(300c) Restructuring of Aggregates and Their Primary Particle Size Distribution During Sintering

Particle
suspensions and films often exhibit unique properties that depend on particle
size distribution, like the opacity of titania pigments, the color of quantum
dot or plasmonic nanoparticle suspensions and the superparamagnetism of iron
oxide nanoparticles to name a few. Typically a narrow size distribution
facilitates harvesting these effects from paints to solar cells, bio sensors
and light emitting devices.

             Aerosol
processes allow rapid and scalable production of nanoparticles over a wide
range of sizes. In such processes, however, particles grow typically by
Brownian coagulation that places a lower limit to the width of the size
distribution, the so-called self-preserving size distribution with a geometric
standard deviation of about 1.45. Such a constraint would limit aerosol-made
particles in applications requiring narrow size distributions. Furthermore,
when primary particles (PP) with different high temperature residence time
histories (e.g. from different reactor streamlines or reaction rates) are
mixed, fractal-like particles with quite polydisperse PP size distributions (PPSD)
are obtained. This polydispersity, however, can be reduced by PP sintering that
proceeds inversely proportional to particle size, similar to condensation that
is routinely used in generation of monodisperse aerosols.

             Sintering
can lead to a narrower PPSD than their parent aggregates. The narrowest PPSD
was obtained when TiO₂ aggregates were produced by TiCl₄
or titanium isopropoxide oxidation followed by coagulation and sintering (Heine
and Pratsinis, 2007). This was observed also with flame-made ZnO
nanocrystalline aggregates exhibiting a blueshift of their absorption spectrum
with decreasing ZnO crystallite size from about 8 to 1.5 nm (Mädler et al.,
2002). A narrow crystal size distribution is required for this quantum-size
effect.

             During
sintering of aggregates of polydisperse PP, restructuring takes place, the
average PP size increases and the PPSD narrows affecting particle performance
in a number of applications (Fig. 1, Eggersdorfer and Pratsinis, 2013). Here,
aggregate sintering by viscous flow (Eggersdorfer et al., 2011), lattice and
grain boundary diffusion (Eggersdorfer et al., 2012) is simulated by
multiparticle discrete element methods focusing on PP growth dynamics and
elucidating the restructuring of aggregates during their coalescence. The
effect of initial PPSD and sintering mechanisms on the evolution of PP polydispersity
and surface area mean diameter are presented. Each sintering mechanism results
in a distinct evolution of PPSD but quite similar growth in average PP
diameter. Grain boundary diffusion has the strongest impact among all sintering
mechanisms and rapidly results in the narrowest PPSD as it has the strongest
dependence on PP size. During sintering of aggregates with initially
monodisperse PPs, the PPSD goes through a maximum width before narrowing again
as PPs coalesce. A power law holds between projected aggregate surface area and
number of PPs regardless of sintering mechanism and initial PP polydispersity.
This law can be readily used in aerosol reactor design and for characterization
of aggregates independent of material composition, initial PP polydispersity
and sintering mechanism.

Figure 1. The geometric standard
deviation Rg of PP size distribution for a) agglomerates and b)
aggregates is calculated with the diameters d of their constituent PPs at
dimensionless time . The sinter neck or grain boundaries between neighboring
particles are sketched with thin lines. For aggregates, the d represents the
maximum extension of the PP or crystal size (truncated sphere). The number of
PPs, np, remains constant while the average PP number, nva, decreases during
sintering due to the decreasing surface area of the aggregate.

Financial support by ETH Research Grant
(ETHIIRA) ETH-11 09-1 and the European Research Council under the European
Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement n°
247283 is gratefully acknowledged.

Eggersdorfer, M.L., Kadau, D., Herrmann,
H.J. and Pratsinis, S.E. (2011) Langmuir 27, 6358-6367.

Eggersdorfer, M.L., Kadau, D., Herrmann,
H.J. and Pratsinis, S.E. (2012) J. Aerosol Sci. 46, 7-19.

Eggersdorfer, M.L., Pratsinis, S.E. (2013)
AIChE J. in press.

Heine, M.C. and Pratsinis, S.E. (2007) J.
Aerosol Sci. 38, 17-38.

Mädler, L., Stark, W.J. and Pratsinis S.E. (2002) J. App. Phys. 92, 6537-6540.