## 3 Results and Discussions
### Liquid Crystalline Phases of TiO\({}_{2}\) NRs
(**b,c**) Hexagonal superlattices of vertically aligned anatase NRs. Inset in (**b**) shows the corresponding FFT pattern illustrating a close-packed hexagonal order. In (**c**), NRs have a tilted orientation, similar to rows of fallen dominoes (yellow arrows) around a vortex structure centered on a small cluster of locally homeotropically oriented NRs. In (**d**), a linear “rail-track” pattern was observed from the side-by-side assembly of the NRs into the rail-tracks of various lengths. (**e**) A sedimenting sample from a dispersion of anatase NRs in toluene (-29 vol%) in a capillary with three distinct regions. From top to bottom: isotropic fluid at the top, (**f**) elongated nematic tactoids floating in the isotropic fluid, and (**g**) coexistence of nematic domains and sharped-edge smectic LC phases. Scale bar in (**e**) is 500 \(\upmu\)m.  
standing normal to the TEM grid evidencing more extended 2D smectic layer formation. The vertically aligned NR layers were seen to form with close-packed hexagonal order within the smectic layers (Figure 5b inset) [39]. Additionally, in some parts of the 2D smectic layers with the rods standing perpendicular most likely the drying forces made parts of the rods end up in a tilted orientation. Some of the rods fell over like dominoes in a certain direction; similar observations were made with different systems of NRs such as TiO\({}_{2}\)[18; 80; 81; 82], CdS [83], CdSe [84], and CoO [85]. By considering the electron diffraction data, we conclude that these structures are otherwise the same as the vertically aligned arrays with a precise orientational and positional order and also the same interparticle separation as observed for the vertical superlattices. In Figure 5b,c we could also observe part of a vortex structure centered on one or a small cluster of locally homeotropically ordered rods. Since the orientation of the individual nanorods changed continuously around the vortex defect, it is similar to a disclination of strength +1 that can be observed in nematic liquid crystal phases [84; 86]. The presence of this structure can be linked to twist or bend distortions of the nematic, and possibly also smectic liquid crystal domains produced by microflows during drying [87; 88; 89]. In Figure 5e-g, polarized optical microscopy (POM) images of the LC domains of anatase NRs are displayed. The initial volume fraction of these NRs was approximately 29 vol% and they were in an isotropic state showing no optical activity between cross polarizers. Analogous to our remarks in the previous report on brookite NRs lyotropic LCs [18], the dispersion of anatase NRs exhibited an equilibrium phase behavior along the concentration gradient that occurred in the capillary. Since these NRs were too small to sediment under gravity, this gradient was most likely formed by phase separation as a result of sufficiently high initial volume fraction and weak long-ranged van der Waals attractions. Along the capillary, three main regions were observed: the isotropic region on the top of the capillary, a biphasic region consisting of nematic tactoids nucleating and floating in the isotropic liquid, and a biphasic region of sharp-edged smectic domains in coexistence with a nematic at the bottom of the capillary that was quite identical to that of smectic-A LC phases of brookite NRs [18]. No striated LC texture indicative of a pure smectic phase was detected at the bottom of the capillary in the case of anatase NRs in comparison to brookite LCs. This could be attributed to the higher level of polydispersity in the length of the anatase NRs or the initial volume fraction could be too low to form such a phase. We also note that similar to the dispersion of brookite NRs reported elsewhere [18], a dispersion of anatase NRs in an isotropic state responded to an external electric field. An induced nematic LC phase was reversibly achieved known as a para nematic phase (results are not shown here). In our follow-up work in the near future, we intend to study these behaviors and dynamics in external electric fields.