Molecular Dynamics Simulation of Amorphous SiO - American

District 10, HochiMinh City, Vietnam. ReceiVed: June 1, 2007; In Final Form: September 5, 2007. Molecular dynamics simulation of amorphous SiO2 spheri...
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J. Phys. Chem. B 2007, 111, 12649-12656

12649

Molecular Dynamics Simulation of Amorphous SiO2 Nanoparticles Vo Van Hoang* Department of Physics, Institute of Technology, National UniVersity of HochiMinh City, 268 Ly Thuong Kiet, District 10, HochiMinh City, Vietnam ReceiVed: June 1, 2007; In Final Form: September 5, 2007

Molecular dynamics simulation of amorphous SiO2 spherical nanoparticles has been carried out in a model with different sizes, 2, 4, and 6 nm, under non-periodic boundary conditions. We use the pair interatomic potentials which have weak Coulomb interaction and Morse type short-range interaction. Models have been obtained by cooling from the melt via molecular dynamics (MD) simulation. Structural properties of amorphous nanoparticles obtained at 350 K have been studied via partial radial distribution functions (PRDFs), mean interatomic distances, coordination numbers, and bond-angle distributions, which are compared with those observed in the bulk. Calculations of the radial density profile in nanoparticles show the tendency of oxygen to concentrate at the surface as observed previously in other amorphous clusters or thin films. Size effects on structure of nanosized models are significant. The calculations show that if the size is larger than 4 nm, amorphous SiO2 nanoparticles have a distorted tetrahedral network structure with the mean coordination number ZSi-O ≈ 4.0 and ZO-Si ≈ 2.0 like those observed in the bulk. Surface structure, surface energy, and glass transition temperature of SiO2 nanoparticles have been obtained and presented.

Introduction Over the past decades, SiO2 nanoparticles have been under intensive investigation through both experiments1-26 and computer simulation27-32 because of their enormous technological importance for advanced quantum-confined electronic and optoelectronic devices. It was found that silica nanoparticles have a number of novel properties including catalysis24 and photoluminescence9,17 resulting from their specific structure, which is different from the bulk. Moreover, SiO2 nanoparticles have been used for gene delivery,12 as carriers for indomethacin in solid-state dispersion,13 and drug release control,15 and their effects on thermal and tensile behavior of nylon-6 have been found.21 On the other hand, although SiO2 nanoparticles can be obtained in both crystalline and amorphous polymorphs, less attention has been paid to amorphous SiO2 nanoparticles, and our understanding of their structure and properties is limited.1,3,9,17,20 Therefore, understanding of the relationship between the structure of SiO2 nanoparticles and their chemical and physical properties is fundamental in material science. However, information on an atomistic level can be provided just by computer simulation. Roder et al. studied the structure and dynamics of surfaces of amorphous SiO2 clusters with different diameters, and they found that the shape of the clusters is independent of temperature, and that it becomes more spherical with increasing size.27 They found the existence of twomembered rings at the surface of nanoclusters, and close to the surface, the diffusion constant is somewhat larger than the one in the bulk. Moreover, a small peak of the density distribution that occurred just below the surface has been found and is related to the aggregation of Si particles for the local charge neutrality versus the concentration of oxygen at the surface of nanoclusters.27 Structure and properties of SiO2 nanoclusters containing 1152 atoms at temperatures ranging from 1500 to 2800 K have been studied via classical MD simulation by Schweigert et al.,28 E-mail: [email protected].

Figure 1. Partial radial distribution functions in amorphous SiO2 nanoparticles at T ) 350 K compared with that of the bulk.

and their results share many trends observed by Roder et al. Structures and properties of much smaller SiO2 nanoclusters have been investigated, and much attention has been paid to the ring structure.29-32 However, there are no comprehensive studies of the structure and thermodynamics of liquid and amorphous SiO2 nanoparticles including surface and core structure analysis, temperature dependence of surface energy, size dependence of glass transition temperature, or effects of different boundary conditions on their structure and properties. These points will be discussed in the present work. Calculation Although there is a variety of potentials for silica, the BKS interatomic potentials seem to be remarkably good in the

10.1021/jp074237u CCC: $37.00 © 2007 American Chemical Society Published on Web 10/18/2007

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TABLE 1: Structural Characteristics of Amorphous SiO2 at T ) 350 K; rij, Position of the First Peaks in PRDFs; gij, Height of the First Peaks in PRDFs; Zij, Average Coordination Number rij (Å)

gij

Zij

materials

SisSi

Si-O

OsO

SisSi

Si-O

OsO

SisSi

Si-O

O-Si

OsO

2 nm 4 nm 6 nm bulk

3.02 3.02 3.03 3.06

1.52 1.52 1.52 1.52

2.53 2.54 2.54 2.55

8.60 9.16 8.83 5.12

30.81 32.42 33.12 16.58

8.98 9.40 9.49 5.10

3.69 3.80 3.87 3.78

3.92 3.96 3.98 3.99

1.96 1.98 1.99 2.00

5.86 6.06 6.16 6.07

description of bulk properties of crystalline and amorphous SiO2.33-36 BKS potentials qualitatively describe surface properties of amorphous SiO2 nanoclusters.27 In the present work, we show an alternative choice by using new interatomic potentials. That is, via comparing the melting temperature and the density profile at high temperatures predicted by potentials in literature for SiO2, it was found that the high temperature behavior was best described by the potentials with weak long range interactions and Morse type potential for short-range interactions37 as given below:

Uij(r) )

qiqj + r

{ [(

D0 exp γ 1 -

)]

r R0

- 2 exp

[ (

)]}

r 1 γ 12 R0

nanoparticles, we adopt the fixed values RSi-Si ) 3.30 Å, RSi-O ) 2.10 Å, and RO-O ) 3.00 Å, where R denotes a cutoff radius, which is chosen as the position of the minimum after first peak in the radial distribution function (PRDF), gij(r), for the amorphous state at the temperature of 350 K and at 2.20 g/cm3. In order to compare, we also show the results for models of liquid and amorphous SiO2 in a cube containing 3000 atoms under periodic boundary conditions, which is considered as a bulk. In order to improve the statistics, we average the results over two independent runs for 2 nm and 4 nm nanoparticles. A single run has been done for 6 nm nanoparticle because of its large number of atoms. Results and Discussions

(1)

where qi and qj represent the charges of atoms i and j, for Si atom qSi ) +1.30e and for O atom qO ) -0.65e (e is the elementary charge unit); r denotes the interatomic distance between atoms i and j; D0, γ, and R0 are the parameters of the Morse potentials representing the short-range interactions in the system. The Morse potential parameters for silica can be found in several works.37-39 The potentials have been successfully used in MD simulations of both structure and thermodynamic properties of silica37-39 and in the investigation of the structure changes in cristobalite and silica glass at high temperatures.38 These potentials reproduced well the melting temperature of cristobalite, and the glass phase transition temperature of silica glass and calculated data were more accurate than those observed in other simulation works in which the traditional interatomic potentials with a stronger electrostatic interaction have been used such as BKS or TTAM potentials.33,40,41 Moreover, the simulations in ref 38 reproduced the density maxima at around 1800 K for cristobalite and 1700 K for silica glass which are very close to the experimental data. The potential (1) has been originally proposed with the charge equilibrium scheme, and then it was slightly modified into a potential with the fixed charges with qSi ) +1.30e for Si atom and for O atom qO ) -0.65e (see ref 38). And therefore, such interatomic potentials have been used again here. We use the Verlet algorithm with the MD time step of 1.60 fs. Coulomb interactions were taken into account by means of the Ewald-Hansen method.42 The simulations were done in spherical nanoparticles with sizes of 2, 4, and 6 nm, which contain the number of atoms corresponding to SiO2 stoichiometry and at the real density of 2.20 g/cm3 for vitreous silica; that is, the total number of atoms is equal to 276, 2214, and 7479 atoms, respectively. We first placed randomly N atoms in a sphere of fixed radius, and the configuration has been relaxed for 50 000 MD steps at 7000 K under non-periodic boundary conditions; that is, we use the simple nonslip with non-elastic reflection behavior boundary. The system was cooled down from the melt at constant volume corresponding to the system density of 2.20 g/cm3. The temperature of the system was decreased linearly in time as T ) T0 - γ × t; here, the cooling rate γ is 4.2945 × 1012 K/s. In order to calculate coordination number distributions in SiO2

Structure of Amorphous SiO2 Nanoparticles Compared with Those in the Bulk. The first quantity we would like to discuss here is the PRDF, gij(r), which clearly depends on the size of nanoparticles and differs from those for the bulk (Figure 1). As shown in Figure 1 and Table 1, the position of the first peaks in PRDFs slightly increases with particle size toward the value for the bulk. In contrast, the height of peaks significantly changes with size of nanoparticles; however, the change is not systematic for the Si-Si pair. The peaks in PRDFs of nanoparticles are broader than those for the bulk, indicating a more disordered structure of amorphous nanoparticles compared with that of the bulk because of the contribution of the surface structure of the formers. Moreover, it was pointed out that the method of linkage of structural units-polyhedra such as AlOn and SiOn essentially defines intermediate range order at scales from roughly 4-10 Å in network silicates.43 Therefore, one can infer that size effects on intermediate range order are more pronounced than those on local range order. However, more details of the structure of amorphous SiO2 nanoparticles can be seen via coordination number and bond-angle distributions. We found that the mean coordination number for all atomic pairs in nanoparticles increases with their size toward the value for the bulk because of the reduction of the surface-to-volume ratio, that is, the reduction of surface effects. On the other hand, because of a very large number of atoms in 6 nm nanoparticle, its structural properties such as mean interatomic distances and mean coordination number are identical with those for the bulk. According to our calculations, amorphous SiO2 has a distorted tetrahedral network structure; that is, Si atoms are mainly coordinated to four O atoms, while O atoms are mainly coordinated to two Si atoms (see Tables 1 and 2). This means that Si atoms with ZSi-O * 4 and O atoms with ZO-Si * 2 can be assumed as structural defects in the system. Table 2 shows that defect concentration is enhanced if the nanoparticle size is smaller because of surface effects, specifically, the number of O with ZO-Si ) 1 and ZSi-O ) 3 significantly increases with decreasing nanoparticle size indicating the breaking of O-Si bonds at the surface and the formation of dangling bonds at the surface. We will return to this problem again below. Another important quantity related to the local structure of the system is the bond-angle distribution. We show in Figure 2 the most important Si-O-Si and O-Si-O angles. The first one

MD Simulation of Amorphous SiO2 Nanoparticles

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Figure 2. Bond-angle distributions in amorphous SiO2 nanoparticles at T ) 350 K compared with that of the bulk.

TABLE 2: Fraction of Si Atoms with Coordination Numbers ZSi-O ) 3, 4, and 5 and Fraction of O Atoms with Coordination Numbers ZO-Si ) 1, 2, and 3 in Models Obtained at T ) 350 K ZSi-O

Figure 3. Density profile in amorphous SiO2 nanoparticles at T ) 350 K.

ZO-Si

materials

3

4

5

1

2

3

2 nm 4 nm 6 nm bulk

0.076 0.041 0.024 0.010

0.924 0.958 0.975 0.990

0.000 0.001 0.001 0.000

0.054 0.032 0.027 0.015

0.929 0.955 0.958 0.975

0.017 0.013 0.015 0.010

describes the connectivity between structural units, that is, between SiO4 tetrahedra, and the second one describes the local order inside them. The O-Si-O angle distribution is similar for bulk and nanoparticles; that is, it has a single peak located at around 108°. For an ideal tetrahedron, the O-Si-O angle is equal to 109.47°, which is slightly larger than the value of 108.40° observed for the bulk model (see Figure 2). It suggests that surface effects almost do not change the local order inside the structural units. In contrast, it strongly affects the connectivity between them; that is, strong changes in Si-O-Si angle with nanoparticle size were found. The occurrence of pronounced additional peaks in the Si-O-Si angle distribution for the 2 nm nanoparticles may be caused by strong surface effects including the possibility of the existence of twomembered rings like those found and discussed in ref 27. In order to get more insights into the structure of SiO2 nanoparticle, we show the radial profile density of the nanoparticles as a function of the distance R from the center of nanoparticle, F(R), in Figure 3. This quantity is determined as follows: we find the number of atoms belonging to the spherical shell with the thickness of 0.20 Å formed by two spheres with the radii of R - 0.10 Å and R + 0.10 Å. Then, we calculate the quantity F(R) for finite large enough values, R g10 Å, as it was done in ref 44. The local density is a rather noisy variable. The shells at the outer radii contain many more atoms than those near the center of the nanoparticle, and it is better to carry out the accurate calculation of the outer part of the density profile for the nanoparticles with a size of 4 nm and 6 nm. Strong fluctuations of F(R) indicate that our statistics are not good, smoother changes of the curves can be obtained via averaging over many independent runs. As previously observed in SiO2 surfaces modeled with the BKS interatomic potentials or at amorphous Al2O3 surfaces, oxygen atoms also have a tendency to concentrate at the surface of amorphous SiO2 nanoparticles27,45 (see Figure 3). It can be seen clearly if one looks at the partial density profile for oxygen separately. The reason is that the system is energetically favored with an oxygen atom at the surface, since only one bond has to be broken, if any,

Figure 4. Snapshot of amorphous 4 nm SiO2 nanoparticle at T ) 350 K. Small spheres denote oxygen atoms and large spheres denote silicon ones.

whereas if a silicon is at the surface, several bonds have to be broken. Because of the excess of oxygen at the surface, Si atoms have a tendency to concentrate in the shell close to the surface in order to achieve the local charge neutrality. It causes a peak of the total density in the vicinity of the surface like those previously observed in liquid SiO2 or amorphous Al2O3 surfaces.27,45 At distances far enough from the surface of SiO2 nanoparticles, that is, in the core of nanoparticle, local density fluctuates around the value of 3.00 g/cm3 as was observed for silica nanoclusters with TTAM interatomic potentials.28 This value of density is larger than 2.20 g/cm3, the density of vitreous silica measured experimentally. In addition, a snapshot of the 4 nm SiO2 nanoparticle has been shown in Figure 4, where we can clearly see the existence of structural defects at the surface. According to our results, the concentration of defects at the surface increases with decreasing nanoparticle size (see below). Surface Structure and Surface Energy of Liquid and Amorphous SiO2 Nanoparticles. Surface structure plays an important role in the structure and properties of nanoparticles, and the determination of the relationship between atomic surface

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TABLE 3: Mean Coordination Number of Atoms at the Surface and Core of Amorphous SiO2 Nanoparticles at T ) 350 K Zij materials 2 nm 4 nm 6 nm

surface core surface core surface core

bulk

SisSi

Si-O

O-Si

OsO

3.213 3.935 3.445 3.886 3.537 3.946 3.78

3.705 4.000 3.772 3.998 3.846 3.999 3.99

1.847 2.017 1.876 2.006 1.905 2.005 2.00

5.234 6.250 5.355 6.313 5.540 6.310 6.07

structure and other physicochemical properties of materials is one of the most important achievements of surface science. Therefore, microstructure and properties of amorphous SiO2 surfaces have attracted great interest.1,10,20,25,27,28,46-53 In the present work, we focus attention to the surface structure compared with that observed in the core of nanoparticles. The surface energy also has been found and discussed. To do it, we need a criterion to decide which atoms belong to the surface and which ones belong to the core of nanoparticles. There is no common principle for such choice of surface or core of the amorphous substances. The definition of thickness of the surface in ref 27 is somewhat arbitrary: all atoms that were within 5 Å of the hull just touched the exterior of the droplet and were considered to belong to the surface; atoms that had the distance between 5 Å and 8 Å from the hull belong to the transition zone, and the remaining atoms belong to the interior. In contrast, no definition of surface was clearly presented for the amorphous Al2O3 thin film; they used the top 1 Å or 3 Å layer of the amorphous thin film for surface structural studies.45 From a structural point of view, it can be considered that atoms belong to the surface if they could not have full coordination, and in contrast, atoms belong to the core if they can have full coordination for all atomic pairs like those in the bulk. And therefore, in the present work, atoms located in the outer shell of a spherical nanoparticle with thickness of 3.30 Å (i.e., the largest radius of the coordination spheres found in the system) belong to the surface of the nanoparticles, and the remaining atoms belong to the core. Tables 3 and 4 show that the structure of a core of amorphous SiO2 nanoparticles is nearly size independent and is close to that of the bulk; that is, we found ZSi-O ) 4 and ZO-Si ) 2 in the core of nanoparticles like those observed in the bulk. In contrast, surface structure is strongly size dependent, as the mean coordination number for all atomic pairs increases with increasing nanoparticle size toward the values for the bulk. Moreover, we found significant concentration of structural defects at the surfaces of nanoparticles, that is, Si atoms with ZSi-O * 4 and O atoms with ZO-Si * 2, which strongly increases with decreasing nanoparticle size because of the surface effects. Specifically, we found a significant number of undercoordinated structural units at the surfaces. The existence of structural defects at the surfaces of amorphous nano-

particles might enhance diffusion of atomic species like those observed and discussed,27,28,52 and it is an origin of different surface properties of SiO2 nanoparticles like those found experimentally. We would like to discuss the structural defects in amorphous SiO2 nanoparticles in more detail because they can play an important role in their structure and properties, including catalysis, adsorption, optical properties, and so forth.1,12,17,18,25,32 Particularly, the strong red photoluminescence of amorphous SiO2 nanoparticles has been attributed to the defects at their inner surfaces,17 and it was pointed out that intrinsic point defects are the origin of optical band gap narrowing in fumed silica nanoparticles.18 First, we look at the local environment of Si atoms in amorphous SiO2 nanoparticles. While amorphous SiO2 bulk and core of amorphous SiO2 nanoparticles have a distorted tetrahedral network structure with ZSi-O ) 4 and ZO-Si ) 2, surfaces of nanoparticles contain large amounts of undercoordinated units such as SiO2 and SiO3. Such units can be assumed as structural point defects with oxygen deficiency,54 and their percentage strongly increases with decreasing nanoparticle size, almost up to about 25% in surface shell of 2 nm nanoparticle (see Table 4). We also found the defects with ZSi-O ) 1; however, their fraction is very small, and their role can be ignored (i.e., less than 1%). It is essential to notice that the existence of threefold silicon at the vitreous silica surfaces has been observed and discussed.50 We found a significant amount of O atoms with ZO-Si ) 1 which can be considered as a nonbridging oxygen (NBO), and their percentage also increases strongly with decreasing nanoparticle size up to about 17% in surface shell of 2 nm nanoparticle compared with around 1.5% in the bulk (Table 4). The fact is that the existence of NBO at the vitreous silica surface has been found previously, and NBO are usually hydrated because of the presence of water as a contaminant in the real systems.48 Significant amounts of O with ZO-Si ) 3, that is, O atoms surrounded by three Si4+ cations, have been found in both the core and the surface of nanoparticles. Their percentage is around 1-2% which is higher than that of the bulk (see Table 4). Such defects are often called triclusters, although their definition is slightly different from the one used here; that is, at least one cation is Al, as observed in aluminosilicates.55 The triclusters with three Si in their composition have also been found and discussed.55 Since triclusters can play an important role in structure and dynamics of aluminoisilicates, their role in the structure and properties of silica nanoclusters cannot be ignored. Indeed, threecoordinated oxygen atoms have been also found and discussed in vitreous silica surfaces; it was found that they are predominantly formed 3-5 Å into the surface.51 The increase of the number of triclusters in amorphous SiO2 nanoparticles might be related to the violation of the right SiO2 stoichiometry at the surface and in the core in order to achieve the local charge neutrality. Indeed, we found the existence of SiO2.03, SiO2.06, or SiO2.01 stoichiometries at the surfaces of 2, 4, and 6 nm

TABLE 4: Fraction of Si Atoms with Coordination Numbers ZSi-O ) 1, 2, 3, 4, and 5 and Fraction of O Atoms with Coordination Numbers ZO-Si ) 1, 2, and 3 in the Surface Shell and in the Core of Amorphous SiO2 Nanoparticles at T ) 350 K ZSi-O materials 2 nm 4 nm 6 nm bulk

surface core surface core surface core

ZO-Si

1

2

3

4

5

1

2

3

0.000 0.000 0.004 0.000 0.002 0.000 0.000

0.033 0.000 0.027 0.000 0.008 0.000 0.000

0.229 0.000 0.163 0.004 0.132 0.002 0.010

0.738 1.000 0.806 0.994 0.858 0.997 0.990

0.000 0.000 0.000 0.002 0.000 0.001 0.000

0.169 0.000 0.128 0.007 0.103 0.012 0.015

0.815 0.983 0.858 0.979 0.887 0.971 0.975

0.016 0.017 0.011 0.014 0.009 0.017 0.010

MD Simulation of Amorphous SiO2 Nanoparticles

J. Phys. Chem. B, Vol. 111, No. 44, 2007 12653

Figure 5. Temperature dependence of potential energy of SiO2 nanoparticles compared with that of the bulk.

Figure 7. Determination of the glass transition temperature, Tg, of 2 nm SiO2 nanoparticle. The temperature dependence of potential energy presents clearly the glass transition in the system since Tg can be deduced from the intersection of a linear high- and low-temperature extrapolation of the potential energy. Depending on the cooling rate, liquid can crystallize or form a glass. If liquid crystallizes, the sudden change of potential energy at the transition can be found because of the first-order nature of the transition.

Figure 6. Temperature dependence of the surface energy of SiO2 nanoparticles at sizes 2 and 4 nm.

nanoparticles, respectively. The deviation from SiO2 stoichiometry in nanoparticles might cause the formation of structural defects like those discussed in ref 54. In addition, because of the lack of periodic order structure, there is a significant amount of another type of point defect in amorphous SiO2 nanoparticles, that is, vacancy like defects. We found large pores at the surface of amorphous SiO2 nanoparticles (see Figure 4). Such large pores can change their position with neighboring atoms and act as vacancies in diffusion processes like those found and discussed previously for amorphous Al2O3 (see ref 42). Because of the small dimension and specific amorphous structure, there is an existence of only typical structural point defects in the surface shells of amorphous SiO2 nanoparticles like those just discussed; that is, it is unlike different types of structural defects observed in crystalline TiO2 surfaces such as step edges, oxygen vacancies, line defects, crystallographic shear planes, and so forth.54 The temperature dependence of the system potential energy is of great interest because from that we can infer important quantities and phenomena, such as glass transition temperature and melting point and related phase transitions. Upon cooling nanoparticles from the melt, we found an evolution of the potential energy per atom, Epot, which is presented in Figure 5. We can see that Epot for nanoparticles is significantly higher than that for the bulk because of the surface energy of the formers. Thus, we can suggest the relation: bulk Enano pot - Epot ) Es/N

(2)

Here, Es is the surface energy of nanoparticle and N is the total number of atoms in the system. We show only the data for 2 and 4 nm nanoparticles. Because of the large number of atoms in the 6 nm nanoparticle (7479 atoms), the curve for this

Figure 8. Inverse size dependence of the glass transition temperature of SiO2 nanoparticles, where d is the diameter of a spherical nanoparticle. The straight line is just a guide for eyes.

nanoparticle almost coincides with that for the 3000 atom bulk model (not shown). Therefore, we focus our attention just to small nanoparticles. From eq 2, we can infer the surface energy of the nanoparticle, which is shown in Figure 6. The surface energy of nanoparticles slightly decreases with decreasing temperature; that is, it ranges from 0.142 to 0.100 J/m2 over the temperature range from 7000 to 350 K. There is no experimental surface energy of amorphous SiO2 nanoparticles in vacuum; however, the value obtained experimentally for the surface energy of amorphous silica in pure water is 0.340 J/m2 (see ref 49). The value is not much larger than that calculated in present work. In contrast, the value of surface energy of SiO2 nanoclusters with BKS interatomic potentials ranged from 0.900 J/m2 at 4700 K to around 1.250 J/m2 at 2750 K. We can infer from such data that at 350 K the value of surface energy for BKS vitreous silica nanosized clusters should be at around 1.660 J/m2; that is, it was strongly overestimated compared with those observed experimentally (see more details in ref 27). On the other hand, we can see that the surface energy of amorphous SiO2 nanoparticles has a slight tendency to decrease with decreasing temperature unlike what is observed for the surface energy of free boundary condition BKS SiO2 nanoclusters27 or for the surface tension.56 The discrepancy might be related to the different boundary conditions used in the simulations, or it could mean that the adopted interatomic potentials do not describe well the temperature dependence of the surface energy of silica nanoclusters. Our fixed nonslip boundary conditions are more similar to the amorphous SiO2 formed in confined

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TABLE 5: Structural Characteristics of Amorphous SiO2 Nanoparticles at T ) 350 K with Two Different Boundaries rij (Å) materials 2 nm 4 nm

non-el. elastic non-el. elastic

gij

Zij

SisSi

Si-O

OsO

SisSi

Si-O

OsO

SisSi

Si-O

O-Si

OsO

3.02 3.01 3.02 3.03

1.52 1.52 1.52 1.52

2.53 2.54 2.54 2.54

8.60 8.78 9.16 8.68

30.81 30.63 32.42 31.95

8.98 8.79 9.40 9.36

3.69 3.69 3.80 3.81

3.92 3.96 3.96 3.96

1.96 1.98 1.98 1.98

5.86 5.93 6.06 6.06

TABLE 6: Fraction of Si Atoms with Coordination Numbers ZSi-O ) 1, 2, 3, 4, and 5 and Fraction of O Atoms with Coordination Numbers ZO-Si ) 1, 2, and 3 in the Surface Shell of Amorphous SiO2 Nanoparticles at T ) 350 K ZSi-O materials 2 nm 4 nm

non-el. elastic non-el. elastic

ZO-Si

1

2

3

4

5

1

2

3

0.000 0.000 0.004 0.000

0.033 0.051 0.027 0.011

0.229 0.237 0.163 0.189

0.738 0.712 0.806 0.800

0.000 0.000 0.000 0.000

0.169 0.197 0.128 0.120

0.815 0.795 0.858 0.876

0.016 0.008 0.011 0.002

geometries than to the free amorphous nanoparticles. The oscillations of the curves presented in Figure 6 might be due to insufficiently good statistics rather than to real physical phenomena. Glass Transition Temperature of Liquid SiO2 Nanoparticles. Glass transition in nanoscaled systems including glass transition in nanoparticles, in thin films, and of liquids in confined geometries have been under intensive investigation.57-61 While the glass transition temperature is typically lower in a confined geometry, experiments have also found cases where Tg increases.62,63 However, the glass transition temperature in liquid SiO2 nanoparticles has not been studied yet. Tg in the present work was found via the intersection of a linear highand low-temperature extrapolation of the potential energy, as it was done for bulk Al2O3-SiO2 liquids55 (see Figure 7). We found that Tg is equal to 1767, 1877, 1987, and 1988 K for 2, 4, and 6 nm SiO2 nanoparticles and bulk, respectively. This means that Tg decreases with reduction of nanoparticles size, as observed experimentally for organic nanoparticles59 (see Figure 8). On the other hand, because of the large number of atoms in the 6 nm nanoparticle, its Tg also coincides with that of the bulk model. However, the increase or decrease of Tg with the size of nanoscaled substances might be related to the different boundary conditions used in practice.60 Moreover, our finding somewhat highlights the finite size effects on the glass transition, which affect the stability of low-dimensional materials, recently found and discussed in literature (see ref 59 and references therein). Particularly, Bares found in 1975 that the Tg of styrene-butadiene-styrene triblock copolymer decreases as its surface-to-volume ratio increases and its molecular weight decreases.64 The finite size effects on Tg cannot be interpreted as readily as that on the melting temperature Tm because of the lack of a consensus on the nature of the glass transition.65,66 There were several attempts for interpreting the finite size dependence of Tg. Among them, a model of finite size effects on Tg borrowing the ideas from the theory of the second-order phase transition has been developed. This model predicts a downward shift and a broadening of Tg, from finite size effects constraints on a correlation length defined for the glass transition.67 A recent study of finite size effects in the dynamics of suppercooled liquids supports the model.68 Effects of Boundary Conditions on the Structure and Thermodynamic Quantities. According to the model developed in ref 60, the size dependence of glass transition temperature of nanosized materials might be related to the boundary conditions. In order to shed some light onto the problem, we show the results obtained by using elastic reflection boundary conditions for our models in addition to the non-elastic reflection

ones observed and discussed above. We can see in Table 5 that the structural properties of amorphous SiO2 nanoparticles obtained by using two different boundary conditions are similar to each other. A significant discrepancy can be found via the study of the surface structure. Applying elastic reflection boundary conditions leads to an increase of structural defects at the surface of 2 nm nanoparticle compared with those observed in non-elastic ones. In contrast, no systematic changes have been found for 4 nm nanoparticle (see Table 6). In addition, we also found the boundary effects on the density profile of 4 nm nanoparticle (Figure 9). Such relatively small effects on static properties might lead to dramatic changes in the dynamics of atomic species in nanoparticles. Moreover, we found almost no boundary condition effects on the temperature dependence of the potential energy of nanoparticles (Figure 10). It suggests that there are no boundary effects on the glass transition temperature in SiO2 nanoparticles. Summary The structural properties and thermodynamic quantities of amorphous SiO2 nanoparticles of three different sizes have been studied via MD simulations, using interatomic potentials, which have weak Coulomb interaction and Morse type short-range interactions. Several conclusions can be drawn: (i) We found that the structural properties of amorphous SiO2 nanoparticles are strongly size dependent and differed from those

Figure 9. Density profile in amorphous 4 nm SiO2 nanoparticles at T ) 350 K under non-elastic reflection and elastic reflection boundary conditions.

MD Simulation of Amorphous SiO2 Nanoparticles

Figure 10. Temperature dependence of potential energy of SiO2 nanoparticles under non-elastic reflection and elastic reflection boundary conditions compared with that of the bulk.

of the bulk although a tetrahedral network structure remains. We found that the structure of the core of nanoparticles is similar to the bulk structure, nearly size independent. In contrast, the surface structure of nanoparticles is strongly size dependent, and it differs from those of the core and the bulk. This indicates the dominant role played by the surface structure in determining the nanoparticle structure, instead of the surface energy. This means that the role of surface energy in determining the cluster structure must be reconsidered.69 (ii) We found a significant amount of structural defects at the surface of amorphous nanoparticles, and their concentration increases with decreasing nanoparticle size because of the increase of the surface-to-volume ratio. These defects are undercoordinated units SiO2, SiO3, or O sites with ZO-Si ) 1. We found a significant concentration of so-called triclusters, that is, O sites with ZO-Si ) 3, and their role in structure and dynamics of atomic species in nanoparticles cannot be ignored. Our results share many trends observed previously in amorphous surfaces of SiO2 nanosized clusters or films. Moreover, it is clearly observed the presence of vacancy like defects in amorphous SiO2 nanoparticles, that is, pores with large radii which can act as vacancies in diffusion processes or in adsorption of small molecules. (iii) We found that the glass transition temperature of SiO2 nanoparticles is size dependent, as it decreases with decreasing nanoparticle sizes, as observed experimentally for organic nanoparticles. (iv) We found the boundary condition effects the structure of SiO2 nanoparticles. Although the effects are not strong, they can cause dramatic changes in the dynamics of atomic species in nanoparticles. In contrast, we found no boundary condition effects on the glass transition temperature of SiO2 nanoparticles in contrast to what has been found and discussed for nanosized systems in confined geometries. Acknowledgment. The author is thankful for the financial support from the Japan Society for Promotion of Science via JSPS Invitation Research Fellow. The author also thanks Professor T. Odagaki for the hospitality during a stay at Kyushu University. The calculations were mainly done in Computational Physics Lab of the College of Natural Sciences of HochiMinh City-Vietnam. References and Notes (1) Meier, A.; Gamsjager, H. React. Polym. 1989, 11, 155. (2) Osseo-Asare, K.; Arriagada, F. J. Colloids Surf. 1990, 50, 321.

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