A molecular dynamics study of surface-directed spinodal decomposition on a chemically patterned amorphous substrate

We employ a molecular dynamics (MD) study to explore pattern selection in binary fluid mixtures ($AB$) undergoing surface-directed spinodal decomposition on a chemically patterned amorphous substrate. We chose a checkerboard pattern with chemically distinct square patches of a side $M$, with neighboring patches preferring different particle types. We report the efficient transposition of the substrate's pattern as a \emph{registry} to the fluid cross sections in its vicinity when the pattern's periodicity $\lambda/\sigma \simeq 2M$ ($\sigma$ being the fluid particle size) is larger than the mixture's spinodal length scale $\lambda_c/\sigma \simeq 2\pi/\xi_B$ ($\xi_B$ being the bulk correlation length). Our correlation analysis between the surface field and the surface-\emph{registries} in the substrate's normal direction shows that the associated decay length, $L_{\perp}(t)$, increases with decreasing pattern periodicity ($\lambda$). $L_{\perp}(t)$ also exhibits diffusive growth with time $\sim t^{1/3}$, similar to wetting-layer growth for chemically homogeneous walls. Our MD results also show the emergence of composition waves parallel to the substrate, whose wavelength exhibits dynamical scaling with a power-law growth in time $L_{||}(z,t)\sim t^{\alpha}$. $L_{||}(z,t)$ shows dynamical crossovers from a transient \emph{surface-registry} regime to universal \emph{phase-separation} regimes for cross-sections with \emph{registries}. We also give an account of the scaling of \emph{registry's} formation and melting times with patch sizes.