Surface-Induced Phase Transition During Coalescence of Au Nanoparticles: A Molecular Dynamics Simulation Study

In this study, the melting and coalescence of Au nanoparticles were investigated using molecular dynamics simulation. The melting points of nanoparticles were calculated by studying the potential energy and Lindemann indices as a function of temperature. The simulations show that coalescence of two Au nanoparticles of the same size occurs at far lower temperatures than their corresponding melting temperature. For smaller nanoparticles, the difference between melting and coalescence temperature increases. Detailed analyses of the Lindemann indices and potential energy distribution across the nanoparticles show that the surface melting in nanoparticles begins at several hundred degrees below the melting point. This suggests that the coalescence is governed by the liquid-phase surface diffusion. Furthermore, the surface reduction during the coalescence accelerates its kinetics. It is found that for small enough particles and/or at elevated temperatures, the heat released due to the surface reduction result in a melting transition of the two attached nanoparticles.


Introduction
Due to the unique electronic, optical and catalytic properties of metallic nanoparticles [1][2][3], an increasingly growing interest is developing to explore nanoparticles technological applications [4][5][6]. In this context, the interactions between nanoparticles and their surrounding objects such as solvents, ion/electron beams, and other nanoparticles are fundamentally and technologically important for their storage and performance [7,8]. In particular, the strong attraction among nanoparticles due to their large surface/volume ratio makes them to stick and agglomerate that change some of their desired functional properties.
Metallic/superconductor conjunctions [9], light scattering and absorption [10], and sorting [11] of nanoparticles are some applicable experimental examples which confront this problem. Hence, studying these interactions can be useful to control and improve synthesize and assembly of nanoscale materials and components.
The interaction among the nanoparticles is driven by a reduction in the surface energy. This can be either preserving the shape of nanoparticles at lower temperatures or changing their shape and size by their coalescence at elevated temperatures. In fact, the surface energy of a nanoparticle can be a large portion of its total energy. In this study, we explore the role of surface reduction during the coalescence of Gold (Au) nanoparticles their evolution using Molecular Dynamics (MD) Simulation method.
Au nanoparticles are one of the well-known noble metal nanoparticles that have found some important applications in biotechnology [12], in synthesis [13] as catalyst and in nanoparticles-networked film [14] as conductor and characterization devices [15] as probes. Here we conduct a systematic study of melting and coalescence behavior of Au nanoparticles. In the first step, the melting behavior of single Au nanoparticles are studies as a function of their size.
Then we study the coalescence of the nanoparticles of the same size at different temperatures. Detailed analyses of Lindemann index (LI) and potential energy distribution across the nanoparticles were performed to study the melting and coalescence mechanisms of nanoparticles. The role of surface melting and surface area reduction are discussed in details, both of which are specific features of the nanosized systems.

Simulation method
In the current MD simulations, a glue potential for Au calculated by force matching method was used [16]. The force matching method is a very effective tool to obtain realistic classical potentials [17] that is based on fitting the potential to ab-initio atomic forces of many atomic configurations. A glue potential is defined by standard pair potential  (rij), a glue function U(n) (an energy associated with coordination n of atoms), an atomic density function  (rij) (shortranged monotonically decreasing function of distance) where rij is the distance between two atoms. This potential has been successfully employed in several previous works [18,19].
In this study, the constant temperature simulations were carried out on Au nanoparticles with 586, 1289 and 2406 atoms. All nanoparticles were initially constructed to a prefect truncated polyhedral structure (Figure 1a). The Verlet velocity algorithm was employed to solve motion equations and, the desired temperature was obtained by uniform kinetic energy scaling method [20]. The chosen time step was 1.7 fs.
For a systematic study, first the melting points of nanoparticles were calculated via the potential energy and LI monitoring as a function of temperature. The nanoparticles were equilibrated during an initial (minimum) 250,000 time steps for each temperature, and then the potential energy and LI were calculated at each temperature during at least 150,000 steps depending on the system size. For some systems the equilibration needed more than 1000,000 time steps. The LI of each atom and of the entire system at each temperature are given as [21]: where rij is distance between two atoms, N is number of atoms, δi is the LI of ith atom and δ is the LI of particle which is simply the normalized square root of mean distance among atoms. This parameter was widely used for solid-solid and solid-liquid transitions analysis and, as discussed in the previous works, the end of a sharp rise in the indices over a small temperature change reveals the melting point of system [22,23]. Applying this index across the nanoparticles help analyzing the surface melting phenomenon. A reference Au bulk system (NVT) with a periodic boundary condition was simulated as well to compare against the current simulation results.
For studying the coalescence of nanoparticles, pairs of exactly the same equilibrated Au nanoparticles were brought to contact (separated by 0.2 nm) at different temperatures below and above the nanoparticle melting point and were studied for 200,000 time steps. No external forces were applied during the coalescence. The complete coalescence of each pair of the nanoparticles was defined for a temperature in which the diameter of the pair nanoparticle differed for less than 10% from its minimum value [24]. This definition is arbitrary but does not affect the conclusions drawn from the current studies.

Results and Discussion
Many theoretical and experimental studies show that the melting points of small particles are far lower than that of the corresponding bulk [25][26][27][28] that also has been confirmed by our simulations.  Table 1. A good agreement has been obtained between the current results and previous works [19,28]. In order to obtain more accurate values of the melting temperatures, a detailed study of transition region is needed. As expected, the Gibbs-Thompson size effect on the melting point of nanoparticles is clearly obtained. Interestingly, the solid-liquid transformation energies (latent heats) are also found to be size-dependent, decreasing for smaller nanoparticles. The results in Figure 1b show that for a given temperature the potential energy levels for smaller systems are much higher than the bulk values (marked by the two-sided arrow). In fact, it is clear that this difference is much larger that the liquid-solid latent heat for the nanoparticles and almost comparable to the liquidsolid transformation energy in the bulk material. This implies the extended effect of the surfaces on the energy state of the nanoparticles, also discussed in our previous works, which is equivalent to the Laplace pressure induced by the surface energy. As a matter of fact, this extended surface effect is responsible for the decrease in the latent heat for smaller nanoparticles. As the size of particles increases the potential energy state approaches the bulk value.     Table   1). Figure 3 shows the evolution of two Au2406 nanoparticles, initially at 1100 K.
During the simulations, the initial contact between the two particles is established by the weak attractive forces between them. When two nanoparticles touch, the surface atoms quickly interact. A rapid diffusion of unstable surface-atoms from high-energy state (lower neighboring atoms) to the more stable low-energy state (more neighboring atoms) was observed. The corresponding size evaluations during the coalescence of the two nanoparticles in Figure 3 are marked in Figure   4a. Analysis of the total potential energy and the average temperature of the two systems, however, reveal interesting details about the mechanisms of coalescence: For the liquid droplets (at 1250 K), coalescence occurs rapidly with a continuous increase in the temperature and potential energy state, that is due to the heat released upon the reduction in the total surface area. In case of the two solid nanoparticles at 1100 K a nontrivial path is taken in which an initial decrease (increase) in the total potential energy (temperature), is inversed sometime during the coalescence. The results show that in this case, the energy released due to the initial coalescence and surface reduction is invested in melting the nanoparticles that results in a drop in the average temperature and increase in the total potential energy. In other words, a synergetic mechanism of coalescence is revealed in which the coalescence accelerates itself by the surface reduction. Our results demonstrate that the leading mechanism of coalescence is surface diffusion (high energy and high mobility surface-atoms) followed by a rapid neck growth and a relatively slow reshaping of the attached nanoparticles. Our observations confirm the Foiles et al. [32] MD simulations results, however they did not account energy and temperature changes in the system. Our simulations show that at elevated temperature nanoparticles rapidly reshape while in lower temperatures (for example Au2406 at 800 K) the coalescence beginning quickly, but cannot be completed, because of the slow diffusion. Because of the surface area reduction, the coalescence is accompanied with an energy release increasing the temperature that accelerates the entire process ( figure 4b and c). This confirms Lehtinen and Zachariah [31] reports on the sintering process of nanoparticles.
Although our simulations times were many orders of magnitude smaller than real experimental times, but the coalescences were completed for nanoparticles at several hundred degrees below their melting points. Therefore, in experimental times, it may be expected that lower coalescence temperatures obtain given a longer time for diffusion.

Conclusions
In current work, the melting and coalescence temperatures of Au nanoparticles and bulk were determined via MD simulation method. The potential energy and LI analyses were performed to understand the mechanism of melting and coalescence of nanoparticles.
The simulation results show that the coalescence occurs at temperatures lower than the corresponding melting points of the nanoparticles. With reference to LIs, it seems that the coalescence is accompanied with surface diffusion/melting. It was shown that the liquid-solid phases may be coexisting in a wide range of temperatures below the melting points in nanoparticles. Moreover, it was found that a surface-induced phase transition can occur where the heat released due to the reduction in the surface area can result in melting of the nanoparticles. This effect accelerates the coalescence process and can play a dominating role in small enough nanoparticles and/or at elevated temperature before the melting point.