Molecular Dynamics Simulation of Water Nanodroplet Bounce Back

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Molecular dynamics simulation of water nanodroplet bounce back from flat and nanopillared surface Takahiro Koishi, Kenji Yasuoka, and Xiao Cheng Zeng Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02149 • Publication Date (Web): 06 Sep 2017 Downloaded from http://pubs.acs.org on September 7, 2017

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Molecular dynamics simulation of water nanodroplet bounce back from flat and nanopillared surface Takahiro Koishi,∗,† Kenji Yasuoka,‡ and Xiao Cheng Zeng∗¶ †Department of Applied Physics, University of Fukui, 3-9-1 Bunkyo,Fukui 910-8507, Japan ‡Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan ¶Department of Chemistry, University of Nebraska, Lincoln, Nebraska 68588 E-mail: [email protected],[email protected]

Abstract Molecular dynamics simulations of impinging nanodroplets were performed to study the bounce back condition for flat and nanopillared surfaces. We found that the bounce back condition can be closely related to the degree of droplet deformation upon collision with the solid surface. When the droplets have little or small deformation, the bounce back condition solely depends on the hydrophobicity of the surface. On the other hand, when the droplet deformation is large, the impinging velocity dependence of the bounce back condition becomes stronger due to the increase of the liquid-vapor interfacial area of colliding droplet, which is proportional to the liquid-vapor surface energy. The impinging droplet simulations with nanopillared surfaces were also performed. The contribution of droplet deformation in this case is relatively small because the surface hydrophobicity is enhanced due to the existence of pillars. Finally, we find that the maximum spreading diameter of the impinging droplets exhibits consistent

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trend, in terms of the Weber number dependence, as the experimental measurements with macrodroplets.

Introduction Impact of water droplets is ubiquitous in nature and has fascinated researchers for decades. 1 Despite of a long history of considerable efforts by researchers, the dynamical behavior of impinging water droplet is still not fully clarified. A better understanding of the phenomenon is required for industrial applications such as surface self cleaning, anti-icing and ink-jet printing. Many types of strongly hydrorepellent surface have been developed to achieve superhydrophobicity with which impinging water droplets can bounce back. 2–10 In particular, the contact angle on the multiscale hierarchical surface structures 5,8 is greater than 165◦ and the contact time of bouncing back is reduced due to the strong superhydrophobic effect. Since air is trapped between a droplet bottom and the surface, the droplet is in contact with the composite solid-air interface which results in lower free energy. This state of droplet is called the Cassie state, the favorable state for the droplet bounce back compared to the Wenzel state in which the droplet is in contact with the surface without air pockets. Nanoscale structure can be fabricated onto a surface with microscale roughness to achieve the hierarchical surface. This hierarchical structure is inspired from water-repellent surfaces in nature, such as lotus leaf, rose petal and water striders’ legs. 11–14 The impinging velocity dependence of bouncing droplet was reported previously by researchers. 15,16 While droplets with lower impinging velocity do not bounce back on the superhydrophobic surface, bounce-back events were observed when the impinging velocity was faster than a critical velocity. If the impinging velocity of a droplet is higher than the other critical velocity, the droplet cannot bounce back due to the Cassie-Wenzel transition in which water can intrude between the surface structures and the contact line of droplet


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can be strongly pinned at the surface. The bounce back behavior can be classified into three distinct regimes: low velocity non-bouncing droplet, moderate velocity bouncing droplet, and high velocity sticky droplet. 15 Many studies have been devoted to investigate spreading dynamics of impinging droplets. 17–20 In the colliding process, the droplet first expands in the radial direction until reaching its maximum diameter, then retracts to recover a spherical shape. It is known that the Weber number governs the spreading dynamics and has been used to compare the maximum diameters of different scale droplets. The Weber number is dimensionless and defined by W e = ρv 2 D0 /γ, where ρ is the density of droplet, v is the impinging velocity, D0 is the initial droplet diameter and γ is the surface tension. Visser et al. performed experiments of impinging micrometer-sized droplets at high velocities (v > 10 m/s) on hydrophilic and hydrophobic surfaces. 20 The Weber number dependences of the normalized maximum spreading diameter of micro droplets were compared with that of millimeter-sized droplets. The results were in fairly good agreement and the scale-invariance of the impinging events were observed. Richard and Quéré studied the energy transfer of impinging droplets bouncing on superhydrophobic surfaces. 21 They observed the restitution coefficient, defined as the ratio of the velocities after and before the bouncing, as a function of the impinging velocity. The observed values, close to 0.9, are independent of the impinging velocity in the wide velocity range. To confirm the effects of viscosity and contact angle hysteresis for dissipating energy, they used rubber balloons filled with a mixture of water and glycerol whose viscosity is larger than that of water. The rubber balloons were employed to represent the droplet bouncing on the superhydrophobic surface. The results are close to those of water droplets, confirming negligibility of the effects of viscosity and contact angle hysteresis. They also found that the source of energy dissipation was the droplet oscillation after the bouncing and a part of the impinging kinetic energy was transferred into internal modes of vibration. Mesoscopic simulations have been performed by previous researchers using the lattice


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Boltzmann method. 22–25 The three distinct regimes of the bounce back behavior 15 were reproduced and a fourth regime was found between the bounce back and the sticky regimes by Hyväluoma et al. 22 In the fourth regime, a non-bouncing droplet that ends up in the Cassie state was observed. They also estimated the energy dissipation during the droplet impact, using the strain-rate tensors. 23 The energy dissipation occurs strongly when the droplet first encounters the surface, and later at the withdrawal of the liquid from between surface pillars. Zhang et al. 24 also used the lattice Boltzmann method to study the impact of water droplets on superhydrophobic surfaces with a wettability gradient. They found that droplet can bounce back toward both directions, i.e., following and against the wettability gradient. Their simulation results indicated that the bounce-back directions depend on the impinging velocity, droplet size, and areal density of surface pillars. Some molecular dynamics (MD) simulations have been performed to investigate the microscopic behavior of impinging droplets. Since the impinging process takes place in a time span of sub-microseconds for nano scale droplets, it is difficult to observe it experimentally. The MD simulation which simulates molecular motion at femto second scale is a useful tool to study the detailed impinging process of nano scale droplets. The MD simulations of impinging metal clusters, such as molybdenum, 26 aluminum 27 and copper, 28 were performed to investigate deposition, deformation and fragmentation on the surface of the same metal species 26,27 and the rigid surface. 28 Tomsic et al. reported both experiments and MD simulations of impinging ice clusters on hot surfaces. 29–32 The evaporation and bouncing of the ice clusters were studied at surface temperatures between 300 and 1400 K. They found the two types of bounce back behaviors; evaporation and elastic bouncing. When the surface temperature was 1400 K, the impinging ice clusters, whose initial temperature was 180 K, were heated by the hot surface and bounce back due to evaporation of monomers and small fragments of water molecules on the surface. 30 When the surface temperature was 300 K, the impinging velocity at which the bounce back observed was 200 m/s for the ice clusters whose initial temperatures were 0 and 47 K in their simulations. 31 The bounce back condition was


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confined to a narrow range of impinging velocities and temperatures of the ice clusters and the surfaces. At a lower impinging velocity, the ice clusters tend to be trapped at the surface because of the less kinetic energy. At the faster impinging velocity, the ice clusters were deformed plastically and also trapped at the surface. When the surface temperature was above 300 K, the ice clusters melted at the surface. Since the melting resulted in a lager contact area and a stronger binding between the cluster and the surface, the ice cluster cannot bounce back. In this work, unlike previous MD studies, we comprehensively estimated the impinging velocities and the surface hydrophobicity dependences of the bounce back conditions for a water droplet at room temperature using MD simulations. The obtained bounce back condition is plotted on a regime map in which the horizontal and vertical axes are the impinging velocities and the surface hydrophobicity, respectively. The map provides the boundary between the bounce back state and non-bounce back state and reveals the contribution of droplet deformation for the bounce back condition. The energy transformation of the kinetic energy of impinging velocity is also discussed. While the droplet oscillation after collision, regarded as the source of energy dissipation experimentally, 21 is not seen here due to the large difference of droplet size, it is shown that a part of the kinetic energy of impinging velocity is transformed to the liquid-vapor surface energy, providing the energy source of the bounce back.

System and Interactions The MD simulation system contains a water droplet and a flat or nanopillared surface. The flat surface is the (0001) graphite surface with hexagonally arranged carbon atoms. During the simulation carbon atoms are fixed. The nanopillared surface consists of an ordered array of quadrangular nanopillars with the lateral size of each nanopillar being 12.3 ˚ A × 12.8 ˚ A. The spatial interval between the nanopillars is 12.3 ˚ A and 12.8 ˚ A in the x and y direction,


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respectively. This near-square-lattice arrangement for the nanopillar array has been used previously by Lundgren et al. 33,34 The height of the nanopillar (Ln ) is varied from 3.4 ˚ A to 20.1 ˚ A, corresponding to Ln = 1, 2, 4 and 6 stacked graphene layers, respectively. The projected area of the surface is 168.3 ˚ A × 169.7 ˚ A. A rigid-body model of water, the SPC/E model, 35 is employed for water droplet modeling. The potential function of the SPC/E model includes two terms, a Coulomb term and a Lennard-Jones (LJ) term. Carbon atoms of the graphite are treated as LJ particles whose size and energy parameters are 3.4 ˚ A and 0.2325 kJ/mol, respectively. 36 The hydrophobicity parameter, khb , is introduced to control interaction strength of the LJ interaction between O atoms of water and C atoms of surface as,

ϕLJ-OC (rij ) = 4khb εOC

(  σ 

)12 OC

rij

(

σOC − rij

)6   

.

(1)

Note that here the hydrophobicity of the surface is defined based on the contact angle of a water droplet. When the hydrophobicity parameter, khb , is 1.0, the contact angle of water droplet on both the flat and pillared surfaces is defined as the inherent contact angle. The contact angle increases with decreasing the hydrophobicity parameter.

Results and Discussion Contact Angles of Droplets To evaluate the hydrophobicity of the flat and nanopillared surfaces, we estimated the contact angle of water nanodroplets equilibrated on both surfaces. The results are shown in Fig. 1. The details of computation method to estimate the contact angle are given in our previous papers. 37,38 In the original graphite surfaces (khb = 1), the inherent contact angle is 90◦ and the contact angles increase with increasing the pillar height clearly. The contact angles also increase as the hydrophobicity parameter, khb , increases. These trends are consistent


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with the results of Landgren et al. 33,34 Although the initial state of droplets is Cassie at all conditions considered, the droplets with (Ln , khb ) = (1, 0.1), (1, 1.0), (2, 1.0) (plotted as solid squares and solid diamonds) change into the Wenzel state. The other droplets maintained the Cassie state (plotted as open squares and open diamonds) and their contact angles converge about 160◦ . These results show that the pillar height has less influence on the contact angles when the hydrophobicity of nanopillared surfaces is very high. 180

contact angle (deg.)

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super hydrophobic

150

Ln=4 Ln=2 Ln=1 Ln=0 (flat)

100

−2

−1

10

10 khb

0

10

Figure 1: Contact angles of water nanodroplets versus the hydrophobicity parameter khb at different height of nanopillars Ln .

Spreading Dynamics Upon Collision with Surface The time dependences of the droplet center of mass was calculated to determine which state of the impinging droplet right after the collision with the surface: bounce back (B) state, or non-bounce back (NB) state. The z-component of the center of mass at different time is shown in Fig. S1. The impinging droplet collided at t = 10 ps on the surfaces of khb = 0.02 have B state. On the other hand, for the surface of khb = 0.10 (less hydrophobicity), the droplet adhere to the surface and exhibits the NB state. Clearly, the surface hydrophobicity, controlled via the parameter khb , has marked effect on the state of the impinging nanodroplet after collision. 7 ACS Paragon Plus Environment

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The spreading dynamics of the impinging droplets can be characterized by the maximum spreading diameter. The latter is related to magnitude of the impinging velocity, the surface tension, and the interaction between the droplet and the surface. The maximum spreading diameter can be also correlated with the Weber number which is dimensionless parameter that includes the factors of surface tension, drop diameter and impact velocity. Note that the dependence of the normalized maximum spreading diameter on the Weber number has been previously studied experimentally to compare the spreading dynamics of the impinging macroscopic droplets. 20 Here, we estimated the maximum spreading diameter from the time dependence of droplet diameter as shown in Fig. S2(a). The initial and maximum diameters are calculated from the average between x- and y-diameters,

D0 = Dmax

D0x + D0y , 2 Dmax-x + Dmax-y = , 2

(2) (3)

respectively, as shown in Fig. S2(b) and (c). The Weber number dependence of normalized maximum spreading diameter is plotted, together with previous experimental results, 17–20 in Fig. 2. Despite of drastically different length scales of the droplets, our results appear to be correlated with the experimental results quite well in the trend of the Weber number dependence. Since the Weber number involves factors of the impinging velocity and the diameter of droplet, it varies when the impinging velocity and/or the diameter are changed. In Fig. 2, the black and green points denote variation of the droplet size in the experiment while the blue and cyan points denote the variation of the impinging velocity in the experiment. It seems that our results for the Weber number near 100 are closer to the blue and cyan points because in our simulations the Weber number is varied with through change of the impinging velocity. The Weber number of our results are limited by the maximum impinging velocity. When the velocity is higher than the maximum, the impinging droplets would splash and split into small droplets. The


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MD simulations of much larger droplets are required to extend the Weber number range for computing their maximum spreading diameters. 6 5 4

Dmax / D0

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D0 = 36 µm-84 µm (Van Dam) D0 = 12 µm-100 µm (Visser) D0 = 50 µm for Glass (Visser) D0 = 50 µm for RainX (Visser) D0 = 6.9 nm (this work)

3

2

1

0

2

10

10

Weber Number

Figure 2: Weber number dependence of normalized maximum spreading diameters


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Bounce Back Conditions on Flat Surface Since whether the impinging droplet selects the B state or NB state upon collision depends on both the surface hydrophobicity parameter and the impinging velocity of droplet, we performed another independent series of MD simulations in which both the surface hydrophobicity parameter and the impinging velocity were changed. The simulation results for the flat surface are summarized in Fig. 3. The boundary between B and NB states can be divided into three ranges: (i) no deformation range (vd ≤ 100 m/s), (ii) small deformation range (100 m/s < vd ≤ 500 m/s), and (iii) large deformation range (500 m/s < vd ). In the first range, the impinging droplets are little deformed upon collision, and the bounce back condition solely depends on the hydrophobicity of the surface. In the second range, the boundary is nearly independent on the impinging velocity. It means that the bounce back condition is solely dependent on the surface hydrophobicity, and the contribution of droplet deformation should be small. The sequential snapshots of B (run A) and NB (run B) states in this range are shown in Fig. 4(a) and (b). The deformation of the droplet upon collision with the surface is relatively small in both run A and B. Hence, the bounce back droplet in run A is largely due to the higher surface hydrophobicity. In the third range, the contribution of droplet deformation is apparent. The sequential snapshots of B (run C) and NB (run D) states are also shown Fig. 4(c) and (d). While the surface hydrophobicity in run C is weaker than that in run A, and the interaction between the surface and the droplet in run C is stronger, the droplet can still bounce back. The reason should be due to the large droplet deformation. Since the deformation increases with increasing the impinging velocity, the boundary between B and NB states moves towards weaker surface hydrophobicity (larger khb ) as the the impinging velocity increases. When the surface hydrophobicity is much weaker and the interaction between the surface and the droplet is much stronger, the droplet shows the NB state in run D. The energy difference between normal and deformed droplets should be the energy source contributed to droplet bounce back. We have also computed temperature-distribution maps and radial components of molecule 10 ACS Paragon Plus Environment

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velocities of the colliding droplet to show the flow of kinetic (thermal) energy. The radial component is defined as the expanding and retracting direction component of a colliding droplet in the xy-plane. The temperature of the lower part of the droplet (near the surface) is higher than that of other parts when the radial velocity is increasing. The friction between the droplet and the surface appears to raise the temperature of the lower part when the droplet is acceleratingly expanding. Figures of these results are shown in Supporting Information (SI). 10

B

run C

run D

2

downward velocity, vd (10 m/s)

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5

run A

0

−2

10

NB

run B

−1

10 khb

0

10

Figure 3: Bounce back condition on flat surfaces. The conditions of B and NB states are plotted as solid circles and triangles, respectively


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6 ?

1 ps

20 ps

50 ps

100 ps

200 ps

(a) run A, vd = 200 m/s, khb = 0.02

?

1 ps

20 ps

50 ps

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(b) run B, vd = 200 m/s, khb = 0.03

6 ?

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(c) run C, vd = 800 m/s, khb = 0.06

?

1 ps

20 ps

50 ps

100 ps

(d) run D, vd = 800 m/s, khb = 0.20 Figure 4: Sequential snapshots of colliding droplets


200 ps

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Bounce Back Conditions on Nanopillared Surface MD simulations of impinging droplet on nanopillared surfaces were performed to study the effect of roughness via controlling the height of nanoscale pillars. The pillar height dependence of the bounce back conditions is illustrated in Fig. 5(a)-(d). The sequential snapshots of runs A and B corresponding to B and NB states for each condition are shown in Fig. S5S8 of Supporting Information. It is known that the apparent contact angle of a droplet on nanopillared surfaces is larger than the contact angle on the corresponding flat surface, both in the Wenzel and Cassie states of droplet. 34,37,38 As a result, the surface hydrophobicity is enhanced due to the existence of pillars. Hence, the boundaries between B and NB states shift to less hydrophobicity region (larger khb ) due to the increase of net hydrophobicity of the nanopillared surface. The summarized boundary curves in Figs. 3 and 5 are shown in Fig. 6. In the impinging velocity range of vd > 500 m/s, the boundary curves of Ln = 1, 2 are similar to that of the flat surfaces and have the khb dependence. It suggests that the contribution of droplet deformation is dominant, and the effect of pillars is limited due to the low pillar height. On the other hand, the khb dependence of the boundary curves is relatively weak for the nanopillared surfaces of Ln = 4, 6. Since the deformation of impinging droplet is less affected by pillars on the higher nanopillared surfaces as shown in Fig. S7 and S8, the difference of B and NB states should depend on the net hydrophobicity of the surface, including the pillar height. The agreement of the boundaries of Ln = 4, 6 suggests that the decrease of hydrophobicity due to the pillar height increase has little effect when the pillar height is Ln = 6 or above. When the impinging velocity is 100 m/s, the droplets cannot touch the bottom surface of Ln = 4, 6, but that of Ln = 1, 2 the droplets can be touched. When the impinging velocity is higher than 400 m/s, all droplets can touch the bottom surface. The droplets which fully penetrate between pillars take the Wenzel state at that moment of the touching. After that, these droplets having the NB state could take the Cassie or Wenzel states. In Figs. 5(a)-(d), 13 ACS Paragon Plus Environment

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the conditions of the NB state plotted as open and solid triangles are for the Cassie and Wenzel state, respectively. The droplets tend to be in the Cassie state near the boundary for the higher nanopillared surfaces, Ln = 4, 6, suggesting that the Cassie state is likely the global minimum state of the free energy due to the higher hydrophobicity. When the hydrophobicity parameter khb is large, the Wenzel state is the most stable state due to the stronger attractive interaction between the droplet and the surface. run B

B

run A

run B

2

run A


10

B

2


10

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5

NB 0

−2

−1

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10 khb

NB 0

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(a) Ln = 1

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10

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(b) Ln = 2 10 run B

B

run A

run B

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run A

2

B


10 downward velocity, vd (10 m/s)

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5

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NB 0

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10

−1

10 khb

NB 0

0

10

−2

10

(c) Ln = 4

−1

10 khb

10

0

(d) Ln = 6

Figure 5: Bounce back conditions on nanopillared surfaces. The conditions of B states are plotted as solid circles. The conditions of NB states with the Cassie and Wenzel states are plotted as open and solid triangles, respectively.


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10 2


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Ln=0 (flat) 5

Ln=1

Ln=6 Ln=2 Ln=4

0

−2

10

−1

10 khb

0

10

Figure 6: The boundary between B and NB states of flat and nanopillared surfaces.


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Energy Transformation To gain more insights into the bounce back conditions, the energy source to offset the adhesive energy between the droplet and the surface should be analyzed in details. Since the N V E ensemble is employed in the MD simulations, the total energy of the system is conserved and as such, the time dependence of the energy transformation between the kinetic and potential energies can be monitored. The time dependence of the kinetic and potential energies of a droplet with impinging velocity of 600 m/s (the hydrophobicity parameter khb = 0.05) is shown, together with that of a static droplet, in Fig. 7(a) and (b). To obtain the result of the static droplet, we performed an additional simulation in which the impinging velocity was zero and no solid surface was included. Here, the droplet was equilibrated in the vacuum and the liquid-vapor coexistence was achieved. The impinging velocity is added to the droplet at t = 0 and its kinetic energy instantly increases 131 K as shown in Fig. 7(a). The kinetic energy of the impinging droplet including the contribution due to impinging velocity decreases when the droplet is colliding to the surface, and reaches the minimum at t ∼ 15 ps. Beyond 15 ps, the kinetic energy increases slightly and then levels off. The difference in temperature between the static droplet and impinging droplet is 37 K, meaning that about 28% of the added energy is kept in the form of kinetic energy which includes the thermal energy and the kinetic energy of upward (bounce back) velocity. Note that the dotted curve in Fig. 7(a) shows the kinetic energy without including the kinetic energy contribution due to impinging velocity so that it corresponds to the net thermal energy of the droplet. As shown in Fig. 7(b), the potential energy of the impinging droplet increases when the droplet is colliding with the surface. At the maximum of the potential energy (t ∼ 15 ps), the droplet deformation is also maximum. Thereafter, the droplet recovers the equilibrium shape. The potential-energy difference between the the impinging droplet at equilibration and the static droplet is 94 K, indicating that 72% of the added energy transforms into the potential energy. The time dependences of the kinetic and potential energies are oppositely changed because of the conservation of total energy of 16 ACS Paragon Plus Environment

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the system. Interestingly, the energy transformation ratio between the kinetic and potential energy is approximately 28:72 for both B and NB states in all conditions with the impinging velocity being higher than 150 m/s, as listed in Tables S1-S10. More studies on why the ratio is more or less a constant will be the focus in a future work. As shown in the inset of Fig. 7(b), the potential energy has a peak value at t ∼ 15 ps. The deformation of a droplet is the maximum at the potential peak and then the droplet recovers its equilibrium shape. A part of the kinetic energy due to the addition of impinging velocity is kept as the potential energy. Hence, the difference between the peak and the equilibrium potential energies can be viewed as the energy source for droplet bounce back. This energy difference, Ep-diff , defined as Ep-diff = Ep-max − 2σp-avr − Ep-avr ,

(4)

where Ep-max is the maximum potential value, Ep-avr is the average value at the equilibrium state, and σp-avr is the standard division of Ep-avr . The reason why −2σp-avr is included in eq. (4) is that Ep-max is the upper limit of the potential energy with fluctuation, and 2σp-avr should be subtracted from Ep-max to compare with the average value Ep-avr . The impinging velocity dependences of Ep-diff in the case of flat surface with khb = 0.02 is shown in Fig. 8. The potential energy of water molecules located in the liquid-vapor interface of the droplet is higher than that in the inner region because the density at the liquid-vapor interface is lower than that in the inner region. So molecules at the liquid-vapor interface give positive contributions to the total potential energy. On the other hand, the potential energy of water molecules located near the solid-liquid interface is low due to the attractive interaction between water molecules and surface atoms. So water molecules near the solidliquid interface give negative contributions to the total potential energy. In the impinging velocity range of vd ≥ 500 m/s which corresponds to the large deformation range in Fig. 3, Ep-diff increases with increasing the impinging velocity while the positive contribution is


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dominant due to the large deformation. In the impinging velocity range of vd ≤ 400 m/s which corresponds to non-deformation or small deformation range of Fig. 3, the positive and negative contributions are expected to be comparable so that the droplet deformation dependence is weak, and the hydrophobicity is the dominant factor to the bounce back condition. Therefore, when Ep-diff is large, the kinetic energy of impinging velocity is kept in the potential energy which is released during the recovering of the droplet shape, and the droplet can detach from the surface and bounce back.

Surface Area and Its Effect on Bounce Back The contact area of the solid-liquid interface typically increases upon collision due to the droplet deformation, and the associated interface energy is transformed to the energy source after the collision to overcome the adhesive energy between the droplet and the surface. Since the attractive interaction between water molecules and surface atoms tends to hold the bounce back, the solid-liquid surface energy should be removed from the energy source for the bounce back. Part of the surface energy of the liquid-vapor interface can transform into the thermal energy and the kinetic energy of upward velocity during the bounce back. To evaluate the energy for bounce back, we calculated the interfacial area of the colliding droplet because the liquid-vapor interfacial area is proportional to the liquid-vapor surface energy. The interface can be defined as the iso-density surface whose water density is 0.014 ˚ A−3 . The time dependence of the surface area reaches the maximum value when the droplet deformation is the largest. Snapshots and interfacial areas of the droplets with the impinging velocity vd = 100 and 800 m/s are shown in Fig. 9. (Other snapshots and interfacial areas are shown in Figs. S10 and S11.) The surface of droplet can be classified into the liquid-vapor and solid-liquid interfaces using the geometric condition. We define the interface located within 6.4 ˚ A from the solid surface as the solid-liquid one. The definition of this threshold and the threshold dependence of the liquid-vapor interfacial area are given in Figs. S12 and S13, respectively. The maximum values of total and liquid-vapor interfacial areas for each 18 ACS Paragon Plus Environment

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impinging droplet are plotted versus the impinging velocity in the case of the flat surface with khb = 0.02, as shown in Fig. 10. While the total interfacial area increases with increasing the impinging velocity, the liquid-vapor interfacial area decreases for low impinging velocity, and increases for high impinging velocity. When the impinging velocity is relatively low, the shape of the colliding droplet is close to a sphere which slightly collapses upon collision while the liquid-vapor interface decreases. When the impinging velocity is high, the shape of the colliding droplet is similar to the shape of a pancake while the liquid-vapor interfacial area increases. The trend for the impinging velocity dependence of Ep-diff is quite similar to that for the liquid-vapor interfacial area when vd ≥ 200 m/s. It means that Ep-diff , the sum of positive and negative contribution to the potential energy of the deformed droplet is proportional to the liquid-vapor interfacial area and the surface energy. When the interfacial area is large enough, the kinetic energy of upward velocity can overcome the adhesive energy between the droplet and the surface, even when the droplet is more strongly adsorbed due to the less surface hydrophobicity (larger khb ). Hence, the boundary between B and NB states shifts to the weaker surface hydrophobicity region as the hydrophobicity of the surface is weaker within the range of khb > 0.02.


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kinetic energy (kcal/mol)

0.9

Downward kinetic energy Eadd = 131K (0.273 kcal/mol)

0.8 Kinetic energy of impinging droplet 334K

0.7 ∆Ek = 37K (0.078 kcal/mol)

0.6

Kinetic energy of static droplet 297K

0

100

200

t (ps)

(a) Kinetic energy −3.5 potential energy (kcal/mol)

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Potential energy of impinging droplet 334K

−3.6

Ep-diff

−3.7

∆Ep=94K (0.195 kcal/mol)

−3.8 Potential energy of static droplet 297K

0

100

200

t (ps)

(b) Potential energy Figure 7: Comparison of kinetic and potential energies between the impinging and static droplets.


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0.03

Ep-diff (kcal/mol)

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0.02

0.01

0 0

2

4

6

8

2

impinging velocity, vd (10 m/s)

Figure 8: Impinging velocity dependence of Ep-diff

side-view of droplets

side-view of droplet surfaces

bottom-view of droplet surfaces

(a) impinging velocity vd = 100 m/s

(b) impinging velocity vd = 800 m/s Figure 9: Snapshots of droplet and droplet interfacial areas with the impinging velocity vd = 400 and 800 m/s when the surface area is the largest. Blue area means the liquid-vapor surface and Red area means the solid-liquid surface.


2

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maximum surface area (nm )

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total interfacial area liquid−vapor interfacial area

300

200

2

4

6

8

2

impinging velocity, vd (10 m/s)

Figure 10: Impinging velocity dependence of the total (open circles with dotted line) and liquid-vapor (solid circles with solid line) interfacial areas.


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Conclusions We performed MD simulations of impinging droplets to investigate the bounce back condition for flat and nanopillared surfaces. The impinging droplet selects either the bouncing state or non-bouncing state, depending on both the surface hydrophobicity and the impinging velocity of droplet. The boundary between bouncing and non-bouncing states is computed from an independent series of MD simulations. We found that the boundary is closely related to the degree of the deformation of colliding droplet. When the droplets have little or small deformation, the bounce back condition solely depends on the hydrophobicity of the surface. On the other hand, when the droplet deformation is large, the impinging velocity dependence of the bounce back condition becomes stronger, and the boundary between bouncing and non-bouncing states moves towards weaker surface hydrophobicity direction. This result suggests that the droplet deformation plays an important role in determining the bounce back condition. The impinging simulations with nanopillared surfaces were also performed. The boundaries between bouncing and non-bouncing states shift to less hydrophobicity region as the pillar height increases. This is because the surface hydrophobicity is enhanced due to the existence of pillars. Since the higher pillars tend to restrict the droplet deformation to higher extent, the influence of impinging velocity becomes weaker for the higher nanopillared surfaces. The effect of the droplet deformation on the bounce back condition can be explained by the increase of liquid-vapor interfacial area of the colliding droplet. Since the liquid-vapor interfacial area is proportional to the liquid-vapor surface energy, the surface energy which contains a part of the kinetic energy due to the addition of impinging velocity to the droplet is also large when the droplet deformation is large. Hence, the surface energy is trapped as the kinetic energy of upward bounce back to overcome the adhesive potential energy between the droplet and the surface. As such, the droplet deformation can have strong influence to the bounce back condition of impinging droplets. 23 ACS Paragon Plus Environment

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Finally, we have also investigated the Weber number dependence of the normalized maximum spreading diameter of the impinging droplet to compare the spreading dynamics of nanodroplet obtained by the MD simulations with the experimental results. Notably, our simulations show consistent trend, in terms of Weber number dependence, as the experimental measurements with macrodroplets.

Simulation Method The long range charge-charge interaction between water molecules is calculated by using the the particle-mesh Ewald (PME) method. 39 The cut-off length of the Ewald real part and LJ interactions is 12.0 ˚ A. Rotational motion of water molecules is calculated using the symplectic quaternion integrator. 40 The MD time step is set at 2.0 fs and the total impinging simulation time is 200 ps. An MD simulation program previously developed in our group 41 is employed to perform all simulations. The initial coordination of water droplets containing 5832 molecules is set as that of a simple cubic lattice with the same density as bulk water. In the beginning of MD simulations, translational motion of water molecules was not involved for 10 ps so that only orientational degrees of freedom of water molecules were relaxed. Next, the water droplets equilibrated for another 10 ps at T = 298 K apart from the solid surface. The distance between the bottom of the droplets and the top of the surface is longer than the cut-off length of the interactions. After the equilibrium runs, a downward velocity is imposed toward z-direction instantly for all water molecules to represent a impinging droplet. The impinging simulations were carried out in an constant-volume and constant-energy (N V E) ensemble to keep the impinging velocity constant. The impinging droplets should decelerate, if the temperature control was employed. The kinetic energy of the impinging velocity transferred to the kinetic (thermal) and the potential energies.


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References (1) Worthington, A. M. A study of splashes; London, New York, Bombay, Calcutta : Longmans, Green, and Co., 1908. (2) Wang, Z.; Lopez, C.; Hirsa, A.; Koratkara, N. Impact dynamics and rebound of water droplets on superhydrophobic carbon nanotube arrays. Appl. Phys. Lett. 2007, 91, 023105 1–3. (3) Tutejaa, A.; Choib, W.; Mabryc, J. M.; McKinleyb, G. H.; Cohena, R. E. Robust omniphobic surfaces. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 18200–18205. (4) Deng, T.; Varanasi, K. K.; Hsu, M.; Bhate, N.; Keimel, C.; Stein, J.; Blohm, M. Nonwetting of impinging droplets on textured surfaces. Appl. Phys. Lett. 2009, 94, 133109–1 – 133109–3. (5) Lee, D. J.; Kim, H. M.; Song, Y. S.; Youn, J. R. Water Droplet Bouncing and Superhydrophobicity Induced by Multiscale Hierarchical Nanostructures. ACS Nano 2012, 6, 7656–7664. (6) Bird, J. C.; Dhiman, R.; Kwon, H.-M.; Varanasi, K. K. Erratum: Reducing the contact time of a bouncing drop. Nature 2014, 505, 436–436. (7) Liu, T. L.; Kim, C.-J. C. Turning a surface superrepellent even to completely wetting liquids. Science 2014, 346, 1096–1100. (8) Liu, Y.; Whyman, G.; Bormashenko, E.; Hao, C.; Wang, Z. Controlling drop bouncing using surfaces with gradient features. Appl. Phys. Lett. 2015, 107, 051604. (9) Lu, Y.; Sathasivam, S.; Song, J.; Crick, C. R.; Carmalt, C. J.; Parkin, I. P. Robust self-cleaning surfaces that function when exposed to either air or oil. Science 2015, 347, 1132–1135.


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(10) Weisensee, P. B.; Tian, J.; Miljkovic, N.; King, W. P. Water droplet impact on elastic superhydrophobic surfaces. Sci. Rep. 2016, 6, 30328 1–9. (11) Neinhuis, C.; Barthlott, W. Characterization and distribution of water-repellent, selfcleaning plant surfaces. Ann. Bot. 1997, 79, 667–677. (12) Gao, X.; Jiang, L. Biophysics: Water-repellent legs of water striders. Nature 2004, 432, 36. (13) Genzer, J.; Marmur, A. Biological and synthetic self-cleaning surfaces. Mat. Res. Soc. Bull. 2008, 33, 742–746. (14) Feng, L.; Zhang, Y.; Xi, J.; Zhu, Y.; Wang, N.; Xia, F.; Jiang, L. Petal Effect: A Superhydrophobic State with High Adhesive Force. Langmuir 2008, 24, 4114–4119. (15) Bartolo, D.; Bouamrirene, F.; . Verneuil,; Buguin, A.; Silberzan, P.; Moulinet, S. Bouncing or sticky droplets: Impalement transitions on superhydrophobic micropatterned surfaces. Europhys. Lett. 2006, 74, 299–305. (16) Jung, Y. C.; Bhushan, B. Dynamic Effects of Bouncing Water Droplets on Superhydrophobic Surfaces. Langmuir 2008, 24, 6262–6269. (17) Rioboo, R.; Marengo, M.; Tropea, C. Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 2002, 33, 112–124. (18) van Dam, D. B.; Le Clerc, C. Experimental study of the impact of an ink-jet printed droplet on a solid substrate. Phys. Fluids 2004, 16, 3403–3414. (19) Visser, C. W.; Tagawa, Y.; Sun, C.; Lohse, D. Microdroplet impact at very high velocity. Soft Matter 2012, 8, 10732–10737. (20) Visser, C. W.; Frommhold, P. E.; Wildeman, S.; Mettin, R.; Lohse, D.; Sun, C. Dynamics of high-speed micro-drop impact: numerical simulations and experiments at frame-to-frame times below 100 ns. Soft Matter 2015, 11, 1708–1722. 26 ACS Paragon Plus Environment

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(21) Richard, D.; Quere, D. Bouncing water drops. Europhys. Lett. 2000, 50, 769–775. (22) Hyvluoma, J.; Timonen, J. Impalement transitions in droplets impacting microstructured superhydrophobic surfaces. Europhys. Lett. 2008, 83, 64002. (23) Hyvluoma, J.; Timonen, J. Impact states and energy dissipation in bouncing and nonbouncing droplets. J. Stat. Mech: Theory Exp. 2009, 2009, P06010. (24) Chen, L.; Kang, Q.; Mu, Y.; He, Y.-L.; Tao, W.-Q. A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications. Int. J. Heat Mass Transfer 2014, 76, 210 – 236. (25) Zhang, B.; Lei, Q.; Wang, Z.; Zhang, X. Droplets Can Rebound toward Both Directions on Textured Surfaces with a Wettability Gradient. Langmuir 2016, 32, 346–351. (26) Insepov, Z.; Moseler, M. Molecular-dynamics simulation of thin-film growth by energetic cluster impact. Phys. Rev. B 1995, 51, 11061. (27) Shimizu, J.; Ohmura, E.; Kobayashi, Y.; Kiyoshima, S.; Eda, H. Molecular Dynamics Simulation of Flattening Process of a High-Temperature, High-Speed Droplet.Influence of Impact Parameters. J. Therm. Spray Technol. 2000, 16, 722–728. (28) Germann, T. Large-scale molecular dynamics simulations of hyperthermal cluster impact. Int. J. Impact Eng. 2006, 33, 285–293. (29) Tomsic, A.; Markovic, N.; Pettersson, J. B. C. Molecular dynamics simulations of cluster-surface collisions: Mechanisms for monomer emission. Phys. Chem. Chem. Phys. 2001, 3, 3667–3671. (30) Tomsic, A.; Andersson, P. U.; Markovic, N.; Piskorz, W.; Svanberg, M.; Pettersson, J. B. C. Molecular-dynamics simulations of clustersurface collisions: Emission of large fragments. J. Chem. Phys. 2001, 115, 10509–10517.


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(31) Tomsic, A.; Markovi, N.; Pettersson, J. B. C. Scattering of Ice Particles from a Graphite Surface: A Molecular Dynamics Simulation Study. J. Phys. Chem. B 2003, 107, 10576– 10582. (32) Tomsic, A.; Andersson, P. U.; Markovi, N.; Pettersson, J. B. C. Collision dynamics of large water clusters on graphite. J. Chem. Phys. 2003, 119, 4916–4922. (33) Lundgren, M.; Allan, N. L.; Cosgrove, T.; George, N. Wetting of Water and Water/Ethanol Droplets on a Non-Polar Surface: A Molecular Dynamics Study. Langmuir 2002, 18, 10462–10466. (34) Lundgren, M.; Allan, N. L.; Cosgrove, T.; George, N. Molecular Dynamics Study of Wetting of a Pillar Surface. Langmuir 2003, 19, 7127–7129. (35) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The missing term in effective pair potentials. J. Phys. Chem. 1987, 91, 6269–6271. (36) Bhethanabotla, V. R.; Steele, W. A. Molecular dynamics simulations of oxygen monolayers on graphite. Langmuir 1987, 3, 581–587. (37) Koishi, T.; Yasuoka, K.; Fujikawa, S.; Ebisuzaki, T.; Zeng, X. C. Coexistence and transition between Cassie and Wenzel state on pillared hydrophobic surface. Proc. Natl. Acad. Sci. USA 2009, 106, 8435–8440. (38) Koishi, T.; Yasuoka, K.; Fujikawa, S.; Zeng, X. C. Measurement of Contact-Angle Hysteresis for Droplets on Nanopillared Surface and in the Cassie and Wenzel States: A Molecular Dynamics Simulation Study. ACS Nano 2011, 5, 6834–6842. (39) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103, 8577–8593. (40) Miller III, T. F.; Eleftheriou, M.; Pattnaik, P.; Ndirango, A.; Newns, D.; Martyna, G. J.


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Symplectic quaternion scheme for biophysical molecular dynamics. J. Chem. Phys. 2002, 116, 8649–8659. (41) Koishi, T.; Takeichi, H. An efficiently extendable and fine-grain parallelised molecular dynamics simulation program: Mid. Mol. Simul. 2015, 41, 801–807.


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For Table of Contents Only lower impinging velocity

Bounce back condition of water droplets liquid-vapor interfacial area

Molecular Dynamics Simulation of Water Nanodroplet Bounce Back

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