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

TL;DR

The paper investigates pattern selection in surface-directed spinodal decomposition of a symmetric binary fluid on a chemically patterned amorphous substrate using molecular dynamics, capturing hydrodynamic effects absent in some continuum models. By employing a checkerboard of chemically distinct patches and controlling the pattern periodicity $λ$ relative to the spinodal length $λ_c$, it shows that a near-surface registry is transposed into fluid layers in contact with the substrate when $λ/σ ≈ 2M > 2π/ξ_B$, with $L_{ot}(t) ∼ t^{1/3}$ and $L_{||}(z,t) ∼ t^{α}$ describing perpendicular and parallel growth, respectively. The study further demonstrates that registry formation scales as $t_{formation} ∼ M^2$ and registry melting as $t_{melting} ∼ M^3$, with hydrodynamics introducing deviations at large patch sizes; the results reveal depth-dependent modulation of SDSD waves and a transition from near-surface registry-dominated regimes to universal phase-separation behavior in non-registry regions. Overall, the work provides insight into how chemically patterned substrates steer nanoscale patterning through SDSD, with implications for thin-film design and nanofabrication where hydrodynamics and pattern commensurability play key roles.

Abstract

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 $λ/σ\simeq 2M$ ($σ$ being the fluid particle size) is larger than the mixture's spinodal length scale $λ_c/σ\simeq 2π/ξ_B$ ($ξ_B$ 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 ($λ$). $L_{\perp}(t)$ 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 $L_{||}(z,t)\sim t^α$. $L_{||}(z,t)$ 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.

Figures (12)

• Figure 1: ($a$) A $3$D perspective of the simulation box employed in our study of SDSD of a binary mixture ($A+ B$) on a chemically patterned substrate. The simulation box is of size $L_x\times L_y \times L_z = 128\times 128\times 68 \;\sigma^3$ that is periodic in $xy$ direction and confined by amorphous walls in $z$-direction. Fluid particles are not shown here to clearly display the bottom pattern. The substrate pattern at $z=-2$ is a checkerboard type with gray (prefers $A$) and white (prefers $B$) square patches of size $M^2$. An impenetrable wall shown by blue-colored particles is at the top edge $z=64$ of the simulation box that uniformly repels $A$ and $B$. ($b$) A $xz$ cross-section of the chemically patterned wall of thickness $2\sigma$ with $\sigma=1$.
• Figure 2: Snapshots of the wetting phenomenon on a chemically patterned substrate at different times. The atomic representations of domains are from the $xy$ cross-sections of width $2$ present next to the patterned substrate and placed upward from $z=0$. The fluid is undergoing SDSD for $T = 0.7T_c$ ( bulk $T_c \approx 1.423$), which starts from a homogeneously mixed state for $T>T_c$. For clarity, only $A$-type particles (pink) are shown here. As stated in Fig. \ref{['fig:figure0']}, the substrate is templated with chemically distinct square patches ($M_x=M_y=16$), and we show here only the projection of gray patches that prefer $A$-type particles. The wetting kinetics of gray patches by $A$ is exhibited by the snapshots belonging to three reduced times of (a) $t=50$, (b) $t=300$, and (c) $t=1000$.
• Figure 3: Snapshots analogous to what shown in Fig. \ref{['fig:figure1']} but for cross-sections of a unit width starting upward from $z=4$. The time series presented here are (a) $t=500$, (b) $t=1000$, (c) $t=3000$, and (d) $t=10000$.
• Figure 4: Snapshots with details similar to Fig. \ref{['fig:figure2']}, but at different depths from $z=0$ for a time $t=5000$ . The depths denoted by the $z$ values are: ($a$) $2$ , ($b$) $6$, ($c$) $12$, and ($d$) $24$.
• Figure 5: The evolution of the order-parameter profiles $\psi (x,z,t)$ vs. $x$ for times $t$ as specified within the plot. The data are for a fixed $y$ set to $M_y/2=16/2$ but at different $z$ values. Different $z$ values are ($a$) $z=0$, ($b$) $z=2$, ($c$) $z=6$, and ($d$) $z=12$. The temporal profiles are obtained from snapshots presented in Figs. \ref{['fig:figure1']} and \ref{['fig:figure3']} after performing the noise removal technique described in the text.