Effect of substrate mismatch, orientation, and flexibility on heterogeneous ice nucleation

TL;DR

This work isolates the effect of lattice mismatch on heterogeneous ice nucleation by using substrate models composed of water molecules with stretched or compressed ice lattices, effectively decoupling structural mismatch from interfacial interactions. Using the mW water model in MD simulations, the authors quantify how the nucleation temperature $T_n$ declines roughly linearly with mismatch at a rate of about $-4\,K$ per unit mismatch, and they show this trend holds for both rigid and flexible substrates. They also find that the three primary ice orientations—basal, pI, and pII—exhibit similar nucleation abilities, with only small differences that align with subtle interfacial structural similarities. Lattice flexibility enhances nucleation by allowing the substrate to adapt to the emerging ice, effectively reducing the apparent mismatch, while interfacial analyses reveal a heterogeneous, ice-like layer near the surface and a nucleus that tilts and gradually recovers ice structure with distance from the interface. Overall, the study provides a clear, fundamental view of how lattice mismatch, orientation, and substrate mobility influence ice nucleation, offering a baseline against which more realistic substrate effects can be benchmarked.

Abstract

Heterogeneous nucleation is the main path to ice formation on Earth. The ice nucleating ability of a certain substrate is mainly determined by both molecular interactions and the structural mismatch between the ice and the substrate lattices. We focus on the latter factor using molecular simulations of the mW model. Quantifying the effect of structural mismatch alone is challenging due to its coupling with molecular interactions. To disentangle both factors, we use a substrate composed of water molecules in such a way that any variation on the nucleation temperature can be exclusively ascribed to the structural mismatch. We find that a one per cent increase of structural mismatch leads to a decrease of approximately 4 K in the nucleation temperature. We also analyse the effect of the orientation of the substrate with respect to the liquid. The three main ice orientations (basal, primary prism and secondary prism) have a similar ice nucleating ability. We finally asses the effect of lattice flexibility by comparing substrates where molecules are immobile with others where a certain freedom to fluctuate around the lattice positions is allowed. Interestingly, we find that the latter type of substrate is more efficient in nucleating ice because it can adapt its structure to that of ice.

Figures (11)

• Figure 1: Sequence of snapshots illustrating our procedure to generate an initial configuration. Left: Snapshot of a side view of a replicated (and stretched for $\delta$ >0) unit cell in contact with a 15Å thick vacuum. Yellow particles correspond to the substrate (exposing the pII plane to the liquid) and blue particles will be melted to give rise to the initial configuration. Middle: At 300 K, a liquid layer is readily formed in the face of the replicated ice lattice in contact with vacuum. Right: At 300 K and in the NVT ensemble the liquid layer propagates up to the substrate surface giving rise to the initial configuration.
• Figure 2: (a) Snapshot shortly after starting a simulation with a $\delta = 0$ rigid substrate at 1 K below the melting temperature. An ice layer wetting the mold is clearly seen. (b) Snapshot shortly after nucleation on a wells substrate with $\delta = 5$ at 255.5 K.
• Figure 3: (a) Potential energy versus time for a trajectory at 272 K (1 K below the melting temperature) on a wells substrate with $\delta = 0$. (b) Potential energy versus time for nine trajectories of a liquid at 245.0 K on a wells substrate with $\delta = 7$. (c) Time evolution of the potential energy (green) compared to that of the average q$_{12}$ local bond order parameter steinhardt1983bond (orange) for a single nucleation trajectory of those shown in (b).
• Figure 4: (a) Heterogeneous nucleation rate versus temperature for the different mismatches and the different kinds of stretched substrates studied in this work as indicated in the legend. These results correspond to the pII orientation (exposing the yz plane of the stretched and replicated unit cell as indicated in table \ref{['tab:sistemas']}). The open diamond (square) corresponds to a $\delta=7$ rigid substrate system having double liquid (substrate) depth than the system with which the filled brown dots were obtained. (b) Heterogeneous nucleation rate temperature dependence of expanded (exp) and compressed (comp) rigid substrates exposing the pII plane to the liquid.
• Figure 5: Nucleation temperature versus the mismatch between ice and the substrate. The two different sorts of substrates studied in this work are compared for the pII orientation. The black point for $\delta=0$ corresponds to the ice melting temperature of the model (273 K). Empty green circles correspond to the rigid compressed substrate. In grey dashed, a line with -4 K/$\delta$ slope starting at the coexistence point is shown for visual reference. Symbol size coincides with that of the estimated error bar.