Dynamic Wetting of Nanodroplets on Smooth and Patterned Graphene

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Dynamic Wetting of Nanodroplets on Smooth and Patterned Graphene-Coated Surface Shih-Wei Hung, and Junichiro Shiomi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01344 • Publication Date (Web): 02 Apr 2018 Downloaded from http://pubs.acs.org on April 2, 2018

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The Journal of Physical Chemistry

Dynamic Wetting of Nanodroplets on Smooth and Patterned Graphene-Coated Surface Shih-Wei Hung, Junichiro Shiomi,*

Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan

AUTHOR INFORMATION

Corresponding Author: [email protected]

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT Wettability of graphene-coated surface has gained significant attention due to the practical applications of graphene. In terms of static contact angle, the wettability of graphene-coated surfaces has been widely investigated by experiments, simulations, and theories in recent years. However, the studies of dynamic wetting on graphene-coated surfaces are limited. In the present study, molecular dynamics simulation is performed to understand the dynamic wetting of water nanodroplet on graphene-coated surfaces with different underlying substrates, copper, and graphite, from a nanoscopic point of view. The results show that the spreading on smooth graphene-coated surfaces can be characterized by the final equilibrium radius of droplet and inertial time constant. The dynamics of spreading of water nanodroplet on graphene-coated surface with patterned nanostructures on graphene is also carried out. Unlike the smooth graphene-coated surfaces, dynamic wetting on the patterned graphene-coated surfaces depends on the underlying substrate: the inhibition of wetting by the surface nanostructures is stronger for a hydrophobic underlying substrate than the hydrophilic substrate.

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INTRODUCTION Vast research efforts have targeted on graphene owing to its unique electronic, optical, chemical and mechanical properties.1–4 The advanced coating technique using graphene also benefits from its extraordinary properties, e.g. excellent chemical resistance, impermeability to gases, anti-bacterial properties, and mechanical strength.5 The practical application of graphene coatings requires further understanding of how the single-atom-thick sheet affects the surface properties of the underlying substrate, such as wetting. Recently, there have been extensive researches6–19 in quantifying the wetting behavior of graphene-coated surfaces in terms of static contact angle. An early work of Rafiee et al.11 found the “wetting transparency” of graphene, i.e. the wetting behavior of underlying substrate, where van der Waals forces dominate the wetting, is not significantly altered by the addition of graphene. However, the follow-up experimental studies demonstrate the graphene is not completely but partially transparent to wetting.9,10,12,14,15 Computer simulations6,7,12,13,15 and theoretical calculations6,8,12,15 also support the partial wetting transparency of graphene. Those researches indicate the monolayer graphene acts like a barrier, reducing the water-underlying substrate interaction. The progress in quantifying the static wetting on graphene-coated surface has been substantial, but the reported study of dynamic wetting on graphene-coated surface is 3



still limited. The dynamic wetting is a multiscale and complex problem as the classical hydrodynamic description breaks down at the moving contact line, and the nanoscopic features at the molecular scale needs to be considered.20 Thus, the dynamic wetting shows different behaviors at different length scales due to the size effect. A recent study of capillary filling in nanochannels21 demonstrates that the dynamic contact angle at the nanoscale differs significantly from the static contact angle. While molecular kinetic theory22 has been formulated to understand the advance of contact line in terms of kinetics of molecules, the most direct method to investigate the details of the dynamics is molecular dynamics (MD) simulation, which have been widely used to study dynamic wetting phenomena, particularly at the nanoscale.23–33 The results of MD simulations on flat surfaces are generally in agreement with the molecular kinetic theory.24–26,33 Although there is a limitation in the diameter of the simulated droplet, typically in the order of tens of nanometers (nanodroplet), MD simulations can trace the evolution of the droplet spreading, from which scaling of contact radius R can be directly obtained. When comparing with the macroscopic experiments of initial rapid wetting on flat surface that are typically studied with millimeter droplets, they exhibit some similarities in the scaling despite the large difference in the length scale; R evolves with time, t, as R~t1/2 for completely wetting surfaces23,34,35 in analogy to the

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scaling of an inertia-dominated coalescence,36,37 and the exponent decreases with decreasing wettability for partial wetting surfaces.30,31,38,39 The dominant physics that counteracts capillarity in the initial rapid wetting phase is expected to be mostly inertia and, for droplets at the microscale, the time histories of R for different droplet sizes coincide with each other by using the inertial scaling even for partial wetting surfaces.38 However, the inertial scaling does not capture the dependence on the wettability. As for the nanodroplets in MD simulations, no scaling for neither diameter nor wettability has been identified. On graphene-coated surfaces, Andrews et al.23 studied the nanodroplet spreading using MD simulation. Unlike the partial wetting-transparency in static wetting, the dynamic wetting of nanodroplet was found to be independent of the underlying substrates; the contact radius followed R~t1/2 regardless of the number of graphene layers or the wetting property of the underlying substrate. The study shed light on the inertia-dominated dynamic wetting of nanodroplets on graphene-coated surfaces. However, the scaling that incorporates both dependences on diameter and wettability is still unknown, and thus we aim to identify such scaling in this work. Furthermore, we investigate the sensitivity of the dynamic wetting on the surface structure with the scope of controlling the wetting phenomena through the geometry of the graphene

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layer, following series of works on macroscale droplets where large controllability by surface structures has been demonstarated.40,41 Here, the surface structure is altered by forming patterned defects in the graphene, which can be achieved using the ion beam technique.42,43

SIMULATION DETAILS MD simulations were performed to study the dynamic wetting of water droplet on a solid surface down to the nanoscale. Three sizes of water droplet with initial radii, Ri = 6.4, 9.0, and 12.8 nm, corresponding to 25,000, 50,000, and 100,000 water molecules, were considered to study the size effect. The model surfaces included graphene, graphite, monolayer graphene coated copper (MGC), bilayer graphene coated copper (BGC), and copper. For droplet at the nanoscale, the measured contact angle is affected by the line tension at the three-phase line.44 To eliminate the line tension effect,45 the quasi-two-dimensional (2D) system, droplet in cylindrical geometry, was implemented as shown in Fig. 1. The periodic boundary conditions were applied in all directions. The system size in the y direction was set to 5.92 nm, leading to an infinitely long cylindrical droplet. The system size in the x direction was set to 77.00 nm to ensure that the droplet does not interact with the periodic images. The cylindrical geometry is

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widely implemented in the studies of dynamic wetting of nanodroplet23,27,31,35 to achieve sufficiently large droplet sizes in a hydrodynamic regime, which is computationally expensive in spherical geometry. Besides, the contact problems such as dynamic wetting are essentially 2D phenomena.35 The previous study31 also demonstrates that even though the evolution of contact radius is different for droplets in the spherical and cylindrical geometries, the local processes at the contact line are independent of the geometry of droplet.

Figure 1. Snapshot of the initial state of dynamic wetting simulation of water droplet (Ri=12.8nm) on monolayer graphene coated copper (MGC) surface.

The Cu(111) surface was chosen and the graphite surface was represented by six graphene

layers.

The

separation

distance

between

copper–graphene

and

graphene-graphene was 0.326 nm46 and 0.34 nm,44 respectively. The extended simple 7



point charge (SPC/E) model47 was applied for water droplets. The Lennard-Jones (LJ) potential was implemented for the van der Waals interaction between water and solid surfaces. The LJ parameters of the interaction between oxygen atom of water molecule and carbon atom were ε=0.392 kJ/mol and σ=0.319 nm,44 while the LJ parameters were ε=5.067 kJ/mol and σ=0.272 nm48 for the interaction between oxygen atom of water molecule and copper atom. The difference between the water contact angles on rigid and flexible substrates has been shown to be negligible,44 and thus all atoms of solid surfaces were kept fixed at their equilibrium positions to reduce the computational cost. All simulations were performed with the GROMACS 4.6.749 and visualized with the software PyMOL.50 The simulations were carried out in a canonical ensemble with integrating time steps of 1.0 fs. The temperature was kept constant at 300 K using the Nosé−Hoover thermostat51,52 with a time constant of 0.2 ps. A cutoff distance of 2.0 nm was used for the nonbonded van der Waals (vdW) interactions. The electrostatic interaction was treated using particle-mesh Ewald summation method53 with a real-space cutoff distance of 2.0 nm. The water droplet was first equilibrated in the system without solid surfaces to achieve the circular shape. The equilibrated droplet was then placed at a location with

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a certain distance from the solid surface so that they start to interact. The droplet spreads on the solid surface spontaneously due to the solid-liquid interaction. To measure the contact radius of droplet, a square binning of local number of water molecules along the x and z directions with a bin size of 0.2 nm was performed. The liquid-gas interface was defined to be the contour of density = 500 kg/m3, which approximately corresponds to the middle value of bulk liquid and gas densities of water. The atom positions were recorded every picosecond to evaluate time histories of the contact radius evolution.

RESULTS AND DISCUSSION The static contact angle of droplet with Ri=6.4, 9.0, and 12.8 nm on graphene was calculated to be 89.6±3.5°, 89.9±3.5°, and 89.9±3.4°, respectively. The obtained contact angle on graphene is consistent with the previous simulation with the same model; the contact angle on graphene is around 90°.7,17 The static contact angles of droplet with Ri=12.8 nm are 64.5±3.5°, 78.4±2.5°, and 80.2±2.5° on MGC, BGC, and graphite, respectively. The copper surface is completely wetting, i.e. contact angle is zero. The values of static contact angles are in good agreement with the previous MD study12 using the same force field. The contact angle is increased significantly by the addition of a monolayer graphene. By adding two layers of graphene, the value of 9



contact angle approaches that of graphite, which indicates that the effect from underlying substrate can be shielded by bilayer graphene. Figure 2(a) shows how the contact radius of droplets with various initial radii evolves in time on surfaces with various wettabilities. The late-time spreading shows a dependence on droplet sizes that larger droplets spread faster than smaller ones. For surfaces with different wettabilities, the droplets spread faster on more hydrophilic surfaces. The observation is consistent with the microscale experimental results.38 The previous studies suggest that the spreading at the nanoscale operates in the inertial-dominated regime,23,35 thus the inertial scaling is adapted in Figure 2(b). The characteristic inertia time constant (ρRi3/γ)1/2, where ρ is the liquid density and γ is the liquid-vapor surface tension, comes from the balance of the inertial pressure inside the droplet and the capillary pressure associated with the droplet curvature.35 The values ρ=1000 kg/m3 and γ=72 mN/m are used in this work. The curves of droplets with different sizes on the same surface collapse onto one curve. However, the curves for surfaces with different wettabilities scatter, which was also observed in the previous macroscopic experiments.38 Now, since the final equilibrium radius, Rf, of droplet is related to the wettability of surface, we scale the radius by Rf instead of Ri, shown in Fig. 2(c). Note that the final equilibrium radius cannot be obtained for the copper

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surface, thus the profiles of copper surface are not included in this scaling analysis. Interestingly, all simulation profiles collapse onto one single curve, which suggests that the appropriate length scale and time scale to describe the dynamic wetting at the nanoscale are Rf and (ρRi3/γ)1/2, respectively. We here call this scaling the “modified inertial scaling”.

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Figure 2. Time histories of contact radius of droplets with varying sizes on surfaces with varying wettability (a) dimensional units, (b) inertial scaling, and (c) modified inertial scaling. The numbers in parentheses in (a) denote the static contact angle of Ri=12.8 nm droplet. 12


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In mind of enhancing the controllability of dynamic wetting, one possible strategy is to nanostructure the surface by restructuring the coated monolayer graphene. To this end, patterned holes with various sizes and shapes are formed to understand the effect of geometries of the surface nanostructures. Note that intentional introduction of such defects are now possible in experiments using the ion beam technique.42,43 Each structure was denoted with R(δx, δy) and T(δx, δy), as shown in Fig. 3, where R and T denote rectangular and triangle and δx and δy are the length of the hole in the x and y directions integer-multiples of 0.43 nm and 0.37 nm, respectively. For example, R(3, 4) indicates that a 1.29 nm × 1.48 nm rectangular hole is periodically repeated 20 times in the x direction and 2 times in the y direction. Two underlying substrate, copper and graphite, are chosen to study the influence of underlying substrate with different wettabilities.

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Figure 3. Top view of the patterned graphene-coated copper surface of (a) rectangular R(3,4) and (b) triangle T(4,4). δx and δy denote the pattern sizes in the x and y directions, respectively.

Figure 4 shows the contact radius profiles of droplet with Ri = 12.8 nm spreading on various patterned graphene-coated surfaces. The results demonstrate the droplets spread more slowly on the patterned-graphene coated surface than that on the smooth graphene-coated surface. Comparison between Fig. 4(a) and Fig. 4(b) indicates that the extent of this wetting inhibition depends on the underlying substrate, where the inhibition is stronger for the case of graphite underlying substrate (Fig. 4(a)) than the copper underlying substrate (Fig. 4(b)). The validity of modified inertial scaling is examined to the patterned graphene-coated surface in Fig. 5. For the graphite underlying substrate case (Fig. 5(a)), the profiles of different sizes of droplet are also analyzed. The results show that the profiles do not collapse as well as in the case of 14


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smooth graphene-coated surfaces. For the copper underlying substrate case (Fig. 5(b)), the profiles of patterned graphene-coated surfaces do not collapse and clearly differ from the profile of smooth graphene-coated surface. It indicates that the effect of the underlying substrate are enhanced because of the surface nanostructures. The importance of other effects, for example the line friction force, may be amplified on the patterned graphene-coated surfaces. Thus, although the modified inertial scaling works for droplets on the smooth graphene-coated surfaces, it no longer holds on the patterned graphene-coated surfaces.

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Figure 4. Time histories of contact radius of droplets on various patterned graphene-coated surfaces with (a) graphite and (b) copper as underlying substrates.

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Figure 5. Time histories of contact radius of droplets on various patterned graphene-coated surfaces using modified inertial scaling with (a) graphite and (b) copper as underlying substrates.

In order to quantify the effect of pattern size on the dynamic wetting, the spreading speeds are calculated. The spreading speed is defined as the average contact line speed over the initial 500 ps (dash line in Fig. 4), i.e., dividing the contact radius at 500 ps by 500 ps. The multiple regression analysis is applied to relate the spreading speed to the

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size of pattern, δx and δy, as shown in Fig. 6. Note that the results of triangular patterned cases are not shown in Fig. 6 because the effect of triangular pattern on dynamic wetting is difficult to separate in the x and y directions, respectively. The results reveal that the effect of surface nanostructures on dynamic wetting is more obvious on the graphite underlying substrate case than that on the copper one. The difference in spreading speed is 18.35% for the graphite underlying substrate case and it is only 7.77% for the copper one. It implies that the dynamic wetting can be manipulated more effectively by the design of pattern size for the graphite underlying substrate than the copper one. Also, it is shown that the spreading speed correlates to δy, which is perpendicular to the spreading direction, more than to δx, which is parallel to the spreading direction. The larger values in δy (larger pattern size in the y direction) induce more resistance for droplet spreading on both underlying substrates. The behavior can be attributed to the contact line pinning effect of spreading. The pinning effect has been shown to be important for the spreading on the textured surfaces with micro-structures.41,54 On nanostructured surfaces, the contact angle hysteresis shows the dependence on the area density of defects, indicating that the defects pin the contact line of droplet.55 It was also shown that the macroscopic pinning behavior is preserved for nanostructures with dimensions down to ~200 nm.56 On the other hand,

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the contributions of δx to the dynamic wetting are opposite for these two underlying substrates, i.e. positive coefficient for the graphite underlying substrate case and negative coefficient for the copper one, as shown in Fig. 6. In order to depict the phenomena clearly, the top views of spreading of water adjacent to the surface, within 0.5 nm, are displayed in Fig. 7 for these two underlying substrates. For graphite underlying substrate case, the contact line is pinned on the boundary of hole in both the x and y directions, as shown from t = 500 ps to 560 ps. The pinning effect in the both directions can also be observed for copper underlying substrate case from t = 430 ps to 490 ps. When water molecules contact the copper surface (t = 520ps), the spreading is enhanced because copper is more hydrophilic than graphene. For graphite underlying substrate case, the larger values in both δx and δy form more resistance for droplet spreading due to the pinning effect. The slower spreading and higher hydrophobicity was also observed on the defective graphene surface.8 For copper underlying substrate case, the larger values in δy slow down the spreading while the larger values in δx enhance the spreading. Due to the competition between these two effects, the spreading processes are insensitive to the pattern sizes in the early regime.

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Figure 6. Spreading speed of droplets as a function of pattern size, δx and δy, on various patterned graphene-coated surfaces with (a) graphite and (b) copper as underlying substrates.

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Figure 7. Top view of spreading of water molecules adjacent to R(7,8) patterned graphene-coated surface with (a) graphite and (b) copper as underlying substrates. Coated graphene in green, graphite in gray, and copper in yellow.

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CONCLUSION MD simulations are implemented to study the dynamics wetting of water droplet on graphene-coated surface with different underlying substrates, copper, and graphite. The influence from underlying substrate on the both static contact angle and dynamic spreading can be weakened significantly by the addition of one layer of graphene. The dimensional analysis demonstrates that the dynamic wetting can be characterized by the inertial time constant and final equilibrium radius for the nanodroplets. For patterned graphene-coated surfaces, the modified inertial scaling does not hold, indicating other effects, such as line friction force, become important due to the surface nanostructures. Unlike the smooth graphene-coated surfaces, the dynamic wetting shows strong dependence on the underlying substrate. For the graphite underlying substrate case, the spreading speed decreases and hydrophobicity increases with the increasing size of holes. The dependence of early-time spreading on pattern size is weaker for the copper underlying substrate case, because of the competition between the strong attraction from copper surface and pinning effect. The results indicate that the manipulation of spreading can be achieved by modifying the nanostructures of graphene on hydrophobic underlying substrate.

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Notes The authors declare no competing financial interests.

AKNOWLEDGEMENTS This work was financially support by Grant-in-Aid for JSPS Fellows (Grant No. 26-04364). S.-W. H. was financially supported by JSPS Postdoctoral Fellowship for Overseas Researchers Program (26-04364).

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Dynamic Wetting of Nanodroplets on Smooth and Patterned Graphene

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