The Leidenfrost Effect at the Nanoscale

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The Leidenfrost Effect at the Nanoscale Jhonatam Cordeiro Department of Industrial and Nanotechnology has been presenting successful applications in several ﬁelds, such as Systems Engineering, electronics, medicine, energy, and new materials. However, the high cost of investment in North Carolina A&T State University, facilities, equipment, and materials as well as the lack of some experimental analysis at 419 McNair Hall, the nanoscale can limit research in nanotechnology. The implementation of accurate 1601 East Market Street, computer models can alleviate this problem. This research investigates the Leidenfrost Greensboro, NC 27411 effect at the nanoscale using molecular dynamics (MDs) simulation. Models of water e-mail: [email protected] droplets with diameters of 4 nm and 10 nm were simulated over gold and silicon sub- 1 strates. To induce the Leidenfrost effect, droplets at 293 K were deposited on heated sub-

Salil Desai strates at 373 K. As a baseline, simulations were run with substrates at room temperature Downloaded from http://asmedigitalcollection.asme.org/heattransfer/article-pdf/4/4/041001/5949632/jmnm_004_04_041001.pdf by guest on 27 September 2021 Department of Industrial and (293 K). Results show that for substrates at 293 K, the 4 nm droplet has higher position Systems Engineering, variability than the 10 nm droplets. In addition, for substrates at 373 K, the 4 nm droplets North Carolina A&T State University, have higher velocities than the 10 nm droplets. The wettability of the substrate also influ- 423 McNair Hall, ences the Leidenfrost effect. Droplets over the gold substrate, which has hydrophobic 1601 East Market Street, characteristics, have higher velocities as compared to droplets over silicon that has a Greensboro, NC 27411 hydrophilic behavior. Moreover, the Leidenfrost effect was observed at the boiling e-mail: [email protected] temperature of water (373 K) which is a significantly lower temperature than reported in previous experiments at the microscale. This research lays the foundation for investigating the fluid–structure interaction within several droplet based micro- and nano-manufacturing processes. [DOI: 10.1115/1.4034607]

Introduction [10] used MD simulation to investigate the failure mechanism of Si molds and reduce defective outputs of nano-imprint lithography Nanotechnology has been presenting several applications (NIL) process. Chen et al. [11] used a hybrid approach of MD despite being a recent field. Applications include compact transis- simulation and experiments and proposed a highly sensitive sen- tors that make faster and energy efficient processors and memory sor to detect molecular conformation. Desai et al. [12] used MD chips [1], long-life battery cells [2], efficient drug-delivery sys- simulations to investigate the wettability of SiO and Si N as a tems [3], DNA sequencing chips [4], stronger structural materials 2 3 4 function of temperature. Borodin et al. [13] used MD simulations [5], superconducting materials [6], and others. These successful to investigate the properties of lithium batteries and minimize applications of components measuring less than 100 nm have interfacial resistance, improving battery safety and battery life. demonstrated the potential of nanotechnology and the need for a This research demonstrates the applicability of molecular better understanding of material properties at the nanoscale. dynamics to investigate the Leidenfrost effect at the nanoscale Working with nanotechnology often requires expensive materials, which is an underexplored phenomenon. Several direct-write specialized equipment, and state-of-the-art facilities. Besides the droplet based manufacturing processes involve the deposition of high cost of these resources, they also require long setup times, micro- and nano-scale droplets on heated substrates. These trained personnel, and complex procedures. The high cost of pro- include scalable inkjet [14,15], aerosol jet [16], electrohydrody- curement and operation of nanotechnology resources can restrict namic jet [17], and other atomized droplet processes where the the development in this field. To the best of our knowledge, there droplet deposition dynamics determines the morphology of the is no microscopy method that can observe droplet at the nano- printed feature. Thus, it is critical that the transport properties of scale, without influencing the measurements of the experiments. droplet be investigated in order to determine the fluid–structure One solution to help optimize the R&D in nanotechnology is to interaction between different substrate materials at elevated tem- use computer models to help optimize design and process parame- peratures. In addition, this research investigates the droplet move- ters of the experiments and products, hence reducing costs and ment on heated substrates, which has an impact on the final increasing design freedom. placement and stabilization shape of the droplet. The phenomena Traditional numerical simulation methods, such as finite ele- of water interfacing with a hot surface were first investigated by ments, predict material properties up to the submicron scale [7,8]. Leidenfrost in 1756 [18]. If a droplet of liquid is deposited over a However, they fail to make correct predictions for components surface around the boiling temperature of the liquid, the liquid smaller than several hundred nanometers [9]. A more accurate boils and evaporates rapidly. However, when the temperature of approach for computer modeling for the nanoscale is to use the surface is significantly higher than the boiling temperature of molecular dynamics models. In MDs models, each atom in the the liquid, the droplet levitates over its own vapor, greatly increas- system and their interaction with other atoms are represented. The ing the evaporation time of the droplet. Also, the thin layer of representation accuracy, freedom of design, and insights that can vapor avoids the nucleation of bubbles, preventing the droplet be gained by using MD modeling have attracted several research from boiling and making it evaporate slowly [19]. This research groups to investigate nanotechnology applications. Tada et al. investigates the Leidenfrost effect at the nanoscale based on variations in droplet size, substrate temperature, and substrate material. 1Corresponding author. We track the droplet trajectory path via its centroid and its veloc- Contributed by the Manufacturing Engineering Division of ASME for publication ity overtime. The tools, parameters, and models used in this work in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received May 30, 2016; final manuscript received August 22, 2016; published online October 10, 2016. can be extended to other materials and substrate geometries to Assoc. Editor: Rajiv Malhotra. enable other scenarios of the Leidenfrost effect to be studied. The

Journal of Micro- and Nano-Manufacturing Copyright VC 2016 by ASME DECEMBER 2016, Vol. 4 / 041001-1 results of this research provide quantitative analysis on the role Table 1 Nonbonded interaction parameters of different process parameters that impact the Leidenfrost ˚ effect at the nanoscale regime. Further, they provide a basis to Atom type eijðkcal=molÞ rijðAÞ investigate several droplet based nano- and micro-manufacturing processes. Si Si 0.31 4.27 Au Au 0.039 1.8436 Methodology In this research, the nanoscale molecular dynamics (NAMDs) [20] source code was used in conjunction with virtual molecular dynamics (VMDs) software to model the materials in the system Table 2 Simulation conﬁgurations and visualize the simulation output. NAMD is robust for parallel computing [20,21] and open source and compatible with most Index Temperature (K) Substrate Droplet size (nm) force ﬁelds for commonly available CHARMM [22] and AMBER [23] packages. The MD simulations were executed on a graphical 1 293 Au 10

2 293 Au 4 Downloaded from http://asmedigitalcollection.asme.org/heattransfer/article-pdf/4/4/041001/5949632/jmnm_004_04_041001.pdf by guest on 27 September 2021 processing unit (GPU) processor (NVIDIA Tesla K40) with 3 293 Si 10 2880 CUDA cores on a 64-bit Linux based system to enhance the 4 293 Si 4 performance of the computations [24]. The NAMD source code 5 373 Au 10 uses the GPU for nonbonded force evaluation while the energy 6 373 Au 4 evaluation is done on the central processing unit [25]. 7 373 Si 10 In this work, MD models of 4 nm and 10 nm water droplets 8 373 Si 4 were used, containing 1108 and 17,267 molecules, respectively. Substrates of gold and silicon measuring 240 A˚ 240 A˚ 40 A˚ in dimensions were used. The water molecules had a TIP3P structure X and were modeled using VMD. All the force fields used in the angle 2 Uangle ¼ ki ðhi h0iÞ (3) simulations are compatible with the CHARMM standard, and the bonds i format of potential energy function shown in Eq. (1) was used to X X represent the atomic interactions. The simulations were performed qiqj with a 2 fs integration time step. Van der Waals interactions were UCoulomb ¼ (4) 4pe0rij computed with a cutoff of 12 A˚ and switching function starting i j>i at 10 A˚ . The long-range electrostatic forces were computed "# X X 12 6 using a particle mesh Ewald (PME) summation method. A canoni- rij rij U ¼ 4e (5) cal ensemble of conserved number of atoms, volume and tempera- vdW ij i j>i rij rij ture was used, and a Langevin thermostat was employed to control the temperature. The water droplets were modeled as The parameters for Eqs. (2)–(5) for water molecules (oxygen spheres and placed on top of the substrates, as illustrated in Fig. 1 and hydrogen) were taken from the CHARMM force fields [26]. The parameters for gold and Si substrates were adapted from U ¼ U þ U þ U (1) total bond angle nonbond Braun et al. [27] and Mayo et al. [28], respectively, as shown in Table 1. where Ubond and Uangle are the stretching and bending interac- The objective of the simulations was to analyze the Leidenfrost tions, as described in Eqs. (2) and (3), respectively. Unonbond is the effect which describes the fluid–substrate interactions at the nano- interaction between nonbonded pairs of atoms that correspond to scale. An important aspect of this research was to investigate the the electrostatic interactions and van der Waal’s forces, expressed variations in the droplet velocity over the substrate as a function by Lennard-Jones 6–12 potentials [20], as described in Eqs. (4) of the substrate material and temperature. The trajectory path of and (5) the droplet was used to analyze the relationship between the X droplet movement and the physics of the Leidenfrost phenomena. bond 2 Ubond ¼ ki ðri r0iÞ (2) The centroid of the droplet was recorded every 2 ps to construct a bonds i trajectory path. The velocity of the droplet was computed by dif- ferentiating the droplet positions over time. Scripts in VMD were used to compute the droplet position, and MATLAB was used to calculate the velocities. Two temperature levels were used in the simulation: 293 K and 373 K. Table 2 shows the design of experiments based on the combination of droplet size, substrate material, and temperature. Simulation runs were conducted to execute the three factors (k) at two levels each (2 k ¼ 23 ¼ 8 runs). The behavior of nanoscale water droplets coming in contact with a heated substrate was simulated. The simulations run at 293 K served as a base line to observe droplet behavior at room temperature. In order to simulate a heated substrate, the entire simulation volume was initially thermalized for 5 ps, wherein the system reaches a temperature of 293 K. After this initial phase, the substrate was heated and maintained at 373 K using a Langevin temperature control thermostat for the entire simulation period.

Results and Discussion Nanodroplets at 4 nm and 10 nm were tracked using their trajectory proﬁles. The effect of droplet size, substrate material, and Fig. 1 Initial conﬁguration of the MD models of 10 nm water temperature on the nanodroplet spreading dynamics was observed droplets over a substrate over time. Further, the presence of the Leidenfrost effect was

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Fig. 2 Simulations at 293 K (time period 5 2 ns): (a) 4 nm water droplet over gold, (b) 4 nm water droplet over silicon, (c)10nm water droplet over gold, and (d) 10 nm water droplet over silicon veriﬁed by tracking the kinetic energy and temperature of different layers of the nanodroplet from the substrate surface.

Droplet Position One of the first evidence of the Leidenfrost effect on a droplet over a flat surface is that the droplet tends to move over the sub- Fig. 3 Top view of moving droplets over (a) gold and (b) silicon strate. Figure 2 shows the top view of 4 nm and 10 nm droplets at 373 K at time 0 ns, 1 ns, and 2 ns deposited over gold and silicon at 293 K after 2 ns of simulation. It can be seen that the droplets deposited over a substrate at According to Leidenfrost [29], droplets move on a heated sub- room temperature (293 K) have minimal displacement within the strate due to a thin layer of vapor that forms between the droplet 2 ns time frame. The droplets have a z-directional displacement and the heated surface. Typically, the vapor layer separates the when they spread over the substrates (see Fig. 10), but remain sta- droplet from the surface and propels it in random directions, tionary in x–y directions. The water nanodroplets display both hydrophilic and hydrophobic interactions with respect to silicon and gold substrates (Fig. 10). The trajectory path of the droplets (bold line) remains at the center of the simulation volume, indicating that the droplets maintain a steady position. However, in contrast, a droplet deposited over a heated substrate (373 K) starts to move in random directions. Figure 3 shows the top view of 4 nm droplets moving over gold (a) and silicon (b) substrates over time at 373 K. From Fig. 3, it is evident that after 1 ns the droplets moved to a different region on the substrate. Droplets deposited over gold have a higher displacement than droplets deposited over silicon. After 2 ns, the 4 nm droplet presents a significant displacement and is positioned at the edge of the substrate. However, the 4 nm droplet over silicon moved significantly less than the droplet over gold. To better illustrate the movement of the droplets, the trajectory path of 4 nm and 10 nm droplets deposited over gold and silicon substrates at 373 K is shown in Fig. 4. The 4 nm droplets over gold at 373 K present the highest displacement and its trajectory path is the longest. Ten nanometer droplets over gold present a significant displacement, but smaller than the 4 nm droplet. Nanodroplets over silicon present a lower displacement as compared to droplets over gold. Similar to the gold substrate, the 4 nm droplets show higher displacement as compared to the 10 nm droplet over the silicon substrate. This is due to the fact that larger nanodroplets have higher aggregate Fig. 4 Simulations at 373 K (time period 5 2 ns): (a) 4 nm water mass which limits its mobility based on the vapor layer formation droplet over gold, (b) 4 nm water droplet over silicon, (c)10nm in between the droplet and the substrate. water droplet over gold, and (d) 10 nm water droplet over silicon

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Fig. 5 (a) Kinetic energy (kcal/mol) and (b) temperature (K) of 4 nm droplet over gold as a function of the distance away from the substrate surface

Fig. 6 (a) Kinetic energy (kcal/mol) and (b) temperature (K) of 10 nm droplet over gold as a function of the distance away from the substrate surface depending on the flow direction of the vapor. Experiments at the nanodroplets are placed over a substrate at 293 K (dashed line), microscale have demonstrated that the Leidenfrost effect occurs at the molecular kinetic energy is similar for all the layer of mole- temperatures above 473 K [19]. One important finding from our cules. Thus, this constant kinetic energy (2000 kcal/mol) illus- simulations with nanoscale droplet reveals that this effect was trates that the droplet has only one water state, which is liquid. observed at 373 K. This temperature to observe the Leidenfrost The main characteristic of the Leidenfrost effect is the fact that effects is significantly lower than temperatures at the microscale. droplets undergoing this phenomenon require a longer time period We further explore this effect by dividing the droplets in layers of for evaporation when placed on a heated substrate. This is because 0.5 A˚ in height and measuring the kinetic energy of molecules in a vapor boundary layer is formed between the substrate and the each layer away from the substrate surface. Figures 5(a) and 6(a) lower layers of the droplet interfacing with the substrate. The show the average kinetic energy of the atoms as a function of the presence of the vapor layer reduces the heat exchange between distance away from the gold substrate surface for 4 nm and 10 nm the substrate and the nanodroplet, resulting in longer evaporation droplets, respectively. It can be observed that at 373 K (solid line times for the droplet. Figures 5(b) and 6(b) show the temperature legend), nanodroplets display higher molecular kinetic energy for profiles of the atoms as a function of the distance away from the layers closer to the substrate. However, there is a steep decrease gold substrate surface for 4 nm and 10 nm droplets, respectively. in the kinetic energy of molecules for distance over 4A˚ from The temperature profiles are analogous to the kinetic energy pro- the substrate. The graphs at 373 K for both 4 nm and 10 nm drop- files and display a steep rise in the temperature of the atoms in the lets depict the presence of two distinct water phases in the simula- vicinity of the substrate. This steep increase in temperature can be tion. This includes a thin layer of vapor next to the substrate with attributed to the formation of superheated steam at the droplet and a higher kinetic energy and a liquid phase in the layers further substrate interface. The rapid escape of these high energy vapor away from the substrate with lower kinetic energy. In addition, molecules from the bottom of the droplet causes it to propel the the 4 nm droplet has higher kinetic energy (9750 kcal/mol) as droplet in the lateral (x–y plane) direction. It is important to note compared to the 10 nm droplet (8300 kcal/mol). This can be attrib- that the temperature and kinetic energies of atoms above the vapor uted to the lower escape velocities of the vapor molecules boundary layer are much lower as compared to the peak values. If from under the nanodroplet for larger droplet sizes due to higher the peak values in kinetic energy and temperature were primarily aggregation of molecules for the 10 nm droplet. In contrast, when convection based, then the average kinetic energy in the

041001-4 / Vol. 4, DECEMBER 2016 Transactions of the ASME subsequent layers of the droplet would also increase over time. This was not observed in our simulation results suggesting that phenomena being observed were in fact the Leidenfrost effect. When the Leidenfrost effect occurs, the heat transfer between substrate and water droplet is signiﬁcantly reduced. The Leiden- frost effect negatively impacts heat-transfer rates for applications which rely on convection-based heat transfer between liquid media and solid surface. Thus, in practical applications such as industrial coolers, chillers, computer chips and other devices, there is a steep drop in thermal heat transfer efﬁciency due to vapor formation based on the Leidenfrost effect. Our research plays an important role to investigate and explain the Leidenfrost effect for nanoscale liquid–solid interfaces to resolve heat-transfer issue in heat exchangers. In addition, this research investigates the

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Velocity The velocity of the droplet calculated based on its centroid (as Fig. 8 Velocity of 4 nm and 10 nm droplet over gold substrate represented in Eq. (6)) was used to infer about the vapor layer at 373 K formation. The position and velocity measurements for the nanodroplets were conducted in a three-dimensional coordinate system. Figures 7–9 show the instantaneous velocities for nanodroplets at 293 K and 373 K on gold and silicon substrates, respectively. As can be seen in the graphs, there is an initial increase in the velocity which can be attributed to the z-directional component of the velocity. This occurs as the droplet undergoes a verti- cal displacement from its initial spherical shape to its stabilization shape on the substrate. This phenomenon is captured within 100–200 ns since the beginning of the simulation depending on the size of the droplet and type of substrate. After attaining equi- librium contact angle (Fig. 10), the droplet is propelled on the substrate due to the Leidenfrost effect in the x–y plane. Thus, the motion of the droplet in the lateral plane (x–y plane) is the primary component to the velocity as shown in Figs. 8 and 9. The higher the droplet velocity, the more intensiﬁed is the vapor formation process. The velocity of the droplets (4 nm and 10 nm) at room temperature was computed to serve as a base case to study the Leidenfrost effect. Figure 7 shows the velocities of 4 nm and 10 nm droplets over gold and silicon at 293 K. The velocities in Fig. 7 represent the random vibration of the droplet around its stationary mean position. These droplet velocities occur when the Fig. 9 Velocity of 4 nm and 10 nm droplet over silicon sub- droplet stays in its original position and is reﬂected as “noise” in strate at 373 K the system. The droplet velocity calculation based on its centroid position is calculated as shown in the following equation: PtðÞþ Dt PtðÞ VtðÞ¼ (6) Dt

where PðtÞ is the three-dimensional droplet centroid position at time t, and Dt is the step size of the simulation (2 fs). Figure 7 shows that the stationary vibration velocities of the 4 nm droplets are higher as compared to 10 nm droplets. This can be explained by the fact that smaller droplets have lower number of molecules (1108). The velocity is based on the position of the droplet center of mass, which in turn is a weighted average of all the molecules positions in the droplet. The bigger the pool of molecular positions used to calculate the center of mass, the lower its position variability. Because the velocity of the droplets is calculated as the derivative of position, the droplet position variability can in turn be derived into velocity. In other words, the random variability noise of the molecular centroid could cause the derivative to be greater than zero, even with the droplet being stationary. In this way, the higher the pool of molecules, the lower the position variability of the droplet and therefore the lower its velocity. The 10 nm droplets have more molecules (17,267), and the individual droplet displacement is an average of the pool of its Fig. 7 Velocity of 4 nm and 10 nm droplets over gold and sili- molecules. One can expect that as the number of molecules grows, con substrates at 293 K the droplet velocity would reduce further, and eventually be close

Journal of Micro- and Nano-Manufacturing DECEMBER 2016, Vol. 4 / 041001-5 Fig. 10 Side view of (a) 10 nm droplet over gold and (b) 10 nm droplet over silicon

to zero for droplets at the mesoscale. The random vibration of sta- occur. Figure 10 shows the side view and the contact angle for Downloaded from http://asmedigitalcollection.asme.org/heattransfer/article-pdf/4/4/041001/5949632/jmnm_004_04_041001.pdf by guest on 27 September 2021 tionary droplets around its mean position can be used as a baseline 10 nm droplets over gold and silicon. velocity to benchmark moving nanodroplets. The velocity of the The contact angle of the 10 nm droplet over gold is 125 deg nanodroplets subjected to the Leidenfrost effect has much higher clearly indicating the hydrophobic interaction of water and gold velocities as compared to baseline velocities of stationary drop- substrate. The contact angle of the 10 nm droplet over silicon is lets. This is evident for the nanodroplet motion on both the sub- 70 deg, thus making a hydrophilic substrate. The silicon substrate strates. The average baseline velocity of 10 nm droplet on silicon slows down the droplets movement because of the higher adhe- substrate at 293 K was around 1 m/s as compared to 4 m/s at 373 K sion between them. This phenomenon restricts the formation of due to the Leidenfrost effect. Similarly, the average baseline vapor layer and limits its lateral motion on the substrate. velocity of 4 nm droplet on silicon substrate at 293 K was around 3 m/s as compared to 6 m/s at 373 K due to the Leidenfrost effect. Conclusions In case of the gold substrate, the average baseline velocity of the 10 nm droplet at 293 K was around 2 m/s as compared to 5 m/s at This research explores the Leidenfrost effect at nanoscale 373 K due to the Leidenfrost effect. The same fact applies to the dimensions using molecular dynamics simulations. Water droplets 4 nm droplet which had an average baseline velocity of 4.5 m/s at at 4 nm and 10 nm were simulated over gold and silicon substrates 293 K as compared to 12.5 m/s at 373 K. Thus, the moving droplet at 293 K and 373 K, respectively. At 293 K, both the droplets velocities are much higher as compared to random vibration of remained stationary on the substrate limiting their displacement stationary droplets which indicates the presence of the Leidenfrost from their original position. However, smaller droplets (4 nm) dis- effect at the nanoscale. played higher random velocity about their mean position as compared to the 10 nm droplets. This can be attributed to the fact that smaller droplets have fewer atoms enabling higher variability for Droplet Size its centroid due to the smaller aggregation pool. The Leidenfrost When the temperature of the substrate is increased to 373 K, the effect was observed when droplets were deposited on the heated droplets undergo random motion along the substrate, representing substrate at 373 K. This result is in contrast with the Leidenfrost the Leidenfrost effect. Figure 8 shows the velocity of 4 nm and effect at the macro- and micro-scale which is typically observed 10 nm droplets over a gold substrate at 373 K. The simulation of for temperatures over 473 K. At 373 K, the 4 nm droplets pre- 4 nm and 10 nm droplets was terminated at 2 ns and 5 ns, respec- sented higher propagation velocities than the 10 nm droplets. This tively. Smaller droplets have a faster stabilization time at room is due to the fact that smaller droplets have a higher surface to vol- temperature (293 K). In addition, droplets deposited over a heated ume ratio which makes the smaller droplets absorb higher energy plate (373 K) display movement and velocity peaks in a shorter per unit volume. Also, molecules at the surface of the droplet time as compared to 10 nm droplets. have fewer hydrogen bonds and require less energy to separate As can be seen from Fig. 8, the 4 nm droplet has significantly from other molecules. Thus, when exposed to a heated substrate, higher velocity as compared to the 10 nm droplet. At 373 K, the the breakage of hydrogen bonds is accelerated on smaller droplets average velocity of the 4 nm droplet is around 12.5 m/s as com- as they possess proportionally fewer hydrogen bonds. In addition, pared to 5 m/s for the 10 nm droplet on the gold substrate. Besides the smaller droplets have a lower inertia and thereby are promi- having fewer molecules that average for the center of mass, the nently influenced by the propelling forces of the vapor layer. smaller droplets also have a higher surface to volume ratio. Thus, Droplets deposited over gold substrate had higher velocities than a smaller droplet has more atoms on its surface, where they are droplets deposited over silicon. Silicon substrates are more hydro- subjected to fewer hydrogen bonds. This facilitates the breakage philic than gold substrates, and the affinity between liquid and of hydrogen bonds and formation of vapor. The accelerated vapor substrate acts as a restrain to the droplet movement. These results formation increases the droplet velocity. Moreover, smaller drop- reveal the interplay of different process parameters which impact lets have lower inertia and a lower resistance to displacement. the Leidenfrost effect, an unexplored phenomenon at the nano- Similarly, higher migration velocities are observed for the 4 nm scale. This research forms a foundation to understand nanoscale droplets when deposited over a silicon substrate at 373 K, compar- droplet propagation and heat transfer within several droplet based ing the 10 nm droplets deposited over the same substrates (shown nano- and micro-manufacturing processes. in Fig. 9). As can be seen from Fig. 9, the 4 nm droplet has higher the Acknowledgment velocity (6 m/s) as compared to the 10 nm droplet (4 m/s) on the The authors extend their gratitude to the U.S. National Science silicon substrate. However, both the 4 nm and 10 nm droplets Foundation (NSF CMMI: Award No. 1435649) and the TMCF- maintain a higher velocity over gold as compared to silicon sub- Army Research Laboratory Faculty Research Fellowship for strate. The reduced velocity of droplets over the silicon substrate support toward this research. is due to the fact that the interaction of water nanodroplets with silicon is more hydrophilic than gold. The higher affinity between Nomenclature water molecules and the silicon substrate implies that more energy angle is necessary to separate the water droplet from the substrate by a ki ¼ bending constant of the bond bond layer of vapor, a condition necessary for the Leidenfrost effect to ki ¼ stretching constant of the bond

041001-6 / Vol. 4, DECEMBER 2016 Transactions of the ASME PðtÞ¼droplet centroid at time t [12] Desai, S., Kaware, R. D., and Rodrigues, J., 2014, “Temperature-Dependent Wettability on Silicon Dioxide and Silicon Nitride Substrates,” J. Nanoeng. qi ¼ charge of atom i Nanomanuf., 4(3), pp. 237–246. ri ¼ bond length [13] Borodin, O., Zhuang, G. V., Ross, P. N., and Xu, K., 2013, rij ¼ distance between atom i and j “Molecular Dynamics Simulations and Experimental Study of Lithium Ion Transport in Dilithium Ethylene Dicarbonate,” J. Phys. Chem. C, 117(15), r0i ¼ reference bond length (length with minimal stretching pp. 7433–7444. potential energy) [14] Desai, S., Esho, T., and Kaware, R., 2012, “Experimental Investigation of Con- t ¼ time (ns) trolled Microdroplet Evaporation Toward Scalable Micro/Nanomanufacturing,” Uangle ¼ potential energy from bending interactions IIE Trans., 44(2), pp. 155–162. [15] Adarkwa, E., and Desai, S., 2016, “Scalable Droplet Based Manufacturing Ubond ¼ potential energy from stretching interactions Using In-Flight Laser Evaporation,” J. Nanomanuf. Nanoeng., 6(3), pp. 1–6. Unonbond ¼ potential energy from nonbonded interactions [16] Werner, C., Godlinski, D., Zollmer,€ V., and Busse, M., 2013, “Morphological Utotal ¼ total potential function Inﬂuences on the Electrical Sintering Process of Aerosol Jet and Ink Jet VðtÞ¼droplet velocity at time t Printed Silver Microstructures,” J. Mater. Sci.: Mater. Electron., 24(11), Dt ¼ time step between position measurements pp. 4367–4377. [17] Erven, J. V., Moerman, R., and Marijnissen, J. C., 2005, “Platinum Nanoparticle eij ¼ depth of potential energy well Production by EHDA,” Aerosol Sci. Technol., 39(10), pp. 941–946.

e0 ¼ electromagnetic permittivity of free space [18] Leidenfrost, J. G., 1756, De Aquae Communis Nonnullis Qualitatibus Tractatus, Downloaded from http://asmedigitalcollection.asme.org/heattransfer/article-pdf/4/4/041001/5949632/jmnm_004_04_041001.pdf by guest on 27 September 2021 hi ¼ angular displacement of the bond Ovenius, Berlin. [19] Biance, A.-L., Clanet, C., and Quere, D., 2003, “Leidenfrost Drops,” Phys. h0i ¼ reference bond angular displacement Fluids, 15(6), pp. 1632–1637. rij ¼ distance between atom i and j at which the interparticle [20] Phillips, J. C., Braun, R., Wang, W., Gumbart, J., Tajkhorshid, E., Villa, E., potential is zero Chipot, C., Skeel, R. D., Kale, L., and Schulten, K., 2005, “Scalable Molecular Dynamics With NAMD,” J. Comput. Chem., 26(16), pp. 1781–1802. [21] Humphrey, W., Dalke, A., and Schulten, K., 1996, “VMD: Visual Molecular References Dynamics,” J. Mol. Graphics, 14(1), pp. 33–38. [1] Wong, H.-S. P., and Salahuddin, S., 2015, “Memory Leads the Way to Better [22] Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S., Computing,” Nat. Nanotechnol., 10(3), pp. 191–194. and Karplus, M., 1983, “CHARMM: A Program for Macromolecular Energy, [2] Zheng, G., Lee, S. W., Liang, Z., Lee, H.-W., Yan, K., Yao, H., Wang, H., Li, Minimization, and Dynamics Calculations,” J. Comput. Chem., 4(2), W., Chu, S., and Cui, Y., 2014, “Interconnected Hollow Carbon Nanospheres pp. 187–217. for Stable Lithium Metal Anodes,” Nat. Nanotechnol., 9(8), pp. 618–623. [23] Pearlman, D. A., Case, D. A., Caldwell, J. W., Ross, W. S., Cheatham, T. E., [3] Suri, S. S., Fenniri, H., and Singh, B., 2007, “Nanotechnology-Based Drug DeBolt, S., Ferguson, D., Seibel, G., and Kollman, P., 1995, “AMBER: A Pack- Delivery Systems,” J. Occup. Med. Toxicol., 2(1), pp. 1–6. age of Computer Programs for Applying Molecular Mechanics, Normal Mode [4] Heerema, S. J., and Dekker, C., 2016, “Graphene Nanodevices for DNA Analysis, Molecular Dynamics and Free Energy Calculations to Simulate the Sequencing,” Nat. Nanotechnol., 11(2), pp. 127–136. Structural and Energetic Properties of Molecules,” Comput. Phys. Commun., [5] Wagner, H. D., 2007, “Nanocomposites: Paving the Way to Stronger Materi- 91(1), pp. 1–41. als,” Nat. Nanotechnol., 2(12), pp. 742–744. [24] Stone, J. E., Hardy, D. J., Ufimtsev, I. S., and Schulten, K., 2010, [6] Piraux, L., Encinas, A., Vila, L., Matefi-Tempfli, S., Matefi-Tempfli, M., “GPU-Accelerated Molecular Modeling Coming of Age,” J. Mol. Graphics Darques, M., Elhoussine, F., and Michotte, S., 2005, “Magnetic and Supercon- Modell., 29(2), pp. 116–125. ducting Nanowires,” J. Nanosci. Nanotechnol., 5(3), pp. 372–389. [25] Kindratenko, V. V., Enos, J. J., Shi, G., Showerman, M. T., Arnold, G. W., [7] Hirai, Y., Konishi, T., Yoshikawa, T., and Yoshida, S., 2004, “Simulation and Stone, J. E., Phillips, J. C., and Hwu, W.-M., 2009, “GPU Clusters for Experimental Study of Polymer Deformation in Nanoimprint Lithography,” High-Performance Computing,” IEEE International Conference on Cluster J. Vac. Sci. Technol. B, 22(6), pp. 3288–3293. Computing and Workshops, CLUSTER’09, New Orleans, LA, Aug. 31–Sept. 4, [8] Song, Z., Choi, J., You, B. H., Lee, J., and Park, S., 2008, “Simulation Study on pp. 1–8. Stress and Deformation of Polymeric Patterns During the Demolding Process in [26] MacKerell, A. D., Bashford, D., Bellott, M., Dunbrack, R., Evanseck, J., Field, Thermal Imprint Lithography,” J. Vac. Sci. Technol. B, 26(2), pp. 598–605. M. J., Fischer, S., Gao, J., Guo, H., and Ha, S. A., 1998, “All-Atom Empirical [9] Yasuda, M., Tada, K., and Hirai, Y., 2010, Molecular Dynamics Study on Mold Potential for Molecular Modeling and Dynamics Studies of Proteins,” J. Phys. and Pattern Breakages in Nanoimprint Lithography, INTECH Open Access Chem. B, 102(18), pp. 3586–3616. Publisher, Rijeka, Croatia. [27] Braun, R., Sarikaya, M., and Schulten, K., 2002, “Genetically Engineered [10] Tada, K., Horimoto, S., Kimoto, Y., Yasuda, M., Kawata, H., and Hirai, Y., Gold-Binding Polypeptides: Structure Prediction and Molecular Dynamics,” 2010, “Molecular Dynamics Study on Compressive Strength of Monocrystal- J. Biomater. Sci. Polym. Ed., 13(7), pp. 747–757. line, Nanocrystalline and Amorphous Si Mold for Nanoimprint Lithography,” [28] Mayo, S. L., Olafson, B. D., and Goddard, W. A., 1990, “DREIDING: A Microelectron. Eng., 87(10), pp. 1816–1820. Generic Force Field for Molecular Simulations,” J. Phys. Chem., 94(26), [11] Chen, Y., Cruz-Chu, E. R., Woodard, J. C., Gartia, M. R., Schulten, K., and pp. 8897–8909. Liu, L., 2012, “Electrically Induced Conformational Change of Peptides on [29] Quere, D., 2013, “Leidenfrost Dynamics,” Annu. Rev. Fluid Mech., 45(1), Metallic Nanosurfaces,” ACS Nano, 6(10), pp. 8847–8856. pp. 197–215.

Journal of Micro- and Nano-Manufacturing DECEMBER 2016, Vol. 4 / 041001-7