The hard sphere diameter of nanocrystals (nanoparticles)

The hard sphere diameter d_HS of a nanocrystal (or nanoparticle) is a very important parameter that determines the nearest neighbor separation of their assembled structure, even in those situations where the nanocrystals have large deformations of the ligand shell that prevent them from being described as hard spheres. The parameter d_HS is a function of the number of grafted ligands and critically depends on the maximum ligand grafting density σ_Max, which we calculate by three different methods for the 351 gold nanocrystals with the number of atoms between 38 and 4033. The use of d_HS in the interpretation of experimental results is analyzed.