**3. Results and Discussion**

#### *3.1. Surface Hydrophilicity and Ice Nucleation*

The role of surface hydrophilicity [53,54] has been a central argument to determine whether ice nucleation and the subsequent growth process can happen [55–57]. In order to understand the impact of surface clearance on ice formation where hydrophilicity is different from peripheral graphene sheets, we performed a series of MD simulations using the interaction strength *ε*w-m as the collective variate to explore a desirable freezing delay surface, as shown in Figure 1a.

Ice formation can be obviously observed on every metal–graphene nanosheet surface as the system cooled down gradually, and the details are shown in Figure S3. The freezing process of liquid water on each metal–graphene nanosheet surface configuration is shown in Figure 2a. Curves with different colors represent various surface hydrophilicities of the metal substrate *ε*w-m. Generally, lower interaction strength between a solid atom and water molecule results in later ice nucleation, which has been demonstrated in other research [54]. However, there was no simple trend for the triggering time of ice nucleation for *ε*w-m ranging from 1.0 to 6.0 kcal/mol, as shown in Figure 2b. Water molecules in the simulation system could interact with substrate atoms freely when *ε*w-m was smaller than 1.0 kcal/mol, as shown in Figure 3a. Note that a layer of water molecules was arranged in an fcc structure gradually with the increasing *ε*w-m, as shown in Figure 3b. This interfacial water layer was formed adjacent to the substrate with a distance of about 1.88 Å, and it could be detected by the count of water molecules along the z direction, as shown in Figure 3b. On one hand, water molecules in this layer were closely packed in an fcc structure that differed from the structure of an ice crystal, which is not beneficial for ice nucleation. On the other hand, other free water molecules were separated from the metal substrate by the interfacial water layer, which decreased the interaction between free water molecules and the metal substrate. Therefore, the interfacial water layer acts as a barrier and hinders the nucleation of an ice nucleus [7,58]. Meanwhile, the surrounding conditions of the graphene nanosheets were not beneficial to ice nucleation, owing to the extremely low surface hydrophilicity of 0.13 kcal/mol. Therefore, ice nucleation was delayed for *ε*w-m ranging from 1.0 to 6.0 kcal/mol because of the hindering effect of the interfacial water layer formed on the metal substrate.

**Figure 3.** The formation of an interfacial water layer on a metal–graphene nanosheet surface. (**a**) Snapshot of the interface between a metal substrate and liquid water. The dense interfacial water layer was not formed at *ε*w-m = 0.13 kcal/mol. (**b**) Snapshot of the interfacial water layer viewed from the top and the side. The right panel is the number of water molecules along the z direction before water freezing. In all cases, the interfacial water layer is colored red for ease of visualization.

However, with the *ε*w-m increasement, a higher surface hydrophilicity of a metal substrate forced more water molecules to arrange in an orderly manner, which was convenient for the formation of an ice structure during the *ε*w-m value range from 6.0 to 14.0 kcal/mol. The competition of both effects lead to the nonlinear dependence, as shown in Figure 2b. Therefore, a proper surface hydrophilicity discrepancy between a graphene nanosheet and metal substrate is considered as a desirable agent for the delayed initiation of ice nucleation. The inset shows the total potential energy of a system changed with simulation time, together with the number of water molecules in the ice nucleus Nice [59]. As a plunge of the potential energy Epot of the system occurred, Nice increased suddenly, indicating the nucleation of an ice embryo. When *ε*w-m was set to 6.0 kcal/mol, i.e., a discrepancy of the surface hydrophilicity *D*ε of 5.87 kcal/mol, the ice nucleation on the metal–graphene nanosheet surface was delayed by 5.25 ns, which was a maximum value compared to that on a pure metal surface, as shown in Figure 2b. We noticed that a higher extent of hydrophilicity could induce a greater thickness of the interfacial water layer. The hindering effect of the interfacial water layer prevailed again, which well explained the jump of the triggering time of ice nucleation for *ε*w-m values between 6.0 to 8.0 kcal/mol.

It should be mentioned that small ice nuclei form and expand constantly under the action of structure and energy undulations in supercooled water [60]. Additionally, these unstable ice nuclei prefer to form at the edge of graphene sheets, where the energy barrier for ice nucleation is lower compared with those in other positions [19,61]. The edge of the graphene sheet is a phase contact area where water molecules interact with carbon and metal atoms simultaneously.
