Multi-Particle Sintering Dynamics: From Fractal-like ...Multi-Particle Sintering Dynamics: From...

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

M.L. Eggersdorfer1, D. Kadau2, H.J. Herrmann2 and S.E. Pratsinis1

1Particle Technology Laboratory, ETH Zürich, CH-8092 Zürich, Switzerland

ObjectiveCharacterizing the morphology and average primary particle diameter, dVA, and number, nVA, of fractal-like agglomerates (physically-bonded) andaggregates (chemically- or sinter-bonded) is needed for monitoring material synthesis of gas-borne nanoparticles, emissions from combustionengines and atmospheric particles. Here the evolution of particle coalescence by viscous flow sintering (e.g. SiO2, polymers) and grain boundarydiffusion (e.g. TiO2, metals) of several agglomerates consisting of 16 – 512 primary particles made by diffusion limited cluster-clusteragglomeration (DLCA) is monitored in detail.

meggers@ptl.mavt.ethz.ch

www.ptl.ethz.chParticle Technology Laboratory, ETH Zürich, CH 8092 Zürich, Switzerland

2Computational Physics of Engineering Materials, ETH Zürich, CH-8093 Zürich, Switzerland

Projected Aggregate Area Scaling1

a) Viscous flowsintering2

b) Grain boundarydiffusion

Figure 1: A power law holds between normalized projected aggregate area Aa/AVA and average number of primary particles nVA during sintering by a) viscous flow and b) grain boundary diffusion(average kA = 0.998 & = 1.069).

α

aVA A

An = k

A

AVA

Average Primary Particle Diameter: dVA= 6V/A = (kAdm2/(6V))1/(2-3)

Figure 2: The evolution of dVA

as a function of aggregate Figure 3: The dVA of Ag nanoparticle agglomerates

VAA

Aa

The dVA can be estimated from agglomerateVolume V , mobility size dm and the relation3: Aa = dm

2/4.

gg gmobility diameter, dm, during sintering. For agglomerates of monodisperse spherical primary particles, dVA = dp

independent of mobility size (horizontal agglomerate or collision line). The dm

decreases during sintering while dVA increases until a compact particle (Df = 3) is

gggenerated by Kim et al.4 is obtained by the proposed equation and compared to particle diameters dp

obtained by TEM4 (grey area represents standard deviation of dp at T = 293 K). Higher furnace temperatures (T = 473 –873K) lead to faster

Effective fractal dimension Df vs. mass mobility exponent Dfm

fD

gp n

p

Rn = k

r

fmD

mp m

p

rn = k

r

reached (coalescence line). sintering and larger dVA.

R

Figure 4: The evolution of Df and Dfm during viscous sintering of DLCA agglomerates. The exponents (Df, Dfm) are obtained by ensemble averaging over 50 agglomerates of each size. Only Dfm exhibits monotonic behavior and thus can be used to characterize the degree or extent of sintering of aggregates

Figure 5: The DMA-APM data of silver nanoparticle aggregates sintered at different temperatures by Kim et al.4 are post-processed here. The Dfm exhibits a monotonic increase consistent with our sintering simulations (Fig 4)

rm

Rg

ConclusionsReferences

[1] A.I. Medalia, J. Colloid Interface Sci. 24 (1967) 393-404.[2] M.L. Eggersdorfer, D. Kadau, H.J. Herrmann, S.E. Pratsinis,

Langmuir 27 (2011) 6358-6367.[3] S.N. Rogak, R.C. Flagan & H.V. Nguyen, Aerosol Sci.

Technol. 18 (1993) 25-47.[4] S.C. Kim, J. Wang, M.S. Emery, W.G. Shin, G.W.

Mulholland & D.Y.H. Pui, J. Aerosol Sci. 43 (2009) 344-355.

1. The projected area scaling is valid during sintering.

2. The and kA are independent of sinteringmechanism.

3. The dVA obtained by this work is in reasonableagreement with counting TEM images.

4. The mass-mobility exponent Dfm increasesmonotonically, while the fractal dimension Df

reaches a minimum. So Dfm can be used tocharacterize the degree of sintering.

Acknowledgments:Financial support by ETH Research grant (ETHIIRA) ETH-11 09-1 and the European Research Council.

α

aVA A

VA

An = k

A

can be used to characterize the degree or extent of sintering of aggregates. consistent with our sintering simulations (Fig. 4).