Anomalous Ostwald Ripening Enables 2D Polymer Crystals via Fast Evaporation

We demonstrate by molecular simulations that the Ostwald ripening of crystalline polymer nuclei within the fast-evaporation-induced 2D skin layer is retarded at suitable temperatures and evaporation rates. Such an anomalous ripening can be attributed to the interplay between the thermodynamically driven diffusion of noncrystalline fragments toward the growing nuclei and the diffusive current away from the free surface caused by the densification in the nonequilibrium skin layer. The growth orientation of the nuclei inside the skin plane can be adjusted during this anomalous ripening process, which is beneficial for fabricating 2D polymer crystals.

Figure 1

Monomer densities of polymers at distinct times $t=0.5\tau$, $1.5\tau$, $3.0\tau$, $6.0\tau$ during the evaporation process at temperature $T=3.0$ and $N=20$. Inset shows the crystallization temperature $T_c$ as a function of monomer concentration ${\rho }_0$. (b) Top view of the typical snapshots for crystalline nuclei at $t=6.0\tau$, $8.0\tau$, $10.0\tau$, $12.0\tau$, and $60.0\tau$ (including the side view). The growing and shrinking nuclei during the Ostwald ripening process are labeled with yellow and other deep colors. The blue square line indicates the position of the free surface.

Figure 2

Histogram of the crystal orientations $\alpha$ for different chain lengths (a) $N=50$, (b) $N=20$, (c) $N=10$. For each chain length, 3 distinct temperatures $T$ are explored as labeled. The histograms colored in blue and black are shifted by $-0.03$ and $+0.03$ on the abscissa for clear display. Each histogram is averaged over 128 independent simulations. The inset in panel (a) shows the angle between the crystalline bond vector and the $z$ axis and the orientation parameter of the crystal is $\alpha =0.25$. Insets in panel (b) and (c) depict vertically and parallelly grown nuclei with $\alpha =-0.5$ and 1.0, respectively.

Figure 3

Time evolution of the average number $⟨N_{\text{nuclei}}⟩$ (black) and size $⟨R_{\text{nuclei}}⟩$ (blue curve) of nuclei for $N=20$ at (a) $T=2.8$ and (b) $T=3.0$. The gray region in panel (a) indicates the slope of $⟨R_{\text{nuclei}}⟩\sim t^{0.33}$, corresponding to the Ostwald ripening process, whereas that in (b) shows the anomalous ripening. (c) Variation of the average nuclei orientation (top) and size (bottom) as a function of the distance $d$ between the free surface and the center of mass of nuclei along the $z$ axis. The temperatures $T=2.8$ and 3.0 correspond to the left and right panels.

Figure 4

(a) The histogram of the nuclei size during the (left) normal and (right) retarded ripening process at $t=9.0\tau$, $12.0\tau$, $15.0\tau$, and $18.0\tau$. (b) The average number of ripening and shrinking nuclei at different times $t$. The critical size that divides the ripening and shrinking nuclei is chosen as $1.5R_{e0}$ for $T=2.8$ and $1.0R_{e0}$ for $T=3.0$. (c) Illustrations of the normal Ostwald ripening in the bulk (left) and the retarded ripening in the nonequilibrium skin layer (right). The dashed blue line shows the typical density profile along the $z$ axis in the bulk and the skin layer. The red arrow indicates the thermodynamically driven diffusion of noncrystalline chain fragments toward the ripening nuclei, whereas the blue arrow shows the off free-surface diffusion within the skin layer.