Sintering Rate and Mechanism of TiO2 Nanoparticles by Molecular Dynamics

Sintering Rate and Mechanism of TiO₂ Nanoparticles
by Molecular Dynamics

B. Buesser, A.J. Gröhn and S.E. Pratsinis

Particle Technology Laboratory, Institute of Process Engineering,

Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland

Titania (TiO₂) nanoparticles have many attractive applications in photovoltaic¹ and photocatalytic² processes, to name a few. The performance of TiO₂ nanoparticles depends considerably on their size and composition which are determined by the sintering rate during their synthesis. The sintering rate is crucial for designing of gas-phase processes with controlled product particle size, structure, composition and eventual performance in a number of applications³.

Kobata et al.⁴ and Seto et al.⁵ have proposed sintering rates for TiO₂ and validated them by accounting for the detailed fluid mechanics of their hot wall reactors forming rather large TiO₂ nanoparticles (d_p = 10 – 100 nm). Little is known, however, for the sintering rate of small TiO₂ nanoparticles (d_p < 10 nm) as it is difficult to reliably measure it.

On the other hand molecular dynamics (MD) simulations have been used to study the sintering to full coalescence of metallic and metalloid nanoparticles^6,7 though much less has been done for ceramic ones as their force fields and potentials are difficult to determine. Koparde and Cummings⁸ investigated the sintering of two TiO₂ nanoparticles up to t = 0.5 ns by tracking the shrinkage of the center-to-center distance and the growth of the sintering neck using the force field of Matsui and Akaogi⁹. They compared MD with phenomenological sintering models and investigated the melting of TiO₂ nanoparticles¹⁰.

The above MD of TiO₂ sintering have reached up to 0.5 ns residence time, a duration that is not sufficient for complete coalescence. So most of the surface area reduction of such small particles has taken place by adhesion and neck growth that limited the detailed understanding of sintering mechanisms and, most importantly, the extraction of quantitative sintering rates that are needed in process design of nanoparticle manufacturing.

Here, sintering of rutile TiO₂ nanoparticles is investigated by graphical processing unit (GPU) accelerated MD¹¹ from adhesion and neck growth to finally full coalescence up to several hundred nanoseconds. This allows determining the sintering rate of very small TiO₂ nanoparticles (d_p < 5 nm) by monitoring the evolution of their surface area (Figure 1). For the smallest particle diameters, the MD-obtained sintering rates were smaller than that predicted by theory developed for larger particles4,5. Ions on the particle surface exhibited higher net displacement than bulk ones revealing that surface diffusion is the dominant sintering mechanism of TiO₂ nanoparticles. An expression for the sintering rate of rutile TiO₂ nanoparticles has been extracted from MD, bridging the gap of knowledge from a few molecules to several nanometers, the key size range for nanoparticle properties and performance. This MD-derived sintering rate facilitates the use of phenomenological models¹² in design of processes for large scale manufacture and processing of small nanoparticles¹³.

Financial support from the Swiss National Science Foundation (SNF) grant # 200021-119946/1 and European Research Council is gratefully acknowledged.

References

1.             Gratzel M. Photoelectrochemical cells. Nature. 2001; 414, (6861), 338-344.

2.             Formenti M, Juillet F, Meriaudeau P, Teichner SJ, Vergnon P. Preparation in a hydrogen-oxygen flame of ultrafine metal oxide particles. Oxidative properties toward hydrocarbons in the presence of ultraviolet radiation. J. Colloid Interface Sci. 1972; 39, (1), 79-89.

3.             Strobel R, Pratsinis SE. Flame aerosol synthesis of smart nanostructured materials. J. Mater. Chem. 2007; 17, 4743-4756.

4.             Kobata A, Kusakabe K, Morooka S. Growth and transformation of TiO₂ crystallites in aerosol reactor. AIChE J. 1991; 37, (3), 347-359.

5.             Seto T, Shimada M, Okuyama K. Evaluation of sintering of nanometer-sized titania using aerosol method. Aerosol Sci. Technol. 1995; 23, (2), 183-200.

6.             Arcidiacono S, Bieri NR, Poulikakos D, Grigoropoulos CP. On the coalescence of gold nanoparticles. Int. J. Multiphas. Flow. 2004; 30, (7-8), 979-994.

7.             Zachariah MR, Carrier MJ. Molecular dynamics computation of gas-phase nanoparticle sintering: a comparison with phenomenological models. J. Aerosol Sci. 1999; 30, (9), 1139-1151.

8.             Koparde VN, Cummings PT. Molecular dynamics simulation of titanium dioxide nanoparticle sintering. J. Phys. Chem. B. 2005; 109, (51), 24280-24287.

9.             Matsui M, Akaogi M. Molecular dynamics simulation of the strucutral and physical properties of the four polymorphs of TiO₂. Mol. Simulat. 1991; 6, 239-244.

10.          Koparde VN, Cummings PT. Sintering of titanium dioxide nanoparticles: a comparison between molecular dynamics and phenomenological modeling. J. Nanopart. Res. 2008; 10, (7), 1169-1182.

11.          Garland M, Le Grand S, Nickolls J, Anderson J, Hardwick J, Morton S, Phillips E, Yao Z, Volkov V. Parallel Computing Experiences with CUDA. Micro IEEE. 2008; 28, (4), 13-27.

12.          Koch W, Friedlander SK. The effect of particle coalescence on the surface area of a coagulating aerosol. J. Colloid Interface Sci. 1990; 140, (2), 419-427.

13.          Pratsinis SE. Aerosol-based technologies in nanoscale manufacturing: from functional materials to devices through core chemical engineering. AIChE J. 2010; 56, (12), 3028-3035.

 

Figure 1 Evolution of surface area of two TiO₂ nanoparticles (d₀ = 3 nm) at 1800 K.