Europhys. Lett., 30 (1995) 37.[4] S. Kai, Y. Adachi and S. Nasuno : in Spatio-Temporal Patterns in Nonequilibrium Complex Systems,SF] Studies in the Sciences o/Complexity, Peoc. Vol. XXI, edited by P.C. Cladis and P. Palffy-Muhoray (Addision-Wesley, New York, 1994).[5] A.Hertrich, W. Decker, W. Pesch and L. Kramer: J. Phys. II France ~ (1992) 1915.- 505-

ELECTROHYDRODYNAMIC CONVECTION IN PLANAR AND HOMEOTROPIC SYSTEMS OF NEMATIC LIQUID CRYSTALS(Session III : Complex Fluids, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)

http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/95793/1/KJ00004737690.pdf

ELECTROHYDRODYNAMIC CONVECTION IN PLANAR AND HOMEOTROPIC SYSTEMS OF NEMATIC LIQUID CRYSTALS(Session III : Complex Fluids, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)

Abstract

Similar works

Full text

Available Versions

Kyoto University Research Information Repository