3.1. Dielectric Studies
An LC’s nematic phase shows dielectric anisotropy, Δ
ε =
ε‖ −
ε⊥, where
ε‖ and
ε⊥ are the dielectric components parallel and perpendicular to the nematic director
, respectively. For a positive dielectric anisotropic LC,
ε‖ >
ε⊥. In a planar parallel-plate cell configuration, the nematic director
is initially oriented perpendicularly to the applied electric field
. When
is above a critical threshold value,
reorients parallel to
, achieving a homeotropic orientation. This reorientation process occurs because the nematic state experiences a torque proportional to Δ
ε E2 [
21] due to its dielectric anisotropy. This is the essence of the Fréedericksz transition. In the isotropic phase of an LC, Δ
ε = 0, and so it does not respond to
. An Automatic Liquid Crystal Tester (Instec, Inc.) was employed to measure the dielectric constant
ε values of the pure LC and LC+
h-BN samples as a function of applied voltage
Vrms (
f = 1000 Hz) at different temperatures, both in the nematic and isotropic phases. The AC field was applied to avoid the effect of ion migration on the dielectric measurements.
Figure 2a shows a typical Fréedericksz transition in the deep nematic phase at
T = 40 °C for the pure LC and LC+
h-BN listed in the legend. The LC and the LC+
h-BN mixture undergo planar (
ε⊥) to homeotropic (
ε‖) orientational transition above the threshold voltage
Vth upon increasing the applied
Vrms. The perpendicular dielectric component
ε⊥ was obtained from the average value of
ε at
Vrms <
Vth. The inset in
Figure 2a shows
ε as a function of inverse applied voltage,
for both the cells. The extrapolated
y-intercept of the linear fit of
ε vs.
gives the value of
ε‖.
Figure 2b shows
ε⊥ and
ε‖ as a function of temperature for the pure LC and LC+
h-BN listed in the legend.
Figure 2c presents the dielectric anisotropy, Δ
ε =
ε‖ −
ε⊥, as a function of temperature for the two samples.
These local PNDs possess a different anisotropy than that of the bulk LC due to the strong LC–
h-BN epitaxial interaction. These domains collectively increase the overall anisotropy and the nematic orientational order in the LC+
h-BN sample.
Figure 2d schematically shows that the PNDs align with their flat planes parallel to the far-field nematic director in the nematic LC to minimize the elastic distortion. When the external electric field rotates the nematic LC, the PNDs also follow the director rotation, as illustrated in
Figure 2e.
Figure 2c shows that the parallel dielectric component
ε‖ is a little higher in the LC+
h-BN sample, as the PNDs contribute their anisotropy to the bulk LC. On the other hand, the perpendicular dielectric component
ε⊥ is slightly lower in the LC+
h-BN sample. Some
h-BN flakes sediment down from the LC and preferentially attach to the alignment substrate. This process promotes planar anchoring and presumably pulls the LC molecules closer to the substrate due to the LC—
h-BN interaction, reducing the average pretilt angle. This reduced pretilt angle results in a slightly lower
ε⊥ in the LC+
h-BN sample. Later in this article, we will present the pretilt angle measurement. A higher
ε‖ and a lower
ε⊥ lead to an enhanced Δ
ε for the LC+
h-BN sample. See
Figure 2c.
The energy associated with LC–
h-BN anchoring mechanisms, |
Uanchoring| = 1.2 eV per molecule [
22]. In the deep isotropic state at
T = 70 °C = 343 K for the LC E7, the thermal energy,
Uthermal ~
kBT = 2.95 × 10
−2 eV <<
Uanchoring. Therefore, the thermal energy is not strong enough to eradicate the LC—
h-BN anchoring mechanisms at the LC—
h-BN interface in the isotropic phase. Thus, the PNDs are expected to exist in the isotropic phase as well.
Figure 3 presents
ε as a function of applied voltage in the isotropic phase for the pure LC and LC+
h-BN listed in the legend. The pure LC shows a featureless behavior in the isotropic phase at
T = 61 °C, as expected. The LC+
h-BN system shows an increase in
ε with increasing applied voltage in the isotropic phase at
T = 61 °C. This phenomenon depicts that the suspended PND-encapsulated
h-BN flakes induce a net orientational order in the isotropic LC system—which responds to the external field
in the isotropic phase. The increase in
ε as a function of applied voltage in the isotropic phase for the LC+
h-BN system and a featureless behavior of the same as a function of the applied voltage for the ethanol+
h-BN system clearly indicates that the PNDs are present in the LC+
h-BN system and interact with
. The individual PNDs, being anisotropic in nature, possess dielectric anisotropy Δ
εPND. Therefore, the PNDs experience a torque proportional to Δ
εPNDE2 in an external electric field
. The increase in
ε for the LC+
h-BN sample indicates the alignment mechanism of the PNDs with
in the isotropic phase, as schematically shown in
Figure 3b,c. There is no distinct threshold voltage (like Fréedericksz threshold) observed to start the increment in
ε in the isotropic phase. This is because the PNDs do not interact directly with the alignment layers due to the absence of any long-range elastic interaction in the isotropic phase. The dielectric anisotropy in the isotropic phase for the doped system is defined as Δ
εiso =
εmax −
εmin, where
εmax and
εmin can be determined from
Figure 3a.
Figure 2c shows the non-zero Δ
εiso values for the LC+
h-BN sample above
TNI. More interestingly, as
Figure 3a shows,
ε does not relax back to its original value on turning the voltage down to zero, showing a dielectric hysteresis effect—which manifests a nonvolatile memory effect. This hysteresis effect is persistent at several higher temperatures in the isotropic phase, as shown in
Figure 3a. After each field cycle at a given temperature in the isotropic phase, the LC+
h-BN sample was cooled down to the nematic phase (
T = 25 °C) at a rate of 0.02 °C/min to erase the memory. For consistency, each time before starting a new field cycle, the LC+
h-BN sample was heated up from the nematic phase to the isotropic phase at
T = 70 °C, at a rate of 0.02 °C/min, and then cooled down to the desired temperature in the isotopic phase at the same rate.
As mentioned above, the PNDs do not interact directly with the alignment layers, since there is no long-range elastic interaction in the bulk isotropic phase, and therefore, when the external field is cycled down to zero, there is no elastic force to torque the PNDs back to the original alignment. The thermal fluctuation disturbs the PNDs to some extent, but cannot completely randomize the PNDs after the external field is turned down to zero. Therefore, PNDs maintain some degree of alignment in the isotropic phase after the external field is turned down to zero; hence the observed hysteresis.
To investigate the effects of the PNDs on the physical properties of the LC, we have obtained the bend (
K33) and splay (
K11) elastic constants employing the Fréedericksz transition method [
23] by fitting the capacitance (
C) vs. voltage (
V) graphs according to the equation
where
γ = Δ
ε/
ε⊥,
κ = (
K33/K11) − 1,
Co is the zero-field capacitance,
φ is the angle between the director and the alignment substrate at applied voltage
V,
φm is the maximum angle in the middle of the cell,
φo is the pre-tilt angle, and
Vth is the threshold voltage for Fréedericksz transition.
Figure 4a shows the Fréedericksz transition threshold voltage
Vth as a function of temperature for the pure LC and LC+
h-BN hybrid. Clearly,
Vth stays unaffected in the presence of
h-BN flakes.
Figure 4b,c present
K11 and
K33, respectively, as a function of temperature for pure LC and LC+
h-BN hybrid. As discussed before, the PNDs collectively increase the overall anisotropy and the nematic orientational order in the LC+
h-BN sample. Therefore, the elastic interaction is also increased in the LC+
h-BN sample.
Figure 4b,c, therefore, reveals the increase in
K11 and
K33 for the LC+
h-BN sample. Now, the threshold voltage is described by
Vth =
π [
23]. Since both
K11 and Δ
ε are increased by a similar percentage, the effective change in
Vth is minimal, as seen in
Figure 4a.
3.2. Rotational Viscosity and Pretilt Angle
The rotational viscosity
γ1 of an LC is an important physical parameter that influences the field-induced switching behavior of the LC. We have therefore performed experiments to measure the rotational viscosity
γ1 for the LC+
h-BN sample. The rotational viscosity for the nematic samples was obtained by measuring an electric field-induced transient current [
24,
25,
26] across the cell. When a DC electric field (much higher than the threshold field) is applied across a planar LC cell, the nematic director goes through a dynamic rotation and induces a transient current
I(
t) in the cell. This current response is given by
where
A is the area of the cell,
E = (
V/
d) is the DC electric field, and
φ is the angle the director makes with the electrodes at a given time. At
φ = 45°,
I(
t) reaches its peak value,
at the peak time,
where
φo is the pretilt angle. A DC voltage pulse of 25 V with a pulse interval of 1 Hz was applied across the cell to generate
I(
t)—which was detected as a function of time by a digital storage oscilloscope through a load resistor in series. A detailed description of the experimental setup is given in reference [
24]. The inset in
Figure 5a shows
I(
t) as a function of time for the pure LC and LC+
h-BN at
T = 25 °C. The peak current
Ip was detected from the
I(
t)
vs. time graph to extract
γ1 from the known values of
E, Δ
ε, and
A.
Figure 5a depicts that the LC+
h-BN sample has a smaller
γ1 than the pure LC. We have recently shown that when an
h-BN nanosheet is utilized as a planar-alignment agent in an LC the cell, the
h-BN nanosheet captures a significant amount of free ion impurities from the LC by ion-trapping process [
11]. It has been also shown that the reduction of free ions in the LC results in a reduced
γ1 [
5,
9,
27,
28,
29]. We believe that the dispersed
h-BN flakes in the LC also trap free ion-impurities and reduce
γ1 in the LC+
h-BN sample.
It has been shown that one of the most accurate methods to measure
φo is the transient current
I(t) method [
26], which has been employed to measure
γ1 in this paper. After extracting
γ1 from the peak transient current, one can use Equation (3) to find
φo from the peak time (see the inset in
Figure 5a) for the pure LC and LC+
h-BN samples.
Figure 5b presents the effective φ
o as a function of temperature for the samples listed in the legend. Evidently, LC+
h-BN exhibits almost a 50% decrease in
φo in the room temperature regime. It is possible that a number of monolayer
h-BN flakes sediment down and/or get stuck to the alignment substrates from the LC+
h-BN mixture and align themselves horizontally on the substrates during the filling process of the LC cell. When some
h-BN flakes are preferentially attached to the alignment substrates, they promote planar anchoring, and presumably pull the LC molecules close to the substrate due to the
h-BN—LC epitaxial interaction. This process reduces the effective
φo in the LC+
h-BN mixture.
3.3. Polar Anchoring Strength
The energy cost of the deviation from a planar orientation to a homeotropic orientation upon the application of an electric field is characterized by the polar anchoring strength coefficient,
Wθ. Intuitively, the spontaneously deposited
h-BN flakes on the alignment substrates would enhance the effective polar anchoring strength for the LC+
h-BN sample. We have, therefore, measured
Wθ for both the pure LC and LC+
h-BN samples. This
Wθ measurement was carried out employing the high field technique—where the optical retardation and capacitance of the LC cell are measured simultaneously as a function of applied voltage [
30]. According to this technique [
30],
Wθ is expressed by assuming the first-order approximation,
where
V is the applied rms voltage;
R and
R0 are retardations with and without the applied voltage, respectively;
ξ and
I depend on the LC’s properties and the cell geometry;
C is the capacitance of the cell;
K11 is the splay elastic constant of LC; and
d is the cell gap. We used
d = 22.5 μm thick planar cells for these measurements. A Soleil-Babinet compensator (Thorlabs, Inc.) was used to measure the retardations as a function of applied
Vrms (
f = 1000 Hz), and at the same time, the capacitance was measured by a
Keysight E4980A LCR meter as a function of the same
Vrms at
T = 25 °C.
Figure 6a shows the retardation (in μm) on the left-hand
y-axis as a function of
Vrms. The right-hand
y-axis in
Figure 6a shows the capacitance as a function of
Vrms.
Figure 6b shows
R/
R0vs. 1/
CV for both pure LC and LC+
h-BN samples.
R/
R0 vs. 1/
CV exhibits an excellent linear behavior in the high field (
Vrms >12 V) region, according to Equation (4). The anchoring strength coefficient
Wθ now can be determined from the extrapolated intersection of Equation (4) with the axis of 1/
CV = 0 (see the inset in
Figure 6b) and from the known values of
K11 and
d. We found that
= 5.15 × 10
−4 J/m
2 and
= 9.70 × 10
−4 J/m
2—which is an 88% increase in the effective polar anchoring strength. When some
h-BN flakes are preferentially attached to the alignment substrates, they modify the substrates’ effective anchoring characteristics by enhancing the planar anchoring energy due to the
h-BN—LC epitaxial interaction. This is consistent with some recent results in the literature that show that the graphene flakes [
9] and carbon nanotubes [
31] can also be absorbed on the alignment substrates from the respective LC-colloidal mixtures and significantly enhance the effective
Wθ.
The
Table 1 summarizes the LC parameters at 25 °C.
3.4. Electro-Optic Switching
Now we will discuss the impact of this enhanced
Wθ on the nematic switching response. The two characteristic times,
τon (voltage on) and
τoff (voltage off), of the nematic director, considering
Wθ, can be described as [
32]
where
V (>>
Vth) is the driving applied voltage and
Vb is the bias voltage.
Since
Wθ and
γ1 influence the dynamic electro-optic response in an LC device mainly, the electro-optic switching times for both the pure LC and LC+
h-BN samples in 20 μm cells have been investigated. These response times in both the cells were measured by employing the standard electro-optical setup [
6,
11,
12,
13], where a 5-mW He-Ne laser beam of wavelength 633 nm was sent through two crossed-polarizers and into a photodetector. The planar LC test cell was placed in-between the crossed polarizers where
in the cell was aligned at 45° with respect to the polarizer. The photodetector output was fed into a digital oscilloscope. A modulated square-wave driving voltage with a |
Vb| = 5 V and a |
V|= 25 V (>>
Vth = 0.95 V) was applied across the cell, and the changes in the transmitted intensity through the cell were measured as a function of time from the oscilloscope. In
Figure 7, the right-hand
y-axis shows the modulated square-wave driving voltage (modulated frequency
f = 30 Hz) profile across the cell. The left-hand
y-axis in
Figure 7 shows the change in the normalized transmitted intensity through both the cells as a function of time.
The optical switching on,
τon is the time needed by the transmitted intensity to drop from 90% to 10% of its maximum value when
V is turned on. After
V is turned off, the transmitted intensity through the test cell increases, and the optical switching turns off,
τoff is the time needed by the transmitted intensity to rise from 10% to 90% of its maximum value. The measured
τon and
τoff are shown in
Table 2.
Note that
τon in
Table 1 shows a slight decrease (≈4%) for the LC+
h-BN sample. However,
τoff is significantly accelerated (≈18%) for the LC+
h-BN sample—which can also be seen in
Figure 7. This faster switching response is mainly attributed to the significant enhancement in the effective
Wθ and decrease in
γ1 in the LC+
h-BN sample.
Note that in this experiment,
Vth ≈ 0.95 V and the driving voltage |
V| = 25 V, and therefore,
V >>
Vth. In this high voltage regime, the electro-optic switching mode is known as the transient nematic relaxation mode [
33,
34], where
τoff is naturally fast (~milliseconds), even for large cell-gaps [
33,
34]. Additionally, since
V >>
Vth, the driving voltage becomes the dominating factor for
τon, and
Wθ has very little effect on
τon [
8,
31]. See Equation (5) for
τon. Therefore, a minimal change in
τon is observed for the LC+
h-BN sample. However, when the driving voltage is turned off,
τoff is purely influenced by the elastic interaction between the LC and the planar-alignment layers—which is primarily driven by the polar anchoring strength in the cell. In the weak anchoring range (
Wθ 10
−4 to 10
−5 J m
−2), the term
in
τoff in Equation (5) plays a significant role [
8,
13] in altering the value of
τoff. Therefore, in this weak anchoring limit,
τoff is found to be faster for the LC+
h-BN sample for a higher effective
Wθ and a lower
γ1.
The two micrographs in the inset in
Figure 7 show the voltage off and voltage on states, respectively, for the LC+
h-BN cell under a crossed polarized microscope. The micrograph for the voltage off state shows a uniform texture with no visible
h-BN aggregates. This confirms a uniform dispersion of the
h-BN flakes at 1.2 × 10
−2 wt% in the LC. Our concentration-dependent investigation showed that when the concentration was more than 3 × 10
−2 wt%, the LC+h-BN texture showed the presence of visible
h-BN aggregates under the microscope. Therefore, we consider the 1.2 × 10
−2 wt% as the optimal concentration, and all the experiments were carried out at this concentration.