Aggregate morphology evolution by sintering: Number and diameter of primary particles

Abstract

The structure of fractal-like agglomerates (physically-bonded) and aggregates (chemically-or sinter-bonded) is important in aerosol synthesis of nanoparticles, and in monitoring combustion emissions and atmospheric particles. It influences also particle mobility, scattering, and eventually performance of nanocomposites, suspensions and devices made with such particles. Here, aggregate sintering by viscous flow of amorphous materials (silica, polymers) and grain boundary diffusion of crystalline ceramics (titania, alumina) or metals (Ni, Fe, Ag etc.) is investigated. A scaling law is found between average aggregate projected area and equivalent number of constituent primary particles during sintering: from fractal-like agglomerates to aggregates and eventually compact particles (e.g. spheres). This is essentially a relation independent of time, material properties and sintering mechanisms. It is used to estimate the equivalent primary particle diameter and number in aggregates. The evolution of aggregate morphology or structure is quantified by the effective fractal dimension (D f ) and mass-mobility exponent (D fm ) and the corresponding prefactors. The D fm increases monotonically during sintering converging to 3 for a compact particle. Therefore D fm and its prefactor could be used to gauge the degree or extent of sintering of agglomerates made by a known collision mechanism. This analysis is exemplified by comparison to experiments of silver nanoparticle aggregates sintered at different temperatures in an electric tube furnace.

Improved sizing of soot primary particles using mass-mobility measurements

“…We have also found that for nearly all cases, agreement can be Figure 5. Sauter primary particle diameter measured from Equation (5) using parameters suggested by Eggersdorfer et al (2012b) and those obtained in this study versus TEM data for both HPDI and GDI engines.…”

“…Average Sauter diameters of the primary particles were estimated at different mass-mobility test points using the prefactor and projected area exponent parameters obtained by Eggersdorfer et al (2012b) (k a D 1:0 § 0:04 and D a D 1:07 § 0:03) and Equation (5). These diameters are compared with those directly obtained from the analysis of the TEM images as shown in Figures S2 and S3 in the online SI.…”

“…Average D a;opt (D k a D 1:0 § 0:04 (Eggersdorfer et al 2012b), the average error in the estimation of the primary particle size was reduced from 41% and 21% to 19% and 12% for different operating conditions of HPDI and GDI engines, respectively. The accuracy of the model using these "modified parameters" is compared to cases where optimized parameters (minimum error) and parameters governed by Eggersdorfer et al (2012b) were used; results are reported for individual operating conditions in Figure 4.…”

“…where v and a are volume and surface area of the aggregate, respectively, and k a and D a are usually extracted from fitting Equation (1) to the results obtained from numerical simulations (Medalia 1967;Meakin et al 1989;K€ oyl€ u et al 1995;Pierce et al 2006;Al Zaitone et al 2009;Eggersdorfer et al 2012b) (Dobbins at al. 1994;Park et al 2004aPark et al , 2004b; here D a;opt D 1800 kg/m 3 is used.…”

“…The accuracy of the model using these "modified parameters" is compared to cases where optimized parameters (minimum error) and parameters governed by Eggersdorfer et al (2012b) were used; results are reported for individual operating conditions in Figure 4.…”