How Do Different Liquid Metal Films Coalesce on Carbon Substrates

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

How Do Different Liquid Metal Films Coalesce on Carbon Substrates? Xingfan Zhang, Tao Li, Yifan Li, Yunrui Duan, and Hui Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12756 • Publication Date (Web): 21 Mar 2018 Downloaded from http://pubs.acs.org on March 27, 2018

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The Journal of Physical Chemistry

How do Different Liquid Metal Films Coalesce on Carbon Substrates? Xingfan Zhang, Tao Li, Yifan Li, Yunrui Duan, and Hui Li* Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, People’s Republic of China * Corresponding author: [email protected]

Abstract

Droplet coalescence plays an indispensable role in diverse natural and industrial processes. However, it is still unclear that how the wettability and microstructure of the substrates influences the coalescence. Molecular dynamics simulations were used to investigate the coalescence behaviors of liquid metal films on carbon substrates. Two different coalescence regimes, climbing-coalescence and coating-coalescence were respectively observed in Cu-Al and Cu-Ag systems on graphene. The balance of metal-substrate and metal-metal interactions was regard as the key factor to determine the coalescence regimes. Additionally, the effects of surface roughness and atomic arrangement of substrates on the movements of droplets were also analyzed on other carbon materials. Our findings offer a thorough understanding of the relationship between coalescence and wettability, and could have important implications in self-assembly, 3D printing, and microfluidic devices.

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1.

Introduction

As one of the most common phenomena in nature, droplet coalescence has attracted our interests for a rather long time. Coalescence also plays an indispensable role in industrial production, such as petroleum industry1, self-assembly2, 3D printing technology3, and microfluidic devices4. Usually, during the coalescence process, a liquid bridge forms between the two droplets, and then the merged droplet transforms from ellipsoid to sphere5. The change in topology during coalescence is mainly controlled by three forces: viscous force, inertia, and surface tension. At first, coalescence was thought to have just two dynamical regimes: an inertial regime for low-viscosity or inviscid droplets, and a viscous regime for viscous droplets6-9. But during the past few years, more and more regimes of coalescence have been discovered in other fluids. For example, an abnormal crossover from the viscous regime to the inertial regime was observed by Paulsen et al.10 in salt water. They also discovered a third regime called “inertially limited viscous regime”11 in silicone oil, which is different from the two classic regimes. These new-found regimes indicate that the mechanism of droplet coalescence still needs to be explored. Coalescence of liquid metals plays a crucial role in metallurgy, especially with the rapid development of 3D printing technology, liquid metals have been applied to build free standing microstructures12, which requires in-depth research of coalescence to broaden the applications in this field. Nevertheless, experiments mainly focus on the structure and properties of the coalescent products, details of the coalescence mechanism are still limited. Therefore, many scholars selected to use molecular


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dynamics (MD) simulations to solve some problems, which provide an opportunity to thoroughly understand the process from the perspective of atomic motion13-20. Besides, how the substrate affect coalescence is still poorly understood. On one hand, surface microstructure of substrates has long been recognized to have a great influence on contact angles21. People have been committed to control the wettability of droplets by modifying the surface microstructure of substrates to produce superhydrophobic or superhydrophilic materials22-24. On the other hand, coalescence of droplets on substrates25 or confined in two substrates26 were found not to consist with the classic coalescence regimes using sessile drops, which could also be associated with wettability. In fact, wetting and coalescence are closely related. For example, Au, Cu or some other liquid metal films which have large surface tension can convert their surface deformation energy into kinetic energy and jump off from the non-wettable substrates, which is called dewetting27-30. Dewetting has important applications in self-assembly nanotechnology31-34, and how to control the coalescence of droplets becomes the key factor to fabricate desired shapes and patterns2,

35-36

. In our previous works, we

reported that nanopillared graphene substrates can enhanced the dewetting property of liquid Cu films, which can be used to promote the coalescence of Cu droplets37-38. In this paper, we studied the coalescence of Cu films with other liquid metal films on carbon-based substrates, which shows some novel coalescence behaviors. The Cu droplet climbed the Al droplet to achieve coalescence, while the Ag droplet coated the Cu droplet to get coalescence due to the wettability difference on carbon-based



substrates. We probed the relationship between coalescence and wettability based on the atomic diffusion and interaction. Additionally, we also analyzed how the microstructure of the substrates affects the movement of droplets during the coalescence.

2.

Methods

MD simulations were performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package39 to study the wettability of metal droplets on carbon-based substrates and their coalescence behaviors. At first, pure metal blocks were melted to 1500 K and then relaxed for 100 ps in the isobaric-isothermal (NPT) ensemble to obtain liquid metals. Then, liquid metal films with the same thickness (15 Å) and diameter (100 Å) were extracted from the liquid metal blocks and placed at a distance of 2.0 Å above the carbon substrates to investigate the wetting behaviors in the canonical (NVT) ensemble. Substrates were fixed during the simulations for the convenience of accurately measuring the contact angles and observing the morphological evolution of droplets. After 300 ps of simulations, the systems reached the equilibrium states, in which the contact angles and the diffusion coefficients can be obtained. In a coalescence set-up, two liquid metal films with the same size were placed together above the substrates at a distance of 2 Å at the initial stage. The Cu-Ag and Cu-Al systems were respectively used to study the different coalescence regimes. The simulations of coalescence were also carried out in the canonical ensemble, while the temperature was maintained constant at 1500 K using the


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Nosé-Hoover thermostat40. The Newton's equation of motion was calculated using the velocity-Verlet algorithm with a time step of 1.0 fs throughout the simulations. AIREBO potential41 was used to describe the C-C interaction of carbon nanomaterials. The Cu-Ag interaction was described by embedded atom method (EAM) potential42. An angular-dependent (ADP) potential was used to calculate the Cu-Al interaction43. Additionally, we also chose the 6-12 Lennard-Jones (L-J) potentials with a well depth ε=0.010 eV and size parameter σ=3.225 Å to describe the Cu-C interaction28; a well depth ε=0.015 eV and size parameter σ=2.900 Å to describe the Ag-C interaction44; a well depth ε=0.0309 eV and size parameter σ=3.422 Å to describe the Al-C interaction45. With these parameters, the simulated contact angles and diffusion coefficients are in good agreements with the experimental ones, which guarantee the accuracy of the results. Mean square displacements (MSD) and the diffusion coefficients (D) of metals were calculated according to the Einstein diffusion law46: MSD =< |r t − r 0| > D = lim

→

(1) (2)

Where ri(t) is the position of atom i at time t and denotes an average overall atoms, qi is numerical constant that depends on dimensionality, qi = 6 for 3-dimensional diffusion in this work. Interatomic pair potential interaction energy used to explain the origin of different coalescence regimes is given as:



! $

E = 4ε " #

−

! % "

# & , ( < ()

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(3)

Where ε is the well depth of the potential wall, σ is the finite distance at which the inter-particle potential is zero, and rc is the cutoff distance which is selected as 10.0 Å. The calculated metal-metal interaction energy values only include the pair potential portion of the EAM interactions, which may cause a certain margin of numerical error, but have no influence on the results.

3.

Results & discussion

The contact angles (CAs) of Al, Ag, and Cu droplets on the graphene substrate at 1500 K are shown in Fig. 1 (a) to illustrate the wettability difference of the metal droplets. At the nanoscale, the CAs of the droplets keep fluctuating so that we measured five values from the last five picoseconds and took the average value as the result. The simulated CAs of Al, Ag and Cu on graphene are 82.1°, 130.3° and 138.4°, respectively, which are in good agreement with the experimental values of 85°47, 129°48, and 140°49, demonstrating the accuracy of the simulations. At the equilibrium states, the Cu and Ag droplets with poor wettability form a sphere and slightly attach to graphene, while the Al droplet with good wettability keeps hemispherical and closely contacts with the substrate. The Al droplet has the best wettability due to the largest metal-carbon interaction energy as shown in Fig. 1 (b). Besides, we used the equilibrium states as the initial structures to calculate the time-evolution mean square displacement (MSD) and the diffusion coefficients (D) of metals on graphene. DAl, DAg, and DCu are computed as 0.854 Å2/ps, 0.433 Å2/ps and 0.445 Å2/ps, respectively.


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In other works which investigated pure metal systems, DAl was calculated as 1.245 Å2/ps (1193 K)50, DAg was calculated as 0.44 Å2/ps (1450 K)51 , and DCu was measured as 0.60 Å2/ps (1533 K)52. By contrast, the calculated diffusion coefficients in this work are smaller than those in other pure metal systems, because the existence of metal-C interactions limits the diffusion of metal atoms on the substrate. Additionally, we compared the time-evolution MSD and metal-substrate interaction energy (Emetal-C) between the droplets and liquid films in Fig. 1 (b) and Fig. 1 (c). It can be seen that the atoms in the Cu and Ag films diffuse much faster than in the droplets because the large surface tension drives the films to rapidly turn into droplets. But the Al film does not show such huge difference due to the largest attraction from the substrate. This result illustrates that the substrate will hinder the atomic diffusion of droplets in different degrees depending on the magnitude of the metal-substrate interaction energy. Coalescence behaviors of two identical Al-Al, Ag-Ag, and Cu-Cu films on graphene are shown in Fig. 1 (d) to compare with the subsequent different metal systems. Different colors of atoms are used to distinguish the atoms in the two droplets. It can be seen that all of the coalescence processes are similar which have three stages: contraction, adjoining, and horizontal interdiffusion. Among these three systems, the coalescence rate of two Al droplets is the fastest, which can be seen from the growth rates of the liquid bridges and the final mixture uniformity of atoms, indicating that the droplets which have better wettability coalesce faster on substrates. These results indicate that the changes in metal types in the coalescence of two identical metal films



will cause the differences in the atomic diffusion rate, coalescence speed and the contact angle on the substrate, but will not change the coalescence regimes. However, the coalescence behaviors of different metal films are quite different. Figure 2 shows the coalescence of Cu-Al films and Cu-Ag films on graphene. From Fig. 2 (a), it can be seen that the coalescence of Cu and Al films follows the “climbing-coalescence” regime with three stages: contraction, climbing, and vertical interdiffusion. At first, both kinds of films begin to contract under the surface tension. At 30 ps, the Cu film turns into a sphere and slightly attaches to the substrate, while the Al film changes into a hemisphere and closely contacts with the substrate due to their wettability difference. Next, the Cu droplet gradually moves to the top of the Al droplet along its surface, like mountain climbing. Finally, the Cu and Al atoms interdiffuse along the vertical direction to complete the coalescence. Fig. 2 (b) shows the coalescence process of Cu and Ag films. Different from the Cu-Al system, the Cu and Ag droplets display a coating-coalescence regime which includes four stages: contraction, adjoining, coating, and radial interdiffusion. It is noteworthy that the coating and radial interdiffusion stages do not exist in the coalescence of two identical droplets. After the adjoining stage, the identical droplets just interdiffuse horizontally as shown in Fig. 1 (d). But in the Cu-Ag system, after 70 ps, like the phagocytosis process53 in biology, the Ag droplet devours the Cu droplet step by step. At about 200 ps, an Ag spherical shell has formed to fully wrap the Cu droplet. Finally, the two types of atoms interdiffuse along the radial direction and complete their coalescence.


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The interatomic interaction energy graphs in Fig. 3 can help us further understand the origin of the coalescence regimes. The calculated interatomic interaction energy describes the sum of all the pair potential interaction energy between the two types of atoms. In these graphs, a bigger negative value of interaction energy indicates the existence of stronger attraction between the two components. Higher Emetal-C means the attraction from the substrates is higher, and lower Emetal-metal means the interatomic bonding force is lower, which both leads to smaller contact angle of droplet on the substrates. In the Cu-Al system, comparing EAl-C and ECu-C in Fig. 3 (a), it can be seen that the substrate has much larger attraction to the Al atoms than the Cu atoms. As a result, the Al droplet keeps attaching to the substrate with small contact angle, while the Cu droplet keeps spherical and slightly attach to the substrate with large contact angle. During their coalescence, the Al atoms easily intrude into the interface of Cu-C and replace the Cu atoms to contact with the substrate due to the relatively higher Al-C interaction energy. After the contraction stage, the contact area between the Cu droplet and the substrate gets smaller and the Cu-Al interaction gets larger, the attraction from the Al droplet exceeds that from the substrate soon, causing the “mountain climbing” behavior of the Cu droplet. Accordingly, we can conclude that the difference in metal-substrate interaction energy determines whether the climbing phenomenon will occur. In the Cu-Ag system, ECu-C and EAg-C are both low as shown in Fig. 3 (b), so the two droplets both have large contact angles on graphene and the climbing phenomenon does not occur. However, ECu-Cu almost doubles EAg-Ag as shown in Fig. 3 (c), which is



the key factor of the coating-coalescence. The relatively higher ECu-Cu indicates the bonding force between the Cu atoms is higher. As a result, the Cu atoms tightly assemble as a spherical droplet, which makes it difficult for Ag atoms to embed into the Cu droplet but easy to move around the surface of the Cu droplet to get coalescence. The movement of metal atoms during the coating stage can be observed in Fig. 3 (d)-(f) in which slices of atomic velocity vectors are shown. These 5-angstrom-thick slices were cut along the directions perpendicular to the Cu-Ag interface. At 70 ps, the Cu atoms at the center of the droplet rush toward Ag under the inertial force, facilitating the coating behavior of the Ag atoms. From 70 ps to 200 ps, the Ag atoms gradually move around the surface of the Cu droplet and form a liquid shell to coat the Cu droplet. Comparing the length of the arrows, it can be seen that the atoms at the surface of the droplet and near the Cu-Ag interface diffuse faster than other atoms. It is concluded that the difference in metal-metal interaction energy determines whether the coating phenomenon will occur. When the two droplets both have low Emetal-C and the effect of the substrate can be ignored, according to the difference in metal-metal interaction energy, there are three kinds of metal droplet coalescence. The Cu-Ag system describes the first case of large difference in metal-metal interaction energy, in which the Ag droplet completely coats the Cu droplet to achieve coalescence. On the contrary, if the two metals have almost the same metal-metal interaction energy, the coating phenomenon will not occur, which can refer to the coalescence of two identical metal films, such as the coalescence of Cu-Cu, Ag-Ag,


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and Al-Al films. In this condition, the coalescence process only has three stages: contraction, adjoining, and horizontal interdiffusion. Finally, if the difference between EA-A and EB-B is small, it is expected to be an intermediate state between the non-coating coalescence and the complete-coating coalescence. For example, if EA-A is slightly higher than EB-B, droplet B will partly coat droplet A during their coalescence. This case may need further verification in other metal systems. However, these conclusions are only suitable for the systems which have negligible droplet-substrate interactions. When the substrate has larger attraction to the droplets, the coalescence behaviors can be different. For example, in the Cu-Al system, the high EAl-C causes the coating phenomenon to be not obvious. We selected another EAM potential54 to compare ECu-Cu and EAl-Al at the initial stage because the used many-body ADP potential could not calculate the pair potential interaction energy. ECu-Cu is calculated as about -8000 eV and EAl-Al is about -2400 eV, indicating that the interatomic bonding force of the Cu atoms is much larger than Al. According to the above conclusions, the Al droplet is supposed to fully coat the Cu droplet. However, the coating phenomenon is covered up by the climbing-coalescence, mainly because of the high EAl-C. As shown in Fig. 2 (a), during the climbing-coalescence, the Cu droplet keeps spherical before the 150 ps, and the Al droplet only partly coats the Cu droplet from the bottom. Due to the large attraction from the substrate, the Al droplet closely attaches to the substrate, preventing it from further wrapping the Cu droplet, so the coating phenomenon is not obvious. As a result, under the balance of Emetal-metal and Emetal-C, the Cu and Al droplet shows the climbing-coalescence from an overall



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perspective. This case illustrates that although the difference between EA-A and EB-B is the key factor of the coating-coalescence, the droplet-substrate interactions may greatly affect the coalescence regimes, which guides us to further investigated the effect of the substrate microstructure in the Cu-Al system. After coating-coalescence, the stabilized EAg-C and ECu-C are -37.32 eV and -21.45 eV in the Cu-Ag system as shown in Fig. 3 (b), which vary from the results in Fig. 1 (b) calculated from the single droplet systems (EAg-C and ECu-C are -22.81 eV and -37.67 eV). The relative magnitude of EAg-C and ECu-C have changed because the Ag atoms partially

replace

the

Cu

atoms

to

contact

with

the

substrate

during

coating-coalescence, resulting in the increased EAg-C and decreased ECu-C. Additionally, the atomic diffusion was also found to be affected by the coalescence behaviors. The Cu atoms diffuse faster than Al atoms during coalescence as shown in Fig. 4 (a), which is similar to the single-film systems in Fig. 1 (c). But in the Cu-Ag system in Fig. 4 (b), the relatively larger MSD of Ag than Cu indicates that the D of Ag atoms is higher than that of Cu, which is contrary to the results of single-film systems. This difference can also be ascribe to the coating behavior of the Ag atoms, which significantly increases their diffusion rate during the coating-coalescence. Next, we investigated the coalescence on rough surfaces: horizontally-placed carbon nanotubes (HCNT) substrate, vertically-placed carbon nanotubes (VCNT) substrate, in which the carbon nanotubes are placed in parallel and perpendicular to the coalescence direction, and capped-carbon-nanotube-pillared graphene (PG) substrate, which are shown in Fig. 5 (a). Firstly, we selected the Cu-Al system to illustrate how


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the substrates affect the coalescence of droplets with different wettability. Snapshots in Fig. 5 (b) show that the climbing-coalescence regime still exists under these three conditions, but the speed of coalescence and the motion of droplets in X-axis are different. It takes the shortest time to coalesce on the HCNT substrate because the grooves on the substrate are parallel to the coalescence direction, which have almost no barriers for the droplet movement. The arrangement of the carbon nanotubes side by side forms some periodic peaks and valleys along the X-axis of the VCNT substrate, which make the droplet move difficultly. This difference illustrates that on anisotropic surfaces, the location of films will affect the coalescence speed. On the PG substrate, some Al atoms penetrate into the gaps of the rough surface and hardly move just like being pinned. Such pinning effect caused by rough surfaces is remarkable for the droplet motion at the nanoscale. From the center-of-mass displacement (CMD) in Fig. 5 (b), the Al droplet is pinned so tightly that it cannot move freely on the PG and VCNT substrates. But the Cu droplet is not that case as shown in Fig. 5 (c). On the contrary, the rougher the surface is, the faster the Cu droplet moves. Due to the large surface tension and low metal-substrate interaction energy, the Cu droplet keeps spherical instead of penetrating into the gaps of the rough surfaces. The pillared surfaces decrease the contact area between Cu and C and further reduce the attraction from the substrate, thus the Cu droplet can move more freely without the restriction from substrates. By comparing the CMD curves in Fig. 5 (c)-(d), the CMD in X-axis of the Cu droplet on the three substrates follows the order PG > VCNT > HCNT, while for the Al droplet follows the converse order HCNT >



VCNT > PG. Therefore, it is concluded that rough surfaces can induce the droplets with good wettability to penetrate into the gaps of the surfaces due to the strong metal-substrate interaction, which will pin the droplets and hinder the coalescence. On the contrary, for the droplets with poor wettability, the metal-substrate interaction is too weak to overcome the surface tension of the droplet. Rough surfaces can reduce the contact area with the droplets instead, and further facilitate the coalescence. We also explored how the atomic arrangement affects the coalescence on smooth substrates by simulating the coalescence behaviors of the Cu and Al films on the (1 0 0), (1 1 0), and (1 1 1) surfaces of diamond (DM). As shown in Fig. 6 (a), the coalescence on DM (1 0 0) is distinctly different from other conditions that the coalescent droplet is closer to the right side of the substrate. CMD graphs in Fig. 6 (b)-(c) show that on DM (1 1 0) and DM (1 1 1), the two droplets move toward each other to achieve coalescence. But on DM (1 0 0), the Al droplet hardly moves along the X-axis and the coalescence is accomplished solely by the movement of the Cu droplet. We found the reason from the atomic arrangement of the substrates. The surface packing densities of DM (1 0 0), DM (1 1 0) and DM (1 1 1) are 15.72, 22.37, and 18.27 atoms/nm2, respectively, demonstrating that there are fewest carbon atoms to contact with the droplets on DM (1 0 0). It can also be proved in Fig. 6 (d) that the interaction energy of Al-C on DM (1 0 0) is the lowest (the interaction energy on DM (1 1 1) is the highest because the top two atomic layers are very close, which evidently increases the interaction). During the contraction stage of coalescence, the Al droplet moves upward for a larger distance on DM (1 0 0) than other conditions as


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shown in Fig. 6 (e). Additionally, it was also found that the single Al droplet on DM (1 0 0) shows the worst wettability that it has the largest contact angle and the highest altitude as shown in Fig. 6 (f). As a result, it is difficult for the Cu droplet to climb over the higher Al droplet, and for the higher Al droplet to intrude into the bottom of the Cu droplet. Therefore, the Cu droplet not only climbs, but also pushes the higher Al droplet to move along the opposite direction. Finally, the two droplets move together along the X-axis and the compound droplet stays near the right side of the DM (1 0 0) substrate. But on DM (1 1 0) and DM (1 1 1), due to the better wettability caused by the lower Al-C interaction energy, the Al droplet is shorter in height, so that the pushing force becomes evidently smaller. As a consequence, the two droplets move toward each other to achieve coalescence. The result illustrates that the atomic arrangement of the smooth substrates will affect the coalescence behaviors of droplets by affecting their wettability. In the Cu-Ag system, the substrate microstructure has much less influence on the droplet coalescence behaviors than in the Cu-Al system. Fig. 7 (a) and Fig. 7 (b) shows the CMD of the Cu and Ag droplets in X-axis during coalescence, respectively, in which solid lines represent the cases on rough surfaces (HCNT, VCNT and PG), and dash lines represent the cases on smooth surfaces (DM (1 0 0), DM (1 1 0), and DM (1 1 1)). It can be seen that the CMD curves do not show evident difference whether on the rough or the smooth substrates, because the low ECu-C and EAg-C significantly reduce the contact area between the droplets and the substrates. These results indicate that the changes in the microstructure of the substrates have little



influence on the coalescence rates of two droplets with low metal-substrate interaction energy. Contact angles (CAs) of the coalescent droplets on different substrates were measured from 200 ps to 1000 ps. In the Cu-Al system, the CAs rise gradually before 700 ps because the Cu atoms diffuse downward as shown in Fig. 8 (a). The CAs show very little change after 700 ps, and the average CAs of the Cu-Al droplets from 700 ps to 1000 ps on G, HCNT, VCNT, and PG are 88.6°, 93.3°, 91.4°, and 93.6°, respectively. But in the Cu-Ag system, as shown in Fig. 8 (b), the CAs become stable after 500 ps, earlier than those in the Cu-Al system, indicating that the Cu and Ag droplets coalesce faster. The average CAs of the Cu-Ag droplets from 700 ps to 1000 ps on G, HCNT, VCNT, and PG are 128.7°, 132.1°, 133.3°, and 134.6°, respectively. In each system, the CA of droplet on the G substrate is the smallest and on the PG substrate is the largest, indicating rough substrates can increase the CAs of metal droplets. Furthermore, compared to the CAs of the pure metal droplets (The CAs of Al, Ag and Cu are 82.1°, 130.3°, and 138.4°, respectively), the CA of the alloy droplet is closer to the lower value of the two components.

4.

Conclusion

In summary, molecular dynamics simulations were performed to study the coalescence behaviors of liquid metal films on carbon substrates. Two different coalescence regimes, climbing-coalescence and coating-coalescence were observed on graphene. The Cu droplet climbs to the top of the Al droplet to achieve coalescence


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in Cu-Al system, while the Ag atoms coats the Cu droplet to get coalescence in the Cu-Ag system. The balance of metal-substrate and metal-metal interactions was regard as the key factor to determine the coalescence regimes. It is concluded that the difference in Emetal-C between the two metals determines whether the climbing phenomenon will occur, and the difference in Emetal-metal determines whether the coating phenomenon will occur. Additionally, we further studied the effect of surface microstructure of the substrates on coalescence. By comparing the coalescence behaviors of Cu and Al films on rough substrates, it is concluded that rough surfaces will pin the good-wettability droplets and restrict their movements, but make the poor-wettability droplets move more freely during coalescence. The atomic arrangement of the smooth substrates was also found to affect the coalescence behaviors of droplets by affecting their wettability. These results offer an applicable method from the perspective of interatomic interaction to investigate droplet coalescence, which could be extended to other systems which have non-bonded liquid-solid interactions, and could have certain guiding significance for new applications in self-assembly, 3D printing, and microfluidic devices.

Acknowledgements

The authors would like to acknowledge the support from the National Natural Science Foundation of China (Grant No.51671114). This work is also supported by the Special Funding in the Project of the Taishan Scholar Construction Engineering and National Key Research Program of China (Grant No. 2016YFB0300501).



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Figure


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Figure 1: (a) Wetting behaviors of liquid metal droplets on graphene. The contact angles of Al, Ag, and Cu are measured as 82.1°, 130.3°, and 138.4°, respectively. (b) Interaction energy between metal and the substrate. Solid lines represent the initial structures are metal droplets at the equilibrium states on graphene, and dash lines represent the initial structures are liquid metal films. (c) Time-evolution mean square displacement (MSD) of Al, Ag and Cu on graphene. (d) Coalescence of two identical



Al, Ag or Cu films on graphene.

Figure 2: Two different coalescence regimes on graphene. (a) “Climbing-coalescence” of Cu and Al films. The Al droplet climbs to the top of the Cu droplet and they achieve their coalescence by vertical interdiffusion. (b) “Coating-coalescence” of Cu and Ag films. The Ag droplet coats the Cu droplet step by step and they finally


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interdiffuse along the radial direction to complete their coalescence.

Figure 3: Interatomic interaction energy and atomic motion during coalescence. (a) Metal-C interaction energy in the Cu-Al system. (b) Metal-C interaction energy in the Cu-Ag system. (c) Metal-metal interaction energy in the Cu-Ag system. Slices of temporal evolution of atomic velocity vectors during the coalescence of Cu and Ag droplets at the Cu-Ag interface at (d) 70 ps, (e) 150 ps, and (f) 200 ps.

Figure 4: Time-evolution mean square displacement (MSD) of metals during the



coalescence processes on graphene in the (a) Cu-Al system and (b) Cu-Ag system.

Figure 5: Coalescence of Cu and Al films on rough substrates. (a) The horizontally-placed carbon nanotubes (HCNT) substrate, vertically-placed carbon nanotubes (VCNT) substrate, and capped-carbon-nanotube-pillared graphene (PG) substrate are used to describe different situations of rough substrates. (b) Coalescence processes of the Cu and Al films on the three substrates. (c) Center-of-mass displacements (CMD) of the Cu droplet in X-axis during coalescence on the three


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substrates. (d) CMD of the Al droplet in X-axis on the three substrates.

Figure 6: Coalescence of the Cu and Al films on different crystal faces of diamond. (a)



Snapshots of the coalescence processes on the (1 0 0), (1 1 0), and (1 1 1) faces of diamond (b) CMD of the Cu droplet in X-axis on the three substrates. (c) CMD of the Al droplet in X-axis. (d) Al-C interaction energy. (e) CMD of the Al droplet in Z-axis. (f) The wettability of the Al droplet on different faces of diamond.

Figure 7: Coalescence of Cu and Ag films on rough (HCNT, VCNT, and PG) and smooth (DM (1 0 0), DM (1 1 0), and DM (1 1 1)) substrates. (a) Center-of-mass displacements (CMD) of the Cu droplet in X-axis during coalescence on the six substrates. (b) CMD of the Ag droplet in X-axis on the six substrates.


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Figure 8: Time-evolutional contact angles (CA) of the coalescent droplets on the G, HCNT, VCNT, and PG substrates from 200 ps to 1000 ps. (a) The coalescent Cu-Al droplet. (b) The coalescent Cu-Ag droplet.

TOC Graphic



Figure 1: (a) Wetting behaviors of liquid metal droplets on graphene. The contact angles of Al, Ag, and Cu are measured as 82.1°, 130.3°, and 138.4°, respectively. (b) Time-evolution mean square displacement (MSD) of Al, Ag and Cu on graphene. Solid lines represent the initial structures are metal droplets at the equilibrium states on graphene, and dash lines represent the initial structures are liquid metal films. (c) Interaction energy between metal and the substrate. (d) Coalescence of two identical Al, Ag or Cu films on graphene. 177x208mm (300 x 300 DPI)


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Figure 2: Two different coalescence regimes on graphene. (a) “Climbing-coalescence” of Cu and Al films. The Al droplet climbs to the top of the Cu droplet and they achieve their coalescence by vertical interdiffusion. (b) “Coating-coalescence” of Cu and Ag films. The Ag droplet coats the Cu droplet step by step and they finally interdiffuse along the radial direction to complete their coalescence. 177x204mm (300 x 300 DPI)



Figure 3: Interatomic interaction energy and atomic motion during coalescence. (a) Metal-C interaction energy in the Cu-Al system. (b) Metal-C interaction energy in the Cu-Ag system. (c) Metal-metal interaction energy in the Cu-Ag system. Slices of temporal evolution of atomic velocity vectors during the coalescence of Cu and Ag droplets at the Cu-Ag interface at (d) 70 ps, (e) 150 ps, and (f) 200 ps. 177x84mm (300 x 300 DPI)


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Figure 4: Time-evolution mean square displacement (MSD) of metals during the coalescence processes on graphene in the (a) Cu-Al system and (b) Cu-Ag system. 177x67mm (300 x 300 DPI)



Figure 5: Coalescence of Cu and Al films on rough substrates. (a) The horizontally-placed carbon nanotubes (HCNT) substrate, vertically-placed carbon nanotubes (VCNT) substrate, and capped-carbon-nanotubepillared graphene (PG) substrate are used to describe different situations of rough substrates. (b) Coalescence processes of the Cu and Al films on the three substrates. (c) Center-of-mass displacements (CMD) of the Cu droplet in X-axis during coalescence on the three substrates. (d) CMD of the Al droplet in Xaxis on the three substrates. 177x178mm (300 x 300 DPI)


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Figure 6: Coalescence of the Cu and Al films on different crystal faces of diamond. (a) Snapshots of the coalescence processes on the (1 0 0), (1 1 0), and (1 1 1) faces of diamond (b) CMD of the Cu droplet in Xaxis on the three substrates. (c) CMD of the Al droplet in X-axis. (d) Al-C interaction energy. (e) CMD of the Al droplet in Z-axis. (f) The wettability of the Al droplet on different faces of diamond. 177x240mm (300 x 300 DPI)



Figure 7: Coalescence of Cu and Ag films on rough (HCNT, VCNT, and PG) and smooth (DM (1 0 0), DM (1 1 0), and DM (1 1 1)) substrates. (a) Center-of-mass displacements (CMD) of the Cu droplet in X-axis during coalescence on the six substrates. (b) CMD of the Ag droplet in X-axis on the six substrates. 177x75mm (300 x 300 DPI)


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Figure 8: Time-evolutional contact angles (CA) of the coalescent droplets on the G, HCNT, VCNT, and PG substrates from 200 ps to 1000 ps. (a) The coalescent Cu-Al droplet. (b) The coalescent Cu-Ag droplet. 177x68mm (300 x 300 DPI)



TOC Graphic 85x34mm (300 x 300 DPI)


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How Do Different Liquid Metal Films Coalesce on Carbon Substrates

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