The temperature dependence of the thickness of thick free-standing ﬁlms is studied using a high-resolution ﬁlm thickness measurement technique. A small discontinuity in the temperature dependence of the smectic layer thickness at every phase transition between ferro-, ferri-, and antiferroelectric phases is observed. We show that the major contribution to it arises from a change in the smectic tilt angle

Blanc, C.

Goodby, J. W.

Lorman, V.

Panarin, Yuri

Panov, V. P.

Vij, J. K.

English

Arrow@TUDublin

Technological University Dublin ARROW@TU Dublin Articles School of Electrical and Electronic Engineering 2007 Discontinuous Change in the Smectic Layer Thickness in Ferrielectric Liquid Crystals V. P. Panov Trinity College Dublin, Ireland J. K. Vij Trinity College Dublin, Ireland Yuri Panarin Technological University Dublin, yuri.panarin@tudublin.ie C. Blanc CNRS V. Lorman CNRS See next page for additional authors Follow this and additional works at: https://arrow.tudublin.ie/engscheleart2  Part of the Electrical and Computer Engineering Commons Recommended Citation Blanc, C. et al. (2007). Discontinuous change in the smectic layer thickness in ferrielectric liquid crystals. Physical Review E vol. 75, pp. 1-4 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 Authors V. P. Panov, J. K. Vij, Yuri Panarin, C. Blanc, V. Lorman, and J. W. Goodby This article is available at ARROW@TU Dublin: https://arrow.tudublin.ie/engscheleart2/170 Discontinuous change in the smectic layer thickness in ferrielectric liquid crystalsV. P. Panov and J. K. Vij*Department of Electronic and Electrical Engineering, Trinity College, University of Dublin, Dublin 2, IrelandYu. P. PanarinDepartment of Electronic and Electrical Engineering, Trinity College, University of Dublin, Dublin 2, Irelandand Department of Electronics, Dublin Institute of Technology, Dublin, IrelandC. Blanc and V. LormanUMR 5587, CNRS, Université Montpellier II, Place E. Bataillon, 34095 Montpellier, FranceJ. W. GoodbyDepartment of Chemistry, University of York, York, YO10 5DD, United KingdomReceived 10 April 2006; revised manuscript received 5 January 2007; published 9 April 2007The temperature dependence of the thickness of thick free-standing films is studied using a high-resolutionfilm thickness measurement technique. A small discontinuity in the temperature dependence of the smecticlayer thickness at every phase transition between ferro-, ferri-, and antiferroelectric phases is observed. Weshow that the major contribution to it arises from a change in the smectic tilt angle.DOI: 10.1103/PhysRevE.75.042701 PACS numbers: 64.70.Md, 61.30.Cz, 61.30.Eb, 77.80.eSmectic liquid crystals form layered liquid crystallinephases. In tilted smectic phases the average direction of theelongated molecules is tilted by an angle with respect to thelayer normal. In chiral smectics the layers are spontaneouslypolarized in the plane of the layer and perpendicular to thedirection of the tilt 1,2. A number of intermediate ferrielec-tric phases had been discovered between ferroelectric smec-tic C* SmC* and antiferroelectric smectic CA* SmCA* 3.The general and well-established phase sequence on coolingfrom paraelectric smectic A SmA is as follows: ferroelec-tric SmC*; four-layer ferrielectric SmC4* also known asSmCFI2* 4 or AF 3; three-layer ferrielectric SmC3* orSmCFI1* 4 or SmC* 3, and finally two-layer antiferroelec-tric SmC2 or SmCA*. Theory 5 predicts a number of inter-mediate phases in a narrow temperature range betweenSmC* and SmCA*. Some of these have been reported experi-mentally see, for example,6–10.The phase transition from orthogonal SmA to tilted SmC*is associated with the appearance of the pseudovector orderparameter = n ·k0nk0, where k0 is the smectic layernormal, and the director is specified as n= sin  cos  , sin  sin  , cos  in terms of the tilt angle and the azimuthal angle . This transition can be describedwithin the mean-field theory by taking the free energy inLandau-Ginzburg form 11:F = a2 + b4 + O6 1where = T−TC /TC is the dimensionless deviation of thetemperature T from the SmA-SmC* transition temperatureTC; a and b are the Taylor expansion coefficients. The moreadvanced approach has suggested b to be a function of tem-perature as well 12.While being mathematically simple, the mean-field theoryis a powerful technique to describe the properties of newexperimental systems and phases. However, it is based on anapproximation of the thermodynamic properties of systemswhere the order parameter is spatially constant. When mod-eling the ferro-, ferri-, and antiferroelectric phases the varia-tion in the azimuthal angle  between the neighboring layersis usually considered as the main distinctive feature in thecharacterization of the molecular arrangement. This featureis ignored in the mean-field approach and the value of the tiltangle as a function of the temperature but not of a particularphase is taken into account. Meanwhile in many experimen-tal works one can see a clear jump in the tilt angle on coolingfrom the SmC* phase down to a low-temperature phase6,13–15. These results cannot be described by the classicalmean-field theory.In this paper we show that the jumps in the tilt anglehappen not only at this, but at every phase transition betweenthe ferrielectric phases, and analyze their influence on theoptical thickness. Recently we developed a high-resolutionfree-standing film FSF thickness measurement techniquewhich is based on using a fiber-optic spectrometer AvaSpec-2048. The liquid crystalline films were stretched across a3-mm-diameter hole drilled in a 0.3-mm-thick steel platemounted within a hot stage with a temperature resolution of0.01 °C. A special algorithm gives fast and reliable fitting ofthe interference fringes formed on reflection from the film inorder to obtain the film thickness. The optical thickness ndwhere n is an effective refractive index and d is the me-chanical film thickness is measured in the range of a fewtens of micrometers with a resolution better than 0.01%. Inthe case when the selective reflection band lies within thespectrometer range 400–1100 nm in our case, the helicalpitch and the thickness of the film are obtained in a singleexperiment. This gives valuable information for characteriz-ing the phases in the liquid crystalline materials under inves-tigation.*Electronic address: jvij@tcd.iePHYSICAL REVIEW E 75, 042701 20071539-3755/2007/754/0427014 ©2007 The American Physical Society042701-1In our experiment the optical thickness of a thick over10 000 layers FSF is measured. For such a thick film, thesurface effects can easily be neglected but we can stillachieve a high-quality homeotropic alignment. In order torule out the thickness change due to a possible destruction ofa few layers during the experiment, the measurements wereperformed during both heating and cooling with a rate asslow as 0.01 °C/min. The measurements were performedusing nonpolarized light incident along the layer normal.Therefore only the components of the biaxial refractive in-dex tensor depending on the tilt angle  of the long molecu-lar axis can cause a detectable change in the effective refrac-tive index n and affect the results of our measurements.A change in the optical thickness can appear as a result oftwo reasons: i a change in the mechanical thickness d of thefilm and ii a change in the effective refractive index n ofthe liquid crystal. In order to estimate the contribution ofthese two factors we have performed numerical simulationsusing Berreman’s 44 matrix method 16. The 44 matrixmethod was used to simulate spectra of the smectic filmswith different tilt angles and unit cell structures. The ob-tained theoretical curves were treated with the same algo-rithm as the experimental data to ensure that the output hasexactly the same meaning as for the experiment. The simu-lation shows that the possible influence of the azimuthal mo-lecular structure of an intermediate phase on the thicknessobtained from the interference pattern of nonpolarized lightpropagating along the layer normal is negligible.The results of the simulation are shown on the inset of Fig1. The thick line b shows the dependence of the measuredoptical thickness nd on the tilt angle for a rigid rod approxi-mation of the molecular length. The parameters used for thesimulations are as follows: mechanical layer thickness d=d0 cos, dielectric tensor components 11=22=2.0,33=2.54. The tensor components here are related to a singlelayer and do not change with phase transitions. The effect ofa temperature change on the components of the dielectricanisotropy is gradual and can easily be neglected over a nar-row range of temperatures involved under discussion. There-fore the effective refractive index n is a function of the tiltangle  only. The dashed line c shows the correspondingchanges of the mechanical film thickness normalized usingthe effective refractive index in the SmA phase n0d=n0d0 cos. As an illustration we also provide a hypotheti-cal change of the optical film thickness in the absence of themechanical layer shrinkage i.e., d=d0=const. See Fig 1a.The index 0 here means that the parameter corresponds to theSmA phase with zero tilt angle . One can see that, for thegiven dielectric anisotropy, the change in the optical filmthickness due to a change in the effective refractive index hasbeen found to have the opposite trend compared to that ob-served experimentally.We also compared our data with the smectic layer thick-ness obtained by the x-ray scattering technique carried out atthe Cu K	 wavelength =0.154 nm University of Mont-pellier II, France. For the studied liquid crystalline materialsthe normalized value of the optically measured film thick-ness departs from the mechanical film thickness by 10–15 %of the total change in thickness when the tilt angle reaches25°. This conclusion is in good agreement with our resultsgiven in the main part of Fig. 1. The small circles representthe results of the optical film thickness measurements for12OF1M7, while the large squares show the normalizedsmectic layer thickness obtained using the x-ray scatteringtechnique. One can see that on cooling the sample in SmC*the x-ray data depart from the optical ones by 10–15 % ofthe total layer shrinkage as also predicted by our simulations.Therefore we conclude that the main contribution to thechange in the optical thickness observed experimentally is achange in the mechanical thickness of the film resulting froma change in the tilt angle. This has also been confirmed bymicroscopic observations of the meniscus of a free-standingfilm, which has to absorb the excess of the material resultingfrom the change in thickness. The x-ray results also confirma jump in the layer thickness due to the change in the tiltangle at the SmC*-AF phase transition. However, the simplex-ray technique is not able to resolve the smaller jumps leav-ing a niche for implementation of our optical technique.To describe the detailed structure of the intermediatephases we use the same notation as in 18, i.e., the four-layer phase has the azimuthal angles of the molecules in itsunit cell defined as 0, 2, 180°, 180° +2, while the three-layer phase has −1 /2, 1 /2, 180°. Here 1=2=0 producesthe ideal Ising model, while 1=90° and 2=120° corre-spond to the uniaxial clock model. The values of the distor-tion angles  were recently measured by many groups17–23. In most experiments 1 /2 does not exceed 45° and2 is normally less than 30°. Therefore as a rough first-orderapproximation we can consider a structure where the mol-ecules in the neighboring layers are either synclinic or anti-clinic.From Fig. 2 it is clear that the tilt angle and therefore thethickness in a particular layer depends not only on the tem-perature as in the conventional mean-field theory but alsoon the relative azimuthal orientation synclinic S or anti-clinic A of the adjacent layers. Let us introduce the orien-tational parameter dT as the difference between the thick-FIG. 1. Color online Comparison of the thickness measure-ments by the x-ray squares and optical FSF thickness circlestechniques. Inset: relative influence of the layer shrinkage and thechange in the refractive index on the results of the optical filmthickness measurements. Curve a, no layer shrinkage considered;curve b, simulation of a realistic material with layer shrinkage andmolecular dielectric anisotropy, and curve c, rigid rod approxima-tion without considering a change in the refractive index.BRIEF REPORTS PHYSICAL REVIEW E 75, 042701 2007042701-2nesses of synclinic and anticlinic layers dST−dAT. Sincethe measured thickness of an N-layer phase is the sum of thethicknesses of a large number of layers, it can be presentedas dN=dAT+dTqTN, where qTN is a fraction of syn-clinic ordering in the N-layer phase: S / S+A and S and Aare the number of synclinic and anticlinic arrangements inthe unit cell of an intermediate phase. While this equation isjust a rough approximation, it is in good agreement withexperimental data shown in Fig. 2. It also demonstrates thatour method can be used to find the intermediate phases anddetermine their unit cell periodicity. Accordingly, the phaseobserved in 120F1M7 6 in between two and three layerphases is estimated to be a five layer phase.The only exception is the transition between the SmC*and SmC	* phases where there is no clear preference towardsynclinic or anticlinic arrangement due to extremely shortvalues of the helical pitch. Moreover, in the case of12OF1M7 this transition is not detectable by our techniquesince it has proven to be continuous 24.The temperature dependence of the optical film thick-nesses for a number of different materials that exhibit inter-mediate ferrielectric subphases between ferroelectric SmC*and antiferroelectric SmCA* phases have been obtained. Thetemperature dependencies of the optical thickness for threecompounds with the following acronyms and phase se-quences are presented in Fig. 2. For MHPOBC on heating, asshown in curve a,SmCA* ——→124.1SmC* ——→124.5AF——→124.9SmC*——→127.1SmC	* ——→128.3SmA*.For 10OF1M7 on cooling, curve b, and on heating curve c,heating Fig. 2cSmCA*82.181.4SmC*82.181.7AF83.683.0SmC*85.385.3SmC	*87.787.7SmA*.For S-12OF1M7 on cooling, curve d,SmCA* ←——77.49SmC5lr* ←——78.3SmC* ←——79.8AF←——83.3SmC*←——93.5SmA*.One clearly sees a stepwise increase in the optical filmthickness at every transition in the phase sequences of thestudied materials.Finally we conclude that a change in the measured FSFoptical thickness is mainly due to a change in mechanicallayer thickness. This is caused by a variation in the smectictilt angle . A small discontinuity in the tilt angle exists atevery phase transition between the tilted smectic phases. Forthe first time, we resolve a change in the smectic layer thick-ness of the order of 0.01% which corresponds to jumps in thetilt angle of 0.05° to 0.5° at the transitions between theSmCA*, SmC5 layer also known as SmCAqT=1/5* 6, SmC*also known as SmCAqT=1/3* , and AF SmCAqT=1/2*  phases.A number of materials possessing these phases includingMHPOBC, 12OF1M7, and its homolog have been investi-gated and all of them possess similar behavior. The techniquehas proven to be useful for detecting the intermediate phasesexisting over extremely narrow temperature regions such asthe SmC5 layer* phase in 12OF1M7. The other advantage of itis that it does not require the application of an external elec-tric field which can disturb the liquid crystalline structure.The tilt angle is found to depend not only on the tempera-ture, but also on the molecular arrangement synclinic oranticlinic, leaving room for further theoretical treatment.We thank A. Fukuda, M. A. Osipov, A. V. Emelyanenko,F. 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Discontinuous Change in the Smectic Layer Thickness in Ferrielectric Liquid Crystals

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Discontinuous Change in the Smectic Layer Thickness in Ferrielectric Liquid Crystals

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