Morphology and Crystallinity of Coalescing Nanosilver by Molecular

Article pubs.acs.org/JPCC

Morphology and Crystallinity of Coalescing Nanosilver by Molecular Dynamics B. Buesser*,† and S. E. Pratsinis‡ †

Smarter Cities Technology Center, IBM ResearchIreland, Dublin, Ireland Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland

‡

ABSTRACT: Sintering and its final stage of coalescence of silver nanoparticles with various morphologies have been investigated in vacuo between 400 and 1000 K by molecular dynamics simulations using the embedded atom method (EAM). It was found that the Ag nanoparticle melting temperature increases with increasing particle size and approaches the bulk melting point of Ag for bigger particles (>10 nm) consistent with simulation literature and experimental data. The motion of surface and bulk Ag atoms within Ag nanoparticles is monitored closely during their sintering. Early on, the sintering or coalescence of nanoparticles is dominated by surface diffusion whereas a transition toward plastic flow sintering can be observed near their melting point. The sintering rate of straight nanoparticle chains is much slower than that of more compact structures. The formation of new crystal domains during Ag particle sintering is demonstrated for the first time to the best of our knowledge, and mechanisms leading to formation of polycrystalline particles are revealed. Pinilla et al.19 characterized Ag nanoparticles by atomic force microscopy and UV−visible spectroscopy and by comparing this data to their MD simulations determined the relative stabilities of nanoparticle shapes and their respective melting temperatures. Here, the sintering rate and mechanism of various silver nanoparticle morphologies with particle diameters up to 4 nm are elucidated and compared through monitoring of their surface area reduction during sintering and coalescence. This is done by MD accelerated with graphics processing units (GPUs) using the EAM to describe the atomic interactions.16 Furthermore, Ag nanocrystal sintering dynamics are investigated in detail by determining the degree of crystalline order in the vicinity of Ag atoms and monitoring their trajectories. The sintering rate and crystallinity of chains and compact Ag nanoparticle aggregates are investigated.

1. INTRODUCTION Silver nanoparticles (nanosilver) are in about 25% of today’s nanomaterial-containing consumer products1 where they have essential roles as catalysts,2 bactericidal materials,3 plasmonic absorbers in organic photovoltaic cells,4 or biosensors.5 The performance of nanosilver thereby depends considerably on its particle size, shape, and crystallinity, especially below 10 nm where the fraction of surface atoms increases dramatically and quantum effects start to appear. For example, the efficiency of solar cells has been enhanced considerably by nanosilver with a diameter as small as 5 nm because of their increased light adsorption in the visible spectrum.4 Silver nanoparticles are produced either by wet-6 or gasphase7 processes. The latter have the advantage of proven scalability to ton/hour combined with facile particle handling (e.g., carbon black, pigmentary TiO2, fumed SiO2).8 In gas phase, nanoparticles grow mainly by coagulation and sintering/ coalescence. The sintering rate determines the product morphology and primary particle diameters when agglomerates and aggregates are produced. This motivates the development of a quantitative understanding of the early stages of particle formation and growth to enable the interpretation of experimental data, efficient process design of nanoparticle synthesis, and eventually target design of optimal product performance.8 Molecular dynamics (MD) simulations have been used to effectively elucidate the sintering of nanoparticles of, e.g., Cu,9 Al,10 Si,11 Au,12 Ni,13 W,14 or TiO2.15,16 In particular for Ag, Zhao et al.17 have used the embedded atom method (EAM) to calculate caloric curves and melting temperatures and demonstrated the early sintering stages of three silver nanoparticles. Xiao et al.18 elucidated with MD how melting of nanocrystalline Ag is starting at grain boundaries. Gracia© XXXX American Chemical Society

2. THEORY 2.1. Molecular Dynamics Implementation. The embedded atom method (EAM)20,21 is used with the parametrization of Foiles et al.22 to describe the interactions of silver atoms: 1 Etot = ∑ Fi(ρh , i ) + ∑ ∑ ϕij(R ij) 2 i j(≠ i) i (1) The first term on the right-hand side accounts for the local electron density whereas the second describes pairwise atom interactions. Nanoparticles were prepared by selecting atoms within a sphere of diameter dp out of a perfect fcc-crystal with lattice constant a = 4.09 Å corresponding to bulk silver. These Received: February 12, 2015 Revised: April 8, 2015

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DOI: 10.1021/acs.jpcc.5b01491 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C nanoparticles were equilibrated first in the microcanonical ensemble (NVE) combined with velocity rescaling to the investigated temperature every 100th time step during 100 ps with a time step of 1 fs followed by a simulation of 100 ps of NVE without velocity rescaling to test the quality of the equilibration by assuring the absence of any drifts in temperature.16 Particle sintering was simulated by placing two such nanoparticles, after 200 ps of equilibration, next to each other with a separation of 3.5 Å between the closest atom centers. The sintering simulations have been carried out in the canonical ensemble (NVT) for a constant time average of temperature with an integration time step of 1 fs. The temperature damping parameter was set to 10 s. The dependence on initial conditions was investigated by simulating the sintering of two particles at each temperature four times by rotating the right-hand-side particle initially by 90° around the axis through the center of mass of the two particles. All simulations were done using LAMMPS23 running on GPUs in double precision on Brutus at ETH Zurich and on CPUs on Pharos at MIT. The heating and cooling simulations to determine melting temperatures started with nanoparticles equilibrated at T = 300 K and increased the temperature with NVT within 107 time steps of 1 fs to T = 1300 K followed by cooling with the same parameters back to 300 K. This corresponds to a heating and cooling rate of 1011 K/s which is a common cooling rate for MD but much longer than the typical cooling rates of 106−107 K/s observed in industrial particle synthesis processes. 2.2. Aggregate Surface Area. The surface area evolution of the sintering/coalescing particles was determined with the program24 MSMS 6.2.1 that calculates the area of the surface created by a probing sphere rolling over overlapping spheres. Here, the overlapping spheres represent silver atoms with their van der Waals radius25 of 1.72 Å while the probing sphere has a radius of 2.25 Å corresponding to that of a N2 molecule. This is consistent with standard experimental measurements16 of surface area by N2 adsorption.26 2.3. Characteristic Sintering Time. Particle dynamics models for the design of aerosol reactors in gas-phase manufacturing of nanoparticles often apply the phenomenological sintering model of Koch and Friedlander27

a − a fc da = dt τ

within the cutoff radius rcut = 2.95 Å around atom j. To improve the accuracy, q was averaged following Lechner and Dellago31 and Kawasaki and Onuki:30 1 q6̅ jm = j [q j + ∑ q k ] nb + 1 6m k ∈ bond 6m (4) The disorder variable Dj was defined as Dj(t ) =

1

∑

Ylm(rjk(t ))

k ∈ bond m =−6

|q6̅ jm(t ) − q6̅ km(t )|2

(5)

3. RESULTS AND DISCUSSION 3.1. Validation: Melting Temperature of Nanosilver. The sintering rate depends strongly on particle temperature, size, and morphology. Therefore, the size-dependent melting and solidifying temperatures have been obtained for the employed EAM force field by simulating caloric curves of particle heating and subsequent cooling between 300 and 1300 K at 1011 K/s, a common cooling rate for MD simulations but larger than typical experimental cooling rates. Figure 1 shows

Figure 1. Melting temperature, Tm (red line and circles), and supercooled solidifying temperature, Ts (blue line and circles), of silver nanoparticles as a function of particle diameter, dp, along with the corresponding regions for solid (blue), metastable (green), and liquid (red) nanoparticles. Literature data are shown for MD simulations in vacuo (open symbols) and experiments (filled symbols) of Ag particles deposited on SiO2 (squares) and tungsten (diamonds) substrates. The Tm and Ts seem to approach the melting (1234 K, dashed line) and supercooled solidifying (974 K, dash-dot line) temperatures of bulk silver for dp > 10 nm.

(2)

nbj(t ) k ∈ bond

6

∑ ∑

where a small value of Dj ≤ 0.005 represents a well-ordered fcccrystal environment.30

to describe the reduction of aggregate particle surface area, a, by sintering until full coalescence (one, single spherical particle) with surface area afc. The characteristic sintering time, τ, is the time needed to reduce the excess surface area (a − afc) of coalescing particles over afc by 63%.28 It depends on particle composition, diameter, and temperature. Here, molecular dynamics simulations16 are used to simulate the evolution of a to determine τ. 2.4. Disorder Variable. The Steinhardt order parameter qlm is defined as29,30 qlmj =

1 j n b( t )

the melting, Tm (red line and circles), and supercooled solidifying temperature, Ts (blue line and circles), of silver nanoparticles as a function of their diameter, dp. Melting temperatures were obtained by monitoring the increase or decrease in the Lindemann index above or below 0.15 during heating and cooling, respectively.32 With increasing dp, the calculated Tm and Ts seem to approach the corresponding bulk silver temperatures of 1234 K (dashed line) and 974 K (dashdot line), respectively, consistent with experimental data of gold and silver nanoparticles.33,34

(3)

where Ylm are spherical harmonic functions of degree l (with −l ≤ m ≤ l) as a function of vector rjk between the centers of atoms j and k, where l = 6 has been shown to be a good choice for analysis of fcc-crystals,30 and nbj is the number of atoms k B


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The Journal of Physical Chemistry C Figure 1 shows also that diameter-dependent melting and solidifying temperatures divide the particle diameter/temperature space into three regions for solid (blue), metastable (green), and liquid (red) particles. At low and high temperatures, all particles are either solid or liquid, respectively. In between there is a metastable region where particles can be either solid or liquid and that narrows with decreasing particle size and cooling rate.9,35 The steep reduction of Tm for dp < 3 nm is consistent with Zhao et al.17(open squares) who had simulated the coalescence of two truncated Marks decahedrashaped particles and in even better agreement with Xiao et al.18 (open diamonds) who had simulated the melting of spherical Ag nanoparticles by MD. Gracia-Pinilla et al.19 had simulated highly symmetric particles with a different force field parametrization and obtained slightly higher melting temperatures for a diameter of 5 nm (open triangles). All these literature melting temperatures are in agreement with the transition between metastable and liquid particles obtained here (red line). Experimental data on the melting temperature of unsupported silver nanoparticles (in vacuo) is not available to the best of our knowledge, but for comparison experimental data for silver nanoparticles deposited on tungsten34 (filled diamonds) or SiO236 (filled square) substrates are shown. These experiments reported melting temperatures slightly lower than the solid−metastable transition of this work in Figure 1 (blue line). This could be explained by the influence of the substrate, impurities, or irregularities in the atomic structure. Furthermore, MD simulations of gold particles have shown that nanoparticle contact angles with the substrate smaller than 90° can significantly enhance the size-dependence of Tm and accelerate melting compared to nanoparticles in vacuo.37 For example, in nanosilver-containing adhesives sinter neck formation was observed for dp = 20 nm already at 473 K.38 3.2. Sintering or Coalescence Dynamics of Two AgNanoparticles. Figure 2 shows snapshots of the cross section of two solid silver nanoparticles with initial diameter dp,0 = 3 nm undergoing sintering/coalescence at t = 0, 1, 10, and 100 ns for (a) 800 K (left column) and (b) 900 K (right column). The atoms that are initially (t = 0 ns) on the particle surface are colored green, while the bulk atoms are red to trace their trajectory during sintering (t > 0 ns).16 At T = 800 K (Figure 2a), a sintering neck is formed immediately (t < 1 ns) by adhesion. Shortly afterward (t = 1 ns), the concave region at the nanoparticle sintering neck fills up (open arrow) with surface atoms (green) from both nanoparticles. This indicates the dominance of highly mobile surface atoms and subsequently sintering by surface diffusion16 while the initially bulk atoms (red) remain nearly undisturbed. Later on (t = 10−100 ns), the two particles have almost fully coalesced into an oval or spherically shaped particle. At this time, few of the initially bulk (red) atoms have been able to reach the particle surface as the initially surface (green) atoms have diffused away (filled arrows) into the concave neck region and started to spread across the surface. At T = 900 K (Figure 2b), which is close to Tm for this particle size (Figure 1), sintering proceeds much faster. Early on (t = 1 ns), surface atoms also fill the neck region between particles forming the characteristic oval particle shape that corresponds to an advanced sintering state. Furthermore, a deformation of the particle bulk (red) takes place along the sinter neck line which indicates a liquidlike (plastic) sintering behavior. At t = 10 ns this becomes even more pronounced as

Figure 2. Snapshots of cross sections of two silver nanoparticles with initial diameter dp,0 = 3 nm undergoing sintering at T = (a) 800 K (below Tm, left column) and (b) 900 K (near Tm = 930 K, right column) at t = 0, 1, 10, and 100 ns. The initial location of the atoms is traced by initially coloring the bulk atoms red and the surface atoms green.

particles coalesce to a more compact, spherical shape. At t = 100 ns the two domains of initially surface and bulk atoms are much less well-defined and separated than for T = 800 K as Ag atoms are quite intermixed between surface and bulk. Figure 3 shows the characteristic sintering time, τ, of two equally sized Ag nanoparticles (Figure 2) with initial diameters dp,0 = 2.5 (circles), 3 (squares), 3.5 (diamonds), and 4 nm (triangles) as a function of sintering temperature, T.16 Symbols represent averages of four independent simulations, each at the same temperature, and error bars show the minimum and maximum value of these four simulations. The width of the error bars decreases considerably with increasing particle size as the fraction of highly mobile atoms, and their variability decreases with increasing particle size. At a given T, increasing dp,0 increases τ as larger particles need longer to fully coalesce than smaller particles. Similarly, at a given initial dp,0, decreasing T increases τ as lower temperatures result in lower atom mobility and subsequently slower particle coalescence.28 The τ approaches a minimum or asymptotic value around the corresponding size-dependent Tm (Figure 1) between 650 and 900 K for 2.5 nm and between 850 and 1000 K for 3 nm. 3.3. Multiparticle Sintering. Figure 4 shows snapshots of the cross section of a straight chain of three equally sized silver nanoparticles with dp,0 = 3 nm undergoing sintering at (a) 800 K (left column) and (b) 900 K (right column) at t = 0, 10, and 100 ns. The initial location (t = 0 ns) of Ag atoms is colored as in Figure 2. At T = 800 K (Figure 4a) similar to Figure 2a, the sintering necks are filled quickly by initially surface atoms (t = C


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The Journal of Physical Chemistry C

Figure 3. Characteristic sintering time, τ, obtained by MD for two equally sized Ag particles with initial diameter dp,0 = 2.5 (spheres), 3 (squares), 3.5 (diamonds), and 4 nm (triangles) as a function of sintering temperature, T. Symbols represent the average of four simulations while the error bars show the minimum and maximum values. Bigger particles sinter slower and have therefore a longer τ while increasing temperature decreases τ.

Figure 4. Snapshots of the cross section of a straight chain of three equally sized silver nanoparticles with initial diameter dp,0 = 3 nm undergoing sintering at (a) 800 K (left column) and (b) 900 K (right column) for t = 0, 10, and 100 ns. The initial (t = 0 ns) location of the atoms is traced by initially coloring the bulk atoms red and the surface atoms green.

Figure 5. Snapshots of cross sections of four silver nanoparticles in star configuration with initial diameter dp,0 = 3 nm sintering at T = 800 K at t = (a) 0, (b) 10, and (c) 100 ns.

10 ns, open arrows) while the initially bulk atoms (red) remain largely in three distinct regions of the aggregate particle. Later on (t = 100 ns), bulk atoms of the initially side particles reach the surface of the aggregate particle (filled arrows) while the bulk of the center particle slightly deforms at the aggregate center. At T = 900 K (Figure 4b), a similar deformation of the bulk regions can be observed as for two particles already at 10 ns (Figure 2b). Later on (t = 100 ns), the side bulk regions are largely disintegrated. The bulk of the center particle can still be recognized while the entire aggregate has become quite compact and nearly spherical. Figure 5 shows snapshots of cross sections of four silver nanoparticles in a star configuration with initial diameter dp,0 = 3 nm sintering at T = 800 K at t = (a) 0, (b) 10, and (c) 100 ns. Again the surface atoms are filling up early on (Figure 5b, t = 10

ns) the concave regions between the peripheral particles and gradually expose the initially bulk atoms to the surface of the aggregate. Even after full coalescence to a spherical particle (Figure 5c, t = 100 ns), the initially surface and bulk atoms remain segregated, although now, the surface of the coalesced aggregate particle consists mainly of the initial bulk atoms of the three peripheral particles. Figure 6 quantifies the evolution of the external surface area of the aggregates during sintering by their characteristic sintering time,16 τ, as a function of sintering temperature, T, for equally sized particles with initial diameters of dp,0 = 2.5 (broken lines) and 3 nm (solid lines) in configurations of two particles (circles), three particles in a straight chain (squares), triangles of three particles (triangles), and stars of four particles D


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Figure 6. Characteristic sintering time, τ, for equally sized particles with initial diameter dp,0 = 2.5 (red broken line) and 3 nm (blue solid line) in configurations of two particles (circles), three particles in a chain (squares) or triangle (triangles), and four particles in a star (diamonds) as a function of sintering temperature, T.

(diamonds). All clusters sinter faster and have a shorter τ at higher temperatures, and clearly all clusters with smaller particles sinter faster than those made of larger particles, which points out the significance of primary particle size in sintering of multiparticle ensembles or aggregates. Configuration, however, matters too. For a given dp, the chain of three particles (squares) sinters slower than just two particles (circles). Most interestingly, however, the more compact three-particle triangle configuration (triangles) sinters even faster than two particles of the same primary particle size! This is even more pronounced for the smaller particles (2.5 nm, red line and symbols) with their increased fraction of high mobility surface atoms. This might be explained by the larger fraction of surface area lost just by neck formation during adhesion of the particles in configurations with more contact points, an effect that increases with smaller particle size.16 The characteristic sintering time of four particles in star configuration is only slightly larger than that of a chain of three particles. These results show that the widely used sintering rates of two particles are roughly on the average (circles) of all these configurations. Also, it seems that more compact agglomerates and aggregates, e.g., those with a higher fractal dimension like triangles, sinter faster than less compact ones like chains. 3.4. Crystallinity Dynamics. An important property of nanoparticles, along with primary particle size and extent of aggregation, is crystallinity, e.g., the composition and number of crystal grains per particle (mono- or polycrystallinity). This property is difficult to follow experimentally in situ, especially in gas phase. Therefore, Steinhardt parameters and a disorder variable, Dj, describing the disorder or deviation from a perfect fcc-crystal have been calculated for each Ag atom using eqs 3−5 to analyze the evolution of the crystal domains during sintering. Figure 7a shows the crystallinity of silver nanoparticles during sintering or coalescence at T = 800 K (the same particles as in Figure 2a) through the Dj of each atom on their cross sections. Blue (Di < 0.02) indicates a nearly perfect fcc-crystal environment while colors from green (Di ∼ 0.05) to red (Di > 0.1) represent increasing deviations from the perfect Ag fcccrystal. At t = 0 ns, the bulk Ag (particle interior) is perfectly fcc-ordered (blue) and small disorders appear mostly near the

Figure 7. (a) Snapshots of the cross section of two equally sized sintering particles (Figure 2a, dp,0 = 3 nm at T = 800 K) colored according to the disorder variable, Di. Blue (Di < 0.02) indicates a perfect fcc-crystal environment and green (Di ∼ 0.05) to red (Di > 0.1) an increasingly distorted crystal. (b) In the right column the righthand-side particle has been rotated by 45° to alter the initial alignment of the crystal planes (red arrow) to demonstrate the role of such lattice defects or mismatches during particle sintering.

surface or because of thermal vibrations. At the surface, atoms minimize their potential energy by leaving the fcc-crystal positions because of their smaller coordination numbers which results in larger disorder (green/yellow/orange/red). As sintering progresses (t = 10 ns), a boundary of increased disorder (greenish-light blue atoms) forms between the two particles. This boundary consists of both initially surface and bulk Ag atoms as can be seen by juxtaposing Figure 2a at t = 10 ns. This boundary is in the center of the aggregate particle and persists until full coalescence (t = 100 ns). By comparing this picture to that of Figure 2a at 100 ns, it is worth noting that some initially surface Ag atoms have attained perfectly crystalline positions at the upper quartile of the aggregate while some bulk ones are part of this low crystallinity boundary. The spatial distribution of this boundary within the coalesced particle was investigated further (with an MRI-like examination) by analyzing slices of atom layers through various particles heights. So it was found that this disorder spans the aggregate particle from side to side resulting in essentially two crystal grains divided by one grain boundary (green). To investigate the influence of initial crystal mismatches and defects, Figure 7b shows the crystallinity dynamics similar to Figure 7a but with the right-hand-side particle rotated initially by 45° (red arrow). At t = 10 ns, three crystal domains and two grain boundaries can be recognized. The change in initial crystal alignment has favored the formation of a third crystal in the upper side of the sintering neck (open arrow) while the lower side remained highly disordered (filled arrow). This crystalline configuration persists until full coalescence (t = 100 ns) which points out the effect of even small crystal defects or initial mismatches on the final particle crystallinity. It also E


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the size-dependent melting temperature. At higher temperatures a transition to plastic flow sintering has been observed. Chains of three particles and stars of four particles have comparable characteristic sintering times which are larger than that for two particles. However, the more compact configuration of a triangle of three particles sinters faster than just two particles. This might indicate that a single characteristic sintering time only depending on particle size and temperature might not be sufficient to describe the influence of particle configuration on the sintering of aggregates accurately, but that the rate for two particles is close to the average of all morphologies and a good approximation. The evolution of crystallinity during sintering has been analyzed using a disorder variable based on Steinhardt parameters. At low temperature even fully compact or coalesced particles retain the crystalline structure of the constituent particles. Initial mismatches in crystal plane alignment can result in the formation of new crystals at the sintering necks, and therefore sintering can be a mechanism that increases polycrystallinity during particle synthesis.

demonstrates nicely how sintering can lead to polycrystalline particles. Figure 8a shows the analysis of Figure 7a for a chain of three particles (the same as in Figure 4a). The three aligned particles

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Figure 8. (a) Snapshots of cross sections colored according to the disorder variable, Di, where blue (Di < 0.02) indicates a perfect fcccrystal environment and green (Di ∼ 0.05) to red (Di > 0.1) an increasingly distorted crystal for three particles in a chain with dp,0 = 3 nm at T = 800 K. (b) In the right column the center particle has been rotated by 45° (red arrow) to misalign its crystal planes with the two other particles.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Swiss National Science Foundation (SNF) Postdoctoral Research Grant PBEZP2-140081 and the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013, ERC grant agreement no. 247283) is gratefully acknowledged.

form sintering necks with rather thin crystalline grain boundaries (t = 10 ns). Closer to full coalescence (t = 100 ns), however, a higher degree of distortion can be observed with few distinct noncrystalline domains (blue). When the center particle in the chain is rotated by 45° (Figure 8b), it aligns better with the left particle upon adhesion (t = 10 ns) than in Figure 8a. As a result, a slightly larger crystal domain is formed in the center-left side with some defects. In contrast, the right-hand-side particle in the chain could not rotate enough upon adhesion16 to line up with the crystal lattices of the center particle. As a result, a new crystal domain was formed on the right side sintering neck of the resulting aggregate (open arrow). On the bottom of this sintering neck, a largely disordered domain (filled arrow) has been formed, temporarily as it can be seen later, similar to that for two particles (Figure 7b, t = 10 ns, filled arrow). Closer to full coalescence (t = 100 ns), however, this polycrystalline structure evolves largely into a particle with only two crystal grains and one grain boundary between the initial center-right particles. These simulations show how minor initial differences or mismatches can lead to formation of distinctly different final crystalline domains in a sintering aggregate made out of otherwise identical nanoparticles and how crystal domains dynamically appear and disappear over the course of sintering. Furthermore, this reveals how sintering actually can introduce nonuniformity into nanoparticles even though they are initially monocrystalline.

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4. CONCLUSIONS The evolution of morphology and crystallinity of silver nanoparticles undergoing sintering in various configurations has been investigated by molecular dynamics. Analyzing the atom trajectories of two sintering particles revealed that surface diffusion dominates their sintering for temperatures well below F


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