Simulation of emergent macroscopic structure based on experimental nanoscale potentials

Inks and paints are made of pigment dispersions stabilized by surfactants. These pigments are comprised of nanoscale, ramified primary particles. ~3nm elemental crystals clustered into 5 to 8 nm 3D primary particles which further form aggregates of about 10 to 100 nm.  Aggregates can form 3D agglomerates or form space-filling networks the latter of which advantageously scatter light and present uniform dispersion. The rate of drying and the film thickness control structural emergence as the concentration increases. Thick films display 3D agglomerates, which are not desirous in applications. For drying in micron thick films, a dual hierarchical network forms which are composed of clusters of aggregates that form micron size networks that are optimal for light scattering. It is desirable to predictably control this multi-hierarchical emergent structure. The interaction potentials of the pigment structural levels are determined experimentally using USAXS, SAXS, and WAXS. These potentials are employed in a Monte-Carlo simulation to model the interplay between the thermodynamic driving force for multi hierarchical structural emergence and transport kinetics. Observed agglomeration and network formation can be recreated using as input the surfactant characteristics.