Enhancement of Birefringence in Reduced Graphene Oxide Doped Liquid Crystal

We investigated the effect of reduced graphene oxide (rGO) doping on the birefringence of 5CB liquid crystal (LC). The characteristics of the synthesized rGO and LC-rGO composite with different rGO concentrations were analyzed by atomic force microscopy, X-ray photoelectron spectroscopy, white light polarized microscopy, voltage-dependent transmission measurement, and differential scanning calorimetry. We found that doping LC with an appropriate concentration of rGO enhances the birefringence of the LC. This is mainly due to the improved anisotropy of polarizability, which stems from the high shape anisotropy of rGO. However, the aggregation of rGO reduces the birefringence by decreasing the anisotropy of polarizability as well as the order parameter. Our study shows the promising potential of LC-rGO for developing various electro-optic devices that offer improved electro-optic effects.


Introduction
Doping liquid crystals (LCs) with nanoparticles (NPs) has attracted increasing attention in various research fields and industries because it not only changes the physical properties of LC but also provides additional functionalities. Various nanoparticles synthesized based on metals [1][2][3][4][5][6], dielectrics [7], semiconductors [8,9], carbon nanotubes [10][11][12], and ferroelectric [13,14] materials have been used as dopants to improve the electro-optic properties of the LC devices including a Fréedericksz transition voltage and a switching time. It has also been reported that ionic impurities could be co-doped with nanoparticles to improve the electro-optic performance of LC independent of temperature [15]. Among various NPs, the one that can increase dielectric anisotropy (∆ε) without significantly reducing orientational order parameter has been considered as a preferred choice because it improves both a Fréedericksz transition voltage (V th ) [16] and a switching time (τ on ) [17] simultaneously through the following relationship: Figure 1a shows the structure of the phase modulator implemented by the rGO doped 5CB LC (LC-rGO). The fabrication of the phase modulator was started from cleaning indium tin oxide (ITO) coated glass substrates (Sigma Aldrich, St. Louis, MO, USA) with acetone, isopropyl alcohol (IPA), and deionized (DI) water in a sonication bath for 5 min, respectively. The thicknesses of ITO and the glass slide were 100 nm and 1.1 mm, respectively. The substrates were then exposed to UV ozone for 1000 s to make the surface hydrophilic. Polyvinyl alcohol (PVA, 2 wt%) was dissolved in DI water. The solution was stirred and heated at 90°C for 2 h. The PVA solution was spin-coated on the glass substrate at the speed of 3000 rpm for 30 s and then baked for 1 h at 90°C on a hot plate. The PVA layers on glass substrates were rubbed with a velvet cloth in an antiparallel direction. Two glass substrates were bonded using double-sided adhesive films (Nitto, Umeda, OSA, Japan) with a thickness of 5 µm, a width of 5 mm, and a length of 35 mm placed on the rims of one substrate. The area where the double-sided adhesive films were placed, was masked using kapton tape (DuPont, Wilmington, DE, USA) during the spin coating of PVA solution. Pressure was applied to the two substrates after assembling and before filling the LC. The LC with different weight concentrations of rGO was prepared by vortex-mixing rGO in a 5CB LC for 60 s, followed by sonicating for 2 h and heating at 90°C for 30 min. At this temperature, the 5CB LC became isotropic and it allowed for better dispersion of rGO. The LC-rGO was filled between two substrates by capillary action at 60°C. Nanomaterials 2020, 10, x FOR PEER REVIEW 3 of 11 area where the double-sided adhesive films were placed, was masked using kapton tape (DuPont, Wilmington, DE, USA) during the spin coating of PVA solution. Pressure was applied to the two substrates after assembling and before filling the LC. The LC with different weight concentrations of rGO was prepared by vortex-mixing rGO in a 5CB LC for 60 s, followed by sonicating for 2 h and heating at 90 for 30 min. At this temperature, the 5CB LC became isotropic and it allowed for better dispersion of rGO. The LC-rGO was filled between two substrates by capillary action at 60 . The rGO was prepared by reducing GO produced by the modified hummers method from the graphite powder. A mixture of 2 g of graphite having a mean size of 200 mesh and purity of 99%, 2 g of sodium nitrate (NaNO3), and 100 mL of sulfuric acid (H2SO4) with 95 wt% was prepared and stirred for 1 h. After cooling down the mixture in an ice bath, 10 g of potassium permanganate (KMnO4) was added and magnetically stirred until the solution became brown. Three hundred milliliter of deionized water was added to the solution slowly during the stirring. To remove excess KMnO4, 10 mL of hydrogen peroxide (H2O2) was added and stirred. Deionized (DI) water was then added and centrifuged. The supernatant was removed and residuals were washed using DI water and centrifuged five times. The GO solution was dried in the oven at 80 for 3 h to obtain the GO powder. One gram of GO were dissolved in 400 mL of DI water during sonication. After heating the GO solution up to 100 , 10 mL of hydrazine was added and heated for 1 h. The resulting rGO was then washed using DI water and dried in the oven at 80 for 3 h. One gram of rGO was then dissolved in 100 mL of isopropyl alcohol and mixed using a rotating mixer for 10 min followed by the solution ball milling for 2 h. Figure 1b presents the survey X-ray photoelectron spectroscopy (XPS) spectrum of rGO, showing the N1s peak in addition to the C1s and O1s peaks. The N1s peak is attributed to the nitrogen doping by hydrazine reduction [38]. Figure 1c shows the C1s XPS spectrum which can be divided into four different peaks centered at 284.70, 285.67, 286.27, and 287.90 eV, corresponding to the C=C, C-C, C-O, and C=O groups, respectively. Figure 1d shows the atomic force microscopy image of the rGO. Figure 1e,f shows the thicknesses of the rGO along the line section 1-1 and 2-2, respectively. The thicknesses were measured to be 1.060 nm and 1.675 nm. Since the thickness The rGO was prepared by reducing GO produced by the modified hummers method from the graphite powder. A mixture of 2 g of graphite having a mean size of 200 mesh and purity of 99%, 2 g of sodium nitrate (NaNO 3 ), and 100 mL of sulfuric acid (H 2 SO 4 ) with 95 wt% was prepared and stirred for 1 h. After cooling down the mixture in an ice bath, 10 g of potassium permanganate (KMnO 4 ) was added and magnetically stirred until the solution became brown. Three hundred milliliter of deionized water was added to the solution slowly during the stirring. To remove excess KMnO 4 , 10 mL of hydrogen peroxide (H 2 O 2 ) was added and stirred. Deionized (DI) water was then added and centrifuged. The supernatant was removed and residuals were washed using DI water and centrifuged five times. The GO solution was dried in the oven at 80°C for 3 h to obtain the GO powder. One gram of GO were dissolved in 400 mL of DI water during sonication. After heating the GO solution up to 100°C, 10 mL of hydrazine was added and heated for 1 h. The resulting rGO was then washed using DI water and dried in the oven at 80°C for 3 h. One gram of rGO was then dissolved in 100 mL of isopropyl alcohol and mixed using a rotating mixer for 10 min followed by the solution ball milling for 2 h. Figure 1b presents the survey X-ray photoelectron spectroscopy (XPS) spectrum of rGO, showing the N1s peak in addition to the C1s and O1s peaks. The N1s peak is attributed to the nitrogen doping by hydrazine reduction [38]. Figure 1c shows the C1s XPS spectrum which can be divided into four different peaks centered at 284.70, 285.67, 286.27, and 287.90 eV, corresponding to the C=C, C-C, C-O, and C=O groups, respectively. Figure 1d shows the atomic force microscopy image of the rGO. Figure 1e,f shows the thicknesses of the rGO along the line section 1-1 and 2-2, respectively. The thicknesses were measured to be 1.060 nm and 1.675 nm. Since the thickness of a chemically reduced monolayer GO sheet is 0.5-0.7 nm, the measured thicknesses correspond to two and three layers, respectively. [39][40][41]

Results and Discussions
The textures for the pure LC and LC-rGO with different rGO concentrations were analyzed by the white light polarized optical microscope (POM) as shown in Figure 2a. For the concentration of 0.02 wt%, the POM image shows the area with a uniform color and dark spots, corresponding to the uniform nematic texture and rGO aggregates, respectively. The uniform nematic texture in the POM image indicates the spontaneous alignment of rGO flakes in parallel to the far-field n-director of LC by the π-π electron stacking between the hexagonal lattices in rGO and benzene rings in the LC [42,43]. The uniform nematic texture also implies that the edges of the rGO flakes do not perturb the n-director of LC unless the rGO flakes agglomerate. The number and size of rGO aggregates increases as the rGO doping concentration increases and the perturbation of the n-director of LC around the rGO aggregates was observed for high rGO concentrations as shown in the inset of Figure 2a (iii-v). Since the rGO aggregates worsen the orientational order of the LC, one of the factors that determine the birefringence of the LC, it is critical to inhibit the aggregation of rGO flakes in order to take advantage of rGO doping. The aggregation of rGO flakes can be further minimized by adding nanosurfactants in the rGO-LC [37].

Results and Discussions
The textures for the pure LC and LC-rGO with different rGO concentrations were analyzed by the white light polarized optical microscope (POM) as shown in Figure 2a. For the concentration of 0.02 wt%, the POM image shows the area with a uniform color and dark spots, corresponding to the uniform nematic texture and rGO aggregates, respectively. The uniform nematic texture in the POM image indicates the spontaneous alignment of rGO flakes in parallel to the far-field n-director of LC by the -electron stacking between the hexagonal lattices in rGO and benzene rings in the LC [42,43]. The uniform nematic texture also implies that the edges of the rGO flakes do not perturb the n-director of LC unless the rGO flakes agglomerate. The number and size of rGO aggregates increases as the rGO doping concentration increases and the perturbation of the n-director of LC around the rGO aggregates was observed for high rGO concentrations as shown in the inset of Figure 2a (iii-v). Since the rGO aggregates worsen the orientational order of the LC, one of the factors that determine the birefringence of the LC, it is critical to inhibit the aggregation of rGO flakes in order to take advantage of rGO doping. The aggregation of rGO flakes can be further minimized by adding nanosurfactants in the rGO-LC [37].    To quantify the changes in the birefringence by rGO doping, the voltage-dependent optical transmission measurement was performed. Figure 3 shows the measurement setup for the voltage-dependent optical transmission of the homogeneously aligned LC-rGO between glass substrates. The setup comprised a He-Ne laser with a wavelength of 543 nm, an attenuator, a spatial filter, a refractive lens, an aperture, a polarizer and the LC-rGO cell, an analyzer, and a power meter. The measurements were performed in crossed polarizers, and the polarizer azimuth angle (polarization direction) was 45 • with respect to the optical axis of the LC-rGO phase modulator. The bipolar square wave pulse with a frequency of 1 kHz and zero DC bias was applied for the measurement. Figure 4a-e shows the voltage-dependent optical transmission of LC-rGO phase modulator with different rGO concentrations. The optical transmission oscillates between the minimum and maximum value as a function of voltage. The voltage-dependent optical transmissions for LC-rGO with rGO concentration of 0.02 and 0.04 wt% exhibit a higher number of oscillations than that of intrinsic LC, indicating increased effective birefringence. Figure 5a shows the voltage-dependent phase retardation of the LC-rGO phase modulator. It should be noted that the phase retardation is strongly dependent on the thickness and birefringence of the LC-rGO. Therefore, the thickness variation among cells should be carefully considered. Figure  The birefringence of a nematic LC is determined by the order parameter and anisotropy of polarizability of the individual molecules. The relationship between the order parameter (S), the anisotropy of polarizability (∆α), and birefringence (∆n = n e − n o ) can be described by following the Vuks expression [44]: where n e and n o are the extraordinary and ordinary refractive index, α = 1/3(α x + α y + α z ), and n = 1/3(n x + n y + n z ).
Nanomaterials 2020, 10, x FOR PEER REVIEW 5 of 11 To quantify the changes in the birefringence by rGO doping, the voltage-dependent optical transmission measurement was performed. Figure 3 shows the measurement setup for the voltagedependent optical transmission of the homogeneously aligned LC-rGO between glass substrates. The setup comprised a He-Ne laser with a wavelength of 543 nm, an attenuator, a spatial filter, a refractive lens, an aperture, a polarizer and the LC-rGO cell, an analyzer, and a power meter. The measurements were performed in crossed polarizers, and the polarizer azimuth angle (polarization direction) was 45° with respect to the optical axis of the LC-rGO phase modulator. The bipolar square wave pulse with a frequency of 1 kHz and zero DC bias was applied for the measurement. Figure 4a-e shows the voltage-dependent optical transmission of LC-rGO phase modulator with different rGO concentrations. The optical transmission oscillates between the minimum and maximum value as a function of voltage. The voltage-dependent optical transmissions for LC-rGO with rGO concentration of 0.02 and 0.04 wt% exhibit a higher number of oscillations than that of intrinsic LC, indicating increased effective birefringence. Figure 5a shows the voltage-dependent phase retardation of the LC-rGO phase modulator. It should be noted that the phase retardation is strongly dependent on the thickness and birefringence of the LC-rGO. Therefore, the thickness variation among cells should be carefully considered. Figure 5b shows the effective birefringence of the LC-rGO extracted from the phase retardation (Figure 5a) and the thicknesses of the LC-rGO layers. The thicknesses of four different positions of each empty LC-rGO cell were measured using a UV-Visible spectrometer and averaged. The average thickness (standard deviation) of an LC-rGO layer with concentrations of 0.00, 0.02, 0.04, 0.06 and 0.08 wt% were 5.704 (± 0.055), 6.402 (± 0.268), 6.041 (± 0.016), 6.284 (± 0.233), and 6.430 μm (± 0.156), respectively. The average effective birefringence (standard deviation) of the LC-rGO with a concentration of 0.00, 0.02, 0.04, 0.06 and 0.08 wt% were 0.174 (± 0.002), 0.198 (± 0.006), 0.189 (± 0.001), 0.167 (± 0.006), and 0.164 (± 0.004), respectively. The birefringence of the intrinsic LC is in good agreement with the value provided by the supplier. The birefringence of LC-rGO exhibits a higher value than that of the intrinsic LC in the range of 0.02 to 0.04 wt% rGO concentrations, and a further increase in doping concentration lowers the birefringence.    The birefringence of a nematic LC is determined by the order parameter and anisotropy of polarizability of the individual molecules. The relationship between the order parameter (S), the anisotropy of polarizability ( ), and birefringence ( can be described by following the Vuks expression [44]: (3) where and are the extraordinary and ordinary refractive index, , and .
To investigate the effect of rGO doping on the order parameter, the nematic to isotropic phase transition temperature (TNI) of the LC-rGO was measured using a differential scanning calorimeter as shown in Figure 6a. This shows that the addition of rGO decreases TNI for all doping concentrations. The relationship between TNI and the order parameter (S) can be described by following Haller's empirical expression [45]:  The birefringence of a nematic LC is determined by the order parameter and anisotropy of polarizability of the individual molecules. The relationship between the order parameter (S), the anisotropy of polarizability ( ), and birefringence ( can be described by following the Vuks expression [44]: (3) where and are the extraordinary and ordinary refractive index, , and .
To investigate the effect of rGO doping on the order parameter, the nematic to isotropic phase transition temperature (TNI) of the LC-rGO was measured using a differential scanning calorimeter as shown in Figure 6a. This shows that the addition of rGO decreases TNI for all doping concentrations. The relationship between TNI and the order parameter (S) can be described by following Haller's empirical expression [45]: To investigate the effect of rGO doping on the order parameter, the nematic to isotropic phase transition temperature (T NI ) of the LC-rGO was measured using a differential scanning calorimeter as shown in Figure 6a. This shows that the addition of rGO decreases T NI for all doping concentrations. The relationship between T NI and the order parameter (S) can be described by following Haller's empirical expression [45]: where T is the temperature at which the measurement is made, and β is a unitless fitting parameter. Therefore, the decrease in T NI is attributed to the reduced-order parameter for all rGO concentrations. This result and Equation (3) imply that increased birefringence for the rGO concentration of 0.02 and 0.04 wt% is mainly due to the increased anisotropy of polarizability which compensates for the decreases in the order parameter. When subjected to an alternating electric field, rGO is polarized and both rGO and LC gain dipole moments. The torque exerted on rGO not only rotates the rGO itself but also facilitates the rotation of LC anchoring on both sides of the rGO surface. Thus, the increased anisotropy of polarizability of the LC-rGO results in increased birefringence of the LC-rGO composite. For higher doping concentrations, the aggregation of rGO lowers birefringence by decreasing both the order parameter and the anisotropy of polarizability. Figure 6b shows the threshold voltage as a function of doping concentrations. For the concentrations of 0.02 and 0.04 wt%, the threshold voltage decreased compared to that of the intrinsic LC, whereas for higher doping concentrations, the threshold voltage increased. The threshold voltage is determined by the dielectric anisotropy (∆ε) and the splay elastic constant (K 11 ) as shown in Equation (1). To investigate the effect of the order parameter and polarizability anisotropy on the threshold voltage, we described dielectric anisotropy and the splay elastic constant in terms of order parameter and anisotropy of polarizability by [46][47][48]: where N is the number density, h is the cavity field factor, F is the Onsager reaction field, ∆α is the polarizability anisotropy, µ is the dipole moment, kT is the thermal energy, β is the angle between the dipole moment and the primary molecular axis. C 11 is the reduced splay elastic constant, and V n is the mole volume. Therefore, the threshold voltage can be described by the order parameter and dielectric anisotropy as follows: where γ = (Fµ 2 /kT)(1 − 3cos 2 (β)). The threshold voltage is proportional to the square root of the order parameter and is inversely proportional to the square root of the polarizability anisotropy. The decrease in threshold voltage for the doping concentration of 0.02 and 0.04 wt% is attributed to the decrease in the order parameter and increase in polarizability anisotropy. For higher concentrations, it can be concluded that both the order parameter and anisotropy of polarizability decrease, however, the decrease in anisotropy of polarizability outweighs the decrease in the order parameter, thus, resulting in an increased threshold voltage.

Conclusions
We have demonstrated that the addition of an appropriate concentration of rGO enhances the birefringence of LC. It has been found that the enhancement of birefringence is mainly due to the increased anisotropy of polarizability, which compensates for the decrease in the order parameter. The high shape anisotropy of rGO provides improved anisotropy of polarizability. However, the aggregation of rGO reduces the birefringence by decreasing the anisotropy of polarizability as well as order parameter. Our study suggests that the LC doped with rGO can be potentially applied to a variety of electro-optic devices for an improved electro-optic effect and reduced device thickness.

Conclusions
We have demonstrated that the addition of an appropriate concentration of rGO enhances the birefringence of LC. It has been found that the enhancement of birefringence is mainly due to the Nanomaterials 2020, 10, 842 8 of 10 increased anisotropy of polarizability, which compensates for the decrease in the order parameter. The high shape anisotropy of rGO provides improved anisotropy of polarizability. However, the aggregation of rGO reduces the birefringence by decreasing the anisotropy of polarizability as well as order parameter. Our study suggests that the LC doped with rGO can be potentially applied to a variety of electro-optic devices for an improved electro-optic effect and reduced device thickness.

Conflicts of Interest:
The authors declare no conflict of interest.