*3.2. Priority of Ice Nucleation*

We noticed that the position of initial ice nucleation on the metal–graphene nanosheet surface depended on the surface hydrophilicity of the metal substrate. For *ε*w-m lower than 1.0 kcal/mol, ice nucleation tended to happen at the top of the graphene nanosheets, as shown in Figure 4e and Figure S4. On this condition, ice nucleation was triggered by the repeated hexagonal carbon ring structure of the graphene nanosheet, which matched better with an ice structure compared to the fcc crystal structure of a metal substrate. However, ice nucleation generally happened at the clearance between the graphene nanosheets, as shown in Figure 4a and Figure S5, when *ε*w-m was higher than the critical value mentioned above, i.e., 1.0 kcal/mol. In this case, a more hydrophilic metal substrate, rather than the hexagonal structure on the basal plane of the graphene nanosheet, dominates the position that a stable ice nucleus would form initially [60].

**Figure 4.** Snapshots of the preferential site of ice nucleation and subsequent growth of ice crystals on a metal–graphene surface. (**a**) Ice nucleation at the clearance of the surface, *ε*w-m = 4.0 kcal/mol. (**b**–**d**) Representative growth trajectories of an ice nucleus that appeared at the clearance, which is indicated by a yellow circle (from the top view). (**e**) Ice nucleation at the top of the graphene nanosheet, *ε*w-m = 1.0 kcal/mol. (**f**–**h**) Representative growth trajectories of an ice nucleus that appeared at the top of the graphene nanosheet. Silver and black spheres represent metal and carbon atoms. White sticks covered on them represent liquid water molecules, and blue and green sticks connect pairs of ice molecules with hexagonal and cubic structure orders, respectively.

Therefore, in this work, we draw the conclusion that an ice nucleus tends to form at the clearance of a surface with surface hydrophilicity discrepancy *D*ε larger than 0.87 kcal/mol. On the contrary, an ice nucleus tended to form at the top of the graphene nanosheets when the *D*ε was lower than 0.87 kcal/mol. Either at the clearance or at the top of the graphene nanosheets, an ice nucleus could grow continuously as the system temperature cooled down, as shown in Figure 4b–d or f–h. Nearly all liquid water molecules on the surface arranged in the regular order finally to form the ice structures. In addition, the growth rate of the ice crystal that nucleated initially at the clearance was much lower than that of the ice crystal that nucleated at the top of the graphene sheets, and the lowest growth rate of an ice crystal on the metal–graphene nanosheet surface could be found under the condition of the surface hydrophilicity discrepancy *D*ε being set to 7.87 kcal/mol.

#### *3.3. Ice Growth and Stunting Effect of Boundary Misorientation*

We also compared the mean growth rate of an ice nucleus under several surface conditions, including metal–graphene nanosheets, pure metal, pure graphene and graphene– graphene nanosheet systems, as shown in Figure 5. Different surface conditions and their models are illustrated in Figure 1b. The ice growth rate was calculated by the method described in Figure S6.

**Figure 5.** Growth rate of an ice nucleus on different surface configurations. (**a**) Number of water molecules in the ice nucleus, Nice, changed with simulation time on the metal–graphene nanosheet surface. (**b**–**d**) Nice on a pure metal, pure graphene and graphene–graphene nanosheet surface, respectively. The data refer to *ε*w-m = 8.0 kcal/mol both in (**a**,**b**). The red line in each figure is the linear fitting of Nice within the first 1 ns after the initiation of icing. (**e**) Comparison of the ice growth rate on different surface configurations. Blue and purple bars represent the original and enlarged size of the simulation box.

The lowest growth rate of an ice crystal was on the metal–graphene nanosheet surface when *ε*w-m was set to 8.0 kcal/mol, i.e., 7.87 kcal/mol surface hydrophilicity discrepancy for the clearance configuration. Compared to the pure metal surface, this ice growth rate was decreased by 71.08%, as shown in Figure 5e. Similarly, for the graphene–graphene nanosheet surface, the growth rate of the ice nucleus decreased by 36.07% compared to that on the pure graphene surface. Ice growth was suppressed on both the metal and graphene substrate, while graphene nanosheets were anchored on them. These alternately distributed graphene nanosheets can restrict the growth of an ice nucleus in the direction parallel to the substrate [42]. An ice nucleus at the clearance tends to grow along the z axis, leading to the curved surface of the ice nucleus. According to the Gibbs–Thomson effect [43,62], the surface curvature of ice would cause additional pressure on the ice–water interface, resulting in an external resistance for the further growth of the ice nucleus. [42,63]. Hence, the free energy barrier for ice growth increases, and the freezing point of liquid water is decreased. However, the suppression effect was more prominent on the metal–graphene nanosheet surface configuration, owing to the proper surface hydrophilicity discrepancy and the rearranged interfacial water layer existing at the clearance configuration. Additionally, we found that ice nucleation occurred at a random position of the graphene–graphene nanosheet surface. The ice growth was suppressed only when the ice nucleus was formed at the clearance; otherwise, the ice nucleus grew on the graphene nanosheet without the suppression effect of the clearance. These results indicate that the suppression effect of the clearance generated by graphene nanosheets does occur both on metal and graphene substrates, and the optimal freezing delay ability of the surface can be achieved in the metal–graphene nanosheet surface system with a proper surface hydrophilicity discrepancy. The suppression effect of these surfaces followed the sequence of metal–graphene nanosheets > graphene–graphene nanosheets > pure graphene, as illustrated in Figure 5e.

On the other hand, we also constructed models with an enlarged size of the simulation box, which means an enlarged clearance width on these surfaces, and performed simulations to investigate the impact of clearance width on the growth of the ice nucleus. Details of the models are shown in Table S2. The simulation parameters of the enlarged systems were the same to that of the systems with the original size for each surface configuration. The initiation of ice nucleation on the metal–graphene nanosheet surface was greatly advanced (10–20 ns) by merely a 1 nm increase of the clearance width, and the ice growth rate increased noticeably by 40.02%, as shown in Figure S7 and Figure 5e. In the enlarged metal–graphene nanosheet system, the ice embryo could still nucleate at the enlarged clearance configuration. However, a stable ice nucleus formed before it contacted the lateral graphene nanosheets. Ice growth would not be restricted and the curved surface of an ice nucleus would not form. Consequently, the suppression effect of the clearance configuration disappeared, when the clearance width was larger than 2 nm on the surface both in metal–graphene nanosheet and graphene–graphene nanosheet systems. Therefore, our investigation leads to the conclusion that a pronounced ice inhibition will exhibit on the metal–graphene nanosheet surface configuration only when the clearance between graphene nanosheets is narrow enough. Further research needs to be developed for a critical size of the clearance configuration. In contrast, the enlarged size of the simulation box had no obvious influence on ice growth on the pure metal and pure graphene surfaces. For the graphene–graphene nanosheet surface, ice nucleation occurred at a random position on the surface in both the original and enlarged systems. When the clearance width was enlarged, ice growth would not be restricted by the graphene nanosheets, even if the ice nucleus was formed at the clearance. The growth rate of the ice nucleus on the graphene–graphene nanosheet surface slightly increased by 18.46% due to the enlarged clearance width, as shown in Figure 5e.

Figure 6a suggests that a stunting effect exists during the growth process of an ice crystal on a metal–graphene nanosheet surface. This is due to the boundary misorientation between ice crystals [47], as illustrated in Figure 6b. Obviously, the ice cluster marked with a red circle has a different orientation with the ice cluster on the right side. Generally, two growing ice nuclei contact each other, and the boundary misorientation forms. With the decreasing entropy and potential energy of a system, ice clusters with a boundary misorientation tended to transform into a consistent crystal, and the disorder boundary structure disappeared gradually, which suspended the growth of the ice crystal on the surface about 0.5–1.0 ns. This stunting effect could take a lot of time during the rapid growth of the ice crystal, as shown in Figure 6a. We also found that the duration of the stunting effect extended by increasing the contact area between ice clusters with different orientations, finally slowing down the growth rate of the ice crystal.

**Figure 6.** Stunting effect of a boundary misorientation during ice growth. (**a**) The inset shows the stunting period (shaded red) in the ice growth process caused by boundary misorientation between ice crystals. (**b**) Top view snapshots of boundary misorientation between ice crystals. (**c**) Side view of the boundary misorientation between ice crystals.

#### **4. Conclusions**

In summary, we carried out molecular dynamics simulations to investigate the freezing delay capability of metal–graphene nanosheet surfaces and gained a microscopic understanding of ice nucleation and growth, which were restricted at the clearance configuration. The interfacial water layer would form when the surface hydrophilicity of the metal substrate *ε*w-m was higher than 1.0 kcal/mol, separating other free water molecules from interacting with the metal substrate. This hindering effect of interfacial water layer competed with the increasing interaction strength between water molecules and the metal substrate. Ice nucleation was delayed when *ε*w-m ranged from 4.0 to 14.0 kcal/mol and the delayed time peaks to 5.25 ns with the surface hydrophilicity discrepancy *D*ε of 5.87 kcal/mol.

The nucleation position of an ice embryo changed from the top of graphene nanosheets to the clearance since the surface hydrophilicity of the metal substrate *ε*w-m surpassed 1.0 kcal/mol. The growth of the ice nucleus at the clearance was restricted by surrounding graphene nanosheets both on metal and graphene substrates. The ice nucleus grew with the lowest rate when *ε*w-m was 8.0 kcal/mol. An enlarged width of the clearance weakened the suppression effect remarkably, which is an important element in the design of anti-icing nanomaterials. Furthermore, the boundary misorientation between ice crystals can also suppress ice growth because of the stunting effect, which is proportional to the contact area between ice crystals. We believe these findings provide a simple model to explore the mechanism of nano-sized graphene and its derivatives on ice nucleation and growth, as well as their potential application for anti-icing materials.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/coatings12010052/s1, Figure S1: Morphology of the simulation system. (a) A typical metal–graphene nanosheets surface, containing four single graphene nanosheets anchored alternately on a metal substrate. (b) Entire simulation box with a water slab covered on the surface. Atoms of metal substrate and graphene nanosheets are colored by silver and black respectively, hydrogen bonds between liquid water molecules are represented by white sticks with a cut off distance of 3.2 Å, which is realized by the Create Bonds modifier in OVITO software; Figure S2: Example of a simulation box used in ice freezing. Periodic boundary conditions (PBC) were applied in x, y and z directions. A 7-nm-thick void region was incorporated in the simulation box to avoid the undesired effect of metal substrate in the adjacent simulation box caused by the PBC in the z direction; Figure S3: Ice formation on the metal–graphene nanosheets surface. (a) Stacking disordered ice formed on the surface (*ε*w-m = 1.0 kcal/mol), from a cross section view. Random layers of ice Ih and ice Ic were colored in bule and green respectively. (b) Count of water molecules above the surface along z direction, which depicts the regular order of ice; Figure S4: Ice growth at the top the graphene nanosheets with a surface hydrophilicity of metal substrate of 0.13 kcal/mol, which is equal to the surface hydrophilicity of graphene *ε*w-g. (a) Ice embryo nucleating at the top the graphene nanosheets owing to the repeated hexagonal carbon ring structure on graphene. (b–d) Growth of the ice crystal on the graphene nanosheets; Figure S5: Ice growth at the clearance, between the peripheral graphene nanosheets, with a surface hydrophilicity of metal substrate of 4.0 kcal/mol. (a) Ice embryo nucleated at the clearance configuration. (b–d) Restricted growth of the ice crystal on the metal–graphene nanosheets surface; Figure S6: Number of water molecules in ice nucleus changed with simulation time on metal–graphene nanosheets surface with different surface hydrophilicity of metal substrate; Figure S7: Initiation time of icing on metal–graphene nanosheets with different size of simulation box. The clearance width is about 2.0 nm in original sized system, whereas it is 3.0 nm in enlarged sized system; Table S1: The size of simulation box; Table S2: The interaction parameters for the Model Systems in this work.

**Author Contributions:** Conceptualization, Y.S.; methodology, Y.X.; validation, B.J., Y.S., J.T., Y.X., H.C., and S.L.; writing—original draft preparation, B.J. and Y.S.; writing—review and editing, J.T. and Y.S.; visualization, W.L. and X.X.; funding acquisition, J.T. and Y.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (Nos. 52075246, 12002364, and U1937206), the Natural Science Foundation of Jiangsu Province (No. BK20211568), the Project Funded by China Postdoctoral Science Foundation (No. 2019M661826), the

Open Fund of Key Laboratory of Icing and Anti/De-icing (Nos. IADL20190202, IADL20200407) and the NUAA Innovation Program for Graduate Education (kfjj20200613, kfjj20200605).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.
