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Melting and Freezing of Au Nanoparticles Confined in Armchair Single-Walled Carbon Nanotubes Jingling Shao, Cao Yang, Xiaolei Zhu,* and Xiaohua Lu* State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing UniVersity of Technology, Nanjing 210009, China ReceiVed: October 28, 2009; ReVised Manuscript ReceiVed: January 18, 2010
The structure, phase transition, and nucleation of Au nanoparticles confined within armchair single-walled carbon nanotubes ((n,n)-SWNTs) are investigated using molecular dynamics (MD) simulation technique. The Au-Au interactions are described by the TB-SMA potentials and the Au-SWNT interactions are represented by Lennard-Jones potential. SWNTs are approximately considered to be rigid. The total energies, structures, Lindemman indices, and radial density distributions are used to reveal the feature of phase transition for Au nanoparticles confined in (n,n)-SWNTs. The classical nucleation theory is applied to perform nucleation analysis. Results demonstrate that confined AuN exhibit multishell structures. The order-disorder transformation of atoms in each layer is an important structure feature of phase transition. Interestingly, the melting starts from the innermost layer and freezing starts from outermost layer for confined Au nanoparticles. SWNTs have a significant effect on the structures and stabilities of the confined Au nanoparticles. On the other hand, some important thermodynamic and dynamic parameters are estimated and compared with available experimental and calculated results. This work provides the primary physical insights into the phase transition and nucleation process of confined Au nanoparticles. 1. Introduction Carbon nanotubes (CNTs) filled with different materials are of great interest in science and technology of nanomaterials due to their novel structures and properties.1–14 It is well-known that metals or metal compounds are inserted into the carbon nanotubes (CNTs) using various techniques.11–14 Metal-filled carbon nanotubes have potential applications, such as nanocatalysts, semiconductor devices, nanomagnetic recording media, fuel cells, and so on. Therefore, they have been the topics of many theoretical and experimental studies. Although people have successfully obtained metal-filled CNTs or nanoparticles by various methods, the structural and physical properties of the confined metals are still not very clear. MD simulations can provide physical insights into metals supported on substrates and have been widely applied to investigate metal-filled carbon nanotubes. For example, Kang et al15 found that the cylindrical ultrathin copper nanowires in carbon nanotubes have multishell packing structures. The results obtained by Kang et al16 suggested that the copper nanoclusters encapsulated in carbon nanotubes tend to move along the tube axis. Also, Kang et al17 found that Na metal confined in carbon nanotube exhibits several phases from an atomic strand to multishell packing structures when the radius of the carbon nanotubes increases. The simulations obtained by Wang18 demonstrated that the melting temperature of the confined icosahedral Pt55 clusters increases with the diameters of SWNTs. The shell structure of free Au nanowires was also investigated computationally19 and observed experimentally.20 Recently, Poulikakos et al.21 have carried out a pioneering work on Au nanoparticle confined in carbon nanotubes using MD simulation technique, and found that the solidification temperatures of Au * To whom correspondence should be addressed. E-mail: xlzhu@ njut.edu.cn (X.Z.);
[email protected] (X.L.).
nanoparticles confined in (n,0)-SWNT are higher than those of the corresponding free clusters and lower than that of its bulk counterpart. Recently, there have been many reports about the surface premelting and the overheating of embedded nanostructures such as liquid-drop formation,22 liquid-shell nucleation and growth,23 lattice-vibration instability,24 surface melting,25 surface-phonon instability,26 and surface bond-order loss.27 The experimental studies about phase transition and nucleation dynamics for Au nanoparticle encapsulated in SWNT have proven elusive. Herein, we carry out MD simulations to investigate the structure, phase transition, and nucleation on Au nanoparticles confined in (n,n)-SWNTs. Results reveal some important features of phase transition and nucleation for confined Au nanoparticles. Some important thermodynamic and dynamic parameters are estimated based on MD simulations, which are valuable for further experimental studies. 2. Computational Details The MD simulations are used to investigate phase transition and nucleation of gold nanoparticles within armchair (n,n)SWNTs with n ) 15, 19, 25, and 30. The diameters of (n,n)SWNTs are 20.34, 25.76, 33.90, and 40.68 Å, respectively. The gold particle is encapsulated in the SWNT. Each system includes a gold cluster confined in the carbon tube and an infinitely long SWNT (simulated by a box of length 22.017 nm replicated using periodic boundary conditions along the tube axis). We investigate Au particles with 467, 818, 1522, and 2230 atoms, respectively. For simplicity, we distinguish the different systems by displaying the number of gold atoms N(Au) and the index n of the (n,n)-SWNT (N(Au)-n). Therefore, the systems studied in current work can be represented as 467(Au)-15, 818(Au)19, 1522(Au)-25, and 2230(Au)-30, respectively. The second-moment approximation of the tight-binding (TBSMA-type potential function) has been widely applied in
10.1021/jp910289c 2010 American Chemical Society Published on Web 02/04/2010
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J. Phys. Chem. C, Vol. 114, No. 7, 2010 2897
simulation studies of ultrathin nanowires28 and nanoclusters,29 and the simulated results obtained from this potential are consistent with the experiments for low-dimensional systems30 and bulk.31 Therefore, the gold-gold interactions are represented with the TB-SMA potential.31 Based on the TB-SMA potential, Au-Au interaction energy, EAu-Au, can be represented by
EAu-Au )
∑ ERi + EBi
(1)
i
where EiBand EiR are the bond and Born-Mayer ion-ion repulsion terms, respectively. These two terms for an atom i can be described in terms of
ERi )
∑ ARβ exp(-pRβ(rij/rRβ0 - 1))
(2)
j
EBi
)-
{∑
2 ξRβ
j
exp(-qRβ(rij /rRβ 0
}
- 1))
Figure 1. Total energy as a function of temperature for AuN confined in SWNTs. The curves of 467(Au)-15, 818(Au)-19, and 1522(Au)-25 are shifted upward by 15, 10, and 5 kJ/mol, respectively.
TABLE 1: Physical Properties Obtained from MD Simulations Cp (J K-1 mol-1)
(3)
The TB-SMA potential parameters for Au-Au can be obtained from ref 30 (A ) 0.2061 eV, ξ ) 1.790 eV, p ) 10.229, q ) 4.036, r0 ) 2.884 Å). Because the interactions between Au atoms and SWNTs are weak, the structures of SWNTs will not be significantly changed in the presence of Au metal.18 In MD simulations, SWNTs are approximately considered as rigid superstructures of fixed atoms, which are similar to those in relevant references.16,17,21,32 The gold-SWNT interaction is described by a Lennard-Jones (LJ) potential using the parameters from ref 33 (σC-Au ) 2.9943 Å, εC-Au ) 0.01273 eV). The software used in our MD simulations is developed based on the modified version of the program MDIONs.34 In phase transition simulation of the four systems studied, the gold particle is inserted into the SWNT and melted by bringing it to a temperature above 1400 K for 0.6 ns. Then, a slow cooling process starts at 1400 K, with a temperature step of 20 K and time step of 3 fs. Each system is first simulated at constant temperature for 20000 time steps and then at constant energy for 20000 time steps. For constant temperature MD simulations, velocities are rescaled at each step to reach the desired temperature.35 MD simulations are continued until the temperatures reach 300 K. The final structure at 300 K is considered as the initial configuration for a slow heating process. In slow heating process, each structure is heated from 300K to 1400K with temperature step of 20K. For each temperature, spend 20000 time steps at constant temperature and 20000 time steps at constant energy. To perform nucleation analysis, for each of melted Au467, Au818, Au1522, and Au2230 clusters confined in SWNTs, heating is continued at 1400 K to generate 80 melted clusters, that is, each of melted Au467, Au818, Au1522, and Au2230 clusters confined in SWNTs is kept in a bath with the temperature of 1400 K. During constant temperature (1400 K) simulation, a structure is saved every running 4000 time steps, from which 80 melted clusters can be obtained. These melted clusters possess different thermal histories and structures. Then, we investigate nucleation and crystallization of Au467, Au818, Au1522, and Au2230 clusters inside SWNTs by quenching the melted Au particles in SWNT to specified temperatures (550, 600, 650, or 700 K) for 180 ps. 3. Results and Discussion Figure 1 represents the temperature dependence of total energies for Au467, Au818, Au1522, and Au2230 confined in SWNTs
systema 467(Au)-15 818(Au)-19 1522(Au)-25 2230(Au)-30 bulk Au (exp)
liquid
solid
34.77 22.43 + 0.01155T 34.73 21.69 + 0.01145T 34.45 17.45 + 0.021.90T 34.25 17.71 + 0.02030T 18.89 + 0.02206T 1.214 × 10-5T2b
Tm(K)
∆Hfus (kJ mol-1)
780 813 830 836 1336c
5.5 6.3 6.4 6.9 12.4b
a We distinguish the different systems by displaying the number of gold atoms N(Au) and the index n of the (n,n)-SWNT (N(Au)-n). b Barin, I.; Knacke, O. Thermochemical Properties of Inorganic Substances; Springer-Verlag: Berlin, 1973. c Weast, R. C., Ed. CRC Handbook of Chemistry and Physics, 63rd ed.; CRC Press: Boca Raton, FL, 1982.
during slow heating processes. In Figure 1, sharp increases in the total energy curves are observed, corresponding to the melting transformations. As shown in Figure 1, Au467, Au818, Au1522, and Au2230 within SWNTs melt around 780, 813, 830, and 836 K, respectively. Results demonstrate that the melting temperatures of confined Au nanoparticles tend to increase with nanoparticle size as expected. Moreover, the melting temperatures are lower than that (1336 K)36 of free bulk Au. The depression of the melting point can be attributed to a large surface-to-volume ratio and low-dimensional structures for confined Au nanoparticles. In addition, the heat capacities and heats of fusion can be derived from heating curves of these four systems, as shown in Table 1,35,37 which is needed for nucleation analysis. The structures of the confined AuN (N ) 467, 818, 1522, and 2230) at 300 K are represented in Figure 2. It is found in Figure 2 that the solid Au nanoparticles confined in SWNTs exhibit cylindrical multishelled structures, which are consistent with previous results obtained by Poulikakos et al21 as well as Xiao et al.38 and are different from those of free Au clusters39 or bulk Au. The multishelled structures of confined Au clusters should be related to the confinement environment provided by SWNT. Although there are free Au nanowires with the multishelled structures,19 the structures of confined Au clusters are relatively more ordered than those of free Au nanowires, suggesting that SWNTs increase the stability of Au clusters. To explore the melting transformation process, we examine the structures of confined Au clusters in cooling and heating processes. During slow cooling and heating stages, the images of projections of the atoms in Au1522 inside SWNTs are displayed in Figure 3. At first sight, before the melting temperature, the Au1522 clusters have multishelled structures
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Figure 4. Lindemann indices as a function of temperature for 467(Au)15: squares, first layer (innermost); circles, fourth layer (outermost); up triangles, entire system.
Figure 2. Images of AuN confined in (n,n)-SWNTs perpendicular to the tube axis of SWNTs (a,c) and parallel to the tube axis (b,d,e,f) at 300 K: (a,b) 467(Au)-15; (c,d) 818(Au)-19; (e) 1522(Au)-25; and (f) 2230(Au)-30. The blue and yellow balls represent carbon and gold atoms, respectively.
(Figure 3c-e) with ordered structure. After the melting temperature, the Au1522 exhibit disordered structures (Figure 3a,b,f,g). Moreover, the multishelled structures of confined Au clusters are observed for these four systems during quenching runs. The Lindemann indices40 are often employed to identify phase transitions. The Lindemann index of each layer δi is represented in terms of
δi )
2 Ni(Ni - 1)
∑ j
