Theoretical investigation on the formation of hexagonal, honeycomb, and kagome superlattices of binary 1D nanoparticles

Superlattices that consist of binary nanoparticles have attracted attention for their potential applicability. However, the synthesis of superlattices composed of two different types of one-dimensional (1D) nanoparticles is still challenging. In this study, we investigate the formation of superlattices composed of binary component 1D nanoparticles by experiments and theory. Our experiments demonstrate that two different superlattices (AB₂ and AB₃ types) can be obtained by tuning particle diameter and mixing ratios. We develop a mean field theory to understand the thermodynamics of the superlattices self-assembly. We calculate the free volume of three different phases (AB₂, AB₃ and random phases) at given size and number ratios, and estimate free energy per site of two types of coexisting phases (AB₂ + random and AB₃ + random). The theory shows that the different types of superlattices formation (observed in experiments) can be understood in terms of the free volume entropy-driven process. Based on the calculated free energy per site, we determine the thermodynamically favorable phase at given particle diameter and mixing ratio, which is consistent with experiments.