Table Of ContentGeneral phase diagram for antiferroelectric liquid crystals in dependence on
enantiomeric excess
1,2E. Gorecka, 1D. Pociecha, 3M. Cˇepiˇc,3B. Zˇekˇs, 4R. Dabrowski
1Chemistry Department, Warsaw University, Al. Zwirki i Wigury 101, 02-089 Warsaw, Poland;
2Department of Microelectronics and Nanoscience, Chalmers University of Technology, S-41296 G¨oteborg, Sweden;
3J. Stefan Institute, Jamova 39,1000 Ljubljana, Slovenia;
4Institute of Chemistry, Military University of Technology, 00-908 Warsaw, Poland.
2
0 (February 6, 2008)
0
The phase diagram of the prototype antiferroelectric liquid crystal MHPOBC in dependence of
2 enantiomeric excesswas measured. It wasshown thattheSm C∗ phasein verypuresamples isthe
β
n SmC∗FI2 phasewithafourlayerstructure,andonlyaftersmallracemization ittransformsintothe
a ferroelectric Sm C∗ phase. The phase diagram was theoretically explained by taking into account
J
longer range bilinear and short range biquadratic interlayer interactions, that lead to the distorted
5
clock structures and first order transitions between them.
1
PACS numbers: 61.30.Cz
]
t ∗ ∗
f In some systems chiral properties can be transferred Sm C phase transforms into the Sm CFI2 phase upon
o
from a molecular to a macroscopic level. The best ex- increasing optical purity. The result solves the long
s ∗
t. amples of such systems are liquid crystals which form known controversy why the smectic Sm Cβ phase in
a chiral phases (cholesteric, blue, twist grain boundary or MHPOBC was first reported as a typical ferroelectric
m polar smectic phases), if built of chiral molecules. The phase [2] and later also as the phase having antiferro-
- variation of the enantiomeric excess influences macro- electric properties [4]. We show here, that this system
d
scopic properties of these phases like the period of the is a nice example of intermediate phases, which appear
n
modulation and the phase transition temperature or it between main phases because of the cancelationof short
o
c can even change the phase sequence. The striking ex- rangeinteractionsandconsecutiverelevanceofsmallchi-
[ ample of the last phenomenon are antiferroelectric liq- ral and/or longer range interactions. We present a new
uid crystals where some phases disappear with racem- phenomenologicalmodel,whichtakesintoaccountlonger
1
v ization [1]. For high optical purity MHPOBC com- range bilinear [5] and short range biquadratic [6] inter-
5 pound, the prototype antiferroelectric material, the se- layerinteractionsandallowsforcorrectenantiomericex-
4 quence of tilted phases Sm C∗ ↔ Sm C∗ ↔ Sm C∗ ↔ cessdependentphasesequencewithfirstordertransitions
α β γ
2 ∗
SmC wasreportedwithdecreasingtemperature[2]. In between experimentally consistent structures.
1 A
the partially racemized sample only two of these phases, Several S-enantiomer rich [7] mixtures of MHPOBC
0
∗ ∗ ∗
2 Sm Cβ and Sm CA, remained. The Sm CA phase is were studied by differential scanning calorimetry(DSC),
0 the phase with the antiferroelectric properties and an- dielectric and optical methods. The DSC measurements
/ tiparalleltiltsinneighboringlayers,i.e.,anticlinicphase. were performed using Perkin Elmer DSC-7 calorimeter
t
a The Sm C∗ phase has been recognized as the ferro- in the cooling and heating runs at scanning rates 0.2-
m β ∗
electric synclinic Sm C phase. Almost ten years later 1 K/min. In the dielectric measurements the glass cells
- structures of the other subphases have been found by ofvariousthickness,with25mm2 ITOelectrodescoated
d
n resonant x-ray scattering in a different compound (S- by polimide, were used. Dielectric spectroscopy studies
o 10OTBBB1M7) [3]. In this compound the phase se- were performed with HP 4192A impedance analyzer. In
c quencewithdecreasingtemperatureis: theSmC∗ phase each phase the dielectric spectra were fitted with Cole-
α
:
v with the periodical modulation of a tilt direction and Cole equation. The selective reflection measurements
i with 5- or more, in general incommensurate, number wereperformedintransmissionmodeatnormalincidence
X
∗
of layers, the Sm C phase with 4-layer modula- (Shimadzu3101PCspectrofotometer)foronesurfacefree
r ∗ FI2
a tion, the Sm CFI1 phase with 3-layer modulation, (made on the quartz plate) or film samples. These stud-
∗ ∗
and the Sm C phase with 2-layer structure. The ies allowed to determine the helical pitch in Sm C and
A A
∗ ∗
Sm C phase in the 10OTBBB1M7 compound cor- Sm C phases.
FI1
∗ ∗ ∗
responds to the Sm C phase in MHPOBC material. IntheSmC andSmC phasesthepitchwasesti-
γ FI1 FI2
Sofartheoreticalconsiderationsfailedto accountforthe matedbythedirectmicroscopicobservationsofperiodic-
correct phase sequences in dependence of enantiomeric ityofthelinedefectsin40micronhomogeneouslyaligned
excess as well as experimentally consistent structures of cell. The thick (250 micron) film samples were used
some phases. for the optical rotatory power (ORP) measurements, in
In this Letter we present the complete phase diagram which a standard setup was used where the analyzer is
for the antiferroelectric system MHPOBC with respect rotatedagainstthepolarizertoobtainaminimumofthe
to the enantiomeric excess. We show that the synclinic light (630 nm) transmission.
1
In the optically pure samples (enantiomeric excess tive reflection in the visible light range. Selective reflec-
x = c − c = ±1 where c and c are correspond- tion wavelength changes from 450 nm to 600 nm within
S R S R
ing concentrations) four tilted smectic subphases with the phase temperature interval. Since the temperature
∗ ∗ ∗ ∗ ∗
historical names Sm C , Sm C , Sm C , Sm C ap- range of the Sm C phase in this mixture is rather
α β γ A FI2
pear below the Sm A phase (Fig. 1). Two phases which narrow it is difficult to observe all five phases in the di-
∗ ∗
appear between the Sm C and Sm C phase, have electric measurements. Due to the small temperature
α A
rather long helical pitch. The periodicity of disclination gradients that are hard to avoid in the sample with the
∗
lines which could be observed in the thick planar cell, big electrode area, the Sm C phase always coexists
FI2
is about 2.5 µm in higher temperature phase (denoted with the additional phase. In this additional phase the
as SmC∗) and about 1.6 µm in the lower temperature dielectric permitivity is an order of magnitude stronger
β
∗
phase (denoted as SmC ). No selective reflection in a thaninallotherphases(Fig.2b)thustypicalforthesyn-
γ
∗
visible range, which is encountered in the lower purity clinic ferroelectric Sm C phase.
∗
MHPOBC materials, could be detected at any tempera- As the optical purity decreases further, the Sm C
FI2
ture. Both intermediate phases have a pronounced opti- phase disappears and in the excess range between 0.88-
calactivity,+35o/µmand-10o/µminSmC∗ andSmC∗, 0.97thephasesequenceSmC∗ ↔SmC∗ ↔SmC∗ ↔
γ β α FI1
∗
respectively,that is only slightly temperature dependent Sm C is observed, that is the phase sequence incor-
A
in the each phase temperature interval. Except for the rectly reported in literature for the pure enantiomeric
temperature region of SmC∗, the results of ORP mea- MHPOBCcompound[2]. Inmixtureswithx<0.88also
β
surements agree with those presented in [8]. Dielectric Sm CFI1 is missing. As the enantiomeric excess is fur-
spectroscopy measurements clearly exclude the presence therreduced(x<0.5),finallytheSmC∗ disappears,and
α
∗ ∗ ∗
of the ferroelectric synclinic Sm C phase (Fig. 2a). In only Sm A, Sm C and Sm C phases are left. Based
A
the Sm A phase, single, high frequency relaxation pro- on above observations the phase diagram in dependence
cess is observed that softens, e.g. the mode frequency on enantiomeric excess as shown in Fig. 3 is proposed.
decreasesandits amplitude increases,whenapproaching Webelievethatthistypeofthephasediagramisgeneral
∗ ∗
the Sm C phase. In the Sm C phase a single mode for antiferroelectric liquid crystals.
α α
at ∼ 60 kHz was observed. In the Sm C∗ phase weak Toaccountforexperimentalobservationstheoretically,
β
(∆ε ∼ 4), high frequency (350kHz) mode was detected, we introduce a new phenomenological model with bi-
typicalforthephasewithanantiferroelectricorder. Sim- linear interlayer interactions between the tilt vectors
ilarly as in the Sm C∗ phase [9] this mode is either re- ξ which are of longer range [5], and with biquadratic
A j
lated to the distortion of the crystallographic unit cell quadrupolarNNinteractions[6],whichbecomemoreim-
or to the rotation of the molecules around their main portant at larger tilts i.e. at lower temperatures. The
axes. Absence of the Goldstone mode excludes that Sm interlayer part of the free energy is
∗ ∗
C phase is the ferroelectric Sm C phase.
β 4 3
Die∗lectric permittivity increases upon entering the Gint = 1 a˜i (ξj ·ξj+i)+ f˜i (ξj ×ξj+i) +
Sm C phase. Here the main contributionto the dielec- 2
γ j i=1 i=1
tric susceptibility comes from the low frequency relax- X X X
ation process at 1-2 kHz, sometimes called the ferrielec- +bQ (ξj ·ξj+1)2 . (1)
tricGoldstonemode[10]. Therelaxationfrequencyofthe (cid:17)
mode detected in the Sm C∗ phase is not well defined. Achiralparametersa˜ andchiralparametersf˜ dependon
γ i i
The parameter α in the Cole-Cole formula, that char- stericandonvanderWaalsinteractionstonearestneigh-
acterizes the distribution of the relaxation frequencies, boring layers (NN), on electrostatic interactions to NN
is about 0.3. The presence of a broad mode is inherent andnextnearestneighboringlayers(NNN),onintralayer
∗
to the Sm C phase. The dielectric permittivity again chiral piezoelectric and NN flexoelectric coupling. They
γ
∗
decreases in the Sm C phase, in this phase two weak are given by Eq.(6) in the Ref. [5]. We assume that for
A
modes (∆ε<1) could be seen in MHz frequency region. the racemic mixture parameter a˜1 is negative favoring
∗
AboveresultsshowthattheSmC phaseistheferrielec- synclinic tilts at higher temperatures and becomes pos-
γ
∗ ∗
tricphaseidenticalastheSmC andtheSmC phase itive favoring anticlinic tilts at lower temperatures. In
FI1 β
istheantiferroelectricphase,biaxialthusopticallyactive chiral samples it gains additional positive contribution
and distinctly different than the Sm C∗ phase. Thus we proportional to x2, thus changes the sign at higher tem-
A
conclude that the Sm C∗β phase has the distorted clock perature. Parameter a˜2 is positive and does not depend
∗
four-layer structure of the Sm C phase. on the enantiomeric excess considerably. Quadrupolar
FI2
In the samples with a slightly lower optical purity NN interactions b are excess independent. All parame-
Q
(x∼0.97) five subphases could be identified below SmA ters are expressed in degree Kelvin [5].
phase from the DSC thermograms (Fig.1) and micro- Numericalanalysisofthe abovemodelgivesthe phase
scopic studies. An additional phase, which appears be- diagramswhichareinqualitativeagreementwiththeex-
∗ ∗
tween the Sm C and the Sm C phases, gives selec- perimentally obtained one Fig. 3. This detailed anal-
α FI2
2
ysis will be published elsewhere and here only the ba- enantiomeric excess is proposed. We also proposed the
sic physical understanding is given. In racemic mixtures new freeenergyforpolarsmectics whichincludes achiral
thesynclinicnegativea˜1 termprevailsoverthe anticlinic and chiral bilinear interlayer interactions to more dis-
positive a˜2 term directly below the transition from the tant layers and quadrupolar NN interactions. This free
∗
Sm A to the tilted phase and the Sm C phase appears. energy allows for the correct enantiomeric excess depen-
Upon decreasing temperature, a˜1 increases and changes dent phase sequence as well as the experimentally con-
its sign at a temperature where quadrupolar term is al- sistentstructures of allphases andfirst ordertransitions
ready significant. Since this term favors both synclinic between them.
and anticlinic tilts in NN layers, direct transition from Acknowledgment: ThisworkwassupportedbyPolish-
∗ ∗
the Sm C phase to the Sm C phases is obtained. In Slovenian exchange program. The financial support for
A
chiral samples, the anticlinic part of the parameter a˜1 E.G. from TFR Swedish Research Council is acknowl-
increases and a˜1 becomes by its absolute value com- edged. E.G. is gratefull to Prof. S. Lagerwall for his
parable to the parameter a˜2 directly below the transi- hospitality during her stay at the Chalmers University.
tion to the tilted phase. This results in a formation
∗
of the Sm C phase with the short pitch modulation
α
which becomes stable over a wider temperature range
upon increasing enantiomeric excess. It evolves into the
∗
SmC phaseduetoincreasingquadrupolarinteractions.
Due to increased enantiomeric excess also the tempera-
[1] A.Fukuda, Y.Takanishi, T.Isozaki, K.Ishikawa and
ture increases where the a˜1 changes sign. Therefore the H.Takezoe, J.Mat.Chem. 4, 997 (1994).
influence of quadrupolar interactions is weaker and can-
[2] A.D.L.Chandani, E.Gorecka, Y.Ouchi, H.Takezoe and
notpreventtheexistenceofmodulatedphases. Withpu- A.Fukuda Jap.J.App.Phys. 28, L1265, (1989);
rificationalsothetemperaturerangeofmodulatedphases
E.Gorecka, A.D.L.Chandani, Y.Ouchi, H.Takezoe and
increases. In the temperature region where a˜1 ≈ 0 the A.Fukuda,Jap.J.Appl.Phys. 29, 131 (1990).
structurewithtwointerchangingphasedifferencesαand [3] P.Mach,R.Pindak,A.-M.Levelut,P.Barois,H.T.Nguyen,
β with α+β ≈ π, is formed. The quadrupolar term b C.C.Huang, and L.Furenlid, Phys. Rev. Lett. 81,
Q
favors values of α = 0 and β = π but chiral NN inter- 1015 (1998). P.Mach, R.Pindak,A.-M.Levelut,P.Barois,
actions increase the value of α and decrease the value of H. T.Nguyen, H.Baltes, M.Hird, K.Toyne, A.Seed,
β. This structure obtained by the minimization of the J.W.Goodby, C.C.Huang, and L.Furenlid, Phys.Rev.E
60,6793, (1999).
Eq. (1) is consistent with a tentatively proposed struc-
∗ [4] J.F.Li, E.A.Shack, Y.K.Yu, X.Y.Wang,
ture for the Sm C phase [11,12]. The structure has
FI2 C.Rosenblatt, M.E. Neubert, S.S.Keats and H.Gleeson
the biaxial unit cell, a negligible polarization and is he-
Jap.J.Appl.Phys.235,L1608(1996);T.Sako,Y.Kimura,
licoidally modulated with the long optical pitch defined R.Hoyakawa,N.Okabe,Y.Suzuki,Jap.J.Appl.Phys.235,
by δ (Fig.4a). Decreasing the temperature further, the L114 (1996); A. Jakli J.Appl.Phys. 85, 1101 (1999).
parameter a˜1 becomes positive and thus simultaneously [5] M.Cˇepiˇc, B.Zˇekˇs, Phys.Rev.Lett 87, 085501 (2001).
with the a˜3 parameter encourages the structure where [6] D.Pociecha, E.Gorecka, M.Cˇepiˇc, N.Vaupotiˇc, B.Zˇekˇs,
tilts inthirdneighboringlayersaresynclinic. Due to the D.Kardas, and J.Mieczkowski, Phys.Rev.Lett. 86, 3048
up down symmetry, the phase difference α is followed (2001).
by two equal phase differences β where α + 2β ≈ 2π. [7] R- or S- octanol-2 with 99.5% enantiomeric excess was
The obtained unit cell is polar and biaxial. The struc- used for the synthesis of the MHPOBC compound as
described by W.J. Drzewinski Phd thesis, (2000).
tureishelicoidallymodulatedwiththelongopticalpitch
[8] M.Sˇkarabot, M.Cˇepiˇc, B.Zˇekˇs, R.Blinc, G.Heppke,
defined by δ (Fig. 4b). It can be recognized as the one
∗ A.V.Kityk,I.Muˇseviˇc, Phys.Rev.E58, 575 (1998)
proposedfortheSmC phase[11,12]. Inpuresamples
FI1 [9] Yu.P.Panarin, O.Kalinovskaya, J. K.Vij, J.W.Goodby
∗
the temperature rangeof the Sm Cα phase and the tem- Phys.Rev.E55, 4345 (1997).
perature rangeofthe modulated phasesare so wide that
[10] S.Merino, M.R.de la Fuente, Y.Gonz´alez, M.A.P´erez
∗
the Sm C phase cannot evolveand direct phase transi- Jubindo, B.Ros, J.A.Pu´ertolas, Phys.Rev.E54, 5169
tion between the Sm C∗α phase and the Sm C∗FI2 phase (1996); M.Cˇepiˇc, G.Heppke, J.M.Hollidt, D.L¨otzsch,
occurs as observed in MHPOBC. B.Zˇekˇs, Ferroelectrics 147, 43 (1993); M.Glogarova,
To conclude, in this Letter we report experimental H.Sverenyuk, H.T.Nguyen, C.Destrade, Ferroelectrics
and theoretical studies which show that in the opti- 147, 159 (1993).
cally pure antiferroelectric liquid crystal MHPOBC, the [11] T.Akizuki, K.Miyachi, Y.Takanishi,
∗ ∗ K.Ishikawa, H.Takezoe and A.Fukuda,Jpn.J.Appl.Phys.
SmC phaseisnottheferroelectricSmC phasebutthe
β∗ 38, 4832(1999).
SmC phasewithfour-layerunitcellandantiferroelec-
FI2 ∗ [12] P.M.Johnson, D.A.Olson, S.Pankratz, T.Nguyen,
tric properties. The ferroelectric Sm C phase appears
J.Goodby, M.Hird and C.C.Huang, Phys.Rev.Lett.84,
only after aslightracemization. Forantiferroelectricliq-
4870 (2000).
uid crystals the general phase diagram with respect to
3
FIG.2. Dielectric losses vs. temperature and frequency in
S-MHPOBC enantiomer (a) and and its mixture with 1,5%
of R-enantiomer (b).
FIG. 1. DSC scans for MHPOBC mixtures with various
percentage of R enantiomer measured in heating scans with
1K/minrate. Forconcentration1.5%thecoolingscanisalso
shown.
FIG.3. PhasediagramforMHPOBCindependenceofop-
tical purity.
4
∗
FIG.4. a)TheSmCFI2 phaseandb)theSmCFI1 phase
obtained for the optically pure material x = 1 and
the set of parameters expressed in K (Eq.(6), Ref.[5]):
a1 = (−4.1+90 θ2), cp = 0.6, µ = 0.77, b0 = 2, b1 = b0/5,
b2 = b0/100, f1 = 0 and for bQ = −17.7. Corresponding
set of effective parameters expressed in mK is: a˜2 = 73.5,
a˜3 = −7.41, a˜4 = 0.65, f˜1 =−231, f˜2 = 23.1 and f˜3 =2.02.
◦
ThetiltangleistakenfromRef.[8]for(a)θ=12.5 andthere-
fore a˜1 =137 mK and for (b)θ=13.2◦ and a˜1 =−69.6 mK.
5
