Molecular dynamics (MD) simulations are performed to investigate the wettability of gold substrate interacting with nanosized droplets of water. The effects of droplet size, temperature variation, and impingement velocity are evaluated using molecular trajectories, dynamic contact angle, spread ratios, radial distribution function (RDF), and molecular diffusion graphs. Droplets of 4 nm and 10 nm were simulated at 293 K and 373 K, respectively. Stationary droplets were compared to droplets impinging the substrate at 100 m/s. The simulations were executed on high-end workstations equipped with NVIDIA® Tesla graphical processing units (GPUs). Results show that smaller droplets have a faster stabilization time and lower contact angles than larger droplets. With an increase in temperature, stabilization time gets faster, and the molecular diffusion from the water droplet increases. Higher temperatures also increase the wettability of the gold substrate, wherein droplets present a lower contact angle and a higher spread ratio. Droplets that impact the substrate at a higher impingement velocity converge to the same contact angle as stationary droplets. At higher temperatures, the impingement velocities accelerate the diffusion of water molecules into vapor. It was revealed that impingement velocities do not influence stabilization times. This research establishes relationships among different process parameters to control the wettability of water on gold substrates which can be explored to study several nanomanufacturing processes.

## Introduction

How water interacts with a surface is important for many physical, chemical, and biological applications. The wetting properties of water for a variety of materials are well understood at the macroscopic scale [14]. However, water plays an important role in many manufacturing processes at the nanoscale such as deposition [57], spray-cooling, fabrication of nanofluidic devices, and biophotonics [810]. Several investigations in the literature have confirmed that the behavior of water at the nanoscale differs from that at the macroscale. These include the dynamics of liquids on top of surfaces [11], polymers [12], graphite [13], and metals [14].

An interface between two phases has an interfacial energy, which is proportional to the contact surface, as proposed by Young [15]. The surface energy induces a surface tension on the liquid surface, that can be determined by the contact angle of that liquid on a flat substrate surface. At the nanoscale, wetting properties of a liquid with a substrate are determined by the molecular interactions between the materials. This interaction is influenced by their chemical composition, the surface geometry of the substrate, ambient temperature, and the dynamics of the liquid over the surface. Molecular dynamics (MD) simulations can explore the nature of the surface interaction between materials. Moreover, by employing a virtual modeling environment, one can eliminate experimental noise and increase repeatability. In addition, molecular simulations can assist in analyzing molecular trajectories, thermodynamics properties, and other data at lower cost and reduced setup times. Many research groups have used MD simulations to investigate material properties, including the wettability of a variety of substrates. Hong et al. [16] used MD simulation to study the variation of the contact angle of a water droplet in equilibrium with a solid with different characteristic energies. They studied the receding and advancing contact angle which is affected in the presence of a body force. Using the water-Lennard-Jones (LJ) solid models, the authors presented density profiles, radial density functions for the water droplet in interaction with solids with different LJ potentials. The spread of nanodroplets on top of polyethylene (PE) and polyvinyl chloride (PVC) surfaces were investigated by Hirvi and Pakkanen [12]. MD simulations were used to evaluate surface contact angles and density profiles to investigate the interaction between water and the polymer substrates. A systematic MDs study was carried out by Werder et al. [13] to investigate the properties of water droplets on graphite. It was revealed that the droplet contact angle changes significantly as a function of the water–carbon interaction energy. Density profiles and hydrogen bond distributions for a water droplet on graphite substrate were presented. Ztekin et al. [17] used MD simulations to investigate the properties of Au metallic systems using P–V and P–T diagrams. By modeling a system of 1372 Au atoms, the authors calculated the bulk modulus, specific heat, elastic constants, and validated their results with from experimental literature. Wu et al. [18] have investigated the effects of temperature, size of water droplets, and surface roughness on nanowetting properties using MDs simulations.

Despite several MDs studies in the field, to the best of our knowledge, the effect of the droplet impingement velocity on substrate spreading behavior has not been investigated at the nanoscale. Impingement velocities of droplets play an important role in determining their initial spread, stability and relaxation times to attain contact angle equilibrium on substrates. This is particularly valuable for different nanoscale processes and phenomena wherein nanoscale droplets impinge on surfaces at high velocities (ranging from 1 m/s to 100 m/s) resulting in agglomerate clusters or disintegrated droplets. Thus, it is critical that nanoscale droplet spreading phenomena be explored, which encompasses variations in droplet size, temperatures, and impingement velocities, for a fundamental understanding of the underlying phenomena.

Freud [19] studied the influence of an applied force on flow in the vicinity of the advancing and receding solid–liquid–vapor contact lines. The liquid droplet was simulated using an atomistic model of a droplet in a thermodynamic equilibrium with its own vapor, moving steadily on top of a smooth surface. Ju et al. [20] investigated the influence of temperature on droplet formation. They concluded that when the temperature is increased the ratio of surface molecules also increases, but the average number of hydrogen bonds in the droplet decreases. Thus, temperature influences the molecular arrangement of droplets and can be used to change the wettability of a substrate [18,21]. Nanodroplets are relevant to many processes that occur at high temperatures such as physical vapor deposition and spray-cooling [22]. In this work, droplets were simulated at the boiling temperature (373 K) of water and at room temperature which enabled the influence of temperature to be investigated in relation to droplet sizes and impingement velocities of the droplet.

In the past, studies have been carried out to investigate the properties of water droplets on different types of substrates and ambient environments spanning micro- to the nano-scale. However, there is limited effort to study the effect of droplet velocity on the dynamics of liquid–substrate interaction at the nanoregime. This research investigates the effect of droplet impingement velocity on the contact angle, stabilization time, and their diffusion rate on a gold substrate. We further explore the wetting behavior of varying sizes of water nanodroplets at different temperatures.

## Methodology

This section presents the force fields, assembled systems, simulation conditions, and simulation analysis tools used. All the simulations were executed using nanoscale molecular dynamics (NAMD). Visual MDs was used for model development, visualization, and analyzing the results of the simulations. NAMD source code was chosen as it is proven to be robust for parallel computing [23,24], is an open source, and compatible with most force fields for commonly available CHARMM [25] and AMBER [26] packages. Both NAMD and visual MDs were developed by the Theoretical and Computational Biophysics Group in Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign [27]. The simulations were executed on a 64 bit Linux system using a graphical processing unit (GPU) board (NVIDIA Tesla C2050) with 448 cores. The compute unified device architecture enabled version of NAMD was used to run the simulations. In GPU-based computational models, the nonbonded force evaluations are performed on the GPU board [28], while the energy evaluations are conducted on the central processing unit [29].

Water droplets of sizes 4 nm and 10 nm were modeled. The water molecules were modeled using a TIP3P molecular model adopted within the CHARMM force field system. The 4 nm and 10 nm droplets consisted of 1108 and 17,267 molecules of water, respectively. The substrates used for the simulations were composed of gold molecules in a perfect face-centered cubic (FCC) structure. Substrates of size 100 Å × 100 Å × 38 Å and 161 Å × 161 Å × 38 Å were used in simulations with 4 nm droplets and 10 nm droplets, respectively. All atoms of the substrate had their atomic coordinates fixed to their initial position, while water molecules were set to move freely. Figure 1 illustrates the MD model for 4 nm and 10 nm. To account for the effect of neighboring atoms, three-dimensional periodic boundary conditions were employed.

The gold–water system simulations were executed using a CHARMM compatible form of the potential energy function, as shown in Eq. (1). The simulations were performed with a 2 fs integration step; Van der Waals interactions were computed with a cutoff of 12 Å and switching function starting at 10 Å. The long-range electrostatic forces were computed using a particle mesh Ewald (PME) summation method. A canonical NVT (constant number (N), volume (V), and temperature (T)) ensemble was used, and a Langevin thermostat was employed to control the temperature. To investigate the effect of temperature, two temperatures were used in the simulation: room temperature (293 K) and boiling temperature of water (373 K).

The effect of droplet impingement velocity on its spreading behavior was investigated by applying velocities of 0 m/s and 100 m/s for the same set of simulations. To simulate impingement velocities, the nanodroplets were placed tangent to the substrate, and forces were applied to the water atoms in a direction perpendicular to the substrate. The velocity component was induced until the contact angle with the substrate was smaller than 90 deg. Further, the effects of velocity were then removed from the water molecules, releasing them during equilibration. Figure 2 presents a progression of a simulation for 4 nm and 10 nm with an initial velocity of 100 m/s at 293 K, respectively.

The effects of three factors which include the droplet size, temperature, and velocity of impact on the nanodroplet wetting behavior were analyzed. The PME method was used to calculate the direct-space interactions of temperature, pressure, and electrostatic forces. Smooth PME was used to compute the full electrostatic interactions. The potential energy function presented in Eq. (1) was used to represent the intermolecular and interatomic interaction forces
(1)
where $Ubond,$$Uangle$, and $Udihedral$ are the stretching, bending, and torsion interactions, respectively,
(2)
(3)
(4)
$UCoulomb$ is the electrostatic interaction. $UvdW$ is the interaction between nonbonded pairs of atoms that corresponds to the van der Waal's forces, expressed by a Lennard-Jones 6–12 potential as shown in Eq. (5). Assuming that every atom experiences a force from other interacting material, this potential force field considers the interaction between all atoms in the simulation volume within the switching and cutoff distances of 10 Å and 14 Å, respectively. The nonbonded force field parameters used to represent Au atoms were availed from another study [30]
$ELj=4εij[(σijrij)12−(σijrij)6]$
(5)

where $σij$ is the finite distance at which the interparticle potential is zero between a nonbonded pair of atoms $i$ and $j$, $rij$ is the distance between them, and $εij$ is the well depth. The results of the simulation are discussed in terms of the atomic diffusion, dynamic contact angle, spread ratio, radial distribution function, and root-mean-square deviation (RMSD) of the molecular displacement.

### Density Profiles.

In order to measure the contact angle of the droplets, it was necessary to isolate the droplet from the water vapor around it. By calculating the density in the region where the molecules were located, the water molecules that compose the vapor were separated from the atoms that compose the liquid in the droplet. Defining density as the average number of water molecules inside a grid region, we divided the volume of the simulation in cubic bins with a side of 3 Å to calculate the number of water molecules within every bin. In order to build a density field, the original molecular densities are smoothed by applications of averages of a bin and its neighbors. Liquid water has an atomic density of approximately 0.096 atoms/Å3 between 293 K and 373 K [31]. The expected molecular density of liquid water in each bin would be 2.592 atoms/bin ($0.096×33)$. We considered that the boundary between water and vapor occurs at 50% of the atomic density of liquid water. Therefore, if a bin had less than 1.3 atoms/bin, it was considered as vapor. Figure 3 illustrates the water droplet and vapor periphery used for the measurement of contact angles.

A script was created in matlab to automate the process of measuring the density profiles of the simulations. The molecules of liquid water were counted using the same script. Thus, all the molecules that were inside a bin with more than 1.3 atoms were counted as liquid molecules. Thereby, the diffusion rate of molecules in the simulation was calculated for different droplet sizes at varying temperatures and impingement velocities. All the simulations were executed for 2000 steps of minimization, while the equilibration was run until the system attained stability which was calculated based on RMSD values. The equilibration was terminated at a point where the RMSD values reached a plateau or constant rate of growth.

## Results and Discussion

### Effect of Droplet Size.

Figures 4 and 5 show the RMSD of the atomic positions of water molecules in the droplet at 293 K and 373 K, respectively. The RMSD measures the average distance between atoms and is used in this study to investigate the stabilization times and the diffusion of the droplet.

Figure 4 shows the RMSD for the 10 and 4 nm droplets on top of a gold substrate at an ambient temperature of 293 K. This figure also shows the RMSD values for droplets with an initial velocity of 100 m/s. The simulations were terminated once the RMSDs attained a plateau or a steady rate of growth, indicating that the system had approached its equilibrium state. The 4 nm droplets attained steady-state RMSDs within shorter time frames as compared to the 10 nm droplets, both with and without the application of velocity component. The higher surface to volume ratio induces molecules to stabilize faster, due to lower average hydrogen bonds in the droplet, reaching a lower RMSD level at a shorter timeframe for smaller droplets.

The size of the droplets also has an influence on the spread ratios and contact angles of the droplets. Spread factor denoted by, D/D0 ratio (ratio of instantaneous contact diameter (D) to the initial diameter of the droplet (D0)) is the measure of substrate wetting phenomenon at a given temperature. In smaller droplets, a greater proportion of water molecules are located at the surface, hence exposed to a fewer number of hydrogen bonds as compared to those in the interior of the droplet. Thus, larger droplets would need more kinetic energy to modify the surface molecular arrangement and increase wettability. Figures 6 and 7 show the spread ratio and the contact angles of 4 nm and 10 nm droplets at 293 K, respectively. The spread ratio for 4 nm and 10 nm droplets after 2 ns are 0.8 and 0.55, respectively. While the contact angles for 4 nm and 10 nm droplets are 117 deg and 145 deg, respectively.

It is clear that 4 nm droplets had a higher spread ratio and a lower contact angle which implies a higher wetting ability and low interfacial energy [15]. This result is in agreement with a previous study that shows that the wettability increases with the reduction of water molecules in droplets on top of metals and polymers [32]. Therefore, in comparison with 10 nm droplets, 4 nm droplets have higher wettability and lower stabilization times due to its closer spaced molecular structure and a higher surface area to volume ratio.

### Effect of Temperature.

There are several applications at the nanoscale, wherein droplets are used at high temperatures which may include convection cooling of semiconductor chips, spray painting, and atomized media deposition. In order to investigate how an increase in temperature would influence the wettability of the gold substrate, the same set of simulations were performed at the boiling point of water (373 K). Four nanometer and 10 nm droplets were simulated both with and without the impingement velocity component. Figure 5 shows the RMSD graphs of the simulations for 4 nm and 10 nm droplets for both stationary and with impingement velocity components on a gold substrate at 373 K. The simulations were terminated once the RMSD attained steady-state values. For both the droplet sizes, an increase in temperature from 293 K to 373 K induced the water molecules to attain a steady level of displacement in a shorter time. This reduction in stabilization time is evident in the 10 nm droplets simulations. The 10 nm droplet without the application of the velocity reached a steady-state RMSD level of ∼53 Å in 2 ns at 373 K as opposed to 7 ns at the ambient temperature of 293 K (see Fig. 4).

The reduction in stabilization time is due to the fact that an increase in kinetic energy leads to the breaking of hydrogen bonds in the droplet at a faster rate which accelerates the spread of the droplet to the equilibrium contact angle. In addition to increasing the kinetic energy, the increase in temperature also makes the molecular structure of water sparser.

Figure 8 shows the radial distribution function (RDF) $g(r)$ function for the 10 nm droplet at 293 K and 373 K with and without the application of the impingement velocity of 100 m/s. The g(r) describes the variation of the atomic density as a function of the distance away from a particular atom. The RDF g(r) is an indication of the density of a structure, i.e., a solid crystal or liquid cluster [18].

The RDF peaks are relatively higher when the droplet is at 293 K as compared to 373 K. This behavior indicates that the molecular structure of the water is closely spaced at 293 K. An increase in the temperature to 373 K will further increase the kinetic energy to break the hydrogen bonds and change the molecular arrangement of the droplet at a faster rate. Lower temperatures have higher RDF peaks and these peaks get lower and spread out at higher temperatures as the water network becomes progressively more disordered, and the hydrogen bond is considerably weakened. Thus, the temperature is an important parameter that can be controlled to tune the wettability of substrates [21]. Figures 9 and 10 show the contact angle and the spread ratio of the 10 nm droplet at 293 K and 373 K, respectively. The 4 nm droplets at 373 K had significant variability on its periphery shape making measurements of contact angle and spread ratio inconsistent. For the 10 nm droplet, the equilibrium contact angle at 293 K was 145 deg as compared to 127 deg at 373 K. Similarly, the increase in temperature resulted in a higher spread ratio of 0.75 at 373 K as compared to 0.55 at 293 K. Thus, the gold substrate had higher wettability at higher temperatures. In the case where wettability of a substrate needs to be controlled, temperature is an important parameter to be considered.

By using density profiles of the droplet and counting the number of atoms that constitutes liquid water in the droplet, it was possible to infer about the atomic diffusion in the droplets. Figures 11(a) and 11(b) show the atom count of the 4 nm and 10 nm droplets at 293 K and 373 K, respectively. Diffusion in the droplet occurs when the water molecules transition from the liquid state to the vapor phase, thereby decreasing the molecular count of the droplets. At 293 K, both the droplets (4 nm and 10 nm) show a steady-state level of atomic count. Thus, indicating that diffusion rate at room temperature (20 °C) is minimal. However, when the temperature is increased to 373 K, there is an increase in the diffusion rate of molecules as they start to transition from the liquid state to the vapor state at a faster rate. The increase in temperature imparts higher kinetic energy to the molecules at the droplet surface. The higher kinetic energy results in breaking of the hydrogen bonds and release of the water molecules from the liquid droplet.

Thus, the wettability of droplets on the gold substrate can be controlled by manipulating the deposition temperature as confirmed by prior studies [18,21]. In addition, water nanodroplets at higher temperatures have a rapid diffusion rate of water molecules and reach equilibrium contact angles in shorter time frames as compared to lower temperatures.

### Effect of Impingement Velocity.

Nanodroplets imparted with a higher impingement velocity (100 m/s) had higher RMSD values as compared to stationary nanodroplets (Fig. 5). The higher RMSD values correspond to higher displacements of water molecules from the droplet surface leading to formation vapor molecules. Figure 11 shows that there is an increase in the diffusion rate of molecules from the droplet due to vapor phase change when the temperature is increased from 293 K to 373 K. In addition, the results indicate that the diffusion rates of nanodroplets are increased by imparting them a higher impingement velocity (100 m/s). Figure 12 shows the atom count of nanodroplets at 373 K with (100 m/s) and without (stationary) the application of impingement velocity. It was revealed that both the 4 nm and 10 nm droplets loose molecules at a faster rate when subjected to an impingement velocity of 100 m/s.

The rapid rate of water molecules transitioning to the vapor phase can be explained by the fact that the impingement velocity introduces higher kinetic energy, facilitating the breaking of hydrogen bonds and thereby accelerating the diffusions of the molecules. This effect is evident in the 4 nm droplet which has a higher diffusion rate as compared to the 10 nm droplet. This is because the smaller droplet (4 nm) requires lower kinetic energy for changing its molecular arrangement and releasing the water molecules into a vapor phase. Table 1 lists the percentage reduction in droplet size for each of droplet size, temperature, and velocity scenario.

Figure 13 shows the dynamic contact angles of 4 nm and 10 nm droplets at 293 K with (100 m/s) and without (stationary) the application of the velocity component. The assignment of impingement velocity did not influence the equilibrium contact angle for both the droplet sizes. The 4 nm and 10 nm droplets attained equilibrium contact angles of 117 deg and 145 deg, respectively. Impingement velocities also do not have any influence on the spread ratio of the droplets. Figure 14 shows the spread ratio for 4 nm and 10 nm droplets at 293 K with (100 m/s) and without (stationary) the application of the velocity component. The 4 nm and 10 nm droplets have a final spread ratio of 0.80 and 0.55, respectively, independent of the velocity.

The application of impingement velocities introduces kinetic energy to the droplet. The additional kinetic energy, in turn, facilitates the break of hydrogen bonds in the liquid droplet, hence accelerating the diffusion rate of water molecules when the water droplets are submitted to a temperature of 373 K. However, submitting the droplets to the impingement velocity did not influence the final contact angles and spread ratios, nor the stabilization times.

## Conclusions

This paper presents a MDs study of the influence of temperature, droplet size, and impingement velocities on the spreading behavior of nanosized water droplets over a thin gold substrate. Droplets of 4 nm and 10 nm were simulated at temperatures of 293 K and 373 K and at velocities of 0 m/s and 100 m/s, respectively. The RMSD analysis revealed that 10 nm droplets attained faster stabilization at higher temperatures (373 K) and induced higher substrate wettability as compared to 273 K. At room temperature, the 4 nm droplets stabilized at a faster rate than the 10 nm droplet, indicating that smaller droplets have faster stabilization times. At 293 K, the 4 nm droplets presented spread ratio and contact angle measurements of 0.8 deg and 117 deg, respectively. Whereas, the 10 nm droplets presented a spread ratio and contact angle of 0.55 deg and 145 deg, respectively. Thus, the 4 nm droplets induced higher substrate wettability as compared to the 10 nm droplets. When subjected to an impingement velocity of 100 m/s, the nanodroplets had higher diffusion rates and evaporation of molecules to the ambient as compared to stationary droplets. Impinging the 4 nm and 10 nm droplets at 373 K presented a diffusion rate of 21.7% and 8.48%, respectively. However, stationary 4 nm and 10 nm droplets presented diffusion rates of 10.45% and 4.64%, respectively. At room temperature (293 K), the velocity of the droplets did not influence the stabilization times and the diffusion rates. In addition, the spread ratios and contact angles for stationary nanodroplets and those with an impingement velocity remained unaffected at equilibrium. This research investigates the effect of different factors on the wettability of gold thin films which has several practical applications. This approach can be extended to study the combinatorial aspects of substrate wettability for colloidal and nanoparticulate liquid media in several nanomanufacturing processes.

## Acknowledgment

This work was funded by National Science Foundation (NSF CMMI: Award 1435649) and the U.S. Army Research Fellowship.

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