Stratification in Drying Films Containing Bidisperse Mixtures of Nanoparticles

Large
scale molecular dynamics simulations for bidisperse nanoparticle
suspensions with an explicit solvent are used to investigate the effects
of evaporation rates and volume fractions on the nanoparticle distribution
during drying. Our results show that “small-on-top”
stratification can occur when Pesϕs ≳ c with c ∼ 1, where Pes is the
Péclet number and ϕs is the
volume fraction of the smaller particles. This threshold of Pesϕs for
“small-on-top” is larger by a factor of ∼α2 than the prediction of the model treating solvent as an implicit
viscous background, where α is the size ratio between the large
and small particles. Our simulations further show that when the evaporation
rate of the solvent is reduced, the “small-on-top” stratification
can be enhanced, which is not predicted by existing theories. This
unexpected behavior is explained with thermophoresis associated with
a positive gradient of solvent density caused by evaporative cooling
at the liquid/vapor interface. For ultrafast evaporation the gradient
is large and drives the nanoparticles toward the liquid/vapor interface.
This phoretic effect is stronger for larger nanoparticles, and consequently
the “small-on-top” stratification becomes more distinct
when the evaporation rate is slower (but not too slow such that a
uniform distribution of nanoparticles in the drying film is produced),
as thermophoresis that favors larger particles on the top is mitigated.
A similar effect can lead to “large-on-top” stratification
for Pesϕs above the threshold when Pes is large
but ϕs is small. Our results reveal
the importance of including the solvent explicitly when modeling evaporation-induced
particle separation and organization and point to the important role
of density gradients brought about by ultrafast evaporation.