In that case, the system has two types of orientational order: (i) the one associated with particle orientations and characterized by a polyhedral nematic order parameter, and (ii) the bond orientational order. As we have demonstrated in earlier works, the SymBOP is natural for the characterization of self-assembly of anisotropic particles. There are two fundamental approaches that one can employ to construct the projection operator P ̂ g, and thus the corresponding SymBOP: In 3D, this typically implies the choice of at least one preferential direction (or several equivalent ones). The results underscore the versatility and robustness of SymBOPs in characterizing ordering phenomena, making them valuable tools for investigating structural properties in various systems.īy its definition, a SymBOP depends on the underlying point symmetry group g. Furthermore, the analysis distinguishes individual sublattices within a single crystalline domain, such as pair of interpenetrating FCC lattices within a cubic diamond. It proved highly sensitive in identifying coherent crystalline domains with different orientations, as well as detecting topological defects, such as dislocations. The SymBOP analysis was applied to experiments on DNA-frame-based assembly of nanoparticle lattices. The present study expands the method initially developed for assemblies of anisotropic particles to the isotropic ones or cases where particle orientation information is unavailable. This approach provides a more sensitive analysis of local order than traditional scalar BOPs, facilitating the identification of coherent domains at the single bond level. Bond-orientational order in DNA-assembled nanoparticles lattices is explored with the help of recently introduced Symmetry-specific Bond Order Parameters (SymBOPs).
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