Dielectric and Electro-Optic E ﬀ ects in a Nematic Liquid Crystal Doped with h -BN Flakes

: A small quantity of hexagonal boron nitride ( h -BN) ﬂakes is doped into a nematic liquid crystal (LC). The epitaxial interaction between the LC molecules and the h -BN ﬂakes rising from the π − π electron stacking between the LC’s benzene rings and the h -BN’s honeycomb structure stabilizes pseudo-nematic domains surrounding the h -BN ﬂakes. Electric ﬁeld-dependent dielectric studies reveal that the LC-jacketed h -BN ﬂakes follow the nematic director reorientation upon increasing the applied electric ﬁeld. These anisotropic pseudo-nematic domains exist in the isotropic phase of the LC + h -BN system as well, and interact with the external electric ﬁeld, giving rise to a nonzero dielectric anisotropy in the isotropic phase. Further investigations reveal that the presence of the h -BN ﬂakes at a low concentration in the nematic LC enhances the elastic constants, reduces the rotation viscosity, and lowers the pre-tilt angle of the LC. However, the Fr é edericksz threshold voltage stays mostly una ﬀ ected in the presence of the h -BN ﬂakes. Additional studies show that the presence of the h -BN ﬂakes enhances the e ﬀ ective polar anchoring strength in the cell. The enhanced polar anchoring strength and the reduced rotational viscosity result in faster electro-optic switching in the h -BN-doped LC cell.


Introduction
The nanoscale interactions between nematic liquid crystals (LCs) and various two-dimensional (2D) hexagonal nanomaterials show interesting phenomena at the macroscopic levels. For example, the epitaxial interactions between the nematic LC and the hexagonal lattice of graphene, molybdenum diselenide, and tungsten diselenide deposited [1][2][3][4][5][6][7][8][9][10] demonstrate that the LC can achieve a planar-aligned state on these 2D hexagonal nanostructures. Our group has recently shown that the 2D hexagonal boron nitride (h-BN) film can be successfully employed as a planar-alignment agent as well as an ion-capturing agent in electro-optic LC devices [11][12][13]. Here we report the effects of ultrafine 2D h-BN flakes as a colloidal dopant in a nematic LC. The alternating boron and nitrogen atoms form the sp 2 conjugated honeycomb structure of h-BN with a lattice spacing of 1.44 Å [14]. This 2D h-BN is an insulator [15] which has very high structural [16], thermal [17], and chemical [18] stability. Here, we experimentally demonstrate that the LC-h-BN epitaxial interaction results in the formation of pseudo-nematic domains-which modifies the LC's dielectric anisotropy, splay elastic constant, rotational viscosity, and pre-tilt angle. In addition, the isotropic phase shows a net anisotropy on the application of an electric field due to the presence of the h-BN-induced pseudo-nematic domains. When some h-BN flakes from the LC+h-BN sample are absorbed onto the alignment substrates, the polar anchoring strength of the cell is found to increase significantly-which has a major impact on the accelerated electro-optic switching effect of the LC+h-BN sample.

Dielectric Studies
An LC's nematic phase shows dielectric anisotropy, Δε = 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 Δε E 2 [21] due to its dielectric anisotropy. This is the essence of the Fréedericksz transition. In the isotropic phase of an LC, Δε = 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, Δε = 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 LCh-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.

Dielectric Studies
An LC's nematic phase shows dielectric anisotropy, ∆ε = ε − ε ⊥ , where ε and ε ⊥ are the dielectric components parallel and perpendicular to the nematic directorn, respectively. For a positive dielectric anisotropic LC, ε > ε ⊥ . In a planar parallel-plate cell configuration, the nematic directorn is initially oriented perpendicularly to the applied electric field → E. When → E is above a critical threshold value, n reorients parallel to → E, achieving a homeotropic orientation. This reorientation process occurs because the nematic state experiences a torque proportional to ∆ε E 2 [21] due to its dielectric anisotropy. This is the essence of the Fréedericksz transition. In the isotropic phase of an LC, ∆ε = 0, and so it does not respond to → E. 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 V rms (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 V th upon increasing the applied V rms . The perpendicular dielectric component ε ⊥ was obtained from the average value of ε at V rms < V th . The inset in Figure 2a shows ε as a function of inverse applied voltage, V −1 rms for both the cells. The extrapolated y-intercept of the linear fit of ε vs. V −1 rms 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, ∆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 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 Δε 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 LCh-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 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 ∆ε for the LC+h-BN sample. See Figure 2c.
The energy associated with LC-h-BN anchoring mechanisms, |U anchoring | = 1.2 eV per molecule [22]. In the deep isotropic state at T = 70 • C = 343 K for the LC E7, the thermal energy, U thermal~kB T = 2.95 × 10 −2 eV << U anchoring . 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 Crystals 2020, 10, 123 5 of 12 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 → E 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 → E. The individual PNDs, being anisotropic in nature, possess dielectric anisotropy ∆ε PND . Therefore, the PNDs experience a torque proportional to ∆ε PND E 2 in an external electric field → E. The increase in ε for the LC+h-BN sample indicates the alignment mechanism of the PNDs with → E 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 ∆ε iso = ε max − ε min , where ε max and ε min can be determined from Figure 3a. Figure 2c shows the non-zero ∆ε iso values for the LC+h-BN sample above T NI . 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.  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 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 → E 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 → E is turned down to zero. Therefore, PNDs maintain some degree of alignment in the isotropic phase after the external field → E 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 (K 33 ) and splay (K 11 ) elastic constants employing the Fréedericksz transition method [23] by fitting the capacitance (C) vs. voltage (V) graphs according to the equation where γ = ∆ε/ε ⊥ , κ = (K 33 /K 11 ) − 1, C o is the zero-field capacitance, ϕ is the angle between the director and the alignment substrate at applied voltage V, ϕ m is the maximum angle in the middle of the cell, ϕ o is the pre-tilt angle, and V th is the threshold voltage for Fréedericksz transition. Figure 4a shows the Fréedericksz transition threshold voltage V th as a function of temperature for the pure LC and LC+h-BN hybrid. Clearly, V th stays unaffected in the presence of h-BN flakes. Figure 4b,c present K 11 and K 33 , 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 K 11 and K 33 for the LC+h-BN sample. Now, the threshold voltage is described by V th = π (K 11 /ε 0 ∆ε) [23]. Since both K 11 and ∆ε are increased by a similar percentage, the effective change in V th is minimal, as seen in Figure 4a. where γ =Δε /ε⊥, = (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 ( / Δ ) [23]. Since both K11 and Δε are increased by a similar percentage, the effective change in Vth is minimal, as seen in Figure 4a.

Rotational Viscosity and Pretilt Angle
The rotational viscosity 1 of an LC is an important physical parameter that influences the fieldinduced switching behavior of the LC. We have therefore performed experiments to measure the rotational viscosity 1 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 1 from the known values of E, Δε, and A. Figure 5a depicts that the LC+h-BN sample has a smaller 1 than the pure LC. We have recently shown that when an h-BN nanosheet is utilized as a planar-alignment agent in an

Rotational Viscosity and Pretilt Angle
The rotational viscosity γ 1 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 γ 1 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 ϕ o 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 I p was detected from the I(t) vs. time graph to extract γ 1 from the known values of E, ∆ε, and A. Figure 5a depicts that the LC+h-BN sample has a smaller γ 1 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 γ 1 [5,9,[27][28][29]. We believe that the dispersed h-BN flakes in the LC also trap free ion-impurities and reduce γ 1 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 1 in this paper. After extracting 1 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 φo 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.

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 righthand y-axis in Figure 6a shows the capacitance as a function of Vrms. Figure 6b shows R/R0 vs. 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 It has been shown that one of the most accurate methods to measure ϕ o is the transient current I(t) method [26], which has been employed to measure γ 1 in this paper. After extracting γ 1 from the peak transient current, one can use Equation (3) to find ϕ o 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 ϕ o 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 ϕ o in the LC+h-BN mixture.

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, W θ . 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 W θ for both the pure LC and LC+h-BN samples. This W θ 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], W θ is expressed by assuming the first-order approximation, where V is the applied rms voltage; R and R 0 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; K 11 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 V rms (f = 1000 Hz), and at the same time, the capacitance was measured by a Keysight E4980A LCR meter as a function of the same V rms at T = 25 • C. Figure 6a shows the retardation (in µm) on the left-hand y-axis as a function of V rms . The right-hand y-axis in Figure 6a shows the capacitance as a function of V rms . Figure 6b shows R/R 0 vs. 1/CV for both pure LC and LC+h-BN samples. R/R 0 vs. 1/CV exhibits an excellent linear behavior in the high field (V rms >12 V) region, according to Equation (4). The anchoring strength coefficient W θ 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 K 11 and d. We found that W LC θ = 5.15 × 10 −4 J/m 2 and W LC+hBN θ = 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 W θ .
Crystals 2020, 10, x FOR PEER REVIEW 8 of 12 in Figure 6b) and from the known values of K11 and d. We found that ϴ = 5.15 × 10 -4 J/m 2 and ϴ = 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.

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 1 influence the dynamic electro-optic response in an LC device mainly, the electrooptic switching times for both the pure LC and LC+h-BN samples in 20 µm cells have been The Table 1 summarizes the LC parameters at 25 • C.

Electro-Optic Switching
Now we will discuss the impact of this enhanced W θ on the nematic switching response. The two characteristic times, τ on (voltage on) and τ off (voltage off), of the nematic director, considering W θ , can be described as [32] where V (>>V th ) is the driving applied voltage and V b is the bias voltage.
Since W θ and γ 1 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 wheren 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 |V b | = 5 V and a |V|= 25 V (>>V th = 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.

Conclusions
In conclusion, we have shown that the presence of h-BN flakes in the LC creates anisotropic PNDs, altering some essential physical and optical properties of the LC. The presence of the PNDs enhances the dielectric anisotropy in the nematic phase. In the isotropic phase, the PNDs still exist and interact with the external electric field. It is observed that the presence of h-BN flakes decreases the rotational viscosity and lowers the pretilt angle. Finally, the polar anchoring strength is enhanced in the LC+h-BN sample, and consequently, this hybrid sample exhibits a faster electro-optic switching than the pure LC. The optical switching on, τ on 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, τ off is the time needed by the transmitted intensity to rise from 10% to 90% of its maximum value. The measured τ on and τ off are shown in Table 2. Note that τ on in Table 1 shows a slight decrease (≈4%) for the LC+h-BN sample. However, τ off 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 W θ and decrease in γ 1 in the LC+h-BN sample.
Note that in this experiment, V th ≈ 0.95 V and the driving voltage |V| = 25 V, and therefore, V >> V th . In this high voltage regime, the electro-optic switching mode is known as the transient nematic relaxation mode [33,34], where τ off is naturally fast (~milliseconds), even for large cell-gaps [33,34]. Additionally, since V >> V th , the driving voltage becomes the dominating factor for τ on , and W θ has very little effect on τ on [8,31]. See Equation (5) for τ on . Therefore, a minimal change in τ on is observed for the LC+h-BN sample. However, when the driving voltage is turned off, τ off 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 (W θ ∼ 10 −4 to 10 −5 J m −2 ), the term