Small-angle x-ray-scattering study of silver-nanocrystal disorder-order phase transitions

A conceptually unique approach was developed to study the interparticle interactions between organized alkanethiol-capped silver nanocrystals. Dense nanocrystal fluids were formed by evaporating the solvent from a “size-polydisperse” $(\sigma \pm 12\%)$ nanocrystal dispersion on a substrate. The sample polydispersity prevented the disorder-order phase transition (i.e., superlattice formation) from occurring. Small-angle x-ray scattering was then used to measure the static structure factors $S\left(q\right),$ of these disordered nanocrystal films as a function of the ratio $〈L〉/R$ between the capping ligand chain length to the core nanocrystal radius. The pair-distribution and direct correlation functions were then calculated from Fourier transformations of $S\left(q\right).$ This enabled the use of the hypernetted chain approximation to calculate the pair interparticle potential $u\left(r\right).$ The 6-12 Lennard-Jones potential provided reasonable fits to all experimentally determined values of $u\left(r\right),$ indicating the predominance of relatively short-range repulsion between nanocrystals. Monodisperse dodecanethiol- and octanethiol-capped silver nanocrystals were then condensed into ordered arrays. Face-centered-cubic (fcc) packing was favored for $〈L〉/R<\mathrm{}0.60,$ and body-centered-cubic (bcc) packing was favored when $〈L〉/R>\mathrm{}\mathrm{0.60.}\mathrm{}$ Lower-symmetry body-centered-tetragonal packing was observed for octanethiol-capped silver nanocrystals with $〈L〉/R>\mathrm{}\mathrm{0.66.}\mathrm{}$ A simple model employing the experimentally determined values for $u\left(r\right),$ predicts that the $\mathrm{fc}\overrightarrow{c}\mathrm{bcc}$ superlattice phase transition occurs when $〈L〉/R\mathrm{0.65.}$