  Halloysite nanotubes (HNTs) are naturally occurring clay minerals found in
Earth's crust that typically exist in the form of high aspect-ratio
nanometers-long rods. Here, we investigate the evaporation-driven self-assembly
process of HNTs and show that a highly polydisperse collection of HNTs
self-sort into a spatially inhomogeneous structure, displaying a systematic
variation in the resulting nematic order. Through detailed quantification using
nematic order parameter $S$ and nematic correlation functions, we show the
existence of well-defined isotropic-nematic transitions in the emerging
structures. We also show that the onset of these transitions gives rise to the
formation of nematic islands - phase coexisting ordered nematic domains
surrounded by isotropic phase - which grow in size with $S$. Detailed image
analysis indicates a strong correlation between local $S$ and the local aspect
ratio, $L/D$, with nematic order possible only for rods with $L/D \ge 6.5 \pm
1$. Finally, we conclude that observed phenomena directly result from aspect
ratio-based sorting in our system. Altogether, our results provide a unique
method of tuning the local microscopic structure in self-assembled HNTs using
$L/D$ as an external parameter.
