When and Why Like-Sized, Oppositely Charged Particles Assemble into Diamond-like Crystals

Abstract

Like-sized, oppositely charged nanoparticles are known to assemble into large crystals with diamond-like (ZnS) ordering, in sharp contrast to analogous molecular ions and micrometer scale colloids, which invariably favor more closely packed structures (NaCl or CsCl). Here, we show that these experimental observations can be understood as a consequence of ionic screening and the slight asymmetry in surface charge present on the assembling particles. With this asymmetry taken into account, free-energy calculations predict that the diamond-like ZnS lattice is more favorable than other 1:1 ionic structures, namely, NaCl or CsCl, when the Debye screening length is considerably larger than the particle size. A thermodynamic model describes how the presence of neutralizing counterions within the interstitial regions of the crystal acts to bias the formation of low-volume-fraction structures. The results provide general insights into the self-assembly of non-close-packed structures via electrostatic interactions.