Introduction

Wettability is a fundamental property of a solid surface and plays important roles in daily life, industry and agriculture. The amazing climbing ability of geckos1,2,3, as well as the self-cleaning effects of lotus leaves and butterfly wings4,5, are all related to the unique micro- and nanostructures on their surfaces. Inspired by these strategies, functional surfaces with special wettability, such as nanopillared surfaces, have elicited great research interest6,7,8,9 and been synthesized by various methods10,11,12,13,14. For example, the superhydrophilic surface15,16 with a water contact angle of almost 0° fabricated by UV irradiation has been successfully used as a transparent coating with antifogging and self-cleaning properties. On the other hand, various phenomena, such as contamination, snow sticking, erosion and water transport are expected to be inhibited on superhydrophobic surfaces17,18,19 with a contact angle larger than 150°.

Much research has been performed to investigate the wetting behavior of liquid nanostructures, including water, polymers and metals20,21,22,23,24,25,26,27,28. In terms of metallic thin films, these materials have attracted much attention not only due to their central importance for thin film technology, such as controlling the homogeneity of thin films and coatings29,30, but also because of their potential applications in catalysis, photovoltaics, sensor, transparent conductors and memory cells31,32,33. Due to the dramatic difference in the physical properties relative to typical polymer and water films, including high surface energy, low viscosity and differences in the long range interaction forces, continuous metallic films contract far from equilibrium and are unstable with respect to forming discrete nanodroplets via dewetting34. Numerous experimental and theoretical investigations have confirmed that the dewetting begins at the edges or corners of films where the surface tension is high35,36,37 and the dewetting evolution undergoes three successive stages: rupture of the film resulting in the occurrence of nanoholes, growth of the holes followed by the mass and energy transmissions and finally the decay of the holes. According to hydromechanics, inertia plays a dominant role in the dewetting dynamics of metallic nanostructures36,37. Recently, a unique property of these films, i.e. jumping off the substrates, has been reported. Habenicht et al.36 first demonstrated that deformed Au droplets could convert their surface deformation energy into kinetic energy, which makes them contract and finally detach from the non-wettable substrate. Fuentes-Cabrera et al.38, Afkhami and Kondic37 have reported that the evolution of the liquid Cu film is strongly dependent on its initial shape and the contact angle (CA). Such a jumping phenomenon had also been found in the evaporation of water droplets on G39. These important findings shed new light on the interfacial interactions and possibly pave the way for self-assembly nanotechnology40,41,42.

Much research has been done for the interfacial behavior of graphene, such as wetting and applications of super-hydrophobicity in self-cleaning materials, however, to our knowledge, fewer efforts have focused on the dewetting-induced detachment of nanodroplets, especially how to use super-hydrophobicity to control the movement of nanodroplets. Wetting and dewetting are important practical issues in physical and material sciences and provide an opportunity for comprehensive and satisfactory understanding of the interfacial properties of nanomaterials. As of yet, although there has been much progress in the understanding of dewetting, some important questions concerning the super-hydrophobic surfaces remain unanswered. Motivated by this and inspired by the amazing wettability of the nanofabricated surfaces mentioned above, we performed molecular dynamics (MD) simulations to explore the dewetting behavior of metallic thin films on pillared graphene (PG) consisting of uniform-distributed canbon nanotube (CNT) pillars, with the aim of controlling the contraction and detachment of liquid films by tuning the sizes of nanopillars. Figure 1 shows the model of the simulated system that a liquid Cu disk is deposited on a nanopillared graphene (PG) constructed with vertically aligned carbon nanotube (CNT) pillars.

Figure 1
figure 1

Schematic plot of the simulated system.

The capped carbon nanotubes (CNTs) are placed at the corners and center of the regular hexagons on the graphene to form a nanopillared graphene (PG), mimicking the super dewetting surfaces. The interval distance, diameter and hight of pillars are defined as a, d and h, respectively. The diameter and thickness of the disk are denoted as D and H, respectively.

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Results

To determine the role of the capped CNT nanopillars on the dewetting properties of surfaces, a comparison between G and PG surfaces is made. Figure 2 shows snapshots of the dewetting dynamics and potential energy distributions of liquid Cu disks with D = 135.6 Å. Notably, when H = 3 Å, the film on either the G or PG first ruptures to form some nanoholes (Figure 2a and b). These nanoholes gradually combine into a large hole, then decay and disappear. This phenomenon provides insight into the evolution process of nanoholes within the ultrathin liquid film (see the video 1 in the Supporting Information for details of the Cu-PG system), which is in good agreement with the experimental results35. When H increases to 5 Å, no holes can be observed. This indicates that whether the nanohole exists during the contraction is mainly dependent on the H of the film rather than the surface structure. Interestingly, further research presents that the PG can detach the nanodroplet from it (see the video 2 in the Supporting Information), while this detachment can not be observed on G, regardless of the fact that H increases to 10 Å. Like PG, another substrate PG2 displays similar dewetting properties, as shown in Figure 2c. The droplets detach from the PG and PG2 surfaces at 41 and 51 ps, respectively. Importantly, the film sizes (initial diameter D, thickness H and radius of droplet R) used in this study and the detaching time td = 41 ps, are far smaller than those in previous studies36,37,38,49. The comparison indicates that the nanopillars would improve the dewetting property of flat surfaces which brings great advantages in detaching droplets from the substrate. These findings are critical in the chemical system, daily life and nanotechnology, as well as guiding nanoparticles toward a tumor. In addition, the switch of dewetting modes with respect to the H also gives us the inspiration to avoid the formation of nanoholes within the superthin films by decreasing the film sizes, which is very important in the practical applications of superthin liquid films, such as homogeneous thin film, coating29,30, anti-adsorption and self-cleaning materials.

Figure 2
figure 2

Dewetting dynamics and potential energy distributions of Cu films (D = 135.6 Å) on substrates.

(a) G. (b) PG, a = 10.2 and h = 13.67 Å. (c) Another pillared graphene (PG2) with the concave-cap CNT as the pillar, a = 3.4 and h = 10.92 Å. For clear observation of the internal energy distribution, one fouth of some liquid droplets has been cut off. When H increases to 5 Å, the droplet detaches from the PG surface at 41 ps due to dewetting. Further increasing H to 7 Å, detachment occurs in the Cu-PG2 system at 51 ps.

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Potential energy distributions indicate that the dewetting begins at the edges of films and nanoholes. As the simulation proceeds, the edge propagates and contracts toward the center of the disk, which makes mass and energy flow and finally forms a spherical droplet when the system approaches the equilibrium (t = 200 ps). A better understanding of the contraction and detachment of the liquid film can be gained by the energy profiles. The total potential energy, Etot, is defined as Etot = EC-C + ECu-Cu + EC-Cu, where EC-C, ECu-Cu and EC-Cu represent the C-C, Cu-Cu and C-Cu interaction, respectively. Naturally, the EC-C is equal to 0 eV due to the fix of the substrate. The EC-Cu is a resisting force which hinders the slipping and ejection of droplets due to its reverse direction to the slipping and detachment. Therefore, ECu-Cu is the driving force. The energy difference, ΔECu-Cu, is partially transformed into kinetic energy of the droplet, which induces contraction and even detachment. Figure 3 gives the ΔECu-Cu, EC-Cu and vz(t) as a function of time. As for those systems without detachment, the ΔECu-Cu (EC-Cu) of the Cu-PG system is much larger (lower) than the Cu-G system, indicating that the PG exhibits a stronger dewettability than the flat G, as shown in Figures 3 a and b. At the first 15 ps, the rapid decrease of ΔECu-Cu and EC-Cu accelerates the contraction of the liquid film and helps the droplet move upward, thus leading to the rapid nearly-linear increase of vz. It is worth noting that there exists a small peak when H = 3 Å (Figure 3c), which is considered to be directly related to the existence of nanoholes and this plays a critical role in determining the dewetting mode of metallic films. When t = 10 ~ 15 ps, the vz in all systems reaches the maximum. Furthermore, the peaks in the Cu-PG system are much higher than those in the Cu-G system, confirming that the surface nanostructures greatly influence the contracting velocity. After 15 ps, the vz decreases rapidly to a value far below 0 m/s due to the combined effects of the EC-Cu and the ΔECu-Cu, which signifies that the elongated droplets spread to the surfaces again and would not jump off the surface. Comparing with those systems without detachment, the systems with detachment present remarkably different results, as indicated in Figures 3 d–f. First, the driving force ΔECu-Cu is much larger either at the beginning or at the equilibrium, which is one of the key factors that the droplet could detach from the pillared surfaces rather than from the G. Second, the hindering force EC-Cu is much lower, which is quite benefit for the droplet to contract and detach. Finally, the much higher vz implies that a large maximum vz is essential for the subsequent detachment. Therefore, from the above analysis, we regard that low EC-Cu and high equilibrium ΔECu-Cu are the key factors for the detachment. The high ΔECu-Cu could generate a large vz and the low ΔEC-Cu ensures that the vz remains at a constant value above zero.

Figure 3
figure 3

ΔECu-Cu, EC-Cu and vz of the systems without (left) and with (right) detachment.

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There still exists the question of what plays the dominant role in determining the contraction and detachment: the inertial force, or the viscous force. To gain insight into this question, we carry out additional analysis from the perspective of hydromechanics. The Reynolds number (Re) is a dimensionless quantity which gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces during the liquid film evolution. Re is given as , where ρ, ν and μ are the density, mean velocity and dynamic viscosity of the fluid, respectively and L is a characteristic linear dimension. For liquid Cu in these systems, Re ≈ 6.10, indicating that the inertial force plays an important role in the contraction and detachment, which accords well with the deductions from Refs. 36 and 37.

Figure 4 provides the dependency of H on the detachment. Notably, as H increases from 5 to 10 Å, td increases monotonously, but vd slightly decreases with some fluctuations. At every point of H, the td (vd) decreases (increases) significantly with the increasing a. These phenomena indicate that the dewetting dynamics of the Cu liquid film is more sensitive to the a than H. That is because increasing every 1 Å of the H results in a much larger increase of the EC-Cu than the ECu-Cu, however, increasing a conversely leads to the decrease of the hindering force EC-Cu. That is, decreasing the EC-Cu is the key to effectively detach the liquid droplet. Therefore, we can conclude from Figure 4 that it is an effective means to control the dewetting dynamics of the liquid film by tailing the interval distance of pillars rather than tuning the initial H of the films.

Figure 4
figure 4

The H effects on the detaching behavior td (a) and vd (b).

The increasing tendency of td and slightly decreasing tendency of vd reflect the important role of H in determining the wetting dynamics.

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The above analysis indicates the great effect of a on detachment. Actually, the height h of pillars may also affect the dewettability. To verify this notion, a series of simulations are carried out on the liquid evolution of Cu films on PGs with h ranging from 13.67 to 17.22 Å. Different from the a, the h presents slight dependency on the detachment. Figure 5 a and b shows the influence of a and h on the td and vd. Clearly, the td exhibits a nearly exponential decrease and vd shows a exponential increase with the increasing a. However, when a is fixed, both the td and vd change slightly with the h increasing from 13.67 to 17.22 Å. It indicates that the detaching properties of the droplet is not sensitive to the height of the pillars, which may bring interesting insights to the design of novel microfluidic devices.

Figure 5
figure 5

The size effects of nanopillars on detachment: td (a) and vd (b).

The solid lines are fit curves, which reveal that the td (vd) exponentially increases (decreases) with the interval distance of pillars a.

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To explore how the shape of the liquid film affects the dewetting behavior, a comparison among the Cu films in the shapes of disk, square and triangle is made. Figure 6 shows snapshots of these films, as well as the corresponding td and vd. From the top view of the dewetting process, it can be seen that the Cu disk always remains circular in shape and the square Cu forms a circle at about 23 ps, but more than 23 ps for the triangle Cu. Interestingly, the snapshot of the triangle Cu clearly indicates that the contraction at the straight lines is faster than that at the corners. Importantly, the td (62 ps) for the triangle Cu is largest, followed by 58 ps for the square, then by 49 ps for the disk. The comparison between these films strongly suggests that the sharp corner does not favor the contraction and detachment. That is, the dewetting behavior of liquid films shows significant dependence on their initial shapes (Figures 6a–c), which is further confirmed by Figures 6 d–f. Notably, after 12 ps, the vz for the disk Cu films is the largest and reaches the maximum of about 128 m/s at 21 ps, but the vz for the square Cu slightly decreases then increases to a much lower maximum of about 114 m/s at 24 ps, especially, the vz for the triangle Cu decreases greatly then slightly increases to the lowest maximum of about 93 at 28 ps (Figure 6d). Moreover, at every point of D, the td (vd) of the triangle and square Cu is much larger (smaller) than those of the disk Cu (Figures 6e and f). These shape effects may possibly be explained by the fact that the sharp corners consume more formation energy to form a circle than the smooth lines during the dewetting process. Additionally, we also note that both td and vd increase with the increasing D, suggesting that increasing D would delay the detachment but increase the vd, due to the increase of the surface energy.

Figure 6
figure 6

The initial shape effects of Cu films on detachment.

The H is fixed at 10 Å. (a)–(c) Snapshots of the detaching process. (d) The vz(t) of the liquid Cu droplet when D = 162.72 Å. (e) and (f) td and vd as functions of D. The black, red and blue lines stand for the results of the disk, square and triangle, respectively.

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To investigate the influence of temperature (T) on the td and vd, we have carried out a series of MD simulations of a Cu disk with D = 135.6 Å on the PG at temperatures ranging from 1500 to 2000 K. As shown in Figures 7 a and b, increasing T from 1500 to 2000 K leads to a 24.44% decrement of td and 82.76% increment of vd for a = 10.2 Å, indicating that the detachment can be controlled by adjusting the temperature. These temperature effects are attributed to the enhanced inertial effects, which result from the decreases of density and viscosity due to the increase of T39. As an example, when T increases from 1500 to 1900 K, the Re increases from 6.10 to 10.13, indicating that the role of inertial effects is very remarkable at high temperatures. The effect of the surface structure change of the PG at high temperatures is presented in Figures 7 c and d, which show that the detaching time (td) averagely decreases 4.36% and the detaching velocity (vd) averagely increases 8.12%, indicating that it is slightly easy for the Cu droplet to detach from the substrate if the surface structure changes at high temperatures.

Figure 7
figure 7

The temperature effects on detachment.

(a) and (b) The curves correspond to those systems with H = 10 Å, h = 13.67 Å and a ranging from 6.8 to 10.2 Å. The dashed lines are fit curves, which reveal that the td (vd) presents an exponential relation with T. (c) and (d) The effect of the surface structure change on the detaching properties at high temperatures. The sample used here corresponds to the system a = 11.9 Å, h = 13.67 Å and H = 5.0 Å. Results show that the td decreases 4.36% and the vd increases 8.12% after considering the surface structure change, indicating that it is relatively easy for the Cu droplet to jump off with the consideration of the structure change.

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Figure 8 presents the detaching properties of the Cu liquid droplet on the PG2 surfaces. Like the detachment on the PG surface, the detachment on the PG2 surface displays strong dependence on both the films and the substrates. Figure 8 a and b show that the td significantly increases but the vd slightly decreases with the increasing H. Additionally, both the td and vd display an exponential relation with a and temperature, as shown in Figures 8 c–f. One difference is that both the gaps of td and vd between a = 6.8 and 10.2 Å are larger than that in the Cu-PG system, indicating that the detachment is more sensitive to a in the Cu-PG2 system.

Figure 8
figure 8

Detaching properties of disk Cu on the PG2 surface at 1500 K.

Similarly, the td (vd) shows a increasing (decreasing) tendency with the increasing H and displays exponential relations with a and T.

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Figure 9 shows dewetting properties of liquid films on the horizontally placed carbon nanotubes (HCNT). Like the PG and PG2 surfaces, the HCNT could also detach the droplet, as shown in Figure 9a. Further research presents that both the td and vd display an increasing tendency with increasing D, as shown in Figure 9b, which is consistent with the results in Figure 6, which reflects the importance of surface nanostructures on the special dewettability and indicates the effective method to control these properties by tuning the sizes of the Cu films.

Figure 9
figure 9

Detaching properties of disk Cu on another C-based substrate.

The H is fixed at 10 Å. (a) Structure of the substrate that consists of horizontally placed carbon nanotubes (HCNTs) with fixed interval distance 3.4 Å and partial snapshots of the detaching process. (b) Detaching properties of the disk with varying D on the HCNT.

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Discussion

In summary, this biomimetic study on the wettability of nanopillared graphene reveals the importance of the surface nanostructures on the special dewettability. The MD results show that the CNT pillars act as the effective dewetting components and this not only leads to the increase of dewettability but also brings great convenience in detaching metallic droplets from the surfaces. The inertia plays a dominant role in the dewetting dynamics, especially at high temperature. The detachment can be controlled by simply tunning the geometrical parameters of the films and the surface nanostructures, as well as the temperature. The switching dewetting mode and the controlled detachment not only shed new light on the special dewttability of nanopillared surfaces, but also pave the way for new and promising applications of these surfaces in daily life, self-cleaning materials, nanofluidic devices and homogeneous coatings.

Methods

The Cu nanodisk is extracted from a bulk liquid, then deposited at a distance of 3.0 Å above the PG surface. The CNT pillars are placed on the G to mimic the lotus leaves which possess superhydrophobicity and self-cleaning effects4,5. MD simulations are performed to study the dewetting properties of metallic liquid films on PG under the constant-volume and constant-temperature (NVT) ensemble, by using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package43,44. The interaction among metal atoms is described by an embedded atom method (EAM) potential45. The C-C interaction is modeled by an adaptive intermolecular reactive empirical bond order (AIREBO) potential46. due to the fact that metal and carbon can only form soft bonds via charge transfer from the π electrons in the sp2 hybridized carbon to the empty 4 s states of metal47,48, we utilize the 12-6 Lennard-Jones (LJ) potential with a well depth ε = 0.018 eV and size parameter σ = 3.0 Å to describe the metal-C interaction38,49. This LJ potential was found to reproduce the equilibrium CA as 132° for Cu on pristine graphene. These values are in good agreement with the experimental one 140°50. The temperature is controlled by the Nose−Hoover method and the time integration of the Newton's equation of motion is undertaken using the velocity Verlet algorithm51 with a time step of 1.0 fs. All of the substrates are fixed during the MD simulations.

The CA of a liquid metal droplet on surfaces is calculated by the method used by Werder52. Firstly, the isochore line of the time-averaged metal number density being about one fourth of the bulk density is defined as liquid-air interface. Secondly, we fit a circle to the interface and then measure the CA. The velocity of the liquid nanodroplet along the z direction vertical to the substrate is defined as , where ZCM is the displacement of the nanodroplet center of mass and t is time. The moment when the C-metal potential energy EC-metal equals zero is defined as the detaching time td. After detachment, the liquid droplets remain at a constant velocity, which is defined as the detaching velocity vd.