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.