Method for Measuring Effective Density and Fractal Dimension of Aerosol Agglomerates

Figures & data

FIG. 1 Parameters varied in density fitting method (see text). The slope of the curve (3-d _f ) depends on the structure of particles.

FIG. 2 Different phases of the fitting procedure and the resulting density versus mobility diameter curve.

TABLE 1 Range of parameter values used in simulation

	Minimum	Maximum
Input parameter	value	value	Unit
CMD	10	400	nm
GSD	1.3	2
ρ i	0.5	10.5	g/cm^3
d f	2	3

FIG. 3 Fitted fractal dimension values versus input values. Simulation result with noise added to individual ELPI and SMPS channel signals.

FIG. 4 Fitted fractal dimension versus input fractal dimension. Simulation result with input CMD 100 nm, GSD 1.7, and input ρ _i 1.0 g/cm³; 100 simulation runs per each input value, with noise in individual channel signals of ELPI and SMPS. The error bars indicate standard deviation of the 100 runs.

FIG. 5 Measurement setup.

FIG. 6 (a) Set of measured silver particle distributions and resulted fractal dimensions. (b) Density values for Aged II particles gained from reference method are compared to results found by fitting method in figure.

FIG. 7 Electron microscope images of fresh silver particles on the left and Aged II particles (ageing time 15 min) on the right.

FIG. 8 Measured fractal dimension values and error limits compared with error limits found in simulations. Note that no reference value for Silver Aged I is available; place in x axis is the average of measured values.

TABLE 2 Summary of the results

	Reference	Fitted
Material	density (g/cm^3)	ρ i (g/cm^3)	Reference d f	Fitted d f
DOS	0.918	0.98 ± 0.02	3 (known)	3.0 ± 0.06
Silver, fresh	6.5 ± 0.8	7.1 ± 0.5	∼ 3	3.1 ± 0.1
Silver, aged I	—	5.3 ± 0.3	—	2.7 ± 0.05
Silver, aged II	2.4	2.0 ± 0.1	2.3	2.3 ± 0.1
The reference d f value for DOS is the known value for spherical liquid particles. The reference values for silver particles are gained from reference method.