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The self-driving of water droplets on textured substrate is momentous for understanding the directional transport of water on biological surface. In this paper, a novel design of monolayer graphene-covered wedge-shaped copper substrate (GWCS) is put forward to realize the directional and ultrafast spontaneous driving of water droplets from the tip of the wedge-shaped substrate to the wide end. The self-driving behaviors of water droplets on GWCS are studied by classical molecular dynamics. The results show that the maximum spontaneous driving velocity of water droplet driven by surface wetting gradient and Young-Laplace pressure gradient can reach 73.8 m/s. The law of energy variation during the whole droplet self-driving on GWCS indicates that there is a competitive relationship between the potential energy of water droplet and the interaction energy between the droplet and GWCS, i.e. the interaction energy between water droplet and GWCS is partially converted into the potential energy of water droplet. The relationship of the maximum displacement of water droplet with the wedge angle, wettability of GWCS and the droplet surface tension is proposed in theory, and the influence of the discontinuous linear increase of the wedge-shaped substrate width on a nanoscale on the self-driving is analyzed and used to explain the little difference between the theoretical and simulation results. Furthermore, a smaller droplet is easier to obtain larger spontaneous driving velocity, and the influence of long-distance decelerating motion of high-speed small droplet on the non-wetting gradient substrate on the droplet displacement law is clarified. Finally, the mechanism of graphene suspended on both sides of the wedge-shaped copper structure to enhance the droplet transport efficiency is determined. The results will have theoretical significance in designing the functional texture surface covered by monolayer graphene to realize droplet self-driving.
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图 1 水纳米液滴在GWCS上定向运输模型 (a)楔形铜基底模型的俯视图和A-A方向剖视图, 楔形铜基底包括中间的楔形基底、楔形基底两侧的凹槽和凹槽底部底板; (b)水纳米液滴在GWCS上的俯视图和正视图. 粉色是铜基底, 黑色是单层石墨烯, 红白相间的球是水纳米液滴
Figure 1. Uni-directional self-driving model of a water nanodroplet on GWCS: (a) Top view and A-A sectional view of wedge-shaped copper substrate, the wedge-shaped copper substrate includes wedge-shaped substrate in the middle, grooves on both sides of the wedge-shaped substrate and a copper plate at the bottom of the grooves; (b) top view and front view of water nanodroplet on GWCS. The pink is Cu substrate, the black is monolayer graphene, and the red and white sphere is water nanodroplet.
图 2 液滴自驱动的速度、位移与时间的关系, 液滴直径为8 nm, 楔形基底角度为40°, 插图分别为液滴在0.35和1.00 ns时的运动状态, 单层石墨烯模型设置为线条结构且未显示铜基底底板
Figure 2. Velocity and displacement of the water droplet self-driving on GWCS. The diameter of the water nanodroplet is 8 nm, and the wedge angle of GWCS is 40°, the illustrations show the motion of the droplet at 0.35 and 1.00 ns, respectively. The monolayer graphene model is set to linear structure and the bottom plate of copper substrate does not show.
图 3 (a) 液滴前进方向所受的合力F和速度随时间的变化关系; (b) 液滴的势能、液滴与GWCS之间的相互作用能随时间的变化关系. Ew-Cu, Ew-G和Ew-GCu分别为液滴与铜基底、石墨烯、GWCS之间的相互作用能, Ew为液滴的势能
Figure 3. (a) Resultant force F and velocity of the droplet in +x direction as a function of time; (b) potential energy of water droplet and the interfacial interaction energy between water droplet and GWCS versus time. Ew-Cu is the interaction energy between water droplet and copper substrate, Ew-G is the interaction energy between water droplet and graphene, Ew-GCu is the interaction energy between water droplet and GWCS, Ew is the droplet potential energy.
图 4 液滴自驱动过程中在GWCS上的两种接触状态的俯视图和正视图(未显示铜基底底板, 且俯视图中的单层石墨烯为线条结构) (a) 液滴在GWCS上的接触面包括楔形基底和沟槽正上方的单层石墨烯; (b) 液滴完全处于楔形基底上
Figure 4. Top and front view of two contact states of the water droplet on GWCS in the self-driving process (the bottom plate of copper substrate is not shown, and the monolayer graphene in the top view is linear structure): (a) Contact area of the droplet on the substrate includes the wedge-shaped substrate and the graphene right above the groove; (b) droplet is completely on the wedge-shaped substrate.
图 5 (a) 液滴在楔形基底上的驱动力示意图; (b) 液滴达到最大位移时所在基底上的位置
Figure 5. (a) Driving force diagram of the droplet on GWCS; (b) position of the droplet on the substrate when the droplet reaches the maximum displacement.
图 6 楔形基底角度对液滴自驱动的影响 (a) 液滴运动速度; (b) 液滴的位移随时间的变化关系
Figure 6. Influence of the wedge angle of GWCS on the droplet self-driving behaviors: (a) Velocity and (b) displacement of the droplet on GWCS with different wedge angles versus time.
图 7 不同角度的楔形铜基底, x方向每间隔距离k, y方向增加两层铜原子宽度
Figure 7. For the GWCS with different wedge angles, when the interval distance is k in x direction, the width of the wedge-shaped copper substrate increases two layers of copper atoms in y direction.
图 8 液滴在不同楔角GWCS上的自驱动最终位移、所在位置楔形基底宽度的模拟值与理论值对比
Figure 8. Comparison of the simulation and theoretical results of the final self-driving displacement and the width of wedge-shaped substrate with different wedge angles respectively.
图 9 液滴直径在6−9 nm范围内时液滴尺寸对液滴自驱动的影响 (a) 液滴的速度和(b)液滴的位移随时间的变化关系, 插图为6 nm液滴的最终位置; (c) 液滴最大位移的模拟值与理论值随液滴直径的变化关系和模拟值与理论值的差值相对于液滴直径的比率
Figure 9. Influence of water droplet size on the droplet self-driving behaviors when the droplet diameter in the range of 6−9 nm: (a) Velocity and (b) displacement versus time, the illustration is the final position of the 6 nm droplet; (c) simulated and theoretical values of the droplet displacement versus droplet diameter, and the ratio of the difference between the simulated value and the theoretical value to the droplet diameter.
图 10 楔形铜结构两侧凹槽深度对液滴自驱动的影响 (a) 液滴的速度和(b)液滴的位移随时间的变化关系; (c) 8 nm直径液滴在凹槽深度为0.904 nm的GWCS上最终运动状态
Figure 10. Influence of groove depth on both sides of wedge-shaped copper structure on the droplet self-driving: (a) Velocity and (b) displacement of droplet versus time; (c) final motion state of 8 nm diameter droplet on GWCS with 0.904 nm groove depth.
表 1 不同原子之间的LJ势能参数
Table 1. Parameters of LJ potential between different atoms.
Atomic pairs σ ε/meV O-C 3.280 5.13 O-Cu 2.737 34.34 C-Cu 2.857 24.96 
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[1] Parker A R, Lawrence C R 2001 Nature 414 33
Google Scholar
[2] Zhang S N, Huang J Y, Chen Z, Yang S, Lai Y K 2019 J. Mater. Chem. A 7 38
Google Scholar
[3] Ju J, Bai H, Zheng Y M, Zhao T Y, Fang R C, Jiang L 2012 Nat. Commun. 3 1247
Google Scholar
[4] Yi S Z, Wang J, Chen Z P, Liu B, Ren L, Liang L, Jiang L L 2019 Adv. Mater. Technol. 4 1900727
Google Scholar
[5] Yang X, Zhuang K, Lu Y, Wang X 2021 ACS Nano 15 2589
Google Scholar
[6] Dai H Y, Gao C, Sun J H, Li C X, Li N, Wu L, Dong Z C, Jiang L 2019 Adv. Mater. 31 1905449
Google Scholar
[7] Daniel S, Chaudhury M K, Gennes P G 2005 Langmuir 21 4240
Google Scholar
[8] Habenicht A, Olapinski M, Burmeister F, Leiderer P, Boneberg J 2005 Science 309 2043
Google Scholar
[9] Ang B T W, Zhang J, Lin G J, Wang H, Lee W S V, Xue J M 2019 ACS Appl. Mater. Interfaces 11 27464
Google Scholar
[10] Lin Y C, Hu Z Y, Gao C L, Guo Z Y, Li C, Zheng Y M 2018 Adv. Mater. Interfaces 5 1800962
Google Scholar
[11] Ju J, Zheng Y M, Jiang L 2014 Acc. Chem. Res. 47 2342
Google Scholar
[12] Wang Q B, Yao X, Liu H, Quere D, Jiang L 2015 Proc. Natl. Acad. Sci. U. S. A. 112 9247
Google Scholar
[13] Liu C R, Sun J, Li J, Xiang C H, Che L F, Wang Z K, Zhou X F 2017 Sci. Rep. 7 7552
Google Scholar
[14] Hu B B, Duan Z F, Xu B J, Zhang K J, Tang Z X, Lu C, He M J, Jiang L, Liu H 2020 J. Am. Chem. Soc. 142 6111
Google Scholar
[15] Zhou H, Jing X S, Guo Z G 2020 Langmuir 36 6801
Google Scholar
[16] Wang F C, Wu H A 2013 Soft Matter 9 5703
Google Scholar
[17] Yuan Q Z, Huang X F, Zhao Y P 2014 Phys. Fluids 26 092104
Google Scholar
[18] Verho T, Bower C, Andrew P, Franssila S, Ikkala O, Ras R H A 2011 Adv. Mater. 23 673
Google Scholar
[19] Chen H W, Zhang L W, Zhang P F, Zhang D Y, Han Z W, Jiang L 2017 Small 13 1601676
Google Scholar
[20] Li J Q, Zhou X F, Li J, Che L F, Yao J, McHale G, Chaudhury M K, Wang Z K 2017 Sci. Adv. 3 eaao3530
Google Scholar
[21] Vakarelski I U, Patankar N A, Marston J O, Chan D Y C, Thoroddsen S T 2012 Nature 489 274
Google Scholar
[22] Liu M J, Li J, Zhou X F, Li J Q, Feng S L, Cheng Y Q, Wang S, Wang Z K 2020 Adv. Mater. 32 1907999
Google Scholar
[23] Rafiee J, Mi X, Gullapalli H, Thomas A V, Yavari F, Shi Y F, Ajayan P M, Koratkar N A 2012 Nat. Mater. 11 217
Google Scholar
[24] Xie Q, Alibakhshi M A, Jiao S P, Xu Z P, Hempel M, Kong J, Park H G, Duan C H 2018 Nat. Nanotechnol. 13 238
Google Scholar
[25] Huang Q J, Zhang Z Q, Liu Z, Zhang F J, Cheng G G, Ding J N 2021 Appl. Surf. Sci. 542 148666
Google Scholar
[26] Ma M, Tocci G, Michaelides A, Aeppli G 2016 Nat. Mater. 15 66
Google Scholar
[27] Zhang Z Q, Zhang F J, Huang Q J, Cheng G G, Ding J N 2020 Appl. Surf. Sci. 515 145976
Google Scholar
[28] Zhang Z Q, Guo X F, Tang H Y, Ding J N, Zheng Y G, Li S F 2019 ACS Appl. Mater. Interfaces 11 28562
Google Scholar
[29] Guo Y F, Guo W L 2006 Nanotechnology 17 4726
Google Scholar
[30] Ye H F, Zheng Y G, Zhang Z Q, Zhang H W, Chen Z 2016 Nanotechnology 27 315702
Google Scholar
[31] Papadopoulou E, Megaridis C M, Walther J H, Koumoutsakos P 2019 ACS Nano 13 5465
Google Scholar
[32] Horn H W, Swope W C, Pitera J W, Madura J D, Dick T J, Hura G L, Head-Gordon T 2004 J. Chem. Phys. 120 9665
Google Scholar
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