## 4 Conclusions  
In this work, we successfully synthesized highly crystalline organic-solvent-dispersible TiO\({}_{2}\) NRs based on a modified procedure from literature via a ligand-assisted nonhydrolytic sol-gel route. X-ray diffraction and selected area electron diffraction results showed the coexistence of anatase and TiO\({}_{2}\)(B) phases of titania in the particles made. This synthesis yielded relatively concentrated dispersions of the anatase NRs (-500 mg/mL), after careful size-selective precipitation steps (yield of nearly 50%) to remove the largest rods as well as semispherical particles, which is twice the amount reported for the same size brookite NRs in ref. [18]. Possible reaction and formation mechanisms for the NRs were discussed based on the unusual observation that relatively early in the synthesis (after 10 min) rods were already present that subsequently reduced in length and increased in thickness during further growth, while semispherical particles were formed as well. Furthermore, we showed that anatase NRs were monodisperse enough to spontaneously self-assemble into smectic liquid crystalline phases on the TEM grid and in bulk. Because of their high refractive indexes and at the same time minimal light scattering due to their size,  
Figure 6: (**a**) van der Waals interaction potentials between two bare TiO\({}_{2}\) NRs of anatase (solid lines) and brookite (dashed lines) phase of the same size in toluene. Vertical gray solid lines represent one and two times the effective ligand length of 1.5 nm corresponding to the interparticle spacing observed in the TEM images. (**b**) Schematic representation of NRs encounter each other in parallel, diagonal, or crossed configuration shown in blue, red, and green colors, respectively. Nanorods are assumed as parallelepipeds of length 27.4 nm and thickness 3.4 nm. both anatase and brookite TiO\({}_{2}\) dispersions are promising candidates for application in electro-optical devices based on inorganic liquid crystals. The following are available online at [[https://www.mdpi.com/article/10.3390/app12031614/s1](https://www.mdpi.com/article/10.3390/app12031614/s1)]([https://www.mdpi.com/article/10.3390/app12031614/s1](https://www.mdpi.com/article/10.3390/app12031614/s1)). Figure S1: (a) A typical UV-Vis absorption spectrum of dilute dispersion of TiO\({}_{2}\) NRs in toluene. The spectrum shows a sharp absorption edge at 380 nm corresponding to band-to-band transitions. (b) Energy dependence of \((\Delta uv)^{0.5}\) versus photon energy \((\hbar v)\) for the determination of the band gap derived from diffused UV-Vis absorption spectrum of TiO\({}_{2}\) NRs based on indirect transitions (\(n=0.5\)) for anatase NRs. The bandgap of the anatase NRs was estimated based on \((\alpha=\mathrm{K(h}v-\mathrm{E}_{g})^{0.5}/\mathrm{h}v)\) where \(E_{g}\) is the bandgap, \(\alpha\) is the absorption coefficient, \(K\) is the absorption constant for indirect transitions, and \(\hbar v\) is the incident photon energy. The bandgap of the anatase NRs is equal to 3.28 eV which is calculated from the extrapolation of the absorption edge onto the energy axis where \(\alpha=0\). Table S1: Calculated parameters used in Scherrer equation (L = \(\mathrm{K}\)\(\wedge\)/g\(\cos\)\(\theta_{\mathrm{B}}\)), where \((\beta\cong 0.041\)b), L is the average size, \(\lambda\) is the X-ray wavelength, \(\beta\) is the full-width at half maximum value calculated in radians by fitting peaks with a 4-parameter Gaussian profile, b is a coefficient in the 4-parameter Gaussian fit profile, \(\theta_{\mathrm{B}}\) is the Bragg angle for the measured peak, and K is a constant equal to 0.94. Conceptualization, S.N.H., A.v.B., A.I., P.J.B. ; methodology and investigation, S.N.H. ; HRTEM analysis, X.C. ; writing--original draft preparation, S.N.H. ; writing--review and editing, S.N.H., A.v.B., A.I., P.J.B. ; supervision, A.I., P.J.B., A.v.B. ; funding acquisition, A.v.B., A.I., P.J.B. All authors have read and agreed to the published version of the manuscript.