Effect of smectic short-range order on the discontinuous anchoring transition innematic liquid crystals
D. Venkata Sai, T. Arun Kumar, W. Haase, Arun Roy, and Surajit Dhara
Citation: The Journal of Chemical Physics 141, 044706 (2014); doi: 10.1063/1.4890532
View online: http://dx.doi.org/10.1063/1.4890532
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THE JOURNAL OF CHEMICAL PHYSICS 141, 044706 (2014)

Effect of smectic short-range order on the discontinuous anchoringtransition in nematic liquid crystals
D. Venkata Sai,1 T. Arun Kumar,1 W. Haase,2 Arun Roy,3 and Surajit Dhara1,a)1

School of Physics, University of Hyderabad, Hyderabad-500046, India
Darmstadt University of Technology, Eduard- Zintl-Institute for Inorganic and Physical Chemistry,Petersenstr. 20, Darmstadt 64287, Germany
3
Raman Research Institute, C. V. Raman Avenue, Bangalore-500080, India
2(Received 17 March 2014; accepted 7 July 2014; published online 25 July 2014)
We report studies on the temperature dependent alignment behavior of a homologous series of trans,
trans- 4, 4 -dialkyl-(1α,1 α-bicyclohexyl)-4β-carbonitrile (CCNs) on a perfluoropolymer coatedcells. Among six compounds in the series, one (CCN-35) has only nematic phase and the remaining five have either smectic-A or smectic-B in addition to the nematic phase. We simultaneously
performed temperature dependent dielectric measurements and optical polarising microscope observation. It is found that except for CCN-35 and CCN-73, the remaining four compounds exhibit discontinuous anchoring transition from planar to homeotropic and vice versa with increasing
thermal hysteresis. We developed a simple theory taking into account the effect of smectic shortrange order at the substrates to explain the experimental observations. © 2014 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4890532]
I. INTRODUCTION

The molecules in liquid crystal displays (LCDs) areoriented in a particular direction with respect to the confining
substrates. Generally, two types of orientations are preferred
for both LCDs and for physical measurements, namely,
planar and homeotropic. In the planar state, the director(the average direction of molecular orientation1 ) is parallel
and in the homeotropic state the director is perpendicular
to the substrates. There are various techniques for aligningliquid crystal molecules on the substrates. One common andinexpensive technique is coating of appropriate polyimides
to get the desired alignments (planar or homeotropic). It
is known that the alignment of liquid crystal molecules
depend upon topograpy of the surfaces, chemistry of theliquid crystals, aligning agents, curing temperatures, andthe rubbing strengths.2–8 The commercial aligning agents
provide stable director alignment in the sense that it does
not change the molecular orientation with temperature.
However, there are some reports that on some unconventionalalignment layers, the director can change its orientationfrom planar to homeotropic and vice versa continuously or
discontinuously with temperature.9–12, 14–22 Consequently,
some theories are developed that shows the effect of various
interactions on the alignment properties such as van der
Waals interaction,23–25 short range dipole interaction, longrange electrostatic interactions,26 and smectic short-rangeorder effect.6, 8 In the recent past, we have reported on the
discontinuous anchoring transition of a nematic liquid crystal(CCN-47) from planar to homeotropic with a large thermal
hysteresis on perfluoropolymer treated cells.27 We showed
the possibility of various interesting applications, for example, rewritable memory device,28–30 optical wave guiding,31a) Electronic address: sdsp@uohyd.ernet.in

0021-9606/2014/141(4)/044706/6/$30.00

bistable dielectric, and conductivity in this system.32 However, the reason for discontinuous anchoring transition inthis system remained unexplored. In this paper, we studied
the alignment properties of the homologous series of CCNs
liquid crystals on perfluoropolymer. Interestingly, we foundthat two compounds do not show any anchoring transition.
The remaining four compounds exhibit strong discontinuous
anchoring transition in the nematic phase with increasing
thermal hysteresis. Our experimental results suggest thatthe effect of smectic short-range order and the temperature
range of nematic is important for the observed discontinuous
anchoring transition. We developed a simple theory taking
into account the short-range smectic order at the substrates
that explains the experimental results.

II. EXPERIMENTThe chemical structure and the phase transition temperatures of compounds are shown in Fig. 1 and in Table I. The
compound CCN-35 shows only one liquid crystalline phase,i.e., nematic (N). CCN-38 and CCN-47 show both nematicand smectic-A (SmA) phases. The remaining compounds
CCN-46, CCN-55, and CCN-73 show both nematic andsmectic-B (SmB) phases. Some physical characterizations
such as X-ray, NMR, and dielectric relaxation studies havealready reported.33–36 The molecules have transverse dipole
moments (cyano group, -CN) and exhibits low birefringenceand large negative dielectric anisotropy.37, 38
The experimental cells were made of two indium tinoxide (ITO) coated glass plates with circularly patterned electrodes. These plates were spin coated with perfluoropolymer,
poly [perfluoro (4-vinyloxy -1-butene)], known as CYTOP.
A solution was prepared by adding 1 part of CTX-809A to
2 parts of CT-Solv.180 by weight39 and these were obtained

141, 044706-1© 2014 AIP Publishing LLC

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TABLE I. Phase transition temperatures (◦ C) of the compounds. K−→ Crystal, SmB−
→ Smectic-B, SmA−
→ Smectic-A, I −→ Isotropic.

FIG. 1. Chemical structure of CCN-mn compounds.

from Asahi Glass Co., Ltd. Japan. The CYTOP coated glass
plates were cured at 100 ◦ C for 30 min. Cells were made byplacing together such that their active areas overlapped. The
typical cell thickness used in the experiment was ∼8 μm.
The empty cell was heated and filled with the sample in theisotropic phase. The phase transitions and the anchoring transitions of the compounds were observed using a polarizing
optical microscope (Nikon, LV100 POL) and a temperature
controller (Instec, mk1000). The temperature dependent
dielectric constant was measured by using a LCR meter(Agilent 4980) in cooling and heating at a temperature stepof 0.1 ◦ C/min. A sinusoidal voltage of frequency 1 kHz andan amplitude 0.2V was used for the dielectric measurements.
The phase transition temperatures of the compounds and theiranchoring transition temperatures were determined from thedielectric data.

SamplePhase transitions (◦ C)

Nematic range (◦ C)

CCN-35
CCN-38
CCN-46
CCN-47
CCN-55
CCN-73

K 38.4 N 49.3 I
K 41 SmA (23) N 49.5 I
K 30 SmB (26) N 54.7 I
K 25.6 SmA 28.2 N 57.3 I
K 25 SmB 30 N 66.4 I
K 38.6 SmB (38) N 50.2 I

10.9
26.5
28.7
29.1
30.4
12.2

III. RESULTS AND DISCUSSIONSWe present some representative textures of four compounds (CCN-35, CCN-38, CCN-55, and CCN-73) in unrubbed CYTOP coated cells at various temperatures in Fig. 2.
In CCN-35, below isotropic-nematic phase transition temperature a Schlieren texture with both half and integer strength
disclinations are observed (Figs. 2(a)– 2(b)). This suggeststhat the director is in the plane (planar anchoring), as any tiltof the director in this case is topologically not allowed.40, 41
It crystallizes at 38.4 ◦ C without any smectic phase. The
Schlieren texture remains the same in the entire nematic range
suggesting no anchoring transition. CCN-38 exhibits similar

FIG. 2. Typical photomicrographs of four compounds at various temperatures during anchoring transition from planar to homeotropic while cooling. (a) CCN35 at 42 ◦ C (b) CCN-35 at 38.3 ◦ C (c) CCN-35 at 37.8 ◦ C (d) CCN-38 at 47.7 ◦ C (e) CCN-38 at 40.7 ◦ C (f) CCN-38 at 38.7 ◦ C (g) CCN-55 at 62.1 ◦ C (h)CCN-55 at 26.9 ◦ C (i) CCN-55 at 26 ◦ C (j) CCN-73 at 43 ◦ C (k) CCN-73 at 37.8 ◦ C (l) CCN-73 at 36.5 ◦ C.

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texture in the nematic phase (Fig. 2(d)). On further cooling, it(CCN-38) shows appearance of small dark regions (Fig. 2(e))
at a particular temperature. These dark regions grow abruptly
and randomly and finally the whole field of view becomescompletely dark within a short temperature range (∼1 ◦ C(Fig. 2(f)). This means that the director orientation spontaneously changes from planar to homeotropic while cooling.
The texture of CCN-55 in the nematic phase (Fig. 2(g)) isalmost similar to that of CCN-38 (Fig. 2(d)). As the sample is cooled, the anchoring transition takes place by forming small dark regions just before the transition to SmB phase(Fig. 2(h)). Finally, the dark regions together with the typical
SmB textures remain in the field of view (Fig. 2(i)). In CCN73, the texture in the nematic phase (Fig. 2(j)) is similar tothat of the previous compounds (Figs. 2(a), 2(d), and 2(g)).
The N to SmB phase transition is observed around 37.8 ◦ C(Fig. 2(k)) and it becomes completely SmB (Fig. 2(l)) without any anchoring transition in the nematic phase. When thesamples (those exhibited anchoring transitions in cooling) areheated up from the homeotropic state, the texture goes to planar state with characteristic umbilic defects beyond a particular temperature. This homeotropic to planar transition takes
place at higher temperature than that observed during cooling(not shown in Fig. 2). Thus the anchoring transition exhibitsa thermal hysteresis in the nematic phase.
In order to find the anchoring transition temperatures andthe range of thermal hysteresis, we measured the effective dielectric constant ( eff ) as a function of temperature in all thesamples. The dielectric measurements were preferred than optical transmission measurements because it does not need rubbing which can modify the surface properties and hence canaffect the anchoring transition temperatures. The temperature
variation of  eff is shown in Fig. 3. The effective dielectric
constant ( eff ) of all the compounds in the planar state (as observed under polarizing microscope) is higher than that of theisotropic phase. This shows that all the compounds have negative dielectric anisotropy, i.e.,  = ( || −  ⊥ ) < 0, where
the subscripts refer to the direction in relation to the director. Thus, the dielectric constant of the planar state is  eff = ⊥ and in the homeotropic state  eff =  || . This was further
confirmed by measuring the dielectric constants in independent planar and homeotropic cells (coated with AL-1254 and
JALS-204), respectively.42 It is observed that in compound
CCN-35, there is no noticeable change in dielectric constantduring heating and cooling in the nematic phase. In case of
CCN-38, CCN-46, and CCN-47, we notice an abrupt decreaseof  eff in the nematic phase at a particular temperature (Tac )(Fig. 3(a)). Similarly, again an abrupt increase in  eff is observed while heating at higher temperature (Tah ). For example, in CCN-38, we observe  eff decreases abruptly while
cooling at about 41.4 ◦ C (=Tac ). Similarly again a abrupt
increase in  eff is observed while heating at about 43.7 ◦ C(=Tah ). Thus the temperature range of thermal hysteresis(Th =Tah -Tac ) is 2.3 ◦ C. The variation of  eff for both CCN55 and CCN-73 is shown in Fig. 3(b) separately. In case of
CCN-55, the planar to homeotropic transition occurs during cooling just before the SmB phase transition as discussed earlier (Fig. 2(h)). Surprisingly, there is no anchoring transition observed in CCN-73. The abrupt decrease of

J. Chem. Phys. 141, 044706 (2014)

FIG. 3. (a) Temperature variation of dielectric constant of CCN-35, CCN46, CCN-38, and CCN-47. (b) Temperature variation of dielectric constantof CCN-55 and CCN-73. The solid and open symbols correspond to the data
while cooling and heating, respectively. The phase transition and anchoringtransition temperatures during cooling and heating are indicated with arrows.
Nematic-isotropic phase transition TNI ; Planar to homeotropic transition incooling Tac ; Homeotropic to planar transition in heating Tah .

the dielectric constant in CCN-73 at 35 ◦ C is due to the
N-SmB phase transition (Fig. 2(k)). The anchoring transition temperatures and the thermal widths of the hysteresis are listed in Table II. It is observed that CCN-35 does
not show any anchoring transition, CCN-38, CCN-46, CCN47, and CCN-55 shows discontinuous anchoring transitionin the nematic phase with increasing thermal hysteresis.
The largest thermal hysteresis is observed in CCN-55 (Th
= 9.5 ◦ C).
There are many experimental studies reported on the anchoring transition in nematic liquid crystals as mentioned
in the Introduction. Various types of molecules such as polar, nonpolar, centrosymmetric with nematic or both nematicand smectic-A phases are chosen in various substrate conditions. Several theories were also developed to explain the
TABLE II. Anchoring transition temperatures and thermal hysteresis, Tac−→ anchoring transition temperature while cooling, Tah −→ anchoring transition temperature while heating. Thermal hysteresis, Th =Tah -Tac .
SampleTac (◦ C)

Tah (◦ C)

Th (◦ C)

CCN-35
CCN-38
CCN-46
CCN-47
CCN-55
CCN-73

41.4
44.7
44.5
27.3

No anchoring transition
43.7
47.8
49.8
36.8
No anchoring transition

0
2.3
3.1
5.3
9.5
0

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experimental observations. For example, Parsons et al. haveshown that the competition between dipole and quadrupole
interaction can lead to the anchoring transition.16 Barbero
et al. have shown that the competition between the nematicnematic and nematic-substrate interaction leads to the anchoring transition.19 Alexe-Inescu has pointed out that the surface anchoring energy can decrease due to the gradient flexoelectric effect and eventually can cause to the anchoringtransition.14 Nazarenko and Lavrentovich proposed that thebalance between orientating tendencies between the electric
double layer and the direct molecular interaction at the surface is responsible for the observed second order anchoringtransition.15 Komitov et al. reported on the anchoring transition in hybrid aligned cell and gave a model that accounts
for the dependence of the elastic constants on the scalar order parameter. Zhang et al. had shown anchoring transition
on micro-structured surface and suggested that it is due tothe frustrated boundary condition in which the elastic energy
due to spatial variation in the molecular orientation compromises an increase in the surface anchoring energy.17 From
the above discussion it appears that there are various possible
mechanisms for different types of the anchoring transitions
in various experimental conditions. In the present system themolecules are highly polar and at a first glance Parsons model
appears to be reasonable16 compared to the other model discussed. However, absence of anchoring transition in CCN-35
rules out the possibility that it is due to the competition between dipolar and quadrupolar interactions. Looking at Tables I and II, it appears that the presence of smectic phaseand relatively wide temperature range of nematic is important
for the occurrence of discontinuous anchoring transition in
the CCNs homologue. In a computer simulation, Chakrabarti
and Bagchi have shown that the onset of the growth of theorientational order in the nematic phase is found to induce
a translational order, resulting in a smectic-like layer in theunderlying inherent structures. Interestingly, they found thatthe inherent structures never seem to sustain orientational order alone if the parent nematic phase is sandwiched between
the high-temperature isotropic phase and the low-temperaturesmectic phase.43 It has been shown by Shioda et al. that SmA
short range order in the nematic phase can lead to continuous anchoring transition from tilted to homeotropic.6 However, discontinuous anchoring transition with a large thermal
hysteresis so far has not been explained theoretically.

where F0 is the free energy in the isotropic phase and ν denotes the outward normal at the two NLC-glass interfaces.
The factor 2 in Eq. (1) is due to the contribution from thetwo surfaces. The nematic tensor order parameter is given by
Qij = 32 S(ni nj − 13 δij ), where S and n being the scaler orderparameter and the director in the nematic phase, respectively.
In the above expansion of the free energy, we have considered
only terms up to second order in Qij . For the samples studiedin our experiments, the first order anchoring transition was observed only for samples which exhibit SmA or SmB phases
below the nematic phase. The anchoring transition was notobserved for the lower homologue of the compounds which
do not exhibit any smectic phase (CCN-35). Therefore, it isreasonable to assume that the surface induced Smectic-like order plays a crucial role in the discontinuous anchoring transition. In fact, the effect of smectic short range order on the anchoring transition has been discussed previously.6, 8 For compounds exhibiting SmA phase, the glass-NLC interfaces tend
to induce a SmA-like layer structure near the interfaces evenin the nematic phase with layers parallel to the interface. The
last term in Eq. (1) denotes the coupling of the surface induced SmA order with the orientational order parameter Qij .
Substituting Qij in Eq. (1), we obtain
F = F0 + β11 S{(n · ν)2 − 1/3} + β20 S 2+β21 S 2 {(n · ν)2 + 1/3} + β22 S 2 {(n · ν)2 − 1/3}2
 d2−3Dq Sψ(z){(n · ν)2 − 1/3}dz,(2)0where β 11 = 3γ 11 , β 20 = 3γ 20 , β 21 = 3γ 21 /2, and β 22
= 9γ 22 /2. Assuming that the surface induced smectic orderdecays exponentially with a correlation length ξ in the bulkof the nematic phase at temperatures above the nematic tosmectic transition temperature (TNA ), the last integral term in
Eq. (2) can be estimated as −6Dq2 Sξ ψ 0 {(n · ν)2 − 1/3}, andthe free energy can be written as
F [S, ξ, (n · ν)] = F0 + F1 [S, ξ ] + F2 [S, ξ, (n · ν)],

(3)

where



 

β22
β11
β21
2
S + β20 ++S2
F1 [S, ξ ] = 2Dq ξ ψ0 −
3
3
9
(4)
is the isotropic part of the surface free energy. The anisotropic
part of the surface free energy (third term in Eq. (3)) is givenbyIV. THEORETICAL

We present a simple theoretical model to account for theobserved discontinuous anchoring transition in the nematic
phase. We assume that the nematic liquid crystal (NLC) of
thickness d is bounded by two identical glass plates with thesurface normals along the z-axis and there is no spatial variation of the orientational order parameter across the cell. The
free energy of the sample per unit area can be written as12, 13
F = F0 + 2[γ11 νi Qij νj + γ20 Qij Qj i + γ21 νi Qij Qj l νl
 d+γ22 (νi Qij νj )2 ] − Dψ(z)q 2 (νi Qij νj )dz, (1)0F2 [S, ξ, (n · ν)] = A(S, ξ )(n · ν)2 + B(S)(n · ν)4 ,(5)where the coefficients A(S, ξ ) and B(S) are defined as




2β22
2
A(S, ξ ) = β11 − 6Dq ψ0 ξ S + β21 −S23B(S) = β22 S 2 .

(6)

The stable surface orientation, φ = cos−1 (n · ν) can be obtained by minimizing the free energy in Eq. (5).
To account for the experimentally observed first order anchoring transitions, we assume that the coefficients

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J. Chem. Phys. 141, 044706 (2014)

β 11 , β 21 > 0 but the coefficient β 22 < 0. Then the stability
conditions for the surface tilt angle φ are given by φ = π /2
if A(S, ξ ) > 0 and φ = 0 if A(S, ξ ) + 2B(S) < 0. In themean field approximation, the smectic correlation length ξdepends on temperature as ξ = ξ 0 [(T − TNA )/TNA ]−1/2 for
T > TNA . As the anchoring transition in our samples occur
at temperature far below the isotropic to nematic transition
temperature TNI , we assume that the orientational order parameter S saturates to a constant value and is independentof temperature during the anchoring transition. This is reasonable because those four compounds which showed anchoring transition have relatively large nematic temperature
range (Table I). Then minimization of Eq. (5) and the stability conditions predict a first order anchoring transition from
φ = π /2 at temperature T > Tah to φ = 0 at temperature
T < Tac with thermal hysteresis between Tah and Tac as observed experimentally, whereTah = TNA + TNA

36D 2 q 4 ψ02 ξ02,[β11 + (β21 − 4|β22 |/3)S]2

36D 2 q 4 ψ02 ξ02.
Tac = TNA + TNA[β11 + (β21 + 2|β22 |/3)S]2(7)

We now estimate Tah , Tac , and Th from Eq. (7). Considering
the case of the compound CCN-47, the layer spacing in thesmectic phase is ∼20 × 10−8 cm giving q ∼ 3 × 107 cm−1 .
We assume that the bare smectic correlation length ξ 0 ∼ 5
× 10−8 cm and D ∼ 3.9 × 10−8 erg/cm.6 The anchoring coefficients β 11 and β 21 are expected to be of similar magnitudes.
We assume β 11 ∼ 2 erg/cm2 and β 21 = 0.9β 11 . The magnitude of the higher order anchoring coefficient β 22 is expected
to be relatively smaller than β 11 and we assume that |β 22 |∼ 0.15β 11 . At temperatures corresponding to anchoring transition in our samples, we assume that the nematic order parameter S ∼ 0.6 and the surface induced smectic order parameter ψ02 ∼ 0.005. Using the above parameters, Tah , Tac ,and Th are estimated to be 323 ◦ K, 318 ◦ K, and 5 ◦ K, respectively, which agree very well with our experimental observations. As reported earlier by Rosenblatt et al., the surface
induced smectic order in the nematic phase can drive an anchoring transition from the planar to homeotropic orientation
which is continuous in nature.6 Here, we demonstrated bothexperimentally and theoretically that such transition can be offirst order with the discontinuous jump in the surface orientation from planar to homeotropic orientation with a thermal
hysteresis.
V. CONCLUSIONSIn conclusion, we studied the anchoring transition ofa homologous series of a liquid crystal (CCNs) on perfluoropolymer treated cells. CCN-38, CCN-46, CCN-47, andCCN-55 exhibits discontinuous anchoring transitions with increasing thermal hysteresis. We found that the compound
CCN-35 which has no SmA or SmB phase does not show
any anchoring transition. CCN-73 has SmB phase but the nematic temperature range is short and does not also show any
anchoring transition. Our experimental results show that thesmectic short-range order and the wide temperature range ofnematic is important for discontinuous anchoring transition.
We developed a simple theory considering the experimental
observations and showed the discontinuous anchoring transition with a finite thermal hysteresis.

ACKNOWLEDGMENTS

We gratefully acknowledge support from the DSTPURSE and V.D. acknowledges UGC for a fellowship. We
acknowledge Ashai Glass, Japan for CYTOP.
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