## 3 Results and Discussions
### Liquid Crystalline Phases of TiO\({}_{2}\) NRs  
In the next step, we investigate liquid crystal phases formed by the self-assembly of the anatase NRs made. As we showed in our early work elsewhere [18] that we are interested in the collective properties of TiO\({}_{2}\) NRs specifically for optical applications. We already showed that brookite TiO\({}_{2}\) NRs exhibit an intriguing LC phase behavior in bulk as well as promising switchability in external fields. Here, to compare anatase TiO\({}_{2}\) NRs with their brookite counterparts, we represent several self-assembled domains achieved on a carbon-coated copper TEM grid in the dry state as well as LC domains along with the sedimentation profile in a capillary in bulk (Figure 5). Similar to brookite TiO\({}_{2}\) NRs, anatase TiO\({}_{2}\) NRs can be fairly well approximated as spherocylinders with an effective aspect ratio (L/T) defined by the total length (L) divided by thickness (T). To obtain the relevant aspect ratio (AR) for self-assembly we also added 3.0 nm to both L and T, reflecting twice the effective length of the ligand molecules based on interparticle spacings measured from TEM images. The phase diagram for hard anisotropic shapes has been determined by [PERSON] and [PERSON] using computer simulations [70]. However, colloidal rods are never all the same due to polydispersity in their length and diameter. Initially, [PERSON] predicted that length polydispersity in the system of hard rods broadens the biphasic region where longer rods preferentially enter the nematic phase [71]. Later, many papers investigated the effects of polydispersity for continuous distributions of rigid rods where they also found that increase in polydispersity shifts the isotropic boundary to lower concentrations while the nematic boundary moves to notably higher ones leading to a broadened biphasic region [39; 72; 73; 74; 75; 76]. In our system, based on the average dimensions of the examined anatase NRs (L = 24.6 \(\pm\) 3.4 nm and T = 3.6 \(\pm\) 0.3 nm measured by TEM images), an effective aspect ratio of 4.2 was calculated which for monodisperse hard rods is close to the AR where next to nematic, also smectic LC phases can be formed and ABC-stacked crystals at high volume fractions [39; 77; 78]. Figure 5a depicts short smectic tracks of NRs aligned side-by-side in  
Figure 4: XRD patterns of synthesized TiO\({}_{2}\) NRs and semispherical NCs. Bragg peaks at 30.5\({}^{\circ}\), 45.4\({}^{\circ}\), 57.0\({}^{\circ}\), 64.6\({}^{\circ}\), 66.1\({}^{\circ}\), and 74.6\({}^{\circ}\) indicate the existence of the anatase phase of TiO\({}_{2}\) (JCPDS No.01-086-1155) for NRs. XRD analyses clearly show the occurrence of other Bragg peaks at 34.6\({}^{\circ}\), 35.9\({}^{\circ}\), 52.7\({}^{\circ}\), and 57.9\({}^{\circ}\) mainly due to semispherical NCs that are fit with the TiO\({}_{2}\)(B) phase of titania with the reference card (JCPDS-00-046-1238). The (002), (\(-\)111), (003), and (020) reflections are typical of TiO\({}_{2}\)(B) titania. several domains. For rods with hard interactions, it has been shown that smectic phases of hard rods nucleate first in 2D smectic layers which are most likely related to why such tracks form on top of a flat wall, but it should also be remembered that the drying forces are large compared to the average kinetic energy \(kT\), where k is the Boltzmann's constant and T the absolute temperature. Therefore, it is also possible that these tracks are formed at the liquid-air interface, as it is known that being attached to the interface induces lateral forces between the rods because of the deformation of the interface [79]. Although the self-assembled arrays in Figure 5a seem to be a single layer, we presented some self-assembled domains in Figure 5b,c where part of the titania NRs were imaged  
Figure 5: TEM micrographs of anatase NRs self-assembled on a TEM grid (**a–d**) and optical micrographs of a dispersion in toluene between crossed polarizers (**e–g**). (**a**) Anatase NRs in small smectic liquid crystal-like domains.