Electroclinic effect in chiral SmA* liquid crystals induced by atropisomeric biphenyl dopants: Amplification of the electroclinic coefficient using achiral additives

Article abstract of DOI:10.1039/b515313a

The atropisomeric compound (R)-2,2′,6,6′-tetramethyl-3, 3′-dinitro-4,4′-bis[(4-nonyloxybenzoyl)oxy]biphenyl ((R)-1) was doped in the achiral liquid crystal hosts 2-(4-butoxyphenyl)-5- octyloxypyrimidine (2-PhP) and 4-(4′-heptyl[1,1′-biphen]-4-yl)-1- hexyl

Full text of DOI:10.1039/b515313a

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PAPER
www.rsc.org/materials | Journal of Materials Chemistry
Electroclinic effect in chiral SmA* liquid crystals induced by atropisomeric
biphenyl dopants: amplification of the electroclinic coefficient using achiral
additives{
C. Scott Hartley,a Nadia Kapernaum,b Jeffrey C. Roberts,a Frank Giesselmannb and Robert P. Lemieux*a
Received 27th October 2005, Accepted 29th March 2006
First published as an Advance Article on the web 24th April 2006
DOI: 10.1039/b515313a
The atropisomeric compound (R)-2,29,6,69-tetramethyl-3,39-dinitro-4,49-bis[(4-
nonyloxybenzoyl)oxy]biphenyl ((R)-1) was doped in the achiral liquid crystal hosts
2-(4-butoxyphenyl)-5-octyloxypyrimidine (2-PhP) and 4-(49-heptyl[1,19-biphen]-4-yl)-1-
hexylcyclohexanecarbonitrile (NCB76), and electroclinic coefficients ec were measured as a
function of the dopant mole fraction x1 in the chiral SmA* phase at T 2 TC = +5 K. The
extrapolated ec values of 3.07 and 2.28 deg mm V21 are comparable to some of the highest ec
values reported for neat SmA* materials. The electroclinic coefficient of a 4 mol% mixture of
(R)-1 in 2-PhP is amplified by achiral 2-phenylpyrimidine additives (5 mol%) that are longer
than 2-PhP; in the best case, ec is amplified by a factor of 3.2 with 5-(tetradecyloxy)-2-(4-
(tetradecyloxy)phenyl)pyrimidine (3g), which is almost twice as long as 2-PhP. However, no
amplification is observed in a 4 mol% mixture of (R)-1 in NCB76 using the same series of
additives. A correlation between ec values and the temperature range of the SmA* phase
suggests that the amplification of ec with increasing length of the additive 3 in the (R)-1/2-PhP
mixture is due primarily to a decrease in the tilt susceptibility coefficient a as the second-order
SmA*–SmC* phase transition moves away from the tricritical point. Measurements of
smectic layer spacing as a function of T 2 TC by small-angle X-ray scattering are consistent
with this explanation. The results show that the variation in reduced layer spacing dA/dC
with T 2 TC for the pure host 2-PhP fits to a square-root law, which indicates that the
second-order SmA–C transition is nearly tricritical. On the other hand, the corresponding
variation in dA/dC with T 2 TC for a 5 mol% mixture of 3g in 2-PhP fits to a linear
relation, which indicates that the second-order SmA–C transition approaches typical
mean-field behavior.
applied field E at low field strengths.3 This relationship is
Introduction
expressed by eqn (1) and (2),
The electroclinic effect is a unique and technologically useful
electro-optical property of the chiral smectic A (SmA*) liquid
crystal phase.1 The SmA* phase is characterized by a diffuse
layer structure in which the molecular long axes of chiral
mesogens are oriented perpendicular to the layer plane, on the
time-average, and it cannot be distinguished from the achiral
SmA phase in the absence of external perturbations. However,
Garoff and Meyer showed that an electric field E applied
parallel to the layers of a chiral SmA* phase induces a
molecular tilt h relative to the layer normal in a direction
orthogonal to the field.2 This electroclinic effect is described by
a phenomenological model derived from Landau theory which
predicts a linear dependence of the induced tilt angle h on the
h = ec E
(1)
(2)
c
ec~
aðT{TCÞ
where ec is the electroclinic coefficient, c is the electroclinic
coupling constant, and a(T 2 TC) is the first coefficient of the
Landau free-energy expansion. The term a is a nonchiral
parameter known as the tilt susceptibility coefficient, or tilt
elastic modulus, which describes the restoring torque taking
the director back to the layer normal. The term c is a chiral
parameter describing the coupling between the spontaneous
polarization and the tilt h in the SmC* phase.1 The relation-
ship between h and E normally deviates from linearity at high
field strengths and/or when the temperature approaches the
Curie point TC corresponding to the second-order transition
from the orthogonal SmA* to the tilted SmC* phase.
aChemistry Department, Queen’s University, Kingston, Ontario, Canada
K7L 3N6
bInstitute of Physical Chemistry, Universita¨t Stuttgart, Pfaffenwaldring
55, D-70569, Stuttgart, Germany
The linear relationship between the induced electroclinic
tilt and E at low field strengths makes it possible to generate
a gray scale display between crossed polarizers, and its
response time may be orders of magnitude faster than a
{ Electronic supplementary information (ESI) available: synthetic
procedures and spectral characterization data (1H and 13C NMR,
low- and high-resolution MS) for compounds 3a–h. See DOI: 10.1039/
b515313a
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surface-stabilized ferroelectric liquid crystal (SSFLC) display.4
Such properties make electroclinic SmA* materials suitable
for a wide range of electro-optical device applications,
including micro-color filters, tunable color filters and spatial
light modulators.5 To develop electroclinic materials for device
applications, several groups have focused their efforts on the
design of chiral SmA* liquid crystals with high electroclinic
coefficients,6–10 including de Vries SmA* liquid crystals,
which are characterized by a tilted molecular orientation with
random azimuthal distribution.11–19 However, the design of
SmA* liquid crystals suitable for device applications is a multi-
variable problem that also requires the optimization of achiral
parameters unrelated to the electroclinic properties. A solution
to this problem, which is widely used in the formulation of
ferroelectric SmC* liquid crystals for SSFLC display applica-
tions,20 is to combine a chiral dopant that induces the desired
electroclinic response at low concentration with an achiral
SmA liquid crystal host mixture.21–23
powers of (R)-2 and (S)-2 increase by factors of 5.5 and 2.8,
respectively, and the sign of polarization induced by (S)-2 is
inverted from negative to positive. These results reflect the
diastereomeric relationship between the two dopant/probe
combinations, and are consistent with long range chiral
perturbations amplifying the polarization power of 2.
As part of a broader study on the influence of the SmC host
composition on polarization amplification in the SmC* phase,
we recently showed that dopant 1 induces an electroclinic
effect in mixtures of 2-PhP and 5-PhP that scales with the mole
fraction of the latter; at a dopant mole fraction of x1 = 0.04,
the electroclinic coefficient ec at 5 K above the Curie point
(T 2 TC = +5 K) ranges from 0.06 deg mm V21 (x5-PhP = 0.0) to
0.34 deg mm V21 (x5-PhP = 0.24).27 The increase in ec was
originally attributed to a more effective propagation of chiral
perturbations via interactions with the non-planar 5-phenyl-
pyrimidine core, and implied that CTF amplification is also
operative in the chiral SmA* phase. In this paper, we report a
more complete assessment of the propensity of 1 to induce
an electroclinic effect in achiral SmC hosts that refutes our
original explanation, and ultimately addresses a question of
fundamental importance: does the SmA* phase under an
electric field have the same structure as the SmC* phase?28–30
In addition, we report a large amplification of ec in 4 mol%
mixtures of (R)-1 in the unsymmetrically substituted host
2-PhP upon addition of symmetrically substituted 2-phenyl-
pyrimidine mesogens that cause a broadening of the tempera-
ture range of the SmA* phase.
Results and discussion
Electroclinic coefficient measurements
Mixtures of (R)-1 in the achiral hosts 2-PhP and NCB76
were prepared, with dopant mole fractions in the ranges of
0.04 ¡ x1 ¡ 0.2 and 0.02 ¡ x1 ¡ 0.08, respectively. The
mixtures were aligned in commercial ITO glass cells with
parallel-rubbed polyimide surfaces and a spacing of 4 mm.
Electroclinic tilt angles h were measured at T 2 TC = +5 K by
polarized optical microscopy (POM) as half the rotation
between the two extinction positions observed upon applying a
0.1 Hz square wave ac field E ranging from 0 to 15 V mm21. In
most cases, plots of h vs. E gave good linear least-squares fits
from which ec values were derived according to eqn (1).
Samples at the high end of the x1 ranges gave plots of h vs. E
that deviate from linearity at high fields; in those cases, the
linear portions of the plots were used to determine ec values.
Plots of ec vs. x1 in 2-PhP and NCB76 gave good least-squares
fits (R2 = 0.991 and 0.999, respectively), as shown in Fig. 1.
Due to the paucity of studies reporting electroclinic coeffi-
cients for induced SmA* phases, it is difficult to assess
the effectiveness of 1 as an electroclinic chiral dopant.
Nevertheless, extrapolations of ec to x1 = 1.0 according to
the least-squares fits give values of 3.07 ¡ 0.17 deg mm V21 in
2-PhP and 2.28 ¡ 0.06 deg mm V21 in NCB76, which are of
the same order of magnitude as the highest electroclinic coeffi-
cients reported for neat SmA* liquid crystals (on the order of
6–7 deg mm V21 at the same reduced temperature).12,31
In general, SmA* liquid crystals with large ec values
exhibit large spontaneous polarizations in the SmC* phase.
We have shown that chiral dopants with atropisomeric
biphenyl cores such as 1 induce ferroelectric SmC* phases
and exhibit remarkably high polarization powers (dp)—up to
1738 nC cm22—in achiral SmC liquid crystal hosts with a
complementary phenylpyrimidine core structure in which the
atropisomeric core propagates its chirality through core–core
interactions with surrounding host molecules.24,25 The result-
ing chiral perturbations are thought to amplify the induced
polarization as a feedback effect (Chirality Transfer Feedback,
CTF) by causing a shift in the conformational distribution
of the chiral dopant favoring one orientation of its transverse
dipole moment along the polar axis of the SmC* phase.
Evidence supporting the CTF amplification was provided by
probe experiments in which the polarization powers of (R) and
(S) enantiomers of a probe dopant exerting much weaker
chiral perturbations (the probe 2) were measured in the
presence of (S)-1 at a constant mole fraction of x1 = 0.04
(4 mol%) in 2-PhP.26 In the presence of (S)-1, the polarization
The difference in extrapolated ec values measured in
the hosts 2-PhP and NCB76 is much smaller than the
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Fig. 2 Electroclinic coefficient ec vs. reduced temperature T 2 TC for
mixtures of (R)-1 (x1 = 0.04) and (R)-2 (x2 = 0.03) (filled diamonds),
and (R)-1 (x1 = 0.04) and (S)-2 (x2 = 0.03) (open circles) in 2-PhP. The
error bars represent the 95% confidence limit about each point.
to out-of-layer fluctuations than in the SmC* phase, in which
the tails are less tilted than the core.33 However, these results
do not rule out completely the contribution of CTF to the
electroclinic effect, but suggest that any chiral perturbations
exerted by (R)-1 in the SmA* phase are on a much shorter
length scale due to less effective core–core interactions.
Although there is no evidence that dopant 2 has a significant
‘chiral’ influence on the electroclinic effect of the 4 mol%
mixture of (R)-1 in 2-PhP, the electroclinic coefficient of the
mixture does increase significantly in the presence of either
enantiomer of 2 at x2 = 0.03 (0.19 vs. 0.12 deg mm V21 at
T 2 TC = +5 K). Since the dopant molecules 1 and 2 are
Fig. 1 Electroclinic coefficient ec vs. mole fraction of (R)-1 x1 in (a)
2-PhP and (b) NCB76 measured at T 2 TC = +5 K. The lines represent
the least-squares fits to the data.
˚
significantly longer than the host molecules (ca. 47 A for 1 and
˚
˚
2 vs. 26 A for 2-PhP and 28 A for NCB76), we sought to
determine whether this discrepancy in molecular length plays
a role in the induction of the relatively large electroclinic
effects reported herein. To investigate the effect of molecular
length discrepancy systematically, we synthesized a series of
2-phenylpyrimidine mesogens 3a–h, which are approximately
equal to or greater in length than 2-PhP and NCB76, and
measured the effect of these additives on the electroclinic
coefficient in 4 mol% mixtures of (R)-1 in 2-PhP and NCB76.
Compounds 3a–h were prepared by dialkylation of 2-(4-
hydroxyphenyl)-5-pyrimidol. Their phase transition tempera-
tures were measured by differential scanning calorimetry, and
the mesophases identified by texture analysis using POM
(Table 1). The compounds 3a–f are known and, with the
exception of 3a, the phase sequences and transition tempera-
tures are in good agreement with the literature values.34 The
phase sequences follow the expected empirical trend, i.e., a
stabilization of the SmC phase at the expense of the nematic
and SmA phases with increasing chain length. Mixtures of
(R)-1 (x1 = 0.04) and 3a–h (x3 = 0.05) in the hosts 2-PhP and
NCB76 were prepared and analyzed by POM; all eight
additives were used in the (R)-1/2-PhP series, but only 3b,
3d, 3f and 3g were used in the (R)-1/NCB76 series. As shown
in the phase diagrams in Fig. 3, the increase in chain length
n of the additive 3 has relatively little effect on the I–N* and
N*–SmA* phase transition temperatures in 2-PhP and
NCB76, but causes a significant decrease in the SmA*–SmC*
corresponding difference in dp values (21555 vs.
2514 nC cm22, respectively), which suggests that the CTF
effect may not play as important a role in the SmA* phase as
in the SmC* phase.32 To determine the influence of chiral
perturbations exerted by (R)-1 on the induced electroclinic
effect in 2-PhP, we performed probe experiments using
mixtures of (R)-1 (x1 = 0.04) and either the (R) or (S)
enantiomer of the probe dopant 2 (x2 = 0.03) in the host
2-PhP. Four replicate mixtures were prepared for each dopant
combination, and electroclinic coefficients were measured for
each mixture at T 2 TC = +1.5, +2.5 and +5 K, and plotted as
a function of T 2 TC. As shown in Fig. 2, there is no
significant difference between ec values for the (R,R) and (R,S)
dopant/probe combinations, which indicates that the con-
tribution of the chiral dopant 2 to the induced electroclinic
effect is too small to be measured at x2 = 0.03, and suggests
that (R)-1 does not exert long range chiral perturbations in the
SmA* phase that would amplify the contribution of 2 to
the induced electroclinic effect. This result is consistent with
the less pronounced host dependence exhibited by ec relative to
dp, and implies that the degree of core–core correlation in the
SmA* phase under an electric field is significantly less than in
the tilted SmC* phase. This would be consistent with previous
observations that molecules tilt as rigid rods in the SmA*
phase under an electric field,28,29 and are therefore more prone
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Table 1 Liquid crystal properties and molecular lengths of achiral
additives 3a–h
a
Phase sequence (uC)b
˚
Length/A
Additive
n
3a
3b
3c
3d
3e
3f
3g
3h
a
6
8
9
10
11
12
14
16
25.6
30.6
33.1
35.5
38.1
40.5
45.5
50.5
Cr 69 SmC 74 SmA 77 N 100 I
Cr 53 SmC 93 SmA 101 N 102 I
Cr 64 SmC 97 SmA 101 I
Cr 58 SmC 104 I
Cr 74 SmC 103 I
Cr 66 SmC 105 I
Cr 77 SmC 104 I
Cr 85 SmXc 86 SmC 102 I
b
Fig. 4 Electroclinic coefficient ec vs. additive chain length n for
Derived from AM1-minimized molecular models. Determined by
differential scanning calorimetry and polarized microscopy.
Unidentified higher order smectic phase.
mixtures of (R)-1 (x1 = 0.04) and 3 (x3 = 0.05) in the hosts 2-PhP (filled
circles) and NCB76 (filled squares). The open symbols represent the
electroclinic coefficients in the absence of additive.
c
n = 14, which is 3.2 times larger than the electroclinic effect
achieved without additive. On the other hand, the additives
have no effect on the electroclinic coefficient in the (R)-1/
NCB76 mixture, despite the fact that they are all longer than
the host. Plots of ec vs. T 2 TC for (R)-1/2-PhP mixtures with
the additives 3a, 3d and 3g give excellent fits to eqn (2) (R2 >
phase transition temperature in 2-PhP, resulting in a broaden-
ing of the SmA* phase. By comparison, the increase in chain
length of 3 has little effect on the SmA*–SmC* phase
transition temperature in NCB76.
The electroclinic coefficients of these mixtures were mea-
sured at T 2 TC = +5 K and plotted as a function of the
additive chain length n. As shown in Fig. 4, the electroclinic
coefficient increases with the chain length of 3 in the (R)-1/2-
PhP mixture and reaches a maximum of 0.38 deg mm V21 at
0.98), with c/a values of 0.66, 1.03 and 1.88 deg K mm V21
,
respectively (Fig. 5). If we consider the results of the probe
experiments, which suggest that chirality transfer does not
contribute to the electroclinic effect in the SmA* phase, it is
reasonable to assume that the chirality-dependent electroclinic
coupling constant c is invariant in this series of mixtures, and
that the electroclinic amplification effect results primarily from
a decrease in the tilt susceptibility coefficient a.
Why do we observe an amplification in ec with increasing
chain length of 3 in the (R)-1/2-PhP mixture, but not in the
(R)-1/NCB76 mixture? Literature precedents paint a rather
inconsistent picture of the relationship between the chain
length of SmA* component(s) and the magnitude of ec. Several
studies have shown that the electroclinic coefficients of
homologous series of SmA* mesogens increase with the length
Fig. 5 Electroclinic coefficient ec vs. reduced temperature T 2 TC
for mixtures of (R)-1 (x1 = 0.04) and 3 (x3 = 0.05; a, filled circles; d,
open circles; g, triangles) in 2-PhP. The lines show the least-squares
fits to eqn (2) (a, c/a = 0.66 ¡ 0.02 deg K mm V21; d, c/a = 1.03 ¡
0.01 deg K mm V21; g, c/a = 1.88 ¡ 0.03 deg K mm V21).
Fig. 3 Phase diagrams for mixtures of (R)-1 (x1 = 0.04) and 3 (x3
=
0.05) in the hosts (a) 2-PhP and (b) NCB76 as a function of the chain
length n of 3.
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of chiral and achiral side-chains,7,35,36 which was attributed to
an increase in molecular flexibility that imparts a greater
mobility to the aromatic cores.35 On the other hand, Beresnev
et al. reported a decrease in ec upon lengthening the side-chains
of a chiral dopant (10% w/w) in a three-component SmA*
mixture.37 Kang et al. also reported a decrease in ec upon
similar modification of a chiral dopant (5% w/w) in a SmA
host.23 In the present case, the amplification of ec may be
explained by considering the effect of the additive on the
temperature range of the SmA* phase. In liquid crystals with
I–N–SmA–SmC or I–SmA–SmC phase sequences, it is well
known that the second order SmA–C phase transition
approaches the tricritical point (crossover from second to first
order), and ultimately becomes discontinuous (first order), as
the temperature range of the SmA phase decreases.38–41 In the
chiral SmA* phase, the approach of a SmA*–C* phase
transition towards the tricritical point (tricritical transition)
causes an increase in a as the fluctuations in tilt h near the
SmA*–C* phase transition decrease in magnitude.42 In the
(R)-1/2-PhP mixtures, the increase in ec with increasing chain
length of the additive 3 correlates with a broadening of the
SmA* temperature range except at very long chain length (3h),
which suggests that the amplification effect is due primarily to
a decrease in a as the second order SmA*–C* phase transition
moves away from the tricritical point. In the (R)-1/NCB76
mixtures, the lengthening of the additive 3 has relatively
little effect on the SmA* temperature range, and on the
corresponding electroclinic coefficient, which is consistent
with this explanation. Indeed, the amplification of ec first
observed with mixtures of (R)-1 in 2-PhP and 5-PhP can also
be correlated to a broadening of the SmA* temperature range
with increasing proportion of 5-PhP,43 which suggests that our
original explanation of this effect based on enhanced chirality
transfer in the SmA* phase is incorrect.27
Fig. 6 Smectic layer spacing d vs. temperature T for pure 2-PhP, 3g,
and a 5 mol% mixture of 3g in 2-PhP.
T 2 TC = 220 K; and (iii) a near linear variation in dC with
temperature that stands in sharp contrast to the concave
curvature shown in the dC(T) plot of pure 2-PhP, the latter
being typical of most materials with second-order SmA–C
transitions.
The change in profile of the dC(T) plots is consistent with a
change in the nature of the SmA–C transition. If we assume in
a first approximation that the mesogenic molecules behave as
rigid rods, the tilt angle h formed by the molecular long axes
and the layer normal in the SmC phase reduces the layer
spacing dC to:
SAXS measurements
To investigate the effects of additives 3a and 3g on the SmA–C
phase transition of 2-PhP, the smectic layer spacings d of pure
2-PhP, 3a, 3g and 5 mol% mixtures of 3a in 2-PhP and 3g in
2-PhP were measured as a function of temperature by small-
angle X-ray scattering (SAXS). As shown in Fig. 6, the layer
spacing of pure 2-PhP undergoes substantial shrinkage
below the SmA–C phase transition temperature TC (86 uC);
dC = dAcosh
(3)
based on simple geometry considerations. For small tilt angles
h, eqn (3) can be expanded as:
!
˚
h2
at T 2 TC = 220 K, the layer spacing dC is reduced by 1.8 A
dC~dA 1{ z . . .
(4)
(ca. 7%) relative to the extrapolated layer spacing dA of the
SmA phase (dashed line). By contrast, the layer spacing dC of
the additive 3g, which undergoes a first-order transition from
isotropic liquid to the SmC phase at 102 uC, increases sharply
due to the rapidly increasing orientational order expected for
such materials on cooling from the isotropic liquid phase.
When compared to the two pure components, the meso-
morphic properties of the 5 mol% mixture of 3g in 2-PhP show
some remarkable features: (i) a lowering of the SmA–C
transition temperature by more than 20 K relative to that of
pure 2-PhP and a broadening of the SmA temperature range
despite the fact that pure 3g forms only a SmC phase that is
stable at much higher temperatures; (ii) a reduction in layer
shrinkage in the SmC phase from 7% (pure 2-PhP) to 4% at
2
or:
dC
dA
h2
&1{
(5)
2
Since h is the primary order parameter describing the
SmA–C phase transition, the temperature variation of h is
described according to the general power law:
h 3 |T 2 Tc|b
(6)
where Tc is the SmA–C transition temperature (critical
temperature), and the order parameter exponent b is related
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to the nature of the phase transition. According to the
generalized mean-field theory of phase transitions (Landau
theory), a b value of K is expected in the case of a pure second-
order transition (mean-field transition), whereas a b value
of J is expected in the case of a second-order transition
approaching the tricritical point (tricritical transition).44,45 We
square-root law in eqn (8), which indicates that the second-
order SmA–C transition in 2-PhP is nearly tricritical. On the
other hand, the dC/dA(T 2 TC) plot for the 5 mol% mixture
of 3g in 2-PhP fits to the linear relation in eqn (8) (at least
for small h values), which indicates that the second-order
SmA–C phase transition approaches the mean-field limit
according to Landau theory. These results are consistent
with the broadening of the SmA phase observed upon addition
of 3g to 2-PhP, and the corresponding enhancement of the
electroclinic coefficient.
therefore obtain:
(
jT{Tcj
jT{Tcj
mean{field
h2!
(7)
1=2
tricritical
To clarify whether this effect depends on the molecular
length of the additive, we studied the effect of the shorter
additive 3a, which also undergoes a SmA–C transition, on the
smectic layer spacing of 2-PhP. As shown in Fig. 8, the layer
spacing of pure 3a undergoes substantial shrinkage below the
SmA–C phase transition; at T 2 TC = 27 K, the layer spacing
By inserting these results into eqn (8), we find that:
(
1{ajT{Tcj
1{ajT{Tcj
mean ꢀ field
dC
dA
&
(8)
1=2
tricritical
˚
dC is reduced by 1.5 A (ca. 6%) relative to the extrapolated
where a is a proportionality constant. According to this result,
the reduced layer spacing dC/dA should vary linearly with
temperature in the case of a pure mean-field transition (at
small tilt angles); in the borderline case of a tricritical
transition, a square-root law is expected. These considerations
are applied to our experimental data in Fig. 7, where dC/dA
is plotted against the reduced temperature T 2 TC, and
compared to the best fits to eqn (8). As shown in Fig. 7a,
the dC/dA(T 2 TC) plot for the pure host 2-PhP fits to the
layer spacing dA of the SmA phase, which is even greater
than that measured for 2-PhP at the same reduced temperature
(ca. 4%). At the SmA–C transition temperature TC, the layer
spacings of the two pure materials are approximately the same
˚
(ca. 25.8 A). The extent of layer shrinkage of a 5 mol% mixture
of 3a in 2-PhP at T 2 TC = = 27 K is approximately the same
as that of pure 2-PhP, and the temperature dependence of
dC appears to be similar in character. However, the layer
˚
spacing of the mixture is ca. 0.5 A smaller than for pure 2-PhP,
which violates the empirical trend described by the ‘additivity
rule’ of Diele that gives the layer spacing of a smectic
mixture as the weighted average of the layer spacings of the
pure components.46 In this case, the SAXS data suggest
that the addition of 3a substantially reduces the orientational
order of the pure host and, consequently, its smectic layer
spacing.14
As shown in Fig. 9, the dC/dA(T 2 TC) plot for the 5 mol%
mixture of 3a in 2-PhP fits to the square-root law in eqn (8).
This suggests that the nature of the SmA–C phase transition
is similar to that of the pure host—near the tricritical point—
which is consistent with the negligible ec amplification
observed with this mixture.
Fig. 7 Reduced layer spacing dC/dA vs. reduced temperature T 2 TC
for (a) pure 2-PhP and (b) a 5 mol% mixture of 3g in 2-PhP. The
solid lines represent the fits to eqn (8) for tricritical and mean-field
transitions, respectively.
Fig. 8 Layer spacing d vs. temperature T in the SmA (open symbols)
and SmC (filled symbols) phases for pure 2-PhP (squares), 3a
(triangles) and a 5 mol% mixture of 3a in 2-PhP (circles).
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Fig. 9 Reduced layer spacing dC/dA vs. reduced temperature T 2 TC
for the additive 3a (triangles) and a 5 mol% mixture of 3a in 2-PhP
(circles). The solid lines represent the fits to eqn (8) for tricritical
transitions.
Spontaneous polarization measurements
The spontaneous polarization (PS) of the chiral SmC* phase is
considered to be a secondary order parameter of the SmA*–C*
phase transition.47 Due to the coupling between PS and h,
the temperature dependence of PS near TC should also reflect
the nature of the SmA*–C* phase transition. However, PS
measurements by integration of polarization reversal current
peaks are complicated by induced polarization contributions
near TC due to the electroclinic effect (soft mode),48 although
the latter can often be minimized by using low triangular
ac fields. The PS(T 2 TC) plot for the 5 mol% mixture of 3a
in 2-PhP (Fig. 10a) was obtained using the lowest possible
triangular ac field (2 V mm21) without compromising the
accuracy of the current peak integration. Despite the low ac
field, the plot still shows some tailing beyond TC that results
from the soft mode contribution to the polarization reversal
current. By comparison, the PS(T 2 TC) plot for the 5 mol%
mixture of 3g in 2-PhP (Fig. 10b) shows a much more
pronounced tailing beyond TC that precludes any attempt at
fitting the plot to a power law similar to eqn (6). The pro-
nounced distortion of this plot near the SmA*–C* transition
is consistent with the higher electroclinic effect observed with
this mixture, but it makes impossible any useful comparison to
the PS(T) profile in Fig. 10a.
Fig. 10 Spontaneous polarization PS vs. reduced temperature T 2 TC
for mixtures of (a) (R)-1 (x1 = 0.04) and 3a (x3 = 0.05) in 2-PhP and (b)
(R)-1 (x1 = 0.04) and 3g (x3 = 0.05) in 2-PhP. The spontaneous
polarizations were measured using a triangular ac field of 2 V mm21
.
previous observations that molecules tilt as rigid rods in the
SmA* phase under an electric field.28,29 The electroclinic
coefficient of a 4 mol% mixture of (R)-1 in 2-PhP is amplified
by achiral 2-phenylpyrimidine additives that are longer than
2-PhP; in the best case, ec is amplified by a factor of 3.2
with the bis-tetradecyloxy derivative 3g, which is almost
twice as long as 2-PhP. However, no amplification is observed
in 4 mol% mixtures of (R)-1 in NCB76 using the same series
of additives.
A correlation between ec values and the temperature range
of the SmA* phase suggests that the amplification of ec with
increasing length of the additive 3 in the (R)-1/2-PhP mixture
is due primarily to a decrease in the tilt susceptibility
coefficient a as the second-order SmA*–SmC* phase transition
moves away from the tricritical point. Measurements of
smectic layer spacing as a function of T 2 TC by SAXS are
consistent with this explanation. The results show that the
variation in reduced layer spacing dA/dC with T 2 TC for the
pure host 2-PhP fits to a square-root law, which indicates that
the second-order SmA–C transition is nearly tricritical. On the
other hand, the corresponding variation in dA/dC with T 2 TC
for a 5 mol% mixture of 3g in 2-PhP fits to a linear relation,
which indicates that the second-order SmA–C transition
approaches typical mean-field behavior. Further work aimed
at establishing the generality of this effect in SmA* phases with
Summary
The atropisomeric dopant (R)-1 induces an electroclinic effect
in the liquid crystal hosts 2-PhP and NCB76 with extrapolated
electroclinic coefficients ec of 3.07 and 2.28 deg mm V21 at
T 2 TC = +5 K, respectively, which are comparable to some
of the highest ec values reported for neat SmA* materials.
In contrast to the polarization power dp of (R)-1 in the
SmC* phase, ec is much less sensitive to the host structure.
Furthermore, the results of probe experiments with (R)-2 and
(S)-2 suggest that any chiral perturbation exerted by (R)-1 in
the SmA* phase under an electric field must be on a shorter
length scale than in the SmC* phase, which is consistent with
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S. T. Lagerwall, in Ferroelectric Liquid Crystals: Principles,
large electroclinic coefficients is in progress and will be
reported in due course.
Properties and Applications, ed. J. W. Goodby, R. Blinc, N. A.
Clark, S. T. Lagerwall, M. A. Osipov, S. A. Pikin, T. Sakurai,
K. Yoshino and B. Zeks, Gordon and Breach, Philadelphia, 1991,
p. 84.
2 S. Garoff and R. B. Meyer, Phys. Rev. Lett., 1977, 38, 848.
3 I. Abdulhalim and G. Moddel, Liq. Cryst., 1991, 9, 493.
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Experimental
Materials
Dopants (R)-1, (R)-2 and (S)-2 were synthesized according to
published procedures and shown to have the expected physical
and spectral properties.32,49 The liquid crystal hosts 2-(4-
butoxyphenyl)-5-octyloxypyrimidine (2-PhP) and 4-(49-hep-
tyl[1,19-biphen]-4-yl)-1-hexylcyclohexanecarbonitrile (NCB76)
were obtained from commercial sources. Synthetic procedures
and spectral data for compounds 3a–h are described in the
Electronic Supplementary Information.{
10 G. P. Crawford, J. Naciri, R. Shashidhar and B. R. Ratna, Jpn. J.
Appl. Phys., 1996, 35, 2176.
Physical measurements
11 F. Giesselmann, P. Zugenmaier, I. Dierking, S. T. Lagerwall,
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19 J. P. F. Lagerwall and F. Giesselmann, Chem. Phys. Chem., 2006,
7, 20.
20 H. Stegemeyer, R. Meister, U. Hoffmann, A. Sprick and A. Becker,
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24 R. P. Lemieux, Acc. Chem. Res., 2001, 34, 845.
25 The polarization power is a measure of the propensity of a chiral
dopant to induce a spontaneous polarization in an achiral SmC
liquid crystal host: K. Siemensmeyer and H. Stegemeyer, Chem.
Phys. Lett., 1988, 148, 409.
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Differential scanning calorimetry analyses were performed at a
scan rate of 5 K min21 on a Perkin-Elmer DSC-7 instrument
(calibrated with indium) interfaced to a Perkin-Elmer TAC
7/DX Thermal Analysis Controller. Polarized optical micro-
scopy analyses were performed using either a Nikon Eclipse
E600 POL or Nikon Labophot-2 POL polarized microscope
fitted with Linkam LTS 350 hot stages. Electroclinic tilt
measurements were performed on samples aligned in rubbed
polyimide/ITO coated glass cells with a spacing of 4 ¡ 0.5 mm
(E.H.C., Japan). The film thickness was determined for each
sample based on the capacitance of the empty cell using a
Displaytech APT-III polarization testbed. Electroclinic tilt
angles h were determined by polarized microscopy as a
function of E using a 0.1 Hz square wave ac field. Tilt angle
values were taken as half the rotation between the two optical
extinction positions corresponding to opposite signs of E.
The electroclinic coefficient ec at a given reduced temperature
T 2 TC was determined according to eqn (1) from the linear
region of a plot of h vs. E; good least-squares fits (R2 ¢ 0.98)
were obtained in all cases. Spontaneous polarizations were
measured on the same aligned samples by the triangular wave
method using a Displaytech APT-III polarization testbed in
conjunction with the Linkam hot stage.50 X-Ray scattering
experiments were performed with Ni-filtered CuKa radiation
˚
(wavelength 1.5418 A). Small angle scattering data from
unaligned samples (filled into Mark capillary tubes of 0.7 mm
diameter) were obtained using a Kratky compact camera
(A. Paar) equipped with a temperature controller (A. Paar)
and a one-dimensional electronic detector (M. Braun).
29 A. G. Rappaport, P. A. Williams, B. N. Thomas, N. A. Clark,
M. B. Ros and D. M. Walba, Appl. Phys. Lett., 1995, 67, 362.
30 J. V. Selinger, J. Xu, R. L. B. Selinger, B. R. Ratna and
R. Shashidhar, Phys. Rev. E, 2000, 62, 666.
31 The ec value of 0.15 deg mm V21 at x1 = 0.04 measured in this study
is ca. twice the value measured in our original study,27 which is
likely due to a weighing error. Given that ec measurements were
carried out over a range of x1 values, and the quality of the least-
squares fit shown in Fig. 1, we are confident of the value reported
in this study.
Acknowledgements
We thank the Natural Sciences and Engineering Research
Council of Canada (Discovery Grant to R.P.L., Postgraduate
Scholarships to C.S.H., and Postdoctoral Fellowship to
J.C.R.), the Canada Foundation for Innovation and the
Deutsche Forschungsgemeinschaft (DFG) for support of
this work.
32 D. Vizitiu, C. Lazar, B. J. Halden and R. P. Lemieux, J. Am. Chem.
Soc., 1999, 121, 8229.
33 R. Bartolino, J. Doucet and G. Durand, Ann. Phys., 1978, 3, 389.
34 K. Ohno, M. Ushioda, S. Salto and K. Miyazawa, Eur. Pat. Appl.,
EP 313991 A2, 1988.
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