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PHYSICAL REVIEW E 83, 020701(R) (2011)

Reentrant orthogonal smectic-A phase below a tilted smectic-C phase in a chiral compound

Vladimıra Novotna,1,* Milada Glogarova,1 Miroslav Kaspar,1 Vera Hamplova,1 Ewa Gorecka,2

Damian Pociecha,2 and Mojca Cepic3

1Institute of Physics, Academy of Science of the Czech Republic, Na Slovance 2, CZ-182 21 Prague 8, Czech Republic2Laboratory of Dielectrics and Magnetics, Chemistry Department, Warsaw University, Al. Zwirki i Wigury 101, PL-02-089 Warsaw, Poland

3Jozef Stefan Institute, Ljubljana, Slovenia(Received 9 July 2010; published 9 February 2011)

A reentrant orthogonal smectic-A (SmA) phase below the tilted smectic-C phase is established in a chiralliquid crystalline compound. The temperature evolution of the layer spacing confirms monolayer structure in bothSmA phases, the upper SmA as well as the reentrant SmA phase. The reentrancy of the SmA phase is explainedon the basis of the mean field free energy taking into account nonmonotoneous temperature dependence of thelowest term coefficient.

DOI: 10.1103/PhysRevE.83.020701 PACS number(s): 61.30.Hn, 61.30.Cz, 61.30.Jf

It is more than usual behavior that as the temperature ofa system decreases, more and more ordered phases appear.However, rather rare materials have been found where aless ordered phase appears below the more ordered one oncooling. Such behavior is called “reentrancy” and phases areusually considered as reentrant phases. The liquid crystals arematerials in which a reentrant phenomenon is relatively oftenobserved because of many complex, competing interactionsexisting in these systems [1].

First, a reentrant nematic phase has been discovered inbinary mixtures of strongly polar materials [2]. For somerodlike molecules with strong longitudinal dipole momentsa reentrant smectic-A (SmA) phase appeared in multiplereentrancy with the nematic phase [3,4]. In these cases theassociation of molecules to dimers occurred, the degree ofdimerization being different in both higher temperature andreentrant phases. As for the SmA phases, the dimerizationor interdigitation of molecules causes different layer spacingin higher and lower temperature phases and the possibleformation of bilayers [1,3–5]. The reentrancy was explained asfrustration between dipole interactions causing various typesof association of molecules and consequent frustration insteric factor. The molecules with shapes intermediate betweendiscs and rods can show reentrant isotropic phase betweenhigher temperature columnar hexagonal phase and lowertemperature smectic phase, because for such compounds insome temperature range the molecular conformation is neithercompatible with lamellar nor columnar structure [6].

The reentrant SmA phase has been reported in binarymixtures of two homologs, one component with the SmA,the other with the smectic-C (SmC) phase only. The reentrantSmA phase SmARE existed only in an overcooled state [7].The other example of the phase sequence SmA-SmC-SmARE

has been detected in a narrow (2 mole %) concentration rangeof binary mixtures of a nonpolar compound with compoundpossessing a dipole at one terminal chain [8]. Anotherexample of entrancy phenomenon is the antiferroelectricphase separating two ferroelectric phases [9,10]. The reentrantphenomena have been found mostly in mixtures, especiallymixtures of compounds having different types of molecules.

*novotna@fzu.cz; http://www.fzu.cz

In pure compounds this effect is rather unique and its studycan help in better understanding the relationship between themolecular structure and physical property.

Here we describe the first chiral liquid crystalline com-pound showing unique sequence of lamellar phases withliquidlike order in the smectic layer: nontilted (SmA)-ferroelectric tilted (SmC*) and nontilted SmARE phase upondecreasing temperature. The phases differ by the tilt thatmolecules make with the normal layer, which is the orderparameter describing the phase transitions. The chirality of thematerial allows for the ferroelectric dipolar order in the SmC*phase. This unusual phase sequence has been established in acompound having a rodlike core made of two biphenyl unitsconnected by an ester group, one of biphenyls being laterallysubstituted by a chlorine atom. One of the end tails attached tothe mesogenic core contains two chiral centers: methyl-buthyland lactate groups (see Fig. 1).

The phase transition temperatures are evaluated fromdifferential calorimetric study (DSC). In DSC scans theSmC*-SmARE phase transitions show small heat flow changebelow <0.01 J mol−1; the other phase transitions exhibitstronger thermal effect. The phases are determined fromtexture observation. In planar 8-μm-thick samples (moleculesparallel to the sample plane) characteristic textures of bluephase, namely, platelike domains with low birefringence,typical oily streaks in the cholesteric phase and pseudo-fan-shaped texture in the twist grain boundary phase (TGBA) [11]were observed. On further cooling, the TGBA-SmA phasetransition was observed as an abrupt sharpening of contrast anda change of fan color. No dechiralization lines accompanyingthe helicoidal superstructure were observed in the SmC*phase. Nevertheless, by a selective refraction the helicity wasestablished with a pith length of about 0.1 μm in a homeotropicsample (smectic layers parallel to the sample plane). In theSmARE fan-shaped texture occurs typically for a nontilted(orthogonal) smectic phase with no in-plane order.

In free-standing 2-to-5-μm-thick films both SmA andSmARE phases exhibit uniform dark texture pointing to opticaluniaxiality of the phase, while the transition to the SmC*phase is observed as an appearance of schlieren texture, withpoint defects characterized by s = ±1. The brightness ofthe schlieren texture gradually decreases as the birefringencecontinuously diminishes on approaching the SmA phases.

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VLADIMIRA NOVOTNA et al. PHYSICAL REVIEW E 83, 020701(R) (2011)

FIG. 1. Chemical formula of 9ZBL and the sequence of phaseson cooling. Melting point is at 47 ◦C.

Continuous changes of birefringence are characteristic of thesecond-order phase transition.

The x-ray diffraction studies [Fig. 2(a)] yield the layerspacing values, d, and clearly confirm that order inside thelayer remains short range in all mesophases, down to thecrystallization temperature. No jumps in d occur at bothtemperature limits of the SmC* phase, which indicates thesecond-order transitions. The distinct minima in the diffractedx-ray intensity reflect fluctuations at the phase transitionsbetween orthogonal and tilted phases. In the SmA phaseregions the layer spacing increases linearly on decreasingtemperature, with nearly the same thermal expansion coef-ficient: −0.018 A/deg in the higher temperature SmA phase

FIG. 2. (a) Layer spacing and intensity of the x-ray signal vstemperature. (b) Tilt determined from layer spacing data measuredin the SmC* phase, dSmC , and value dSmA linearly extrapolated fromthe SmA phase. The line shows a polynomial fit to the third order intemperature.

and −0.023 A/deg in the SmARE phase. The temperatureevolution of d values excludes formation of smectic bilayersor any other molecular association in the SmARE phase. Inthis point this SmARE phase differs from any other smecticreentrant phases reported so far.

The tilt extracted from the layer spacing data θ =arccos dSmC/dSmA, where dSmA is extrapolated for temperaturerange of the SmC phase, reaches a maximum of 8◦ [Fig. 2(b)].This value is slightly higher than the optical tilt measured by di-rect electroptical method reaching a maximum of 5◦ [Fig. 3(a)].It is not typical and may suggest that molecules do not adoptzigzag conformation which is usually expected for moleculesin tilted phase [12]. The direct tilt measurements show strongelectro-optic effect in higher and lower SmA phases far behindthe SmC* phase [Fig. 3(a)]. The susceptibility of the tilt toelectric field is also pronounced in the SmC* phase region; forlow electric field, it is 1.2 deg μm/V. It is necessary to applymore than 15 V/μm to obtain saturated value of the tilt.

The electric spontaneous polarization (Ps), due to the linearpiezoelectric coupling between the tilt and the polarization

FIG. 3. Temperature dependence of (a) the tilt angle measuredelectro-optically and (b) polarization evaluated from hysteresisloops. The measuring fields are indicated. The vertical arrows showtransition temperatures without a bias field and the dotted linesconnect the transition temperatures at different bias fields taken fromdielectric spectroscopy and extrapolated for higher fields.

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REENTRANT ORTHOGONAL SMECTIC-A PHASE BELOW . . . PHYSICAL REVIEW E 83, 020701(R) (2011)

[Fig. 3(b)], follows the changes of the tilt. Its maximumvalue 41 nC/cm2 occurs in the middle of the SmC* rangeat 82 ◦C. The dielectric dispersion study performed in afrequency range of 101–106 Hz on cells with planar alignmentshows a monodispersive relaxation process in the mesophasesstudied. These measurements make it possible to establishpolar fluctuations that are coupled to the tilt fluctuations. Thetemperature dependence of relaxation frequency has clear dipsat the SmA-SmC* and SmC*-SmARE transitions showing thaton approaching the tilted-nontiled phase transition temperaturecollective molecular tilt fluctuations slow down and finallymolecules freeze to form tilted ferroelectric phases [Fig. 4(a)].The soft mode relaxation frequency reaches about 2 kHzat the SmA-SmC* phase transition and 260 Hz at theSmARE-SmC* phase transition. The critical dependence ofthe relaxation frequency is also visible at the SmC* sides ofthe phase transitions, if the collective tilt azimuthal fluctuations(Goldstone mode) are suppressed by external bias electric field.The relaxation frequency decrease is accompanied by increasein the mode intensity. The linear temperature dependenceof inverse mode strength [Fig. 4(b)] indicates that bothSmA-SmC* and SmC*-SmARE phase transitions could beconsistently described by the mean field model with molecular

FIG. 4. Temperature dependence of (a) the dielectric strength andrelaxation frequency and (b) the reciprocal value of dielectric strength,1/�ε, under indicated bias fields. Arrows mark the SmA-SmC* andSmC*-SmARE phase transitions on cooling.

tilt angle as an order parameter. The phase transition to thepolar SmC* phase neglecting the helicoidal superstructure isdescribed by the simple form of the free energy [13]:

G = 1

2aξ 2 + 1

4bξ 4 − C(P × ξ )z + 1

2εP 2 − E · P. (1)

Here the free energy is expressed in terms of order pa-rameters, polarization P and tilt ξ . If the transition takesplace, the first coefficient changes sign in dependence of thetemperature. Usually this temperature dependence is consid-ered as linear in the first approximation as a = a0(T − T0),T0 being the temperature, where the coefficient a changessign and the phase transition to the tilted phase occurs. Othercoefficients are considered as temperature independent in thefirst approximation. If the rare case occurs in which twoor even more ordering processes and subsequent competinginteractions take place close to the transition, the linear Taylorexpansion of the a coefficient may not satisfy. After all, thelinear dependence of the coefficient a is valid only closeto the transition temperature, but in general the temperaturedependence of the a coefficient is nonlinear [Fig. 5(a)] ornonmonotonous. The nonmonotonous behavior of a aroundthe phase transition temperature [Fig. 5(b)] is probably thereason for the reentrancy of the SmA phase.

In the most crude approximation the effective temperaturedependence of a may be expressed like

a = a0(T − T0) + a′(T − T0)2 + a′′(T − T0)3 − εC2, (2)

where a0 < 0, a′ > 0, and a′′ > 0. The last term describes theincrease of the transition temperature due to the piezoelectri-cally induced polarization. In the region where a is negative,the system is tilted. However, when it becomes positive atlower temperatures again, the SmA phase reenters. In theabsence of the electric field the tilt is

θ =√

a − εC2

b. (3)

In the presence of the field the tilt is the solution of thethird-order polynomial and has to be determined numerically.

FIG. 5. The possible temperature dependence of a: (a) nonlinearand (b) nonmonotonous near the transition temperature. Temperatureregions of phases are below the diagrams. The crystalline phase, Cr.,is the lowest temperature phase.

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FIG. 6. Temperature dependence of (a) tilt (in degrees) and(b) relaxation frequency of dielectric response for different values ofapplied electric field obtained by numerical minimization of equation(1). Coefficients used in calculation were a0 = 2.6 × 102 J m−3 K−1,a′ = −1.0 × 103 J m−3 K−2, a′′ = 6.7 × 102 J m−3 K−3, b = 7.0 ×105 J m−3, and εC = 0.02. Units for the relaxation frequency arearbitrary.

Temperature dependence of the tilt for increasing field can beseen in Fig. 6(a). It is in good agreement with the measured data[cf. with Fig. 3(a)]. The corresponding relaxation frequency of

the dielectric response is given in Fig. 6(b). It shows softeningin both SmA phases when approaching the transition to theSmC* phase. This softening is seen in measured dielectricdata (cf. with Fig. 4). The possible temperature dependence ofcoefficients originates in changes of average intermoleculardistances as van der Waals forces are strongly nonlinearand/or in changes of molecular conformations due to theentropy. It is especially important for complex moleculeshaving many molecular conformations with close energies.Rodlike molecules of liquid crystals are a good example ofsuch systems, especially if molecules contain several chiralcenters. Therefore, one can easily understand that the lineartemperature dependence of the coefficient a is violated andbecomes nonmonotonous even near the transition temperatureT0, which would be a reason for the reentrancy of theSmA phase.

This work was supported by Project No. 202/09/0047 of theCzech Science Foundation and Project No. IAA100100911 ofthe Grant Agency of AS CR.

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