Correlation between the surface wettability and the contact angleThe simulation system was constructed based on LAMMPS simulation package (Supplementary Fig. 1). The smooth surface wettability is characterized by the contact angle. The correlation between the contact angle θ and the water-surface energy parameter ε is clarified (Supplementary Fig. 2). As the energy parameter ε increases, the contact angle decreases. For θ < 90°, the solid surface is hydrophilic. For θ > 90°, the solid surface is hydrophobic. For θ > 150°, the solid surface is superhydrophobic. For θ < 15°, the solid surface is superhydrophilic. When ε exceeds the critical value, the droplet completely wets the surface with θ = 0°.Liquid-solid phase transition: the effect of temperature on 2D ice in coexistence with 3D ice without confinementAt a constant temperature, the contact angle of nanodroplets decreases with the enhancement of nanodroplet and surface interaction, which is attributed to the larger surface energy and the stronger wettability of the solid surface (Supplementary Fig. 2). As the temperature increases, the potential energy per water molecule basically increases. The potential energy per water molecule at 250 K is significantly higher than that of per water molecule at other temperatures (Supplementary Fig. 3). In the NVT ensemble, the volume of the simulation system box is constant. As the temperature increases, the pressure of the system increases, so does the potential energy of water molecules. Figure 1a shows the change of the potential energy per water molecule with the surface energy parameters at 205 K. The potential energy per water molecule for the energy parameter ε ≤ 0.43 kcal·mol−1 is significantly higher than that of the energy parameter ε > 0.43 kcal·mol−1. As energy parameter ε increases, the potential energy suddenly drops by ~0.43 kcal·mol−1. The potential energy declines sharply between ε = 0.40 kcal·mol−1 and ε = 0.50 kcal·mol−1. Figure 1b displays the mean-square displacement of water molecules on the solid surface at 205 K. The mean-square displacement of ε = 0.50 kcal·mol−1 corresponds to the vertical axis on the right-hand side, which is one order of magnitude higher than that of ε = 0.43 kcal·mol−1 and 0.30 kcal·mol−1 corresponds to the vertical axis on the left-hand side. The mean square displacement of ε = 0.50 kcal·mol−1 increases sharply at first, showing some water molecules of the droplet diffuse rapidly along the wall to form 2D ice. In this process, the liquid water exists at the same time as the 2D ice solid. Then the inflection point appears and tends to increase slowly, indicating that the liquid water molecules nucleate and grow into 3D ice. At this time, both 2D ice solid phase and 3D ice solid phase are present. The whole freezing process has two phase transitions. The first phase transition produces 2D ice, and the second phase transition produces 3D ice. The appearance of the inflection point means that the liquid water molecules nucleate and crystallize in an instant to form 3D ice, and only the solid state exists. For the mean square displacement of ε = 0.43 kcal·mol−1, there is only liquid phase after equilibrium. The critical value of energy parameter ε for phase transition is estimated to be 0.43 kcal·mol−1.Fig. 1: Determination of energy parameter for phase transition.a Potential energy per water molecules versus energy parameter ε on the Pt surface at T = 205 K after equilibrium. Data are presented as mean values +/− SD (standard deviation), n = 20. b Mean-square displacement <Δr2> of water molecules versus time t on the solid surface at T = 205 K. r is the positions of atom. The mean-square displacement of ε = 0.50 kcal·mol−1 corresponds to the right-hand vertical axis. The mean-square displacement of ε = 0.43 kcal·mol−1 and 0.30 kcal·mol−1 corresponds to the left-hand vertical axis.The dynamic processes of nanodroplets on surfaces with different energy parameters show characteristics of the nanodroplets supercooled to nucleation and crystallization (Supplementary Fig. 4 and Fig. 5). The nucleation process is a phase-transition activation process. Overcoming the free energy barrier to form critical nucleus, the nucleus grows spontaneously (Supplementary Fig. 6). The phase transition and crystallization process of nanodroplets on surfaces with different energy parameters can be summarized as: (1) Droplets supercooled; (2) Critical nucleus formation; (3) Rapid phase transition; (4) Ice crystals growth. Near the gas-liquid, liquid-solid and gas-liquid-solid regions, the appearance of critical nucleus is spatially selective. The simulation results show that the surface nucleation process with different wettabilities after quenching displays different characteristics: For ε = 0.10 kcal·mol−1, the formation of critical nucleus preferentially occurs inside the droplet rather than on the solid surface, which is attributed to the superhydrophobic state of the surface (θ > 150°). The extremely low free energy of the solid surface causes the migration of nanodroplet. For ε = 0.20–0.43 kcal·mol−1, nanodroplet nucleation occurs preferentially on solid surface due to the surface being between hydrophobic and hydrophilic state (70° <θ < 150°). With the increase of wettability, the interaction between nanodroplet and the surface enhances, so the contact angle of nanodroplet decreases and the contact radius increases. Nanodroplet on surface with higher wettability is more likely to nucleate and crystallize due to the very high adsorption energy of the surface. Nanodroplet crystallization is not a single cubic or hexagonal structure, but a mixture of cubic and hexagonal structure stacking on each other. The stacking direction is controlled by the growth direction of ice nucleus. In the process of water freezing, a relatively long-lived hydrogen-bonded network is generated between water molecules. For the liquid-solid phase transition, from the perspective of dynamics, the decrease in temperature leads to slower molecular motion and lower kinetic energy. When the kinetic energy of the molecule is small, the potential energy between the molecules is sufficient to confine the molecules, so that the molecules are usually arranged in a regular crystal structure. The nucleation and crystallization of nanodroplets mainly occur on the solid surface (ε = 0.20–1.0 kcal·mol−1), and the latent heat released by local crystallization can provide enough energy for growth and crystallization52. The variation of the potential energy with time displays the nucleation and crystallization process of nanodroplets after quenching and cooling (Supplementary Fig. 7). The nucleation event is detected by recording the sudden decrease of the potential energy Epot of water molecules during the formation of critical ice nucleus. For ε = 0.10–0.43 kcal·mol−1, the potential energy change of the nucleation and crystallization process of nanodroplets on the solid surface is divided into three continuous characteristic stages: In the first stage, the potential energy of water molecules changes slightly. In the second stage, the potential energy Epot of water molecules decreases sharply, and the critical nucleus is formed. In the third stage, the potential energy of water molecules is in an equilibrium, and the remaining water molecules slowly crystallize.For 0.43 kcal·mol−1 < ε ≤ 1.0 kcal·mol−1, the nanodroplets first form 2D ice and then form 3D ice during the supercooled process. Taking ε = 0.50 kcal·mol−1 as an example, the dynamic process of the formation of 2D-3D coexisting ice is shown in Fig. 2a. After quenching and cooling, some water molecules on the surface droplets diffuse rapidly to form 2D ice. The 2D ice is formed by two layers of interlocking 5-, 6-, 7- membered rings water molecules. The double-layers are connected by hydrogen bonds. Each water molecule forms three hydrogen bonds with water molecules in the same layer, and forms a hydrogen bond with water molecules in the upper and lower layers. Therefore, all hydrogen bonds are saturated and their structures are very stable39. 2D ice formation mechanism without nanoscale confinement is that appropriate water-surface interactions can compensate for the entropy loss in the freezing transition process41. The supercooled unfrozen droplets are promoted by 2D ice. After overcoming the free energy barrier and forming a critical nucleus, the crystal nucleus grows rapidly and crystallizes to form 2D and 3D coexisting ice. The 3D ice is formed by the mixed accumulation of hexagonal ice and cubic ice. The 2D ice underlying growth mechanisms could be revealed by capturing the growth and merged of the metastable edge structures (Supplementary Fig. 8). Firstly, the edges of the 2D ice on both sides are formed by the non-rotating stacking of double-layer 4-, 5-, 6-, 7-membered ring ice. Then, with the diffusion of water molecules, the 2D ice growth edge is composed of double-layer 5-, 6-, 7-membered ring water molecules. The 2D ice boundary has metastable characteristics. At the moment of merging at the edge of the 2D ice double layer, the 6-membered ring in the white circle in the picture contributes a single water molecule, which is connected with the left 5-membered ring, and then forms two metastable 4-membered rings to connect the water molecules on both sides. After that, the two 4-membered ring water molecules become relatively stable 5-membered ring water molecules, and the water molecules on both sides merge and grow. During the growth process, the zigzag growth mode and the armchair growth mode of the 2D ice appears. When the calculation time reaches 200 ns, the 2D-3D coexisting ice structures are relatively stable. The 2D ice is still composed of double-layer 5-, 6-, 7-membered ring water molecules, and the proportion of 5-, 7-membered ring water molecules is basically unchanged, indicating that the 2D-3D coexisting ice is not sensitive to the calculation time when it is sufficiently long (Supplementary Fig. 9). The intensity of the first peak is slightly larger than that of the second peak as shown in Fig. 2b, revealing that the growth of 2D ice starts from the bottom layer (near the solid wall), which is consistent with the results in ref. 39. Figure 2c shows the growth of the number of ice molecules. After quenching and cooling, 2D ice grows rapidly and its number reaches a stable value. After that, the unfrozen droplets overcome the free energy barrier to form 3D ice quickly, and the number of 2D ice and 3D ice molecules reaches the maximum.Fig. 2: Growth characteristics of 2D ice in coexistence with 3D ice.a A sequence of snapshots of the coexisting ice growth process (Front view and top view) for ε = 0.5 kcal·mol−1. Dark yellow, light blue, light gray (3.08 ns) and light red balls represent hexagonal ice, cubic ice, 2D ice and solid substrate, respectively. b Density profile of the 2D ice. Density represents the size of 1D density. Height is the size of z axis. c The number of ice molecules versus time. d Phase diagram of liquid water, 2D ice and 3D ice with respect to temperature T and energy parameter ε. Phase diagram consists of liquid water, 2D ice in coexistence with liquid water, 3D ice and 2D-3D coexisting ice.Based on the molecular simulation calculation, the critical value of the surface energy parameter is estimated to be 0.43 kcal·mol−1. The evaluation system of liquid water, 2D ice and 3D ice on the temperature and energy parameter ε on the Pt surface is predicted. As shown in Fig. 2d, the influence of multiple temperature conditions and multiple energy parameters on the liquid-solid phase transition of water molecules is clarified. For 210 K < T ≤ 250 K and ε ≤ 0.43 kcal·mol−1, the supercooled nanodroplet is in liquid phase without phase transition. For 210 K < T ≤ 250 K and ε å 0.43 kcal·mol−1, the supercooled nanodroplet is in the coexistence of 2D ice and liquid phase. For 130 K ≤ T ≤ 210 K and ε ≤ 0.43 kcal·mol−1, the supercooled nanodroplet is in solid phase with phase transition, and the 3D ice is disorderly accumulated by hexagonal ice and cubic ice. For 130 K ≤ T ≤ 210 K and ε å 0.43 kcal·mol−1, the supercooled nanodroplets undergoes phase transition, and the ice is in the coexistence of 2D ice and 3D hexagonal ice and cubic ice. The mechanism for the 2D-3D coexisting ice without nanoscale confinement is attributed to overcoming the free energy barrier and the satiation of the Bernal-Fowler ice rules and the appropriate water-surface interaction, which can compensate for the entropy loss caused by the freezing transition process.Liquid-solid phase transition: the effect of pressure on 2D ice in coexistence with 3D ice without confinementIn order to investigate the influence of pressure on coexisting ice, five pressure conditions were chosen for molecular dynamic simulation at 205 K. In the NVT ensemble, pressure regulation is achieved by adding different numbers of nitrogen molecules (Supplementary Fig. 10). Due to the limited size of the system box, 20, 50, 100, 200 and 300 nitrogen molecules were added to obtain approximate pressures of 1.0, 2.5, 5.5, 11.0 and 17.5 atmospheres, respectively. Figure 3b shows that the contact angle of nanodroplets decreases with increasing gas pressure, and the droplet curvature decreases first and then increases with increasing gas pressure for energy parameter ε = 0.4 kcal·mol−1. Taking pressure of 11.0 atm as an example, for 0.1 kcal·mol−1 ≤ ε < 0.43 kcal·mol−1, the liquid-solid phase transition only generates 3D ice with disordered stacking of hexagonal ice and cubic ice (Supplementary Fig. 11). For 0.43 kcal·mol−1 ≤ ε ≤ 1.0 kcal·mol−1, the liquid-solid phase transition produces coexisting ice, which is composed of 2D ice and 3D ice stacked disorderly with hexagonal ice and cubic ice (Supplementary Fig. 12). With increasing wetting characteristics, the contact angle of droplets decreases, and droplets gradually spread on the wall. After quenching, 2D ice begins to form instantaneously, and 3D ice is formed after overcoming the nucleation energy barrier. The variation of potential energy with time also reflects the occurrence of nucleation and icing process (Supplementary Fig. 13). When the surface energy parameters is 0.5 kcal·mol−1, 2D ice grows and merges slowly for pressure 11.0 atm (and 17.5 atm) as shown in Fig. 3a, which is attributed to the combined effect of surface wettability and gas pressure. After calculation of 200 ns, the 2D ice is still composed of double-layer 5-, 6-, 7-membered ring water molecules.Fig. 3: Effect of gas pressure on growth characteristics of 2D-3D ice.a A sequence of snapshots of the coexisting ice growth process (Front view and top view) for gas pressure P = 11 atm and energy parameter ε = 0.5 kcal·mol−1. Dark yellow, light blue, light gray (200.0 ns) and light red balls represent hexagonal ice, cubic ice, 2D ice and solid substrate, respectively. b Variation of contact angle θ and curvature R-1 versus pressure for ε = 0.4 kcal·mol−1. A density colorbar shows the meaning of the contact angle heatmaps. Data are presented as mean values +/− SD (standard deviation), n = 5. c Phase diagram of 3D ice and coexisting ice with respect to gas pressure and energy parameter ε. Phase diagram consists of 3D ice and 2D-3D coexisting ice.The phase diagram about energy parameters and pressure is predicted to distinguish 3D ice and 2D-3D coexisting ice by a large number of molecular dynamic simulations. The critical value of the surface energy parameter is estimated to be 0.43 kcal·mol−1, which is the same as that of the nitrogen-free system, indicating that the formation of 2D-3D coexisting ice on the platinum surface is not very sensitive to the applied gas pressure conditions. The effects of multiple pressure conditions and multiple surface wetting characteristics on the liquid-solid phase transition of water molecules are revealed as shown in Fig. 3c. For 1.0 atm ≤ P ≤ 17.5 atm and ε < 0.43 kcal·mol−1, the supercooled droplet undergoes liquid-solid phase transition to solid phase, and the 3D ice is composed of disordered hexagonal ice and cubic ice. For 1.0 atm ≤ P ≤ 17.5 atm and 0.43 kcal·mol−1 ≤ ε ≤ 1.0 kcal·mol−1, liquid-solid phase transition occurs, and the coexisting ice consists of 2D ice and 3D hexagonal ice and cubic ice. For 0.43 kcal·mol−1 ≤ ε < 0.8 kcal·mol−1, the 2D ice in coexisting ice is composed of double-layer 5-, 6-, 7-membered ring water molecules. For 0.8 kcal·mol−1 ≤ ε ≤ 1.0 kcal·mol−1, the 2D ice in coexisting ice is finally composed of a layer of 5-, 6-, 7-membered ring water molecules and a layer of 4-, 6-membered ring water molecules near solid surface (Supplementary Fig. 14). The appearance of the 4-membered square ring water molecules is attributed to the surface being too hydrophilic and gas pressure.De-icing mechanism of 2D ice in coexistence with 3D iceThe detachment processes of nanoscale coexisting ice from smooth Pt surface are used to investigate the de-icing characteristics (Supplementary Fig. 15). Ice adhesion strength is the ice adhesion force divided by the ice-solid substrate contact area (σ = F / A). The tension is applied to the ice by applying acceleration to all water molecules in the +z direction (perpendicular to the solid substrate), increasing the vertical acceleration at a constant rate, so that the tension is stably loaded throughout the ice. With the superposition of force fluctuations, the attractive force between the coexisting ice and the solid substrate increases linearly (Supplementary Fig. 16a). When the coexisting ice is completely detached from the solid substrate instantaneously, the attractive force decreases suddenly. The coordinates of the intersection point of fluctuating attractive force fitting curve (the black line) and the expected attractive force (the red line) are the detachment force and detachment time (Supplementary Fig. 16b). When the tension is greater than the maximum adhesion between the ice and the solid substrate, the ice will be completely detached from the solid substrate, and the ice detachment is related to the sudden decrease of the adhesion force. MD simulation is able to capture the ice detachment process at the atomic level55, and provide nanoscale mechanism of ice detachment dynamics. Figure 4a reveals that the ice adhesion force of 2D ice in coexistence with 3D ice is significantly larger than that of 3D ice. Figure 4b shows that the adhesion strength of 2D-3D coexisting ice is smaller than that of 3D ice, which is attributed to the combined effect of ice adhesion force and ice contact area. Ice adhesion strength depends on the ice adhesion force and the ice contact area. The contact area between 2D-3D coexisting ice and solid substrate is 2.35 times that between 3D ice and solid substrate (A2D-3D / A3D = 2.35). The 2D-3D coexisting ice has a larger contact area with a solid substrate, which could provide a higher adhesion force. However, the adhesion force of 2D-3D coexisting ice is no more than 2 times that of 3D ice (F2D-3D / F3D < 2). Therefore, ice adhesion strength for 2D-3D coexisting ice is lower than that of 3D ice. Figure 4c, d shows the dynamic process of coexisting ice and 3D ice detachment from the solid substrate, respectively. The coexisting ice is first detached from the surface at the left junction of the 2D ice and the 3D ice, then the 2D ice and the 3D ice on the left side are detached from the surface, and finally the 2D ice on the right side is detached from the surface. The 3D ice is first detached from the surface at the right edge, becoming increasingly tilted relative to the substrate and eventually detached from the substrate. This angular ice detachment mechanism is consistent with the experimental observation results54, which is attributed to the sharp edge or corner of the ice having the maximum tensile stress due to its singularity. Therefore, the thermal fluctuation of ice molecules is most likely to cause ice to break away from the edge corner. The calculated ice adhesion strength is two orders of magnitude larger than the experimental ice adhesion strength ( ≤ 1 MPa), which is mainly attributed to the fact that the typical loading rate used in MD simulation is about 6–7 orders of magnitude higher than the experimental study55, the nano-size of ice and the separation stress of ice increase logarithmically with the loading rate56. If the same loading rate is used in MD simulation and experiment, the de-icing stress of the two methods is not much different.Fig. 4: Comparison of ice adhesion strength between the 2D-3D coexisting ice and 3D ice.a Correlation between fluctuating adhesion force and time for 2D-3D coexisting ice and 3D ice detached from smooth Pt surface. FA is the fluctuating adhesion force between ice and solid substrate. Set is the pulling force acting on ice as a function of time. It represents that the initial value of acceleration is 0 and increases linearly with 5.734*10−9 nm·fs−2. Bidoseresp fitting is the least-square fitting of the datas for the part below the “set” line using the bidirectional-dose-response function. εw-Pt means the energy parameter between the 2D ice or 2D-3D ice and the walls. b Ice adhesion strength σ vs energy parameter ε. Data are presented as mean values +/- SD (standard deviation), n = 3. c A sequence of snapshots of the 2D-3D coexisting ice detachment process. d A sequence of snapshots of the 3D ice detachment process. e Variation of ice adhesion strength versus the ratio εw-Pt/(kBT) for the 2D-3D coexisting ice and 3D ice systems. The dash lines are obtained by linear fitting of the data.The adhesion strength of coexisting ice is significantly lower than that of 3D ice for different temperatures and the same energy parameters (Supplementary Fig. 17). At the same temperature, the adhesion strength of 3D ice and coexisting ice is linearly related to the energy parameter εw-Pt between nanodroplets and solid substrate, indicating that the surface wettability energy parameter εw-Pt is directly related to the ice adhesion strength. Based on the concept of depletion layer, the linear correlation between cos θ and ε of water droplets on the solid substrate is derived57. By assuming the homogeneous solid density ρS and liquid density ρL, and ignoring the electrostatic or interfacial entropy, the work H12 of each surface area required to separate the liquid from the solid is calculated theoretically.$${H}_{12}={{{{{{\boldsymbol{\gamma }}}}}}}_{{{{{{\rm{SV}}}}}}}+{{{{{{\boldsymbol{\gamma }}}}}}}_{{{{{{\rm{LV}}}}}}}-{{{{{{\boldsymbol{\gamma }}}}}}}_{{{{{{\rm{SL}}}}}}}=-\pi {\rho }_{{{{{{\rm{L}}}}}}}{\rho }_{{{{{{\rm{S}}}}}}}{\int }_{{Z}^{\ast }}^{{R}_{0}}dzz{(z-{z}{\ast })}^{2}u(z)$$
(1)
$$1+\,\cos \theta=({{{{{{\boldsymbol{\gamma }}}}}}}_{{{{{{\rm{SV}}}}}}}+{{{{{{\boldsymbol{\gamma }}}}}}}_{{{{{{\rm{LV}}}}}}}-{{{{{{\boldsymbol{\gamma }}}}}}}_{{{{{{\rm{SL}}}}}}})/{{{{{{\boldsymbol{\gamma }}}}}}}_{{{{{{\rm{LV}}}}}}}={H}_{12}/{{{{{{\boldsymbol{\gamma }}}}}}}_{{{{{{\rm{LV}}}}}}}\sim {\varepsilon }_{{{{{{\rm{W}}}}}}-{{{{{\rm{Pt}}}}}}}$$
(2)
$${{{{{\boldsymbol{\sigma }}}}}}\sim 1+\,\cos \theta$$
(3)
$$1+\,\cos {\theta }^{\ast }=\,{\phi }_{{{{{{\rm{s}}}}}}}(1+\,\cos \theta )$$
(4)
where γSV, γLV and γSL are the surface tensions between solid-vapor (SV), liquid-vapor (LV) and solid-liquid (SL), respectively. u(z) represents the solid-liquid interaction energy. The LJ interaction simulation analysis is used. Since the LJ potential is linearly related to ε, H12 is also a linear function of ε. Equation (2) is obtained by combining Young’s equation. The ice adhesion strength is linearly related to the cosine of the receding angle of water droplets on the solid surface58, that is, σ ~ 1+cosθrec. The atomic plane does not exhibit contact angle hysteresis, indicating that the receding angle of the water droplet is the same as the equilibrium contact angle. Therefore, the ice adhesion strength and the linear variation of the contact angle cosine of water droplets on the solid surface is given by Eq. (3). From Eqs. (2) and (3), it is obtained that the ice adhesion strength is a linear function of the water-solid substrate interaction force σ ~ ε. The slope of linear function of coexisting ice adhesion strength and energy parameter ε on solid surface is smaller than that of linear function of 3D ice adhesion strength and energy parameter ε (Supplementary Fig. 17). As the interaction energy between ice and solid substrate decreases, the ice adhesion strength of solid surface decreases.The ice temperature and the ice-solid substrate interaction force are important parameters affecting the ice adhesion strength. The increase of temperature enhances the fluidity of water molecules in ice, which reduces the ice adhesion strength. Temperature and ice-solid substrate interaction have opposite effect on ice adhesion strength. For a given ice-solid substrate interaction, higher temperature corresponds to lower ice adhesion strength. For different temperatures, the ice adhesion strength is still linearly related to the surface energy parameter. Considering the opposite effects of temperature and water-substrate interaction on ice adhesion strength, Fig. 4e shows the linear relationship between ice adhesion strength and dimensionless number ε/kBT. The linear correlation slope of ε/kBT of coexisting ice on solid surface is smaller than that of 3D ice on solid surface, which is consistent with the results shown in Supplementary Fig. 16. With the decrease of ice-solid substrate interaction, the ice adhesion strength on solid surface decreases. At different temperatures, the ice adhesion strength is linearly related to the ice-solid surface interaction. For the coexisting ice and 3D ice on the solid surface, the MD data of ice adhesion strength are fitted to obtain two straight lines, namely, the ice-solid substrate interaction force and ice temperature ratio function.In NPxyT ensemble, after 200 ns of calculation, the 2D ice composed of metastable double-layer 5-, 6-, 7-membered ring water molecules is transformed into steady-state 6-membered ring 2D ice. 3D ice structure in coexisting ice is not sensitive to the calculation time (Supplementary Fig. 18). At 30 ns, the 2D ice is composed of double-layer 5-, 6-, 7-membered ring water molecules. At 200 ns, the 2D ice is composed of double-layer 6-membered ring water molecules. With the increase of energy parameter εw-Pt, the ice adhesion force at 200 ns is gradually larger than that at 30 ns, which is attributed to the combined effect of surface wetting characteristics, 2D ice structure and ice freezing time (Supplementary Fig. 19).Gas-solid phase transition: 2D ice in coexistence with 3D ice without confinementA gas-liquid-solid three-phase system is established to simulate vapor deposition (Supplementary Fig. 20). The dynamic processes of vapor deposition display the characteristics of nucleation and crystallization (Supplementary Fig. 21 and Fig. 22). For different surface wettabilities, dropwise condensation mode or film condensation mode can appear in supercooled process. For ε = 0.10 − 0.20 kcal·mol−1, water vapor is difficult to deposit on the solid surface because the surface is too hydrophobic. For ε = 0.30 − 0.40 kcal·mol−1, with the progress of vapor deposition, the gas-liquid phase variation occurs, and independent nanodroplets appear on the solid surface. The water vapor condenses in dropwise condensation mode, and then the liquid-solid phase transition occurs. The nucleation of the nanodroplet preferentially occurs on the solid surface. Nanodroplet crystallization is a stacking disordered arrangement of cubic and hexagonal structure. For ε = 0.43–0.50 kcal·mol−1, the solid surface is hydrophilic. With the progress of vapor deposition, the gas-solid phase transition occurs, and the gas phase molecules diffuse to form 2D ice. The 2D ice is composed of double-layer 5-, 6-, 7-membered ring ice without rotation and stacking. Then the gas-liquid phase transition occurs, and a large number of gas molecules condense in the dropwise condensation mode. With the progress of vapor deposition, the liquid-solid phase transition is activated. The free energy barrier is overcome to form a critical nucleus. The critical nucleus is close to the 2D ice, and the crystal nucleus grows rapidly and crystallizes to form 3D stacking ice with hexagonal structure and cubic structure. 2D ice promotes the nucleation and growth of 3D ice, thus forming 2D and 3D coexisting ice. The formation mechanism of 2D ice without confinement is attributed to the fact that appropriate water-surface interactions can compensate for the entropy loss41. For ε = 0.60 kcal·mol−1, the solid surface is hydrophilic. Firstly, the gas-solid phase transition occurs to form 2D ice. Secondly, the gas-liquid phase transition occurs and condenses in dropwise condensation mode. Then, the liquid-solid phase transition occurs, the crystal nucleus grows rapidly and crystallizes, and the gas-solid phase transition occurs at the same time. The gas molecule directly becomes a component of the 3D ice, and finally only 3D ice is formed. For ε = 0.70–1.0 kcal·mol−1, firstly, the gas-solid phase transition occurs to form 2D ice, and then the gas-liquid phase transition occurs and condenses in dropwise condensation mode. Secondly, 2D ice is covered by a complete liquid film, showing the film condensation mode. Finally, the liquid-solid phase transition occurs, forming 3D hexagonal structure and cubic structure disordered accumulation ice. For ε = 0.10–0.20 kcal·mol−1, the potential energy of gas molecules keeps in equilibrium without phase transition. For ε = 0.30 − 1.0 kcal·mol−1, the potential energy of gas molecules decreases twice (Supplementary Fig. 23). The first drop is gas-liquid phase transition or the gas-solid phase transition coexists with gas-liquid phase transition, and the second drop is liquid-solid phase transition, which verifies the different surface condensation crystallization phase transition characteristics mentioned above.For 0.43 kcal·mol−1 ≤ ε ≤ 1.0 kcal·mol−1, the vapor deposition first forms 2D ice during the supercooled process, and then forms 3D ice. For ε = 0.50 kcal·mol−1, the formation process of 2D and 3D coexisting ice is shown in Fig. 5a. As the vapor deposition progresses, the gas-solid phase transition occurs. The gas molecules first form a single 2D double-layer 5-membered ring ice on the solid surface, then form a dispersed 2-dimensional ice on the solid surface composed of the non-rotating stacking of double-layer 5-, 6-, 7-membered ring ice. The dispersed 2D ice merge and grow. The gas molecules are condensed in dropwise condensation mode. The critical nucleus forms and grows rapidly to form 3D ice. Finally, 2D and 3D coexisting ice is formed. Figure 5b shows the relationship between temperature and potential energy. The first potential energy drop corresponds to the coexistence of 2D ice and nanodroplet, including gas-solid phase transition and gas-liquid phase transition. The second potential energy drop corresponds to the formation of 3D ice critical nucleus, including only liquid-solid phase transition. The second potential energy drop corresponds to the temperature jump, indicating that the heat released by local nucleation crystallization can increase the temperature.Fig. 5: Growth characteristics of 2D ice in coexistence with 3D ice.a A sequence of snapshots of the coexisting ice growth process (Front view and top view) for ε = 0.5 kcal·mol−1. ε is the energy parameter between the water vapor and the wall. Dark yellow, light blue, light gray (10.35 ns) and light red balls represent hexagonal ice, cubic ice, 2D ice and solid substrate, respectively. b Variation of the temperature T and potential energy Epot versus time t. c Phase diagram criterion of gaseous water, liquid water, 2D ice and 3D ice regarding temperature T and energy parameter ε. Phase diagram consists of gas, 2D ice in coexistence with dropwise liquid water, 2D ice in coexistence with film liquid water, 3D dropwise ice, 3D film ice and 2D-3D coexisting ice.Through a large number of the molecular dynamics simulations, the critical value of surface energy parameter is estimated to be 0.43 kcal·mol−1. The evaluation system of temperature and energy parameter ε of gaseous water, liquid water, 2D ice and 3D ice is predicted as shown in Fig. 5c. For 200 K ≤ T ≤ 250 K and ε ≤ 0.20 kcal·mol−1, there is no phase transition. For 200 K ≤ T ≤ 210 K and 0.20 < ε <0.43 kcal·mol−1, the gas-liquid-solid phase transition occurs. The system only has dropwise 3D ice. For 200 K ≤ T ≤ 210 K and 0.43 ≤ ε < 0.60 kcal·mol−1, the system has 2D and 3D coexisting ice. For 200 K ≤ T ≤ 210 K and 0.60 ≤ ε ≤ 1.0 kcal·mol−1, the gas-liquid-solid phase transition occurs. The system only has film-like 3D ice. For 210 K < T ≤ 250 K and 0.20 < ε < 0.60 kcal·mol−1, the system exists 2D ice and dropwise droplet. For 210 K < T ≤ 250 K and 0.60 ≤ ε ≤ 1.0 kcal·mol−1, 2D ice and film-like water coexist in the system.
Two-dimensional bilayer ice in coexistence with three-dimensional ice without confinement
