Directional Motion of Water Droplet on Nano-Cone Surface Driven by

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C: Physical Processes in Nanomaterials and Nanostructures

Directional Motion of Water Droplet on Nano-Cone Surface Driven by Curvature Gradient: A Molecular Dynamics Simulation Study Awais Mahmood, Shuai Chen, Chaolang Chen, Ding Weng, and Jiadao Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02642 • Publication Date (Web): 05 Jun 2018 Downloaded from http://pubs.acs.org on June 5, 2018

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The Journal of Physical Chemistry

Directional Motion of Water Droplet on Nano-Cone Surface Driven by Curvature Gradient: A Molecular Dynamics Simulation Study Awais Mahmood, † Shuai Chen, ‡Chaolang Chen, † Ding Weng, † and Jiadao Wang†* †

‡

State Key Laboratory of Tribology, Tsinghua University, Beijing, 100084, China Institute of High Performance Computing, A*STAR, 138632, Singapore

ACS Paragon Plus Environment

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ABSTRACT: This research work focuses on the wetting behavior and directional motion of water droplet on nano-cone surface through molecular dynamics simulation approach. A total of five nano-cones having different apex angle were utilized to observe the wetting characteristics. In addition, water droplets of different sizes based on containing number of molecules were also considered in this study. The results show that the water droplet spontaneously travels from the tip of the nano-cone towards its larger diameter direction in all cases. The average velocity of water droplet on the nano-cone surface with smaller apex angle was found to be higher than that with larger apex angle. Moreover, it was found that the energy parameter of nano-cone surface and the size of water droplet have a significant effect on the wetting characteristics and velocity of droplet. Furthermore, three different equilibrium states of the water droplet on the nano-cone surface were observed; un-wet, partially-wet, and fully-wet. The velocity of the droplet was comparatively higher in the fully-wet state as compared to the partially-wet equilibrium state.


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1. INTRODUCTION In many of the recent studies the spontaneous movement of droplet on solid surface has been a subject of interest due to its potential applications in the field of atomic force microscopy (AFM),1 biomedical applications,2 nanofluidics,3 fog collection,4 oil and water separation,5 environmental protection,6 and so on.7 In order to design more efficient nanofluidic systems for water transport, research on nanowetting properties of solid surfaces is of great importance. Many plant and animal species have developed intriguing appeal and surface structures, which facilitate them in efficiently gathering water from fog.8-10 The water harvesting mechanism of these species can be utilized to design smart materials for water collection,11,12 and also for oil-water separation.13 It is believed that Laplace pressure and surface-free energy gradients are the main driving forces in water collection mechanism. Even though an ample amount of research is conducted on these living species, the process of fog collection is still poorly understood. By understanding the water harvesting mechanism of these species at nano scale, more efficient devices could be developed. Computer aided simulations, specifically molecular dynamics (MD) simulation could be an effective way to understand the water transport behavior of these natural species at nano-scale. Numerous studies have been conducted on wetting behavior of surfaces on nano-scale in recent years.14-16 While plenty of researchers have studied motion of liquid on flat surface,17,18 others analyzed the transport of liquid inside microchannels.19-21 As the droplet can spontaneously travel inside the conical channel, a droplet can also move on a conical fiber due to Laplace pressure gradient.22 In a recent study, the speed of nano-droplet on graphene nano-cone is predicted by using MD simulation, the predicted velocity of nano-droplet was found to be around


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100 m/s.23 In an another study, impregnation of water molecules through vertically aligned carbon nanotubes is studied by MD simulation, the results show that the permeability of water is dependent on the volume fraction of carbon nanotubes.24 These studies can provide an insight on how water molecules travel outside the nano-surface and which factors influence the movement of water molecules at nano-scale. Although many experimental and analytical studies have been conducted on the flow investigation of liquids inside a nano-channel,25-28 but according to author’s best knowledge, the wetting behavior of nano-cone has not yet been reported in previous studies. To understand the wetting behavior of nano-cone at different wetting conditions a virtual solid surface having specific lattice structure could be used to design the solid surface.29,30 The potential parameters can be altered artificially to obtain a continuous range between the hydrophilic and hydrophobic conditions of existing design.15 The velocity of a nano-droplet on the conical surface at each time step is an important factor to analyze and it can be helpful to understand the liquid transport mechanism on this surface.23 This paper analyzes the equilibrium states of a droplet on a nano-cone surface. In addition, the effect of number of water molecules and energy parameter on the wetting conditions and transport mechanism of water molecules is also investigated. This research work is compelling for understanding the characteristics of water-solid interface, including the wettability of diverse conical surfaces having different apex angle.

2. METHODS The simulation model contains water molecules located at the tip of the nano-cone surface (Figure 1(a)). In this research a rigid extended simple point charged potential water model


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(SPC/E) is utilized,31 each molecule contains two hydrogen atoms with +0.4238e and one oxygen atom with ˗0.8476e charge on it. The bond length of O˗H atoms was 1Å and the bond angle between H˗O˗H atoms was 109.47°. The conical structure is constructed by utilizing a single layer of cubic diamond structure consisting of lattice constant, a, which is equal to 5.43Å (the Si crystal structure is obtained from Material Studio library).45 This single layer of Si lattice atoms is then cut in to a circular disc. Next, a sector is cutoff from the disc at an angle of 90°, 135°, 180°, 225° and 270° to obtain five different discs, as show in Figure S1. In order to analyze the wetting behavior of nano-cone these cutoff discs were then rolled to obtain nano-cone with different apex angle,41 five nano-cones with apex angle θ of (S1=113°, S2=92°, S3=71°, S4=53°, S5=34°), were obtained as shown in Figure 1(c), and S2. The top diameter dtop of each cone was kept equal to 150Å but the length of each cone was different. The water molecules were located at the tip of the cone and the distance between the nano-cone surface and the water molecules is kept equal to 3Å. In order to observe the effect of the size of water droplet on wetting characteristic of nano-cone, five different sizes of water droplets with 500, 1000, 1500, 2000, and 2500, water molecules in each were modeled as shown in Figure 1(b). As it has been reported in previous studies,32,33 to improve and simplify the calculation efficiency, the gas molecules are not considered in this study.


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Figure 1. Initial structure of the ensemble containing (a) nano-cone made by silicon atoms and water molecules placed at its tip (b) nano-cone having different number of water molecules (c) nano-cone having different apex angle. White, red, and green spheres represent the hydrogen, oxygen and nano-cone atoms, respectively. The intermolecular interaction forces between the molecules is a combination of electrostatic interaction, which is calculated by using Coulomb’s Law while the repulsion and dispersion forces were calculated by utilizing Lennard-Jones (L-J) potential.34 4

,

(1)

In the above equation i and j represent oxygen (O), Hydrogen (H) and nano-cone (S) atoms, also qi and qj represent the charges on the atoms, and σij and εij represent the distance where the depth of the potential and interatomic potential wall is zero. The cutoff potential is represented by rc and it is kept 12Å, which means Uij =0 when rij ≥ 12Å. The interatomic mixed-atom potentials were calculated by using Lorentz-Berthelot mixing rules.35


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×

(2) (3)

The values for εij of O, and H atoms are 6.748 and 0meV, while the εij of the nano-cone surface had the following values (1, 5, 10, 17.5, 30, 40, 50, 60meV) in order to obtain different wetting conditions. A flat surface of similar atomic lattice structure as of nano-cone surface is modeled to calculate the contact angle of 2500 water molecules on the flat surface at these different potential parameters. The contact angle was found to be in a range of (150° to 8°), which represent a surface with superhydrophobic to a superhydrophilic characteristics. All simulations were featured under periodic boundary condition having fixed (Number, Volume, and Temperature) NVT ensemble in LAMMPS (MD) molecular dynamics software.36 Initially the momentum of the droplet is kept constant for 0.1ns at the initial condition of the droplet in order to obtain thermal equilibrium. Then the droplet is released and simulation is run for another 0.4ns. All models were run for 0.5ns duration with a 0.1fs time step. The angle and the bond length of water molecules were fixed by SHAKE algorithm.37 The long-range electrostatic interaction was estimated by using particle-particle particle-mesh (PPPM) algorithm, which was set to be equal to 10-4. The simulation box was coupled with Nose-Hoover thermostat with the temperature of 300K. The diameter of the nano-cone surface was about three to five times more than the length of the water cube and periodic image interactions had a minor effect on the droplet behavior. The length of simulation box was kept twice the size of the model, and the impact of molecules on the action of droplet in the duplicate domain can be neglected. The solid surface atoms were fixed to their initial position and can be considered as an inert wall. The temperature of water molecules was kept stable during the simulation and a deviation of less than 5.0K was observed.


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3. RESULTS AND DISCUSSION In this paper, at first the mean square displacement (MSD) of different size of water droplet on nano-cone surface at each time step (0.1fs) is captured and its average velocity is calculated. Moreover, the effect of number of water molecules contacted to the surface of nano-cone on the velocity of droplet is studied. Furthermore, the influence of interaction energy between the water atoms and nano-cone atoms on the wetting condition is calculated. Secondly, the MSD of water droplet on the nano-cone having different apex angle is measured at each time step and the average velocity of water droplet during 0.5ns duration on each nano-cone is analyzed. At last, the wetting condition of nano-cone at different energy parameter (hydrophobic to hydrophilic) is analyzed visually and the MSD of water droplet is measured to compare the results at different wetting conditions. In addition, nano-cones made up by rolling graphene discs were also utilized to analyze the MSD and average velocity of water droplet in 0.25ns simulation time. 3.1 Directional Motion of Water with Different Droplet Size To find out whether velocity of the water droplet on the nano-cone surface is affected by the droplet size, nano-cone S3 with an apex angle θ of 71°, is simulated with different number water molecules and with energy parameter of 17.5meV, which represent the potential parameter of silicon surface.38 The average velocity of different sizes of water droplet on nano-cone surface is shown in Figure 2(a). The results show that the average velocity of droplet can be correlated with the droplet size, and as the size of the droplet is increased the average velocity is reduced. Furthermore, figure 2(b) reveals that the number of water molecules touching with the nano-cone surface is inversely proportional to the velocity of the droplet. A water droplet with a large number of molecules can cause an increase in contact area between the water molecules and


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nano-cone surface which then result in reduction in its velocity. The MSD at each time step for different size of water droplet is measured and plotted in Figure 2(c), results show that smaller water droplet (500 molecules) has more displacement in 0.5ns duration as compared to larger water droplet (2500 molecules), which is associated with its higher velocity. The trend also indicates the directional movement of water droplet over nano-cone surface due to curvature gradient. Besides, the MSD and the number of contacted water molecules on the nano-cone surface, the other reason for this change in the velocity of droplet could be explained by the change in interaction energy between nano-cone and water atoms. Interaction energy is the interaction between per water molecule and nano-cone. As it is shown in Figure 2(d), the interaction energy for 500 water molecules reduces more quickly than that of the 2500 water molecules during 0.5ns simulation time, resulting in larger velocity of 500 water molecules. The maximum average velocity was found to be around 14.33nm/ns in case of 500 water molecules droplet, and the minimum average velocity was found to be 8.41nm/ns in case of the 2500 water molecules droplet. As the difference between the maximum and minimum velocity is considerable so it can be concluded that the droplet size does have a significant effect on the velocity of droplet on the nano-cone surface. The reason behind categorizing the significance of droplet size is linked to the wetting condition of the water droplet on the nano-cone surface, which is further associated to the change in average velocity of the droplet on nano-cone surface. In the section 3.3, the effect of energy parameter and droplet size on the wetting conditions and the average velocity of nano-cone are further discussed in detail.


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Figure 2. Simulated results of nano-cone S3 with an apex angle 71° during 0.5ns simulation time (a) shows the average velocity of different number of water molecules, i.e., 500, 1000, 1500, 2000, and 2500 on nano-cone surface (b) average velocity of water droplet with respect to the number of water molecules touching the nano-cone surface. (c) MSD plot of water molecules on nano-cone surface with fitting curve y = 656 - 30796x + 295769x2 + 163447x3 - 240567x4 (500 molecules) and y= -427 + 26420x - 221257x2 + 1.19E6x3 - 1.2E6x4 (2500 molecules). (d) Interaction energy between water and nano-cone atoms with fitting curve y = 0.12 - 23.8x + 23.9x2 (500 molecules) and y = -0.03 - 4.47x - 1.31x2 (2500 molecules). The velocity of a water droplet on nano-cone surface can be measured by a two-step method. First, the total mean squared displacement (MSD) data of each group of atoms is taken from the


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simulation output file. Second, the square root of the difference of two consecutive average displacements is divided by the time step to obtain the velocity of a droplet at each time step. At last, the velocity at each time step is sum up and divided by the total number of time steps during the 0.5ns simulation time to get the average velocity. The MSD is a measure of the deviation of the position of total water molecules with respect to their initial positions over time. In LAMMPS, MSD function calculates each and every effect due to the motion of atoms through its periodic boundaries. The total squared displacement can be calculated by, (dx*dx+dy*dy+dz*dz), which is summed and averaged over atoms.36 3.2 Directional Motion of Water Droplet on Nano-Cone with Different Apex Angle In this section the displacement of water droplet on nano-cone surface having different apex angle is studied in detail. Five different nano-cones having an apex angle of (S1=113°, S2=92°, S3=71°, S4=53°, S5=34°) were modeled and analyzed, as shown in Figure S2. The simulation was run for 0.5ns in all cases and the average velocity of the 1500 water molecules droplet on each nano-cone is calculated. The average velocity of the droplet and the number of water molecules touching the different apex angle nano-cone surface is plotted as shown in Figure 3(a). The MSD of water droplet on two different nano-cones S4 with apex angle 53° and S5 with apex angle 34° at each time step are plotted in Figure 3(b).


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Figure 3. Simulated results of (a) average velocity of 1500 water molecules and the number of water molecules touching the surface of each type of nano-cone (b) MSD plot of 1500 water molecules on S4 cone (53°) with fitting curve y = 312 - 17074x + 22484x2 - 717849x3 + 1.76E6x4 and on S5 cone (34°) with fitting curve y = -874 + 63863x - 901130x2 + 4.48E6x3 4.47E6x4 during 0.5ns simulation time. As shown in Figure 3 (a), the number of water molecules touching the nano-cone surface is higher on the larger apex angle as compared to the smaller apex angle nano-cone. This further confirms that the increase in contact area of water molecules on the nano-cone surface results in lower velocity. In addition, the average velocity of water droplet on each nano-cone model is found to be different from each other. The results indicate that, the average velocity of droplet is low for nano-cone with large apex angle and the velocity increases as the apex angle decreases. The average velocity on the surface of S1 (113°) was around 8.71nm/nsec, which is minimum in all types and the velocity is increased as the apex angle is decreased, with a maximum of 12.85nm/nsec in the case of S5 (34°), as shown in Figure 3(a). The energy parameter during all these cases was set to be equal to17.5eV. The results show that the MSD of a droplet at each time step varies significantly due to the spontaneous movement of the droplet on the nano-cone


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surface. The MSD curve of S4 (53°) and S5 (34°) reveals that the nano-cone having smaller apex angle has greater MSD than the nano-cone with the larger apex angle, as shown in Figure 3(b). 3.3 Directional Motion of Water on Nano-Cone with Different Wettability In order to observe the wetting behavior of the droplet on the nano-cone surface, the energy parameter of the nano-cone is altered. A flat surface, made up of a similar atomic structure as that of the nano-cone is modeled to observe the contact angle of 2500 water molecule droplet at different energy parameters. The energy parameter of the flat surface is altered, and contact angle of the droplet on the flat surface is measured and plotted as shown in the Figure 4(a). The results show that the surface has different wetting states, i.e. hydrophobic to hydrophilic, depending on the energy parameter. The surface was superhydrophobic when the energy parameter was equal to 1meV and had a contact angle of 150° while the surface was superhydrophilic when the energy parameter was equal to 60meV and had a contact angle of around 8°. These above mentioned energy parameter values are utilized to alter the wettability of the nano-cone surface.


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Figure 4. Simulated contact angle of (a) 2500 water molecules on flat surface at eight different energy parameters and (b) Snapshot of different equilibrium states of nano-cone containing 2500 water molecules with different energy parameter, ranging from 1meV to 60meV. The nano-cone S3 (71°) was utilized for this analysis and its wetting behavior was observed at different L-J potential and water droplet size. There were a total of eight different potential parameter cases which were analyzed for each droplet size. In this paper only images of 2500 molecules water droplet are shown, which can be seen in Figure 4(b). The results show that when the cone has superhydrophobic characteristics the water droplet is repelled away from the cone surface and stayed away from the nano-cone surface throughout the simulation time, this can be seen in figure 4(b), despite of its initial condition where the droplet is placed on the tip of the nano-cone. This equilibrium state is called an un-wet state and can be observed during the superhydrophobic state of a nano-cone. As the energy parameter was increased and is brought to 10meV the droplet got attached to the surface of the nano-cone and subsequently travelled towards the larger diameter direction on the nano-cone structure. The contact angle of water droplet on flat surface at 10meV was around 105°, which is hydrophobic state. So, it can be concluded that the droplet does not attach to the


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surface of nano-cone when it is in superhydrophobic state but it does attach to the surface of nano-cone when its hydrophobicity is reduced. This equilibrium state is called as the partiallywet state and it can be observed when the energy parameter is below 45meV and the contact angle of water on flat surface is greater than 30°. In the partially-wet state the water drop maintains a continuous contact with the nano-cone surface and keeps its droplet shape intact, as shown in Figure 4(b). The trend is similar for all sizes of water droplet used in this study. As the energy parameter is further increased, the hydrophilicity of the surface is also increased which compels the water droplet to spread completely over the nano-cone surface. This fully-wet equilibrium state can be observed when the potential parameter is equal or greater than 50meV, as shown in Figure 4(b). At this potential parameter the contact angle of water droplet on flat surface was around 15° which represents a superhydrophilic surface. The results reveal that the droplet has circular shape in un-wet state, a semicircle shape due to contact with the nano-cone surface in its partially-wet state, and later it completely spreads over the cone surface and take the shape of a nano-cone in its fully-wet state. The results indicate that the water molecules keep on moving towards the increasing diameter side of the nano-cone despite the size and energy parameter of the water droplet and nano-cone surface respectively. All these different equilibrium states are illustrated in figure 4(b).


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Figure 5. Simulated results of (a) average velocity of 2500 water molecules at eight different energy parameters (b) MSD plot of 2500 water molecules with fitting curve y = -374 + 24016x 176075x2 + 872149x3 - 760367x4 at 17.5meV and y = 24 + 3665x + 26482x2 + 335938x3 122312x4 at 60meV during 0.5ns simulation time. The average velocity and MSD of the 2500 water molecules at different energy parameters is plotted in Figure 5(a) and (b), respectively. It was observed that the velocity of the droplet was higher and negative in direction when the surface was superhydrophobic. As the droplet detached from the nano-cone surface and travelled inside the simulation box so this data is not plotted. The average velocity was found to be around 8.43nm/ns at an energy parameter of 10meV. Moreover, the velocity started to decrease as the energy parameter increased and it kept on decreasing until the energy parameter was equal to 40meV and the minimum velocity at this energy parameter was found to be around 8.03nm/ns. However, the average velocity of droplet started to increase as the energy parameter was further increased from 40meV. The maximum calculates velocity was equal to 8.63nm/ns at an energy parameter of 60meV. The reason for this increase in velocity is because of complete spreading of the water droplet on the nano-surface which eventually causes water molecules to move more smoothly over the nano-cone surface. It


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can be concluded from the results that the droplet has high velocity in un-wet state and fully-wet state, while it has comparatively lower velocity during partially-wet equilibrium state. Furthermore, in case of 500 water molecules droplet the velocity started to increase when the potential parameter is increased from 30meV, while for the 2500 water molecules droplet the velocity started to increase after 40meV, the result is plotted in supporting information Figure S4. The reason behind this delay in increase in velocity of a bigger water molecule is linked to its size. A droplet of larger size is tends to spread slower than the droplet of smaller size. This trend in average velocity reflects that the size of water droplet has significant influence on the wetting condition, which further alters the average velocity of the droplet. Therefore, it can be concluded that the average velocity is altered due to size of the droplet.

Figure 6. Simulation results of (a) average velocity of 500 water molecules during 0.2ns simulation on five different graphene nano-cones having different apex angle (b) MSD plot of 500 water molecules droplet on graphene nano-cone surface with fitting curve y = 279 - 36182x + 1.20E6x2 - 1.11E7x3 + 3.57E7x4 for G3 = 71° and y = 298 - 38198x + 1.27E6x2 - 1.19E7x3 + 4.05E7x4 for G4 = 52° during 0.2ns simulation time.


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In order to validate the results obtained from the nano-cone made with silicone lattice atom, a nano-cone is made from rolled graphene disc. Graphene or carbon nano-cones are ideally suited for their use in scanning probe tips and electron field emitters.39 There are plenty of molecular dynamics simulation studies done on carbon nano-cones,40-42 so it can be assumed that the graphene nano-cones are a well suited material to compare the results obtained from our model. There were five graphene nano-cones namely (G1, G2, G3, G4, and G5) designed with an apex angle comparatively equal to that of nano-cone presented in previous sections, as shown in Figure S2. The average velocity and MSD of the 500 water molecules droplet on graphene nanocone is measured and plotted in Figure 6(a) and (b), respectively. The average velocity of water droplet on graphene nano-cone was found to be around two times the one obtained from our modeled nano-cone. The reason could be associated to the lattice structure and strong sp2 bonding found in carbon atoms and also due to strong hydrogen bonding between water molecules and graphene surface.43 The other reason for the higher velocity could be the low energy parameter of graphene surface, which was set to be equal to 2.445 meV.44 The effect of apex angle on the average velocity of a droplet is found to have a similar trend as was observed in silicon nano-cone. The velocity was high in case of the nano-cone with small apex angle and was low in case of the nano-cone with large apex angle. However, the maximum and minimum velocity in case of graphene nano-cone was found to be around 17.15 and 19.45nm/ns, respectively. Here forth, it can be concluded that both type of nano-cone do behave similarly and can be utilized for analyzing the wetting behavior and movement of water droplet on the nano-cone surface.


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4. CONCLUSION This research work provides a molecular level understanding about the wetting behavior and directional motion of a nano-droplet on the surface of nano-cone having different size (apex angle) and type (hydrophobic to hydrophilic). In order to analyze the wetting behavior of water on nano-cone surface, droplet with different number of water molecules (500, 1000, 1500, 2000, and 2500) were placed at the tip of the nano-cone. It was observed that the influence of the droplet size on the wetting characteristics and the velocity of water droplet were considerable. In addition, the wettability of the nano-cone surface was also altered and the influence of this change in energy parameter on the wetting behavior and velocity of water droplet was studied. There were total eight different energy parameter values (1meV, 5meV, 10meV, 17.5meV, 30meV, 40meV, 50meV, and 60meV) that were used to alter the wettability of the nano-cone from (superhydrophobic to superhydrophilic). The results show that the energy parameter has strong effect on the wetting condition and the velocity of the droplet. The droplet dethatches from the tip of the nano-cone when it is in superhydrophobic state while the droplet spontaneously travels on the nano-cone surface when it is hydrophobic or hydrophilic in nature. However, the velocity of the droplet changes in correlation to the potential parameter and to the wetting state of the droplet. Furthermore, the wetting state of water droplet determines the velocity of the droplet, which is comparatively higher in fully-wet state as that of in partially-wet equilibrium state. ASSOCIATED CONTENT Supporting Information This material is available free of charge via the Internet at http://pubs.acs.org.


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1. Movie of the equilibrium states of water droplet on nano-cone surface at different energy parameter. This movie demonstrates the three equilibrium states, i.e., un-wet, partiallywet and fully-wet state, in which white, red, and green spheres represent the hydrogen, oxygen and nano-cone atoms, respectively. (ZIP) 2. Figure S1-S4 and Table S1. (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Tel: +86-010-62796458. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China Project under grant nos. 51775296 and 51375253. The authors also acknowledge the support of this work from the Tsinghua National Laboratory for Information Science and Technology, China. CONFLICT OF INTEREST The authors declare no competing financial interest. REFERENCES (1) Calò, A.; Domingo, N.; Santos, S.; Verdaguer, A. Revealing water films structure from force reconstruction in dynamic AFM. J. Phys. Chem. C 2015, 119, 8258-8265. (2) Daniel, M. C.; Astruc, D. Gold nanoparticles: assembly, supramolecular chemistry, quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology. J. Chem. Rev. 2004, 104, 293-346.


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Directional Motion of Water Droplet on Nano-Cone Surface Driven by

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