(200e) The Structure of Agglomerates Consisting of Polydisperse Nanoparticles

The
Structure of Agglomerates Consisting of Polydisperse Nanoparticles

M.L. Eggersdorfer and
S.E. Pratsinis

Particle Technology Laboratory,
Institute of Process Engineering, Department of Mechanical and Process
Engineering, ETH Zurich, Sonneggstrasse 3, CH-8092 Zürich, Switzerland.

Ph. +41 (0) 44 632 31 80; Fax. +41 (0)
44 632 15 95

Agglomeration is encountered in many natural or
industrial processes, like growth of aerosol particles in the atmosphere,
material synthesis by aerosol processes or even flocculation of minerals in
oceans or colloidal particles. These particles collide by different mechanisms
and stick together forming irregular or fractal-like agglomerates. Typically,
the structure of these agglomerates is characterized with the fractal dimension,
D_f, and pre-exponential factor, k_n, of
simulated agglomerates of monodisperse primary particles (PP) for ballistic or
diffusion-limited particle-cluster and cluster-cluster collision mechanisms.
This concept has served well a wide spectrum of aerosol and colloidal
particles, in particular by coagulation. In fact, a number of characterization
techniques and process design concepts have been developed capitalizing on
these D_f values to extract other particle properties (e.g.
collision diameter, primary particle size) and design reactors for
manufacturing such particles. What might have been overlooked in
characterization and simulations of such particles is that the above D_f
values have been developed for agglomerates of monodisperse primary particles. For
coagulating aerosols and colloids, however, this needs to be carefully examined
as Brownian coagulation-driven particle formation leads to polydisperse
particles. Figure 1 shows a TEM image of a fractal-like zirconia nanoparticle
made by scalable flame spray pyrolysis having a primary particle size
distribution with geometric standard deviation of s_g
≈ 1.58.

             Here, the effect of PP polydispersity
on D_f and k_n is investigated with
agglomerates consisting of 16 ? 1024 PP with closely controlled size
distribution (s_g
= 1-3). Figure 2 shows a snapshot of a numerically generated diffusion-limited
cluster-cluster agglomerate (DLCA) with s_g
= 1.58. These simulations are in excellent agreement with the classic structure
(D_f and k_n) of agglomerates consisting of
monodisperse PPs made by four different collision mechanisms as well as with
agglomerates of bi-, tri-disperse [1] and normally distributed PPs [2].
Broadening the PP size distribution of agglomerates decreases monotonically
their D_f and for sufficiently broad PP distributions (s_g
> 2.5) the D_f reaches about 1.5 and k_n
about 1 regardless of collision mechanism [3]. Furthermore with increasing PP
polydispersity, the corresponding projected area exponent, D_a,
and pre-exponential factor, k_a, decrease monotonically from
their standard values for agglomerates with monodisperse PPs. So the PP
polydispersity determines for s_g
> 2.5 the agglomerate structure rather than the collision mechanism. So D_f
as well as D_a
can be an indication for PP polydispersity in mass?mobility and light
scattering measurements, if the dominant agglomeration mechanism is known, like
diffusion-limited and/or ballistic cluster-cluster coagulation in aerosols or
colloidal systems.

[1]
Bushell, G. and Amal, R. J. Colloid Interface Sci. 205 (1998) 459.

[2]
Tence, M., Chevalier, J. P. and Jullien, R. J. Phys. 47 (1986) 1989.

[3]
M.L. Eggersdorfer, S.E. Pratsinis,
Aerosol Sci. Technol. 46 (2012) 347.

Figure
1: TEM image of a size-selected zirconia agglomerate with a mobility diameter, d_m
= 110 nm, and a primary particle size distribution with geometric standard
deviation of s_g
≈ 1.58.

Figure
2: Snapshot of a diffusion-limited cluster-cluster agglomerate (DLCA)
consisting of 256 primary particles with s_g
= 1.58.