The coalescence of heterogeneous liquid metal on nano substrate

Accepted Manuscript The coalescence of heterogeneous liquid metal on nano substrate Long Wang, Yifan Li, Xuyan Zhou, Tao Li, Hui Li PII: DOI: Reference:

S0301-0104(16)30650-4 http://dx.doi.org/10.1016/j.chemphys.2017.04.009 CHEMPH 9777

To appear in:

Chemical Physics

Received Date: Accepted Date:

16 August 2016 14 April 2017

Please cite this article as: L. Wang, Y. Li, X. Zhou, T. Li, H. Li, The coalescence of heterogeneous liquid metal on nano substrate, Chemical Physics (2017), doi: http://dx.doi.org/10.1016/j.chemphys.2017.04.009

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The coalescence of heterogeneous liquid metal on nano substrate Long Wang, Yifan Li, Xuyan Zhou, Tao Li, 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. E-mail: [email protected]

Table of Contents

The asymmetric coalescence of heterogeneous liquid metal and the shell structure of the final drop.

Abstract Molecular dynamics simulation has been performed to study the asymmetric coalescence of heterogeneous liquid metal on graphene. Simulation results show that the anomalies in the drop coalescence is mainly caused by the wettability of heterogeneous liquid metal. The silver atoms incline to distribute on the outer layer of the gold and copper droplets, revealing that the structure is determined by the interaction between different metal atoms. The coalescence and fusion of heterogeneous liquid metal drop can be predicted by comparing the wettability and the atomic mass of metallic liquid drops, which has important implications in the industrial application such as ink-jet printing and metallurgy.

Keywords: asymmetric coalescence; heterogeneous liquid; carbon nano substrate; wettability

Introduction The coalescence of liquid drop is of great importance in the field of practical application such as the self-cleaning materials, spray painting or spray coating, separation of emulsions and metallurgy industry1-7. Considerable work has been done to study the drop formation on substrate. Early theoretical models by J. Eggers et al. 8 focused on the early-time behavior of the radius of the small bridge between the two drops. Experimentally, the initial stage of coalescence in a molecular system with a variable viscosity was studied by Aarts et al9 who demonstrated that the coalescencing

dynamics of droplets is slowed down by viscosity for low Reynolds numbers and by inertia for high Reynolds numbers. These models typically focused on the wettable drop, but, there is also significant interest in the dewetting process. Jumping drops on the super-hydrophobic surfaces has been investigated by several groups10-12 theoretically and experimentally. Liu et al13,

14

studied the self-propelled jumping upon drop coalescence on non-wetting

surfaces and Leidenfrost surfaces. Wang et al

15

accurately predicted the nearly

constant jumping velocity of drop when scaled by the capillary–inertial velocity. Considerable efforts have been devoted to studying the driving force and retardation force in the drop coalescence. Liu et al16 studied the jumping mechanism of a condensed drop on super hydrophobic surfaces. The initially coalesced drop is unstable so that it has the driving force to reduce its radius toward its equilibrium as possible as it can. Studies of such phenomena have led to important new insights into the dynamics of drop formation. Almost all the present studies are focused on two identical drops, but the coalescence of two different drops is less mentioned. Zheng et al.17 have studied the asymmetric coalescence of reactively wetting droplets, whose results show that ridge at the contact line changes the coalescence dynamics so that when two droplets touch they coalesce with the resulting center of mass located at the projected center of the larger droplets. Besides, to our knowledge, studies of drop coalescence of heterogeneous liquid are limited. The heterogeneous coalescence is relevant to a wide variety of fields, ranging from welding and casting manufacturing to metallurgy

industry. For instance, practical applications of the heterogeneous coalescence are found in the welding industry that require joining of different metals because the heterogeneous coalescence of high-temperature liquid metal can affect the structure and properties of the weld line. So far this phenomenon remained largely unexplored. In this study, we carry out molecule dynamics simulations to study the heterogeneous coalescence of metal drop on nano substrate.

Methods and modeling MD

simulations

are

carried

out

under

the

constant-volume

and

constant-temperature (NVT) ensemble, by means of the large-scale atomic/molecular massively parallel simulator (LAMMPS) package18,19. The temperature is 1500k which is controlled by the Nose−Hoover method and the time integration of the Newton's equation of motion is undertaken using the velocity Verlet algorithm20 with a time step of 1.0 fs. All the MD simulations are run 1000ps. During the simulation, the circular metal films are all deposited on the double-wall graphene with the connecting line of the center of each film parallel to the substrate as shown in Fig.1. All the substrates are fixed during the MD simulation and periodic boundary conditions are applied in x and y directions. The interaction among metal atoms is described by an embedded atom method (EAM) potential.21, 22 The C-C interaction is modeled by an adaptive intermolecular reactive empirical bond order (AIREBO) potential.23 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 4s states of metal24-26, we utilize the 12-6 Lennard-Jones (L-J) potential to describe the metal-C

interaction. The well-depth and size cross LJ parameters are 0.00873 eV and 2.99943 Å for Au-C, 0.0301 eV and 3.006 Å for Ag-C, 0.0180 eV and 3.000 Å for Cu-C respectively. In this work, the contact angle of Au drops on flat graphene is measured as 133.7° that was fitted to ab initio and experimental data.11 The LJ potential of Cu-C has been widely determined by the equilibrium contact angle similar to the theoretical and experimental results.27,28 The parameters of Ag-C have been applied to calculate the Ag-carbon interaction for the water-graphite system by Akbarzadeh.29 These result strongly demonstrate that the LJ potential can accurately describe the interaction between atoms.

Fig. 1 Schematic of the simulated system. (a)The nonwetting process of single metal film. (b)The adjacent metal films located on the graphene. The diameter and thickness of films are defined as D = 108.48 Å and H = 15 Å respectively. The double-wall graphene is 260 Å long and

150 Å wide, which is determined to make sure the distance between the liquid metal and the edge is about 20 Å. The atoms are in different colors to identify the different metals.

Results and discussion

Fig.2 Snapshots of the coalescence of different metal drops on flat graphene. (a) Cu-Ag (b) Au-Ag (c) Au-Cu. TABLE 1. the height (Å) of the simple metal drop during the contraction. metal

10 ps

20 ps

30 ps

40 ps

50 ps

60 ps

70 ps

Cu(Cu-Ag)

26.1

33.5

49.2

58.9

62.6

64.6

66.1

Ag(Cu-Ag)

24.4

26.0

30.3

35.5

39.7

44.1

46.9

Au(Au-Ag)

26.8

32.9

43.2

53.4

61.4

68.0

73.2

Ag(Au-Ag)

24.5

25.6

29.6

33.9

36.8

39.8

42.6

Au(Au-Cu)

27.9

33.2

41.8

51.8

61.1

69.4

76.9

Cu(Au-Cu)

27.6

36.7

49.6

58.6

65.4

70.2

74.0

Fig. 2 shows side view of the drop forming process of two different metal films that just contact each other. We have already measured that the contact angles of single liquid Au, Ag, Cu on the graphene, are 133.7°, 92.6° and 123.1°, which indicates that the order of wettability is Ag>Cu>Au. As the two films gradually become drops, the meniscus bridge between two films expands in the direction perpendicular to the center line of the films. As the simulation progresses, the films which contracts rapidly are expected to further coalesce and combine into one elliptical droplet before 100ps. This binary droplet has the form of asymmetrical distribution such as Cu-Ag in Fig. 2a which shows that the Cu atoms distribute in the left-up part while all the Ag atoms accumulate at the bottom, then it takes a long time to get a uniform drop. The contact angles of the final Cu-Ag, Au-Ag and Au-Cu drops are measured as 98°, 95° and 128°. Here, we focus on the initial rapid growth of the meniscus bridge between adjacent films in the first 100ps. During this period of time, the metal films gradually contract and the drop coalescencing shows asymmetric which is similar with Hernandez-Sanchez30 who studied the coalescence of viscous drops on a substrate experimentally and theoretically. Hernandez-Sanchez put two drops with same viscidity but different shape together and the results show that the universal shape of the asymmetric bridge is accurately described by similarity solutions. Unlike Hernandez-Sanchez’s research, the metal films in our simulation are initially in the same size and shape, but our results also show the asymmetric coalescence. Table 1 shows the height of the drop which can represent the shape of the liquid metal during the coalescence. The driving forces of coalescence can be

understood from a balance between surface tension, inertia and viscosity in this regime. When put on the graphene, the metal droplets convert their surface deformation energy into kinetic energy, which makes them contract rapidly. During the contraction, the interaction of the metal atoms reflects the viscous force, and the interaction between carbon atoms and metal atoms reflects the inertial force. When the drop exhibits a better wettability on the surface, the repulsive force is less due to the weaker interaction between carbon and metal, resulting a faster contraction. This rule is in agreement with our simulations in Fig. 2a-b in which the height of both Au drop and Cu drop is bigger than the Ag drop during the coalescence. However, when Au and Cu films are put together on the graphene, the shape of Cu drop is obviously higher and thinner than Au before 70ps, which are contrary to our expectation. It could be confirmed that the repulsive force between Au liquid is larger, so the asymmetric coalescence is not only relevant with the wettability of metal itself, but also the different mass of the different metal. To well understand the movement of metal drops in the initial stage, Fig. 3b shows the velocity-time curves of different drops in z direction. Actually, because the mass of Cu drop is much bigger than that of Au drop, the mass center of Cu has the higher acceleration and more quickly upward velocity than Au at the same time, which results in the abnormal coalescence of Au and Cu films.

Fig. 3. The velocity of metal drop as a function of time. (a-c) X-component of velocity VX (d-f) Z-component of velocity Vz.

Fig.3 shows the velocity of metal drop as a function of time. The most drastic changes of velocity are all appeared during the first 100ps. By comparison of the peak value of the curves, it can be found that the order of horizontal velocity is Cu>Ag>Au, indicating that the velocity along x direction is independent of the wettability of liquid metal. Further analyses indicate that the x-component velocity is inversely proportional to the relative atomic mass. However, the maximum of Vz, to some extent, can reflect the wettability as we can see from Fig. 3(d-f). The Cu drops can reach about 0.8 Å/ps, while Au drops can reach about 0.5 Å/ps, and Ag drops which have the best wettability can only reach 0.2 Å/ps. The maximum velocity all appears at about 30 ps, which means that inertial forces play a leading role in acceleration

stage, but after 30ps, the dynamics are described by a fully viscous regime where inertial forces are neglected, meaning that the shared interaction between surface tension and viscosity can be considered as the driving forces of coalescence. More interesting, the trend of velocity-time curve distribution shows symmetrical distribution along the center line which is slightly higher than the central line. The symmetry is particularly obvious for Ag and Cu which have similar atomic mass, indicating that the forces during the mixing stage between the two connect drops are mutual and related to the relative atomic mass.

Fig. 4 The trajectories of the mass center of metal drops in x-z plane. (a) Cu-Ag (b) Au-Ag (c) Au-Cu. Color shows the velocity, colder traces signify slower speeds. The drop center of Au can rise to 40 Å high from the initial, and the maximum velocity is 0.6 Å/ps. The Cu drops, which are nonwettable on carbon, rising with a speed of 1 Å/ps, arrive at peak which is 25 Å above the substrate. As for Ag drop, it accelerates to 0.8 Å/ps firstly, and then decelerates until the drop center rises to 10 Å above the surface, and starts mixing with the other metal drop slowly.

Fig. 4 shows the trajectories of the mass center of metal drops in x-z plane. It can be seen that the drop center of Au can rise to 40 Å high from the initial, and these maximums are almost the same whether contacting with Ag or Cu which shows great different wettability. Moreover, the velocity of Au drops also remain unchanged, and the maximum velocity is 0.6 Å/ps. It is suggested that the formation process is obviously different if the adjacent drop is changed, but the movement of single drop is unchanged. During the mixing stage, for the distance between different metal atoms, the interaction between heterogeneous metal is weaker, resulting the less impacts on the adjacent metal drops. The color of the track curves shows that the maximum velocity appears in the rising process after a quick acceleration due to the inertial. Fuentes-Cabrera12 has already studied the velocity of jumping droplets and found that the velocity depends on the initial shape and temperature. The dependence of the ejected velocity on shape is ascribed to the temporal asymmetry of the mass coalescence during the droplet formation, but the dependence of the ejected velocity on temperature is ascribed to the changes in density and viscosity. After about 200ps, for all metal drops, the displacement curves increase linearly, which indicate that the different metal atoms are uniform mixing. During this period, the binary drop always moves along x axis and the direction is regular to the order of wettability (Ag>Cu>Au). Whether two different metal drops were put together, the binary drop is more likely to move to the position of good wetting metal. It can be seen from Fig. 3a that the movement is independent of the horizontal velocity by comparing the x-component of velocity from the figure which shows that VXCu>VXAg>VXAu. The

moving direction could be explained from two aspects: one is the repulsive force between metal and substrate, the other is the interatomic interaction of metal atoms. In addition, the attracting force of the Au or Cu atoms is stronger than the Ag atoms, resulting the different viscosity of the metal liquid.

Fig. 5 Mean square displacements (MSDs) of metal atoms on graphene (a) Au-Cu (b) Au-Ag (c) Ag-Cu

The diffusivity of metal drops, one of the physical characteristics to describe the metal drops on the substrate, is further explored by the mean square displacements(MSDs). Fig. 5 shows the MSDs of metal atoms on graphene. Before 200ps, the diffusion speed of Cu and Au are higher than that of Ag, suggesting that the order of the diffusion speed agrees well with the order of the wettability of metal drops during the early-stage of coalescence. And after 200ps, it can be seen that the diffusion speed of Ag and Cu increase rapidly and eventually surpass the Au, intensely implying that during this stage, the x-component velocity plays a role in the diffusion. Fig. 5a shows that the diffusion curves do not intersect with each other

because the x-component velocity of Ag and Cu have not much difference as shown in Fig. 4. Furthermore, a striking discovery from Figure 5 is that the diffusion speed of Ag is significant increased when the adjacent drop changes from Cu to Au, which means that the diffusion of metal drops is closely related to the adjacent metal.

Fig. 6 Cross section views of binary drops during the latter stage of coalescence. (a) Cu-Ag (b) Au-Ag (c) Au-Cu

We finally consider the mixing stage for the three different coalescence cases. Fig. 6 shows the snapshots of cross section views during this stage, the three cases are much different. There is a kind of shell structure during the mixing of Cu and Ag. Ag atoms are wrapped around Cu atoms which contract rapidly into a ball. In both sides of the interface, the interdiffusion of components is evident. As for the case of Au-Ag, Au atoms appear on the top while Ag atoms appear on the bottom due to the great

different wettability between Au and Ag. After a long mixing time, both Cu-Ag and Au-Ag stay stable with internal uniform structures, but their outermost layers are mainly composed of Ag atoms. The mixing process of Au-Cu is distinctive. Fig. 6c shows that the new droplet is formed at 60ps and the uniform structure is presented before 500ps. The different phenomenon during the coalescence is closely related to the intrinsic characteristics of the metal. The Ag atoms always distribute at the bottom and outer because of the good wettability of Ag drop and the viscosity of Au and Cu. The stronger attraction between Ag and graphene makes the Ag atoms accumulate near the substrate at the initial stage of the mixing. The cohesion of Au or Cu atoms is much stronger than that of Ag atoms, causing the shell structure of heterogeneous metal drop.

Conclusion MD simulations have been performed to study the coalescence and mixing of heterogeneous liquid metal on graphene. The asymmetric coalescence behavior is determined by not only the wettability of metal, but also the mass of the drop. Because of the interaction between metal atoms, the formation process is obviously different if the adjacent drop is different. The x-component velocity is inversely proportional to the relative atomic mass, indicating that the forces during the mixing stage between the two connect drops are mutual and related to the relative atomic mass. Moreover, it can be found the shell structure when liquid Ag participate in the coalescence, revealing the stronger attraction between Ag and graphene. This study

would provide a better insight into the relevance coalescence and interfacial properties, and aid in the development of an effective method for controlling the coalescence of metal films.

Acknowledgements The authors would like to acknowledge the support from the National Natural Science Foundation of China (Grant No. 51271100). This work is also supported by the National Basic Research Program of China (Grant No.2012CB825702). This work is also supported by the Special Funding in the Project of the Taishan Scholar Construction Engineering.

References 1. W. W. Grabowski and L.-P. Wang, Annu Rev Fluid Mech, 2013, 45, 293-324. 2. A. Raza, Y. Si, X. Wang, T. Ren, B. Ding and J. Yu, RSC Adv, 2012, 2, 2804-12811. 3. N. Gao and Y. Yan, Nanoscale, 2012, 4, 2202-2218. 4. D. Wu, P. Wang, P. Wu, Q. Yang, F. Liu, Y. Han, F. Xu and L. Wang, Chem. Phys, 2015, 457, 63-69 5. C. Belgardt, E. Sowade, T. Blaudeck, T. Baumgärtel, H. Graaf, C. von Borczyskowski and R. R. Baumann, Phys Chem Chem Phys, 2013, 15, 7494-7504. 6. M. W. Lee, D. K. Kang, S. S. Yoon and A. L. Yarin, Langmuir, 2012, 28, 3791-3798.

7. M. K. Rana and A. Chandra, Chem. Phys, 2015, 457, 78-86 8. J. Eggers, JR. Lister and HA. Stone, J Fluid Mech, 1999, 401, 293-310 9. D. G. Aarts, H. N. Lekkerkerker, H. Guo, G. H. Wegdam, and D. Bonn, Phys Rev Lett, 2005, 95, 164503-164503. 10. X. Li, Y. He, Y. Wang, J. Dong and H. Li, Sci. Rep, 2014, 4. 11. A. Habenicht, M. Olapinski, F. Burmeister, P. Leiderer and J. Boneberg, Science, 2005, 309, 2043-2045. 12. M. Fuentes-Cabrera, B. H. Rhodes, M. I. Baskes, H. Terrones and J. D. Fowlkes, Acs Nano, 2011, 5, 7130-6. 13. F. Liu, G. Ghigliotti, J. J. Feng and C. H. Chen, J Fluid Mech, 2014, 752, 22-38. 14. F. Liu, G. Ghigliotti, J. J. Feng and C. H. Chen, J Fluid Mech, 2014, 752, 39-65. 15. J. Wang, S. Chen and D. Chen, Phys Chem Chem Phys, 2015, 17, 30533-30539. 16. T. Q. Liu, W. Sun, X. Y. Sun and H. R. Ai, Colloids Surf. A, 2012, 414, 366-374. 17. C. X. Zheng, W. X. Tang and D. E. Jesson, Appl. Phys. Lett. 2012, 100, 017903. 18. S. Plimpton, J Comput Phys, 1995, 117, 1-19. 19. J. D. Fowlkes, L. Kondic, J. Diez, Y. Wu and P. D. Rack, Nano Lett, 2011, 11, 2478-2485. 20. Y. V. Naidich and G. Kolesnichenko, Soviet Powder Metallurgy and Metal Ceramics, 1968, 7, 563-565. 21. X. W. Zhou, R. A. Johnson, and H. N.

G. Wadley, Phy. Rev. B, 2004, 69,

1124-1133. 22. S.P. Huang, D.S. Mainardi，P.B. Balbuena, (2003). Surf. Sci. 2003, 545, 163-179.

23. H. Ren, L. Zhang, X. Li, Y. Li, W. Wu and H. Li, Phys Chem Chem Phys, 2015, 17, 23460-23467. 24. S. J. Stuart, A. B. Tutein and J. A. Harrison, The Journal of chemical physics, 2000, 112, 6472-6486. 25. P. Sutter, M. Hybertsen, J. Sadowski and E. Sutter, Nano Lett, 2009, 9, 2654-2660. 26. Y. He, H. Li, Y. Li, K. Zhang, Y. Jiang and X. Bian, Phys Chem Chem Phys, 2013, 15, 9163-9169. 27. S. Afkhami and L Kondic, Physics, 2013, 111, 1115-1141. 28. B. Deng, A.W. Xu, G.Y. Chen, A. R. Song and L Chen, J. Phys. Chem. B, 2006, 110, 11711-6. 29. H. Akbarzadeh, H. Yaghoubi and S Salemi, Fluid Phase Equilib. 2014, 365, 68-73 30. J.F. Hernández-Sánchez, L.A. Lubbers, A. Eddi and JH Snoeijer, Phys. Rev. Lett. 2012, 109, 3368-3375