Molecular Dynamics Study of Temperature Influence on Directional

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C: Physical Processes in Nanomaterials and Nanostructures

Molecular Dynamics Study of Temperature Influence on Directional Motion of Gold Nano-Particle on Nano-Cone Surface Awais Mahmood, Shuai Chen, Chaolang Chen, Ding Weng, and Jiadao Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12405 • Publication Date (Web): 28 Jan 2019 Downloaded from http://pubs.acs.org on February 5, 2019

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The Journal of Physical Chemistry

Molecular

Dynamics

Study

of

Temperature

Influence on Directional Motion of Gold NanoParticle on Nano-Cone Surface Awais Mahmood, Ъ Shuai Chen,ЫChaolang Chen, Ъ Ding Weng, Ъ and Jiadao WangЪ* Ъ

State Key Laboratory of Tribology, Tsinghua University, Beijing, 100084, China

Ы

Institute of High Performance Computing, A*STAR, 138632, Singapore

ACS Paragon Plus Environment

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ABSTRACT: In this work, the directional motion and underlying mechanism of a circular shaped gold nano-particle (AuNP) on nano-cone (NC) surface were studied with the aid of molecular dynamics simulation. Three specific sized AuNP(s) having a particular number of atoms, and three nano-cones having distinct apex angle, were utilized in this work. The simulation was run in a temperature range of 300K to 1300K to observe the effect of temperature on the directional motion of AuNP located outside of NC surface. The results revealed that the AuNP tend to move towards the larger diameter direction of the NC at higher temperature range while it stayed intact on the area around the tip of NC at lower temperature range. It was observed that the average velocity of AuNP located outside the NC surface with large apex angle was comparatively lower than that on the NC surface having small apex angle. Furthermore, it was inspected that the interaction energy of the AuNP is reduced heavily as the temperature is increased and it decayed more in the large diameter AuNP which resulted in higher velocity of large diameter AuNP on NC surface. Moreover, the contact angle of AuNP on flat silicon surface is observed. It was found that the AuNP stayed intact at low temperature but it started to deform at higher temperature due to its transition from unmolten (solid) to molten (liquid) state. In addition, the melting temperature of AuNP is also measured by analyzing the potential energy results at different temperatures during the simulation.


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1. INTRODUCTION The tremendous development in the field of nanotechnology in recent years has given rise to new topics of interests, such as, nano-manipulation. In plenty of recent studies the interaction and control of nano-scale phenomenon using gold nano-particles (AuNPs) has been studied intensively due to its probable utilization in the research field of light absorption enhancement of solar cells,1 atomic force microscopy (AFM) for imaging of AuNP,2 biomedical applications,3 disease recognition,4 dip-pen lithography,5 granularity,6 inkjet printing,7 and sensing.8 For the efficient development of nano-devices with good control of the nano-particles, it is of great importance to realize the directional motion of AuNP(s) and understand the transport phenomenon of AuNP(s). In above mentioned applications, the directional motion of AuNP(s) is usually realized by increasing the temperature with the help of heat transduction or a light source. The AuNP(s) are prone to approach and coalesce with each other even at solid state when subjected to heat.9 Recently, we found that the liquid droplet could move directionally and spontaneously on the NC surface.

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Is it possible for the AuNP to move directionally on the NC surface when heated? If

so, this phenomenon can be utilized for the development of micro- nano-sized electrical devices,11,12,13 and also for nano-alloy manufacturing.14 It is considered that the interaction force between the particle and the tip is particularly distinct from what exists between macroscopic particles and it usually consist of electrostatic force, van der waals, chemical, and capillary force.15,16,17 It has been established that arbitrary force related to the temperature is explicitly important for micro-particle.18,19,20,21


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It has been found that computer aided simulation and more specifically molecular dynamics (MD) simulation provides a powerful tool to understand the AuNP(s) transport behavior and underlying mechanism at nanoscale. Recently, plenty of research has been conducted on understanding

the

coalescence and

spontaneous movement

of heated

AuNP(s)

at

nanoscale.22,23,24 It is well known that at temperatures above melting point, solids becomes liquid. In previous studies it is reported that AuNP(s) behave like liquid well below the melting point.25 The transport mechanism of liquid/like liquid and solid-liquid interface interaction has been studied by numerous researchers.26,27 In another work, properties of AuNP(s) at air-liquid, liquidliquid and solid-liquid interface is examined with the help of MD simulation and the results revealed that the contact angle of nanoparticles at fluid interface is affected by the amount of adsorbed fluid.28 The above mentioned studies present an insight on how heated nanoparticles move on the nanostructured surface and what factors influence their movement at nanoscale. Although plenty of analytical and experimental work has been done on understanding the solid-liquid interaction at nanoscale,29,30,31 but to the best of the author’s knowledge, the directional motion and underlying mechanism of AuNP on conical surface have not been studied to date. In order to fathom the transport mechanism of AuNP on NC surface, a fundamental solid surface consisting of definite lattice structure can be utilized to model the conical surface.32,33 The temperature could be varied in order to observe its influence on the transport mechanism of heated AuNP(s).34 The time averaged velocity of AuNP on the conical surface can give an insight on how to interpret the spontaneous movement of AuNP on solid surface with a curvature gradient.35 In this research work the equilibrium states of AuNP on NC surface is analyzed. Furthermore, the effect of the size of AuNP and the applied temperature on the directional motion and


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transport mechanism are also investigated. This study provides fundamental understanding about the characteristics of solid-solid/like liquid-solid interface interaction and also describes the transport mechanism of AuNP on different conical surfaces with distinct apex angle.

2. METHODS In this research work, classical MD simulation was performed to analyze the directional motion and transport mechanism of AuNP(s) on NC surface. A cubic diamond structure containing single layer was utilized to model NC structure having a lattice constant, a, equals to 5.43Å (Material Studio library is used to retrieve the crystal structure of Si).36 The modeled unit layer of Si lattice atom was then used to obtain a disc of circular shape. Then, three cutoff discs were produced by removing a sector from the circular disc at an angle of 90°, 180°, and 270°. In order to observe the transport behavior of AuNP on NC surface the above mentioned cutoff discs were rolled to achieve three distinct NC,37 having an apex angle ș of (C1=113°, C2=71°, C3=32°), as shown in Figure 1(c). The top diameter d top and the length of each NC were different from each other. The AuNP atoms were placed around the tip of the NC, the gap between the tip of NC and the bottom of AuNP was around 3Å. In order to discover the effect of the size of AuNP on its transport mechanism, three circular shaped AuNP having diameter of 8nm, 10nm, and 12nm, were modeled as shown in Figure 1(b). Moreover, the gas molecules were ignored in this study in order to simplify the computation model and to improve the calculation efficiency which has also been reported in the previous research work.38,39


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Figure 1. Simulation model containing (a) A NC surface (32°) and AuNP (8nm) located at the tip, (b) AuNP(s) of three different diameter (8nm, 10nm, 12nm), and (c) NC with three apex angle (113°, 71°, 32°). Where, yellow and green spheres represent the gold, and NC atoms, respectively. The interatomic interaction force between Au atoms is represented by an Embedded Atom Method (EAM) potential.40 The total energy of an N atom system can be calculated by the following relation. ଵ

௜ஷ௝ ܷ௧௢௧௔௟ = σ௜ ‫ܨ‬௜ (ߩ௘ ) + σ௜,௝ Ø௜௝ (‫ݎ‬௜௝ ) ଶ

(1)


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Where Ø௜௝ (‫ݎ‬௜௝ ) represent two-body central potential between atom i and j having a separation distance ‫ݎ‬௜௝ and ‫ܨ‬௜ (ߩ௘ ) is the embedding energy of the atom i with electron density ‫ܨ‬௜ (ߩ௘ ). While the interaction between the NC and the AuNP(s) atoms is measured by using LennardJones (L-J) potential.41

ܷ௜௝ = 4ߝ௜௝ ቈ൬

ఙ೔ೕ ௥೔ೕ

ଵଶ

൰

െ൬

ఙ೔ೕ ௥೔ೕ

଺

൰ ቉ , ‫ݎ‬௜௝ < ‫ݎ‬௖

(2)

Where i and j represent NC (Si), and AuNP(s) (Au) atoms, and ߪ௜௝ and ߝ௜௝ means the space where the depth of the interatomic potential wall and the potential is zero. Also, r c represent the cutoff potential and it is kept equal to 20Å in this study, it means U ij =0 when r ij 20Å. The Lorentz-Berthelot mixing rules were utilized to calculate the interatomic mixed-atom potentials.42,25

ߪ௜௝ =

ఙ೔೔ ାఙೕೕ ଶ

ߝ௜௝ = ඥߝ௜௜ × ߝ௝௝

(3) (4)

The values of ߝ௜௝ and ߪ௜௝ for Au and Si atoms are set to be ߝ஺௨ି஺௨ = 534.4ܸ݉݁, ߝௌ௜ିௌ௜ = 17.5ܸ݉݁ ,ߪ஺௨ି஺௨ = 2.57Å , and ߪௌ௜ିௌ௜ = 3.826Å.43,44 In addition, a surface modeled by an atomic lattice structure similar to that of NC surface is utilized to determine the potential energy of 8nm, 10nm, and 12nm diameter AuNP ball on the flat surface in a temperature range of 300K to 1600K. A sharp change in potential energy at certain temperature can be regarded as the melting temperature of AuNP. This will be helpful in analyzing the spreading and transport mechanism of heated nanoparticles on the NC surface as a function of temperature.


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A fixed boundary condition is used to display all simulations with a fixed (Number, Volume, and Temperature) NVT ensemble in LAMMPS (MD) molecular dynamics software.45 In the beginning the whole system is equilibrated for 250ps at the temperature of 300K.10 After attaining equilibrium the system is heated to a certain targeted temperature (300K, 500K, 700K, 900K, 1100K, and 1300K) in 250ps duration and this temperature is then maintained by using Nose-Hoover thermostat till the end of simulation. The simulation is then run for another 2.5ns and the time step is set to be at 1fs. The length and the top diameter of the NC structure were around two to four times bigger than the diameter of the AuNP. Furthermore, the size of the simulation box was kept twice the dimension of the simulation model. Moreover, an inert wall was constructed by fixing the NC atoms to their initial position. Once a specific temperature is obtained, it is then controlled to be stable inside the simulation box and a discrepancy of less than 5.0K was detected during the simulation.

3. RESULTS AND DISCUSSION In this research work, firstly, the influence of change in temperature (300K to 1300K) of 8nm diameter AuNP on the movement conditions is measured. Secondly, the MSD and average velocity of different sized AuNP (8nm, 10nm, 12nm) on NC surface at different temperatures (300K to 1300K) is inspected. Thirdly, in order to observe the melting temperature of AuNP the potential energy of 8nm, 10nm, and 12nm, AuNP on flat silicon surface at different temperatures is also calculated. In addition, the contact angle of 10nm AuNP on flat silicon surface is measured at different temperatures. Lastly, the transport mechanism of AuNP on different types of NC is analyzed visually; and physical parameters such as MSD, average velocity, and


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interaction energy of AuNP are measured in order to fully understand its directional motion and transport characteristics 3.1 Motion of AuNP at Different Temperature To observe the effect of the temperature on the velocity of 8nm diameter AuNP placed at the tip of NC surface, nano-cone C3 having an apex angle ș of 32°, is simulated at six different temperatures (300K, 500K, 700K, 900K, 1100K, and 1300K). With an AuNP of 8nm diameter the MSD curve of AuNP at specific temperature is calculated and plotted in Figure 2(a). While the averaged velocity of AuNP on NC surface at different temperature is shown in Figure 2(b). The simulation results exhibit that the average velocity of AuNP can be linked to the applied temperature which is increased with the increase in temperature. Furthermore, it is evident that the increase in temperature can cause spreading of AuNP on the NC surface which results in stronger directional movement due to its like liquid characteristics.10 In all cases the AuNP shifted its position from the tip towards the side of the NC but it did not move further at temperature below 900K. It can be seen in Figure 2(a-I), which represents the final state of the AuNP at 1300K, while Figure 2 (a-II) shows the AuNP at 300K after 3ns simulation. The MSD results show that AuNP at low temperature (300K) has low displacement during 3ns simulation while it has large displacement at higher temperature (1300K), which is associated with its higher velocity. As shown in Figure 2(b) the maximum average velocity was around 7.53 nm/ns at 1300K and at 300K the minimum average velocity was measured around 3.08nm/ns. In addition, the transport mechanism can also be described by analyzing the interaction force between the gold and NC atoms. It can be seen in Figure 2(c) that the interaction energy of AuNP at 300K did not


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change much, as compared to interaction energy at 1300K. The sharp decline in the interaction energy at 1300K resulted in the high driving force of AuNP on NC surface. It is evident that the divergence between the highest and lowest velocity is considerable which further justifies that the temperature of AuNP has compelling effect on the movement of nano-ball on the NC surface. The reason in classifying the importance of temperature is associated to the spontaneous movement of the AuNP on the NC surface at high temperature, which is related to the change in average velocity of the AuNP on NC surface. In section 3.2, the effect of the size of AuNP, and in section 3.4, the effect of apex angle of NC on the average velocity and transport mechanism of AuNP are discussed in detail. While, in section 3.3 the melting temperature of different sized AuNP(s) is calculated with the aid of potential energy data and the effect of temperature on the morphology of AuNP is also inspected with contact angle calculations.

Figure 2. Simulated results of C3 (32°) during 3ns simulation time (a) shows the MSD curve of 8nm diameter AuNP at 300K, 900K, and 1300K (b) average velocity of AuNP at different temperatures and (c) shows the interaction energy of curves of 8nm AuNP at 300K, 900K, and 1300K. The average velocity of an AuNP on NC surface is calculated by a two-step method. Firstly, the simulation output file gives the total MSD data of each group of atoms. Then, the square root of the difference of two successive MSD values is calculated which is then divided by the time


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step (1fs) to attain the velocity of AuNP atoms at each specific time step. Secondly, the calculated velocities are summed up and then divided by the total number of time steps to get the average velocity during 3ns simulation time. The MSD gives the alteration of the position of gold atoms with respect to their initial position during the simulation time. The MSD function is used to calculate all the effects caused by the motion of atoms in the fixed boundary by using LAMMPS software. The total squared displacement which is averaged and summed over atoms is measured by using this relation (dx×dx+dy×dy+dz×dz).35 3.2 Effect of Particle Size on the Motion of AuNP In order to examine the effect of the size AuNP on its motion on NC, C3 (32°) surface, three different sizes of AuNP(s) having diameter of 8nm, 10nm, and 12nm are utilized in this study. In addition, the time-averaged interaction energy of gold and NC atoms is also calculated to analyze the effect of particle size in detail. The results show that MSD of 12nm particle is higher than the 10nm AuNP at 300K temperature as shown in Figure 3(a). Furthermore, at this temperature the AuNP showed little movement which is due to the shift of the AuNP from the tip towards the side of the NC surface. The plot in Figure 3(a) represent that the smaller diameter particle has less MSD as compared to the large diameter AuNP at 300K. The measured displacement at 300K is quite low as compared to the displacement of the AuNP(s) measured at high temperature. The thermal fluctuation is also responsible for the shift of AuNP from the tip of the NC and towards its side at low temperature range. On the other hand, when the temperature was raised to 1300K, the MSD also increased due to spreading of AuNP on NC surface as shown in Figure 3(b). It was observed that the displacement of 12nm diameter AuNP increased slowly in beginning and then increased sharply


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at the end of simulation due to increment in the contact area of AuNP on NC surface after 1.5ns of simulation time. The increment in the contact area of the particle is due to the fact that the particle was placed on the tip of the NC surface at the beginning of the simulation. During simulation the droplet started to move towards the larger diameter of the NC surface, resulting in the increase in the contact area with the NC surface and the increase in the velocity of the particle. The average velocity of different sized AuNP is also calculated and plotted in Figure 3(c). The minimum average velocity was calculated around 0.92nm/ns in case of 10nm AuNP and 1.27nm/ns in case of 12nm AuNP. However, the maximum measured velocity was equal to 9.14nm/ns in case of 12nm AuNP and 8.56 nm/ns in case of 10nm AuNP. The results revealed that the average velocity of AuNP is increased by the increase in temperature. Moreover, the trend shows that the velocity of AuNP is directly proportional to the applied temperature despite the size of the AuNP. The reason behind low velocity of AuNP at low temperature is linked to the stationary state of the AuNP after shifting from the tip of the NC. At temperature above 800K the AuNP started move towards the larger diameter side of the NC, which is linked to its dominant liquid characteristics at higher temperature. To understand the underlying mechanism behind the movement of AuNP, further analysis on interaction energy between different sized AuNP and NC surface during the simulation period is analyzed. The interaction energy between 10nm and 12nm size AuNP atom and the NC atom at 1300K is calculated and plotted in Figure 3(d). The initial and final interaction energy for 10nm AuNP was measured around -0.76eV and -383eV, respectively, while initial and final interaction energy of 12nm diameter AuNP was calculated around -0.95eV and -547eV, respectively. The interaction energy curve shows that 12nm diameter AuNP has higher decaying rate of interaction


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energy in relation to the time than that of 8nm diameter AuNP and that is the reason why small diameter has low displacement than that of large diameter AuNP. It is evident that as the interaction energy is decreased the driving force is increased. Moreover, the results show that the interaction energy was minimum at the end of simulation and maximum at the beginning of the simulation despite of the size of AuNP. In addition, it can be seen in Figure 2(c) that at higher temperature the interaction energy has fast decaying rate which results in high driving force and velocity of AuNP. Therefore, it can be concluded that the temperature has significant influence on how AuNP interact with the NC surface.

Figure 3. Simulated result of 10nm and 12nm AuNP (a) MSD curve at 300K (b) MSD curve at 1300K (c) Average velocity at different temperatures (d) Interaction Energy of 10nm, and 12nm AuNP during 3ns simulation time.


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3.3 Effect of Temperature on Wetting States of AuNP In order to observe the influence of temperature on the spreading mechanism of AuNP on silicon surface, an 8nm, 10nm, and 12nm gold ball was placed on the flat silicon surface. The temperature was altered from 300K to 1600K and the change in potential energy of AuNP was measured during 3ns simulation time. It has been reported in the literature that the solid-liquid transition point of nano-sized AuNP is lower than the bulk Au (1337K) and it is dependent on the size of the particle.46,47,48 The transition temperature can be measured by calculating the change in potential energy of the AuNP as a function of change in applied temperature.

Figure 4. (a) Potential energy curves of 8nm, 10nm, and 12nm AuNP on flat silicon surface (b) contact angle of 10nm Au nano-ball on flat silicone surface at different temperatures.


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It can be seen in Figure 4(a) that potential energy is increased gradually with the increase in temperature followed by a sharp increase at temperature around 1000K. In previous research, it has been reported that the sharp increase indicates the melting of AuNP from solid to liquid state.46,47 In our simulation, it is revealed that the particles spread over the surface at temperature higher than 1000K. In addition the contact angle of 10nm AuNP on flat silicon surface is measured at different temperatures and plotted in Figure 4(b). The change in contact angle represents the deformation in the structure of AuNP which is linked to its wetting state. The AuNP stayed in solid state below 900K temperature and started to deform at temperature higher than 900K which result in increase in its contact angle and contact area with the solid surface. At 1300K the AuNP has the highest contact angle of around 50° which represents that the particle is deformed and melted. Thus, it can be concluded that the increase in temperature results in higher contact between AuNP and the silicon surface. Moreover, the AuNP behaves more like liquid at higher temperature and that is why the velocity of the particle is increased by the increase in temperature which is in accordance with our previously reported work.10 3.4 Effect of Curvature on the Motion of AuNP There were three different types of NC used in this study based on their apex angle. An 8nm diameter AuNP ball was placed at the tip of each NC and the simulation was run for 3ns. The temperature was altered in each case in order to observe the transport mechanism of the AuNP on each type of NC. It can be observed in Figure 5(a-b) that the MSD of AuNP is higher at 1300K as compared to at 300K in case of both C1 and C2 nano-cones. The MSD is increased sharply in the beginning and stabilized afterwards which is due to the shift of AuNP from the tip of the NC towards the larger diameter side at 300K. The particle is shifted from tip of the NC towards its side but it did not further move upward at this temperature. This is similar to the


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results observed in C3, where the particle shifted to the side of the NC and stayed intact at the bottom side of the NC throughout the simulation time. The reason behind this shift is the thermal fluctuations and lower number of contacted gold atoms at the tip of the NC surface. The AuNP requires a bigger contact area with the NC surface which is not possible when it is located at the tip of the NC. As soon as the AuNP moves towards the side of the NC the number of contacted gold atoms with the NC surface increases and results in the intact position of the AuNP. At low temperature the AuNP did not climb high on the NC surface due to dominant solid characteristics, while it moved upward at temperature above 800K. The other reason behind the shift and motion of AuNP is linked to the temperature, at higher temperature the particles behave more like liquid and move spontaneously towards the higher diameter side of the NC.


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Figure 5. Simulated results (a) MSD curve of C1 at 300K and 1300K (b) MSD curve of C2 at 300K and 1300K (c) Average velocity C1 and C2 at different temperatures (d) Number of contacted Au atoms with the C1 , C2, and C3 surface at different temperatures. The trend of AuNP movement on different types of NC surfaces is similar. At higher temperature the AuNP spread on the NC surface and result in increase in contact area of AuNP and NC surface. The large contact area between the liquid and the solid surface result in increase in the displacement of liquid over solid surface by the influence of curvature gradient.10,35 It is evident that the displacement of AuNP at solid state is not affected by the curvature gradient but it does get affected by the curvature gradient at semi-solid or liquid state. The average velocity of 8nm diameter AuNP on the C1 (113°) and C2 (71°), NC surface is plotted in Figure 5(c). It is revealed that the velocity of AuNP was high at 1300K than that on 300K on both C1 and C2 surface. This is due to the fact that at low temperature, the AuNP is less sensitive to thermal fluctuations and has lower contact area with the NC surface, resulting in low velocity. The velocity is increased with the increase in temperature which is similar in all types of NC. It is because the droplet started to deform at temperatures higher than 900K, resulting in high contact area with the NC and increase in velocity of the AuNP. The minimum average velocity was calculated around 2.23 nm/ns at 300K in case of C1, while the maximum velocity was measured around 6.64 nm/ns at 1300K in case of C2. The AuNP has high displacement at the beginning due to the shift of particle from the tip of the NC towards the side, while at high temperature the velocity increase is linked to the spreading of the AuNP over NC surface. These results further justify the influence of curvature gradient on the spontaneous movement of the liquid over solid surface.


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In Figure 5(d) the number of contacted gold atoms with the NC surface is calculated and plotted. The results show that as the temperature is increased the number of contacted atoms is also increased. It is also evident that the high number of contacted atoms results in high velocity of AuNP over the surface of each specific type of NC. This further justifies the trend of velocity and displacement of AuNP over NC surface at different temperatures. Furthermore, it is certain that the number of contacted gold atoms is affected by the applied temperature and the size of the AuNP. The trend is similar in all types of NC despite of its apex angle.

4. CONCLUSION This study provides a molecular level understanding about the directional motion and underlying mechanism of AuNP on NC surface having different size based on its apex angle. In order to analyze the motion of AuNP on NC surface, nanoparticles with different diameters (8nm, 10nm, and 12nm) were located on the tip of NC. It was examined that the impact of the particle size on the transport mechanism and the velocity was considerable. The AuNP stayed intact at 300K temperature but it started to deform at higher temperature and did spread significantly on the solid surface at 1300K due to its prominent liquid-like characteristics. In addition, potential energy of AuNP revealed that its melting temperature is around 1100K and it behaved like liquid at temperature higher than its melting point. There were a total of six different temperatures (300K, 500K, 700K, 900K, 1100K, and 1300K) that were used to alter the state of the AuNP in order to observe its motion on NC surface. The results exhibited that the temperature has considerable effect on the velocity and directional movement of the AuNP. The AuNP stayed intact at the bottom side of the NC when the temperature was low, while the droplet spontaneously traveled towards the larger diameter side of the NC when the temperature was


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increased. However, the velocity of the AuNP changed in correlation to the applied temperature which is further linked to the state of the particle. The AuNP at solid state showed little to negligible movement, while it showed significant movement in like liquid and liquid state. ASSOCIATED CONTENT Supporting Information This material is available free of charge via the Internet at http://pubs.acs.org. 1. Movie of the equilibrium states of AuNP on nano-cone surface at different temperatures. This movie demonstrates the three temperatures representing three equilibrium states, i.e., solid state (300K), transition state (900K), and liquid-like state (1300K) in which yellow, and green spheres represent the gold, and nano-cone atoms, respectively. (ZIP) 2. Figure S1-S4. (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. 51375253, and 51775296. The authors also acknowledge the support of this work from the State Key Laboratory of Tribology, China, under grant code SKLT2017C06. CONFLICT OF INTEREST The authors declare no competing financial interest. REFERENCES


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Molecular Dynamics Study of Temperature Influence on Directional

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