Approach and Coalescence of Gold Nanoparticles Driven by Surface

Approach and Coalescence of Gold Nanoparticles Driven by Surface Thermodynamic Fluctuations and Atomic Interaction Forces Jiadao Wang,*,† Shuai Chen,† Kai Cui, Dangguo Li, and Darong Chen State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China S Supporting Information *

ABSTRACT: The approach and coalescence behavior of gold nanoparticles on a silicon surface were investigated by experiments and molecular dynamics simulations. By analyzing the behavior of the atoms in the nanoparticles in the simulations, it was found that the atoms in a single isolated nanoparticle randomly fluctuated and that the surface atoms showed greater fluctuation. The fluctuation increased as the temperature increased. When there were two or more neighboring nanoparticles, the fluctuating surface atoms of the nanoparticles “flowed” toward the neighboring nanoparticle because of atomic interaction forces between the nanoparticles. With the surface atoms “flowing”, the gold nanoparticles approached and finally coalesced. The simulation results were in good agreement with the experimental results. It can be concluded that surface thermodynamic fluctuations and atomic interaction forces are the causes of the approach and coalescence behavior of the gold nanoparticles. KEYWORDS: nanoparticles, approach, coalescence, surface thermodynamic fluctuation, atomic interaction force example, both Groza et al.17 and Yeadon et al.18 studied the sintering and found that neck sizes were well below those were predicted from conventional scaling models. They concluded the reason was the increased curvature that occurred as the particle size decreased. Schwesig et al.19 studied the evolution of density during the sintering process of nanoparticles and observed that density fluctuated on the micrometer scale. Similarly, Yeadon et al.20 demonstrated that the nanoparticles reoriented upon heating. Asoro et al.21 summarized the possible reasons for the differences in sintering of nanoparticles between models and experimental results: (1) unique defect structures in nanoparticles (twins and facets); (2) enhanced diffusivity due to size effects; and (3) enhanced, localized agglomeration present in nanoparticles. It is obvious that the nanoparticles show quite different characteristics from macroparticles when melt. However, so far, the researchers were mainly focused on the coalescence of AuNPs when melt, and how they approached were not reported. Arcidiacono et al.22 carried out molecular dynamics (MD) simulations to study the coalescence of a wide range of AuNPs.

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old nanoparticles (AuNPs) have exhibited peculiar electronic,1 optical,2 thermal,3 and catalytic properties4 that differ from those of bulk materials because of their large ratio of surface area to volume. In addition, these properties can be designed on a molecular level.5−7 Therefore, AuNPs are widely utilized in applications such as solar cells,8 photodetectors,9 disease recognition,10 drug delivery,11 and sensing.12 In these applications, AuNPs are easily heated by the effects of light, heat transduction, and so on. It has been reported that AuNPs have a strong tendency to approach and coalesce when heated, even below the melting temperature of AuNPs,13 which leads to significant changes in behavior and performance of AuNPs. However, making good use of the approach and coalescence of AuNPs is a great method of bottom-up fabrication of micro- and nanosized electrical devices.14−16 Whether trying to prevent or exploit the approach and coalescence, it is important to have a good understanding of the mechanisms of the approach and coalescence. In recent years, substantial research has been conducted to study the coalescence of nanoparticles.17−28 Generally, the situations of the coalescence can be classified into two categories. Above melting temperatures, a mass of nanoparticles melts to coalesce, called welding and sintering.17−24 For © XXXX American Chemical Society

Received: December 31, 2015 Accepted: January 12, 2016

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DOI: 10.1021/acsnano.5b08236 ACS Nano XXXX, XXX, XXX−XXX

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Figure 1. SEM images of AuNPs (ai) initially deposited at room temperature and (aii) after being heated at 573 K for 1 h. (aiii) Calculated islands in image ai. SEM images of AuNPs (bi) initially deposited at room temperature and (bii) after being heated at 873 K for 1 h. (biii) Calculated islands in image bi. The probability density of AuNP radius when heated at (ci) 573 K and (cii) 873 K. Images ai and aii are in the same area, and bi and bii are in the same area. Regions A−E in images bi and bii are in the same region.

Contrary to previous works, they found that classical “neck” theories could predict the first stage of the sintering process in nanoscales. However, they also did not study the approach process. It is a remarkable fact that their results show that the MD approach is a reliable method to study such nanoscale phenomena. Similarly, Buesser et al.23 and Grammatikopoulos et al.24 performed a number of MD simulations to study the coalescence of two or more nanoparticles, in which Grammatikopoulos et al. used embedded-atom method (EAM) to simulate the interaction between metal atoms. Buesser et al. revealed that surface diffusion was the dominant sintering mechanism of nanoparticles, and grain boundary diffusion was that of larger particles. Below melting temperatures, a pair or group of nanoparticles might coalesce when they contact, but the number of related researches is much less than that above melting temperatures. Moreover, the coalescence mechanisms were analyzed based on adhesion (contact).13,25 For example, Lim et al.13 carried out a real-time in situ transmission electron microscopy (TEM) and kinetic Monte Carlo (MC) study of the coalescence of individual pairs of AuNPs, and compared the rate of growth of the neck that joins two particles during coalescence in observation to classical continuum theory and to atomistic kinetic MC simulations. They found good agreement between the observations and the simulations but also not with the classical continuum model, which was attributed to the faceted nature of the particles. Ingham et al.25 used synchrotron X-ray diffraction (XRD) and small-angle X-ray scattering (SAXS) to study the coalescence mechanism of AuNPs below melting

temperature when the AuNPs were initially contacted, and pointed out that surface diffusion was the dominant mechanism for the coalescence of nanoparticles. As far as we know, until now, the coalescence mechanisms were analyzed based on adhesion (contact), but the reasons why the separated nanoparticles could move to contact have not been reported. However, the approach behavior of separated nanoparticles is quite important to the subsequent coalescence behavior. Studying the approach mechanism of the separated nanoparticles is significant for controlling the coalescence of the nanoparticles. In this paper, the approach and coalescence behavior of AuNPs was studied, and the cause of the approach was analyzed. The coalescence behavior was observed experimentally by scanning electron microscopy (SEM). Furthermore, MD simulations were carried out to track the approach and coalescence process. Based on the behavior of AuNPs in the approach and coalescence process, the cause of the approach was analyzed, which is important for the preparation of nanoparticles with controlled stability and is significant for industrial applications.

RESULTS AND DISCUSSION Approach and Coalescence Phenomena of AuNPs. Figure 1 shows the initial image of AuNPs deposited on the silicon surface (Figure 1ai,bi) and the image of AuNPs heated at 573 K (Figure 1aii) and 873 K for 1 h (Figure 1bii). To quantify the variation of AuNPs before and after heating, the probability density of AuNP radius and number of islands when B


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Figure 2. Initial structures of two AuNPs on a solid silicon surface: (a) side view, (b) top view. Snapshots of two AuNPs (c) when they just contacted and (d) after they coalesced. Red and green spheres represent the gold and silicon atoms, respectively.

Figure 3. (a) Equilibrium states and (b) snapshots in the approaching process of two AuNPs on a silicon surface at different temperatures.

to study the coalescence process (cf. Figure 2c,d), in which EAM potential instead of LJ potential was used to simulate the interactions between two AuNPs (i.e., all Au atoms were interacted by EAM potential). The equilibrium processes of AuNPs at different temperatures (300, 400, 500, 600, 700, 800, 900, 1000, 1100, and 1200 K) are shown in section S1 of the Supporting Information, and the equilibrium states and snapshots in the approaching processes are displayed in Figure 3. The results indicate that the coalescence of AuNPs was not obvious when the temperature was lower than 800 K. However, when the temperature increased to 800 K, the two AuNPs approached and coalesced. The approach and coalescence behavior of AuNPs at 1100 to 1200 K were different from that at 800 to 1000 K. The reason was the AuNPs melt when the temperature was higher than 1100 K, which is in accordance with Taherkhani et al.’s simulations.27 Taherkhani et al. implemented MD simulation with EAM, Sutton−Chen potential, and quantum Sutton−Chen potentials to study the melting temperature of AuNP and found that the melting temperature of AuNP with 55 gold atoms for EAM was 1182.5 ± 1.5 K. Therefore, the AuNPs changed from solid state to liquid state when heated to 1100 K, and these two small liquid droplets flowed together to form a large droplet, which is shown in the approach process of AuNPs in Figure 3b. The AuNPs at 800 K were still in solid state; however, they also approached and coalesced, which corresponds with the experimental results. Both the experimental and simulation results indicate that AuNPs approach and coalesce below melting temperature. Approach and Coalescence Mechanism of AuNPs. The positions of all atoms in the AuNPs during the simulations were stored in output files every 0.001 ns. On the basis of the positions of the atoms in the AuNPs at different temperatures, the diameter of AuNP as a function of temperature was calculated and shown in Figure 4a. The results show that the AuNP diameter increased slightly from 8.18 to 8.43 nm, and this variation (0.25 nm) was much smaller than the separation between AuNPs (2.0 nm). It indicates that the diameter change as a function of temperature was not obvious, and not the main

AuNPs were initially deposited and heated were calculated and plotted in Figure 1ci,cii. The islands in Figure 1ai,bi were calculated and are shown in Figure 1aiii,biii, in which a number of AuNPs that connected together was counted as an island (i.e., the loop curve in Figure 1aiii,biii). The results show that the number of islands initially deposited and after heated at 573 K were 278 and 261, respectively. There was a slight decrease (from 278 to 261) in the number of islands after AuNPs heated, and the average radius of AuNPs remained unchanged at about 9.6 nm. It is concluded that the approach and coalescence of AuNPs were not obvious when heated at 573 K for 1 h. The results in Figure 1biii show that the number of islands decreased from 266 to 124, and the average radius of AuNPs increased from 9.2 to 18.2 nm after AuNPs were heated at 873 K for 1 h. It demonstrates that the single isolated AuNP approached and coalesced with near neighbors to form larger AuNPs. The variations of AuNPs in region A, B, C, D or E in image bi and bii also prove that the AuNPs approached and coalesced. The results in Figure 1ci,cii showed that the radius of the smallest sized AuNPs was about 4 nm. Luo et al.26 studied the melting points of free AuNPs and AuNPs on three different substrates (tungsten, amorphous carbon, and graphite) by experiments. They found that the melting points of AuNPs, whose radii were larger than 4 nm, were all higher than 1100 K. Therefore, the phenomena in Figure 1bi,bii show that AuNPs approached and coalesced below melting temperature. The shapes of the islands in regions C, D, and E of Figure 1bii show that the coalesced AuNPs formed in different shapes, such as hexagon, triangle, and strip-type, which should be resulted from the coalescence under melting temperature and not the result of melted reformation. Similar simulations were carried out to track the approach and coalescence process, in which the model was composed of two AuNPs on a solid silicon surface (cf. Figure 2a,b). The simulation processes were divided into two steps. First, in an approach process, Lennard-Jones (LJ) potential was used to simulate the interactions between two AuNPs (cf. Figure 2b,c). Second, once two AuNPs were contacted, another simulation with this state (cf. Figure 2c) as an initial state was carried out C


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To investigate the approach and coalescence mechanism of the AuNPs, the displacement values of the atoms induced by thermal motion in the AuNPs were calculated based on the positions of the atoms at two neighboring moments. The calculation method is shown in Figure 4b, in which point O were the average positions of all atoms in an AuNP at 0.10 and 0.28 ns. If the atom at point P moves to point P′ from 0.10 to 0.28 ns, the displacement of this atom is the length of the vector M, and the distance from this atom to the center of AuNP is the length of the vector OP. The average displacement value of a group of atoms when their distances to the nanoparticle center were larger than i − 1 and smaller than i + 1 (i = 2, 4, ..., 40 Å) were calculated, in which their average distance was represented by i. Therefore, 20 average displacement values and their corresponding distances were achieved and are plotted in Figure 4b. The results showed that the displacement values of atoms in two neighboring AuNPs were always larger than those in a single isolated AuNP over a period of time regardless of whether the temperature was 300, 600, or 800 K. To find out why the atoms had larger displacement values when there were two neighboring AuNPs, the displacement directions and values of the atoms in one time step (between the positions at 0.100 and 0.101 ns) for three different temperatures (300, 600, and 800 K) were calculated and are shown in Figure 5a. The red arrows (cf. Figure 5a) were plotted on the basis of the positions of the atoms at 0.100 and 0.101 ns. The origins of the red arrows were the positions of the atoms at 0.100 ns, and the ends were the positions of the atoms at 0.101 ns. Therefore, the directions and lengths of the red arrows represent the directions and values of the atoms’ displacements, respectively. The scale bar was 1 Å, and the sizes of the arrows were directly comparable. The results of directions show that the displacements of the atoms in a single isolated AuNP were random and were thermodynamic fluctuations. The displacements of atoms in two neighboring AuNPs at different times (between the positions at 0.160 and 0.161 ns and between the positions at 0.200 and 0.201 ns) at 800 K are shown in Figure 5b. The results indicate that when there were two neighboring AuNPs, the surface atoms in the AuNPs moved toward the neighboring AuNP, which was called “flow”. Surface atoms “flowed” toward the neighboring AuNP because

Figure 4. (a) Diameter of AuNP on a silicon surface as a function of temperature. (b) Displacement values of atoms at different temperatures in two neighboring AuNPs (represented by Au2800, Au2-600, and Au2-300 K) and one single AuNP (represented by Au1-800 K, Au1-600, and Au1-300).

course to induce the approach and coalescence, which corresponds with the results of Buesser et al.23 Buesser et al. revealed that grain boundary diffusion was not the dominant coalescence mechanism of nanoparticles.

Figure 5. Displacements of the atoms in (a) a single isolated AuNP at 0.1 ns for 300, 600, and 800 K and (b) two neighboring AuNPs at 0.16 and 0.20 ns for 800 K. The directions and lengths of the red arrows represent the directions and distances of the atoms’ displacements, respectively. D


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Figure 6. Calculation method and results of the approaching speed at different temperatures.

Figure 7. (a) Calculation method and (b) results of the surface mobility at different distances between nanoparticles. Results of (c) the approaching speeds at different distances and (d) the atomic interaction forces at different distances between atoms.

variation, the approaching speed of the AuNPs is (L1 − L2)/(T2 − T1). All of the approaching speeds of the AuNPs at different temperatures were calculated on the basis of the initial positions (T1 = 0 ns) and the positions at T2 = 0.20 ns for 300 to 700 K or when they just contacted (0.22 ns for 800 K, 0.20 ns for 900 K, 0.19 ns for 1000 K, 0.17 ns for 1100 K, and 0.15 ns for 1200 K). At each temperature, five simulations were carried out. The average value of the approaching speeds in five simulations at the same temperature was chosen as the approaching speed at this temperature, and the deviation was calculated (shown in Figure 6). The results showed that the approaching speed increased as the temperature increased. The approaching speed represented the results of the average effect of all the atoms in the AuNPs. The approach was mainly attributed to the flow ability of the atoms at the surface of AuNPs. Apart from the surface thermodynamic fluctuations, atomic interaction forces were also the cause of the approach behavior of AuNPs. Therefore, the approaching speed and surface mobility of the AuNPs was also affected by the atomic interaction force. The approaching speeds and surface mobility of the AuNPs at different average distances in the approach and

of the atomic interaction forces between AuNPs. Because of the directional flow of the surface atoms to the neighboring AuNPs in most timesteps, the surfaces atoms had larger displacement values in a period of time when there were two neighboring AuNPs, which resulted in the approach and coalescence of AuNPs. The results agree with that of Grammatikopoulos et al.24 Grammatikopoulos et al. reported that the reorientation of nanoparticles was followed by the creation of an interface between nanoparticles. Analysis on the Approaching Speed and Mobility of AuNPs. The approaching speeds of two AuNPs were calculated to analyze the approach process, in which the calculation method is shown in Figure 6. This method includes three steps. First, the average positions of all atoms in each AuNP at two moments (T1 and T2) are determined and are marked by dotted lines. The time interval between these two moments is T2 − T1. Second, the distances between the average positions of the atoms at two moments are calculated, which are the distances between the dotted lines (called average distances). The difference between distances at two moments is L1 − L2. Third, according to the calculated time interval and distance E


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ACS Nano coalescence process at 800 K were calculated and are shown in Figure 7b,c. The calculation method of surface mobility is shown in Figure 7a, which is similar to that in Figure 4b, but only includes the atoms whose distances to the particle center are larger than 30 Å. The atomic interaction potential between the Au atoms in different AuNPs is Lennard−Jones potential (cf. eq 2). On the basis of this potential, the atomic interaction forces at different distances between atoms were also calculated and are shown in Figure 7d, which corresponds with the calculated interaction force by Feke et al.29 The results show that the total atomic interaction force consists of van der Waals (VDW) attractive force and Pauli repulsive force. When the distance between atoms was larger than r0, Pauli repulsive force was small enough, and VDW attractive force was the mainly force. The total atomic interaction force was attractive and increased as the distance decreased. When the distance between atoms was smaller than r0, Pauli repulsive force increased rapidly as the distance decreased. The total atomic interaction force was still attractive but decreased as the distance decreased when the distance was larger than r1 and smaller than r0. When the distance decreased to be smaller than r1, the total atomic interaction force became repulsive, and the value of the force increased as the distance decreased. Based on the values of the average distances, the results in Figure 7b,c can be classified into three regions: approach, contact, and coalescence. In each region, the variation of the approaching speed and surface mobility with the average distance was different. All variation trends correspond with the calculated atomic interaction forces in Figure 7d. In the approach region, the approaching speed and surface mobility increased rapidly as the average distance decreased. The reason was that, for two separated AuNPs, the distances between the atoms in two AuNPs were large, and the VDW attractive force was the mainly force. The VDW attraction increased with the decreasing average distance, resulting in the increase of the approaching speed and surface mobility. In the contact region, the approaching speed and surface mobility reached the highest value (cf. Figure 7a). After contact, the AuNPs continued to coalesce. In the coalescence region, the approaching speed and surface mobility decreased as the average distance decreased. This was because most atoms in two AuNPs became close enough, resulting in the large increases of the repulsive forces between them. The total atomic interaction forces of all the atoms were still attractive but the value of the forces decreased as the distance decreased,30 leading to the decrease of the approaching speed and surface mobility. The results in Figure 7 indicate that the flowing ability of the AuNPs reflected by the surface mobility is affected by the atomic interaction force. Therefore, it is concluded that the atomic interaction force is also the cause of the approach behavior of AuNPs. Analysis on the Influence of Simulation Parameters on Approach and Coalescence. To investigate the influence of simulation parameters on approach and coalescence, such as the size of simulation box, the potential model of Au, the form of Au (such as three AuNPs or Au film), and the material (such as Ag or Cu), additional simulations were carried out. The original simulation box were 2220 × 2220 × 2220 Å3. The results of AuNPs at 300, 800, and 1200 K with different simulation box sizes are shown in Figure 8. It indicates that the results remained unchanged when the simulation box decreased to 220 × 220 × 220 Å3 or increased to 4220 × 4220 × 4220 Å3.

Figure 8. Results of AuNPs at 300, 800, and 1200 K with different simulation box sizes.

The accuracy of MD simulation critically depends on the choice of interatomic potential. For studying the approach and coalescence of AuNPs, the potentials must accurately predict lattice constant, cohesive energy, and vacancy formation. Zhou et al.31 concluded that one such potential is EAM potential. The EAM potential developed by Daw et al.32 were widely used to simulate the interaction between Au atoms. For example, Delogu et al.,33 Hussain et al.34 and Lewis et al.35 studied the thermal behavior, sintering and coalescence of AuNPs by this potential, respectively. The previous simulations in this paper, were also carried out by this EAM potential. Another EAM potential developed by Zhou et al.31 was also employed recently. For example, Ding et al.36 studied the coalescence process of Ag−Au nanowires by Zhou et al.’s potential. Apart from the EAM potential, modified EAM (MEAM) potential37,38 and Finnis−Sinclair (FS) potential39 were also used to simulate the behavior of AuNPs. To evaluate the robustness of the approach and coalescence mechanism, the AuNPs with Zhou et al.’s EAM potential, MEAM potential, and FS potential were simulated. The results are shown in Figure 9. The AuNPs at 800 and 900 K in these three potentials (cf. left side of Figure 9) were still in the solid state, and they coalesced to form an elongated nanoparticle, which corresponds with the coales-

Figure 9. Equilibrium states of AuNPs at (a) another EAM potential, (b) MEAM potential, and FS potential. F


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Figure 10. Equilibrium states of three AuNPs on a silicon surface at different temperatures when the initial distributions of three AuNPs were (a) a straight line, (b) a right triangle, and (c) an equilateral triangle.

The initial model of Au film is shown in Figure 11a, in which the model in y and z directions is periodic. Therefore, they were two infinite surfaces in y and z directions. The distances between the surfaces of two Au films, Ds, were 2 nm, which was same as the separations between AuNPs in the abovementioned simulations. The atoms far from the surfaces were fixed to represent the substrate (cf. Figure 11a). The Au film did not coalesce after being heated to 800 K, and the displacement values of atoms in two AuNPs and Au film were compared in Figure 11b. The results showed that the surfaces mobilities of Au film at 300 and 600 K were less than 0.5 Å. When it was heated to 800 K, the surface mobility of the Au film increased to about 0.7 Å, which was still much smaller than that of AuNPs (6 Å). Becasue the surfaces mobility of Au film was so slight that the Au films could not coalesce. To discover whether the approach and coalescence behavior would happen in nanoparticles of other materials, the simulations of Ag nanoparticles (AgNPs) and Cu nanoparticles (CuNPs) were carried out. The equilibrium states and snapshots are displayed in Figure 12a,b. The results show that the similar approach and coalescence phenomena of AuNPs under melting temperature occurred in Cu nanoparticles (CuNPs) but not in Ag nanoparticles (AgNPs). At temperatures of 900 and 1000 K (cf. Figure 12a), even though the spherical AgNPs deformed, the coalescence between them did not appear. To analyze why these phenomena appeared, the displacement values of atoms in CuNPs and AgNPs at 800 and 1000 K were compared with that of atoms in AuNPs at 800 K (cf. Figure 12c). The results show that when the temperature was 800 K, the displacement values of atoms in CuNPs and AgNPs were much smaller than that in AuNPs. Therefore, the CuNPs and AgNPs did not approach and coalesce. When the temperature increased to 1000 K, the displacement values of atoms in CuNPs increased rapidly to as much as that in AuNPs, which resulted in the approach and coalescence of CuNPs. At 1000 K, however, the displacement values of atoms in AgNPs were still very small, and the surfaces of AgNPs could not approach to contact. It further demonstrates that the directional flow of the surface atoms under the atomic interaction forces is the main cause of the approach and coalescence behavior of nanoparticles.

initial distribution of three AuNPs was a straight line (cf. Figure 10a), a right triangle (cf. Figure 10b), or an equilateral triangle (cf. Figure 10c). It indicates that the AuNPs did not coalesce at any initial distribution from 300 to 700 K. When the temperature increased to 800 K, however, the AuNPs approached and coalesced. When the initial distribution of three AuNPs was a straight line (cf. Figure 10a) or a right triangle (cf. Figure 10b), two AuNPs started to approached and coalesced first. Because these two AuNPs approached, the distance between the third AuNP and its neighbor AuNP increased. Therefore, the third AuNP was hard to coalesce with its neighbor AuNP. When the temperature continued to increase to 1100 K, the AuNPs melt and flowed together, resulting in the coalescence of three AuNPs. When the initial distribution of three AuNPs was an equilateral triangle (cf. Figure 10c), the distance between the third AuNP and the two coalesced AuNPs decreased after the two AuNPs coalesced. Therefore, the third AuNP also approached toward these two AuNPs, resulting in the coalescence of three AuNPs at 800 K. The coalescence mechanism of three AuNPs are quite corresponding with that of two AuNPs.

CONCLUSIONS In summary, this paper presents an experimental and simulation study of the approach and coalescence behavior of AuNPs. First, both the experimental observations and the simulation found that the approach and coalescence of AuNPs were dependent on the temperature. The experimental results show that the coalescence of AuNPs was not obvious when heated at 573 K for 1 h. However, upon heating the AuNPs to 873 K for 1 h, the single AuNP approached and coalesced with near neighbors to form larger AuNPs. Similarly, the simulation results indicate that the two AuNPs did not coalesce when the temperature was lower than 800 K. However, when the temperature increased to 800 K, the two AuNPs approached and coalesced, which is in excellent agreement with the experimental results. Second, the analyses of the behavior of gold atoms in the approach and coalescence processes at different temperatures indicate that the surface atoms showed “flow” characteristics and “flowed” toward the neighboring AuNP because of the atomic interaction forces between the AuNPs. With the atoms “flowing”, the surfaces of the AuNPs approached and contacted, which resulted in the coalescence. It

cence phenomena in experiments. It demonstrates that AuNPs in these three potential types also appeared coalescence phenomena under melting temperature, in which there was only a little difference in the equilibrium shape. Therefore, the choice of interaction potential had little influence on the qualitative description of the approach and coalescence mechanism. To inquire about the approach and coalescence behavior of different Au forms, simulations with three AuNPs and Au film were carried out. The equilibrium states of three AuNPs at different temperatures are shown in Figure 10, in which the

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Figure 11. (a) Simulation model of Au film. (b) Displacement values of atoms at different temperatures in two AuNPs (represented by Particle-800 K, Particle-600 K, and Particle-300 K) and Au film (represented by Surface-800 K, Surface-600 K, and Surface-300 K).

Figure 12. Equilibrium states of (a) AgNPs and (b) CuNPs when heated to different temperatures. (c) Displacement values of atoms in AuNPs, CuNPs and AgNPs.

is concluded that surface thermodynamic fluctuations and atomic interaction forces are the causes of the approach. Third, to investigate the influence of simulation parameters and evaluate the robustness of the mechanism, additional simulations with different simulation box sizes, Au potential models, Au forms and other materials were carried out. The results show that the choices of simulation box and interaction

potential have little influence on the qualitative description of the approach and coalescence mechanism. The results on three AuNPs, Au film, AgNPs, and CuNPs further demonstrate that the directional flow of the surface atoms under the atomic interaction forces is the main cause of the approach and coalescence behavior of nanoparticles. H


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METHODS

ASSOCIATED CONTENT S Supporting Information *

Experimental Details. The method for AuNPs assembly was similar to that previously reported by Zhu et al.40 First, silicon substrate surfaces were modified with a (3-aminopropyl)triethoxysilane (APTES) self-assembled monolayer by immersing them in an APTES/ethanol solution for 2 h. After successive rinsing with ethanol and water, the APTES-coated substrate was then immersed in a citrate-reduced colloidal gold suspension at pH 5 for 6 h. Last, the samples were thoroughly dried in a stream of high purity nitrogen gas. AuNPs were successfully deposited on the silicon surface and results are shown in Figure 1ai and 1bi. To study the approach and coalescence behavior of AuNPs, they were heated to 573 and 873 K, respectively. Simulation Section. For the simulations, a model composed of two AuNPs on a solid silicon surface was constructed, which is shown in Figure 2. A cubic diamond structure with the lattice constant, a, equal to 5.43 Å, was used to represent the solid surface. Both the length, Ls, and the width, Ws, of the solid surface were 217.20 Å (40a), and the height was two layers of (001) surface, which equaled 10.86 Å (2a). The diameter of each AuNP, DD, was 80 Å, and the separation of the two particles, DS, was 20 Å. The Au atoms in the same particle interacted via an EAM potential.32 The total energy of a N atom system takes the form

Utotal =

∑ Fi(ρe ) + i

1 2

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.5b08236. Movie of equilibrium processes of AuNPs (AVI) Results of approach and coalescence behavior at different approaching speeds (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel: +86-01062796458. Author Contributions †

J.W. and S.C. contributed equally to this work.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We acknowledge funding support from the National Natural Science Foundation of China Project under Grant Nos. 51375253 and 51321092. We also acknowledge the support of this work from the Tsinghua National Laboratory for Information Science and Technology, China.

i≠j

∑ ϕij(rij) i,j

(1)

REFERENCES

where ϕij(rij) is a two-body central potential between atom i and j with a separation rij and Fi(ρe) is the embedding energy of the atom i with electron density ρe. The Au atoms interacted with Si atoms using a L− J potential41

⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij Uij = 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠

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(2)

where i and j are Au and Si atoms. σij and εij are the distance where the interatomic potential is zero and the depth of the potential well, respectively. The mixed-atom interatomic potentials are obtained through the Lorentz−Berthelot mixing rules42

σij = 1/2(σii + σjj)

(3)

εij = (εiiεjj)1/2

(4)

where the values of σii and εii for Au and Si are σAu−Au = 2.57 Å, εAu−Au = 0.5344 eV, σSi−Si = 3.826 Å, and εSi−Si = 0.0175 eV.43−45 As for the interaction between the Au atoms in different nanoparticles, the simulation processes were divided into two steps. First, in the approach process, LJ potential was used to simulate the interactions between two AuNPs (cf. Figure 2b,c). Second, once two AuNPs contacted, another simulation with this state (cf. Figure 2c) as an initial state was carried out to study the coalescence process (cf. Figure 2c,d) in which the EAM potential instead of the LJ potential was used to simulate the interactions between two AuNPs (i.e., all Au atoms interacted by EAM potential). The large-scale atomic molecular massively parallel simulator (LAMMPS) developed by Sandia National Laboratories46 was used to carry out the simulations. All simulations were in the periodic boundary conditions with the NVT (fixed number of particles, volume, and temperature) ensemble. The simulation time was 1 ns with an integration time step of 1 fs, and the samples of the trajectories were stored every 0.001 ns. The Si atoms were fixed at their initial positions and represented an inert wall. The initial temperature of the ensemble was 300 K, and the Au atoms were heated to the setting temperature (400, 500, 600, 700, or 800 K) with a heating time of 0.1 ns. I


Article

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Approach and Coalescence of Gold Nanoparticles Driven by Surface

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