Stratification in Drying Films Containing Bidisperse Mixtures of Nanoparticles

TL;DR

This study uses molecular dynamics simulations to explore how evaporation rates and particle concentrations influence nanoparticle stratification in drying films, revealing the significance of explicit solvent modeling and thermophoresis effects.

Contribution

It demonstrates the critical role of explicit solvent effects and thermophoresis in nanoparticle stratification during drying, challenging existing implicit solvent models.

Findings

Small-on-top stratification occurs when Pe_s * phi_s exceeds a threshold near 1.

Slower evaporation enhances small-on-top stratification due to thermophoresis.

Explicit solvent modeling is essential for accurate prediction of particle organization.

Abstract

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 ${\rm Pe}_s\phi_s \gtrsim c$ with $c\sim 1$, where ${\rm Pe}_s$ is the P\'{e}clet number and $\phi_s$ is the volume fraction of the smaller particles. This threshold of ${\rm Pe}_s\phi_s$ for ``small-on-top'' is larger by a factor of $\sim\alpha^2$ than the prediction of the model treating solvent as an implicit viscous background, where $\alpha$ 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 ${\rm Pe}_s\phi_s$ above the threshold when ${\rm Pe}_s$ is large but $\phi_s$ 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.