(72b) Sintering Rate and Mechanism of TiO2 Nanoparticles by Molecular Dynamics Using GPUs

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 gas-phase processes with controlled
product particle size, structure, composition and eventual performance in a
number of applications³.

Seto et al.⁴ have proposed a sintering
rate similar to Kobata et al.⁵ for TiO₂ and
validated it by accounting for the detailed fluid mechanics of their hot wall
reactor 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 have investigated the
sintering of two TiO₂ nanoparticles, with CPU's reaching up to 1 ns
in residence time, 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, while comparing
MD with phenomenological sintering models and investigating the melting of TiO₂
nanoparticles¹⁰.

Here¹¹, sintering of rutile TiO₂
nanoparticles is investigated by MD on graphical processing units (GPU)¹² of a consumer graphic
card that was originally developed for the visualization of highly realistic
computer games. The acceleration achieved by the GPU, compared to a single CPU
(Figure 1), allowed simulating TiO₂ nanoparticle sintering from
adhesion and neck growth to finally full coalescence over several hundred
nanoseconds for the first time and determining the sintering rate of very small
TiO₂ nanoparticles (d_p < 5 nm) by monitoring
the evolution of their surface area (Figure 2). For the smallest particle
diameters, the MD-obtained sintering rates were smaller than that predicted by
theory developed for larger particles^4,5. 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 could facilitate the use of
phenomenological models¹³ to design processes for
large scale manufacture and processing of small nanoparticles¹⁴. The low costs for consumer
GPU hardware and low energy consumption combined with extremely high
computational power make GPU's suitable for scientific computing.

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

References

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Figure 1 The Number of timesteps for molecular dynamics of TiO₂
nanoparticles undergoing sintering on GPU (circles) and CPU (triangles) as
function of number of atoms.

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