Measurements were made of the surface fractal dimension of materials produced by commercial aerosol processes. A nitrogen adsorption technique was used that requires the measurement of only one adsorption isotherm, in contrast to other methods that require multiple isotherms. The materials analyzed were titanium dioxide (fumed and chloride process) and fumed silica. The chloride process titanium dioxide samples showed evidence that surface roughness is controlled by process conditions, and the fumed titanium dioxide appeared to have a surface structure that is not fractal. Results for fumed silica were compared with data from the literature that were obtained using small angle X-ray and neutron scattering. Adsorption surface fractal dimensions were lower, which is believed to be caused by the smoothing of adsorbed layers of nitrogen, resulting in the loss of replication of surface roughness. (C) 1996 American Association for Aerosol Research.

A linear rate law has been derived for the final stages of decay of the excess surface area of a spheroidal solid particle approaching a spherical shape. Solid-state diffusion within the particle, driven by stress gradients resulting from nonsphericity, is assumed to be the controlling mechanism. The derivation is based on a solution to Laplace's equation for the chemical potential inside the solid particle, which satisfies the boundary condition for the chemical potential on the particle surface. The characteristic frequency for the decay is 16v(m)(2)L sigma/R(3) where v(m) is the molecular volume, sigma the surface tension, and R the radius of the sphere. The phenomenological coefficient L appears in the diffusional flux, driven by the chemical-potential gradient.

Aerosol agglomerates can sometimes be described by a characteristic size, a power-law exponent (fractal dimension), and a dimensionless proportionality constant (A). The importance of A has been generally overlooked, although it is necessary for the calculation of agglomerate size. Values of A were calculated from previously published data for the radius of gyration and mobility diameter of fractal-like agglomerates. The value of A is approximately one, but depends on the detailed kinetics of the coagulation mechanism, the fractal dimension, and the characteristic agglomerate size.

Solid particles in the 1 nm < d(p) < 100 nm size range form in gases as a result of gas phase condensation, particle collision processes, and solid-state processes. The relative rates of sintering and collision determine the size and morphology of the spheroidal primary particles. Rapid sintering is equivalent to the classical theory of coagulation with instantaneous coalescence. When the sintering rate is slow compared with the collision rate, fine primary particles form and aggregate into irregularly shaped agglomerates. The growth of primary particles in an aerosol generator that is cooling at a constant rate was studied theoretically. The most important process parameter determining particle diameter is the maximum gas temperature, because the rate of sintering is a sensitive function of temperature. Aerosol volume loading and cooling rate are important when the rate of particle growth is limited by collision processes. Experiments on the formation of alumina particles were made to study these effects. Predictions of primary particle size did not agree well with experimental measurements, which is attributed to an inadequate understanding of solid-state diffusion processes in nanosized particles. Other experiments showed that low concentrations of sodium and potassium additives reduce the primary particle size of silica.

Aerosols generated at high temperatures tend to form agglomerates which can be characterized by a power law exponent, similar to a fractal dimension. The coagulation dynamics of these particles can be described by a modified collision kernel for the free molecule regime. The collision kernel for power law (fractal-like) particles is a homogeneous function, and the equation is solved using self-preserving size distribution theory for fractal dimensions between 2 and 3.The effects of fractal dimension and primary particle size on agglomerate growth and the size distribution are very strong. Agglomerate growth is rapid at low fractal dimension and fine primary particle size, because the collision cross-section is much larger for the same agglomerate mass. The effect of primary particle size on the rate of particle growth becomes more significant with decreasing fractal dimension, and the particle size distribution becomes much broader at low fractal dimensions.

Aerosols generated at high temperatures tend to form irregular agglomerates which can be characterized by a power law exponent, similar to a fractal dimension. The coagulation dynamics of these particles can be described using self-preserving size distribution theory. The value of the power law exponent has a large effect on agglomerate growth and particle size distribution in the free molecule regime.