Electrooptic spectroscopy of an antiferroelectric liquid crystal is carried out over a range of frequencies from 1 Hz to 100 kHz. In the antiferroelectric SmCA phase two relaxation processes are found, one at the fundamental frequency of a mode and the second at twice the frequency of a different mode. A comparison of the results of the electro-optic spectroscopy with a theoretical study of the motion of the director of an antiferroelectric helix subject to a weak alternating ﬁeld enables a determination of the origin of the relaxation processes in antiferroelectric phases. © 1998 American Institute of Physics

Kalinovskaya, O.

Panarin, Yuri

Vij, J.K.

English

Arrow@TUDublin

Technological University Dublin ARROW@TU Dublin Articles School of Electrical and Electronic Engineering 1998 The Investigation of the Relaxation Process in Antiferroelectric Liquid Crystals by Electro-Optic Spectroscopy Yuri Panarin Technological University Dublin, yuri.panarin@tudublin.ie O. Kalinovskaya Trinity College Dublin, Ireland J.K. Vij Trinity College Dublin, Ireland Follow this and additional works at: https://arrow.tudublin.ie/engscheleart2  Part of the Electrical and Computer Engineering Commons Recommended Citation Panarin, Yu. P. et al. 1998. The investigation of the relaxation process in antiferroelectric liquid crystals by electro-optic spectroscopy. Applied Physics Letters , vol. 72, no. 14, pg. 1667-1669. doi:10.1063/1.121147 This Article is brought to you for free and open access by the School of Electrical and Electronic Engineering at ARROW@TU Dublin. It has been accepted for inclusion in Articles by an authorized administrator of ARROW@TU Dublin. For more information, please contact yvonne.desmond@tudublin.ie, arrow.admin@tudublin.ie, brian.widdis@tudublin.ie. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License The investigation of the relaxation processes in antiferroelectric liquidcrystals by electro-optic spectroscopyYu. P. Panarin, O. Kalinovskaya, and J. K. Vija)Department of Electronic Engineering, Trinity College, University of Dublin, Dublin 2, Ireland~Received 25 August 1997; accepted for publication 6 February 1998!Electrooptic spectroscopy of an antiferroelectric liquid crystal is carried out over a range offrequencies from 1 Hz to 100 kHz. In the antiferroelectric SmCA phase two relaxation processes arefound, one at the fundamental frequency of a mode and the second at twice the frequency of adifferent mode. A comparison of the results of the electro-optic spectroscopy with a theoreticalstudy of the motion of the director of an antiferroelectric helix subject to a weak alternating fieldenables a determination of the origin of the relaxation processes in antiferroelectric phases.© 1998 American Institute of Physics. @S0003-6951~98!01114-0#Antiferroelectric liquid crystals ~AFLC! are prospectivematerials for the flat panel displays1 for the reason that atleast one additional stable state can be added to the bistableswitching discovered by Clark and Lagerwall2 in FLCs. Adetermination of the origin of the collective modes will allowfor a further improvement in these materials to occur withregard to their switching speeds and hence increase their use-fulness for displays and electro-optic devices. A study of therelaxation processes has been made using dielectricspectroscopy,3–6 electro-optics,4 and photon correlationspectroscopy.7 Nevertheless, the problem of finding themechanisms governing the various relaxation processes inthe antiferroelectric phase has not yet been solved and theaim of this letter is to unambiguously establish these mecha-nisms using electrooptic spectroscopy of a AFLC. Thoughthe nature of the relaxation process in SmCA phase has some-what been speculated in earlier experimental publications3–5and theoretical works,8,9 nevertheless no clear evidence isgiven and theoretical investigations are divorced from theexperiments. In this letter, the mechanism of the collectiveprocesses is found on comparing the results of the dielectricand electro-optic spectroscopy with those from the theoreti-cal investigations.We investigated the dynamics of an AFLC in the 20 mm.The sample used in experiments was AS-573 ~Hull, UK!with the phase transition sequence being as follows:6SmCA 78 °C SmCg 81 °C AF 83 °C FiLC 90 °CSmC* 93 °C SmA 106 °C Is.The cell is placed between the crossed polarizers. For theelectro-optic spectroscopy, the signal from the photo diode isfed to a lock-in amplifier with a facility of the latter beinglocked,to both the fundamental and the second-harmonic fre-quency of the signal applied across the sample.The relaxation processes observed in the SmCA phasehave been found in the previous papers.3–6 The dielectricspectra in the frequency range from 10 Hz to 1 GHz showthe existence of two collective relaxation processes and twomolecular relaxation processes in the SmCA phase and theseare denoted as Processes 0,1,2,3 with increasing of the relax-ation frequency.6 The lower frequency processes ~Process 0and Process 1! are found to exist6 only in the two antiferro-electric phases SmCA and AF phases. The frequency of Pro-cess 0 is ;2.5 kHz, whereas that of Process 1 lies between10 and 70 kHz depending on the temperature.5 Hence it canonly be concluded that these processes are specifically re-lated to the common characteristics of antiferroelectricphases; however the origin of these processes is still to beexplained. Four possible physical mechanisms, some of thesealready suggested3–5 for the collective molecular reorienta-tions in the antiferroelectric phase, are schematically pre-sented in Fig. 1:~i! A deviation from the antiferroelectric order by theazimuthal angle w, such that w changing in the oppositesense3 in the adjacent layers @Fig. 1~a!#. The mode concern-ing the fluctuation in w of the type shown in Fig. 1~a! in theantiferroelectric phase was called antiferroelectric Goldstonemode by Hiraoka et al.4 However, rotations of the directorsin the opposite directions is termed as ‘‘the antiphase mo-tion’’ by Buivydas et al.3 The terminology ‘‘antiphase mo-tion’’ or the distortion of the antiferroelectric order causedby the antiphase motion is more appropriate for the reasonthat it depicts the mechanism more clearly. The antiferro-electric Goldstone mode in our view be reserved for anotherrelaxation process @Fig. 1~c!#, the mechanism of which issimilar to that of a ferroelectric Goldstone mode.a!Author for correspondence.FIG. 1. Four different physical mechanisms for the molecular rearrange-ments in the antiferroelectric SmCA phase under the applied voltage. Ps isspontaneous polarization vector, C being the C director.APPLIED PHYSICS LETTERS VOLUME 72, NUMBER 14 6 APRIL 199816670003-6951/98/72(14)/1667/3/$15.00 © 1998 American Institute of PhysicsDownloaded 28 Jan 2012 to 147.252.227.64. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions~ii! Fluctuations in the tilt angle ~u! or the antiferroelec-tric soft mode as depicted in Fig. 1~b!.~iii! Helical Goldstone mode due to the existence of‘‘antiferroelectric’’ polarization dP @as shown in Fig. 1~c!and also see Fig. 2#. The explanation for the existence of theantiferroelectric polarization is given later, and~iv! A disturbance of antiferroelectric helix due to thedielectric anisotropy, DeE2, Fig. 1~d!.Origin of Process 0: The C directors in the adjacentsmectic layers are not completely antiparallel to each othereven in the antiferroelectric phases.3 This will give rise to the‘‘antiferroelectric spontaneous polarization’’ dP as shown inFig. 1~c!. This is found to be almost parallel to the C direc-tors ~Fig. 2!. The magnitude of such an ‘‘antiferroelectricpolarization’’ dP is estimated as follows: Taking into ac-count the typical value of the helical pitch '2000 Å and thesmectic layer thickness '40 Å, a calculation shows that theangle between the spontaneous polarization vectors in thetwo adjacent smectic layers is ;176° – 177° and the magni-tude of dP is approximately 3% of the spontaneous polariza-tion Ps . Such an ‘‘antiferroelectric polarization’’ will spiralalong the helical axis as does the polarization in a ferroelec-tric phase. Hence we can expect the dielectric relaxation pro-cess to arise from the distortion of the antiferroelectric helixsimilar to that of a ferroelectric helical Goldstone mode.Origin of Process 1: The relaxation frequency of Process1 is higher than that of Process 0. The mechanism can eitherbe the antiphase motion of the type shown in Fig. 1~a! or softmode @Fig. 1~b!# Hiraoka et al.4 suggested ‘‘antiferroelectric-like’’ Goldstone mode for this type of motion, a misleadingterminology as mentioned before. In certain investigations ofthe samples having a direct SmCA – SmA transition, this pro-cess was also assigned10 to the soft mode for the reason thatit followed a typical behavior for this mode close to thetransition temperature, i.e., relaxation frequency increasedwith temperature on either side of the transition temperature.Nevertheless, 20 °C below this temperature, the relaxationfrequency was found to decrease with decreasing tempera-ture. Although a decrease in the relaxation frequency can beexplained with an increase in the rotational viscosity by de-creasing temperature, nevertheless an unusual dependence ofDe such as that observed6 has got no proper explanation, i.e.,De decreasing instead of increasing close to the transitiontemperature. Therefore we rule out the ‘‘antiferroelectric softmode’’ as a possible physical mechanism for the Process 1.The relaxation Process 1 is therefore tentatively assigned tothe distortion of the antiferroelectric order4 caused by theantiphase motion @Fig. 1~a!#. The mechanism will later beconfirmed through electro-optic spectroscopic investigations.However, in the literature no direct evidence for the mecha-nism is given before. Note that among the four proposedmechanisms for the collective relaxation processes, the firstthree @Fig. 1~a!–1~c!# can be shown to be dielectrically ac-tive. The first two @Figs. 1~a!, 1~b!# are also electroopticallyactive at the fundamental frequency and the forth mechanismis electrooptically active at twice the frequency ~second har-monic! of mode shown in Fig. 1~c!. Therefore a comparisonof the results of the dielectric spectroscopy with electroopticscan clarify the origin of the two collective relaxation pro-cesses in SmCA phase seen in the dielectric spectra.On assuming the existence of the antiferroelectric polar-ization dP, the equation for the director motion in the anti-ferroelectric phase can be written as follows:g]w]t5K]2w]z21dPE0 cos vtcos w1De*E02 cos2 vt sin 2w , ~1!where g5gwsin2 u, K5Kwsin2 u, De*5De sin2 u/8p , gw isrotational viscosity, Kw is elastic constant, u is molecular tiltangle, w is the azimuthal angle, De is the dielectric anisot-ropy. On using the formula cos w sin w5sin(2w)/2, Eq. ~1!can be written in complex form asg]w]t5K]2w]z21dPE0e jvt cos~w!1De*2 E02~e j2vt11 !sin~2w!. ~2!On assuming E0 to be sufficiently small, and on applying thestandard perturbation technique, let the solution be of thefollowing form:w~z ,t !5qz1 f ~z ,t !5qz1cos~qz ! f 11e jvt1sin~2qz !3~ f 22e j2vt1 f 20!, ~3!where f 11 and f 20 , f 22 are the coefficients of Fourier seriesproportional to E0 and E02. On substituting Eq. ~3! into Eq.~2!, we find the coefficients f 11 , f 22 , and f 20 :f 115dPE0Kq21~ jvt111 ! , f 225De*E028Kq21~ jvt211 ! , ~4!f 205De*E028Kq2 ,wheret15g/Kq2, t25g/2Kq2. ~5!Figure 3 shows the dependence of the amplitude part andthe phase part of the electro-optic response at the same fre-quency as the applied signal for a homogeneously alignedcell. The relaxation frequency is found to be ;20– 30 kHzand is almost of the same magnitude as for the dielectricrelaxation Process 1. Therefore we can unambiguously as-sign this relaxation process in the antiferroelectric phase tothe distortion of antiferroelectric order by the electric fieldcaused by a change of angle w arising from the type of mo-tion shown in Fig. 1~a!. This may also be called ‘‘antiphaseFIG. 2. Schematic presentation of the arrangement of the C directors(C1,C2) local spontaneous polarization (Ps1 ,Ps2) of two neighboringsmectic layers in helical antiferroelectric phase with respect to the labora-tory frame of reference.1668 Appl. Phys. Lett., Vol. 72, No. 14, 6 April 1998 Panarin, Kalinovskaya, and VijDownloaded 28 Jan 2012 to 147.252.227.64. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsGoldstone mode.’’ We rule out the assignment due to thesoft mode @Fig. 1~b!# due to the reasons already given in theprevious section.Figure 4 presents the dependence of the amplitude andthe phase part of the second-harmonic electro-optic responseat twice the frequency of the signal for an unaligned cell. Therelaxation frequency for this process is found to ;6 kHz,which is two times the frequency of Process 0 in the dielec-tric spectra. As mentioned before, the relaxation Process 0 isfound to exist in the dielectric spectra without bias voltage3or only under the bias voltage.4 The nonlinear electro-opticresponse appears to be caused by the distortion of the helixdue to the dielectric anisotropy. The relaxation frequency forthis response being approximately two times that for Process0 in the dielectric spectra is in a good agreement with theo-retical predictions @see Eq. ~5!#. It may be reemphasized thatthe helical distortion is caused by two mechanisms: polarinteractions dP.E @Fig. 1~c!# and the interactions due to thedielectric anisotropy De .E2 @Fig. 1~d!#. The latter cannot bedetected dielectrically but is clearly observed in the absenceof bias voltage in the electro-optic response at the secondharmonic frequency of the applied field for Process 0.We summarize the findings as follows:~1! The higher frequency relaxation process ~Process 1! isdue to the distortion of the antiferroelectric order causedby the antiphase motion shown in Fig. 1~a!. This mayalso be called the antiphase antiferroelectric Goldstonemode. It is also observed in the electro-optic response atthe fundamental frequency.~2! The lower frequency relaxation process ~Process 0! inthe dielectric relaxation spectra is the helical distortionmode. Antiferroelectric Goldstone mode is suggested tobe the appropriate terminology as its mechanism is simi-lar to that of a helical Goldstone mode. The distortion ofthe helix caused by the dielectric anisotropy gives rise toan electro-optic response at twice the frequency of theapplied field for this process. The reasons for havingdifferent frequencies for Process 0 using different tech-niques are provided by solving a equation that governsthe motion of the director of an antiferroelectric helixsubject to a weak alternating field.The authors thank J. W. Goodby, A. J. Seed, and M.Hird of the University of Hull for supplying the sample.Research was partially funded by Forbairt Ireland.1 A. Fukuda, Yo. Takanishi, T. Isozaki, K. Ishikawa, and H. Takezoe, J.Mater. Chem. 4, 997 ~1994!.2 N. A. Clark and S. T. Lagerwall, Appl. Phys. Lett. 36, 899 ~1980!.3 M. Buivydas, F. Gouda, S. T. Lagerwall, and B. Stebler, Liq. Cryst. 18,879 ~1995!.4 K. Hiraoka, H. Takezoe, and A. Fukuda, Ferroelectrics 147, 13 ~1993!.5 S. Merino, M. R. de la Fuente, Y. Gonzalez, M. A. Perez Jubindo, and J.A. Puertolas, Phys. Rev. E 54, 5169 ~1996!.6 Yu. P. Panarin, O. Kalinovskaya, and J. K. Vij, and J. W. Goodby, Phys.Rev. E 55, 4345 ~1997!.7 H. Orihara, Ya. Igasaki, and Yo. Ishibashi, Ferroelectrics 147, 67 ~1993!.8 H. Sun, H. Orihara, and Yo. Ishibashi, J. Phys. Soc. Jpn. 60, 2066 ~1991!;62, 2066 and 2706 ~1993!.9 I. Musˇevicˇ, M. Cˇ epicˇ, B. Zˇ eksˇ, M. Cˇ opicˇ, and D. Moro, and G. Heppke,Phys. Rev. Lett. 77, 1769 ~1996!.10 H. Moritake, Ya. Uchiyama, K. Myojin, M. Ozaki, and K. Yoshino, Fer-roelectrics 147, 53 ~1993!.FIG. 3. Frequency dependence of intensity (I) and the phase part ~F! of thelinear response for a well homogeneously-aligned 20 mm cell at 75 °C.FIG. 4. Frequency dependence of the intensity (I) and the phase ~F! attwice the frequency of the applied signal for an unaligned 20 mm cell at75 °C.1669Appl. Phys. Lett., Vol. 72, No. 14, 6 April 1998 Panarin, Kalinovskaya, and VijDownloaded 28 Jan 2012 to 147.252.227.64. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

The Investigation of the Relaxation Process in Antiferroelectric Liquid Crystals by Electro-Optic Spectroscopy

https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1170&context=engscheleart2

The Investigation of the Relaxation Process in Antiferroelectric Liquid Crystals by Electro-Optic Spectroscopy

Abstract

Similar works

Full text

Available Versions

Arrow@TUDublin