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Figure 9.8 Ratio of the mass of a fractal to that of a spherical particle as a function of the fractal dimension and Rg/a.

based on time-consuming image analysis of electron micrographs of individual chain aggregates. However, recently, a method has been described which makes it possible to relate aggregate surface area and volume distributions to the electrical mobility diameter [137, 138]. This method is only applicable for aggregates composed of uniform primary particles, with all surfaces directly exposed to collisions with molecules from the surrounding gas, i.e. a mass fractal dimension less than two. The analysis takes into account the friction coefficient and charging efficiency of chain aggregates, under the assumption that the primary particles composing the aggregates are at least one order of magnitude smaller than the mean free path of the surrounding gas.

Lall and Friedlander [138] compared the surface area and the volume of aggregates with those of a sphere with an equivalent mobility diameter. Their results indicate that the surface area distributions are somewhat underpredicted if the calculations are based on the assumption of spherical particles. However, the volume distributions are greatly overpredicted, by an order of magnitude in some cases. Figure 9.10 shows the difference in the surface area distribution for spherical particles and idealised aggregates. For a primary particle of 18.5 nm diameter the difference in peak heights of the distributions was 17 % and the total aggregate surface area based on mobility diameter is underpredicted by about 15 %. For smaller primary particles, the ratio of

Figure 9.9 Fractal surface area enhancement as a function of the fractal dimension and Rg/a.

Fractal Dimension

Figure 9.9 Fractal surface area enhancement as a function of the fractal dimension and Rg/a.

Figure 9.10 Surface area distribution based on spherical particles compared with the surface area distribution for silver aggregates using the theory of Lall et al. [138] for idealized aggregates. Primary particle size: 18.5 ± 3.5 nm. Reproduced with permission of Elsevier.

Mobility diameter (nm)

Figure 9.10 Surface area distribution based on spherical particles compared with the surface area distribution for silver aggregates using the theory of Lall et al. [138] for idealized aggregates. Primary particle size: 18.5 ± 3.5 nm. Reproduced with permission of Elsevier.

the surface area of the aggregates to that of spheres with the same mobility diameter is expected to be much higher.

Aggregate volumes calculated from the theory agreed well with those measured by electron microscopy. The precision of the technique is limited by the accuracy of estimation of charge distribution on aggregates, which is about 10 %. Hence, this method appears to give realistic information on aggregate volumes and surface areas without the use of electron microscopy. Therefore, it should be possible to determine aggregate surface area and volumes in real time without time-consuming image analysis.

Section 9.3.3 reported that the fractal morphology may be altered in the atmosphere. This restructuring modifies the surface area available for heterogeneous reactions. Adsorption and exchange of molecules at the surface also lead to partial or complete saturation of the chemically active sites. However, the results demonstrate that accounting for the fractal morphology of carbonaceous aggregates can substantially improve calculations of their properties or dynamics. Errors in deriving soot surface areas or uptake rates may prevent quantitative analysis of the impact of soot on atmospheric chemistry.

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