Geometric model describing the banded morphology of particle films formed by convective assembly

Nanoparticle films coated on smooth substrates by convective assembly from dilute suspensions in dip-coating configuration are known to have discrete film morphologies. Specifically, the film morphology is characterized by alternating bands of densely packed particles and bands of bare substrate. Convective assembly is a frontal film-growth process that occurs at the three-phase contact line formed by the substrate, the suspension in which it is submersed, and the surrounding air. The bands are parallel to this contact line and can be either monolayered or multilayered. Monolayered bands result whenever the substrate is withdrawn from the suspension at a rate too high for particles to assemble into a continuous film. We report a new insight to the mechanism behind this banding phenomenon, namely, that inter-band spacing is strongly influenced by the constituent particle size. We therefore propose a geometric model relating the inter-band spacing to the particle size. By making banded films with systematically varied particle sizes (silica/zeolite, 20 to 500 nm), we are able to quantitatively validate our model. Furthermore, the model correctly predicts that multilayered banded films have higher inter-band spacings than monolayered banded films comprising the same particles.