Topological ferroelectric bistability in a polarization-modulated orthogonal smectic liquid crystal

Article abstract of DOI:10.1021/ja3009314

We report a bent-core liquid crystal (LC) compound exhibiting two fluid smectic phases in which two-dimensional, polar, orthorhombic layers order into three-dimensional ferroelectric states. The lower-temperature phase has a uniform polarization field which responds in an analog fashion to applied electric field. The higher-temperature phase is a new smectic state with periodic undulation of the polarization, structurally modulated layers, and a bistable response to applied electric field which originates in the periodically splay-modulated bulk of the LC rather than by surface stabilization at the cell boundaries.

Full text of DOI:10.1021/ja3009314

Article
pubs.acs.org/JACS
Topological Ferroelectric Bistability in a Polarization-Modulated
Orthogonal Smectic Liquid Crystal
Chenhui Zhu,† Renfan Shao,† R. Amaranatha Reddy,‡ Dong Chen,† Yongqiang Shen,† Tao Gong,‡
Matthew A. Glaser,† Eva Korblova,‡ Per Rudquist,§ Joseph E. Maclennan,† David M. Walba,‡
and Noel A. Clark*,†
†Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, United
States
‡Department of Chemistry and Biochemistry and Liquid Crystal Materials Research Center, University of Colorado, Boulder,
Colorado 80309, United States
§Department of Microtechnology and Nanoscience, Chalmers University of Technology, S-41269 Goteborg, Sweden
̈
S
* Supporting Information
ABSTRACT: We report a bent-core liquid crystal (LC) compound exhibiting
two fluid smectic phases in which two-dimensional, polar, orthorhombic layers
order into three-dimensional ferroelectric states. The lower-temperature phase
has a uniform polarization field which responds in an analog fashion to applied
electric field. The higher-temperature phase is a new smectic state with periodic
undulation of the polarization, structurally modulated layers, and a bistable
response to applied electric field which originates in the periodically splay-
modulated bulk of the LC rather than by surface stabilization at the cell
boundaries.
modulated, orthogonal smectic phase which we call the
SmAPFmod, in which the inherent tendency for the polarization
to splay results in the formation of a periodic array of domains
with linear polarization splay and modulated layer thickness.
Filling space with a preferred splay of P requires the
introduction of energetically costly defects, and in typical
solid and LC ferroelectrics this tendency is therefore sup-
pressed. Periodic polarization splay modulation is, however,
observed in tilted phases of bent-core mesogens such as the B7
and B1-Rev,24−27 where the modulation and the layer chirality
combine to produce a complex family of structures. Here we
extend the observation of periodic polarization splay to the
much simpler, higher-symmetry case of an orthogonal phase,
where the polarization modulation is manifested by (i) a
combination of high in-plane polarization with low in-plane
birefringence; (ii) bistable (i.e., ferroelectric) switching
behavior mediated by the field-induced motion of topological
singularities in the polarization field; and (iii) smectic layer
undulations evident in freeze-fracture transmission electron
microscopy (FFTEM) images and in small-angle X-ray
reflections.
INTRODUCTION
■
Bent-core liquid crystals (LCs) have attracted considerable
interest because they exhibit smectic phases with spontaneously
polar layers,1 a possibility suggested theoretically by Brand et
al.,2 and form fluid chiral phases from achiral molecules.3 A
large variety of novel bent-core phases and textures have been
observed experimentally,4,5 including smectic A-like phases with
the molecules aligned normal to the layer planes in which the
presence of in-plane orientational order leads to both polar6−19
and nonpolar20,21 biaxial structures. These orthogonal phases
have 2D fluid layers with in-plane translational symmetry and,
respectively, polar (SmAP) or quadrupolar (SmAb) ordering of
the molecular polar axes about the layer normal, with the layers
stacking to form 3D phases with orthorhombic point symmetry.
The polar phases include the SmAPA, with macroscopic, layer-
by-layer antiferroelectric ordering of the layer polarizations, and
the recently discovered SmAPF phase,22,23 where the molecules
are arranged in a state with macroscopic polar order, as
evidenced by the analog reorientation of the polarization P in
response to applied electric field.
The SmAPF phase was first reported in the mesogen W586,
an unsymmetric bent-core LC with a highly polar cyano group
at one end and a carbosilane tail at the other which exhibits
smectic A (SmA) and SmAPF phases on cooling from the
isotropic. In this paper, we describe W596, an analogue of
W586 in which the terminal −CN group is replaced by −CF3.
The structures and phase sequences of both materials are
shown in Figure 1a. W596 possesses a low-temperature SmAPF
phase but at high temperature has a novel, polarization splay-
EXPERIMENTAL SECTION
■
The phase sequence of W596 was determined using differential
scanning calorimetry (DSC), powder X-ray diffraction, depolarized
transmission light microscopy (DTLM), electro-optic (EO) measure-
Received: January 29, 2012
Published: April 30, 2012
© 2012 American Chemical Society
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Figure 1. Molecular structure and X-ray diffraction. (a) Chemical structure and phase sequences of W586 and W596. The molecular long axis is
along l, the molecular bows (collinear with the dipole direction pi) are along p, and o is perpendicular to the molecular bow plane defined by l and p.
The corresponding refractive indices are nl, np, and no, with nl > np > no. The calculated extended molecular length L (of either molecule) with the
tails in all-trans conformation is about 52 Å. (b) Smectic layer spacing of W596 as a function of temperature. The inset depicts the partial bilayer
structure of the SmAPF phase, where the 57 Å repeat distance is longer than the extended molecular length. Small-angle X-ray scattering from a
powder sample of W596 in the SmAPFmod phase shows (c) weak reflections from the layer modulation and (d) a strong Bragg reflection from the
smectic layering (T = 155 °C). (e) Temperature dependence of the smectic (black filled circles) and layer modulation peaks (at lower right). The
symbols correspond to those marking particular peaks in (c) and (d). The filled triangles and diamonds are harmonics of the open triangles and
diamonds, respectively. The SmAPFmod reflection with smallest q (red filled circles) corresponds to a modulation wavelength dmod ≈ 27 nm.
ment, and FFTEM. DSC was carried out with 5 °C/min heating and
cooling rates. X-ray diffraction on several powder samples (with the
LC in glass capillaries) was done on beamline X10A at the National
Synchrotron Light Source at Brookhaven National Laboratory, with a
wave vector resolution of 0.0004 Å−1. DTLM studies were carried out
on LC cells with the alignment either planar (molecular long axes
parallel to substrates) or homeotropic (molecular long axes
perpendicular to substrates). Electro-optical measurements were
performed using indium tin oxide (ITO) cells with planar alignment
induced by rubbed Teflon, with a.c. (Vmax ≈ 30 V/μm, 5 Hz < f < 200
Hz) or d.c. electric fields applied normal to the glass plates. FFTEM
was carried out by quenching the LC, sandwiched between 2 × 2 mm2
Cu planchettes, from the SmAPFmod phase to 77 K by rapid immersion
in liquid nitrogen or propane, and fracturing cold in a vacuum.
Replicas of the fracture surfaces were imaged using TEM.
suggesting that the compound adopts an interdigitated, partial
bilayer structure (Figure 1b) similar to that proposed for
W58622 and other related compounds.7
Synchrotron-based X-ray studies in the small-angle region
show a single layer peak in the SmAPF phase, and several weak
reflections at smaller wave vector (Figure 1c) in addition to the
main smectic layering peak in the SmAPFmod phase (Figure 1d).
The smallest wave vector, which we presume to be the
fundamental, is around q = 0.023 Å−1 at 150 °C (red filled
circles in Figure 1e), corresponding to a modulation periodicity
dmod = 27 nm, similar to the wavelength of the modulations
seen in FFTEM images of this phase (Figure 2). In the
polarization-modulated B7 bent-core phase (a SmCP variant),
the X-ray scattering is well explained by a 2D reciprocal lattice,
on the basis vector set kl = s(2π/d) along the layer normal
direction and km = h(2π/dmod) along the modulation direction,
where s and h are integers.24 In the case of the SmAPFmod phase,
however, no X-ray peak with q > 2π/d has been observed,
probably because the layer modulations (undulations) are weak,
and the scattering pattern is qualitatively different from that of
the B7 phase. It is not clear why there is no simple indexing of
all of the small-angle reflections, but it may be due to the fact
that this is a disordered focal conic sample, and the modulation
may be affected by variations in the layer curvature.
RESULTS AND DISCUSSION
■
The variation with temperature of the smectic layer spacing, d,
measured using powder X-ray diffraction, indicates that there is
a phase transition (the SmAPFmod−SmAPF transition) at 133
°C (Figure 1b). After increasing steadily on cooling through the
SmAPFmod range, the layer spacing remains practically
unchanged throughout the SmAPF phase. The layer spacing is
continuous across the transition, implying that it is either
second-order or weakly first-order, consistent with the results of
DSC, which shows a very small enthalpy (Figure S1). The layer
spacing in the SmAPF phase is about 57 Å, which is 5 Å more
than the fully extended molecular length (Figure 1a),
When the cell is cooled from the isotropic in the absence of
electric field, the SmAPFmod phase orients with the smectic
layers locally normal to the plates (the bookshelf geometry)
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We first discuss the electrooptics of the low-temperature
phase. The SmAPF phase is optically biaxial and ferroelectric,
with a local polarization density P that is spatially uniform and
of magnitude PF. The response to applied field in the SmAPF
phase is fundamentally the same as in W586, with the W596
molecules rotating around their mean molecular long axes. The
polarization P, corresponding to the mean orientation of the
molecular dipoles pi, is aligned in an applied field but relaxes to
be essentially parallel to the cell plates (φ = 90°, φ defined
below in Figure 5) when the field is removed, as indicated in
Figure 3a.
In cells with uniform planar alignment, the director is
oriented parallel to the cell plates, along the rubbing direction,
giving a refractive index nl for light polarized along the layer
normal in the absence of applied field. The orientation of the
principal axes of the optical dielectric tensor of the SmAPF
index ellipsoid (o,l,p) are shown in Figure 3a. When a triangle-
wave voltage V is applied, the SmAPF phase shows a single
current peak centered about V = 0 during each half-cycle
(Figure 3b, bottom), with Δn decreasing and then increasing
again as the voltage varies in the range −Vsat < V < Vsat, a
feature typical of the V-shaped, analog switching that is
observed in polar smectic LCs with large spontaneous
polarization, including the SmAPF phase of W586.22,29−31
This analog behavior is indicative of a polarization field that is
rendered uniform by charge stabilization and is free to reorient
continuously in response to an applied field, the width of the
current peak being determined by the voltage range over which
a full 180° reorientation of the polarization field takes place.32
With a triangle wave applied, the orientation of the polarization
field varies as φ = cos−1(εILV/2tP), where εIL is the dielectric
constant of the insulating alignment layers and t the thickness
of an alignment layer.30 In the SmAPF phase, when V = 0 the
molecular bow planes and P in the bulk are oriented parallel to
the cell plates (φ = 90°, Figure 3a lower left), giving an
apparent cell birefringence Δn = nl − np, plotted as the solid
blue circles in Figure 4a. An applied voltage reorients the
polarization even though when |V| ≤ Vsat = 2tP/εIL the electric
field in the liquid crystal ELC = 0, being completely screened by
polarization charge. The birefringence at V = Vsat, the highest
voltage for which there is no field in the LC, is plotted as solid
red triangles in Figure 4a. The birefringence increases slightly in
an even stronger applied field (|V| > Vsat) because the nonzero
electric field in the LC further increases the orientational order
by quenching fluctuations in φ. In this regime, the molecular
bow planes are aligned essentially normal to the cell plates (φ =
0°, Figure 3a, lower right), and the apparent cell birefringence is
Δn = nl − no, the largest attainable value of optical anisotropy
since no < np, shown as solid squares in Figure 4a. The
difference in birefringence with and without an applied field,
Δn(φ=0°) − Δn(φ=90°) = 0.02, corresponds to the in-plane
birefringence or biaxiality δn = np − no of the SmAPF phase.
The EO response of the SmAPFmod phase is distinctly
different from that of the SmAPF, exhibiting a single current
peak which occurs at finite field (Eth) during each half-period of
the applied triangle-wave (Figure 3b top and Figure S2). The
hysteretic response of the polarization indicates that in this
phase there is orientational bistability, with two stable
polarization states with P oriented on average normal to the
cell surfaces, designated UP and DOWN in Figure 5. The
threshold field Eth decreases on cooling but has a finite value Eth
≈ 2 V/μm even at the transition to the SmAPF phase (Figure
S2). The SmAPF and SmAPFmod phases coexist over a broad
Figure 2. Layer modulation in the SmAPFmod phase. (a) FFTEM
image of a Pt−C replica showing the topography of a W596 sample
quenched from the SmAPFmod phase (at T = 155 °C) and fractured.
The smectic layers here are oriented on average parallel to the image
plane. The fracture surface exhibits single smectic layer steps (two of
these are indicated by white arrows) and a long-range, periodic bulk
undulation of wavelength dmod ≈ 20 nm along m. The modulations in
the white box in (a) are shown enlarged in (b). (c) Model polarization
splay stripe, showing molecular dipoles (black arrows) and domain
walls (red lines). Modulations of the director/polarization field are
coupled to layer undulations in the SmAPFmod phase. No layer
modulation is observed in the SmAPF phase (see FFTEM images in
the Supporting Information).
and with the layer normal z exhibiting a tendency to align along
the rubbing direction, an alignment that is retained in the
SmAPF phase. Extinction brushes inside remnant cylindrical
focal conic domains are oriented along the polarizer (P) and
analyzer (A) directions, as is typical in DTLM images of
smectics where a principal axis of the optical dielectric tensor is
along the layer normal. Optical studies of such planar-aligned
cells confirm that both the SmAPFmod and SmAPF phases are
responsive to electric field applied normal to the substrates, as
illustrated in Figure 3a. In the SmAPFmod phase, the
birefringence increases slightly upon application of an electric
field (E = 10 V/μm). Once the field is removed, the
birefringence decreases slowly, returning to its original level
after some minutes. When the same field is applied in the
SmAPF phase, the birefringence increases much more (Figure
3a) but, in contrast to the higher-temperature phase, returns
very quickly to its original level once the field is removed; this
EO behavior is identical to that of the SmAPF phase of the
analogue mesogen W586. In both phases of W596, the
birefringence variation is independent of the polarity of the
applied field. The extinction brushes in regions with cylindrical
focal conics remain aligned along the polarizer and analyzer
directions independent of whether a field is applied or not, in
both the SmAPFmod and SmAPF phases. Since even in an
applied electric field there is no hint of optical tilt, and
considering that the molecules in W586 have been shown to be
oriented along the layer normal,22 we conclude that this is also
the case in the SmAPF and SmAPFmod phases of W596, i.e., that
the phases are truly orthogonal rather than of the anticlinic
SmCAP class.28
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Figure 3. Optical birefringence and current response. (a) Optical textures of the SmAPFmod and the SmAPF phases in a 20 μm thick cell with planar
alignment, the molecular long axes l (and hence the layer normal z) being oriented along the rubbing direction except in a few remnant focal conic
domains along the edges of the ITO electrode. An applied field of E = 10 V/μm aligns the mean polarization P in the ITO-coated area along the field
direction E. In the SmAPFmod phase, the birefringence increases only slightly upon application of the field, whereas in the SmAPF phase the
birefringence increases substantially. The models show the director structure in the middle of the cell, with the molecular dipoles (bows) pi
periodically splayed in the SmAPFmod phase but uniformly aligned in the SmAPF. The smectic layer interface and stripe domain boundaries are shown
in green and red, respectively. White arrows indicate increasing birefringence. The scale bar is 100 μm. (b) Polarization current response to a
triangle-wave applied electric field on cooling from the SmAPFmod (top) to the SmAPF phase (bottom). Coexistence of the two phases gives rise to
two partially overlapping current peaks at intermediate temperatures. The shaded area at T = 158 °C indicates a region where the mean polarization
is in the same direction as the electric field. The times at which the threshold voltage for bistable switching in the SmAPFmod is reached are marked as
Vth, and the saturation voltage for V-shaped switching in the SmAPF as Vsat. (c) Spontaneous polarization vs temperature in the SmAPFmod (filled
circles) and SmAPF (triangles) phases. The polarization drops to about 70% of its value at the SmAPF−SmAPFmod transition. The total polarization
of the two phases in coexistence is shown as an open circle.
temperature range (132 °C < T < 140 °C) as shown in Figure
3b, indicating that the transition between them is in fact first
order.
The extremes of Δn with and without applied field in both
orthogonal phases are shown as a function of temperature in
Figure 4a, while the apparent cell birefringence vs applied field
in the SmAPFmod phase is plotted in Figure 4b. At high
temperatures in the SmAPFmod phase, we find Δn ≈ 0.09, close
to the average of the φ = 0° and φ = 90° birefringence limits of
the SmAPF phase (Δn = 0.093, blue dashed line in Figure 4).
This is significant because in a modulated cell in which φ is
uniformly distributed, the effective in-plane refractive index is
δn ≈ (np + no)/2 and the cell birefringence is the corresponding
average Δn = [Δn(φ=0°) + Δn(φ=90°)]/2. This indicates that
at high temperatures the effective biaxiality δn must be quite
small (as confirmed by the low birefringence observed in
homeotropic cells; see Figure S3), and thus that φ is indeed
widely distributed. This is a rather striking result, given that the
polarization Pmod(T) is not very different from that of the low-
temperature SmAPF phase (Figure 3c) and that the molecular
moments must therefore remain substantially aligned in the
SmAPFmod. A proposed structure of narrow, splayed polar-
ization stripes (sketched in Figures 3a, 4, and 5) qualitatively
resolves this apparent contradiction: a splay domain with
The birefringence and polarization current of planar-aligned
cells were recorded while applying a triangle-wave voltage. The
magnitude of the spontaneous polarization, determined by
integrating the polarization reversal current and plotted in
Figure 3c, is somewhat smaller in the SmAPFmod phase than in
the SmAPF, a consequence of nonuniform director structure. In
the coexistence region, the polarization reversal current shows
two peaks (Figure 3b) corresponding to contributions from
both SmAPF and SmAPFmod domains in the cell.
The optical transmission through the cell was measured
using a focused HeNe laser with the layer normal oriented at
45° to the crossed polarizer and analyzer. The apparent cell
birefringence Δn was extracted from the variation of the
transmitted light intensity during switching using I = I0
sin2(πΔnD/λ) + Ibg, where D is the cell thickness, λ the
wavelength of the laser, I0 the incident light intensity, and Ibg
the background intensity. The birefringence was then used to
infer how the polarization field varies in time.
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Figure 4. Birefringence variation with temperature and applied field.
(a) Birefringence Δn deduced from optical transmission under various
applied field conditions. The dynamic birefringence observed during
switching at E = 0 (circles) changes drastically at the SmAPF−
SmAPFmod phase transition as the mean orientation of molecular
dipoles P in the ground state changes from being parallel to the
substrates to pointing toward them. The squares show the apparent
birefringence in a strong applied field (E = 10 V/μm). The triangles
show Δn at the saturation voltage, with ELC = 0. The dashed lines
mark the birefringence in the field-on (φ = 0°) and field-off (φ = 90°)
states in the SmAPF phase, as well as the average birefringence. The
cartoons show the “average” polarization field in the bulk of the cell.
The SmAPFmod in the absence of applied field (lower right), has a total
polarization splay ψ = 180°. An applied electric field causes a reduction
in the total splay (upper right) and a corresponding increase in
birefringence (gray arrow). The birefringence in the SmAPF phase in
the absence of field (lower left) is lower than in the SmAPFmod but
increases when a field is applied (upper left). (b) Birefringence Δn in
the SmAPFmod phase vs temperature and applied field. At high T, the
field-induced change in Δn is small but on cooling toward the SmAPF
phase, Δn increases more rapidly with E and saturates near the
maximum birefringence value obtained in the SmAPF phase in an
applied field. The blue curves show the results of computer simulations
using the director field model described in the Supporting
Information. The model responses were obtained by changing the
parameter w2P/K from about 0.12 at T = 138 °C to 5 at T = 162 °C,
corresponding to an increase in the effective elastic constant by a
factor of about 40 over this temperature range.
Figure 5. Model SmAPFmod splay domains in applied fields. (a)
Unlatched polarization DOWN state. (b) Unlatched polarization UP
state. The polarization orientation φ is measured from the cell normal.
Polar anchoring along the splay stripe boundaries and anchoring at the
glass leads to s = −1 topological line singularities in the bulk
polarization field, indicated as red dots in the stripe domains, and half
+1 defects at the glass surfaces with P directed into the LC, shown in
blue. The cell substrate is shown in blue, the smectic layers in green,
and the splay stripe boundaries in red. Applied field-induced molecular
rotation about the layer normal leads to motion of the s = −1 line
singularities and expansion of either the UP or DOWN splayed states.
(c) When the singularities arrive at the top surface, if the surface
anchoring is sufficiently weak the singularity can combine with the
surface defect (creating a new defect shown in purple) to change the
surface orientation. This latching at the stripe boundaries leads to
bistability.33
Supporting Information, with Figure S4 showing the full
dependence of Δn, δn, and Pmod on ψ.
The fact that the SmAPF phase has an analog response
suggests that the usual surface stabilization mechanism resulting
from orientational anchoring at the glass33 is probably not
solely responsible for the bistability of the SmAPFmod phase, but
rather that it originates in the periodically modulated bulk of
the LC. The splay-modulated cell structure shown in Figure 5
illustrates the proposed polarization UP and DOWN states that
appear with the confinement of P(r) by the splay stripes. In this
model, orientational anchoring at the stripe boundaries and
orientation of the bow planes parallel to the glass surfaces, as
found for W586, requires a topological singularity in P(r)
within each stripe, in this case a −1 defect (red core), identical
polarization azimuths ranging from φ = −90° to φ = +90°
across its width is essentially uniaxial, with δn = 0, and would
appear optically isotropic for light incident along the layer
normal. Nevertheless, the net polarization, Pmod = PF⟨cos(φ)⟩,
averaged over each stripe is nonzero and substantial, with Pmod
= (2/π)PF, if we assume that the magnitude of the molecular
polarization is the same as that in the SmAPF phase (Figure
S4). The polarization and effective birefringence when the
range of φ is varied between the general limits −ψ/2 < φ < ψ/2
(where ψ is the total splay angle) are discussed further in the
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to those found in freely suspended films of W586,22 and a half
+1 defect at each glass plate, which can have P directed out of
(purple) or into (blue) the LC at its center. Applied field-
induced molecular rotation about the layer normal leads to
motion of the −1 defect and expansion of either the UP or
DOWN splayed states, depending on the sign of the field. In
sufficiently large fields, the −1 defect is expelled from the bulk
by combination with the surface defect, in which case the x
component of P at the cell surface changes sign, latching the
orientation change (Figure 5c). Trapping of the defect at the
surface stabilizes the latched UP or DOWN state, producing a
hysteretic response of two states separated by a barrier. Once
the surfaces have switched, further increasing the applied field
tends to reduce the splay in the interior of the cell, especially at
lower temperatures in the SmAPFmod phase.
The energetics and stabilization of the SmAPFmod splay
domains can be probed by studying the field dependence of the
cell birefringence during times that the average polarization in
each stripe is along E (in the shaded region of the top graph in
Figure 3b, for example). In our experiments, the field
dependence of Δn in the UP state was measured by monitoring
the optical transmission as the applied voltage was reduced to
zero, with results shown in Figure 4b. At high temperatures, the
birefringence varies only weakly with applied field, indicating
that the splay domain structure is rather stiff, with the
polarization maintaining its ψ ≈ 180° range in spite of the
field-induced torques. At low temperatures, in contrast, Δn
increases readily with field, attaining a saturated value close to
that of the SmAPF phase birefringence, indicating substantial
alignment of P along the field direction in each splay domain.
The zero-field birefringence increases upon cooling, indicating
that the polarization in each stripe becomes more uniform on
approaching the SmAPF phase transition. The limiting behavior
of Δn vs temperature in the modulated phase is shown in
Figure 4a, both in the absence of applied field, where P(r) is
uniformly distorted within the splay stripes (E = 0, circles), and
in a strong field, where P is more uniform (E = 10 V/μm,
squares).
We assume in analyzing the field response that to first order
the magnitude of the molecular polarization is independent of
temperature and that the apparent decrease in P on heating in
the SmAPFmod phase is a manifestation of the averaging in φ
due to the increasing splay. The effects of the self-interaction of
polarization charges in confined polar LCs are well understood,
tending to render P(r) uniform away from bounding surfaces,
with transition walls of thickness ξP = (εK/P2)1/2, where ε is the
permittivity of the LC, mediating the reorientation of φ to the
angle preferred by the surfaces.34 If we assume a Frank elastic
constant appropriate for the reorientation about the long
molecular axis of a bent-core LC of K ≈ 1 pN and a
polarization P ≈ 3 × 10−3 C/m2, we obtain ξP ≈ 1 nm. Since
the observed undulation periodicity w ≈ 20 nm, such a ξP value
would result in uniform orientation of φ over most of each
stripe domain and large δn, contrary to the observations. The
fact that there is significant splay at high temperature, where Δn
and P are small, indicates that in this regime ξP must be much
bigger than our first estimate, as it would be if the effective
elastic constant K were much larger than 1 pN.
change in the birefringence resulting from small deformations
of φ(y) in each stripe. The extent of field-induced deformation
is determined by the dimensionless parameter λ3 = w/ξE =
(PEw2/K)1/2, where ξE is the electric field coherence length
determined by the competition between the elastic and
electrical torques,35 with deformation of the splayed ground
state appearing when λ3 > 1. If we assume K = 1 pN as before,
and use the measured parameters P = 3 × 10−3 C/m2 and E =
107 V/m, we obtain λ3 ≈ 3.5 at the highest fields applied in our
experiments, a regime where, for domains with w = 20 nm, the
model would predict a substantial reorientation of the
polarization field and a large change in Δn. This appears to
be consistent with the observed response at temperatures low
in the SmAPFmod phase. The experimentally observed lack of
field susceptibility at high temperatures suggests, however, that
in this regime the effective K must be much larger than our
assumed value, a condition which we attribute to renormaliza-
tion of the bare splay elastic constant by polarization charge,
giving KS = KS,bare + λDP2, where λD is the electrostatic
screening length determined by the ion concentration.36,37
The behavior of ions in the SmAPF phase, where the
polarization reorients as a uniform block and a distinct current
peak due to ion flow is observed,32 is clearly illustrated in
W623, an isomer of W586, The ion current peak occurs at
finite voltage, with the peak position moving to lower voltage
(Figure S5a) and the integrated area under the peak (the ion
concentration) increasing (Figure S5b) with rising temperature.
Since the ions in the LC only respond when the internal field
ELC is nonzero, during dynamic switching in the SmAPF phase
there is no ion current until |V| > Vsat. The ions are then swept
across the cell, with the integrated area of the ion current peak
proportional to the number of ions transported during this
switching event. The magnitude of the ion current is
determined both by the ion mobility in the LC and by the
frequency of the applied triangular voltage, with more ions
being transported through the LC at high T because of their
higher mobility. In cells with nonuniform P, in contrast, such as
in the SmAPFmod phase of W596, ELC is nonzero for any applied
voltage. The ions therefore start moving immediately after a
voltage is applied to the cell, and their motion may terminate
long before reorientation of the polarization is complete. As a
result, after only a short time there are very few ions left in the
LC to screen the polarization charge. Indeed, at high
temperatures, the viscosity of the LC is so small and the
mobility of the ions so large that they are quickly swept out of
the cell, resulting in minimal ionic screening of the polarization
charge, a long electrostatic screening length λD, and a large
effective splay elastic constant KS. This makes the preferred
polarization splay structure, which according to Figure 4a has
180° reorientation across each stripe, quite rigid and non-
responsive to the applied field. As the temperature is lowered
toward the SmAPF transition, the mobility decreases such that
the average ion concentration in the LC during switching is
higher and KS(T) decreases as screening becomes more
effective, leading to a larger field response.
CONCLUSION
■
We have described the structure and electro-optic response of
two orthogonal, polar phases of a new bent-core liquid crystal
compound. The lower-temperature (SmAPF) phase has a
uniform polarization field which responds in an analog fashion
This conclusion is consistent with the observation that at
high temperatures Δn hardly changes with applied field. The
highly nonuniform orientation field structure φ(y) postulated
for the splay domains can be maintained only if the orientations
at the domain wall boundaries are essentially fixed, with any
to applied electric field. The higher-temperature (SmAPFmod
)
phase is a new smectic state with periodic undulation of the
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dx.doi.org/10.1021/ja3009314 | J. Am. Chem. Soc. 2012, 134, 9681−9687

Journal of the American Chemical Society
Article
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polarization, structurally modulated layers, and a bistable
response to applied electric field. The confinement of the
splayed polarization structure between stripe domain bounda-
ries leads to an unusual topological ferroelectric bistability. The
experimentally observed weak field susceptibility at high
temperatures in the SmAPFmod phase suggests that, in this
regime, the effective Frank elasticity must be much larger than
expected, a condition which we attribute to renormalization of
the bare splay elastic constant by polarization charge.
ASSOCIATED CONTENT
■
S
* Supporting Information
DSC thermogram; hysteretic behavior of the SmAPFmod phase;
homeotropic cell textures; polarization, apparent cell birefrin-
gence, and in-plane birefringence vs splay angle; current peak
from ions in W623; splay stripe simulations; FFTEM of the
SmAPF phase; synthesis of W596. This material is available free
of charge via the Internet at http://pubs.acs.org.
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̌
̌ ̌
(23) Guo, L. F.; Gorecka, E.; Pociecha, D.; Vaupotic, N.; Cepic, M.;
AUTHOR INFORMATION
■
Reddy, R. A.; Gornik, K.; Araoka, F.; Clark, N. A.; Walba, D.; Ishikawa,
K.; Takezoe, H. Phys. Rev. E 2011, 84, 031706.
Corresponding Author
noel.clark@colorado.edu
(24) Coleman, D. A.; Fernsler, J.; Chattham, N.; Nakata, M.;
Takanishi, Y.; Korblova, E.; Link, D. R.; Shao, R. F.; Jang, W. G.;
Maclennan, J. E.; Mondainn-Monval, O.; Boyer, C.; Weissflog, W.;
Pelzl, G.; Chien, L. C.; Zasadzinski, J.; Watanabe, J.; Walba, D. M.;
Takezoe, H.; Clark, N. A. Science 2003, 301, 1204.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
(25) Coleman, D. A.; Jones, C. D.; Nakata, M.; Clark, N. A.; Walba,
D. M.; Weissflog, W.; Fodor-Csorba, K.; Watanabe, J.; Novotna, V.;
Hamplova, V. Phys. Rev. E 2008, 77, 021703.
■
This work was supported by NSF Materials Research Science
and Engineering Center grant DMR 0820579, NSF Materials
World Network grant DMR 1008300, NSF grant DMR
0603223, and by Swedish Research Council grant 90362101.
Use of the National Synchrotron Light Source was supported
by the U.S. Department of Energy, Divisions of Materials and
Chemical Sciences.
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