GISAXS analysis of 3D nanoparticle assemblies--effect of vertical nanoparticle ordering.

We report on grazing-incidence small-angle x-ray scattering (GISAXS) study of 3D nanoparticle arrays prepared by two different methods from colloidal solutions-layer-by-layer Langmuir-Schaefer deposition and spontaneous self-assembling during the solvent evaporation. GISAXS results are evaluated within the distorted wave Born approximation (DWBA) considering the multiple scattering effects and employing a simplified multilayer model to reduce the computing time. In the model, particular layers are represented by nanoparticle chains where the positions of individual nanoparticles are generated following a model of cumulative disorder. The nanoparticle size dispersion is considered as well. Three model cases are distinguished-no shift between the neighboring chains (AA stacking), a shift equal to half of the mean interparticle distance (AB stacking) and random shift between the chains. The first two cases correspond to vertically correlated nanoparticle positions across different chains. A comparison of the experimental GISAXS patterns with the model cases enabled us to distinguish important differences between the 3D arrays prepared by the two methods. In particular, laterally ordered layers without vertical correlation of the nanoparticle positions were found in the nanoparticle multilayers prepared by the Langmuir-Schaefer method. On the other hand, the solvent evaporation under particular conditions produced highly ordered 3D nanoparticle assemblies where both laterally and vertically correlated nanoparticle positions were found.