**1. Introduction**

Understanding and regulating the crystallization of supercooled water on surfaces is essential in both basic research and engineering applications [1,2]. The freezing of water on surfaces is, in fact, a complicated phenomenon that requires collective understanding of nucleation, crystal growth, surface science and thermodynamics [3–5], and plenty of research has been done theoretically and experimentally [6,7]. According to previous studies, ice nucleation can be affected by many factors, including surface morphology [8,9], wettability [10,11], shear flow [12], ions and contamination particles [13–15], etc. For example, Yue et al. and Wang et al. found that micro-hierarchical structures or patterns on a silicon surface would delay ice nucleation due to enhanced free energy for nucleation [16,17]. He

**Citation:** Jiang, B.; Shen, Y.; Tao, J.; Xu, Y.; Chen, H.; Liu, S.; Liu, W.; Xie, X. Patterning Configuration of Surface Hydrophilicity by Graphene Nanosheet towards the Inhibition of Ice Nucleation and Growth. *Coatings* **2022**, *12*, 52. https://doi.org/ 10.3390/coatings12010052

Academic Editors: Eduardo Guzmán and Alicia de Andrés

Received: 28 October 2021 Accepted: 29 December 2021 Published: 2 January 2022

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et al. reported the effect of counter ions on heterogeneous ice nucleation on a polyelectrolyte brush and discovered that a distinct efficiency of ions in turning ice a freezing temperature follows a certain sequence [18].Their study revealed that counter ions have a profound ion-specific effect on the relaxation of the hydrogen bond and the formation rate of interfacial water molecules.

Over the past few years, it has been investigated that graphene and its derivatives could influence ice nucleation and growth [19–21]. The two-dimensional material, graphene, has become one of the most promising materials in recent decades due to its potential applications in high performance electronics, sensors and energy storage devices [22–27]. It can be made into fibers, membranes and can be drop-casted onto various substrates [28–30]. Using a molecular dynamics simulation, Lupi and Molinero studied the heterogeneous ice nucleation of liquid water in contact with graphitic surfaces of various dimensions and curvatures, which were reported in experimental characterizations of soot [31,32]. Their results indicated that the ordering of interfacial liquid water on a graphene surface was the main reason for the facilitated heterogeneous nucleation [33]. Not only a promoting material, graphene and its derivatives can also restrain ice formation under specific conditions [22,34]. The exceptional Joule's heating effect and electrothermal effect of graphene-based composites have received much attention in the design of antiicing systems [35,36]. The lightweight graphene-based material is expected to be an ideal heater to prevent ice freezing. Specifically, there are numerous studies taking advantage of these properties for anti-icing and de-icing applications [37,38].

Recently, graphene oxide (GO) was used to mimic antifreeze proteins (AFPs) and considered to be an advanced icing inhibitor [39–42]. The repeated hexagonal carbon ring structure arranges the functional groups on the basal plane of GO to match with an ice crystal lattice, leading to the preferred adsorption of GO on existing ice in liquid water. Thus, the growth of the ice crystal is suppressed owing to the Gibbs–Thomson effect; that is, the curved surface lowers the freezing temperature [43,44]. The curved surface of the ice crystal derives from the special surface configuration, which involves different surface hydrophilicity and a crystal structure between the two materials. By using molecular dynamics simulations, Zhang and Chen studied ice nucleation on graphene surfaces functionalized by several kind of ions and methane molecules [45]. Their results indicated that the ice nucleation ability of the functionalized surfaces was weakened compared with that of the smooth graphene surface, depending on the type and the number of functional groups. Akhtar et al. presented an anti-icing coating based on fluorinated graphene, which could strikingly delay ice formation in a high humidity environment [46]. The anti-icing performance of fluorinated graphene was attributed to a robust liquid layer arising from the interface confinement effect that increases the ice-water contact angle and viscosity of water molecules near the surface. Additionally, the coupling of surface crystallinity and surface hydrophilicity was found to be a controlling factor for heterogeneous ice nucleation [7]. With an appropriate hydrophilicity, the arrangement of the water layer in contact with crystalline graphene can be changed; thus, the ice nucleation rate decreases consequently. The interplay between surface morphology and hydrophobicity on heterogeneous ice nucleation was also studied by Martin [4]. They showed that lattice mismatch of the surface with respect to ice is desirable for a good ice nucleating agent. Hence, it is interesting to investigate the synergistic effect of a surface hydrophilicity discrepancy and the clearance configuration created by an anchored graphene sheet on ice nucleation and growth.

In this work, a graphene nanosheet was introduced to design a special surface configuration of surface hydrophilicity on a metal surface. The characteristics of ice nucleation and growth on the surface were investigated using a molecular dynamics (MD) simulation. We constructed a series of surface configurations with various surface hydrophilicity discrepancies between a graphene nanosheet and metal substrate and explored the initiation of ice nucleation and growth processes under specific surface conditions. Besides, we studied the growth process of an ice nucleus and computed the growth rate of the ice nucleus. A

different surface configuration resulted in varying levels of ice growth inhibition. We also discussed the misorientation between grain boundaries of the ice crystal [47].

#### **2. System and Simulations**

The simulation system contained four graphene nanosheets anchored on a metal substrate, which were cleaved in the (100) surface of a face-centred cubic (fcc) crystal. The lattice parameter afcc was 4.0495 Å, and 6189 water molecules were covered on this surface, as shown in Figure 1a. The simulation box had dimensions of *L*x = 9.758 nm, *L*y = 9.744 nm and *L*<sup>z</sup> = 10.000 nm. A void space was set in the simulation box to avoid the influence of a periodic boundary condition in the z direction. Four graphene nanosheets with a size of 2.85 nm × 3.27 nm were fixed atop of the metal substrate with a distance of 6 Å [33,48], resulting in a 2-nm-wide cross-shaped clearance between the graphene nanosheets, as shown in Figure S1.

**Figure 1.** Illustrations of simulation systems. (**a**) Model of the metal–graphene nanosheet surface that was covered with a box of liquid water. A typical ice nucleus formation is illustrated on the surface. (**b**) Models of three other simulation systems. Pure metal, pure graphene and graphene–graphene nanosheet surface systems.

The system described above is defined as a metal–graphene nanosheet system. Additionally, we constructed three other simulation systems for comparison, which were pure metal, pure graphene and graphene–graphene nanosheet surface systems. Details are shown in Figure 1b and Table S1.

The coarse-grained monatomic water (mW) model was employed in this paper to describe the interaction between water molecules [49]. This specific water model has excellent structural properties and a melting point close to the experiment. The mW model treats water molecules as a single particle that interacts through short-range two-body and three-body interactions [50]. Since it is monatomic, it exhibits faster dynamics, which allows for the alleviation of computational costs of our simulations for the ice freezing process. Detailed information about the mW water model is provided in Supplementary Note 1. The Lennard-Jones (LJ) potential was used to model the interaction between water molecules and substrate atoms. Length and energy parameters, *σ*w-g and *ε*w-g, were set to 2.488 Å and 0.13 kcal/mol, respectively, for each water molecule interacting with carbon atoms [31]. Otherwise, for interactions between water molecules and metal atoms, *ε*w-m was tuned from 0.13 kcal/mol to 14.0 kcal/mol in each simulation to obtain a different surface hydrophilicity of the metal substrate, while *σ*w-m was fixed in 2.8798 Å [51]. As a result, the difference between *ε*w-g and *ε*w-m is defined as surface hydrophilicity discrepancy *D*ε. There is no need to define the metal–metal and carbon–carbon interaction potentials, because they are fixed in the simulation system. Periodic boundary conditions were applied in three dimensions, and the integration time-step for the velocity Verlet algorithm was set to 5 fs. After 0.2 ps of relaxation at temperature 290 K, the whole system was cooled down to 200 K gradually with a cooling rate of 0.9 K/ns in the canonical ensemble (NVT), and the

process of water freezing was studied during the quenching period. To obtain statistically reasonable results, we performed 5 repetitions of each cooling simulation for every system. All MD simulations were performed using the LAMMPS simulation package. Phase and structure identification was carried out by the Identify Diamond Structure modifier in OVITO software (version 3.6.0) during the freezing process of liquid water on each surface configuration [52]. The initiation and ending times of the icing process were recorded through the entire simulation. The initiation time of icing was identified as the moment when the number of water molecules in the ice nucleus (Nice) started to increase rapidly. Conversely, the ending time of icing was identified as the moment when Nice tended to be stable, which is marked in Figure 2a.

**Figure 2.** Freezing of liquid water in different surface conditions. (**a**) Number of water molecules in the ice cluster on metal–graphene nanosheet surfaces with different surface hydrophilicities. The interaction strength between the metal and water molecule *ε*w-m varied from 0.13 to 14.0 kcal/mol. (**b**) Initiation time of icing with different surface hydrophilicities of a metal substrate. Inset shows total potential energy Epot of the system and the number of water molecules in the ice nucleus, Nice, during the whole simulation time. The data refer to the metal–graphene nanosheet system, and *ε*w-m was fixed to 1.0 kcal/mol in the inset of (**b**).
