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.

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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.