Optical Properties of Liquid Crystalline Alkoxy Benzoic Acids with Dispersed Citrate-Capped Gold Nanoparticles

2.1 Synthesis of Citrate-Capped Gnps

The citrate-capped Gnps were synthesized with the citrate reduction process from the standard literature data [30]. The chemical ingredients for the synthesis, the reducing agent trisodium citrate dehydrate (Na₃C₆H₅O₇ ⋅ 2H₂O) 99 % and hydrogen tetrachloroaurate (III) trihydrate (HAuCl₄ ⋅ 3H₂O) ACS, 99.99 %, were purchased from Sigma Aldrich Laboratories, USA (Sigma Aldrich, St Louis, MO, USA) and used as such. From the Inductive Couple Plasma Optical Spectrometry report (ICAP6500 Thermo Fisher Scientific), the amount of Gnps present in the solution of 1 ml (1000 μl) of citrate-capped Gnps was 96.75 μg. The author has dispersed very small amounts of citrate-capped Gnps; 30, 50, 70 and 90 μl contain Gnps of amounts 2.90, 4.83, 6.77 and 8.70 μg, respectively.

2.2 Homogeneous Dispersion of Citrate-Capped Gnps in LC Compounds

The LC compounds 11oba and 12oba were purchased from Sigma-Aldrich Laboratories (USA) and used as such. Citrate-capped Gnps (30 μl) was dispersed homogeneously into 100 mg of LC material 11oba in the isotropic state, which was dissolved in toluene and stirred well for about 3 h (Remi DHMS 2432 magnetic stirrer, Vasai, India) and termed as 11oba mix 1. The same process was repeated with the dispersion of 30, 50, 70 and 90 μl in 100 mg of 11oba and 12oba, separately termed as 11oba mix 2, 11oba mix 3 and 11oba mix 4, and 12oba mix 1, 12oba mix 2, 12oba mix 3, and 12oba mix 4, respectively. After cooling, the 11oba and 12oba mixtures were subjected to examination of both phase transition temperatures and textures using polarizing thermal microscopy (POM) (SDTechs) attached with a hot stage (SDTECHS-SDVPM 2727, Machilipatnam, Andhra Pradesh, India). The substance was filled in 4-μm cells in planar alignment, and the temperature was measured with a thermometer designed by Gray [31]. The transition temperatures of LCs with nanomixtures at the phase transition were studied through differential scanning calorimetry (DSC) (Perkin Elmer Diamond DSC, Thane, Mumbai, India) along with the enthalpy values of the endothermic and exothermic regimes. Then, 11oba and 12oba with a homogeneous dispersion of citrate-capped Gnps in each concentration and characterized by the experimental techniques UV-visible spectroscopy (using Shimadzu UV-2450 UV-Visible spectrophotometry, Shimadzu, Tokyo, Japan) and SEM and the presence of citrate-capped Gnps in 11oba and 12oba were further studied.

3.1 Ultraviolet-Visible Spectroscopy

UV-visible spectroscopy is a powerful characterization tool for the citrate-capped Gnps due to the surface plasmon resonance emerging as a broad absorption band in the visible region from ∼510 to ∼580 nm. It is found that no peak is observed in the spectrum for 11oba and 12oba pure compounds in the wavelength range of 500–600 nm. However, the spectra of 11oba mix 3 and 12oba mix 4 show the prominent peak at 550 nm [32], which is the characteristic peak of citrate-capped Gnps shown in Figure 1a and b.

Figure 1:

(a) UV data of citrate-capped Gnps 11oba mix 3. (b) UV data of citrate-capped Gnps in 12oba mix 4.

3.2 SEM Analysis

SEM gives the surface morphology and chemical composition of elements, which are presented in the sample for the characterization of nanomaterials [33]. The SEM image and EDS data of citrate-capped Gnps are shown in Figure 2a, while those of 11oba mix 3 and 12oba mix 4 are shown in Figure 2b and c, respectively. From the EDS data, the occurrence of citrate-capped Gnps in 11oba and 12oba is confirmed. SEM device used Zeiss from Zeiss, Oberkochen, Germany.

Figure 2:

(a) SEM image and EDS data of citrate-capped Gnps. (b) SEM image and EDS data of 11oba mix 3. (c) SEM image and EDS data of 12oba mix 4.

3.3 Gradient Measurement Technique (GMSD)

Image gradient is a directional change in force or shading in an image, and it is an essential component since it can adequately catch the confined structures of the image. Image gradients might be utilized to separate two critical parameters from images. The first one is known as the magnitude of the gradient, which is how rapidly the image power is changing, and the other one is the course of the gradient, which reveals the bearing in which the image force is changing rapidly.

The image gradients are delicate to image contortions, while distinctive neighborhood structures in a mutilated image experience the ill effects of the different degrees of debasements. The most generally experienced image contortions, including commotion defilement, obscure and pressure ancient rarities, will prompt exceptionally the unmistakable auxiliary changes that “fly out” of the gradient area. Inspiring by this, we investigate the utilization of global variation of gradient-based local feature map for the variation in texture images due to change in temperature at phase transitions [34].

This image processing with statistical parameters technique will give information with regard to the phase transition temperature of the compound without taking assistance from the DSC instrument. The mean of all the collected images at various temperatures is used to find the phase change in this strategy. This will allow for the phase transition of the LC compound to be obtained in less time and at low cost [35]. The textures at the phase transition from the POM are shown in Figure 3a–d for 11oba mix 1, in Figure 3e–h for 11oba mix 2, in Figure 3i–l for 12oba mix 1, in Figure 3m–p for 12oba mix 2 and in Figure 3q–t for 12oba mix 4. Table 1 provides the data of the phase transitions of the LC mixtures, and DSC thermograms along with GMSD technique are shown in Figure 4a–d. The DSC thermograms of 11oba and 12oba along with various mixtures are shown in Figure 4e–h.

Figure 3:

POM textures of 11oba mix 1: (a) isotropic to nematic phase at 136.9 °C; (b) nematic at 134.3 °C; (c) SmC at 125.8 °C; (d) solid I at 85.1 °C. POM textures of 11oba mix 2: (e) nematic phase at 136.2 °C; (f) SmC at 124.4 °C; (g) solid I at 83.2 °C; (h) solid II at 73.2 °C. POM textures of 12oba mix 1: (i) nematic phase at 132.8 °C; (j) SmC at 128 °C; (k) solid I at 86.1 °C; (l) solid II at 63.9 °C. POM textures of 12oba mix 2: (m) nematic phase at 132.8 °C; (n) SmC at 128.2 °C; (o) solid I at 86.6 °C; (p) solid II at 62.8 °C. POM textures of 12oba mix 4: (q) nematic phase at 129.9 °C; (r) SmC at 128.8 °C; (s) solid I at 85.9 °C; (t) solid II at 62.8 °C.

Figure 4:

(a) 11oba mix 1 with the DSC and GMSD techniques. (b) 11oba mix 2 with the DSC and GMSD techniques. (c) 12oba mix 1 with the DSC and GMSD techniques. (d) 12oba mix 4 with the DSC and GMSD techniques. (e) DSC thermogram of 11oba pure and with mix 1 and mix 3. (f) DSC thermogram of 11oba pure and with mix 2 and mix 4. (g) DSC thermogram of 12oba pure and with mix 1 and mix 3. (h) DSC thermogram of 12oba pure and with mix 2 and mix 4.

3.4 Measurement of Refractive Indices Using Modified Spectrometer

The refractive indices of the LC compound and with dispersed citrate-capped Gnps in different concentrations are measured with a wedge-shaped glass cell similar to the one used by Haller et al [36] using a modified spectrometer [37], [38] (SDTechs SDMS 6336). The accuracy in the measured refractive indices is ±0.0005, and the temperature accuracy of the heating block is ±0.1 °C. The cell containing the LC sample is enclosed with a heating block mounted on a prism table. The whole system is attached to a modified spectrometer kept in minimum deviation position (SDTECHS-SDMS 6336, Machilipatnam, Andhra Pradesh, India). The refractive indices are measured from the readings of deviations observed in a modified spectrometer by using formula

Here, d is the deviation and A is the angle of the wedge in which the sample is placed.

The variation of the refractive indices with temperature is calculated during the cooling of the LC compound from the isotropic state to the nematic state. At the isotropic state (n_iso) while cooling, the deviated ray splits up into two rays: one is the extraordinary ray (higher value of n_iso), and the other is the ordinary ray (lower value of n_iso), and their corresponding refractive indices (n_e and n_o) are calculated with variations of temperature in the nematic region at various wavelengths 460, 500, 570 and 635 nm. The refractive indices increase with a decrease in wavelength [39] as expected, (shown in Fig. 5a–j).

Figure 5:

(a) Refractive indices (n_e, n_o) vs. temperature in 11oba pure. (b) Refractive indices (n_e, n_o) vs. temperatue in 11oba mix 1. (c) Refractive indices (n_e, n_o) vs. temperature in 11oba mix 2. (d) Refractive indices (n_e, n_o) vs. temperatue in 11oba mix 3. (e) Refractive indices (n_e, n_o) vs. temperature in 11oba mix 4. (f) Refractive indices (n_e, n_o) vs. temperatue in 12oba pure. (g) Refractive indices (n_e, n_o) vs. temperature in 12oba mix 1. (h) Refractive indices (n_e, n_o) vs. temperature in 12oba mix 2. (i) Refractive indices (n_e, n_o) vs. temperature in 12oba mix 3. (j) Refractive indices (n_e, n_o) vs. temperature in 12oba mix 4.

From Figure 5a–e, it is observed that the value of n_e increased from 1.4 % to 13.1 % for 11oba mix 1 to 11oba mix 4 in comparison with the 11oba pure compound, while the value of n_o increased from 1.5 % to 14.1 %, respectively, and in the case of 12oba mix 1 to mix 4, the values of n_e and n_o have been increased, with small amounts from 0.2 % to 2.3 % in comparison with the 12oba pure compound in the saturated nematic thermal region.

3.5 Determination of Birefringence (δn)

The birefringence (δn) with temperature plays an important role in display devices. It is the difference between n_e and n_o measured for different nanocomposites mix 1, mix 2, mix 3 and mix 4 at different wavelengths (460, 500, 570 and 635 nm). The value of δn obtained increased with the decrease in wavelength as shown in Figure 6a–r.

Figure 6:

(a) Birefringence δn vs. temperature in 11oba pure at various wavelengths. (b) Birefringence δn vs. temperature in 11oba mix 1 at various wavelengths. (c) Birefringence δn vs. temperature in 11oba mix 2 at various wavelengths. (d) Birefringence δn vs. temperature in 11oba mix 3 at various wavelengths. (e) Birefringence δn vs. temperature in 11oba mix 4 at various wavelengths. (f) Birefringence δn vs. temperature in 12oba pure at various wavelengths. (g) Birefringence δn vs. temperature in 12oba mix 1 at various wavelengths. (h) Birefringence δn vs. temperature in 12oba mix 2 at various wavelengths. (i) Birefringence δn vs. temperature in 12oba mix 3 at various wavelengths. (j) Birefringence δn vs. temperature in 12oba mix 4 at various wavelengths. (k) Birefringence δn vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations for 460 nm. (l) Birefringence δn vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations for 500 nm. (m) Birefringence δn vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations for 570 nm. (n) Birefringence δn vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations for 635 nm. (o) Birefringence δn vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations for 460 nm. (p) Birefringence δn vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations for 500 nm. (q) Birefringence δn vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations for 570 nm. (r) Birefringence δn vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations for 635 nm.

As the concentration of the dispersed citrate-capped Gnps increased, the nematic transition temperature reduced in all concentrations measured. At first, I-N transition, i.e. in the high temperature regions, the difference in the values of birefringence will be smaller and increases more prominently in the low-temperature region, after crossing the fluctuation-dominated non-linear region in a short thermal range. The values of δn in the pure LC compounds 11oba and 12oba at the stabilized nematic region are enhanced from 2.81 % to18.86 % (460 nm), 1.62 %–18.91 % (500 nm), 1.54 %–18.35 % (570 nm) and 1.4 %–17.79 % (635 nm) with the dispersion of citrate-capped Gnps in increasing concentrations. This shows that the increment in values of δn in 11oba and 12oba with the dispersion of various concentrations of citrate-capped Gnps improves the molecular alignment along with orientational order parameter S of the LC molecules. The same phenomenon is observed in the other LC materials by the dispersion of ZnO and TiO₂ [25], [39]. The citrate-capped Gnps captures the impurity ions in 11oba and 12oba, and the citrate-capped Gnps have greater dipole moment relative to LCs. Thereby, citrate-capped Gnps produce higher electric torque than molecules of the LC compound. Because of this, the electro-optical properties of 11oba and 12oba are enhanced by the dispersion of citrate-capped Gnps [40], [41].

Figure 6a–j shows the variation in δn with respect to temperature at different wavelengths, and Figure 6k to r shows the variation of δn at a particular wavelength for different concentrations with respect to temperature for the compounds 11oba and 12oba, pure and with mix 1, mix 2, mix 3 and mix 4, respectively. In all the graphs, systematic enhancement has been obtained in δn with respect to the different temperatures. The δn values at the stabilized nematic region are enhanced from 2.8 % to 18.9 % in 11oba and from 5.6 % to 22.1 % in 12oba for various wavelengths and with relatively increased concentrations of dispersed citrate-capped Gnps.

3.6 Order Parameter (S)

After the investigations of different optical studies were carried out, the important parameter of LC is order parameter, the parameter which gives the average direction of all LC molecules oriented about the optic axis. The order parameter is determined from the refractive indices data by several methods [42], such as the Kuczynski method (without considering the internal molecular field), the Vuks model (considering the isotropic nature of LCs), the Haller approximation method and the effective geometry parameter model.

3.6.1 Kuczynski Method

The author chose the Kuczynski method for the determination of order parameter S from the birefringence measurements δn without considering the local field experienced by the molecule in the LC nematic phase [43], [44], [45]. The order parameter of LC uniaxial crystal is calculated by the given formula

(2)S=δnΔn

where δn is the birefringence and Δn is the hypothetical birefringence in the case of perfect order (crystalline state). According to Kuczynski et al. [45], [46], the order parameter S can be determined from birefringence δn, a function of temperature, and is built in to the following equation.

(3)δn=Δn{1−(T/T∗)}β

(4)logδn=logΔn+βlog(T∗−TT∗)

where T^∗ and β are constants (T^∗ is about 0.1–4 °C higher than the I–N transition temperature; the exponent β is near to 0.20). The three adjustable parameters T^∗, Δn and β are obtained by varying T^∗ and fitting the experimental data for δn to the logarithmic equation. The values of log Δn and β were obtained with the linear regression method by maintaining regression through adjusting the parameter T^∗, which is obtained by adding a varied value from 0.1 to 4 °C to the I-N transition temperature to get the best correlation coefficient of the linear regression. The log-log plots of 11oba and 12oba with dispersed citrate-capped Gnps at different wavelengths for a particular concentration are shown in Figure 7a and b. The values of slope(β), regression(R) and log(Δn), Δn and T^∗ of the 11oba pure and with mix 1, mix 2, mix 3 and mix 4 are shown in Table 2, while the corresponding values of 12oba pure along with the mixtures are shown in Table 3.

Figure 7:

(a) Log-log plot of 11oba mix 1. (b) Log-log plot of 12oba mix 4.

Table 2:

Values of T^∗, slope(β), regression(R), log(Δn) and Δn of the 11oba pure and with mix 1, mix 2, mix 3 and mix 4.

S. No	LCNPs	T∗	Slope	Regression	Log(Δn)	Δn
	11oba + citrate-capped Gnps – 460 nm
1.	11oba pure	411.70	0.1500	0.9890	−0.4573	0.3491
2.	11oba mix 1	410.77	0.1432	0.9931	−0.4535	0.3519
3.	11oba mix 2	410.03	0.1529	0.9926	−0.4486	0.3560
4.	11oba mix 3	408.84	0.1423	0.9747	−0.4349	0.3673
5.	11oba mix 4	408.62	0.1327	0.9912	−0.4193	0.3805
	11oba + citrate-capped Gnps – 500 nm
6.	11oba pure	411.71	0.1544	0.9889	−0.4695	0.3471
7.	11oba mix 1	410.03	0.1529	0.9926	−0.4338	0.3485
8.	11oba mix 2	409.99	0.1488	0.9888	−0.4509	0.3540
9.	11oba mix 3	408.84	0.1462	0.9752	−0.4379	0.3648
10.	11oba mix 4	408.62	0.1365	0.9915	−0.4223	0.3780
	11oba + citrate-capped Gnps – 570 nm
11.	11oba pure	411.7	0.1583	0.9893	−0.4626	0.3446
12.	11oba mix 1	410.76	0.1524	0.9928	−0.4626	0.3446
13.	11oba mix 2	409.985	0.1546	0.9884	−0.4567	0.3494
14.	11oba mix 3	408.84	0.1548	0.9750	−0.4380	0.3647
15.	11oba mix 4	408.62	0.1427	0.9932	−0.4238	0.3768
	11oba + citrate-capped Gnps – 635 nm
16.	11oba pure	411.69	0.1611	0.9886	−0.4645	0.3431
17.	11oba mix 1	410.76	0.1580	0.9929	−0.4644	0.3433
18.	11oba mix 2	409.99	0.1617	0.9896	−0.4583	0.3481
19.	11oba mix 3	408.84	0.1657	0.9759	−0.4486	0.3562
20.	11oba mix 4	408.62	0.1517	0.9959	−0.4243	0.3765

Table 3:

Values of T^∗, slope(β), regression(R), log(Δn) and Δn of the 12oba pure and with mix 1, mix 2, mix 3 and mix 4.

S. No	LCNPs	T∗	Slope	Regression	Log(Δn)	Δn
	12oba + citrate-capped Gnps – 460 nm
1.	12oba pure	412.53	0.1561	0.9803	−0.5657	0.2718
2.	12oba mix 1	412.16	0.1565	0.9701	−0.5501	0.2817
3.	12oba mix 2	410.56	0.1535	0.9970	−0.5449	0.2852
4.	12oba mix 3	409.90	0.1520	0.9874	−0.5399	0.2885
5.	12oba mix 4	408.36	0.1443	0.9968	−0.5242	0.2989
	12oba + citrate-capped Gnps – 500 nm
6.	12oba pure	412.51	0.1577	0.9806	−0.5697	0.2693
7.	12oba mix 1	412.14	0.1591	0.9704	−0.5578	0.2792
8.	12oba mix 2	410.52	0.1559	0.9972	−0.5508	0.2813
9.	12oba mix 3	409.89	0.1465	0.9872	−0.5449	0.2852
10.	12oba mix 4	408.35	0.1454	0.9964	−0.5289	0.2958
	12oba + citrate-capped Gnps – 570 nm
11.	12oba pure	412.51	0.1608	0.9805	−0.5710	0.2685
12.	12oba mix 1	412.13	0.1645	0.9702	−0.5578	0.2768
13.	12oba mix 2	410.51	0.1629	0.9971	−0.5560	0.2779
14.	12oba mix 3	409.89	0.1498	0.9876	−0.5466	0.2840
15.	12oba mix 4	408.35	0.1518	0.9967	−0.5301	0.2951
	12oba + citrate-capped Gnps – 635 nm
16.	12oba pure	412.51	0.1657	0.9802	−0.5728	0.2674
17.	12oba mix 1	412.12	0.1702	0.9700	−0.5612	0.2747
18.	12oba mix 2	411.51	0.1719	0.9970	−0.5583	0.2765
19.	12oba mix 3	409.86	0.1531	0.9839	−0.5490	0.2824
20.	12oba mix 4	408.35	0.1557	0.9966	−0.5340	0.2924

The various values of the order parameter S of the molecules of the LC compounds along with citrate-capped Gnps are found wherein as the concentration of citrate-capped Gnps increases, they improve the alignment and have the tendency to orient the LC molecules more properly to the director direction.

The birefringence δn as well as the orientational order parameter S values of 11oba and 12oba pure agreed with the values which are previously determined [47]. δn and S increased with the increase in the concentration of citrate-capped Gnps in pure LCs, and these values agree with the values that were obtained from the experimental techniques.

The order parameter values for 11oba and 12oba pure and with dispersed citrate-capped Gnps are presented in Figure 8a and j. Similarly, the variations of the order parameter of 11oba and 12oba pure and mix 1, mix 2, mix 3 and mix 4 across temperature are shown in Figure 8l and n, respectively.

Figure 8:

Order parameter S: (a) S vs. temperature in 11oba pure at various wavelengths from the Kuczynski model. (b) S vs. temperature in 11oba mix 1 at various wavelengths from the Kuczynski model. (c) S vs. temperature in 11oba mix 2 at various wavelengths from the Kuczynski model. (d) S vs. temperature in 11oba mix 3 at various wavelengths from the Kuczynski model. (e) S vs. temperature in 11oba mix 4 at various wavelengths from the Kuczynski model. (f) S vs. temperature in 12oba pure at various wavelengths from the Kuczynski model. (g) S vs. temperature in 12oba mix 1 at various wavelengths from the Kuczynski model. (h) S vs. temperature in 12oba mix 2 at various wavelengths from the Kuczynski model. (i) S vs. temperature in 12oba mix 3 at various wavelengths from the Kuczynski model. (j) S vs. temperature in 12oba mix 4 at various wavelengths from the Kuczynski model. (k) S vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations from the Kuczynski model at 460 nm. (l) S vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations from the Kuczynski model at 500 nm. (m) S vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations from the Kuczynski model at 460 nm. (n) S vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations from the Kuczynski model at 500 nm.

3.6.4 Effective Geometry Parameter Model

In this method, the order parameter could be obtained in terms of the effective geometry parameter, α_eg = n_o/n_e, using following equation, order parameter is calculated.

Sαeg=3⟨n2⟩(Δn)(1−αeg1+2αeg)

The same procedure for the determination of S for the above three methods is repeated for all the four wavelengths (460, 500, 570 and 635 nm). The values of S obtained nearly agree with the values obtained from the Kuczynski method. The variations of S with respect to temperature at various wavelengths and various mixtures from the Kuczynski, Vuks, Haller and effective geometry parameter models are shown in Figures 8a–n, 9a–j, 10a–f, 11a–l and 12a–d.

Figure 9:

(a) S vs. temperature in 11oba pure at various wavelengths from the Vuks model. (b) S vs. temperature in 11oba mix 1 at various wavelengths from the Vuks model. (c) S vs. temperature in 11oba mix 2 at various wavelengths from the Vuks model. (d) S vs. temperature in 11oba mix 3 at various wavelengths from the Vuks model. (e) S vs. temperature in 12oba pure at various wavelengths from the Vuks model. (f) S vs. temperature in 12oba mix 1 at various wavelengths from the Vuks model. (g) S vs. temperature in 12oba mix 2 at various wavelengths from the Vuks model. (h) S vs. temperature in 12oba mix 3 at various wavelengths from the Vuks model. (i) S vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations from the Vuks model at 460 nm. (j) S vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations from the Vuks model at 460 nm.

Figure 10:

(a) S vs. temperature in 11oba pure at various wavelengths from the Haller extrapolation model. (b) S vs. temperature in 11oba mix 3 at various wavelengths from the Haller extrapolation model. (c) S vs. temperature in 11oba mix 4 at various wavelengths from the Haller extrapolation model. (d) S vs. temperature in 12oba pure at various wavelengths from the Haller extrapolation model. (e) S vs. temperature in 12oba mix 3 at various wavelengths from the Haller extrapolation model. (f) S vs. temperature in 12oba mix 4 at various wavelengths from the Haller extrapolation model.

Figure 11:

(a) S vs. temperature in 11oba pure at various wavelengths from the effective geometry parameter method. (b) S vs. temperature in 11oba mix 1 at various wavelengths from the effective geometry parameter method. (c) S vs. temperature in 11oba mix 2 at various wavelengths from the effective geometry parameter method. (d) S vs. temperature in 11oba mix 3 at various wavelengths from the effective geometry parameter method. (e) S vs. temperature in 12oba pure at various wavelengths from the effective geometry parameter method. (f) S vs. temperature in 12oba mix 1 at various wavelengths from the effective geometry parameter method. (g) S vs. temperature in 12oba mix 2 at various wavelengths from the effective geometry parameter method. (h) S vs. temperature in 12oba mix 3 at various wavelengths from the effective geometry parameter method. (i) S vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations from the effective geometry parameter method. (j) S vs. temperature in 11oba with dispersed citrate-capped Gnps at various concentrations from the effective geometry parameter method. (k) S vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations from the effective geometry parameter method. (l) S vs. temperature in 12oba with dispersed citrate-capped Gnps at various concentrations from the effective geometry parameter method.

Figure 12:

Variation of order parameter S in four models in 11oba and 12oba with dispersed citrate-capped Gnps: (a) Comparison of S among four models in 11oba pure at 500 nm. (b) Comparison of S among four models in 11oba mix 3 at 635 nm. (c) Comparison of S among four models in 11oba mix 2 at 570 nm. (d) Comparison of S among four models in 12oba mix 1 at 570 nm.

The dispersed citrate-capped Gnps induce realignment of neighboring 11oba and 12oba molecules, which produce more tendency to align the rod-like molecules along the direction of the director (optic axis) in the nematic phase, i.e. rotational isotropy of the molecules at the isotropic to nematic transition is broken, and they tend to well aligned due to the dispersion of citrate-capped Gnps. This increases the view angle more useful in display devices.

The order parameter S estimated from Δn, birefringence in perfect order (Kuczynski method) is compared with the values of S obtained from the Vuks, Haller and Effective geometry parameter methods; it is found that the percentage of deviation in S is almost less than 11 % in different concentrations in the stabilized nematic region, which is found to be reasonable (shown in Tab. 4).

Table 4:

Percentage of deviation of order parameter S in 11oba and 12oba in various mixtures.

Compound	Wavelength	% of deviation of order parameter S in various models with respect to the Kuczynski model from
		Vuks method	Haller’s method	Effective geometry model αeg
11oba pure	460 nm	10.72	2.05	0.29
	500 nm	9.68	2.07	0.30
	570 nm	8.97	2.15	0.30
	635 nm	8.61	2.17	0.29
11oba mix 1	460 nm	10.19	2.23	0.24
	500 nm	9.99	2.43	0.22
	570 nm	9.80	2.43	0.21
	635 nm	8.82	2.57	0.21
11oba mix 2	460 nm	10.68	0.20	0.18
	500 nm	10.70	0.46	0.19
	570 nm	9.40	0.63	0.17
	635 nm	8.06	3.11	0.18
11oba mix 3	460 nm	10.09	0.41	0.12
	500 nm	9.43	0.38	0.12
	570 nm	7.24	0.40	0.16
	635 nm	7.14	1.35	0.14
11oba mix 4	460 nm	11.16	3.98	0.46
	500 nm	10.4	3.06	0.75
	570 nm	7.88	3.82	0.54
	635 nm	4.81	3.37	0.44
12oba pure	460 nm	4.83	7.27	0.17
	500 nm	4.38	6.80	0.17
	570 nm	4.53	7.02	0.18
	635 nm	4.73	7.23	0.18
12oba mix 1	460 nm	6.34	7.00	0.23
	500 nm	5.94	6.95	0.23
	570 nm	5.72	7.69	0.21
	635 nm	5.07	8.21	0.22
12oba mix 2	460 nm	5.02	5.37	0.24
	500 nm	4.18	6.13	0.23
	570 nm	4.11	6.95	0.21
	635 nm	4.99	8.48	0.22
12oba mix 3	460 nm	2.29	2.40	0.27
	500 nm	0.84	2.02	0.29
	570 nm	0.38	2.08	0.27
	635 nm	1.93	2.05	0.28
12oba mix 4	460 nm	4.75	2.38	0.40
	500 nm	4.23	1.50	0.38
	570 nm	4.35	2.54	0.43
	635 nm	4.50	1.78	0.36