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

Abstract

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'' $(\ensuremath{\sigma}\ifmmode\pm\else\textpm\fi{}12%)$ 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 $S(q),$ 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 $S(q).$ This enabled the use of the hypernetted chain approximation to calculate the pair interparticle potential $u(r).$ The 6-12 Lennard-Jones potential provided reasonable fits to all experimentally determined values of $u(r),$ 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 $〈L〉/R<0.60,$ and body-centered-cubic (bcc) packing was favored when $〈L〉/R>0.60.$ Lower-symmetry body-centered-tetragonal packing was observed for octanethiol-capped silver nanocrystals with $〈L〉/R>0.66.$ A simple model employing the experimentally determined values for $u(r),$ predicts that the $\mathrm{fc}\stackrel{\ensuremath{\rightarrow}}{c}\mathrm{bcc}$ superlattice phase transition occurs when $〈L〉/R0.65.$