(420p) Multi-Particle Sintering Dynamics: From Fractal-Like Aggregates to Compact Structures

Multi-Particle Sintering Dynamics: from
Fractal-like Aggregates to Compact Structures

Multi-particle sintering is encountered in
almost all high temperature processes for material synthesis (titania, silica, nickel) and energy generation (e.g. fly
ash formation) resulting in aggregates of primary particles (hard- or
sinter-bonded agglomerates). This mechanism of particle growth is investigated
quantitatively by mass and energy balances during viscous sintering of
amorphous aerosol materials (e.g. SiO₂, polymers) that typically
have a distribution of sizes and complex morphology¹. Once coalescence or sintering starts
between constituent primary particles, sinter necks are formed between them
converting the agglomerates to aggregates. During sintering, the latter
progressively densify until complete compact (e.g. fractal
dimension D_f = 3) structures are formed at
sufficiently long process times at high temperatures. In reality, however, it
is rather seldom to have enough process time to complete particle coalescence.
As a result, aggregates are formed with D_f in-between
those predicted by particle collision alone.

Here a new and rather simple model is introduced that describes
sintering of two differently sized particles and multi-particle aggregates of amorphous spherical particles (e.g.
silica) by mass² (or volume) and energy balances³. This model is validated at limited cases of sintering between two (equally
or unequally sized) particles, and chains of particles. The evolution of morphology,
surface area and radii of gyration of multi-particle aggregates are elucidated
for various sizes and initial fractal dimension. For each of these structures
that had been generated by diffusion limited (DLA), cluster-cluster (DLCA) and
ballistic particle-cluster agglomeration (BPCA) the surface area evolution is
monitored and found to scale differently than that of the radius of gyration
(moment of inertia). Expressions are proposed for the evolution of fractal
dimension and the surface area of aggregates undergoing viscous sintering. These
expressions are important in design of aerosol processes with population
balance equations (PBE) and/or fluid dynamic simulations for material synthesis
or minimization and even suppression of particle formation. Figure 1 shows the
temporal evolution of the effective fractal dimension of a
DLCA agglomerate with 256 primary particles during viscous sintering. At
the beginning of sintering (Fig. 1, at t/t₀ = 0 - 2) the highly ramified
aggregate branches straighten when primary particles approach each other
(reduction of center-to-center distance). This internal restructuring
practically unfolds the aggregate and D_f is reduced.
However the branches continue shrinking while conserving mass. Further downstream D_f
increased as aggregates compacted by sintering-coalescence consistent with in-situ measurements by
small angle X-ray scattering (SAXS)⁴.

Figure 1: Evolution of the effective
fractal dimension D_f during viscous sintering of an
agglomerate with 256 primary particles.

1. Eggersdorfer, M.L., Kadau, D.,
Herrmann, H.J. and Pratsinis, S.E., Multi-particle sintering
dynamics: from fractal-like aggregates to compact structures, Langmuir in press
(2011).

2. Kadushnikov,
R.M., Skorokhod, V.V., Kamenin,
I.G., Alievskii, V.M., Nurkanov,
E.Y., Alievskii, D.M., Computer simulation of
spherical particle sintering, Powder Metall. Met. Ceram.
40 (2001) 154-163.

3. Frenkel, J.,
Viscous flow of crystalline bodies under the action of surface tension, J.
Phys. (USSR) 9 (1945) 385-391.

4. Camenzind, A.,
Schulz, H., Teleki, A., Beaucage,
G., Narayanan, T., Pratsinis, S.E., Nanostructure
evolution: from aggregated to spherical SiO2 particles made in diffusion flames,
Eur. J. Inorg. Chem. (2008) 911-918.