Temperature dependence and characteristics of relaxation ...

1 Full Terms & Conditions of access and use can be found TransitionsA Multinational JournalISSN: 0141-1594 (Print) 1029-0338 (Online) Journal homepage: dependence and characteristics ofrelaxation modes in achiral polar smectic phasesDina Juki & Mojca epi To cite this article: Dina Juki & Mojca epi (2018) Temperature dependence and characteristicsof relaxation modes in achiral polar smectic phases, Phase Transitions, 91:9-10, 994-999, link to this article: online: 19 Jul your article to this journal Article views: 18 View Crossmark dataCiting articles: 1 View citing articles Temperature dependence and characteristics of relaxation modesin achiral polar smectic phasesDina Juki aand Mojca epi b,caFaculty of Electrical Engineering, Computer Science and Information Technologies Osijek, StrossmayeraUniversity of Osijek, Osijek, Croatia;bFaculty of Education, University of Ljubljana, Ljubljana, Slovenia.

2 CJo ef StefanInstitute, Ljubljana, SloveniaABSTRACTThe paper studies relaxation modes and their corresponding amplitudes inantiferroelectric polar smectic phases made of achiral bent-corecompounds. The analysis identifies two types of modes in theorthogonalSmAPAphase. The nature of these modes is either pure polaror quasi tilt, but they are split into phase and amplitude modes. One ofthe amplitude tilt modes is a soft mode and the correspondingrelaxations time becomes infinite at the transition to the tilted phase.

3 Intilted phases, characteristic modes change the phase of equilibriumorder parameters, the amplitude or both simultaneously. Of thesemodes, two are predominately polar, soft mode and Goldstonemode are predominately tilt modes and the rest are mixed. Thenature of characteristic modes is Temperature independent in all HISTORYR eceived 7 May 2018 Accepted 2 July 2018 KEYWORDSF luctuation amplitudes; orderparameters; polar smectics; relaxation modesIntroductionBanana molecules, as they are trivially named because of their bent-core shape, have been widelystudied after the realization that they can form antiferroelectric and ferroelectric phases, in spiteof achiral molecular constituents [1].

4 Although bananas form a rich variety of phases [2], thispaper focuses on antiferroelectric polar smectics, in which polarity originates from biaxial packingof molecule the section The model , we present stable solutions derived from the minimization offree energy expressed in terms of polar and tilt order parameters. The section Relaxationmodes contains an analysis of the non-equilibrium free energy expressed in a matrix matrix form allows for straightforward analysis of the dynamic properties of the , we discuss the nature of obtained characteristic modes and the amplitudes of modelIn achiral smectic phases made of bent-core molecules, the degree of order is measured in twoorder parameters, the two-dimensional tilt and polarization vectors.

5 Polarization orderparameters can appear independently of the tilt as in the studied orthogonal polarSmAPAphase. More common, they appear simultaneously as in the studied tilted and polarSmCSPAandSmCAPA phases. 2018 Informa UK Limited, trading as Taylor & Francis GroupCONTACTDina Juki TRANSITIONS2018, VOL. 91, NOS. 9 10, 994 999 order parameter is defined with respect to thej-th layer director jj={nj,xnj,z, nj,ynj,z}(1)wherenx,nyandnzare components of the director parameter polarization describes the average orientation of the bent core, and averagepolarization of molecules is either parallel or anti-parallel to this direction Pj={Pj,x,Pj,y}(2)Free energy of achiral smectic system made of bent-core molecules, expressed in order parametersis [ 3]G= j12a0pP2j+14b0pP4j+12a0tj2j+14b0tj4j+12V ( jj Pj)2z+14a1pPj( Pj 1+ Pj+1)

6 +14a1tjj( jj 1+ jj+1)(3)First four terms give energy contributions because of the polarization and tilt order caused by vander Waals T0is the only Temperature -dependent coefficient. Next term, with thenegative coefficientV, describes the intralayer interaction between tilt and polarization, whichfavours mutual perpendicular orientation. Couplings between polarizations and tilts in the neigh-bouring layers are given by last two terms. For the purpose of this study, we choose the positivevalue of the coefficienta1p, characteristic of antiferroelectric ordering in polarization.

7 The coefficienta1tis negative for preferred synclinic, or positive for anticlinic ordering of tilts in structures are described in a coordinate system, where thez-axis corresponds to the layernormal, they-axis is parallel to the polarization order parameters and thex-axis is parallel to thetilt order parameters. In general, order parameters vary in direction from one layer to the other,but they have constant magnitudes. In order to minimize the free energy, the following Ansatzesfor structures were used:SmAPASmCSPASmCAPA j0=0 j0j=u0{1, 0} j0j=u0{1, 0} P0j=P0{0, 1} P0j=P0{0, 1} P0j=P0{0, 1} P0j+1=P0{0, 1} j0j+1=u0{1, 0} j0j+1=u0{ 1, 0} P0j+1=P0{0, 1} P0j+1=P0{0, 1}(4)By inserting (4) in (3) and minimizing with respect tou0andP0, one obtains a time-independentsolution for the parametersu0andP0(Figure 1)

8 SmAPASmCSPASmCAPAu0=0u20= a0tb0p a1tb0p a1pV+TVb0pb0t V2u20= a0tb0p+a1tb0p a1pV+TVb0pb0t V2P20=a1p Tb0pP20=a1pb0t+a0tV+a1tV b0tTb0pb0t V2P20=a1pb0t+a0tV a1tV b0tTb0pb0t V2 relaxation modesA system that has been deviated from equilibrium relaxes through its characteristic modes. Accord-ing to the Goldstone theorem, the characteristic frequency of one of these modes is zero if the phasePHASE TRANSITIONS995transition is continuous [4]. A consequence of this zero-frequency mode is an energy non-changingcoherent rotation of all molecules by the same angle when the liquid crystal is reoriented in a specificdirection.

9 In polar smectics, the Goldstone mode represents the rotation of the sample as a other continuous transitions below theSmA, the frequency of one of the other characteristicmodes also approaches zero as the Temperature reaches the phase transition [5]. Towards the tran-sition, the pseudo forces returning the system to the equilibrium structure decrease,fluctuationsincrease and the system becomes softer. Therefore, this characteristic mode is called the softmode; it condenses at the transition Temperature and breaks the symmetry of the begin the analysis of dynamic properties by inserting time-dependent tilt and polarizationinto free energy Equation (4).

10 J(t)= j0+d j(t) P(t)= P0+d P(t)(5)The time-dependent order parameter is a sum of a time-independent equilibrium order par-ameter and smallfluctuations that can change its magnitude (subscript ) or direction, that is, itsphase (subscript ) j(t)=j0 e +dj e +dj e P(t)=P0 e +dP e +dP e (6)where e and e are unit vectors parallel or perpendicular to stable order parameters locally in energy is then developed around equilibrium. The contribution offluctuations to freeenergy isdG=12xiG2xi(7)Figure dependence of polarization and tilt on the Temperature .